Empirical mode decomposition (EMD) is an adaptive method for nonlinear, non-stationary signal analysis. However, the upper and lower envelopes fitted by cubic spline interpolation (CSI) may often occur overshoots. In this paper, a new envelope fitting method based on the flattest constrained interpolation is proposed. The proposed method effectively integrates the difference between extremes into the cost function, and applies a chaos particle swarm optimization method to optimize the derivatives of the interpolation nodes. The proposed method was tested on three different types of data: ascertain signal, random signals and real electrocardiogram signals. The experimental results show that: (1) The proposed flattest envelope effectively solves the overshoots caused by CSI method and the artificial bends caused by piecewise parabola interpolation (PPI) method. (2) The index of orthogonality of the intrinsic mode functions (IMFs) based on the proposed method is 0.04054, 0.02222±0.01468 and 0.04013±0.03953 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is lower than the CSI method and the PPI method, and means the IMFs are more orthogonal. (3) The index of energy conversation of the IMFs based on the proposed method is 0.96193, 0.93501±0.03290 and 0.93041±0.00429 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is closer to 1 than the other two methods and indicates the total energy deviation amongst the components is smaller. (4) The comparisons of the Hilbert spectrums show that the proposed method overcomes the mode mixing problems very well, and make the instantaneous frequency more physically meaningful. EMD is a new adaptive data analysis method for analyzing nonlinear and non-stationary data, which was proposed by Huang et al. in 1998 Although the EMD is still in developing, it has been successfully applied in various science and engineering fields Many approaches have been proposed to substitute the CSI, such as the B-spline interpolation In this paper, a new envelope fitting approach for EMD, called the flattest constrained piecewise cubic Hermite interpolation (FC-PCHI), is proposed which is based on the optimization of the piecewise cubic Hermite interpolation (PCHI). The proposed method consists of PCHI and the optimization of the derivatives of the interpolate points. The proposed method was tested on three different types of data: ascertain signal, random signals and real electrocardiogram (ECG) signals. The experimental results proved that the new method can solve the overshoots caused by CPI and the artificial bends caused by PPI effectively, and let the IMFs more accurate and more reasonable. This method can overcome mode mixing well, which is one of the major drawbacks of the original EMD.The rest of this paper is organized as follows. Section 2 describes the background of EMD and the FC-PCHI method, which is based on analysis and comparison of the interpolation methods. Section 3 shows the experimental results from using different interpolation methods. Section 4 provides a discussion and conclusion.The main idea of the EMD is to decompose signals into oscillatory components from the fastest (high frequencies) to the lowest ones (low frequencies). Following Huang et al. nth-order IMF, low-order IMFs capture fast oscillation modes while high-order IMFs typically represent slow oscillation modes.At the end of the decomposition, the signal The common linear interpolation method only considers the adjacent two points and is simply constructed. However, the fitted curve is not smooth and may cause cusps at the interpolation points. The interpolation accuracy of the low order polynomials interpolation method is relatively poor. But when the order of the interpolation polynomials increases, the Lunge phenomenon The CSI method is a widely used interpolation method, which uses piecewise polynomials as interpolation functions. To keep the smoothness of the fitted curve, the first and second order derivatives of the interpolation points must exist. However, overshoots often occur when using CSI method because of its second-order smoothness. The overshoots shift the mean value curve of the upper and lower envelopes. Another hand, the CSI method is a global interpolation method, which means if one of the interpolation points changes, the whole fitted curve will change. These issues caused the CSI method with global property may not be suitable to analyze the non-stationary signals emphasized on the local characteristics.The PCHI is an effective interpolation method which can express local information of signals effectively To overcome the overshoots caused by the CSI functions, the interpolation functions should be flattened i.e., the difference between the minimum and maximum should be smaller. When the difference reaches the smallest one, the corresponding curve should be regarded as the flattest one. Therefore, it is reasonable to require that the PCHI functions should be not only smooth, but also the flattest one with the smallest ups and downs among the numerous smooth curves. So how to optimize these first order derivatives in the PCHI method, and make the PCHI curve be the flattest one is the target of the proposed method.The PCHI functions are cluster functions with the first order derivatives of the interpolation points. The key of optimization on PCHI method is the derivatives. Taking the upper envelope as an example, we describe our approach in details as follows.Let The fitted upper envelope can be written as Obviously, The problem to find the flattest PCHI curve equals to the problem to find the optimized Similarly, we can find the flattest lower envelope The proposed method was tested on three types of signals: ascertain and stationary signal, 100 random Gaussian signals and 200 segments of real ECG signals.To evaluate the performance of the proposed FC-PCHI envelope, the proposed method is compared with the CSI envelope and the PPI envelope. Let us first consider the following signal,The CSI envelopes are shown in To measure the index of orthogonality (IO) N+1)-th IMF. If the IO is close to zero, then the IMFs and the residual are close to orthogonal. The IEC reflects the fact that the sum of IMFs represents the signal minus the trend given in the residual. If the IEC is close to one, then the decomposition is close to lossless.Based on the test results summarized in The Gaussian type random signal like 100 random signals as mentioned above are decomposed using three methods, respectively. The average index of orthogonality (AIO), average index of energy conversation (AIEC) and standard deviations are compared in The ECG data used in this study are from MIT-BIH Arrhythmia Database ECG signal is one type of weak biological signals. It is a typical non-stationary random signal. ECG signal is easily contaminated by high frequency noise such as electromyographic interference and low frequency noise such as baseline wander The results of IMFs based on the PPI envelope method are shown in The results of IMFs based on the proposed FC-PCHI envelope method are shown in By adding up the IMFs decomposed based on three methods except the first-order IMF and the residual respectively, the preliminary ECG denoising results with three methods are shown in 200 random segments of ECG signals from all 48 records in the MIT-BIH Arrhythmia Database, which include typical ECG morphologies and typical kinds of noise, are decomposed using three methods, respectively. The comparison of AIO and AIEC results are listed in There are some interesting clues to the actual function of EMD that can be drawn based on both the CPSO method and the simulation examples. As we saw, CPSO method attempts to approach a set of the flattest upper and lower envelopes, and EMD performance appeared to be improved significantly. This may due to that EMD performs as a high-pass filter on the signal in each sifting iteration. This is possible since the local extrema, on which the sifting iteration is based, mainly carries information about the fast oscillating signal.The interpolation method plays an important role in the sifting process. The PCHI is a local interpolation method in the sense that the corresponding piecewise polynomials depend only on the two nearest nodes. This renders the later interpolation method easier to handle mathematically than natural cubic spline.In this paper, we proposed an alternative envelope fitting method for EMD, the FC-PCHI method. The analysis results of the proposed method on three different types of data: ascertain signal, random signals and real non-stationary signals showed that the proposed method has obtained much more accurate and reasonable results than those obtained by the classical CSI method and the PPI method.In summary, our contributions are as follows:The proposed FC-PCHI method effectively solves the overshoots caused by cubic spline interpolation (CSI) and the artificial bends caused by piecewise parabola interpolation (PPI).In the IO test, the IO/AIO of the proposed method is 0.04054, 0.02222±0.01468 and 0.03953±0.04013 for the simulation signal, random signals and ECG signals respectively, which is lower than the IO/AIO of the IMFs based on either the CSI method or the PPI method, which means the IMFs are more orthogonal.To get an idea of the energy conversation, the IEC or AIEC is adopted. The IEC/AIEC of the proposed method is 0.96193, 0.93509±0.03290 and 0.93041±0.00429 for the simulation signal, random signals and ECG signals respectively. It is closer to 1 than the IEC/AIEC of the IMFs based on both the CSI method and the PPI method, which indicates the total energy deviation amongst the components is smaller.The comparisons of the Hilbert spectrums show that the proposed method overcomes the mode mixing problems very well, and make the instantaneous frequency more physically meaningful.However, if there are many extreme points in a data, the CPSO may take a long time. This will affect the pace of the EMD. That is to say, the proposed FC-PCHI method is not suitable for long and very noisy data. The research toward the reduction of the time cost for the proposed FC-PCHI method is still in the investigation.In addition, as the interpolation procedure may lose original information or create additional information which has nothing to do with the original data, the inherent problems during the SP such as end issue, overshoot and mode mixing may be caused by the interpolation issues. The interpolation may make the SP and corresponding IMFs depending on the interpolants. Therefore, free-interpolation models for SP are also our future research interests.


The leg muscles of legged animals show differentiation with regard to the contraction velocity of the fibres in them.Thus one can distinguish between slow, fast and intermediate muscle fibres according to their contraction velocities.Accordingly, they are innervated by specific motoneurons bearing the corresponding name. The stick insect, because of its relative simplicity, suits particularly well to studying the properties of these muscle types and their neuronal control. Thus a large amount of experimental data is available from this order of animals. We shall therefore refer to them in the following. Bässler et al.  showed tTo take account of this fact, we extended our existing model  by dividBy means of our model, we first demonstrated that locomotion (stepping) is indeed primarily determined by the activity of the fast muscle fibres, even though the slow ones are co-active. We also showed that in static positions the residual stiffness of the slow muscles is capable of maintaining the posture. We then applied our model to elucidate intra-leg coordination of the muscle activity when the animal stops and when it re-starts. According to our model, intra-leg coordination at stopping is brought about by inhibiting the individual motoneurons via inhibitory interneurons, rather than switching off the central pattern generators associated with the antagonistic muscle pairs of the leg. The simulations showed that the leg completes a stance phase after the touch-down of the tarsus until the femur reaches its static horizontal position, and the tibia its static flexion. Depending on the steady-state horizontal position (angle) of the femur, the stepping commenced with a swing or a stance phase. The above simulation results are in good agreement with the relevant experimental findings. The model thus provides a putative intra-leg coordination mechanism that can account for the processes that take place at stop and at re-start of stepping of a multi-joint leg, like that of the stick insect.


In this work we demonstrate the principles of a systematic modeling approach of the neurophysiologic processes underlying a behavioral function. The modeling is based upon a flexible simulation tool, which enables parametric specification of the underlying neurophysiologic characteristics. While the impact of selecting specific parameters is of interest, in this work we focus on the insights, which emerge from rather accepted assumptions regarding neuronal representation. We show that harnessing of even such simple assumptions enables the derivation of significant insights regarding the nature of the neurophysiologic processes underlying behavior. We demonstrate our approach in some detail by modeling the behavioral go/no-go task. We further demonstrate the practical significance of this simplified modeling approach in interpreting experimental data – the manifestation of these processes in the EEG and ERP literature of normal and abnormal (ADHD) function, as well as with comprehensive relevant ERP data analysis. In-fact we show that from the model-based spatiotemporal segregation of the processes, it is possible to derive simple and yet effective and theory-based EEG markers differentiating normal and ADHD subjects. We summarize by claiming that the neurophysiologic processes modeled for the go/no-go task are part of a limited set of neurophysiologic processes which underlie, in a variety of combinations, any behavioral function with measurable operational definition. Such neurophysiologic processes could be sampled directly from EEG on the basis of model-based spatiotemporal segregation. The manner by which the brain represents information is the subject matter of many models . Then we demonstrate that the ERP manifestations of the modeled processes seem to emerge from a comprehensive bottom-up signal analysis. Finally, we demonstrate how effective EEG markers for behavioral function vs. dysfunction (in this case ADHD), could be derived from harnessing differences in spatiotemporal characteristics of the modeled processes to untangle the superposition of the manifestations of the various processes in the sampled EEG signal.We finish by emphasizing that the modeling of the go/no-go task and the EEG/ERP interpretation and untangling presented, in the context of ADHD, should be considered a mere example of a general approach, applicable to any operationally definable behavioral function or dysfunction. We touch upon the significance of this possibility.The first challenge we encountered when trying to model the go/no-go process is how to present the temporary relations between the go stimulus and its related response and between the no-go stimulus and its avoid response. Depending on the sensory modality employed, we expect the involvement of certain sensory regions in the go/no-go task: primary sensory, higher unimodal, and heteromodal. Similarly, depending on the specification of the go and avoid responses, we expect the involvement of specific motor-related regions: primary as well as higher motor and prefrontal regions. Specifically, the no-go or avoid response may involve mainly such higher regions  are known to have significant excitatory effects upon the motor regions, including the primary motor region  and the primary motor region: primary sensory region → posterior thalamus → amygdala → substantia nigra pars compacta → dorsal striatum → ventral thalamus → motor cortex (including primary). Figure Theoretical chains like the one described above are somewhat fragile. For example, it appears that meticulous modeling of the dopamine effect in the context of the general function of the basal ganglia may result in changes in the preliminary model we presented. Another weakness in the proposed chain relates to the anatomical connections between the posterior thalamus and the central amygdala, and between the central amygdala and the substantia nigra pars compacta. Our knowledge regarding these connections stems mainly from several animal studies, and may be imprecise. Alternative chains may be possible, as well as potential shortcuts in the presented chain. Furthermore, as was stated previously for the hippocampus, the schema we described above hardly touches upon the possible functional features of the amygdala or of the basal ganglia.Nevertheless, the requirement of a process for promoting responsiveness, which is likely to involve subcortical regions, is derivable directly from the processes described above as being necessary for modeling the go/no-go task. Furthermore, we cannot find many alternative regions and region chains that could underlie promotion of responsiveness aside from perhaps some shortcuts in the chain suggested above. Involvement of the basal ganglia, and in particular of its dopaminergic system, seems to be supported especially for strong, significant, or infrequent stimuli . The effect of methylphenidate, mediated through dopaminergic synapses, on the results of versions of go/no-go tests in ADHD, is also touched upon below in this context. Note that even if the pathophysiology can be related to other (non-dopaminergic) parts of the pathway, enhancement of relevant dopamine effect may still improve functionality.To summarize this section, we found it necessary to model three processes that can possibly underlie the go/no-go task, and suggested a rough anatomic embodiment for their implementation. The neurophysiologic processes are: (i) memory maintenance, (ii) evoking perception by stimulus, and (iii) response enhancement (responsiveness).Electroencephalography is a long standing technology with many aspects of practical use. Vast clinical and non-clinical research results seem to support the possibility of yet much wider practical use. This is further supported by the relative availability of this technology, in terms of usability and cost, which has been even further advanced over the last years. This is the motivation to search the manifestation of the modeled neurophysiologic processes in the EEG signal. We hope that sufficient specification of such manifestations will yield accurate and useful markers for the processes.Not unlike other sampling technologies, the EEG signal has its limitations in representing the intricacy of neurophysiologic processes. It does not present the activity with a resolution of single units of representation , it is less sensitive to activities in deep structures of the brain and its resolution of spatial localization is rather limited. Nevertheless, we suggest below a preliminary approximation of the manner in which neurophysiologic processes are manifested in the EEG signal.Various theories have been raised regarding the source of the EEG signal  in perception. Thus, a relatively short activation, at least on the scale of tens of milliseconds , may be expected over the relevant sensory and associated motor regions after stimulus presentation.In the model we suggested an important role of these ventral thalamic nuclei in the activation of relevant motor regions as part of the responsiveness process following the sensing of task-related stimuli. These nuclei appear to be heavily influenced by major subcortical motor-associated structures such as the cerebellum  seems to be evoked by both types of stimuli to a similar degree  activity prevalent among subjects diagnosed with ADHD , which replaces the longer (N2-P3) activation that is manifest in control subjects and lacks in ADHD subjects.The soundness of the ERP characteristics of ADHD is further demonstrated by its susceptibility to treatment, for example by methylphenidate. The above-mentioned ERP activities, particularly the P3 activity, often tend toward normalization following such treatment . Detailed description of the experimental setup could be found  comprehensive search for activity events consistent across subjects of the same experimental group and stimulus type; and (ii) analysis of spatiotemporal continuity between the events. Details on each step are presented below.First step: division into frequency bands. As shown in Figure Second step: discretization to events of peak time and amplitude. The eight frequency bands selected  were sufficiently narrow to produce near symmetrical half-waves  can also be seen in all experimental conditions in some central (C), some temporal (T), and often some frontal (F) electrodes in the alpha frequency band. In some experimental conditions such early alpha events are also found at Pz. Overall, both early (average<200 ms) and late (average>200 ms) delta events are more prevalent in the control than in the ADHD condition and in the no-go than in the go condition. Figure Figure Overall, the activities found belong either to an early set, in the alpha frequency band at 50–200 ms post-stimulus, or to a prolonged set in the delta frequency band beginning around stimulus onset until 600 ms post-stimulus. Such a summary of two sets is presented in Figure early, seems to manifest strongly at 50–200 ms following the stimulus in the alpha frequency band, mainly at the temporal and centrofrontal electrodes. The second process, which is termed prolonged, seems to manifest strongly at 0–600 ms following the stimulus in the delta frequency band, mainly at centrofrontal and parietal electrodes. There is a clearly notable spatial overlap between the two suggested activities in the time range of 50–200 ms at the centrofrontal electrodes. The early activity appears in both controls and ADHD subjects and for each group, both in the go and in the no-go conditions. The prolonged activity, however, is most evident in the control-no-go condition, to a lesser degree in the ADHD-no-go condition and in the control-go condition, and least in the ADHD-go condition.The analysis results suggest that the go/no-go task ERP activity emerges from two processes spread over time and space. The first process, which is termed In spatiotemporal terms these activities are consistent with the predicted manifestations of the perception (early) and responsiveness (prolonged) processes, as they are modeled in the first section. The responsiveness-related prolonged activity seems to overlap spatiotemporally with the P3 and late N2 activities, characteristic in the literature of the control group and of the no-go condition. The activity related to the enhanced early responsiveness, characteristic of the ADHD group  and sensorimotor regions seems to be in accordance with this interpretation.Overall, we demonstrated in this section the matching between a comprehensive bottom-up data analysis approach, as well as the relevant up-to-date literature, with the predictions of the theoretical model of underlying neurophysiologic processes and their manifestation in EEG.As was stated above there are spatiotemporal differences between the EEG manifestations of the perception and responsiveness processes, However there is also significant overlap, both theoretically driven and experimentally demonstrated. This overlap may have significant impact upon the precision of most ERP analysis methods – for example of standard ERP wave amplitudes and latencies. Instead we suggest emphasizing the differences in the manifestations of the processes.Even simple temporal segregation seems to suffice. In Figure Thus it is possible to derive a theory-based simple markers for the functionality of the neurophysiologic processes underlying behavioral function vs. dysfunction, as is demonstrated for ADHD. This is done by harnessing precisely of elementary differences in the spatiotemporal manifestations of the processes.In the present study we demonstrated the possibility that a rather limited number of neurophysiologic processes can underlie the EEG signal. To demonstrate this possibility, we employed a top-down model-derived analysis, based on the assumption that the neurophysiologic processes manifest in EEG relate to a set of thalamic nuclei. We further matched the modeled processes with a bottom-up analysis of the literature as well as with a comprehensive data analysis method, and showed the precision, which could be derived from it. In the context of the go/no-go task, we discussed five types of neurophysiologic processes that seem to have such an associated thalamic center: memory maintenance, perception, responsiveness, arousal, and sensation. We are aware of only one additional relevant thalamic center and thereby neurophysiologic process, which could manifest in EEG – the executive function, which seems to be related to the dorsal medial thalamic nuclei , touched upon another two in the context of EEG manifestation , and mentioned an additional one (executive function). Each of these processes can be detailed, for example, by specifying different sensory modality involved in one task or another. Furthermore, it is clear that some additional processes are involved in various behavioral functions. For example, it seems necessary to model the processes involving activity-dependent change, which are relevant to exploration and learning behavior. But it is not unrealistic to conceive of a rather limited and comprehensive set of such neurophysiologic processes that underlie any behavior as long as it is operationally measurable. It is likely that most of these processes are among those measurable with EEG (or with other techniques not discussed in our work), as the interaction between cortex and thalamic nuclei occurs in most significant neurophysiologic processes. Future work should demonstrate the applicability of the above approach to other types of operationally defined behavioral function and dysfunction.Operational definitions exist for much of behavioral function and dysfunction, though there are often significant variations in the definitions offered for the same behavior. We hope and believe it will be possible to derive from such a limited core of underlying neurophysiologic processes a clear-cut definition of the spectrum of possible behavioral functions and dysfunctions in a comprehensive manner. This may enable comprehensive assessment, unification, and sharpening of current operational definitions. The possibility that these core neurophysiologic processes, which underlie behavior, are measurable directly with the available technology of EEG, via simple and precise markers, may have major practical significance, both clinical and non-clinical.Finally we discuss the impact the approach we present may have on the research of neuronal representation. The characteristics upon which we based our model are elementary. The evaluation of the impact of more fine-tuned may be a neuropsychological eye-opener and we call for such a systematic effort. Undoubtedly throughout the modeling and further on in the relation of the modeled processes with the EEG signal, we employed sometimes less sound assumptions regarding neuronal representation. Evaluation and correction of the characteristics seems to us of major significance.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


This electrically driven sandwich-type monolayer molecular rotor device showed an on/off ratio of approximately 104, a read window of about 2.5 V, and a retention time of greater than 104 s. The rotation speed of this type of molecular rotor has been reported to be in the picosecond timescale, which provides a potential of high switching speed applications. Current-voltage spectroscopy (I-V) revealed a temperature-dependent negative differential resistance (NDR) associated with the device. The analysis of the device I–V characteristics suggests the source of the observed switching effects to be the result of the redox-induced ligand rotation around the copper metal center and this attribution of switching is consistent with the observed temperature dependence of the switching behavior as well as the proposed energy diagram of the device. The observed resistance switching shows the potential for future non-volatile memories and logic devices applications. This review will discuss the progress and provide a perspective of molecular motion for nanoelectronics and other applications.The use of a functional molecular unit acting as a state variable provides an attractive alternative for the next generations of nanoscale electronics. It may help overcome the limits of conventional MOSFETd due to their potential scalability, low-cost, low variability, and highly integratable characteristics as well as the capability to exploit bottom-up self-assembly processes. This bottom-up construction and the operation of nanoscale machines/devices, in which the molecular motion can be controlled to perform functions, have been studied for their functionalities. Being triggered by external stimuli such as light, electricity or chemical reagents, these devices have shown various functions including those of diodes, rectifiers, memories, resonant tunnel junctions and single settable molecular switches that can be electronically configured for logic gates. Molecule-specific electronic switching has also been reported for several of these device structures, including nanopores containing oligo(phenylene ethynylene) monolayers, and planar junctions incorporating rotaxane and catenane monolayers for the construction and operation of complex molecular machines. A specific electrically driven surface mounted molecular rotor is described in detail in this review. The rotor is comprised of a monolayer of redox-active ligated copper compounds sandwiched between a gold electrode and a highly-doped P However, as the physical limitation comes closer, further scaling of the basic components of the microelectronic circuit such as memory and switch are now being questioned. The anticipation of this limitation has led researchers in academia and industry alike to consider many conceptually new materials and structures from the molecular scale point of view. The above scenario provides an opportunity for exploring molecular machines and nanomachines which can be functionalized as nanoscale electronic devices. These devices based on functional molecular units acting as state variables  are attractive due to their potential ultimate small size, low-cost, low variability, highly integratable characteristics and the ability to self-assemble themselves .etc. The focus of discussion here is on potential devices which could be integrated with conventional semiconductor technologies.A specific kind of molecular machine can be a particular molecular device designed to perform mechanical movements under control of appropriate energy inputs ,8. TriggIn this paper, we limit our discussion to the rotational motion and we first describe the different types of rotary motors generally. Then we will focus on a specific electrically driven surface mounted molecular rotor because of its potential capability of integration with standard semiconductor fabrication technologies, which provides the realization possibility in the near future. In particular, we will discuss their molecular structures, mechanisms and operation principles, respectively. Finally we will provide a perspective of scalability, challenges and potential applications. This review will concentrate on a real prospect of integrating a bottom-up approach, based on molecular design and micro-fabrication, in order to construct molecular electronic devices that can store information with very high densities.1.1.Besides the linear motion, as mentioned in the previous section, the rotary motion is another category of molecular machines. Like the linear motion of molecules, these molecules can be activated to make rotation movement chemically, optically, or electrically as a switch, and the recognition of the change of positions of the chemical elements by the charge transport through the layer results in the off and on states.The molecular rotor usually consists of two parts that can easily rotate relative to each other. The different types of rotors can generate different rotation angles due to the specific rotating ligands. Normally the part with a larger moment of inertia is defined as the stator and the part with a smaller moment of inertia as the rotator, while the term rotor refers to the whole molecule. The distinction is somewhat arbitrary except the stationary part is fixed on or sits within a much more massive object, or on a solid substrate. In the absence of a fixed mounting, the rotator and the stator both turn around the same axle.Showing proper electrical characteristics, some molecule rotors foray into the new field of molecular electronics. The idea is the use of molecular building blocks for the construction of electronic components, both passive  and active . The concept of molecular electronics is attractive and excites scientists and engineers alike due to its prospect of size reduction in electronics offered by molecular-level control of assembly. Hence it provides means to go beyond the anticipated physical size of the conventional CMOS in view of fundamental limiting processes  and cost of top down micro-fabrication technology. However, to realize logic functions using molecular devices, we may face the challenges that the dynamics of molecules in contact with electrodes is far from easy grasp in determining its mechanism as the effects of electrodes and interfaces and others tend to complicate the characterization of the behaviors. In particular, the effect of different switchable and nonswitchable compounds on the observable electrical signals, such as current flow and voltage thresholds, complicate the problem and thus has to be carefully studied to obtain a microscopic understanding of what is really happening inside a particular molecular electronic device. Consequently, appropriate control experiments need to be performed and great care must be exercised in order both to understand the principle of operation and to attribute specific models to the observed switching effects. Although in many cases, results obtained and conclusions drawn may not be as definitive as those of traditional semiconductor physics, where analytical techniques have been relatively mature, hypothesis testing and detailed investigation can help further fundamental understandings.Molecule-specific electronic switching has been reported for several device structures, including nanopores containing oligo(phenylene ethynylene) monolayers ,12 and pi.e., macroscopic gold electrodes) to achieve its different states. In particular, transition metals offer useful features in controlling these state variables due to their accessible oxidation states. This process can results in low power consumption. The variables which can be controlled in the transition metals include coordination number, color, and geometry [i.e., the metal in the center can be used to drive intra-rotational motion. The next section will address rotational molecular switches.Molecular switches use a state variable for which information storage relies on physical changes of the molecule. For example, a bistable molecular switch may be immobilized onto a bottom electrode and the molecular layer is then sandwiched by a top metal electrode  on a solid support; and the surface mounted molecular rotor is that is attached or bonded to the surface of a solid support. As discussed above, for solution phase rotors, the distinction between the rotator and the stator may be sometimes ambiguous, as both parts of the molecule rotator are related to each other. For solid phase rotors, the molecule close to the solid support is normally the stator. And, for a surface-mounted molecule, one can clear specify the stator, which is rigidly attached to the surface, and forms a part of the molecular structure. In addition, the axle of rotation about which the rotator turns can be perpendicular  or parallel  to the surface . For solWithin each category of solution phase, solid phase and surface mounted molecular rotors; a subdivision may be made based on the chemical nature of the axle, such as a single bond, a triple bond, or a metallic atom. This chemical nature of the bond strongly influences one of the fundamental energy terms in the system, the intrinsic barrier energy and width of rotation.In addition to the above structural classification, the other method to categorize rotors is by their nature of dynamics under a given set of environmental conditions. Two extreme cases of thermally activated systems are: (i) the rotor with a small rotational potential energy barrier such that it is easy for the rotor to reorient at a sufficient temperature; and (ii) those having a stator lying in the lowest energy state and thus a large barrier. Switching will normally not occur unless the system is perturbed by an external force. It is obvious that the interplay of the different energy terms in a system determines the rotor dynamics; the environment temperature also plays an important role in determining the energy barrier of rotation.2.Previously reported rotary motions such as a rotational actuator based on multi-walled carbon nanotubes , fluorestransoid sandwich with two pairs of carbon vertices reflected through a center of symmetry, but that of the Ni(IV) species is cisoid  around a nickel axle . The Ni [The schematic structure of this molecular device is shown in  Ni(III)  and Ni(I Ni(III)    with a N Ni(III) ,74.trans configuration [commo-bis-7,8-dicarbollyl metallacarboranes, while some forms the cisoid configuration (such as in Ni(IV)) with its pairs of carbon vertices on the same side of the molecule [versus the standard calomel electrode (SCE)). The authors also showed experimentally and theoretically that the interconversion acts as a rotating molecular machine in their paper. In their model, the photoexcitation induced geometrical changes were simulated to compare with the results caused by electrochemical reduction. Therefore reduction places an electron in the lowest unoccupied molecular orbital (LUMO); photoexcitation removes an electron from the highest occupied molecular orbital (HOMO) and places it in the LUMO. There are other solution phase molecular rotors. For example, in suitably designed rotaxanes, the swinging movement of the ring around the axle can be electrochemically driven as well.The interconversion of the geometries of Ni(III) and Ni(IV) controlled by the change of the nickel oxidation state provides the basis for the controlled, rotational, oscillatory motion, and can be achieved electrochemically by redox reactions or photochemically. It is based on the presence of two adjacent CH vertices, which introduces localized regions of reduction negative charge . The resguration ,72,76  molecules of around 1.5 nm in diameter  on a solid support. A good example is that of single-molecule rotors, and it was found that the rotor, from a study of scanning tunneling microscopy (STM) in ultrahigh vacuum , was surdiameter . It showdiameter . Interesdiameter . It shouSupported by experiments of this kind and, by the existence of a wealth of nanometer scale natural molecular machines ,80, it s4.As we mentioned in the section of solution phase molecular rotors, previously reported rotary motions including a rotational actuator ,83, fluoi.e., eVs per molecule, where Vs is the voltage for which the redox event occurs. Because information storage is based on the nanoscopic movement of atomic nuclei about the copper center, the maximum rate of switching process is fundamentally limited by the frequencies of the relevant rotational vibrational modes of the compound, giving a minimum switching speed on the order of a picosecond [The use of transition metal ions as templates to construct multicomponent chemical systems with interlock or knotted topologies has been extensively exploited . Some ofcosecond . The het+ Si) and a Cu axle), the metal axle (Cu), and a diimine rigid rotator  on the doped Si  Cu(I) and bis Cu(II) complexes in methylene chloride. An absorption peak, corresponding to a metal-to-ligand charge transfer (MLCT) indicative of tetrahedral geometry, was observed near 450 nm for the Cu(I) complex but not for the Cu(II) complex. Two additional peaks observed in both Cu(I) and Cu(II) complexes and centered at approximately 280 nm and 340 nm are attributed to ligand-to-ligand transitions, 2 with a peak-to-valley ratio (PVR) near 5. This RT-PVR exceeds that observed in typical heterostructure resonant tunneling diodes. The author also performed temperature dependent I-V measurements of the device from 77 K to room temperature as illustrated in I-V characteristics of the monolayer device are shown in a is the activation energy, ΔI is the peak minus background current, which is related to the rate constant of chemical reactions, T is the temperature and R is the gas constant. Curve fitting of the data for the temperature range of T > 244 K shown in The results have been further analyzed to extract the activation energy. From the well-known Arrhenius equation below:+ Si substrate shifts the energy position of the molecular state relative to both gold electrode and P+ Si band-edges. As the rotary motion around the molecular axle is controlled by electron transfer, a portion of the applied potential is used to initiate the redox process within the molecular layer. First, calculations of the band gaps for the Cu(I) and Cu(II) complexes by TD-DFT yielded values of approximately 2.7 eV and 3.4 eV, respectively. Additional calculations of the molecular redox energy produced a value of 1.05 eV, which is of the same magnitude as the 0.7 eV difference of the band gaps between the Cu(I) and Cu(II) complexes. The 0.35 eV difference between these two values may be attributed to the rotational energy contribution. Finally, the electron affinity of the Cu(I) complex is estimated to be 3.7 eV, which anchors the LUMO energy state with respective to the gold Fermi level .The switching process begins with the low conductivity state of the Cu(II) complex under a positive bias as shown in + Si substrate was estimated. Since this molecular rotor is sufficiently large, the rotation speed can be estimated classically based on the kinetic energy of rotation and rotational inertia. As the angle between the Cu(I) and Cu(II) systems is 90 degrees, the rotation speed can be estimated as 1.4 ps, ignoring acceleration components of rotation during the beginning and the end of the movement. This value is reasonable as compared to previous simulation results of rotation in solution giving a speed of 0.5 ps [An additional attractive property of functional molecules based on rotational motion is their fast operational speed. In most cases, previous studies have focused on solution-based molecular rotors. With the perspective of exploiting the switching speed in mind, the rotation speed of the molecular rotor on Pf 0.5 ps .To achieve logic functions, the molecular switches have to be able to be compatible with conventional CMOS manufactory technology. From this perspective, the surface mounted molecular device is the most likely candidate for the molecular electronics.5.As we have described above, this review deals with molecular rotors from the point of view of their potential utility for molecular switches and logic devices. In gases, liquids, and certain solids, entire molecules can rotate as a whole around independent axes freely, but they cannot be used as a stable electrical device and furthermore certain process flows have to be developed to be compatible with the traditional CMOS technology; so we restrict the scope of this section to the surface mounted molecular rotors, in which groundwork was laid down for the current developments –93. As s5.1.In the advent of nanoelectronics, the question of inherent physical limits as well as possible technological barriers to scaling is among the most important. In this section, we will start with discussions on the fundamental physical limits of scaling; then we focus on the scalability of molecular rotor devices based on the redox assisted electron tunneling transport.−25 kg, while that of free electron is 9.1 × 10−31 kg, four orders of magnitude higher than a free electron. Therefore the molecular rotor device can in principle be scaled down to below 5 nm. In fact, the designed monolayer molecular rotor device discussed in the last section is on the order of 3 nm scale. However the transport of this device is still controlled by electron tunneling instead of the atomic molecular tunneling if an electrical field is applied even though the tunneling barrier height may be larger than Si, for example. Nevertheless as to be discussed later, the redox energy adds additional tunneling barrier height.It was pointed out that the logic device of the size below 5 nm may preferably use a state variable that has a heavier effective mass than that of an electron . In prinAs we discussed in the last section, the surface mounted molecular rotor is based on a redox-assisted electron tunneling transport model for the device operation. An applied electric field can induce the rotation associated with the redox reaction, thus change the energy barrier height and thus alters the availability of the states to be tunneled to. When the device operates at the Cu(II) state, the energy barrier is increased and electron transport only happens through a barrier to access the available states. Conversely when the device operates at the Cu(I) state, the energy barrier becomes lower and, the accessible states are readily available; thus electrons can easily tunnel through it. In general, the current at the Cu(II) case is lower and strongly unidirectional since the barrier behaves like a Schottky barrier due to the use of Si substrate; while the current at the Cu(I) case is larger and bidirectional, showing close to ohmic behavior.The transition between the Schottky and tunneling modes is achieved by simply changing the polarity of the bias, which activates the redox reaction associated with the rotation movement. Thus the I-V data shows a nonlinear behavior with hysteresis as well as giving rise to negative differential resistance as described in It is important to note that the operation of this device is based on both electron transport and Redox reaction. Although the ultimate limiting factor of scalability of this device is still the leakage current as a result of the quantum tunneling of electron, the energy required by the redox reaction adds an additional energy barrier to the total tunneling barrier so that the probability of the tunneling becomes smaller. Due to the redox reaction, the scalability of this redox-assisted tunneling device should be better than the pure electron tunneling devices, in term of minimizing the leakage.The suggestion that heavier particles might be preferred for nanoscale devices has attracted the attention of several research groups –96. A nuFurther improvement of the scalability of this surface mounted molecular rotor can be achieved by replacing the metal electrode with a solid electrolyte. The idea is to build a pure ion transport system. It is important to carefully choose the solid electrolyte which determines the energy barrier as well as transport ions that are responsible for the current flow where a low bias is applied to move ions while electron tunneling does not occur. A mimic system may be human brain . In huma5.2.Although specific organic molecules have their advantageous electronic properties, the reliability is always a challenge. The problem may be due to poor material uniformity because of inherent impurities, material interfaces, and electrode contacts. Therefore, the inherent characteristics of these molecules are easily masked by effects from the electrode materials and experimental conditions. Great cares must be exercised in attributing mechanisms and in constructing models to the observed switching behaviors and thus critical control experiments are required to obtain fundamental physical understanding. Once we fully understand the particular switching mechanism, studies of reliability, including a thorough investigation of all conceivable failure mechanisms, and subsequent development of optimization steps to correct them can follow.The heat dissipation is another issue to be considered. The specific heat capacity and thermal conductivity of materials affect the device performance and limit the scalability of the molecular device. Proper selections of materials for their favorable heat diffusion rates and for controlled material interfaces on the atomic scale may circumvent the heat dissipation problem to the point to allow for scaling beyond the ultimate tunneling limit.5.3.To date, most of resistive memory devices are based on the change of resistance caused by an applied external electrical field or current . The bas3) [A number of organic MIM devices have been reported to show resistive switching. Among the earliest work, Gregor ,102 used3) ,106, N,N3) , 2-amino3) , several3) ,110, and3) ,112. RepThe redox-based nanoionic memory becomes attractive to the semiconductor industry because experimental demonstrations of scalability, retention and endurance are encouraging ,114. TheAlthough the devices we discussed above are all two terminal devices. In principle, a three terminal device could be designed with a barrier height controlled by a gate similar to conventional Field Effect Transistor (FET) devices. Such approach could reduce the leakage current due to the presence of an additional energy barrier as well as the use of heavier particles. Proper selections of materials for their electron affinity and controlled material interface on the atomic scale may also allow this device for going beyond the ultimate tunneling limit of electron and offers a potential to realize future non-volatile memory or logic devices for information processing applications.To achieve these devices comparable to molecular devices of the size scale of <5 nm, the cost of conventional top down lithography may become prohibitively high for manufactory of these devices of integrated circuits. The patterning size variability due to the presence of subatomic particles and processing fluctuations at this scale increases the rate of faults. Beside to these fabrication challenges, nanoscale circuits also likely contain defects so numerous that some forms of defect tolerance will be necessary to achieve acceptable yields.The above challenges of nanoscale devices in general and the yield issues associated with the molecular devices described above lead us to address on configurable crossbar architectures –123, wheThe crossbar structure possesses many attractive features as it offers the highest possible device density and the simplest interconnect configuration that still allows for external access to each nanodevice . It is aHybrid nanocrossbar/CMOS architectures have also been proposed to complement the limited functionalities of two-terminal switches by integrating with CMOS components to expand their functionalities –130. It If a crossbar structure is referred to as a passive matrix architecture, the two-terminal molecular device, however, can also be integrated to become active matrix architecture by introducing a select transistor at each node by which the storage cells can be decoupled for those not addressed. This concept significantly reduces crosstalks, interferences and disturbing signals in the conventional crossbar system.Overall, the concept of molecular memory emphasizes extreme scaling; in principle, one bit of information can be stored in the space of a single molecule. Because of their small size, very dense circuits could be built, and bottom-up self-assembly process could be applied to augment top-down lithography fabrication techniques. Computing with molecules as circuit building blocks is an exciting concept with several desirable advantages over conventional circuit elements. However, referring to the 2011 ITRS on emerging research devices, the molecular memory device still stands at a long term research state because of our limited understanding of the phenomena accompanying molecular switching, where currently many questions remain. In addition, the variability and reliability will need to be established.In summary, there are a lot of interesting works in this field under progress such as ferroelectric molecular rotors , design


Traumatic dislocation of the interphalangeal of the fifth toe is an unusual foot injury.We report the case of a 47-year-old woman who sustained a minor foot injury for more than 30 years, resulting in chronic, irreducible dislocation of the proximal interphalangeal joint of the fifth toe. The affected proximal interphalangeal joint was accessed via a dorsal incision over the unstable interphalangeal joint. It was found that the interposed interphalangeal joint capsule and attenuated lateral collateral ligament were reconstructed, and it was stabilized by temporary insertion of a Kirschner wire. The affected joint was found to be stable, well-positioned and pain-free at the 12-month post-surgical check-up.This unusual presentation of a chronic joint dislocation responded favorably to open reduction, soft tissue reconstruction and restabilization of the affected joint. It is suggested that this approach will provide a good and functional outcome even in cases of very long-standing joint injury. Isolated, traumatic dislocation of interphalangeal (IP) toe joint is an uncommon foot injury more usually occurring in association with other foot injuries . The greNon-resolving, chronic IP joint dislocation affecting the PIP joint of the fifth toe is an uncommon foot injury. When it occurs, it is usually the result of abductory forces causing dorsolateral displacement of the distal segment of the fifth toe . The joiIt is shown that the case of chronic irreducible dislocation of the PIP joint of the fifth toe occurs and it can be resoluted by opening the reduction of the dislocation. The mid-term (a 12-month post surgery) results in the intervention are presented.A 47-year-old woman in good general health, with no other co-morbidities presented with a long history of chronic right fifth toe pain for 30 years. She reported a history of injuring her right foot when playing sport for 30 years. She when landing recalled that she had twisted her right foot; moreover, the foot was not well treated at that time of the injury. The only treatment for the fifth toe was with the temporary bandage to reduce the deformity. Then, the PIP joint of the fifth toe was redislocated for several times in 6 months after the first injury and the same treatment was attempted each time. After that, the fifth toe gradually became permanently swollen and painful on movement. When the patient presented in the out patient clinic with chronic right fifth toe pain and swelling, Figure , the toeThe decision was made to attempt the correction of the chronic dislocation by open reduction, as the problem had been present for many years and all previous attempts at closed reduction had been non-successful. The dislocated PIP joint was exposed via a dorsal incision, revealing that the joint capsule and attenuated lateral collateral ligament were interposed within the PIP joint space, and the articular cartilage at lateral condyle of proximal phalanx of the fifth toe became eroded Figure . The joiFor the 12-month post-surgery, the PIP joint of the fifth toe remained stable, painless and aesthetically pleasing Figure . The patDislocation of the PIP joint of the toe is an uncommon injury of the forefoot. The mechanism of injury usually occurs from hyperdorsiflexion or sudden application of a dorsolateral force causing traumatic abduction of the PIP joint of the toe. This is a common injury to both the great and lesser toes -7,9,10. Closed reduction is usually successful in correction of IP joint dislocation in hallucal or lesser toes. The digital deformity is initially accentuated. The longitudinal traction, allowing the joint to resume this deformity was applied and then released, so it corrected the anatomical relationship . StientrOpen reduction is best accomplished through a dorsal approach -7. TempoTraumatic dislocation of the interphalangeal joint of the fifth toe should be diagnosed at the earliest stage which was treated initially by adequate tractional reduction of the joint incongruency with relating to soft splintage immobilization in order to prevent subsequent complex chronic joint subluxation. In cases where this approach is not successful or pain persists open reduction, reposition and restabilization of the dislocated joint and its associated soft tissue structures are indicated to achieve a functional toe.Written informed consent was obtained from the patient for the publication of this report and any accompanying images.The authors declare that they have no competing interests.All authors read and approved the final manuscript.


Kulldorff's spatial scan statistic has been one of the most widely used statistical methods for automatic detection of clusters in spatial data. One limitation of this method lies in the fact that it has to rely on scan windows with predefined shapes in the search process, and therefore it cannot detect cluster with arbitrary shapes. We employ a new neighbor-expanding approach and introduce two new algorithms to detect cluster with arbitrary shapes in spatial data. These two algorithms are called the maximum-likelihood-first (MLF) algorithm and non-greedy growth (NGG) algorithm. We then compare the performance of these two new algorithms with the spatial scan statistic (SaTScan), Tango's flexibly shaped spatial scan statistic (FlexScan), and Duczmal's simulated annealing (SA) method using two datasets. Furthermore, we utilize the methods to examine clusters of murine typhus cases in South Texas from 1996 to 2006.When compared with the SaTScan and FlexScan method, the two new algorithms were more flexible and sensitive in detecting the clusters with arbitrary shapes in the test datasets. Clusters detected by the MLF algorithm are statistically more significant than those detected by the NGG algorithm. However, the NGG algorithm appears to be more stable when there are no extreme cluster patterns in the data. For the murine typhus data in South Texas, a large portion of the detected clusters were located in coastal counties where environmental conditions and socioeconomic status of some population groups were at a disadvantage when compared with those in other counties with no clusters of murine typhus cases.The two new algorithms are effective in detecting the location and boundary of spatial clusters with arbitrary shapes. Additional research is needed to better understand the etiology of the concentration of murine typhus cases in some counties in south Texas. In recent years, there has been a significant increase in public concern about environmental hazards and disease events . The nec) . These s) . Among t) ,7.a priori, this method uses a scan window of varying sizes, corresponding to varying population and varying number of incidents. This method has been applied to many research fields. Examples of these applications include disease pattern analysis [Inspired by the work of Openshaw et al. 1987) [7 [8] andanalysis , criminoanalysis ,11, netwanalysis , as wellanalysis . Howeveranalysis ,15. AlthRecently, many methods and strategies have been proposed to improve the detection of clusters with arbitrary shapes by constructing scanning windows of irregular shapes. Tango and Takahashi (2005) presented a "flexibly shaped spatial scan statistic" (FlexScan) which uses a limited exhaustive search to detect arbitrarily shaped clusters by aggregating its nearest circular neighboring areas . The spaOne solution to this problem involves setting a constraint to guide the search process so as to reduce the number of candidate scan windows. Patil and Taillie (2004) introduced the concept of "upper level set" and developed an "upper level set scan statistic" . Based ou) to prevent the generation of large super-clusters from smaller clusters [GGS cannot avoid the local maximum problem . Many alclusters . These aAnother famous improvement is a "simulated annealing strategy" proposed by Duczmal and Assuncao 2004). This method is based on graph theory in which nodes present centers of areas, and edges present the geographical relationships among areas 04. This . Most ofIn this article, we report the development of two algorithms that use a new neighbor-expanding approach based on the assumption that any subset of adjacent areas could make up a potential cluster, and that the shape of this cluster might not be circular or rectangular. These two algorithms are called the maxima -likelihood-first (MLF) algorithm and non-greedy growth (NGG) algorithm. These two algorithms build upon the existing cluster detect techniques, and adopt neighbor-expanding tactics to construct a set of scan windows instead of just using the scan windows in some predefined shapes. Furthermore, the proposed algorithms improve the arbitrarily-shape cluster detection method in avoiding the local maximum problem since the algorithms search for the globally most likely cluster at each step in the search process.Because the two algorithms were built upon the spatial scan statistic, it is necessary to review the spatial scan statistic first. Kulldorff's scan statistic method starts from choosing an appropriate probability model of data to compute the likelihood ratio test statistic λ(z) for any scan window z. After identifying primary cluster candidates with the maximum λ(z), a Monte Carlo hypothesis procedure tests the statistical significance and obtains a p-value .H0  and the alternative hypotheses H1 (the specific area z has a larger probability than outside areas) using either a Bernoulli model or a Poisson model. For a given region z, the likelihood function based on the Bernoulli model can be expressed using expression (1):In Kulldorff's method , one tesμ(G) and μ(Z) are the total population of the study area and population in region Z; nG and nZ are the total number of observed cases in the study area and in region Z; p is the probability that an incident falls in region Z, and q is the probability that an incident falls in the rest of the study area. The likelihood of observing n(Z) in region z is given by the function shown below:where, Where, Therefore the likelihood ratio λ(z) can be obtained as the quotient through dividing the observed likelihood by expected likelihood:Kulldorff 1997) also gave the formula to calculate the likelihood ratio based on the Poisson model as shown below [ also gavp-value, derived from the Monte Carlo simulation, is used to assess the statistical significance of the detected clusters. The Monte Carlo simulation, proposed by Dwass in 1957 [p-values can be calculated based on the sorted likelihood ratio of the real data and simulated data. For example, if there are N simulated datasets and one real dataset and the total number of datasets will be N+1. Within these total datasets, there are n simulations having a larger or equal maximum likelihood ratio compared to the one obtained from the real data. That is, the rank of the real data is n when we sort the data by their maximum likelihood ratios. The p-value for the significant testing in this example will be equal to n/(N+1). Theoretically, the smaller the p-value, the more likely the cluster is not due to chance. Due to the uncertainty associated with cluster validation, it is suggested that the proposed approach be used as an exploratory rather than a deterministic cluster detection tool.Once the most likely cluster has been identified, the next step is to test the statistical significance of the detected clusters. To do so,  in 1957 , was firk+1 by combining a k length region and one of its neighboring areas. One can easily figure out the number of regions with k+1 length based on a k length region. If the number of the neighbors around k length region is j, then one can obtain j regions at k+1 length. To clarify, we illustrate this process using an example as shown in Figure A new neighbor-expanding approach is proposed here to detect clusters with arbitrary shapes. Suppose we have a map consisting of a tessellation of component areas. These areas are associated with case numbers and the total population at risk. Two areas are considered as neighbors when they share the same boundary. We assume that a region with any set of connected areas may make up a potential cluster and a cluster may appear in different shapes depending on how many and how aggregated the set of connected areas are. Our goal is to find such clusters with the likelihood ratio in the scan statistic. In the search process, we sweep a large subset of connected areas, constructing a new region at each step by aggregating one of its neighbor areas, until certain thresholds are met or we obtain the expected results. For the sake of simplicity, we use the length to indicate the number of areas that constitute a region. We are always able to get a new region with a higher length If we choose {16} as a seed region at first length, we find it highlighted by red color in Figure While this search process continues, the number of regions increases exponentially as we aggregate more areas. This process is computationally very intensive. In order to reduce the number of regions, we developed two alternative algorithms for the construction of regions or scan windows: maxima-likelihood-first (MLF) algorithm and non-greedy growth (NGG) algorithm.The principal goal of this algorithm was to direct the new region construction process to obtain a global maximum. This maximum refers to the highest value we were able to obtain by the proposed approach. After analyzing equations (4) and (5), we found that it is hard to determine which of the following factors make the most contribution to the likelihood ratio: the number of cases, population size, or the relationship between them. Thus, there is no clear guidance that could help us construct scan windows which would have the highest likelihood ratios. Rather than construct scan windows randomly, we try to focus on the generation of windows for the most promising clusters. We name this approach as the maximum-likelihood-first (MLF) approach because it always constructs new promising clusters by expanding from the current best candidate, yielding the maximum likelihood ratio.The proposed approach is illustrated in the flowchart in Figure When we detect the cluster using the neighbor-expanding approach described above, it is very likely that the procedure may stick to some areas with high LLRs and unable to search the entire study area. Usually, LLRs of candidate clusters depend on the risk rates of their neighbors . That isAs shown in Figure The non-greedy growth (NGG) algorithm is an improved version of greedy growth algorithm . SeveralThe greedy growth approach sounds tempting, but it has an inherent deficiency in that it does not guarantee to find either the best solution or the global maximum. This method easily falls into the trap of local maximum since it excludes some areas which might potentially form a more promising cluster when they combine with other areas.To solve this problem, we propose a new algorithm to minimize the impact of the local maximum problem. To distinguish it from traditional greedy growth approaches, we name it "the non-greedy growth algorithm". The algorithm allows not only the neighboring area with the local maximum to be included but also includes many other neighboring areas in the search procedure. Usually the number of newly formed regions relies on the number of candidate regions and the number of neighbors of each region. With this method, we can set a constraint on each of these two numbers control the number of newly formed regions at the next step of the search process. Previous studies suggest that the number of candidate regions increase exponentially, while the number of neighbors of each region does not change dramatically. Therefore, it is more reasonable to set a threshold on the number of candidate regions. Theoretically, if we choose only one candidate and one of its neighbors with the highest LLR each time, this method degrades to the traditional greedy growth search method. The inverse extreme of this approach is the naïve exhaustive approach where no limitation is set.In the NGG algorithm, we set a threshold (M) on the maximum expected number of new regions at each iteration. Given that threshold and the average number of neighbors, we could easily determine how many candidate regions should be chosen to participate in the aggregation process. There are a few options in the choice of candidate regions. One is to choose M most promising regions, directly from the pool of candidates, or to choose them randomly. In the actual implementation reported in this paper, we used a combination of the two, that is, part of M candidates are from the top regions and the rest are chosen randomly.The flowchart showing the NGG algorithm is given in Figure This case study was conducted in the southeast counties in Texas, one of the areas having the most murine typhus cases in the United States Figure . Since tThe data used in the present study include geographic boundary shapefiles, population data, and disease data issued by the Texas Department of State Health services. In this study, the cluster detection was performed at the census tract block group level and the geographic boundary shapefiles are obtained from Environmental Systems Research Institute (ESRI) website and ESRI Data DVD . There aWe evaluated the performance of the two new algorithms and compared them with the simulated annealing (SA) strategy method, flexible-shape scan statistic (FlexScan), and spatial scan statistic (SaTScan) before we applied the algorithms to the south Texas data. The simulated data consisted of a tessellation of approximately 300 hexagon component areas Figure . These hFigure A further comparison was performed among these methods using the benchmark real disease data. The data were collected from 11 states and the District of Columbia in the Northeast US from 1988 - 1992, consisting of 58,943 deaths from breast cancer among women. Figure The spatial distribution of murine typhus in the south Texas from 1998 - 2008 is identified using the new neighbor-expanding approach developed in this study and traditional SaTScan, FlexScan, and SA methods. The most likely clusters and the secondary clusters detected by the methods are showed in figure As shown in the figures, all the most likely clusters found by the algorithms are significant with a p-vaule of 0.01 and high LLR values. The LLR value of the most likely cluster detected by the MLF algorithm 186.43) and NGG algorithm 197.51) are slightly higher than that of the SA algorithm (177.15) and significantly higher than that of the FlexScan method (42.95) and Circular SaTScan (97.60)  and median house value  than the average value  for all 18 counties. Driven mainly by tourism and the petrochemical industry, the main economic support of Nueces County depends upon its largest coastal city, Corpus Christi, which also drives the development of related commercial real estate and other industries.For the socioeconomic analysis at the census block group level, we have illustrated the location and distribution of the most likely clusters detected by MLF, NGG, SA, FlexScan, Elliptic SaTScan, and Circular SaTScan within Nueces County Figure  and the There is an important difference among the performance of traditional SaTScan, FlexScan, SA, and the two algorithms (MLF and NGG) introduced in this paper. Kulldorff's method tries to search the maximum likelihood ratio using a predefined geometrical shape (circle or ellipse) while the FlexScan method would search for the nearest maximum. For most circular-shape clusters, the spatial scan statistic method will promise fast and efficient cluster detection in many applications. That is why this method is popular in providing an initial analysis for most cluster studies. The two new algorithms make it easy to find out the exact location and boundaries of clusters with arbitrary shapes. Moreover, by adopting the idea of global-optimization strategies, the two new algorithms reduce the effects of the local maximum problem by searching for the global maximum of the likelihood ratios at each step.We compared the detected clusters from the two new algorithms and those from SaTScan, FlexScan, and SA and found the performance of the neighbor-expanding method has been significantly improved in the cluster with arbitrary shapes. However, the computation time of the NGG algorithm was much longer than that of the MLF algorithm. This might be caused by the no-constraint rule when the NGG selects the seed to detect the next level cluster in the search process. Without any penalty on the shape of the result, the NGG allows more detected clusters than the MLF and SA. One possible solution for this problem is to set the degree allowing irregular shape in the detected cluster according to some appropriate criteria, minimizing the occurrence of false clusters. Or we could post-process the entire detected result after cluster analysis to remove the highly irregular ones. But this solution will require more detection time and expert knowledge in selecting an appropriate threshold.One of the most critical components of environment epidemiology is to estimate the associations between human exposures and health outcomes ,34. In oThe choice of scale/resolution in cluster analysis deserves some attention. In most of case studies, we would prefer to choose a resolution small enough to represent most disease distribution in a relatively homogeneous area. Furthermore, the spatial aggregation of areal data may change the pattern of disease and bring some difficulty in validating the results due to effects of the modifiable areal unit problem (MAUP). A possible solution to this problem involves performing the cluster analyses at different scales of area units to estimate the effects of MAUP and this issue will be addressed in future research. If possible, it would be much better to conduct an analysis of scale effect before conducting a cluster analysis. The choice of scale/resolution for specific cases or specific diseases at different regions should be treated differently. Although there is no specific rule to follow, users of the algorithms should be very familiar with the characteristics of the disease in question as well as the study area before the cluster detection is conducted.The authors declare that they have no competing interests.All authors intensively participated in the study reported in the article. ZY and FBZ conceptualized the study design and analyzed the results. ZY and JT interpreted the results and prepared the initial drafts of the manuscript. All authors participated in the writing of the manuscript and approved the final version.


Neurons react differently to incoming stimuli depending upon their previous history of stimulation. This property can be considered as a single-cell substrate for transient memory, or context-dependent information processing: depending upon the current context that the neuron “sees” through the subset of the network impinging on it in the immediate past, the same synaptic event can evoke a postsynaptic spike or just a subthreshold depolarization. We propose a formal definition of History-Dependent Excitability (HDE) as a measure of the propensity to firing in any moment in time, linking the subthreshold history-dependent dynamics with spike generation. This definition allows the quantitative assessment of the intrinsic memory for different single-neuron dynamics and input statistics. We illustrate the concept of HDE by considering two general dynamical mechanisms: the passive behavior of an Integrate and Fire (IF) neuron, and the inductive behavior of a Generalized Integrate and Fire (GIF) neuron with subthreshold damped oscillations. This framework allows us to characterize the sensitivity of different model neurons to the detailed temporal structure of incoming stimuli. While a neuron with intrinsic oscillations discriminates equally well between input trains with the same or different frequency, a passive neuron discriminates better between inputs with different frequencies. This suggests that passive neurons are better suited to rate-based computation, while neurons with subthreshold oscillations are advantageous in a temporal coding scheme. We also address the influence of intrinsic properties in single-cell processing as a function of input statistics, and show that intrinsic oscillations enhance discrimination sensitivity at high input rates. Finally, we discuss how the recognition of these cell-specific discrimination properties might further our understanding of neuronal network computations and their relationships to the distribution and functional connectivity of different neuronal types. Since the beginnings of electrophysiology it has been observed that neuronal firing rate in sensory systems carries information about the presented stimulus Many biophysical mechanisms have been proposed as feasible candidates in decoding a temporal code. At the network level, a combination of delay lines (possibly tuned by spike timing-dependent plasticity) and an array of coincidence detectors allow the recognition of certain sequences of Inter-Spike Intervals (ISIs) When dealing with temporally selective neuronal mechanisms, most attention has been drawn on the role of short-term synaptic dynamics The present study focuses on the other side of the engram In any moment in time, a neuron carries information about its history of stimulation through its dynamical variables. In particular, the history-dependence of ion channel dynamics has long been recognized as a single-cell substrate for transient memory In this paper we present a formal measure of the neuron's state directly related to spike generation, namely the History-Dependent Excitability (HDE), which lumps the different history-dependent dynamical variables of an arbitrary model neuron to a single, scalar value that describes its propensity to firing in any moment in time. This dynamical mnemonic trace allows the interpretation of newly incoming information in the context of the previously received inputs, and hence the discrimination of information at the single-cell level. The comparison between the HDE trajectories arising from different input histories quantifies the intrinsic discrimination capabilities of single neurons, and their dependence upon the input statistics and the neuronal dynamics.Since different physiological processes can yield similar dynamical effects, it is useful to consider general, dynamical neuronal models which abstract from the specific molecular mechanisms involved. In particular, we illustrate the concept of HDE with two very general dynamical mechanisms: the RC behavior of a passive membrane, captured by a simple Integrate and Fire model, and the inductive RLC behavior of a neuron with a resonant current, described in its simplest (linear) form by a Generalized Integrate and Fire model see . These mIn the most general mathematical framework a neuron is described as a dynamical system:where The neuron's state vector On the other hand the state vector Depending on the local context that the neuron ‘sees’ through the synapses impinging on it in the immediate past, it will differently treat the information it receives. As we will show in this paper, this context-dependent processing is a very general property of dynamical systems and it can be presented in its simplest form with linear models such as the IF and GIF neuron models.The state vector contains all relevant information about the dynamic state of the neuron, hence it can be used to predict the neuron's response to an arbitrary stimulus. Nevertheless, it is not easy to deal with directly. In a model neuron the state vector's dimensionality can be high, and obviously it depends upon the specific model considered, making the comparison between different neuron models difficult and somewhat arbitrary. In a real neuron the state vector depends upon the description level one wishes to adopt, and even when just a few channels' activation-inactivation kinetics are taken into account, it is impossible to measure experimentally. Hence, it is useful to introduce a lumped, functional and physiologically motivated measure of the neuron's state, directly related to spike generation. To this end we propose a formal definition of History-Dependent Excitability (HDE) at any moment in time as the minimal synaptic strength Traditionally the detection capabilities of neurons have been assessed by observing how their output changes as a function of their input. For example, two stimuli are considered to be indistinguishable as long as they both result in a single postsynaptic spike, or in the lack of it. We show that this is not necessarily the case: two different input stimuli can still be distinguished if they bring the neuron to a different internal state, and hence change its response properties to future stimuli.In the case depicted in hort ISI . Both inrization . Neverthst state : the  vacould discriminate between them based on the intrinsic memory brought about by its HDE trajectory. The actual binary discrimination is only realized if some specific inputs are received.This history-dependent free evolution of the model neuron allows for spike-mediated discrimination between the two different histories by a synaptic event with proper time and amplitude: a presynaptic spike with a time and an amplitude indicated by the black filled diamond in ISI,ISI) . In thisIf the same input trains are delivered to an IF neuron with the same membrane time constant, they are still distinguishable but in this case the absolute difference between the two HDE trajectories decreases exponentially after the last spike of the train . ConversFor these linear models, we are able to derive analytical expressions for the discriminability between two input histories in vivo typically receive synaptic signals from thousands of presynaptic cells. It seems that the synaptic strengths of the inputs converging to a given neuron are not exponentially distributed, but might be better described by a log-normal distribution Living neurons In this study, we consider the linearization of the neuron's dynamics around its “working point”, determined by its intrinsic properties and by the collective balance of the weak and asynchronous synaptic events it receives. The synaptic events will be considered as instantaneous, voltage-independent shifts in the This approximation allows us to calculate the neuron's response to a train of presynaptic events with an iterative formula, and to calculate the discriminability based on intrinsic properties analytically see . The diswhere the last equality is due to the fact that in these linear models the firing threshold depends upon the voltage variable where In the case of an IF neuron the instantaneous discriminability is an exponentially decreasing function of time, meaning that the intrinsic memory about the previous history will quickly vanish, and practically be lost after a few membrane time constants. In the case of a GIF model with real eigenvalues, the picture does not differ much, with the exception that now the exponential decay is governed by more than one time constant. In the case of a GIF model with intrinsic oscillations, that is a GIF model with complex conjugate eigenvalues In this case, the instantaneous discriminability is an exponential decreasing function of time multiplied by a sinusoid. This means that for certain input histories The instantaneous discriminability is a measure of the square difference between two HDE trajectories originating from two input histories After some analytical calculations  plane . Our resreasing  .The values of the discriminability on the bisectrix ISIayed see .The evaluation of (6) and (5) along  the dynamic encoding of input history, which determines how subsequent presynaptic spikes affect the dynamic variables of the model in a history-dependent manner, and 2) the free evolution of the system after the last spike of the train see also .Both these ingredients are represented in These results suggest that the dynamical encoding mechanisms provided by intrinsic oscillations increase the sensitivity of short-long vs. long-short ISI discrimination. To clarify this point, we made the hypothesis that requency .In the case of the IF neuron, The corresponding expression (6) for the GIF neuron is not invertible, hence we set Decreasing t trains . This ismall ISI . At highThe effect of the intrinsic frequency plicated . For higsee also . When thsee also . For lowNote that as we increase the membrane rate constant In order to separate the effects due to The results exposed in this section can be directly applied to the characterization of biological neurons, and might be used to test the physiological relevance of the phenomenon for different cell types and in different brain areas. For instance, from standard electrophysiological measures such as a neuron's (complex) impedance, we could obtain estimated values for the neuron parameters In the previous section, we analyzed the input discrimination capabilities based on intrinsic single-cell dynamics between some particular, well defined inputs. In this section, we wish to generalize the previous analysis and characterize the intrinsic discriminability as a function of input statistics and intrinsic properties for random input trains. In particular we considered input trains composed of exponentially distributed ISIs. This distribution is particularly significant in neuroscience, since neurons in many brain regions exhibit a firing statistics that is well fitted by an exponential distribution with a refractory period The average discriminability between pairs of input trains that only differ in their second to last spike can be easily calculated by integrating (4) over the exponential probability density:where Expressions (8) and (7) are shown in rons see . For theain axes . This beSI = ISI . Rate seEvaluation of (7) and (8) along ISIs see  with a vISIs see , indicatAs the intrinsic frequency l neuron . The fornability . Note thncreased . In addiIncreasing quencies . As in tThe standard deviation of the mean discriminability values depicted in Note that as we increase the membrane rate constant Taken together, these results can be summarized as follows: 1. Increasing the intrinsic frequency Neurons are dynamical entities which act on several time scales; this endows them naturally with a capacity for short-term memory or context-dependent processing. The history of inputs to a neuron is dynamically encoded in its state-dependent, time-varying properties: each synaptic event induces some modifications in the neuron dynamical state which depend upon the previously received stimuli and their timing. In order to map intrinsic neuronal state to a physiologically, spike-related measure, we introduced the concept of History-Dependent Excitability (HDE), which we define as the minimal strength of a synaptic event that can cause the neuron to fire. As the neuron's dynamics unfolds in a history-dependent manner, the time evolution of the HDE carries information about the history of stimulation in the immediate past, allowing for context-dependent signal processing. This framework allows us to compare the context-dependent processing capabilities of different neuron types.For the sake of illustration we considered linear models with a fixed voltage threshold for spike generation, namely the IF and (oscillating) GIF neuron models. Their simplicity is useful in dissecting the relative contribution of very general dynamical mechanisms (such as passive and inductive membrane dynamics) to the emergence and properties of history-dependent processing. The IF neuron, described by a single dynamical variable with a single time constant, is a standard model of a passive membrane. The GIF neuron is a natural extension of the single variable IF model which includes an additional dynamical variable that varies linearly with voltage, and comes to represent the (linearized) net effect of voltage gated ionic currents. Of particular interest when dealing with temporally selective dynamical mechanisms is the oscillating GIF neuron, where the effect of the slow variable is to counteract voltage changes and the model dynamics is characterized by a pair of complex conjugate eigenvalues, thus exhibiting damped oscillatory responses to perturbing inputs. These simple linear models allowed the use of iterative formulae for calculating their response to input trains, and analytic expressions for the calculation of the intrinsic discriminability between pairs of input trains. The consequences and possible drawbacks of using these models are discussed in detail in the section “Limitations of the current approach”.Both the IF and the GIF neuron exhibit history-dependent processing capabilities, which could allow the discrimination between different input trains even when they share the same average frequency or even the same constituent ISIs. In fact, history-dependent responses are a general feature of any dynamical system, and can be studied conveniently with any dynamic description of neuronal behavior . In this case, the neuron model does not implement a static input-output transformation, but one that is modulated by its state variables, which in turn reflect the previous history of stimuli and responses. The GIF model, though, is particularly sensitive to the precise timing of input stimuli, while the IF neuron discriminates better between inputs with different average frequencies . This suOne of the most important differences between the IF and the oscillating GIF model is that the intrinsic discriminability between two different input histories decreases exponentially with time for the IF neuron, while intrinsic oscillations result in an intrinsic discriminability that is an exponentially decreasing function of time multiplied by a sinusoid. This means that for certain input histories and neuron parameters, the instantaneous discriminability can reach its maximum a few u.t. after the last spike of the input train . Thus, wAnother important difference between oscillating and non-oscillating neurons regards the sensitivity to small differences in the input histories. For instance, when the discriminability between an accelerating and a decelerating input triplet with the same constituent ISIs is considered, the discriminability as a function of input ISI difference grows faster in the oscillating GIF neuron than in the purely passive IF neuron . Hence, ecreases . These rFinally, the theoretical framework provided by the History-Dependent Excitability concept allowed the assessment of the temporal extension of the intrinsic memory (section “Intrinsic discriminability between input trains that only differ in the their second spike time”). As the neuron receives successive EPSPs in a train, each EPSP drives the neuron's dynamical variables so that they come to reflect mainly the last input ISI, and the relative contribution of previous ISIs to the HDE gradually wanes. In these linear models the intrinsic discriminability of the first and second ISIs in a train decreases exponentially with the train length, and the rate of decay is not influenced by intrinsic oscillations. The exponential forgetting is a consequence of the small number of time scales interacting in these simple linear models . It would not be surprising if a subthreshold dynamics with multiple time scales might lead to a more gradual forgetting, for instance a power-law forgetting, as it is observed in multiple time scale synaptic models The originality of this work lies in characterizing the discriminability properties of neurons based on their HDE trajectories, and not on their spiking output. This is an important shift in perspective because, as shown in Computer simulations allow the assessment of History-Dependent Excitability for arbitrary neuron models, and with arbitrary accuracy. In the absence of an analytical description for the HDE, it can be computed numerically by generating, in any moment in time, multiple branches of a given simulation, corresponding to different values of the conductance of an applied synaptic event. This technique allows the numerical measurement of the HDE, defined as the minimal conductance of a synaptic event capable of generating a spike, in a certain instant. Iterating this procedure over successive time steps allows the reconstruction of the HDE trajectory with arbitrary temporal resolution. The measurement of the HDE in living cells is constrained by the stability of the cell's properties, which will inevitably posit some limit upon the achievable resolution. Nevertheless, we believe that the experimental confirmation of the ideas exposed in this work is possible. In particular, an optimized dynamic clamp protocol Even if the computational mechanisms outlined in this work are general and apply to both living and model neurons, and might be relevant even to non-neural systems with history-dependent dynamics Another simplification adopted is the spike generation mechanism, implemented as a fixed voltage threshold in the IF and GIF models. It is possible that in certain conditions this simplification might provide a biased estimate of the HDE (which depends on both the synaptic dynamics and the spike generation mechanism). For instance, the interplay between the spike generation mechanism and the synaptic filtering properties can affect single-neuron processing, especially at high input rates In this work we have assessed the influence of subthreshold damped oscillations arising from intrinsic neuronal dynamics upon information discrimination. In several brain areas and functional conditions sustained oscillations of the membrane potential have been observed. These oscillations are thought to arise mainly through network mechanisms In this article we considered an idealized scenario in which the neuron sits at its stable point, receives a train of instantaneous EPSPs with constant amplitude, and it is then free to evolve according to its intrinsic dynamics alone. The adoption of linear models guarantees that the presented results also hold if the input histories include fluctuating currents (“frozen noise”), as long as they are equal among different input histories. Furthermore, intrinsic discriminability does not depend upon the neuron state at the moment of input arrival in linear models. Nevertheless, it is not clear whether intrinsic discriminability could still serve as a reliable indicator of the current context in a complex, non-linear neuron as the input histories include unknown time-varying components. From a dynamical perspective, the consistent encoding of incoming information could still be achieved if the neuron state is driven to a restricted portion of its state space before receiving its temporally-structured inputs. This task could be accomplished by network oscillations et al. proposed a new mechanism for the discrimination of spatiotemporal inputs based upon NMDA receptor dynamics, along with the impedance gradient resulting from dendritic tapering et al. seem to lack prominently active dendrites, and the kind of selectivity they report can be summarized as a consistently greater somatic depolarization in response to centripetal, rather than centrifugal, patterns of stimulation. Our work suggests an important role for active dendritic properties in the discrimination of spatiotemporal inputs. In particular, the distribution of active ion channels could be a key ingredient in achieving greater flexibility and modularity in the discrimination of spatiotemporal inputs at the single-cell level.Recently, Branco One last remark regards the definition of History-Dependent Excitability as the minimal excitatory synaptic strength capable of firing the neuron. In the translation from the state vector to a scalar, spike-related measure of the neuron's propensity to firing, we defined HDE as the minimal excitatory synaptic strength capable of firing the neuron. While such a translation is useful for the comparison between different neuron types, the exact definition we propose might sound arbitrary. For instance, neurons receiving an intense barrage of EPSPs and IPSPs might fire mostly because of a reduction in the total inhibitory conductance, rather than because of an increment in the total excitatory drive The presence of an intrinsic memory in each processing unit is likely to have profound consequences at the network level, and to foster the emergence of complex functions in biological circuits. It is now widely accepted that network function is not entirely specified by the network connectivity, but depends upon its neuromodulatory state, and its history of activity and afferent inputs , described by a single linear differential equation:The model is endowed with an after-spike reset mechanism, so that when Another simple model that linearly describes the subthreshold dynamics is the Generalized Integrate and Fire (GIF) model. This model includes an additional dynamical variable, which represents the linearized effect of voltage-gated ion currents, and is described by the following equations:with the same after-spike resetting as in the IF model for the The canonical GIF model that we used for most of the paper has ues  see , but theFor the sake of simplicity, and for carrying out analytical calculations, we considerThis approximation reduces the synaptic dynamics to an instantaneous and voltage independent shift in the voltage variable. If the considered intrinsic dynamics is slow with respect to the synaptic dynamics, and if the membrane voltage stays in a narrow range with respect to the distance from the synaptic reversal potential, this approximation is reasonable. The model trajectories have been calculated with iterative formulae see .In the simulations, random trains of synaptic events have been generated by concatenating two or more ISIs generated from an exponential distribution, using the Matlab routine “random”. For each value of the ranged parameters, 1000 different trials have been simulated, and the corresponding results have been represented in Text S1Appendix.(PDF)Click here for additional data file.