Constraints placed upon the phenotypes of organisms result from their interactions with the environment. Over evolutionary time scales, these constraints feed back onto smaller molecular subnetworks comprising the organism. The evolution of biological networks is studied by considering a network of a few nodes embedded in a larger context. Taking into account this fact that any network under study is actually embedded in a larger context, we define network architecture, not on the basis of physical interactions alone, but rather as a specification of the manner in which constraints are placed upon the states of its nodes. We show that such network architectures possessing cycles in their topology, in contrast to those that do not, may be subjected to unsatisfiable constraints. This may be a significant factor leading to selection biased against those network architectures where such inconsistent constraints are more likely to arise. We proceed to quantify the likelihood of inconsistency arising as a function of network architecture finding that, in the absence of sampling bias over the space of possible constraints and for a given network size, networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them. Our results identify a constraint that, at least in isolation, would contribute to a bias in the evolutionary process towards more hierarchical -modular versus completely connected network architectures. Together, these results highlight the context dependence of the functionality of biological networks. On the one hand, parameters in a probabilistic model can be fit to data obtained by measuring the levels of each variable. For example, in gene-regulatory networks, gene expression can be measured using microarray or sequence census methods –3. On thAn important feature of experimental science is that it involves partial information. In the course of a single measurement, one typically is not able to observe a biological network in its entirety. Rather, one observes a subnetwork at a time and only obtains a more complete picture by later combining these partial views. This contrasts with theory, where one makes a representation of a closed system that provides explicit values for all quantities of interest. In order for a probabilistic model to serve its purpose, it should also accomodate partial information and thus we will explicitly consider the effects of (i) carving out a subnetwork from its context and (ii) coarse-graining observables. Observables representing partial information will generally arise in situations where a system is interacting with another system. This situation arises in the context of interpreting the potential existence of modular substructure within biological network data deriving from any given organism as well as with respect to the interactions between an organism and its environment.Inconsistency arises when a network context places more constraints on a subnetwork than it is capable of satisfying. The impact of this issue on genetic interactions has been considered previously in the context of population genetics . We exhiIn §2, we describe the relationship between representations of biological networks and an abstraction of these referred to as network architecture that indicates the manner in which a subset of a network is connected to its context. We explain the connection between stochastic process models of biological networks and a generalization of the genotype–phenotype map applying to arbitrary biological networks referred to as network–network state maps in §3. Sections 4–6 contain examples of the underlying mathematical justification for our claims , and they can be skipped by readers who are primarily interested in the intuitive implications of our analysis. In §4, we introduce the concept of network modules and define probability distributions over their states. Sections 5 and 6 describe the different compatibility conditions that arise for different biological network architectures and demonstrate how these compatibility conditions lead to a set of inequalities determining a space of probability distributions for each network architecture. Sections 7 and 8 examine these constraints for the example of the three-cycle network architecture. Section 9 computes the likelihood of unsatisfiable constraints for all biological network architectures on four variables that possess cycles. Finally, §10 explains implications for the evolution of biological network architectures of the result that networks with a larger number of cycles are more likely to have unsatisfiable constraints placed upon them.2.environment or context. In figure 1b. The transformation from SBGN to the AI network is given simply by collapsing the disconnected components of the ancestors of each node in the focal subnetwork into single AI nodes. This results in a bipartite graph that captures the dependencies among the environmental factors as experienced by the subnetwork and nothing more.Most studies of biological networks focus on one type of variable in isolation. For example, many studies focus on one of metabolic networks, protein–protein interaction networks, signalling networks, gene-regulatory networks, or population and community dynamics in the context of ecological networks. A true biological network involves all of these acting together to produce biological phenomena at all scales. Models that integrate information about biological networks, rather than focusing exclusively on particular types of molecules, will likely become more common in the near future –10. The c for each of the simple examples of the SBGN form of biological networks. Considering all possible hypergraphs of this kind is equivalent to examining all possible environmental dependency structures the subnetwork could be subjected to. Because the AI is fundamental to understanding how subnetworks depend upon their contexts, it is the structure of the AI and equivalent SH graphs that we refer to as network architecture throughout the paper. We note from this perspective that cycles in the SBGN representation of the biological network do not result in corresponding cycles in the AI graph and vice versa. For instance, in example four of This AI graph is precisely equivalent to an undirected hypergraph if one considers each of the AI nodes as a hyperedge containing all of the nodes to which it connects. This is shown as the SH graph in figure 1L. The different subsets, O, of biological variables, L, making up the hypergraph representation of the AI are each referred to as modules. A biological network architecture, 𝒢, may then be represented by a subset of all possible such modules subject to two conditions . The first represents the fact each variable of the focal subnetwork must be included in at least one module. The second represents the fact that any pair of constraints that are imposed upon overlapping sets of variables must agree on those overlapping variables. In expressing the latter condition, all of the information present in a collection of lower order constraints can be expressed as an effective higher order constraint if any such higher order constraint exists at all. So, if there is a constraint that is imposed simultaneously upon two distinct variables and another independent constraint imposed upon only the first of the two variables, this situation can be expressed in terms of a single constraint on both of the two variables.More precisely, the collection of variables comprising the subnetwork under consideration is referred to as frustration arises in the couplings among the magnetic dipole moments of three nearest neighbour atomic spins [When there is a relatively larger degree of independence in the network context compared with the subnetwork, it is possible for inconsistency to arise. One canonical example of such inconsistency arises in the study of ferromagnetism via the Ising model on a triangular lattice where so-called ic spins –14. In t3.a shows a simplified representation of two different biological networks, the correlation strengths among whose variables are not known but are to be derived from observation of the levels of the entities corresponding to each variable. For example, in the context of a gene-regulatory network, the amount of a given transcript present in a cell can be binned into a smaller number of discrete classes by setting a collection of thresholds on the original dataset. If only a single threshold is given, then the data can be binned into two classes depending upon whether or not the original measurement surpasses the given threshold in figure 2b. The time series that results from such observations can be used to infer various statistics that characterize the dynamics of a biological network such as correlations between pairs of variables.Figure 2P gives the probability of observing n1, n2 and n3 molecules of each of the three variables, respectively, and M(k) is a Markov transition rate matrix that depends upon some rate functions k that are determined by the network architecture and the dynamics of the interactions. The solution to this equation will converge towards a stationary distribution Ps in the limit of long times. Any environmental variable having a characteristic time scale longer than that of the variables in the focal subnetwork would not be sensitive to transients and would only exhibit control over or be influenced by this stationary distribution.If a large enough number of thresholds is available to distinguish among all possible counts of the variables under investigation, then this observational protocol becomes complementary to mechanistic models. There may be several sources for stochasticity in the dynamics including small numbers of the causal molecules and products as well as environmental fluctuations upon which these dynamics are conditioned –23. Regain are natural numbers, then a function f taking any number less than or equal to some threshold T to 0 and any number greater than T to 1 is a very simple example of such a coarse-graining. For this specific form of the coarse-graining function f, the coarse-grained stationary probability distribution takes the formb1, b2, b3 ∈ {0,1}. It is also possible to consider the case where each variable is coarse-grained according to a different threshold and into a different number of classes. An abstract algebraic formulation of the coarse-graining process is provided in electronic supplementary material, §S4.Interactions between variables may be mediated by a coarse-graining over counts of each variable using a function that maps the states representing molecule counts as vectors of natural numbers into some other variables. For example, if The most familiar example of such a coarse-graining process in biology is the genotype–phenotype map. The genotype of an organism has a relatively straightforward definition in terms of the sequence of nucleotides comprising its genome. Phenotypes, on the other hand, can be described at different levels of organization ,25. The L of variables and a finite set P of coarse-grained levels of each of those variables. These levels may have different units, but they can all be mapped into unitless quantities that account for the relevant scale of each variable. In general, each variable could take values in a distinct set Pi, i ∈ I ranging over the variables, whereby P would be required to represent e: L → P and coarse-graining a stationary distribution will lead to a probability distribution on the set of all maps, denoted LP, from subnetworks represented by subsets of L to the respective states of the variables that comprise them. We will refer to this more fine-grained generalization of the genotype–phenotype map, where arbitrary biological networks are substituted for genes and arbitrary networks states are substituted for phenotypes, as network–network state maps.A more realistic basis upon which to build phenotypes than this outline of the historical trajectory contains is one that is not limited to genes alone, but includes all entities constituting a biological network. A phenotype must be a function of the levels of, for example, all of the molecular constituents that comprise it over time, even if more information is required to fully specify it. The aforementioned coarse-grained levels of biological network variables can thus be viewed as collectively determining the lowest level in a hierarchy of abstract phenotypes. In what proceeds, we will assume that we have a finite set 4.O, of the variables, L, in the subnetwork. If we consider the case in which we have two variables L = {l1, l2} and there are two values, P = {0, 1}, then there are four possible assignments of values to variables each of which constitutes a state of the system. We will write the probability of each of these states as v1 is assigned value s1 and variable v2 is assigned value s2. A probability distribution over the states of the system for L is then given byL given by O = {l1}, then a probability distribution over its states is given byHere, we describe examples of probability distributions over network modules. A more general presentation is provided in electronic supplementary material, §S3. As explained in §2, for a given biological subnetwork, the hypergraph representing the dependencies in the network context consists of subsets, 5.l1, l2} and {l1, l3}, then we can obtain a probability distribution on the set {l1} either by marginalizing probabilities defined over {l1, l2} as was done above or by marginalizing probabilities defined over {l1, l3} to obtainHere, we provide an example of compatibility conditions on network–network state maps. A more general mathematical characterization of these constraints is provided in electronic supplementary material, §S5. When one has a non-trivial network architecture .More generally, given a hypergraph 𝒢, we will be interested in two types of consistency conditions. We will say that a collection of probabilities associated to a hypergraph is globally consistent if there exists a joint probability distribution on the totality of variables associated to the hypergraph such that the probabilities associated to any hyperedge are marginals of that joint distribution. In terms of our example, that would mean that there exist probabilities We will say that a collection of probabilities associated to a hypergraph is Because marginalizing from a set of random variables to a smaller set of variables can be accomplished by first marginalizing to an intermediate set and then marginalizing from the intermediate set down to the smaller set, it follows that global consistency implies local consistency. We will now see what conditions are needed in addition to local consistency to ensure global consistency.L of all variables down to a hypergraph 𝒢 in the form v = Gx, where x is a vector whose components are probabilities associated to L, v is a vector whose components are probabilities associated to 𝒢, and G is a suitable matrix. The consistency conditions can be expressed in terms of the fundamental spaces (kernel and cokernel) associated to this matrix [v to be expressible as Gx for some x, we must satisfy the condition that v · u = 0 for all u ∈ coker(G). In our example, the cokernel of the matrix is spanned by the following two row vectors:u · v = 0 for all u ∈ coker(G) will always be exactly the local consistency conditions .As in our example, we can express marginalization from the set s matrix . In ordev = Gx, then we also have v = Gy for any vector y such that x−y lies in the kernel of G. Choose a subspace T of column vectors which is transverse to ker(G) such that the union of T and ker(G) span the column space. Then the equation v = Gx has a unique solution if we restrict x to lie in T. In order for a column vector to represent a legitimate probability distribution, its components must all be non-negative. Hence, we conclude that v being globally consistent is equivalent to the following system of equations and inequalities having a solution:To obtain the global consistency conditions, we note that, if x and y from this system to obtain inequalities involving only the components of v. These are the global consistency conditions.By using a method, such as Fourier–Motzkin elimination, to remove redundant inequalities, one can eliminate the quantities G) is spanned by the following two column vectors:T, we will choose the space spanned by the following basis:x ∈ T reduces to the equations x4 = x8 = 0. The conditions x − y ∈ ker(G) then becomex's, substitute the result into the equation v = Gx and eliminate the y's between the resulting equations and the inequalities y ≥ 0, we find the conditions v ≥ 0. This, of course, is just the condition that the probabilities be positive. Thus, for the case of this simple hypergraph, local consistency suffices to ensure global consistency. In §6, we will see that this is not always the case and that the inequalities obtained by elimination impose more conditions on the probabilities than just positivity.In our example, ker to simultaneously take on a given pair of values. Note that this does not imply the existence or absence of a physical interaction between the variables represented by these two nodes. Together, these probabilities represent constraints that the network context may impose upon the network. We assume three variables are observed via all possible pairwise combinations and that via the coarse-graining process we have binned the state of each variable into one of two classes. Each node of the graph in figure 3a represents a probability distribution over the observation of each variable in either of the two states established in the coarse-graining process. Each of the probability tables adjacent to each edge in the graph assigns a probability distribution to the set of maps from the nodes connected by the edge to all possible combinations of the network states. As these maps take collections of biological network variables as input and produce collections of network states as outputs, we refer to them as network–network state maps and thus to the associated probability distributions as probability distributions over network–network state maps.Each node of the SH graph in figure 3a are meant to represent the ostensible structure and parameters of a biological process. It is often necessary to attempt to infer the parameters of such a model from data under the assumption that the structure of a given network architecture falls within the model class defined by a given graph. Figure 3b represents a case in which a hypothetical dataset is consistent with its derivation from a joint probability distribution, whereas figure 3c represents a case of inconsistency where the pairwise distributions are each individually consistent distributions, but, together, the three pairwise distributions are not consistent with any joint distribution over the states of all three network variables. This inconsistency is made possible by the fact that the network architecture in figure 3a contains a cycle [Suppose the normalized contingency tables in figure 3 a cycle –31 and tIf this situation arises, it indicates some systematic error in the transfer of information whether it occurs intrinsically to the system, wherein a network has inconsistent constraints placed upon it by its network context or as part of the scientific data collection process. In the former case, this can be resolved by modifying the inconsistent constraints in such a manner that they become consistent with or without modifying the network architecture in doing so. In the latter case, this may result from employing a model which (i) takes insufficient account of the network context and (ii) relies on coarse-grained observations. In either case, the synthetic gene circuit schematized in electronic supplementary material, figure S4, serves as one mechanism implementing the example presented in electronic supplementary material, §S5.1. It consists of four genes each of which is capable of taking on three different states . Howevera, and moreover for any network architecture of any size that contains one or more cycles, the possibility of finding a joint distribution over all network variables that satisfies all constraints capable of being imposed upon it requires the implicit assumption that the structure of the network context can be viewed simultaneously as that of figure 2c top and that of figure 2c bottom. The spaces of probability distributions corresponding to the constraints that can be imposed upon the two network architectures contrasted in figure 2c are different. We can now apply the process described in §5 to classify the geometries and thus relationships among the spaces of probability distributions associated to constraints that can be imposed on all possible network architectures with a given number of variables.For the case of the architecture in figure 38.a shows the lattice of reduced subsets of three variables. We are only interested in those subsets that contain at least one instance of each variable. Restricting to the subsets of variables satisfying this condition corresponds to the region highlighted with a grey background in figure 4a. Each network architecture corresponds to a different modularization of the network–network state maps by the network context. For example, figure 4b shows in the same vertical order the different maps induced by the three architectures highlighted in green in figure 4a.The relationships among possible network architectures are given by the lattice, which in this case indicates ordering by subset inclusion, of reduced subsets of biological network variables . For example, figure 4a to be of higher modularity because each corresponds to the increasing restriction from placing constraints on higher- to placing constraints on lower- order correlations among variables. Figure 4b top corresponds to the least modular network architecture because constraints are placed upon correlations among all three variables. Figure 4b middle exhibits an elevated degree of modularity because constraints are placed upon correlations among pairs of variables. Similarly, figure 4b bottom is even more modular because constraints are placed upon each variable individually.We consider those network architectures found lower in the lattice of figure 4a can be associated to a pair of spaces of probability distributions over network–network state maps. These correspond to the spaces of globally, 𝕄(𝒢), and locally, 𝕃(𝒢), consistent distributions described in §5 and electronic supplementary material, §S5. Figure 4c schematically depicts the relationships among the probability distributions associated to the corresponding architectures and network–network state maps in figure 4b. For figure 4c(i), 𝕄(𝒢) = 𝕃(𝒢). The inconsistency noted in the previous section between the architectures figure 4b(i) and (ii) is a result of the differing geometries in figure 4c(ii). There, the smaller darker grey region, 𝕄(𝒢), defined by the inequalities expressed in equations (figure 4b(ii). Similarly, the lighter grey region defined by equation (figure 4b(ii) and thus 𝕄(𝒢) < 𝕃(𝒢) in the latter case.Each of the network architectures in figure 4quations  and  occur for all network architectures defined over any number of variables so long as there exists at least one cycle in the corresponding network architecture, §7. For the case of three variables, there is only one class of graphs containing a cycle, which is that of figure 4b(ii). For the case of four variables, there are nine different classes of hypergraphs containing cycles and these nine classes can be split into two groups depending upon whether or not the edges of the graphs are each restricted to represent correlations among only two variables. Electronic supplementary material, figure S5, shows the components of the analogous lattice to that of figure 4a as well as these different classes of network architectures on four variables having cycles.Relationships between spaces of potential constraints placed upon patterns of network states like that of figure 4c(ii)) of probability distributions over network–network state maps. We assess the likelihood of choosing a point in 𝕄(𝒢) at random by computing the ratio of the volume of 𝕄(𝒢)  with a single edge containing all four variables), whose architecture and thus volume is fixed, to that of 𝕃(𝒢), whose volume varies according to each of the cyclic graphs associated to a network architecture on four variables. We refer to this number as the global : local volume ratio or Vol(𝕄(𝒢))/Vol(𝕃(𝒢)) . The comparison defined by this ratio is meaningful since 𝕃(𝒢)  and 𝕄(𝒢)  are of the same dimension. In the case where the constraints defining 𝕃(𝒢) are eliminated, the analogue of this volume ratio would be 0 for all 𝒢. This volume ratio determines the a priori likelihood of observing inconsistency for a given network architecture. The consistency check involved in computing this ratio can be used as a test demonstrating, for those cases exhibiting inconsistency, that the model being used is incorrect in the sense that it does not correspond sufficiently to the actual network context determining the constraints placed upon the network. Consider the probability of locally versus globally consistent observations (p(𝕃(𝒢)O) versus p(𝕄(𝒢)O), respectively) separately from the probability of locally versus globally consistent models (p(𝕃(𝒢)M) versus p(𝕄(𝒢)M), respectively) that accurately reflect the underlying process. We can then estimate the probability of having a locally consistent model despite obtaining globally consistent observations, p(𝕃(𝒢)M|𝕄(𝒢)O), via a simple application of Bayes' theoremp(𝕄(𝒢)O|𝕄(𝒢)M) = 1, the volume ratio described above corresponds to p(𝕄(𝒢)O|𝕃(𝒢)M), and one could consider the impact of different prior probabilities, p(𝕃(𝒢)M), of having a locally consistent model.Given this larger collection of network architectures with cycles, we can assess the relative sizes of the spaces 𝕄(𝒢) and 𝕃(𝒢) . For the nine network architectures in figure 5a,b containing cycles, the volume ratio is strictly less than one. This quantifies the probability that the network architecture depicted along the x-axis will be able to satisfy the constraints that the associated network context is capable of placing upon it.Figure 510.The satisfiability of constraints capable of being placed on the various architectures is logically a function of whether or not the network architecture is cyclic or acyclic. For those network architectures containing cycles, there are certain functional requirements that can be achieved so long as only local and not global consistency is required of them. Once global consistency is imposed as in the structure corresponding to the joint correlations among all variables, those functions that were accessible when only local consistency was imposed are unavailable. For acyclic network architectures, there is no difference between the satisfiability of locally or globally imposed constraints. When selective pressure is induced equivalent to the distribution located at the blue point, or at any other point within the dark grey region, either of the architectures are essentially equivalent with respect to the statistics of samples from their corresponding probability distributions and they can thus be considered as members of an evolutionarily neutral space. On the other hand, selective pressure equivalent to the probability distributions located at the red point differentiates between the networks of the top and bottom row or equivalently between the network of the bottom row when global consistency is imposed versus the same network when only local consistency conditions are imposed. The same qualitative relationship holds true for the spaces of probability distributions of all network architectures of any size and for any number of different levels in the discrete coarse-graining of network states so long as the graph associated to the relevant correlations among variables contains at least one cycle.The distinction between cyclic and acyclic network architectures with respect to the ability to have unsatisfiable constraints placed upon them is sharp. However, within the class of cyclic network architectures, the likelihood of having unsatisfiable constraints imposed on a given network architecture increases, at least approximately, with the number of cycles in the given network architecture  and §9. 11.When biological networks are studied, we remove a subnetwork from a larger context . DependiOne salient feature applying at any scale is that the structure of the network context plays a crucial role in determining whether or not unsatisfiable constraints on the stochastic dynamical patterns of network states may arise at all. We note based on previously existing results that mutually incompatible constraints are only capable of arising when the network architecture contains a cycle. Moreover, our results suggest the likelihood of mutually incompatible constraints arising relative to network architecture increases with the number of cycles in that network architecture. An evolutionary process exhibiting uniform sampling over the space of network architectures and the space of possible constraints within each network architecture would thus be expected to exhibit a bias towards the breakage of cycles. One would not expect such a bias to eliminate the existence of cycles in biological networks. However, it is reasonable to expect on the basis of this result a kind of hierarchical modularity: where modules that may possess cycles and are small relative to the overall size of the network exist within a globally hierarchical network structure. Of course, there are other factors which may contribute to the development of such network architectures.cis-regulation that enables the breakage of statistical dependence in a time-dependent manner . But such a scenario seems much less plausible than the ability to resolve inconsistency by breaking cycles in the network architecture. In the long term, the latter corresponds to what is observed in hierarchically organized transcription factor networks [It will be important in future work to examine this prediction more closely in the context of developing bottom-up stochastic process models that allow for the explicit encoding and solution of models of more complex biological networks ,35. It inetworks ,36–38. Tnetworks .To contribute to the broader goal of establishing an integrated framework that synthesizes hypothesized intrinsic and extrinsic constraints necessary to understand the functioning and evolution of biological systems, here we have traced a path from biological network architecture to network state constraint satisfiability, and, via the impact of network states on higher level properties culminating in macroscopically observable phenotypes, to evolutionary processes. In the particular context of gene-regulatory networks, one goal of measuring gene expression at transcriptomic scale is to uncover the structure of the generative process encoded in the interactions involved, but, so far, even the most sophisticated methods of describing them at the mechanistic level are only solvable for extremely simple regulatory network architectures ,35. This


Nanoporous carbon material (NCM) was obtained from the raw materials of plant origin by carbonization and subsequent activation in potassium hydroxide. It is established that there is an optimal ratio of 1:1 between content of KOH and carbon material at chemical activation, while the maximum specific capacity of NCM is 180 F/g. An equivalent electrical circuit, which allows modeling of the impedance spectra in the frequency range of 10 One of the modern trends in the development of rechargeable energy sources is the creation of highly efficient electrochemical capacitors (EC), working on the charge/discharge principle of the electrical double layer (EDL) in polarized electrodes with large specific surface area. The EDL charge/discharge mechanism is reversible and reproducible up to thousands of cycles, each of which lasts a fraction of a second ,2. GreatThe value of the specific capacitance of a capacitor depends on the type of the electrolyte, the structure and condition of the developed surface of the electrode material, and its pore size distribution. The electrolyte defines the internal resistance (IR) of EC and the operating voltage that should not exceed the expansion potential of the solvent .2π hybridization  with a complex framework of condensed aromatic layers. The degree of graphitization and amorphousness of the obtained carbon structure depends on the temperature and chemical treatment conditions. The surface of the obtained nanoporous carbon material (NCM) is significantly different according to the method of chemical activation. The final properties of the obtained NCM depend on several factors such as temperature of carbonization of the feedstock and the environment in which it occurs, future conditions, and modes of the chemical activation. Electrodes based on NCM are separated by a separator and placed in the electrolyte. They are an essential part of EC and working on the EDL charge/discharge principle at the interface of electrode ║ electrolyte. Electrochemical charging process can be represented as , where ЕS is the surface of NCM porous structure, C+ and А− are cations and anions of the electrolyte, and ║ is EDL which accumulates charge through the physical adsorption mechanism , where I is a charge/discharge current, td is the discharge time, Um is the maximum voltage, ΔU is the voltage drop at the closure of the discharge circle, and m is weight of the NCM. The IR was determined by the potential jump after ten charge/discharge cycles: ΔU = IR.Galvanostatic measurements were conducted in voltage range of 0 to 1 V and charge/discharge current changed within 10 to 100 mA. The specific capacity was calculated by the formula: C = 2I/s ⋅ m, where I is a current in anodic or cathodic branches of voltammograms, s is a scan rate, and m is weight of the NCM.The values of specific capacity according to potentiodynamic measurements were calculated as C = 1/(2mf ⋅ ImZ), where f is a frequency, Im Z is imaginary part of the impedance, and m is weight of the NCM. EIS data were modeled with standard electrical equivalent circuit (EEC) using the software ZView-2.According to the EIS, the specific capacity of the electrochemical capacitor reduced to weight unit of active electrode was calculated by the formula: The main method for NCM receiving is the carbonation of a feedstock at different temperatures, followed by chemical activation. The output of the final product and its structure Figure  depends When considering the sample surface C31 .In order to detect the possible occurrence of chemical reactions that contribute to the overall capacity of the condenser systems, potentiodynamic research was conducted in the potential range of 0 to 1 V. Figure With increasing scan rate, an insignificant distortion of voltammograms and its deviation from the rectangular shape can be associated with the increase of the EC IR. This is the initial stage of the ‘fasting electrolyte’ effect when the electrolyte ions are removed by their adsorption on the EDL edges . It shous = 1 mV/s, the curves have a symmetrical, almost rectangular shape with no obvious redox peaks, indicating the dominance of the electrostatic electric charge accumulation processes at the interface electrode/electrolyte [− groups), we can conclude that there is a possible intercalation process of these groups into the pores of the electrode material. Using these cyclic voltammograms, we calculated the values of the specific capacity of the samples at the scan rate of 1 mV/s  [This method is most appropriate for solving the abovementioned problems, since it allows conducting research in a wide frequency range (10 106 Hz) .Z = f(ReZ)  Figure .Figure 8L1 reflects the inductive behavior of the electrochemical system, which is due to the metal of the case. Resistance Rs includes the resistance of the electrolyte, contacts, and supply cables. The following circuit elements are responsible for the diffusion processes in the pores of the carbon material and the accumulation of electric charges at the interface electrolyte-carbon. In particular, the link C2║R2 is responsible for the processes in the transport pores, which include macro-and mesopores in the NCM, the link CPE3║R3-CPE4 in the micropores. The use of this EEC has made it possible to approach quite well the experimental spectrum to calculate one and to obtain the parameters that the scheme includes , the impedance of which is defined by equality Therefore, to approximate the experimental curves that describe the process of electrode polarization at all stages of electrochemical implementation, we used EEC, shown in Figure Tjω−CPEP . This CPTjω−CPEP  and the 3 element is responsible for the diffusion restrictions on the transport of electrolyte ions into the micropores , and its behavior is similar to change of the parameter R2. In our opinion, it is also caused by an increase in the proportion of micropores of the NCM, consequently the deviation of the element behavior from the ideal . The value of the resistance R3 remains almost unchanged, indicating a negligible effect of the thermochemical processing of the NCM on its electronic configuration and electrical properties. The option CPE4 changes more significantly, which according to Table 4-P is close to 1), which reflects the capacity of the EDL at the interface electrolyte-NCM in micropores.Based on this data and simulation, we see that the СРЕBased on the analysis of the results, it has revealed that one of the best ways to get a carbon electrode material is the carbonization of the feedstock of the plant origin in a closed furnace at 250°C to 350°C and the following chemical activation with potassium hydroxide in the different ratios of KOH/C in the temperature range 850°C to 920°C.According to the electrochemical studies, we found that an increase in the percentage of KOH during chemical activation leads to a decrease in specific capacity of the NCM by 8% to 12% and an increase in the IR of EC by 10%.Using synthesized activated carbon as electrode material of EC with aqueous electrolyte (KOH) provides a maximum value of the specific capacity of 160 to 180 F/g in the range of operating currents (10 to 100 mA) at a maximum charging voltage of 1 V.For supercapacitors based on NCM, we chose the EEC diagram, which is describing the processes occurring at the interface electrode/electrolyte and is consistent with the results of EIS.


The loss of a loved one adversely affects the bereaved.Using data from the 2010 and 2012 waves of Health and Retirement Study (HRS), we estimate the risk for death in a 2-year span after the loss of a parent, spouse, or child for adults aged 50 to 70 years.A respondent with a loss was twice as likely to die when compared similarly aged persons with no loss . Loss of either a parent , or a child  also increased respondent mortality. This elevated risk persists after adjustment for gender and other high-risk health conditions. Any physical activity reduces survivor death rates during this critical period by more than 85 %. The death of a parent or spouse adversely affects the bereaved , 2. LikeN = 5757).We estimated the risk that loss poses for a survivor’s subsequent mortality with data from the 2010 and 2012 wave of the Health and Retirement Study (HRS). HRS is a representative sample of Americans aged 50 years and older. For purposes of these analyses, and in congruence with our previous research , 7, our N = 2). We did retain these numbers when constructing a summary figure .The primary exposure in this study is reported death of a parent, spouse, sibling, or child. We categorized the death in three ways: any loss (yes or no), relationship between respondent and decedent, and the number of losses experienced by the respondent. The survey did not measure deaths outside of these relationships. The final generalized linear models did not include loss of a sibling due to low numbers of events , and health insurance (any versus none). We also included a measure of satisfaction with current health status as well as a four-level measure of insomnia symptoms.We used Stata 12  for all descriptive statistics, measures of association , and generalized linear models using the logit link function The mortality rate increased twofold from the youngest to oldest age categories between survey waves. A respondent with a loss was twice as likely to die when compared similarly aged persons with no loss . Loss of either a parent , or a child  also increased respondent mortality.Table In a longevity society, parents and children can live together for more than 50 years. The new science of social network provides a mechanism for the propagation of illness caused by negative emotions . Our res


Joint and individual variation explained (JIVE), distinct and common simultaneous component analysis (DISCO) and O2-PLS, a two-block (X-Y) latent variable regression method with an integral OSC filter can all be used for the integrated analysis of multiple data sets and decompose them in three terms: a low(er)-rank approximation capturing common variation across data sets, low(er)-rank approximations for structured variation distinctive for each data set, and residual noise. In this paper these three methods are compared with respect to their mathematical properties and their respective ways of defining common and distinctive variation.The methods are all applied on simulated data and mRNA and miRNA data-sets from GlioBlastoma Multiform (GBM) brain tumors to examine their overlap and differences. When the common variation is abundant, all methods are able to find the correct solution. With real data however, complexities in the data are treated differently by the three methods.All three methods have their own approach to estimate common and distinctive variation with their specific strength and weaknesses. Due to their orthogonality properties and their used algorithms their view on the data is slightly different. By assuming orthogonality between common and distinctive, true natural or biological phenomena that may not be orthogonal at all might be misinterpreted.The online version of this article (doi:10.1186/s12859-016-1037-2) contains supplementary material, which is available to authorized users. I) is usually much smaller than the number of variables (J) (e.g. transcriptomics data) which prevents the use of classical regression models. Data-analysis and interpretation of the huge number of variables is possible when the number of variables can be summarized in fewer factors or latent variables , with J = J1 + J2), DISCO starts with an SCA routine on the concatenated matrix X. This is followed by an orthogonal rotation step of the SCA scores and loadings towards an optimal user-defined target loading matrix P* (i.e. a matrix in which each component is either distinctive for a specific data-set or common for any data-set). As an example, for two data-sets, X1 (I × 2) and X2 (I × 3), with one common component (cc = 1) and one distinctive component for each data-set (c1 = c2 = 1), the total number of components ct for the whole model is 3.After concatenation of the two matrices, P* is:And P*, the zeros are a hard constraint while the ones are not restricted and can be any value. The first two rows relate to the (two) variables in the first data-set, the last 3 rows relate to the variables for the second data-set. The first column relates to the first distinctive component (for data-set 1). The second column is reserved for the distinctive component for the second data-set and the third column is the loading for the common component in both data-sets. Through orthogonal rotation the best rotation matrix (Bopt (ct × ct)) to rotate the Psca loadings (Pr) towards the target loadings P* is found by minimizing the squared sum of the 0 entries in the Pr matrix. To do just that a weight matrix (W = 1 − P*) is used, in which all the 1 entries are set to 0 and the 0 entries to 1:In BtB = IBopt is used to calculate the final rotated scores and loadings (Tr = TscaBopt and Pr = PscaBopt). Consequently the smallest distance criterion is based only on the 0 entries (in P*) and thus on the distinctive components only. A perfect separation of the distinctive components is often not achieved; the positions where P* is 0 are not exactly 0 in Pr. Furthermore, the common variation is forced to be orthogonal to these distinctive parts which clearly could lead to sub-optimal estimations of this common variation. The effects of the orthogonality constraints are discussed later. The final decomposition of the DISCO algorithm is:Tc) for both data-sets are the same and are obtained by optimizing on the distinctive components.The common scores (X). The common parts for both data-sets (Ck) are estimated simultaneously, C = [C1|C2] = TscaPscat (I × J), but now with only the number of common components (cc) and not all the components (ct) like in DISCO. The distinctive parts (D1 and D2) are estimated separately and iteratively based on an orthogonal residual (Rk − TscaTscatRk) matrix with ck distinctive components. Using the same example as before;The JIVE algorithm is also based on an SCA of the concatenated data-sets (C + D). By using the iterative and alternate optimization of the common and distinctinve parts, the orthogonality between the two distinctive parts that does exist in DISCO is no longer enforced. The resulting fit should be able to accommodate more types of data (e.g. the data has to conform to less criteria) than DISCO. Similar to DISCO the common parts are estimated from an SCA on both data-sets simultaneously and like DISCO there is no guarantee that both blocks take part in the common loadings Psca. As a consequence, the optimal solution could for example be one where Psca(=[P1|P2]) only has values for P1 and not P2 which hardly can be considered common.The steps are repeated until convergence of the combined common and distinctive matrices (The resulting decompostion Eq.  in scoreTc) for both data-sets are the same. Because SCA is a least squares method and the common parts are determined first, those variables with much variance are likely to end up in the common parts. Because JIVE is an iterative solution the initial guesses for common and distinctive parts can change considerably during these iterations ) for an analysis of the common variation. Similar to JIVE, the common components are estimated first and from the orthogonal remainder to X1 and X2;In contrast to DISCO and JIVE, that use an SCA on the concatenated data-sets, O2-PLS starts with an SVD on the covariance matrix  the algorithm itself is less restrictive than JIVE. With different common scores per data-set the decomposition of Eq. Tc invariant for a block) so Eq. As a post-processing step the common scores can be combined and by means of a regression model , for exaThe similarity between the three methods is large in terms of scores and loadings that are created in accordance with the algorithms. The methods however are different in terms of constraints that are applied during the decompositions which leads to different orthogonality properties and consequently different independence of the different common and distinctive parts.C1D1t = 0, C1D2t = 0, D1D2t = 0, C2D1t = 0 and C2D2t = 0. The error terms (E1 and E2) are orthogonal to each respective common part and distinctive part only. Orthogonality between the distinctive and common part per data-set in JIVE is enforced by estimation of the distinct components orthogonally to the common scores (Ek) is orthogonal to the distinctive part but not to the common part.The similarity between DISCO and JIVE is a consequence of the use of SCA in both methods. Because the final step in DISCO involves an orthogonal rotation of scores and loadings, the orthogonality between all the rotated scores and loadings remains. This rotation also forces orthogonality between the separate terms: C1 and C2) to have different loadings and scores. The common scores for each block (E1 and E2) in O2-PLS are found to be orthogonal only to the distinctive parts that are calculated as a final step.The decomposition in scores and loadings using the O2-PLS algorithm Eq.  is similA summary of the different orthogonality constraints for the three algorithms can be found in Table CktDl = 0) and therefore do not optimally describe the total variation in the residual block (Rk) which would limit the interpretation of these distinctive parts. The fact that we did not fully observe CktDl = 0 but still find some small residuals originates from the updated scores . The best Prot however, is an approximation of P* and because of orthogonality constraints, situations can occur where the rotation is not perfect. In such cases the elements set to zero in the original target matrix are different from zero in Prot. The exact estimation of Xk is:∥ Xk, the variation in Xk that is explained by the distinctive components of the other data sets, is minimized during the DISCO iterations and is indicative for the influence both data-sets have on each others individual loadings and thus affect direct interpretation. The size of the cross-over part depends on the data and the number of distinctive components reserved for the other data-sets. The model selection procedure is based on minimization of this cross-over content.The cross-over  is selected based on proportion of variance accounted for by the simultaneous components for each individual data block. The second step finds the “best” performing model from all possible combinations of common (cc) and distinctive components  are (still) larger than the permuted ones (with a certain α). For the distinct components per data set Xk, the rows of each variable in that data-set are permuted to disturb the variable object relationship. Again the eigenvalues of the original data set are compared to the eigenvalues of the permuted data sets to find the optimal number of distinct components for each Xk. These setting are used as input for a new start of the estimation of the number of components. This process is repeated until convergence of the number of common and distinctive components.In JIVE the configuration of the model is based on the analysis of permuted versions of the original matrix. For the common components complete rows of each data-set are permuted. This removes the link between the objects from the different data-sets, but does not remove the correlation structure inside each block. The eigenvalues for a large number of permuted matrices are determined. The number of common components is defined as that number where the eigenvalues of the original matrix  individual component(s) per data-set. To generate the data we use the score and loading structure from Eqs.  individuTc, E1 and E2 are based on pseudo numbers drawn from a standard normal distribution. The data-sets have 70 observations each (I = 70) and X1 contains 100 variables (J1 = 100) and X2 50 variables (J2 = 50). The data of each data-set is column-centered and the variance of each block is scaled to unit variance. In our examples we have chosen a set of spectral loadings for illustrative purposes. In functional genomics data-sets e.g. transcriptomics or metabolomics data a similar situation can be envisioned when in functional groups the features are expected to highly correlate. The latent components then describe structured variation of the functional groups over the objects.The scores Scenario 1, abundant variation in common loadings, almost orthogonal loadingsScenario 2, low abundant variation in common loadings, almost orthogonal loadingsThe three methods will be evaluated using the model settings that were suggested by the original model estimation procedure of each method respectively and if different from the actual model, with the real model settings as well. Two different scenarios are evaluated in which two different situations are simulated for the two data-sets:c1/0.28d1 and 0.85c2/0.13d2), scenario 2: (0.11c1/0.88d1 and 0.62c2/0.36d2)). The first scenario should give insight in the performance of the methods under conditions well suited to find the common variation. The second scenario should reveal issues for data that is more realistic like for example, the detection and removal of batch effects.Figure The three methods will also be applied to experimental data from GlioBlastoma Multiform (GBM) brain tumors available at The Cancer Genome Atlas (TCGA). The mRNA (234 × 23293) and miRNA (234 × 534) data-sets describe the messenger RNA’s and small RNA’s profiles of 234 subjects that suffer from different kinds of brain tumors. The same data was already analysed by JIVE in its original paper . Here west scenario did not lead to any problems. All three methods properly select the model of common and distinctive components . The results of DISCO, JIVE and O2-PLS almost exactly match the simulated scores and loadings, which from a mathematical point of view is also expected (see The data sets in the 1Xk and the common and distinctive variance combined (Ck + Dk). In this case however, the data was fabricated with orthogonal common and distinctive scores and we were able to calculated the error as the difference. Furthermore ∥CkCk+Ek∥2 ≪ ∥Ek∥2 which implies that the projection of Ek on Ck is very small indeed.Additional file In the second scenario the model was made more complex with less abundant common variance and more distinctive components per data-set. The difference between the methods already becomes apparent in the model selection. Additional file For completeness, the loading plots and score assessments of the decompositions of JIVE and DISCO with the suggested model settings are included in the Additional file C1D1t = 0 and C1D2t = 0., the real common component in data-set 2 cannot be selected anymore which results in a score vector of zero (the blue line). The two remaining distinctive components are used to fit the two loadings with the largest variation.The DISCO results with the ‘real’ model settings show a perfect decomposition in loadings and scores for both data-sets. The JIVE results show that all three components of the first data-set are fitted perfectly but that the common component is identified incorrectly; the component with the largest variance is identified as common. Because of the orthogonality restriction of In JIVE the first step is to select the allocated number of common components. At this stage this selection is only determined by the largest variance, regardless whether or not this is ‘real’. If this selected part happens to be the distinctive part, the ‘real’ distinctive part is designated as common variance. In these cases the JIVE algorithm is not able to classify it as common, even after all the iterations. This behavior is investigated further by generating different data-sets with increasing variation in the common component. For each data-set the JIVE decomposition is run and the proper identification of the common and distinctive components is recorded . For completeness the optimal number of components for the models was estimated again with each model selection method and the results are shown in Additional file CkCk+Ek∥2 ≪ ∥Ek∥2 for both data-sets). In comparison to DISCO and O2-PLS, JIVE describes less common variation but more distinctive variation. This phenomenon can possibly be accounted for by the iterative behavior of JIVE. By iteratively estimating the common and distinctive parts from only a selected part of the variation in the data, the common part seems less affected by over fitting. This phenomenon is further discussed in the Additional file As an example the O2-PLS score plots for both mRNA and miRNA for the common and distinctive parts are presented in Fig. To study the overlap in the three methods, the percentages explained variation in the common part and in the distinctive part per gene are plotted against each other in Fig. For the miRNA, the situation is similar to the mRNA data. Again JIVE has a lower explained variation for each miRNA in the common part and a higher explained variation in the distinctive part compared to DISCO and O2-PLS. The distribution of the explained variation of the distinctive part is clearly different than for the mRNA. For miRNA, still many features are not well described. This could be related to a lower amount of systematic variation in the miRNA’s and consequently, lower correlation between the different miRNA’s. Therefore, each component only describes few miRNA features.One explanation for DISCO is that orthogonality restrictions prohibit optimal fitting and as a result the cross over variation (i.e. the variation for miRNA explained by the distinctive score for the mRNA) is significant. For miRNA this was 13 % and for mRNA this was 4 % of the total variance. This amount of cross over variation is much larger for miRNA than mRNA because the 33 distinctive mRNA components all add to the cross over variation of miRNA compared to only 13 components vice versa.Pk) and original data (Xk). The distinctive components are removed from the remainder Xk is updated. However, in the final step  from the original JIVE paper. This represents the variability within subtypes  as a proportion of total variability. A lower score indicates better class separation. Table The high correspondence in explained variation for each mRNA and miRNA feature between DISCO and O2-PLS is corroborated by their scores. Table The three methods discussed in this paper to separate common from distinct information all use different approaches, which lead to slightly different models of the data. What is exactly common variation and what is distinctive depends on the different orthogonality constraints applied and the algorithms used to estimate these different parts. When the common variation is abundant, all methods are able to find the correct solution. With real data however, complexities in the data are treated differently by the three methods.Due to fewer orthogonality constraints that are imposed by JIVE and O2-PLS, there is more freedom to select the scores and loadings for the two data-sets. This freedom is not present in DISCO which has the most severe orthogonality restrictions. In the two scenarios shown in this paper, all scores and loadings were chosen orthogonal. Therefore DISCO was able to find the correct scores and loadings while JIVE and O2-PLS found variations thereof that still obayed their orthogonality assumptions. In case of less abundant common variation, both JIVE and DISCO failed to detect the proper amount of common components which can be understood from the methods themselves. Not knowing the real model however can give rise to unexpected results while decomposing the data in common and distinctive components.Even with the optimal model settings selected the JIVE method is the most susceptible to identifying the wrong common components. Due to the SCA of the concatenated matrix JIVE has problems finding common components especially when they are smaller than a distinctive component in one of the blocks. If the common and distinctive variation is approximately of the same magnitude, JIVE is able to properly identify them due to its iterative nature. JIVE re-estimates the common and distinctive parts until they converge, while O2-PLS, which only once re-estimates the common part once, seems to be stuck in a sub optimal solution for the distinctive part.k < I) are used, these data sets may not be well represented by the common scores in JIVE, and even worse, the common scores present information that is not even present in these blocks. This may lead to misinterpretation of both common scores and distinctive scores of such a block [When small data sets with a low number of features .In summary, all three methods have their own approach to estimate common and distinctive variation with their specific strength and weaknesses. Due to their orthogonality properties and their used algorithms their view on the data is slightly different. By assuming orthogonality between common and distinctive, true natural or biological phenomena that may not be orthogonal at all might be misinterpreted.


A. minus hook after a biomimetic methodology has been applied, this paper describes an investigation into the most appropriate method of shape acquisition for the purposes of reproduction and product development towards manufacture. This morphological study investigates confocal microscopy, SEM and other microscopy techniques. Confocal microscopy was selected as being most appropriate and small structures of cellulose and insect cuticle imaged. The benefits and disadvantages of this approach are noted. This paper is the result of research into microscopy techniques coupled with state-of-the-art manufacturing techniques. The result is this experiment with a single-phase confocal microscope to capture their 3-D images, both of cellulose and of chitin, without any specimen-specific treatment. Emphasis must be placed upon the cleanliness of the process since so many Natural attachment mechanisms are of this order of size and confocal microscopy offers opportunities for physical examination of microstructures and their interaction, in situ, with non-destructive inspection. This methodology has to develop further for the source of Nature’s designs to be rifled for ideas.To create a model of a biomimetic product from the  This project received funding from the EPSRC under the title: “The Functional Ecology and Mechanical Properties of Biological Hooks”, a wide field that was subsequently refined to three research papers.The first part of the series  exploresThe study now proceeds to the broader case of studying all Natural Hooks and the available technology for examining these small (~200 μm) structures with new eyes and the opportunities they present for modelling, stress analysis and virtual reality. Confocal microscopy, in particular single-phase confocal microscopy, comes to be the technique of choice and is used here in this part, the second research paper, to examine the structural, frictional and other types of probabilistic attachment mechanisms that are the burdock hook and the tarsal structures of two insects, a common honey bee and a common grasshopper, to Great Britain.There is much in the literature about many aspects of this study, from studies of the biomaterials  to studiThis work was done in September 2003. At that time rapid prototyping and layered manufacture were in their infancy. Ill health lead to a delay in the release of the results and a destruction of all relationship with the Institution (the University of Bath) where the research took place and subsequently the Centre for Biomimetics and Natural Technologies was shut down in 2008, preventing me from re-joining the group and publishing.This phase of the study concerns itself with recording 100-micron range hook shapes for the purposes of engineering analysis and reproduction, looking at the nature of the outputs of various microscopy techniques and their transferability to the domain of manufacturing. The aims of [The functional ecology of a system is the forces that are exerted within that system and their interactions and how they influence the property being studied. In the case of being manufactured/formed/grown it is the case that harvesting hooks may be a better idea than manufacturing them. Cladistically speaking it makes sense that there should be some join between the cellulose and chitin that does not exist in Nature, but it was found that Archeopteryx had feathers and scales so this does not preclude a future discover that mounts the shape of things to come as being brown and chitin-esque. All the more for a procedure that generates an impeller to bring these secrets to light.The scaling effect observed in , namely It has yet to be heard of, an engineer designing in artificial cellulose or chitin and this is accepted as a fact, because of the severe limitations of the reach of technological progress. However, as a study that produces insight into both surface strata of attachment as well as methods of study thereupon, it is though it retains its import whether years old or not.Shape acquisition has a history in biological studies. From the first cave drawings man has endeavoured to reproduce that which he observes in nature. Today, shape is used to provide clues as to internal composition of a biological structure when considered in the context of biomaterial strengths and behavior and the use of the principle of shape optimization.Dai, Gorb and Schwarz  used metBeraldin et al.  in theirFinite element analysis comprises the precise division of a 3-D morphology into vertices and edges to compute stresses at a distance from an applied load in a structure. It was judged that to be of most use, the output file format from the microscopy/imaging technique would allow for both computer vision and finite element analysis as well as rapid prototyping and so the investigation began for a microscopy technique that support this ambition for the purposes of study of microsurgical instrumentation and other probabilistic and specific fasteners in particular of varying textures.What forms were the outputs of the available microscopy techniques and did they lend themselves to virtual reality/mechanical analysis?Can small structures be imaged using a confocal microscope without the use of the casting methods of Evans et al.?With reference to confocal microscopy output, can a mesh formed from random points of light intensities be used to form a finite element analysis mesh? Since light intensities are the recorded outputs of the sensors in the microscope, a voxel.Can a mesh formed from random points of light intensities be used to form a mesh for conversion to.stl format and sent to a rapid prototyping device?The above introduction prompted the following questions:The principles of fluorescence microscopy.Epi-fluorescence microscopy.Confocal microscopy.2-photon microscopy.Near-field scanning optical microscopy.The following techniques were the focus of preliminary investigation, through the lectures of Dr I Jones, then of the Neuroscience Department at the University of Bath :The prinThe fluorescence effect is produced by irradiating atoms with a high-energy light source (laser) which causes excitation of orbiting electrons. These electrons jump “outwards” to high-energy orbitals before returning to their normal state, releasing energy at a specific wavelength which is detected via an emission filter.Confocal microscopy makes use of a laser light source whereas epi-fluorescence microscopy makes use of a normal bright light source and two filters, an excitation filter and an emission filter. Samples are viewed through an eye-piece.reduced blurring;increased effective resolution;improved signal to noise ratio;z-axis scanning;depth perception;magnification is electronically adjusted;scope for clear/good examination of relatively (~100 μm) thick specimens.The advantages of confocal microscopy using a laser light are the following:From a mechanical engineering/manufacturing perspective it is the output of the confocal microscope that makes it most apparently attractive, voxels and.tif files, as well as the huge convenience as a data acquisition source, using simply mounted slides. Stacked an image is produced in.avi format ready for virtual reality applications.The following procedure is described by Evans et al. for the production of cubic voxels and virtual reality applications from his paper on the imaging of mammalian teeth . It noteIn capturing an image it must be borne in mind that the goal was an accurate 3-D model for both virtual reality applications. It is important to set the slice thickness accordingly to arrive at an undistorted image, i.e. cubic voxels. The paper by Evans et al. details a method of taking a cast of a tooth which is more technically cumbersome than simply putting a microscope slide with specimen under the objective and so some of his paper is not relevant here (the details concerning the casting of the teeth).x, y plane where each slice was square (e.g. 256 × 256) pixel 8-bit image at medium scanning speed.Optical slices were taken through the Slices must be taken at the same distance as the interval between pixels to make cubic voxels.x, y point ). In most of the tests run by Evans et al., the cubic voxels  were 7.8 μm long, generated using one of two following methods:For the ×5 mm lens—a 256 × 256 pixel image was scanned at zoom 1 (field of view (FOV) of 2 × 2 mm), or a 128 × 128 pixel image was scanned at zoom 2 (FOV 1 × 1 mm).For the ×10 mm lens, a 128 × 128 pixel image was scanned at zoom 1 (FOV 1 × 1 mm).Software such as Zeiss is used to generate a 3-D image from the stack of slices, where pixel intensity represents height and the z-height is found by comparing the intensities for each Therefore using a lens with a field of view (FOV) of 2 × 2 mm at a setting of zoom 2 reduces the field of view to 1 × 1.accumulation and averaging. Accumulation is to accumulate and average several images at each z height and then create an image from the accumulated image slices. On the microscope, for example, an “Accumulation 2” scan stands for the number of slices that are averaged (two).Surface noise can affect the image and give a false indication of where the true surface lies. Evans et al. did experiments with the ×5 and ×10 lens to see how best to obtain the most accurate surface image. They used two techniques to try to reduce surface noise; The second method was to take the average of a number of reconstructed 3-D images of the same area. This was tested using a specially prepared and dimensionally precise standard glass specimen and comparing resultant images. The specimen was cubic and so without any undercuts but with a 45° fillet. the inner width was 1.3 mm and outer width 1.7 mm.It was found that averaging produces better results than accumulation. Sanson et al. used a resin casting of their teeth specimens which was coated with eosin, a fluorescent dye. Sanson et al. used their generated model to study the interactions of teeth, not for stress analysis or reverse engineering purposes.Conventionally confocal microscopy is used in neuroscience to study cell organelles. It was decided that small biological specimens many times larger than the average organelle could possibly be translucent enough to laser light such that it might not be necessary to use the casting method of Evans et al. Instead it was decided to attempt to image plain untreated specimens of cellulose and insect chitin. This seemed a rational cross-pollination of technology. The first step was to mount the specimen and the simplest possible well-mount in distilled water was used.A. minus bract was mounted upon a “well” microscope slide in distilled water  and placed under the objective of a confocal microscope.A specimen A Zeiss Axiovert single photon confocal microscope (inverted microscope with the objectives underneath the platform).1 × Argon (488 nm).2 × HeNe (543 and 633 nm).Zeiss LSM 510 module (laser scanning microscope) with 2 lasers.all ×10, 40 (oil), 63 (oil) and 63(water).digital zoom up to ×200.differential interference contrast.The field of view: 1 × 1 mm.Pinhole setting: 1 optical unit.Scanning slice thickness: 19 nm.Well slides which are microscope slides with a bowl ground out in the centre to receive specimens that are not flat.Distilled water as a medium for slide mounting.It is important to get the hooked specimen in the right orientation on the slide to avoid displaying an undercut surface to the laser light.It is important to optimise the strength of the laser and reduce the required depth of penetration to prevent excess bleaching.The same specimen can be remounted a number of times in different orientations in the slide to fully expose the complete detail of the structure.AlsoA. minus hook fluoresced well under the green laser light. Under the red and blue light the resulting image was less distinct but these colours worked well for the insect tarsi. The stacked image is then output to file and stored as a sequence of.tif files that are viewed in.avi format (see below for the full range of.tif images).When suffused with the laser light at three different frequencies it was found that the cellulose Stereogram images of the hook follow Fig. . The datThe individual .tif images that make up the above stereogram below see Fig.  were imaNote that the images from the confocal microscope show some internal structure of the hook, particularly the cellulose microfibrils. These microfibrils were visible in  which frFigures It is observed that there are two hooked claws to the walking structure that must interfere in some way with the substrate to produce a ground turbulent like effect such that is necessary to do finite element analysis on the posture of said structure. Gate is the most common effect of the entire school of thought with regards to insect tarsi but in fact it is a probabilistic fastener like the burdock of the product now known as Velcro that could be suited to robotic clasping mechanisms or some such structure that maintained a machine control over its structures, in handling.Therefore, it is important to preserve its nature so that it can be studied and reproduced via inorganic or organic means for the purposes of micro surgery, visual reality and insecticide problems with genetics.It is shown here that the arolium is interacting with the two claws as it gains a foothold on the surface. Again it is important that we understand the efficacy of the bee population if we are to gain another glimpse of the wain of the sound of the fall of the migrant pine tree in the winds of chiming suns. In other words it is of use only to the known predators of the bee and its new neighbours, us, who seek to abstain from this dissipation from life as we know it but they do disappear too you see? So we must protect against the environment from being assailed by the new time called the age of the dawn of the endangered species as foodstuffs such as the bee’s pollen gathering produces, a ground turbulent like effect and with it, our appetite for it.The successful imaging of the two biomaterial specimens in simply mounted slides shows that it should be possible to accumulate a library of data of samplings of these material micro-structures and frictional devices and thereby extrapolate to an even further degree to produce those needed shapes that require a sensitive beginning like self-assembly.To have self-assembly without life is a strange concept yet it is with us already. The control system that dictates the layers is complex yet it does so.The success of the experiment depended upon capturing the.stl file of the shapes, all three of them. This was not done so it fails. But it does illustrate the possibility at large for a further increase in the rate of research into micro-robotics and nano/self-assembled material structures  and theiConfocal microscopy is commonly used in the field of neuroscience. Its application to the field of biomimetic study could be controversial since it is expensive hardware and memory intensive. This notwithstanding, memory capacities are increasing and technology advancing at a speed which may make its use more frequent in the future.A. minus hook or of the chitin tarsi then we have need to consider the options open to us. Reflecting upon our need for CAD/CAM systems it becomes surmountable to be able to nurture the growth of these micro-organisms or organelles through our attempt at life-creation through self-assembly. In the meantime if one asks oneself for real reason to produce something it is to be sold and to create a market is not an impossible thing, to sell whatever you like to manufacture. So one begins by asking is this going to be the real produced product and the answer is no and, therefore, the test proceeds at a pace set for this.In reality a confocal microscope and its output is a laser scanner like many others on the market, engineered for microscopic applications. The random nature of measurement of light wavelengths is not suitable for conversion to .stl file and as of this moment has not been found. In order to proceed with the biomimetic process of developing a product that had the same or approximated the characteristics as the It proceeds now with the acquiring of the sought after .stl file that is required for the production of a resin model in a layered manufacturing laboratory.The generation of a biomimetic product from a biological structure combines prescriptive and descriptive processes. At present technology does not allow us to make the transition smoothly. Finite element analysis and graphical representation  utilise the 3-D meshing of data points for differing purposes.Small biological structures of cellulose and insect chitin are translucent to laser light and, therefore, can be scanned with non-destructive results. This may also be true of other biomaterials. Commercially available software can be utilised to convert the resultant data to 3-D models but this does not mean that the model is suitable for mechanical analysis.In terms of efficiency based upon cost and computational effectiveness including memory storage, confocal microscopy is more expensive than conventional methods of sectioning and digitising. However, in terms of operator time it is by far the cheapest.It is yet to be proved possible to use the confocal microscope to perform data capture and export the product to a finite element package, thereafter to re-mesh to perform finite element analysis.It has been established in part 1 that the burdock hook consists of a uniform biomaterial which is anisotropic. It exhibits scaling effects, being stronger than indicated by Newtonian modelling.This is the property that must be emphasised as it is this that would give a potential useful structure a reason for being and derive a desire to reproduce it in a controlled fashion a la mass production.Given the applications of this technology it must be said that the end of the silence is near as we begin to delve into the world of soft tissue reproductions of living things as we develop new materials.Many surface structures and arresting mechanisms are frictional in nature and this too is a scaled effect to be taken into account or to be applied. They are also non-homogenous and utilise differing qualities to achieve their end goal, be it adhesive by glues, anchorage by hooking or physical interference of structures or probabilistic frictional fastening for instance. Often taking the form of secondary structures themselves they are integrated into the design and function of the primary such as joint hinges, wing arrestors or the locking of two large separate body parts by sex organs by varying viscosity of interior gel-like plasm and structural membranes. These simple mechanisms are appreciated for their reduced energy usage and they are homogenous and isolated, thermodynamically speaking, within closed systems of low energy self-assembly.A.minus hook is suitable for fibres, already a feasible substrate for illustration of a viable frictional, probabilistic attachment mechanism that is biomimetic to A.minus, whereas the grasshopper and bee tarsi would be suitable for a silent probabilistic frictional attachment mechanism with further work on a suitable supplementary substrate.To discuss the choice of design to advance further in this discourse, the three specimens all subjected to confocal microscopy are frictional devices and their physical forms are important to their function. The


The advent of smartphones and tablets, means that we can constantly get information on our current geographical location. These devices include not only GPS/GNSS chipsets but also mass-market inertial platforms that can be used to plan activities, share locations on social networks, and also to perform positioning in indoor and outdoor scenarios. This paper shows the performance of smartphones and their inertial sensors in terms of gaining information about the user’s current geographical location considering an indoor navigation scenario. Tests were carried out to determine the accuracy and precision obtainable with internal and external sensors. In terms of the attitude and drift estimation with an updating interval equal to 1 s, 2D accuracies of about 15 cm were obtained with the images. Residual benefits were also obtained, however, for large intervals, e.g. 2 and 5 s, where the accuracies decreased to 50 cm and 2.2 m, respectively. Image recognition based (IRB) positioning is a good technology for navigation in Global Navigation Satellite System (GNSS) denied environments such as indoors  platforms built with MEMS  technology can be used and considered   of the sensors installed inside the smartphones considered and the benefits of wavelet filtering techniques, such as data obtained by the inertial internal phones. The tests results are also described in terms of accuracy achieved for different time intervals  between two different IRB positioning procedures.The IRB navigation procedure can also be adopted for mass-market devices; the most popular sensors available today are smartphones that now include many useful sensors for geomatics applications.The performance of the most well-known devices available was tested in Piras et al. In this paper, only the Samsung Galaxy S5 and iPhone 4 were considered and their technical information is shown in Table These devices include sensors whose characteristics are needed to obtain a good and feasible positioning. In particular, to achieve a positioning with a photogrammetric approach, it is fundamental to characterize the noise level of the inertial sensors and to calibrate the camera, thus, removing the lens distortion.The main aspect that needs to be considered when a new sensor is analysed is the stability of the internal inertial sensors, whose performance is not usually declared by the manufacturers. We, thus, performed a 6-h static test to acquire the raw data (angular velocity and accelerations) of each smartphone to analyse the stability.Figures The stability and the performance of the iPhone 4 are described in Figs. Table The inertial measurements acquired by these types of sensors are very noisy, due to the MEMS technology of the sensors themselves . Although accurate positioning with this device has been extensively investigated; some key information on the navigational purposes with INS instruments is not known, such as the reference systems of the internal sensors.Various experiments were, thus, performed to determine the reference systems of the internal inertial platforms of smartphones, by performing calibration tests using the external reference inertial measurement unit (IMU).On a non-magnetic plate, the two smartphones shown in Table By performing rotations of known angles and displacements, the determination of the internal reference systems of each smartphone was possible, which is essential for the surveying and data processing phases Fig. .Fig. 11EThe second step of the work was based on writing software that performs real-time positioning through images based localization and inertial sensors installed within the smartphone Fig. .Fig. 12Rn with INS instrumentation, together with the positions and attitudes obtained at epoch n − 1.To analyze the quality of the positioning achieved with the internal sensors, a software was written in Matlab, considering a system with six states (three position components of position and three attitude angles); three different time windows were considered for the dynamic estimation of the inner-state system, due to biases, drift and speed of motion, which are useful parameters for predicting the position and attitude at the generic epoch In the scenario of hybrid IRB and INS positioning, the states are periodically estimated with IRB positioning which provides absolute values for both attitude and position Woodman . INS meak, vector of coordinates; vk, the vector of velocities; Rh, rotation matrix from body to navigation frame; ak, the acceleration vector; dt, time interval; bias, bias vector; drift, drift vector; k, attitude expressed as three orientation angles; ωk, angular velocity vector; k, index for the sequence of positions based on sensor measurement rate; n, sequence of INS epochs between two IRB epochs .In this context considering IRB + INS techniques, real-time position and attitude are estimated by evaluating the following equations:It is therefore necessary to estimate the bias used in  and the n, n + 1 and n + 2 with IRB fix (i.e. epochs with positions and attitudes estimated by the IRB technique) and the bias is assumed to be constant over the two time intervals, the three components of velocity at time n (vn) and the bias of the three accelerometers (one for each axis) can be estimated by solving the following linear system of six linear equations:If the position is evaluated in three consecutive epochs n and n + 1 are needed: a linear system in three unknowns  needs to be solved:For the drift estimation, attitude measurements coming from two consecutive epochs After an initial alignment phase of about 3 s, during which the initial attitude of the smartphone is estimated, some IMU data (accelerations and angular velocities) are acquired, ensuring that they are all turned in the navigational reference system.IMU data are also acquired from the Microstrain sensor integrating a GPS receiver, in terms of absolute position and orientation, together with IMU three axis acceleration and three axis angular velocities. An initialization phase of 3 s is required by the IMU and GPS data fusion algorithm for absolute attitude estimation.On the basis of Woodman  and BeauNote that in this phase of the prototyping algorithm, measures from image positioning are replaced with ones from the output data available with the Microstrain sensor (position and attitude).If there are measures arising from the total station (or later from images), the software can use this information source to estimate acceleration and attitude biases along the three components and determine the new rotation matrix that can be used at the next epoch. When the total station position information is exploited, attitude information is not available and Microstrain information is used. Figure A non-optimal simplified approach with respect to the Kalman filter process was followed. This is because the characterization parameters of the inertial platform, the stability of the biases and drift estimation are not required by our system.The objective of the study, however, was to evaluate how INS technology can be applied to compensate for the latency due to image positioning using the cloud database, as described in  with external antenna (c);A 360° retroflector (d).The test was performed by walking on the same path using the two different smartphones (a) mounted on a special support Fig. , designeDuring the tests each smartphone sensor recorded its own inertial sensor data using a dedicated app: for the smartphone with the android Tarapata  operatinThe reference trajectory was defined by tracking the position of the smartphone continuously with a total station, through the retroflector. Thus, the position of the support was measured with millimetre accuracy.In addition, the data from the external IMU (Microstrain) was stored using a computer, to have reference values for the attitude.Samsung S5: images;iPhone 4: images and videos.For this application different types of data were acquired from the devices, in particular:No substantial differences in precision and accuracy can be obtained considering images or videos, thus in this paper only results obtained with images are shown.After the tests, all the IMU data files concerning each sensor, the images of the tracks and the reference data for the comparison between the estimated and the real solution were processed.The primarily goal of these tests was to assess the accuracy of the estimated position by varying the rate in which the displacement was evaluated based on the data of the inertial platform.The Microstrain inertial platform was chosen as an inertial sensor because it is the type of inertial sensor that will be installed on board the next generation of smartphones, considering both the costs of production and size. The effect of denoising with wavelets was also evaluated: the use of wavelet filtering did not add any benefits because the raw measures were too noisy and a shape variation of the bias was not identified.Regarding the navigation, the results can be considered as satisfactory: considering an interval of 1 s Table  between When the positioning obtained with an interval of 2 s between the images is analyzed, the mean planimetric error increases to 61 cm at 67 % and 1.49 m at 95 %.The tables show that in these tests the measurements of angular velocities were already adjusted for drift, according to the estimation made by the Microstrain itself, and it was not necessary to estimate the drift of the gyro at this stage, because the attitude measurements are already correct.The results obtained with an interval between two epochs  with total station are shown in Fig. While in the previous cases the results were obtained considering the attitude and the drift estimation provided by the Microstrain sensor, the accuracy results were obtained with different drift estimation modes. Table Tables In Table These tables highlight that the results obtained with images are nearly the same as those obtained with the bias and drift estimation from the Microstrain sensor. In this context, 1 or 2 s is the best intervals for positioning estimation with smartphones.This approach, based on the decoupling of the estimated accelerometer biases from the estimated drift of the gyros, using measures of attitude not available in the usual techniques when GPS and INS are coupled, provides comparable results with those obtained by the Kalman filter implemented on the Microstrain, under the condition that the update rate is the same (i.e. 1 s). This is highlighted by comparing Table However, to use a Kalman filter it is necessary to make assumptions about the dynamics of motion and have knowledge of the noise of accelerometers and gyros, as well as the drift variation of the INS, none of which are required in the described approach.Our tests demonstrated that INS measurements can be coupled with image based positioning to reduce latencies of a cloud architecture, if these latencies are less than 2 s. Under this hypothesis, the 1.5 m error boundary is always respected, although an error of this order may lead to various drawbacks for augmented reality. In fact many applications in indoor environments are characterized by limited spaces where the camera position should be more precise in order to provide more accurate information on the localization. For navigation applications, a latency interval of 2 s can be compensated by INS instruments with an error less than 1.5 m.The PDR is a more efficient technique for a longer frame rate. On the other hand, INS with the approach described in this work may be more useful in a short time range, because after 1 s the obtained 2D accuracy is 14 cm while after 5 s it becomes 1.5 m, if the attitude estimated by the Microstrain is considered.Considering the attitude and drift estimation obtained with images, the results obtained are very similar. The estimated drift is effective if the updating intervals are in the order of 1 s. Residual benefits are obtained, however, also for larger intervals . With this study we have demonstrated that the automatic techniques coupled with an INS instrument is useful for indoor navigation because errors are less than 1 m with intervals of about 2 s between two images, even if it could be not optimized for the worst cases (e.g. some indoor environments where there are few details that brings to have less descriptors). An alternative solution can be represented by the range camera coupled with INS instruments, that will be investigated in the future.