We provide a self-consistent mean field approximation in the framework of Mie scattering theory to study the optical bistability of a metallic nanoparticle coated with a nonlinear shell. We demonstrate that the nanoparticle coated with a weakly nonlinear shell exhibits optical bistability in a broad range of incident optical intensity. This optical bistability critically relies on the geometry of the shell-coated nanoparticle, especially the fractional volume of the metallic core. The incident wavelength can also affect the optical bistability. Through an optimization-like process, we find a design with broader bistable region and lower threshold field by adjusting the size of the nonlinear shell, the fractional volume of the metallic core, and the incident wavelength. These results may find potential applications in optical bistable devices such as all-optical switches, optical transistors and optical memories. Optical bistability has attracted remarkable attention in recent years because of its promising applications in logic functions23489In this reports, we study the optical bistability of a metallic nanoparticle coated with a nonlinear shell based on a self-consistent mean field approximation in the framework of Mie scattering theory. We decompose the scattered fields of the coated nanosphere into spherical waves with Debye potentials in order to establish the relationship between the local field of the shell and the incident field. The self-consistent mean field approximation is then adopted to study the optical bistability. Our results match well with the previous quasi-static solution of the Laplace equations at a deep-subwavelength scalea and a shell with outer radius b. The relative permittivity and permeability of the core (the shell) are x direction:We first consider electromagnetic wave scattering from the coated metallic nanoparticle. The coated particle, as shown in wherer = a and r = b, the scattered field in the surrounding medium and the fields in the core and shell can all be solved for both transverse-electric (TE) and transverse-magnetic (TM) waves (see details in Methods). Since the nanoparticle under consideration is much smaller than the wavelength, the 1st order TM wave is generally sufficient for numerical calculation. More orders can be included if more accurate results are required.In time-harmonic cases, Maxwell’s equations in the core, shell and surrounding media can be written as Now, we consider the case in which the coated shell is a Kerr material with weak nonlinearity. The electric displacement χs Here where Following Refs Method. After replacing the linear permittivity where The optical bistable response of a coated sphere has been studied previously using quasi-static approximationwhereOur results of full-wave solutions will be compared with previous results using quasi-static approximationIn our calculations, we set the linear permittivity of the shell as where Method). It can be seen that resonance enhancement can be found when the size of the coated nanoparticle b, or the fractional volume of the core η). In b). The near field properties of the linear coated nanoparticle at different wavelengths are shown in In Next, we introduce weak nonlinearity into the shell. The nonlinear relative permittivity of the shell is set asThen, we study the influence of the fractional volume of metallic core The shell size can also affect the bistable behavior. As shown in In ttivity  , the swiAt last, we fix the incident field amplitude In this reports, we adopt self-consistent mean field approximation within the framework of Mie scattering theory to study the optical bistability of a nonlinear coated metallic nanoparticle. Introducing weak nonlinearity to the shell, we demonstrate numerically that the metallic nanoparticle coated with a nonlinear shell has broad bistable region. We study the effect of the size of the coated spheres, the fractional volume of the metallic core, the permittivity of the surrounding medium, as well as the incident wavelength on the hysteresis loops and the switching-up and switching-down threshold fields. While our results match well with the previous quasi-static results, our full-wave solutions based on Mie scattering are valid in a much wide range of parameters, and thus are more suitable for design of optical bistable devices in optimization.We express the Debye potentials of the incident fieldsThe Debye potentials of the scattering wave areThen, in the shell, the Debye potentials areIn the core, they should be written aswhere To solve the coefficients, we apply the boundary conditions on andSubstituting the boundary conditions into the Debye potentials, we can obtain the coefficients as follows,andHow to cite this article: Chen, H. et al. Optical bistability in a nonlinear-shell-coated metallic nanoparticle. Sci. Rep.6, 21741; doi: 10.1038/srep21741 (2016).


NeuroFlow is a scalable spiking neural network simulation platform for off-the-shelf high performance computing systems using customizable hardware processors such as Field-Programmable Gate Arrays (FPGAs). Unlike multi-core processors and application-specific integrated circuits, the processor architecture of NeuroFlow can be redesigned and reconfigured to suit a particular simulation to deliver optimized performance, such as the degree of parallelism to employ. The compilation process supports using PyNN, a simulator-independent neural network description language, to configure the processor. NeuroFlow supports a number of commonly used current or conductance based neuronal models such as integrate-and-fire and Izhikevich models, and the spike-timing-dependent plasticity (STDP) rule for learning. A 6-FPGA system can simulate a network of up to ~600,000 neurons and can achieve a real-time performance of 400,000 neurons. Using one FPGA, NeuroFlow delivers a speedup of up to 33.6 times the speed of an 8-core processor, or 2.83 times the speed of GPU-based platforms. With high flexibility and throughput, NeuroFlow provides a viable environment for large-scale neural network simulation. Reverse engineering the brain is one of the grand engineering challenges of this century. Various projects have been working on a number of aspects of this problem, including characterizing neuronal types and their genetic transcription  modules to enable simulation of networks in the order of 100,000 neurons on a single FPGA. The size of network that can be simulated on a single processor is larger than a number of previous FPGA neural simulators such as those described by Graas et al.  and ThomOur platform has a number of novel aspects in comparison to existing simulators:We use PyNN to develop a high-level API which provides users with a model description and simulation environment. It is the first FPGA-based simulator to support the use of PyNN to configure the hardware processor and to automate the hardware mapping of neural models. This means that users do not need special hardware knowledge to use the accelerator, allowing them to benefit from flexibility and performance of specialized hardware with only software effort without the need to understand the details of the low-level implementation.NeuroFlow can automatically determine hardware design parameters based on the neural model used in the simulation to optimize the hardware resources, such as the degree of parallelism and the number of FPGAs to be used. It increases the performance and reduces the effort and time to use the hardware processor for researchers with little or no prior knowledge in hardware systems.We implement spike-time dependent plasticity (STDP) using the host processor as a co-processor. It demonstrates the possibility of workload allocation based on the computation to achieve optimal performance for neural simulation.The aim of NeuroFlow is to simulate large-scale SNNs with flexible model options. We develop the simulation platform based on FPGA systems from Maxeler Technology. It has a number of advantages over existing hardware accelerators, including high portability, flexibility, and scalability owing to the design of the hardware system. We develop a compilation flow to translate a neural network description in PyNN to that used by NeuroFlow as an abstraction layer for the underlying hardware. The high level description also aids in automatically determining hardware parameters such as the degree of parallelism, the number of FPGAs to use, and the optimizations that require additional hardware resources. As in previous work, we use software synapses written in memory as look up tables instead of physical wiring between modules , FPGAs update the neuronal parameters and spiking record stored in large off-chip DRAM memory storage. They are retrieved and updated by the FPGA during the simulation. The neuron state update modules update the dynamics of neuronal states in parallel using ordinary differential equations-based neuronal models, which are computed in floating-point arithmetic. The number of parallel neuronal modules, typically ranging from 2 to 32, is determined by the number of neuronal parameters and memory bandwidth available. These customizable modules are implemented in a time-multiplexed, parallelized and pipelined manner to optimize the throughput with a range of model options to choose from.In the second phase (ii), the FPGAs retrieve and store the incoming synaptic data into the fast on-chip BRAM memory storage. The Synaptic Integration Kernel retrieving synaptic data from off-chip memory and subsequently computes the synaptic input for the neurons. The computation is carried out by up to 48 parallel synapse modules, constrained by the available bandwidth and timing delay of hardware logic resources. Accessing synaptic data from memory and subsequent synaptic processing is triggered by spikes hence the overall processing time is roughly proportional to the activity level of the network. The synaptic data are preprocessed and packed in a specific format in fixed precision before being stored in the off-chip memory to speed up the simulation.Our simulator also supports nearest-neighbor STDP using both the FPGA and multi-core processors in a coordinated fashion. It demonstrates that conventional multi-core processors can be used along with the FPGA during a neural simulation in this system. Nearest-neighbor STDP is a common plasticity algorithm for learning in SNNs  to reduce the communication overhead.To efficiently implement the STDP rule, we use a scheme similar to the deferred event model  and the number of neuronal parameters per neuron.Additional weight caching mechanism for synaptic memory access. It makes use of extra on-chip BRAM buffers to store the data. Currently the additional resources required is estimated from previous builds. Together with the FPGA used and the network size to be simulated, the information can determine whether this mechanism can be accommodated in the design.Synaptic organization method to use based on density of neuronal connectivity. A densely-connected network can be packed in a more compact format which can lead to reduction in hardware resources.Dynamic parameters are runtime simulation parameters read by the host processor which do not need hardware recompilation. The parameters cannot be modified during a simulation but can be changed between different simulations in the same program. The parameters include the number of FPGAs to use, the allocation of simulated neurons and the number of neurons handled by each FPGA.PyNN is an open-source, Python-based neural simulation package for building neuronal network models developed by Davison et al. . It offeTaking advantage of its popularity, we adopt PyNN to provide a standardized interface for building neuronal models. Code To automate the process of running neural models and determine hardware parameters, we develop a pipeline of compilation processes to translate a high-level specification to hardware configuration for the FPGA system.The general compilation flow is depicted in Figure In the next step, we make use of tools provided from Maxeler to compile code written in Java describing the computation and architecture into hardware descriptions readable by the FPGA. The compiler reads in the static parameters and chooses which models to implement in the synthesis phase according to user specifications. Instead of soft processors which are used by a number of other FPGA approaches  and the system configuration, such as off-chip memory and inter-processor communication. When a different system is used, only the system configuration needs to be changed, rather than the entire computation engine code, thus facilitating portability across various systems. The hardware is also automatically customized based on the high-level description, meaning that performance gain is obtained without compromising the usability of the system. At the lowest FPGA-specific hardware description level, the program is translated to a hardware description language such as VHDL, which is then compiled to the actual FPGA bit stream using back-end vendor specific synthesis tools.NeuroFlow offers a number of common models and functionalities used in neural simulation which is summarized in Table The current scheme assumes synaptic weights are linear and additive for both excitatory and inhibitory synapses, which are accumulated in the on-chip memory, and can be changed if required. The user can define various synaptic current input functions, such as exponential decay function, alpha-function, or delta-function.The user can specify arbitrary external current injection to the neurons, and the parameters such as amplitude, time, and target neuron index are stored in on-chip memory. A number of random number generators are available to generate noise input to the neurons, including uniform and normally distributed random number generators. The user can also monitor the spiking and membrane potential of specified neurons, which are stored on FPGA during the simulation, and are sent back to the host processor after the simulation is completed.The current implementation of the system maps the neurons into hardware by sequentially assigning the neurons to the FPGAs according to their indices. While this approach is simple and efficient, the communications between the FPGAs may not be optimized and could lead to longer simulation time when using more than one FPGA. In theory the connectivity between the FPGAs and the mapping can be done in a similar manner as Furber et al.  which inTo evaluate the performance of the platform, we simulate a number of models to test the accuracy, speed, and power consumption of our platform. The models vary in size and complexity to test the full range of capability offered by NeuroFlow.In the first set of experiments, we test the precision and accuracy of the computations by simulating two adaptive exponential integrate and fire neurons (aEIF) with external stimulation and STDP Figure . The memL, reversal potential EL, spiking threshold VT, slope factor ΔT, adaptation coupling parameter a, and adaptation time constant τw. Brette and Gerstner , where nsyn ranges from 1000 to 10,000 in the simulations. The synaptic strength values are set to random values between 0 and 0.5, and are adjusted by a scaling factor nsyn in order to produce a similar level of network activity across scenarios of different nsyn. The connection probability follows a Gaussian probability of the synaptic distance, with standard deviation (S.D.) of varying σ for connections from excitatory neurons, and S.D. of 16 for inhibitory neurons. We test σ ranging from 32 to 512 to evaluate the effect of connection sparsity on the performance of the system. Conductance delays of the synapses are proportional to the distance between neurons, with a maximum of 16 ms delay for excitatory synapses and 1 ms delay for inhibitory neurons to ensure fast inhibition from the inhibitory neurons and rhythmic activity of the network.The network has a toroidal structure and the connection probability is spatially constrained. Each neuron connects to varying number of post-synaptic neurons ni in Figure j.When mapping the network onto FPGAs, each FPGA handles the computation of 98,304 neurons with close spatial proximity, and a maximum of six FPGAs are used for the simulations. Due to the locality of synaptic connections, the neurons connect to targets on the same or neighboring FPGAs, thus the hardware mapping of neurons facilitates the retrieval of synaptic data. Neurons that are closer to the border, such as neuron Figure For simulations involving STDP, we simulate a network with 55,000 neurons with STDP applied to excitatory synapses using the STDP profile in Section Computation Phases and Core Structure. The inhibitory synapses are set as non-plastic as described in previous literature . The number of patterns can be larger than the number of neurons in the network, showing the potential computational capacity spiking neurons have over the traditional rate-based neuron models. The network also exhibits a range of rhythmic activity and a balance of excitation and inhibition similar to biological networks. Due to the long simulation required to demonstrate the effect of STDP on the firing patterns, it is a good example to demonstrate the need for neural simulation platforms such as NeuroFlow and other FPGA-based implementations such as that by Wang et al.  and the requirement of long communication paths for large networks, the platform does not handle well cases with a large number of events, such as dense connectivity, STDP, or a highly active network (Furber et al., In the design of customized neurocomputers, flexibility is sometimes sacrificed to achieve higher speedup, but it makes the platform less useful for neuroscientists who usually carry out specific and rapid model modifications. ASIC designs have the lowest programmability and flexibility. The spiking neuron models are fixed during fabrication and synaptic connections are often non-plastic, low precision and have constraints in the number and patterns of connections. In comparison the SpiNNaker system, based on ARM processors, offers a high degree of flexibility, but due to the small number of neurons handled by each processor (at the order of 10Integrating of PyNN into the design of NeuroFlow simulator offers a number of advantages in terms of model development and performance gain. PyNN shortens the time in model development, allowing model builders to port the simulation to a new simulation environment with less time and cross-check the correctness of their models in other simulators. It also allows automated customization of hardware which can optimize the utilization of hardware resources. Currently development with the PyNN framework faces a number of challenges, such as backward incompatibility, minor defects, and the lack of technical support; but the idea of integrating a high-level neural description language with a hardware platform for accelerating simulation is attractive and useful.Neural networks for different purposes require various levels of abstractions and precisions. To date there is no consensus on what is the optimal level of abstraction to describe a biological neural network. Generally models with higher complexity have a richer dynamics which contributes to their higher computational capacity. For example, non-linear dendrites can solve linearly non-separable classification problems (Cazé et al., In this regard, one possible use of NeuroFlow is for prototyping of neurocomputers. Engineers can test various configurations using FPGA-based neurocomputers and find the optimal precision for a given application and use the minimal complexity and precision as system configurations. Similar to ASIC prototyping using FPGAs, prototyping using NeuroFlow can reduce the cost of chip modification and can benefit future neural-based computation systems.5–106 neurons using simple interconnect, more work has to be done on the neural mapping scheme and intercommunication between nodes, such as similar work on SpiNNaker (Khan et al., As illustrated in the experiments, NeuroFlow demonstrates good performance and flexibility, but it has a number of issues to address in order to broaden its appeal. While changes in neuronal, synaptic and simulation parameters only require generating new data files, FPGA requires considerable synthesis time to recompile the hardware configurations. However, there have been a number of attempts to reduce the synthesis time by using precompiled modules, such as hard macro stitching (Lavin et al., Currently there is a major gap in our understanding between small neuronal networks and the neural system as a whole. Models such as the work by Izhikevich and Edelman  incorporKC, SS, and WL conceived the idea for the study, KC carried out the study and prepared the figures, KC, SS, and WL wrote the manuscript. All authors reviewed the manuscript.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.


Sensorimotor control theories propose that the central nervous system exploits expected sensory consequences generated by motor commands for movement planning, as well as online sensory feedback for comparison with expected sensory feedback for monitoring and correcting, if needed, ongoing motor output. In our study, we tested this theoretical framework by quantifying the functional role of expected vs. actual proprioceptive feedback for planning and regulation of gait in humans. We addressed this question by using a novel methodological approach to deliver fast perturbations of the walking surface stiffness, in conjunction with a virtual reality system that provided visual feedback of upcoming changes of surface stiffness. In the “predictable” experimental condition, we asked subjects to learn associating visual feedback of changes in floor stiffness (sand patch) during locomotion to quantify kinematic and kinetic changes in gait prior to and during the gait cycle. In the “unpredictable” experimental condition, we perturbed floor stiffness at unpredictable instances during the gait to characterize the gait-phase dependent strategies in recovering the locomotor cycle. For the “unpredictable” conditions, visual feedback of changes in floor stiffness was absent or inconsistent with tactile and proprioceptive feedback. The investigation of these perturbation-induced effects on contralateral leg kinematics revealed that visual feedback of upcoming changes in floor stiffness allows for both early (preparatory) and late (post-perturbation) changes in leg kinematics. However, when proprioceptive feedback is not available, the early responses in leg kinematics do not occur while the late responses are preserved although in a, slightly attenuated form. The methods proposed in this study and the preliminary results of the kinematic response of the contralateral leg open new directions for the investigation of the relative role of visual, tactile, and proprioceptive feedback on gait control, with potential implications for designing novel robot-assisted gait rehabilitation approaches. The etymology of the word “Anthropos”, the Greek word for Human, includes one of the defining characteristics of human beings, which is the ability to stand upright and walk. Locomotion is one of the most important sensorimotor behaviors in humans that has enabled important evolutionary behaviors covering a wide range of interactions with the environment, including survival and exploration. From the perspective of neural control and biomechanics, the control of gait requires kinematic and dynamic coordination of the limbs and muscles, multi-sensory fusion, and robust control mechanisms.Locomotion results from intricate dynamic interactions between a central “program” and feedback mechanisms. The central program relies fundamentally on a genetically determined spinal circuit capable of generating basic locomotion patterns, as well as neural drive through various descending pathways that can trigger, stop, and/or steer locomotion. Sensory feedback from muscle and skin afferents, as well as other sensory modalities , dynamically adapt the locomotion pattern to the requirements of the environment  that was consistent with visual feedback. In the “unpredictable” experimental condition, the floor stiffness was perturbed at unpredictable instances during gait while visual feedback of changes in floor compliance was absent or inconsistent with tactile and proprioceptive feedback. This experimental approach allowed us to quantify the relative roles of visual and proprioceptive feedback on gait control.x), the amount of force required to extend the spring (S), and thus controls the effective floor stiffness. The distance (r) between the spring and the pivot point does not change. More details can be found at Skidmore et al.  using a custom-made device built by LiteGait. The system is capable of supporting the entire weight of the subjects, or a portion of the subject’s weight. The subject wears a harness similar to those used for rock-climbing, which buckles in to straps hanging down from an overhead beam. Two load sensors separate the straps from the beam, allowing both the weight supported and the left-right distribution of the weight supported to be calculated. In addition to providing support against gravity, the harness helped ensure that the subject remained centered on the treadmill. This measure was necessary due to the subject’s inability to visually sense the location of the treadmill when walking in the virtual world (see below).Two high-speed (200 frames per second) infrared cameras  were used to track the position of infrared emitters  attached to the subject’s legs. The two cameras were placed on the left and right side of the subject, facing inward to the subject’s legs. Six markers were placed on each leg facing laterally outward. Two markers were placed in line with the bones on each thigh, shank and foot, in order to be aligned with the three main segments of the legs. The positions of the markers were used to calculate the hip, knee, and ankle joint angles for both legs in real time. The virtual reality system sampled the calculated joint angles every 60 ms (16.7 Hz) for display in the visual interface. The positions of the two markers on the left foot were averaged to determine the position of the subject’s left foot along the treadmill Figure  which waThe visual stimuli were presented to the subject using a virtual reality headset . The headset contains a 1280 × 800 LCD, and one lens per eye. The screen is split in half, so that each eye sees a slightly shifted image. This provides the user with a stereoscopic view of the media sent to the device, offering three-dimensional depth perception. The headset also tracks the rotational orientation of the user’s head and alters the virtual view accordingly. The stereoscopic sense of depth and the view tracking gave subjects the feeling of immersion in a custom designed virtual environment.The virtual walking environment was designed with the game development package Unity3DAlong the virtual walkway Figure , patchesThe VST was used to effect changes in floor stiffness to the left track of the treadmill, in conjunction with visual stimuli. The perturbations consisted of a change from 1 MN/m to 20 kN/m, starting at left HS, enduring through the left stance phase and ending at left toe off Figure .In order to match the subject’s visual expectations with the change in stiffness, two conditions had to be met for a stiffness change to occur. First, the virtual avatar’s left foot had to break the vertical plane of the nearest edge of the sand patch. The second condition required that the subject’s actual, physical left foot was moving forward. Once both of these conditions were met, the VST would lower the floor stiffness upon the next HS of the left foot, and return to infinite stiffness upon toe off. This design allowed subjects to see that when the virtual avatar stepped on a sand patch, the floor stiffness would be decreased.We delivered three types of perturbations: visual and physical (VP), visual only (VO), or physical only (PO). Out of the 120 patches we used, we delivered 100 VP perturbations, 10 VO perturbations, and 10 PO perturbations.VP perturbations were used as control perturbations to train subjects to associate stepping on sand patches with a drop in floor stiffness. VO perturbations were used to quantify the kinematics of the perturbed and unperturbed leg in response to an expected reduction in floor stiffness. The visual appearance of the sand patch was identical for VP and VO perturbations, the only difference between these two conditions being that for the VO perturbation, floor stiffness was not changed when the subject stepped on the sand patch. The PO perturbation was used to quantify the kinematic response of the perturbed and unperturbed leg to a reduction of floor stiffness change but without visual warning. This was accomplished by inducing a stiffness change halfway between two patches. Visually, the sand patch would appear normal, but the treadmill controller was triggered as if the sand patch was halfway between its actual location and the previous patch. Hence, in the PO perturbation, a stiffness change would happen without a patch being located underneath the subject’s foot.Subject performed one trial consisting of a total of 120 perturbations as described above. As most perturbations were VP (83%), subjects could learn to associate visually-cued sand patches with a drop in stiffness. However, all perturbations  were presented in random order using the following design. For the 10th patch, subjects experience either a VO or PO perturbation, followed by a PO or VO perturbation every 6 ± 2 patches. Within the trial, each subject experienced 10 VO and 10 PO perturbations.Four healthy subjects  walked on the treadmill at a speed of 0.70 m/s while wearing the virtual reality headset. Subjects walked between 620 and 860 m over the course of the experiment, depending on the random distances between consecutive patches. Subjects were provided with 30% bodyweight support. Before starting to walk, subjects were given approximately 30–60 s to look around the virtual world and familiarize with the virtual avatar’s legs and congruence with their own movements. Once the subject informed the experimenter that he/she was ready, the treadmill was brought up to speed and the virtual avatar began moving towards the first sand patch. After walking over all 120 sand patches, the treadmill was slowed to a stop, and the subject was allowed to dismount the treadmill. All subjects gave informed consent for the experimental protocol approved by the Arizona State University Institutional Review Board.Although the left leg was directly perturbed through the left treadmill stiffness change, our analyses focused on the effects of the perturbation on the contralateral (right) leg response. Our previous work has shown that the ipsilateral-perturbed leg kinematics are significantly affected by the stiffness perturbation , VP, VO and PO. As shown in Figure The kinematics of the right leg were also represented in phase space (angular position vs. angular velocity). This space offers a better understanding of the behavior of a periodic system after a perturbation, and allows the analysis of the stability and robustness of the system in general. Angular velocities for all three joints investigated were computed by differentiating the angular position data, after low-pass filtering them . The phase plots of each of the three joints of the right leg are shown in Figure Figure Figure Figure For the VO condition, the phase representation provides further insight about two main features: (1) the evoked responses have similar characteristics to the ones associated with VP and PO perturbations, but delayed with respect to the latter; and (2) the kinematics for the VO condition converge to the normal ones within the gait cycle. It should be emphasized that the VO response in phase space resembles that observed for the VP and PO conditions in terms of acceleration profile of the gait cycle, but lies between the normal cycle and the VP and PO cycles in the phase space. The latter is obvious when examining the loop of the hip phase that includes the HS on the right bottom corner of the graph. A similar behavior can be observed in the corresponding loops of the knee and ankle joints.The presented method of analyzing the interplay between visual and proprioceptive and tactile feedback in gait resulted in important observations. First, when there is no physical perturbation, and therefore proprioceptive feedback is not elicited, visual feedback can evoke contralateral leg responses that resemble those caused by proprioceptive feedback in response to a mechanical perturbation of the opposite leg. This leads to the validation of the hypothesis that a learnt mapping between visual and proprioceptive feedback creates or activates mechanisms, that are probably supraspinally mediated, that control inter-leg coordination.late responses. These responses appear to be independent from proprioceptive feedback, as suggested by time shift of visually-cued responses relative to proprioceptive-dependent responses. Moreover, our results support the existence of only late responses associated with visual feedback of upcoming changes in floor stiffness. This is supported by the observation that in the early phases of the gait cycle, VP and PO responses are almost identical, which suggests that the predictive role of visual feedback does not activate any early motor mechanisms.However, evoked responses associated with only visual feedback of floor stiffness changes (VO) were significantly delayed relative to those caused by a physical perturbation. These data can be interpreted as follows. Visual cues (warning) act to mediate anticipatory/predictive control of gait, however they only evoke The results of the present study should be considered as preliminary due to the small sample of subjects. Furthermore, more work is needed to identify the neural mechanisms underlying the observed kinematic responses of the unperturbed leg to mechanical perturbations delivered to the contralateral leg. Nevertheless, our findings are promising as they shed new light on inter-leg coordination mechanisms and open new avenues for research, However, the scope of this paper is to introduce a novel method of investigating the inter-play of visual and proprioceptive feedback in gait. The proposed method, facilitated by a novel and unique technological architecture (the VST setup), can be potentially beneficial not only for understanding sensorimotor control of gait, but also for significantly improving neural rehabilitation protocols for impaired walkers by applying the identified principles and developing model-based protocols for gait therapy.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.


We addressed the principles of micro-level organization of neuronal circuits and explored how the neuronal morphology constrains this organization. Several studies have demonstrated the non-trivial properties of the network connectivity using in vitro recordings from multiple neurons -3, yet iWe analyzed a model that emphasizes the role of single-cell morphology, a homogeneous population of neurons in a planar space without boundaries. Each neuron is composed of two displaced neurite fields defined on the limited support. A neurite field describes the likelihood of finding a neurite segment at a certain point in the plane. Using a proximity criterion (Peters' rule) the expected number of potential synapses is estimated between each pair of neurons. Alternatively, this number can be estimated from the realistic morphology of a simulated neuron, or from the morphologies reconstructed from in vitro/in vivo recordings. The number of potential synapses depends on the axon-dendrite distance, which leads to a definition of the expected radius. An axon-dendrite pair that is expected to form at least one synapse must be on a distance not larger than the effective radius. All considered statistical measures of network connectivity are expressed as the functions of the effective radius normalized with the neuron size. In this study, we considered the standard graph theoretic measures of network connectivity, the motif counts, clustering coefficient, path length, and small-world coefficient. It has been demonstrated that they have a significant impact on the population activity in simulated networks .Changing the normalized effective radius from small (<0.3) to big (>10) we vary the network properties between the two extremes. For the small values of the effective radius, the networks favor unidirectional connections and sparse local connectivity. The clustering coefficient and the path length are similar to those obtained in uniform random networks, i.e. in the networks independent of topology. For the large values of the effective radius, the local connectivity is dense with the majority of bidirectional connections. As the normalized effective radius increases, the clustering coefficient increases towards the values obtained for the networks with dominant local connectivity, while the path length remains close to the one of the uniform random networks. The normalized effective radius on the interval 1-2, provides the biggest variability of connectivity patterns and the optimized properties relevant for the information transfer.We present a theoretical framework that relates neuromorphology with the connectivity in neuronal circuits, and that can be solved analytically. The normalized effective radius was found to be the key morphological property that dominantly affects considered connectivity measures. By tuning it we can obtain the networks with the biggest variability of local connectivity patterns. At the same time, those networks acquire the key characteristics of the small-world networks, known to optimize the information transfer.


The secondary xylem (wood) of trees mediates several functions including water transport and storage, mechanical support and storage of photosynthates. The optimal structures for each of these functions will most likely differ. The complex structure and function of xylem could lead to trade-offs between conductive efficiency, resistance to embolism, and mechanical strength needed to count for mechanical loading due to gravity and wind. This has been referred to as the trade-off triangle, with the different optimal solutions to the structure/function problems depending on the environmental constraints as well as taxonomic histories. Thus, the optimisation of each function will lead to drastically different anatomical structures. Trees are able to acclimate the internal structure of their trunk and branches according to the stress they experience. These acclimations lead to specific structures that favor the efficiency or the safety of one function but can be antagonistic with other functions. Currently, there are no means to predict the way a tree will acclimate or optimize its internal structure in support of its various functions under differing environmental conditions. In this review, we will focus on the acclimation of xylem anatomy and its resulting mechanical and hydraulic functions to recurrent mechanical strain that usually result from wind-induced thigmomorphogenesis with a special focus on the construction cost and the possible trade-off between wood functions. Secondary xylem (wood) arises as a result of cell divisions of the vascular cambium and is referred to as a type of secondary growth. After division, these cells go through phases of differentiation, enlargement, and maturation. During this process, the cell wall develops, most significantly, the secondary cell wall composed of organized layers of  cellulose microfibrils and lignin. Lignin deposition also occurs in the middle lamella region between cells. At the end of the maturation process, the conducting cells  die through a process of autolysis, the living components (cytoplasm and organelles) are reabsorbed by the tree, and the water-filled cell lumen becomes physiologically functional providing hydraulic conductivity. The resulting structure is a complex porous network of interconnected cells that fulfills several functions that are required for the continued life of the tree in a variable environment. In both dicotyledonous trees and in conifers the vascular cambium can continue to produce new layers of wood throughout the life of the stem or root and so the response to environmental cues is ongoing.The xylem of the stem mainly provides three types of functions: (i) the xylem is the hydraulic pathway for the transport of water from the soil to the transpiring leaves, providing hydration to all living cells along the way; (ii) the stem mechanically supports the heavy structure of the tree; (iii) the xylem is a place where many biochemical components that are required for the tree in order to withstand external stresses  are stored as well as the storage of photosynthate  over the winter for future growth in the subsequent spring . Water sAs a result of an acclimation process, plants modify their growth when they experience mechanical loading: plants are able to perceive external mechanical stresses that generate the strain of the living tissues . These lAt the anatomical level, Figure 1A). The tracheid performs both the conductive and supportive functions within the secondary xylem. The ray parenchyma cells are aligned radially and are usually small compared to angiosperms. On the contrary, the annual ring of angiosperms is composed of more specialized cell types. In addition to ray parenchyma, angiosperms can have axial parenchyma, fibers, fiber tracheids, and vessels depending on the species of tree .Gymnosperm wood is mainly composed of non-living tracheids with a small portion of living ray parenchyma and when resin ducts are present, living epithelial cells lining the ducts. The earlywood portion of gymnosperms is characterized as large diameter cells with thin cell walls, whereas the latewood is composed of smaller diameter cells with thicker cell walls , which occurs on the lower side of non-vertical branches. Compression wood tracheids are shorter than normal wood tracheids. In the transversal direction, they are more rounded and show intercellular spaces at would have been cell corners that do not appear in normal wood. At the cell wall level, the compression wood cells usually possess an S3 layer that is not common for normal wood and the thicker S2 layer has a higher microfibril angle (MFA) than normal wood , called the G-layer. This G-layer exhibits very particular physical property that generate the differential mechanical states on opposite sides of the organ thus forcing it to modify its curvature via contraction of the tension wood fibers upon maturation. The G-layer is mainly made of cellulose and hemicellulose, has a very small MFA and high degree of crystallinity . This chamber is separated into two parts by a thin and flexible continuous membrane resulting from the remaining primary wall. In gymnosperms, the membrane is not continuous: the central structure, the torus, is reduced to a central plate; which is physically linked to the cell wall by the margo made of thin threads of cellulose microfibrils .In angiosperms, pits are made of a pit chamber that occurs in the double cell wall and is connected to the cell lumens by the way of holes called apertures , and the second moment of cross sectional area I, which varies with the fourth power of stem diameter D (Eq. 1). The ecologically important parameter of stem strength is the flexural stiffness ELI that drives the ability of an elongated organ to deform when it experiences bending loads.The mechanical functions include: self-support against the pull of gravity in the form of axial compression upon the trunk , 1994, aEL of wood refers to the stiffness of the wood vertically. Since wood is a porous material with longitudinally oriented cells, EL is mainly linked to porosity . Thus, in a first approximation, EL can be estimated as proportional to the wood density . The end result is an overall stiffer stem composed of more pliable xylem capable of absorbing more mechanical energy in response to wind loading  and the maximum strain σmax the stem experiences is proportional to the ratio D/I (Eq. 3).On the other hand, all the works that dealt with responses to mechanical stimulation of trees reported a large increase in radial growth that increases the second moment of cross sectional area I . This is loading . MoreoveMb is the bending moment applied on the stem (by wind for example). Thus thigmomorphogenesis tends to reduce the strain and stress the stem experiences, making it less likely to fail under mechanical loading.Where Trees have developed efficient hydraulic networks to transport water from the roots into the leaves . This prKs varies with the fourth power (Eq. 4) of the conduit diameter .Xylem is the main long distance transport pathway for water and soluble mineral nutrients from roots to the leaves. One of its main functions is to provide a low resistance pathway for water transport. Transport is provided by vessel elements (angiosperms) or tracheids (gymnosperms). This water transport does not involve energy consumption by the hydraulic network that act as passive conduits. Conduction efficiency is driven by the Hagen–Poiseuille equation that indicates that hydraulic conductivity diameter . Thus, tHowever, comparing gymnosperm and angiosperm structure, P. elliottii compared to staked seedlings was reported by P. contorta exposed to more wind sway. They concluded the reduction in conductivity was due to sway induced functional damage to sapwood. High positive correlations have been observed between water conduction efficiency of the xylem and the growth rate . This isP is inversely proportional to the diameter of the pores, d, according to the Jurin’s law:According to the cohesion–tension theory  water aswhere τ is the liquid surface tension, 𝜃 is the contact angle of the liquid with the pore walls. Thus, the plant structural parameter that determines the vulnerability to drought-induced xylem embolism is the diameter of the largest inter-vessel pore (Eq. 5).The main sites of air seeding to the xylem pathway are inter-vessel or inter-tracheids pits. What is the physical role of the pits during the cavitation process? Many anatomical measurements have been performed on gymnosperm and angiosperm pits. There are statistical correlations between anatomical parameters like pit membrane thickness, aperture diameter, torus diameter, etc., with the cavitation sensitivity. The mechanical behavior of the pit membrane was investigated by the way of modeling . They shDespite the cavitation mechanism not being clearly elucidated, several correlations were investigated in order to focus on the relevant anatomical parameters. At the macroscopic scale, the wood density is often investigated and species that show denser wood usually show higher cavitation resistance . This isELI) is proportional to stem diameter to the fourth power due to the second moment of area calculation, and conductive efficiency is proportional to vessel or tracheid diameter to the fourth power, following the Hagen–Poiseuille law. To increase the hydraulic conductivity the obvious solution is to increase vessel or tracheid diameter, but those solutions could weaken the wood. Is there a necessary trade-off between strength and hydraulic conductivity, and what are the other ramifications of this trade-off? . If so, what are the consequences for cavitation and implosion resistance? What is the effect on hydraulic capacitance?Considering trees need to continuously manage all their vital hydraulic and vital mechanical functions, it is suspected that trade-offs could exist. Possible trade-offs between mechanical and hydraulic properties are inherently complex since both are subject to fourth power relationships. As noted above, axial stiffness  and resistance to cavitation followed a power function with exponent ≈-2, consistent with the existence of a trade-off between conductivity and security in the xylem. However, they suggested that this relationship was consistent with a linear relationship between vessel diameter and the size of inter-vessel pores, which has never been demonstrated. For instance, Although the existence of a trade-off between conductive efficiency and resistance to cavitation or implosion (efficiency versus safety) has not been consistently reported in the literature , availabb) and the cell wall thickness (t). The higher the thickness to span ratio (t/b)2, the greater the resistant to implosion. This safety factor was then used for evaluating the implosion resistance of vessels. All these works suggest that wood density, which is highly correlated with conduit size and cell wall thickness, may impact the both functions in the same way, with thicker cell walls that make the tissues stiffer and more mechanically resistant (Xylem safety (resistance to cavitation or conduit implosion) and mechanical strength have been found to be positively correlated . Hacke eesistant . HoweverArabidopsis mutant deficient in the deposition of secondary cell wall cellulose. Arabidopsis. Genetically modified hybrid poplar trees  with reduced cell wall lignin have also shown collapsed xylem . This can be easily demonstrated assuming that the Young’s modulus is proportional to the wood density ρ At the trunk level, increasing the organ size is an efficient option too. D3.When a beam experiences a bending moment Mb, the Eq. 2 tell us that the maximum strain varies as the inverse of Figure 6B)Assuming the allocated biomass m can be estimated as :Merging Eqs 6, 7, and 8, we can write that the strain varies as the square root of the density and the maximum strain varies according to ρEL is higher in this last case .These Eqs 9 and 10 demonstrate that, for the same biomass allocation m, the mechanical strain and stress increase with the wood density and put the trunk at risk. This conclusion is still available even if we consider that the critical stress increases in a proportional way to the wood density . FinallyAs seen previously, the optimization of conduction properties and biomass allocation leads to large cells with thin cell walls. Thus, finally, low density wood that includes large lumens would be the best way to manage both mechanical and conduction properties. But what is the cost for building cavitation resistant xylem tissue? The pit is probably the very relevant level of observation. This suggests that building resistant pits has a cost and should take account in maintaining the conduction efficiency. And what is the relative importance of resistant pit members to prevent air seeding, versus mechanical support by walls of tracheids or fibers, to prevent implosion? If both parameters are relevant, and have co-evolved, this could explain some contradictions in the literature. The existence or otherwise of functional trade-offs in wood structure is still unclear and has been debated for the past several years. The anatomical parameters that drive the mechanical properties are now well identified and most of the drivers of the conduction efficiency are identified too. But the way the trees build wood that is resistant to cavitation is still a key question that needs to be elucidated in the next years.Table 1). The acclimation process differs between angiosperms and gymnosperms and the consequences on the hydraulic and mechanical properties of wood are highly variable. Because of the lack of experimental data, there is a crucial need for new investigations in order to characterize the mechanical and hydraulic properties of flexure wood. Moreover, in many windy regions, wind is often directional. Hence, bending occurs in a non-symmetric way, with the leeward part of the stem experiencing more compression stress and the windward portion experience more tension stress. Thus, what is really flexure wood? We suggest to the need to investigate separately the thigmomorphogenetic response of wood formation of both elementary stress (compression or tension) to better understand the acclimation process. On the one hand, there is a real need to investigate the relationships between the mechanical stimuli and the modifications of the anatomical structure and its associated construction cost. For this task, there is a real need to investigate the wood formation process, including at the level of cell division and the cell differentiation. This also requires new studies regarding the molecular mechanisms that link mechanical perception to the mechanical stress induced wood formation.Trees have many ways, at the cell wall level or at the organ level, to acclimate their xylem structure to recurrent mechanical stimuli , may be a promising mean of elucidating mechanisms of xylem construction that may be constrained by the functional trade-offs.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.


Species composition and habitats are changing at unprecedented rates in the world's oceans, potentially causing entire food webs to shift to structurally and functionally different regimes. Despite the severity of these regime shifts, elucidating the precise nature of their underlying processes has remained difficult. We address this challenge with a new analytic approach to detect and assess the relative strength of different driving processes in food webs. Our study draws on complexity theory, and integrates the network-centric exponential random graph modelling (ERGM) framework developed within the social sciences with community ecology. In contrast to previous research, this approach makes clear assumptions of direction of causality and accommodates a dynamic perspective on the emergence of food webs. We apply our approach to analysing food webs of the Baltic Sea before and after a previously reported regime shift. Our results show that the dominant food web processes have remained largely the same, although we detect changes in their magnitudes. The results indicate that the reported regime shift may not be a system-wide shift, but instead involve a limited number of species. Our study emphasizes the importance of community-wide analysis on marine regime shifts and introduces a novel approach to examine food webs. Despitelimited set of micro-level processes, in such ways as to push the system beyond a critical threshold where these changes will escalate and finally drive the whole system into a new regime. We however acknowledge that other conceptualizations of regime shifts do exist within the broader complexity literature. Nonetheless, complexity science in large part suggests that systems can be understood as networks of interacting components, and the complex pattern in which these components interact with each other can inform on large-scale systems behaviour .Ecosystems constitute prototypical examples of CAS , and areIn spite of the important insights previous motif-based studies of food webs have provided , these e1), e.g. [Our overall aim is to address this gap by re-interpreting patterns of motif occurrences in species interactions in food webs through applying a recent network modelling framework developed in the social sciences , e.g. ). ERGM iconfigurations instead of motifs. We will use that term unless we explicitly refer to earlier motif-based approaches. Motif-based approaches calculate the frequency of different configurations in the empirical network and compare these frequencies with the same configurations' frequencies derived from a large set of random networks (thus representing the null model). ERGM differs from this descriptive approach in that it encourages and supports identifying the minimal but sufficient (core) set of micro-level configurations that explains the whole structure of the network. Hence, ERGM indirectly takes into account ‘dynamic effects' in that the prevalence of specific configurations in shaping the structure of the network can give rise to over/underrepresentation of other configurations. ERGMs are in a sense conceptually similar to multivariate regression models, where the explanatory variables are represented by a set of configurations, and the dependent variable is the network itself. As when using multiple predictors in a regression, multiple configurations in ERGM can be considered together to examine which are most important in explaining the structure of the entire network. To emphasize this even further, when fitting an ERGM to empirical data, the aim is to make empirical inferences about those configurations required to explain the structure of the network: the frequency of other configurations can be interpreted as a secondary phenomenon/effect. This ability to differentiate between configurations is an important feature that distinguishes ERGM from earlier approaches.ERGM, like previous motif-based studies, builds on the conceptualization of the network being built up by different micro-scale network substructures (motifs). In ERGM terminology, these network substructures are usually called processes that together give rise to the observed system-level network structure. In addition, ERGM facilitates off-the-shelf analyses of configurations that have not previously been conceptualized as motifs [In other words, ERGM encourages a process-oriented approach, which is more congruent with CAS theory in that it supports the identification of these specific configurations that represent the underlying s motifs . FinallyWe use the Baltic Sea as a case study to demonstrate the applicability of ERGM in empirical research on regime shifts in marine systems. The Baltic Sea is a heavily exploited sea that experienced rapid, persistent and large changes in some key state variables  in the late 1980s, and thus is presumed to have undergone a regime shift –32. We s2.a–d) in the entrance to the Northern Baltic Sea. The food webs are directed networks with circa 30 nodes and (un-weighted and directed) links based on predation–prey interactions in which the link (arrow) is the direction of energy transfer, namely from prey to predator. Cannibalism is neglected, and thus intra-specific size-structured interactions are not included. The selection of species was based on their relative biomasses within their functional group. In this way, the constructed food webs reflect changes in species biomass.We constructed four food webs using sampling data (when available), literature and expert opinions. Two food webs were constructed for the offshore area in the central Baltic Sea, representing the decades before and after the documented regime shift, i.e. the 1980s versus the 2000s, and two food webs were constructed for the same time periods for the coastal region of the Åland Islands  weighted by parameters (θs) inside an exponential and c is a normalizing constant [ERGM is a stochastic model in which links among network nodes are random variables. The probability of a given network constant Each network statistics corresponds to a specific network configuration. Similar to multivariate regression analysis, ERGM assesses the effect of each selected core configuration in explaining the observed network structure through parameter estimates. A parameter estimate signifies the magnitude, driving/inhibiting character and the significance of a configuration, given the presence of other selected configurations . For insIn ERGM, as in multivariate regression analysis, one needs to distinguish between the significance of the individual configuration and the appropriateness of a specific model specification taking the ensemble of configuration into account. A parameter estimate for a given configuration depends on which other configurations are included in the model. This is a fundamental difference of ERGM compared with a descriptive frequency analysis where the count of any given motif is independent of the count of other motifs. Further, even though ERGMs are conceptually similar to multivariate regression models, this similarity is merely conceptual. Multivariate regression models assume data independency, whereas network models like ERGM assume the network is formed through processes of interaction. Also, ERGMs are in general capable of picking apart highly correlated effects deriving from configuration entanglements .http://sna.unimelb.edu.au/PNet, see the electronic supplementary material for further details).The GoF procedure is performed to assess how well the model manages to capture the observed frequencies of various configurations of the empirical network that both were, and were not, explicitly modelled . If the Finally, we studied the potential regime shift changes. Parameter estimations from each Baltic Sea ERGM model were compared and the difference from one regime to another was calculated as the percentage difference in parameter values from the 1980s to 2000 . Offshore and coastal food webs are compared separately, following the cross-system consideration guidelines .3.Earlier research has identified tri-trophic food chains, omnivory, apparent competition and exploitative competition  as the fThe configurations explaining the Baltic Sea food web structures are tri-trophic food chain ,17,18, aComparing the ERGMs before and after the reported regime shift, we detect clear changes in the coastal region: the parameter estimate for apparent competition has decreased close to 30%, followed by a decrease in the tri-trophic chain by nearly 20% . Thus, t4.Our results present the minimal set of processes that give rise to the Baltic Sea food webs. The results indicate that this set of configurations is sufficient to explain the entire food web structure, and that no other processes (i.e. configurations) are taking part in significantly shaping the food webs. In all, the similarity of the set of configurations across all four food webs shows that the coastal and offshore food webs are shaped by similar processes. The results however indicate that the offshore food web is less functionally complex since only three configurations came out as significant in the ERGM . In compBy examining the detected sets of configurations, we can obtain insights about the community ecology processes that assemble food webs.The highly predated-species configuration is significant in the coastal food webs. A plausible explanation could be that the coastal food web includes many fish species in comparison to offshore food webs for which the highly predated species was not a significant configuration. All else being equal, if the number of fish species increase whereas the number of prey species in lower trophic levels remains largely the same , the number of predators per each prey species becomes larger. Thus, it becomes likely that patterns of aggregation emerge in which some specific prey species becomes exploited by a large number of predators. This can explain the significant and positive parameter estimate for the highly predated-species configuration in the fish-species-rich coastal food web. A similar argument can help to explain the estimates for the generalist configuration in the coastal and the offshore food web. Fish species are often found at higher trophic levels, and the higher the level a species occupies, the more opportunities there are to feed on different species . Therefore, the more fishes in the food web relative to other species, the higher the likelihood that some species will adopt the behaviour of generalist . Lastly, the estimate for apparent competition is significant and negative before and after the regime shift in the coastal food web, and never significant in the offshore food web. In interpreting the negative estimate for apparent competition, the generalist configuration needs to be taken into account. Both these configurations capture a process in which predator species prey on multiple prey species. Since the generalist configuration is given a high and positive parameter estimate for the coastal food webs at all times whereas apparent competition is negative, it suggests that the tendency to feed on a comparatively large set of prey is stronger than the tendency to feed on just two or a few more species.Moving on from the interpretation of sets of configurations to changes in the functioning of the food webs, our results show that the same underlying processes predominantly drive the Baltic food webs before and after the regime shift. This finding indicates no major shifts in the ways species interact at the community level despite changes in species composition, which include nine species in the coastal food web, and additions of three species in the offshore food web and one in coastal food webs. However, the magnitudes of the estimates for some of the configurations in the ERGM have changed, and these changes are most pronounced in the coastal food web. The largest percentile change is the decrease in the apparent competition in the coastal food web, which indicates that predator competition over a set of common prey species is further reduced after the regime shift.In the offshore food web changes are not especially big and concern generalists, tri-trophic food chains and keystone species. These minor changes could be explained by the increase of intermediate species. Finally, in both the coastal and the offshore food webs, we see an increase in generalism, indicating that processes in which predator species feed on a large number of prey species have become more common after the regime shift.It seems plausible to assume that an ecosystem-wide regime shift would, if interpreted from a complex systems perspective, result in large changes in the ERGM . In addition, if a new regime were the result of biodiversity degradation and other large disturbances, one would assume a simpler food web that could be explained by a smaller number of configurations. None of these changes were however seen in our case, instead we observed remarkable similarities of the food webs before and after the regime shift. Thus, our results give only very limited support for the occurrence of a system-wide regime shift in the Baltic Sea, albeit we acknowledge more research is needed to precisely define what constitute a system-wide regime shift in food web structure. We also wish to emphasize that we are here discussing system-wide regime shift, and our findings do not in any way invalidate previous finding suggesting that the Baltic Sea has undergone a regime shift as seen from the perspective of a more limited number of interacting species.We suggest that the maintenance of the dominant species interaction processes in the Baltic Sea before and after the reported regime shift is caused by the high connectivity and the absence of compartmentalization in the observed food webs . Theoretical studies have argued that these structural features allow the species to compensate for local losses by, for example, switching predation to new prey species ,37. AgaiIrrespectively of whether a system-wide regime shift has occurred or not, our interpretations of the results outlined above provide evidence that ERGM is able to analytically capture the causal link between the existence of different micro-level species interaction processes and the emergent and observable structure of the entire food web. Further, it seems capable of doing so under the assumption that the actual number of processes that gives rise to complex structures (and high-level phenomena) is often quite low. Indeed, the parsimonious character of ERGM seemingly provides a powerful tool in the search for these core processes, which are often very hard to reveal in complex systems (cf. ).Our study however suffers from several limitations. First, we are aware of uncertainties caused by the applied food web assembly process , and acknowledge that this can affect the modelling results. Second, fitting an ERGM involves lots of manual trial and error since model convergence is challenging, which presents inherent limitations in terms of the number of configuration combinations that can be tested practically. A noted difficulty in ERGM is which criteria to use in selecting the best fitting model   and tesRegime shifts are, in complexity theory, often  assumed to result from critical changes in the ways the components of the system interact with each other. When contextualizing this general assumption in food webs where the components constitute species and the interaction processes constitute the ways in which species feed on each other, ERGM can provide an important analytical modelling framework contributing to empirical and theoretical research of regime shifts in ecological communities. Our results from analysing the food webs of the Baltic Sea before and after a reported regime shift highlight the importance of considering the entire ecological community in the analysis. We conclude that our results emphasize the importance of future studies to further address the empirically and theoretically challenging question of whether the previously reported regime shift constitutes a system-wide shift or if it only involves a limited but commercially important set of species.


Medical ultrasound (US) image segmentation and quantification can be challenging due to signal dropouts, missing boundaries, and presence of speckle, which gives images of similar objects quite different appearance. Typically, purely intensity-based methods do not lead to a good segmentation of the structures of interest. Prior work has shown that local phase and feature asymmetry, derived from the monogenic signal, extract structural information from US images. This paper proposes a new US segmentation approach based on the fuzzy connectedness framework. The approach uses local phase and feature asymmetry to define a novel affinity function, which drives the segmentation algorithm, incorporates a shape-based object completion step, and regularises the result by mean curvature flow. To appreciate the accuracy and robustness of the methodology across clinical data of varying appearance and quality, a novel entropy-based quantitative image quality assessment of the different regions of interest is introduced. The new method is applied to 81 US images of the fetal arm acquired at multiple gestational ages, as a means to define a new automated image-based biomarker of fetal nutrition. Quantitative and qualitative evaluation shows that the segmentation method is comparable to manual delineations and robust across image qualities that are typical of clinical practice. Typically, purely intensity-based methods do not lead to good segmentation results. Several approaches are available at present for segmenting S images . Among tS images , has proS images , registrS images , image eS images , tissue S images , and feaS images , since lAmong the many image segmentation methods that are currently available, the fuzzy connectedness (FC) framework can potentially deal with the fuzziness inherently present in US images and is defined by a discrete mathematical formulation, which makes it easy to implement. Fuzzy connectedness  is a regThe particular segmentation challenge considered in this paper is 2D fetal US image segmentation. Previous automatic methods developed for this task have focused on extracting standard biometry (size) parameters over a narrow gestational age range. Examples include methods developed for the fetal head , the fetIn 3D ultrasound, Most previous studies were designed to work over a particular gestational age range . This avoids the main challenges (articulated later in the paper) of developing segmentation solutions applicable across gestation. To our knowledge, the only previous work to propose estimation of a fetal ultrasound biomarker across a large gestational age range is the framework  that accNone of the previous works have attempted to relate the quality of the images to the quality of segmentation results which is an original contribution of this paper, and most prior work only uses a small number of images to develop and validate a method.As with the work of The contributions of this article are three fold. First, we consider how to extend the Absolute Fuzzy Connectedness (AFC) approach to US images by defining a new affinity function. This is done by incorporating information extracted from local phase features instead of image intensities into the AFC framework affinity function. The resulting local phase-based FC framework becomes invariant to contrast and thus is well-suited for US image segmentation. Second, we present a new shape-based method for object completion of one or more ‘gaps’, to deal with missing information resulting from regions without an ultrasonic signal response (for example due to ultrasonic shadows). The result of object completion is then regularised by mean curvature flow. Thirdly, we introduce an approach to quantify the image quality (which can vary considerably between US image acquisitions) of an ultrasound image segmentation validation dataset to appreciate the accuracy and robustness of the developed analysis methodology across clinical data of varying appearance and representative of potential real world applications. The latter is especially important for US image analysis methods, where results are normally linked to the quality of the images and general practice (with few exceptions) is to report findings on good acoustic window data.Preliminary versions of parts of this article appeared in The outline of the remainder of the paper is as follows. In 2The overall segmentation framework is composed of several steps summarised in 2.1f(t) and its Hilbert transform A(t) and local phase φ(t) of f(t) defined as Let MI of an image I generalises the analytic signal to 2D (and higher dimensions) using the Riesz transform instead of the Hilbert transform. From the monogenic signal, the local phase, local energy, and local orientation can be estimated.The monogenic signal  IMH1, H2) define the Riesz transform.In the spatial domain, the convolution kernels of the Riesz transform are defined asσ is the selected scale of the filter.The implementation requires a pair of bandpass quadrature filters to extract the local properties of an image . The image e filter  defined This filter was empirically chosen, giving better visual maps than other candidate bandpass filters. This is not a critical part of the methodology and other filters, such as Cauchy , may be local amplitude (energy) local phaselocal orientationThe monogenic signal 2.2feature asymmetry FA measure, calculated over a number of scales, and defined ass represents the scale, N is the total number of scales, ε is a constant that avoids the division by zero , in this paper we have chosen to employ one of the original formulations of FC, namely Absolute Fuzzy Connectedness (AFC), to study how it would perform using the affinities specially formulated for US imagery.global fuzzy relation that assigns a strength of connectedness to every pair of pixels in an image to define objects via dynamic programming. The key step of this region-based approach relies on the definition of a local fuzzy relation κμ, called affinity, which defines the local “hanging togetherness” between any two adjacent pixels. If two pixels c and d are adjacent, the affinity depends on how homogeneous the region is and on how close the intensity values at c and d are from the expected intensity value of the object of interest. The affinity is equal to 0 for non-adjacent pixels.The Absolute Fuzzy Connectedness strategy  is basedglobal relation, called Fuzzy Connectedness, where the strength of connectedness between any two pixels is calculated as the largest of the strengths of all paths between c and d on the discrete image grid. Each path corresponds to a sequence of adjacent pixels starting from c and finishing in d and has a corresponding strength value, which is the smallest affinity of any pair of consecutive pixels along the path (weakest link). The Absolute Fuzzy Connectedness is represented as a connectivity map, where the object of interest is obtained by thresholding the image at FCT. The detailed mathematical description of the method can be found in  E, derived from the feature asymmetry image, directly gives a measure of homogeneity, since smooth regions have small values and regions near boundaries have large values (cf. c) be the local phase at pixel c and E the thinned pixel edge derived from feature asymmetry between pixels c and d. The homogeneity-based component E is close to 0 in homogeneous regions and close to 1 at edge features, we can express the homogeneity component asg3 is a function of E. The object feature-based component om and oσ are the mean and standard deviation of the intensity values of the object of interest, previously calculated in a training stage, and g4 is a function of φ(c) and φ(d).The AFC framework was adapted to US segmentation by defining a new affinity function that uses structural and edge feature information instead of intensities and intensity gradients. The affinity function was designed as follows. Assume that every fuzzy subset lues cf. . Therefomulation  was applκμ (I(c) and I(d) correspond to the intensities at pixels c and d, respectively 2.4The segmentation resulting from the feature-based FC only incorporates regions of the object of interest present in the image. However, it is unable to delineate object boundaries in shadowed areas , is defined as the set of connected points at a distance smaller than a threshold t from the line connecting the two end points of the set (red dashed curve in C(p) is obtained after symmetrically and progressively examining the adjacent boundary elements to p until the distance is no greater than a threshold t.At each point  segment , called hc-scale value C(p) (green dashed line in C(p), which is the length of the straight-line segment between the end points in C(p). Large hC(p) values indicate small curvature at p, whereas small values denote high curvature  passing through p  in the segmented object. Two normals on each side of each detected gap are then identified at a fixed distance 2.5The resulting object boundary is finally smoothed using a mean curvature flow (MCF)2.6sT was obtained from statistical properties of the local phase image  at the Nuffield Department of Obstetrics and Gynaecology, John Radcliffe Hospital, University of Oxford, Oxford, U.K. The fetuses involved in this clinical study are part of the INTERGROWTH-21st (2009)INTERBIO-21st (2012)The protocol used for the acquisition of the US fetal arm cross-sections was as follows. First, the sagittal view of the humerus  and delineation specificity by 1-FPAF where FPAF is the false positive area fraction. These two independent metrics are sufficient to quantify the general accuracy of a segmentation method. In each case, a larger value indicates a better segmentation performance.In this subsection, we quantitatively assess the proposed segmentation method by using a number of established region-based and distance-based metrics. First, region-based evaluation metrics, defined as area overlap measures, were selected as a way of assessing image segmentation precision (repeatability of the method) and accuracy (sensitivity and specificity). These metrics are as defined in We also report the commonly used Dice similarity metric. Distance-based metrics , as described in The segmentation evaluation results of the proposed approach were then compared to both experts and to the average manual segmentation, as shown in The proposed method performs similarly to manual delineation with mean results very close to those obtained for each metric calculated for the inter-expert variability cf.  in terms3.4This subsection firstly explains how we define image segmentation quality for our dataset and then interprets the automated algorithm performance with respect to the resulting image segmentation quality metrics.It would be greatly beneficial to report segmentation results with a measure of image quality to characterise the dataset used and how well the method performs considering the quality of the images. However, establishing overall image quality measures is difficult, since the quality of images relies on tissue appearance. Ultrasound image quality can vary considerably between acquisitions, which may affect the performance of different segmentation methods.In this paper, we propose a new solution to quantify image quality of a clinical dataset designed to provide deeper insight into segmentation performance. This is, to our knowledge, the first attempt to correlate segmentation results with a quantitative measure of US image quality.US image quality depends on a number of factors including: the US machine , the object being scanned (tissue properties (speckle), effects of attenuation (depth), shadows, and reverberations), and the orientation of the probe with respect to the object.In fetal ultrasound imaging, object appearance varies with gestational age with the structures surrounding the object of interest showing high variability. Overall fetal US image quality tends to decrease towards later gestation as a result of the fetus becoming bigger with relatively less amniotic fluid, thus the fetal structures are more likely to be compressed resulting in the clear soft tissue/fluid interface. The bone density in the fetus also increases, creating more shadows and artefacts in the images. Another factor that can affect ultrasound image quality is the increase of maternal body mass index, attenuating the signal especially towards the end of pregnancy. Specifically, the proposed quantitative image quality assessment method relies on the principle that different tissues have specific sound propagation properties characterised by the complexity of the speckle pattern. These tissues do not evolve in the same way across gestation and surrounding structures vary depending on the acquisition angle and fetal position at that particular time. This is why an overall global image measure would not be as appropriate as a regional quality measure.Traditional image processing quality measures such as SNR  and CNR (contrast-to-noise ratio) rely on the estimation of the signal and noise from the entire image or regions. In the case of ultrasound image processing, and particularly the literature on speckle-reduction, speckle has typically been treated as the noise component. In our case a speckle-based measure would only capture texture differences, not contrast changes, and requires access to the RF signal to estimate a statistical model, for instance see rp, is first estimated from the gray-level histogram of that region. The normalised histogram of a region rA is defined for each intensity value ka with M being the maximum number of intensity levels in rA. In our case, H of the random variable rA can then be calculated asThe proposed new method quantifies the complexity of each region (resulting from the speckle distribution) and the relationship amongst tissues in an image without estimating a speckle model . Specifically, first a manual image partitioning is made to each image resulting in manual delineations of different regions of interest. An entropy-based measure is then computed on each of the image partitions to estimate the information content in each region of interest. This quality measure is based on the appearance and complexity of each region and not on contrast, absolute intensity, or edge information. The probability density function of a region, denoted The proposed quantitative image quality assessment method was applied to the fetal arm dataset introduced in In the evaluation dataset used within this study, we deliberately  selected examples with a wide range of image quality. The examples discussed below are typical examples taken from the whole dataset and were chosen to facilitate the understanding of how entropy values relate to the fetal image regions analysed. We have studied in detail the relationship between all the image regions in the dataset and the entropy values before concluding how to generalise our findings which are reported below.The entropy of the background region is shown in Similarly, the entropy for the adipose tissue region , H(Abackground), and H(Amuscle) as defined in Having looked at the entropy  for different tissues of interest we now consider how to define image segmentation quality metrics. Recall, that the goal is to segment the adipose tissue layer. Thus the two interfaces of interest are background–adipose tissue, and adipose tissue–muscle. Therefore, we define two scores to assess the difference of entropy between the background region and the adipose tissue region, and the adipose tissue region and the muscle region for each image in the evaluation dataset. Let Sab and Sam, derived from adjacent regions as previously defined. Score values are low when adjacent regions are similar, and hence image quality overall is lower. Higher score values translate into more distinct adjacent regions, and hence higher image quality overall. Gestational age is incorporated into Sab values, where the entropy in the background is higher than the information of the adipose tissue layer. This can happen when the arm is surrounded by other organs  as shown in Having explained how to define image segmentation quality metrics for our clinical dataset we can now look at how the automated segmentation method performs with respect to these metrics. The repeatability of the method is presented in Sab values). However, high precision and accuracy values (red and yellow colours) can also be observed in that same quadrant. It is worth pointing out that the lowest accuracy values observed are above 80%, which is good in terms of segmentation performance. Therefore, we conclude that the proposed segmentation method is robust across the variety of image qualities present in the clinical evaluation dataset.As shown in 4This paper has presented three main technical contributions: a feature-based segmentation strategy adapted to US images, a gap completion method, and a novel quantitative image quality assessment approach to assess segmentation performance.The complete US image segmentation framework introduced in this paper is based on a feature-based fuzzy connectedness segmentation method and requires manual placement of the seeds, after which the remaining steps are performed automatically. The selection of the threshold was fixed for this application, in future might be automated by, for instance, the method of Although more conceptually advanced fuzzy connectedness methods exist, such as RFC and IRFC, it remains to be seen how these would perform in US images. This paper reports results on AFC applied to US images, which is the most basic form of FC with affinities specially formulated for US image segmentation. Once this basic investigation is reported and the behaviour of AFC understood in its most fundamental form, we can then take on investigations to study how more advanced forms of FC with the same forms of affinities on a multi-object setting would perform.We argued that all segmentation methods should report their results in conjunction with a quantitative image quality analysis to show that the dataset used is representative of a clinical application, and not selected to best suit a particular methodology. A novel quantitative image quality assessment protocol based on entropy was presented and applied to different image partitions to derive interface scores to show the variability of qualities existing in the dataset, representative of a real clinical application. This technique could readily be adapted to suit images from different clinical applications.A qualitative and quantitative evaluation was performed on 81 cross-sectional images of the fetal arm across gestation, by using region and distance-based metrics. The results showed a similar performance to manual segmentations. Furthermore, the quantitative image quality assessment method showed that the performance of the method was robust across a variety of image qualities representative of a real clinical environment.The proposed method has undergone clinical assessment on pilot data  and is nThe 2D feature-based FC implementation could readily be extended to 3D, as local phase and fuzzy connectedness can be easily extended to 3D. Finally, the proposed framework is motivated by, but not limited to this particular application or imaging modality and could equally be applied to other soft tissue segmentation problems, such as myocardium segmentation , includi


Studies of the global mean surface temperature trend are typically conducted at a single  time scale. The used scale does not necessarily correspond to the intrinsic scales of the natural temperature variability. This scale mismatch complicates the separation of externally forced temperature trends from natural temperature fluctuations. The hiatus of global warming since 1999 has been claimed to show that human activities play only a minor role in global warming. Most likely this claim is wrong due to the inadequate consideration of the scale-dependency in the global surface temperature (GST) evolution. Here we show that the variability and trend of the global mean surface temperature anomalies (GSTA) from January 1850 to December 2013, which incorporate both land and sea surface data, is scale-dependent and that the recent hiatus of global warming is mainly related to natural long-term oscillations. These results provide a possible explanation of the recent hiatus of global warming and suggest that the hiatus is only temporary. Global warming has been widely studied over the past few decades1et al. who found that the global warming trend continued over the recent decades when maximum extreme temperatures rather than average temperatures were usedThe Selection of temporal scales is essential for climate change studies, because different scales used for the same system can produce very different results. For instance, in the study of large-scale forest harvesting on the hydrology in the willow watershed of central British Columbia, Lin and Wei reported that forest harvesting significantly increased the mean and peak flows at the annual scale, whereas the mean and peak flows in the summer and winter periods  were not significantly affectedIn most previous studies of global warming, the used temporal scales  are arbitrarily selected and typically do not correspond to the intrinsic scale of the studied geophysical phenomenon or process in itself. Despite the evidence for a continuum of time scales7Some natural cycles, like the daily and seasonal cycles, are well known to scientists. However, some cycles or quasi-cycles, especially on lower frequencies, are either unknown to us or even ignored in data analysis. In this case, we are very likely to mistake the downward part of a cycle as an externally forced trend. To complicate matters further, there is also a continuous background spectrum on all time scales7The mismatch between the intrinsic natural scales and data analysis scales might present us with misleading or spurious trends. The downward part of a long-term natural oscillation can give us a picture of the global warming pause. Is this the cause of the recent hiatus? In addition, temperature change rates, commonly used in global warming studies, are sensitive to outliers in temperature time series resulting from small-scale variability or events. Is this small-scale variability one of the reasons for the hiatus of global warming? Here we attempt to answer these questions with the Multi-Resolution Analysis (MRA) and the wavelet power spectrum analysis of global surface temperature anomaly (GSTA) time series.http://cdiac.ornl.gov/trends/temp/jonescru/jones.html.Here we use the monthly mean GSTA (relative to the 1961–1990 mean) time series, which incorporates both land surface air temperature and sea surface temperature data and spans the time period from January 1850 to December 2013, to study the global mean surface temperature trend. In spite of the low quality of the pre-1880 data, the inclusion of these data is very useful for understanding the GSTA long-term evolution. For more details about the GSTA data please refer to Wavelet analysis provides a systematic way to obtain information that is not readily available in the raw data. Wavelet analysis has two main applications, namely, cleaning (noise and blur reduction) and signal analysis , which are based on discrete wavelet transforms (CWT) and continuous wavelet transforms (DWT), respectively. The DWT based MRA decomposes the original  series into a low frequency component  and a high frequency component  and this process can be repeated for the approximation part at various levels, producing a series of overall pictures of the geophysical time series at various scales and detail parts corresponding to various decomposing levels or scales as well. MRA undoubtedly increases the chance of scale match between intrinsic scales of a natural process or pattern and the data analysis scale in that many scales rather than a single scale are used in multi-resolution analysis. The continuous Wavelet transform, which decomposes a time series into time-frequency space, can be used to determine both the dominant modes of variability and how those modes vary in time by means of Wavelet power spectrumsWavelet transformation coefficients or wavelet powers (defined as the square of wavelet transform coefficients) yield information as to the correlation between the wavelet  and the data series or array (at a particular location). The large wavelet power value at a given scale (s) and at a particular time location (t) means that the oscillation at the frequency related to that scale (s) exists at the time period centered on the time location (t). As we are interested in the questions whether short-term natural variability causes the hiatus and whether the hiatus affects the long term warming trend, cleaning and the signal analysis, the two main functions of wavelet analysis are both used in this paper.In the process of wavelet transforms, whether discrete or continuous, the distortion problem with the wavelet transform coefficients at the beginning and end of the data series arises due to the finite time series length11et al.et al.111) and 0.882 (α2) at the lags of 1 and 2, respectively. These value are then used to calculate the value for α in Eq. (16) in Torrence and Compo (1998)According to Liu The relationship between the Wavelet scale (s) and the equivalent Fourier period (λ) is very useful to get the information on the duration of the oscillations determined by wavelet powers. According to the formula in table 1 of Torrence and Compo (1998)The global temperature evolution is composed of many oscillations of various frequencies which are the result of the nonlinearity of the climate system and the many periodic and aperiodic natural forces. The existence of such oscillatory components of high frequency  can arise even if the analyzed signal is pure noisehttp://washington.cbslocal.com/2014/08/06/nasa-climate-scientist-explains-15-year-global-warming-hiatus/). However, our statistical results at the scales of 6, 9, 12, 15, 18 and 21 months  do not support this claim. In contrast, the role of long-term oscillations of long duration in the recent hiatus of global warming is statistically supported. The increased heat transfer to the deep sea with a duration of about 30 yearsAccording to NASA, the EI Nino pattern of climate variability that has historically coincided with a slowing in global warming is perhaps a major cause for the recent hiatus . The pattern of the GST evolution is scale dependent and the same GST evolution process when observed at different scales will produce different resultsHow to cite this article: Lin, Y. and Franzke, C. L. E. Scale-dependency of the global mean surface temperature trend and its implication for the recent hiatus of global warming. Sci. Rep.5, 12971; doi: 10.1038/srep12971 (2015).