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As the scale of distributed generations connecting to the power system increases continuously, communication system considering the requirements of real-time control is becoming much more important in active distribution system. Therefore, in order to improve the responsiveness of the distribution network during the communication interruption, an offline backup strategy is proposed considering the combined output of distributed generations and energy storage systems involving the characteristics of the active distribution system. Based on a typical set of clusters which describe the features of wind turbines and photovoltaics, the strategy analyses operational vulnerability combining structural characteristics of the active distribution system and solves the output level of each distributed generation according to the improved algorithm. A numerical case study is presented to demonstrate the effectiveness of this model.

Modern scientific approaches to building a comprehensive assessment of the quality of automated control are not possible without the use of systematic analysis methodology. System analysis provides the completeness and comprehensiveness of the study of a complex system, allows you to combine into a whole set of processes that occur in different fields, such as economic, social, environmental, military. Today, all the links between complex military systems are poorly formalized and generally investigated. At the same time, the complex system itself is poorly structured and interconnected. On this basis, the authors propose the use of system-cognitive analysis to describe and study such systems. The Geospatial Intelligence system is an integral part of the military intelligence system and the overall monitoring system of Ukraine's allies, coalitions and blocs, and there are pro-functions that are detailed into a typical set of tasks performed through the composition of internal functions and basic information-technological algorithms of system functioning. In turn, the automation of the Geospatial Intelligence is aimed at improving the efficiency of the system as a whole. In the development of an automated control system for the Geospatial Intelligence, the priority is to build a correct mathematical model of the control object. It is shown that the Geospatial Intelligence system is a multi-purpose weakly structured system in which the deterministic and bifurcation stages are distinguished. Managing such a system is a multi-criteria task that is complicated by the need to take into account group preferences of decision-makers. The quality of the decision support problem in the management process cannot be evaluated by one function or even by several scales. In such cases, the rational choice mechanism requires additional indirect information, which allows at least to compare alternatives to the choice of management strategies. Therefore, it is necessary to formulate and solve the problem of steady control of the system of Geospatial Intelligence in different conditions and states of its functioning on the basis of system-cognitive analysis. Theoretical studies of computational methods of decision theory prove the importance of determining the requirements for the procedure for forming a vector criterion. These requirements include the completeness of the set of criteria, the redundancy, the ability to decompose, the minimum, the ability to measure. The procedure for constructing such a vector criterion is quite complex, ambiguous and sometimes unformalized. The purpose of the article. The purpose of the article is to improve the scientific and methodological apparatus based on the use of system-cognitive analysis to determine the vector criterion in solving the problem of steady control, determine the value and influence of input parameters on the functioning and choice of strategy management of the Geospatial Intelligence system.

Millions of people own and wear pied-de-poule (houndstooth) garments. Thepattern has an intriguing basic figure and a typical set of symmetries. The originof the pattern lies in a specific type of weaving. In this article, I apply compu-tational techniques to modernize this ancient decorative pattern. In particular Idescribe a way to enrich pied-de-poule with a fractal structure.Although a first fractal line pied-de-poule was shown at Bridges 2015, a numberof fundamental questions still remained. The following questions are addressedin this article: Does the original pied-de-poule appear as a limiting case whenthe fractal structure is increasingly refined? Can we prove that the pattern isregular in the sense that one formula describes all patterns? What is specialabout pied-de-poule when it comes to making these fractals? Can the techniquebe generalised?The results and techniques in this article anticipate the future of fashion wheredecorative patterns, including pied-de-poule, will be part of our global culture,as they are now, but rendered in more refined ways, using new technologies.These new technologies include digital manufacturing technologies such as laser-cutting and 3D printing, but also computational and mathematical tools suchas Lindenmayer rules (originally devised to describe the algorithmic beauty ofplants).

A significant body of research in the data sciences considers unfair discrimination against social categories such as race or gender that could occur or be amplified as a result of algorithmic decisions. Simultaneously, real-world disparities continue to exist, even before algorithmic decisions are made. In this work, we draw on insights from the social sciences brought into the realm of causal modeling and constrained optimization, and develop a novel algorithmic framework for tackling pre-existing real-world disparities. The purpose of our framework, which we call the “impact remediation framework,” is to measure real-world disparities and discover the optimal intervention policies that could help improve equity or access to opportunity for those who are underserved with respect to an outcome of interest. We develop a disaggregated approach to tackling pre-existing disparities that relaxes the typical set of assumptions required for the use of social categories in structural causal models. Our approach flexibly incorporates counterfactuals and is compatible with various ontological assumptions about the nature of social categories. We demonstrate impact remediation with a hypothetical case study and compare our disaggregated approach to an existing state-of-the-art approach, comparing its structure and resulting policy recommendations. In contrast to most work on optimal policy learning, we explore disparity reduction itself as an objective, explicitly focusing the power of algorithms on reducing inequality.

Data Analytics is rapidly expanding within the healthcare domain to help develop strategies for improving the quality of care and curbing costs as well. Natural Language Processing (NLP) solutions have received particular attention whereas a large part of clinical data is stockpiled into unstructured physician or nursing notes. In this respect, we attempt to employ NLP to provide an early prediction of the medical specialties at hospital admission. The study uses a large-scale dataset including more than 260K ED records provided by the Amiens-Picardy University Hospital in France. Our approach aims to integrate structured data with unstructured textual notes recorded at the triage stage. On one hand, a standard MLP model is used against the typical set of features. On the other hand, a Convolutional Neural Network is used to operate over the textual data. While both learning components are conducted independently in parallel. The empirical results demonstrated a promising accuracy in general. It is conceived that the study could be an additional contribution to the mounting efforts of applying NLP methods in the healthcare domain.

A new class of structured codes called quasi group codes (QGCs) is introduced. A QGC is a subset of a group code. In contrast with the group codes, QGCs are not closed under group addition. The parameters of the QGC can be chosen, such that the size of $\mathcal {C}+\mathcal {C}$ is equal to any number between $|\mathcal {C}|$ and $|\mathcal {C}|^{2}$ . We analyze the performance of a specific class of QGCs. This class of QGCs is constructed by assigning single-letter distributions to the indices of the codewords in a group code. Then, the QGC is defined as the set of codewords whose index is in the typical set corresponding to these single-letter distributions. The asymptotic performance limits of this class of QGCs are characterized using single-letter information quantities. Corresponding covering and packing bounds are derived. It is shown that the point-to-point channel capacity and optimal rate-distortion function are achievable using QGCs. Coding strategies based on QGCs are introduced for three fundamental multi-terminal problems: the Korner-Marton problem for modulo prime-power sums, computation over the multiple access channel (MAC), and MAC with distributed states. For each problem, a single-letter achievable rate-region is derived. It is shown, through examples, that the coding strategies improve upon the previous strategies based on the unstructured codes, linear codes, and group codes.

Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients count flags of finite vector spaces with prescribed length and dimensions. In particular, the $q$-binomial coefficients count vector subspaces of given dimension. We obtain this way a combinatorial explanation for the nonadditivity of the quadratic entropy, which arises from a recursive counting of flags. We show that statistical systems whose configurations are described by flags provide a frequentist justification for the maximum entropy principle with Tsallis statistics. We introduce then a discrete-time stochastic process associated to the $q$-binomial probability distribution, that generates at time $n$ a vector subspace of $\mathbb{F}_q^n$ (here $\mathbb{F}_q$ is the finite field of order $q$). The concentration of measure on certain "typical subspaces" allows us to extend the asymptotic equipartition property to this setting. The size of the typical set is quantified by the quadratic entropy. We discuss the applications to Shannon theory, particularly to source coding, when messages correspond to vector spaces., Comment: Presented in part at the Latin American Week on Coding and Information 2018 (Campinas, Brazil)

Distributed detection with multiple sensors and a fusion center over binary symmetric channels has been investigated. The fusion center receives noisy observations of the local binary decisions. A fundamental tradeoff between achievable information rate and the error exponent of the missing probability exists. The tradeoff is well characterized by the rate-exponent region. The paper first derived a closed-form analytic expression for the error exponent and information rate by means of the theory of relative entropy typical set. Second, the properties of the optimal error exponent and information rate are discussed in detail. It was demonstrated that they are monotonically decreasing in the bit error probability of the binary symmetric channel. Simulation results validated the conclusions.

In this paper, we propose a practical low delay digital scheme for lossy transmission of a Gaussian source over Gaussian broadcast channel when there is correlated side information at the receivers. Focusing on two receivers scenario, a bit-filling criterion is applied at the transmitter, to establish a connection between the common layer and refinement layer data. Then, we complete the dirty paper coding according to jointly typicality and finally superimpose the two layers for transmission. At the receiver, we propose a modified log-likelihood ratio-belief propagation decoding algorithm to utilize side information. And a typical-set based decoding algorithm is introduced to be an effective supplement if the decoding decision of the successive canceling method fails. Simulated results show that the proposed typical set decoding algorithm plays an excellent part in refinement layer recovery, and on the whole, the proposed digital scheme renders better reconstruction accuracy than the corresponding low delay separate source channel coding.

The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given the enormous consequences for the understanding of the system's dynamics, and its role underlying the presence of stable, almost deterministic statistical patterns, a question arises whether typical sets exist in much more general scenarios. We demonstrate here that the typical set can be defined and characterized from general forms of entropy for a much wider class of stochastic processes than it was previously thought. This includes processes showing arbitrary path dependence, long range correlations or dynamic sampling spaces; suggesting that typicality is a generic property of stochastic processes, regardless of their complexity. Our results impact directly in the understanding of the stability of complex systems, open the door to new data compression strategies and points to the existence of statistical mechanics-like approaches to systems arbitrarily away from equilibrium with dynamic phase spaces. We argue that the potential emergence of robust properties in complex stochastic systems provided by the existence of typical sets has special relevance to biological systems., Comment: 15 pages, 4 figures

Class-modelling methods aim to predict the conformity of new unknown samples with a single target class, using statistical decision rules built exclusively with objects of that class. This article introduces a novel class-modelling method for spectral data. The method uses the concept of β%-prediction band for functional data to classify spectra. The band is defined by an upper and a lower limiting spectra which delimit critical trajectories for β% of future spectra of the target class. It is constructed in three main steps: firstly, a naive bootstrap sample of calibration spectra is projected onto a parsimonious principal component (PC) basis and their scores are estimated. The posterior predictive distribution of the scores on each PC is estimated using a Bayesian zero-mean normal model. This procedure is repeated on naive bootstrap estimations of the PCs to obtain the predictive distribution of the scores. These enable to account for all modelling uncertainties including the random deviation of scores from their zero-mean on each PC, uncertainty in the variance of scores (eigenvalue) on each PC, and uncertainty in the PC estimations. Secondly, the predicted scores are back-transformed to the original signal scale to obtain the predictive distribution of future spectra. Thirdly, the predicted spectra are ranked to select the β% most central ones as typical set, whose ranges of variation are used to construct the simultaneous limits of the band. Once the band is constructed, reconstructions of future unknown test spectra by bootstrap PC models are projected onto it, and the extent to which they overlap with it is used to decide their acceptance or rejection. The statistical properties and classification performances of the proposed prediction band are evaluated on real near-infrared datasets and compared to the well-known soft-independent modelling of class analogy (SIMCA) model. The results of the evaluation provide evidence that the proposed prediction band possesses satisfactory predictive performances. It even outperforms the SIMCA while offering attractive advantages like risk-management and straightforward physical interpretability of outlyingness patterns of tested spectra.

Subject: The article contains investigation of the questions related to semantic and syntactic analysis of the texts, decomposition of sentences into component processes, the construction of the syntactic structure of sentences; semantic interpretation of the fragments of a natural language sentence into fragments of an M-language; the composition of the fragments of the M-language in the structure of the abstract, describing the problem environment. Purpose: development of a method for analyzing and processing information on the DSS ACS. Objective: To analyze the research of recent years related to the solution of analyzing the content of the language structure problem from the point of view of creating dialogue systems software, to make a conclusion about the appropriateness of research directions. Perform a detailed description of the stages of performing semantic and parsing with a description of the input, intermediate and output data. Determine the recommendations for the input data variability depending on the structure of the sentences of the subject area (the text described in natural language). Suggest rules for the formation of predicates for different parts of the Ukrainian language. Determine the typical set of service awards for filling the reference dictionary. Justify the implementation of each of the above operations for combining into a single computing structure, which is performed at certain stages. Develop procedures for passing each of the stages. Suggest rules for the formation of syntactic groups for certain pairs of tokens. Conclusions: The application of the developed method based on certain rules in predicates will allow to sample informatively significant information from a set of textual information and present it as an annotation (abstract).

Nowadays, the integrated energy system (IES) has become a hot topic in the field of energy research. In this paper, a bi-level optimal configuration strategy is proposed for a community integrated energy system (CIES), which is based on energy supply-demand responses and robustness adjustable scenarios. First, from the perspective of energy supply and demand, various energy equipment on the community side and aggregated energy loads on the user side are analysed and qualitatively modeled, and a multi energy supply-demand of CIES is established. Next, according to the robustness requirements of IES planning, the scenario sampling, sorting, screening and reduction are performed subsequently to obtain a typical set of robustness adjustable scenarios. On this basis, a bi-level optimal configuration model that coordinates the aggregated configuration and operation is developed to design the CIES. While the upper-level model takes the lowest total annual cost as the goal to configure the quantity and capacity of energy equipment, the lower-level model optimizes the scheduling scheme with the aim of the best operation economy under typical scenarios. Finally, case studies are carried out based on a practical town area, and simulation results show the effectiveness and advantage of the proposed strategy.

This paper focuses on an entropy based formalism to speed up the evaluation of the Structural SIMilarity (SSIM) index in images affected by a global distortion. Looking at images as information sources, a visual distortion typical set can be defined for SSIM. This typical set consists of just a subset of information belonging to the original image and the corresponding one in the distorted version. As side effect, some general theoretical criteria for the computation of any full reference quality assessment measure can be given in order to maximize its computational efficiency. Experimental results on various test images show that the proposed approach allows to estimate SSIM with a considerable speed up (about 200 times) and a small relative error (often lower than 5%). HighlightsFast method for the computation of SSIM from a subset of image blocks.Theoretical and practical method for the estimation of the typical set of the quality metric.Speed up for SSIM of about 200 times with relative estimation error lower than 5%.

An information theoretical analysis of nonadaptive group testing schemes based on sparse pooling graphs is presented. A pooling graph is a bipartite graph for which the adjacency matrix is a pooling matrix. The binary status of the objects to be tested are modeled by independent identically distributed. Bernoulli random variables with probability $p$ . An $(l, r, n)$ -regular pooling graph is a bipartite graph in which the left nodes have degree $l$ , the right nodes have degree $r$ , and $n$ is the number of left nodes. The main contribution of this paper is a direct coding theorem that gives the conditions for the existence of an estimator that can achieve an arbitrarily small probability of error. An estimator is a function that uses observations to infer the state of an object. The direct coding theorem is proved by averaging the upper bound on the probability of the estimation error of the typical set estimator over an $(l, r, n)$ -regular pooling graph ensemble. Numerical results indicate sharp threshold behaviors in the asymptotic regime. These results can provide a concrete benchmark for nonadaptive group testing of existing and emerging detection algorithms over a noiseless system.

Andrey Kolmogorov put forward in 1933 the five fundamental axioms of classical probability theory. The original idea in my complex probability paradigm is to add new imaginary dimensions to the experiment real dimensions which will make the work in the complex probability set totally predictable and with a probability permanently equal to one. Therefore, adding to the real set of probabilities $ {\sc{R}} $ the contributions of the imaginary set of probabilities $ \sc{M} $ will make the event in $ \sc{C}= \sc{R} + \sc{M} $ absolutely deterministic. It is of great importance that stochastic systems become totally predictable since we will be perfectly knowledgeable to foretell the outcome of all random events that occur in nature. Hence, my purpose here is to link my complex probability paradigm to Claude Shannon’s information theory that was originally proposed in 1948. Consequently, by calculating the parameters of the new prognostic model, we will be able to determine the magnitude of the chaotic factor, the degree of our knowledge, the complex probability, the self-information functions, the message entropies, and the channel capacities in the probability sets $ \sc{R} $ and $ \sc{{M}} $ and $ \sc{C} $ and which are all functions of the message real probability subject to chaos and random effects.

Determining a single-letter secrecy-capacity formula for the arbitrarily varying wiretap channel (AVWTC) is an open problem largely because of two main challenges. Not only does it capture the difficulty of the compound wiretap channel (another open problem), it also requires that secrecy is ensured with respect to exponentially many possible channel state sequences. By extending the strong soft-covering lemma, recently derived by the authors, to the heterogeneous scenario, this paper accounts for the exponential number of secrecy constraints while only imposing single-letter constraints on the communication rate. Through this approach, we derive a single-letter characterization of the correlated-random (CR)-assisted semantic-security (SS) capacity of an AVWTC with a type constraint on the allowed state sequences. The allowed state sequences are the ones in a typical set around a single constraining type. The stringent SS requirement is established by showing that the mutual information between the message and the eavesdropper’s observations is negligible even when maximized over all message distributions, choices of state sequences, and realizations of the CR-code. Both the achievability and the converse proofs of the type-constrained coding theorem rely on stronger claims than actually required. The direct part establishes a novel single-letter lower bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained by any convex and closed set of state probability mass functions. This bound achieves the best known single-letter secrecy rates for a corresponding compound wiretap channel over the same constraint set. In contrast to other single-letter results in the AVWTC literature, this paper does not assume the existence of a best channel to the eavesdropper. Instead, SS follows by leveraging the heterogeneous version of the strong soft-covering lemma and a CR-code reduction argument. Optimality is a consequence of a max-inf upper bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained to any collection of type-classes. When adjusted to the aforementioned compound WTC, the upper bound simplifies to a max–min structure, thus strengthening the previously best known single-letter upper bound by Liang et al. that has a min–max form. The proof of the upper bound uses a novel distribution coupling argument. The capacity formula shows that the legitimate users effectively see an averaged main channel, while security must be ensured versus an eavesdropper with perfect channel state information. An example visualizes our single-letter results, and their relation to the past multi-letter secrecy-capacity characterization of the AVWTC is highlighted.

Online set intersection operations have been widely used in network processing tasks, such as Quality of Service differentiation, firewall processing, and packet/traffic classification. The major challenge for online set intersection is to sustain line-rate processing speed; accelerating set intersection using state-of-the-art hardware devices is of great interest to the research community. In this paper, we present a novel high-performance set intersection approach on FPGA. In our approach, each element in any set is represented by a combination of Group ID (GID) and Bit Stride (BS); all the sets are intersected using linear merge techniques and bitwise AND operations. We map our online set intersection algorithm onto hardware; this is done by constructing modular Processing Element (PE) and concatenating multiple PEs into a tree-based parallel architecture. In order to improve the throughput on a state-of-the-art FPGA, we feed all the inputs to FPGA in a streaming fashion with the help of the synchronization GIDs. Post place-and-route results show that, for a typical set intersection problem in network processing, our design can intersect $\text{eight}$ sets, each of up to $32$ K elements, at a throughput of $47.4$ Thousand Intersections Per Second (KIPS) and a latency of $94.8\,\mu$ s per batch of inputs. Compared to the classic linear merge or bitwise AND techniques on state-of-the-art multi-core processors, our designs on FPGA achieves up to $66\times$ throughput improvement and $80\times$ latency reduction.

Although both novice and experienced researchers can struggle with what theoretical frameworks are and why they are necessary, it is nevertheless clear that they are an important part of designing, carrying out, and reporting on research in our field. In this chapter, we attempt to clarify the roles played by theoretical frameworks in mathematics education and to explain why they are important and useful, both to individual researchers and to the field as a whole. Finally, we provide some examples of how different frameworks might be applied to a typical set of data: videotaped whole-class, teacher-student, and student-student interactions in a mathematics classroom.

We introduce a method for measuring the number and durations of processing stages from the electroencephalographic signal and apply it to the study of associative recognition. Using an extension of past research that combines multivariate pattern analysis with hidden semi-Markov models, the approach identifies on a trial-by-trial basis where brief sinusoidal peaks (called bumps) are added to the ongoing electroencephalographic signal. We propose that these bumps mark the onset of critical cognitive stages in processing. The results of the analysis can be used to guide the development of detailed process models. Applied to the associative recognition task, the hidden semi-Markov models multivariate pattern analysis method indicates that the effects of associative strength and probe type are localized to a memory retrieval stage and a decision stage. This is in line with a previously developed the adaptive control of thought-rational process model, called ACT-R, of the task. As a test of the generalization of our method we also apply it to a data set on the Sternberg working memory task collected by Jacobs, Hwang, Curran, and Kahana (2006). The analysis generalizes robustly, and localizes the typical set size effect in a late comparison/decision stage. In addition to providing information about the number and durations of stages in associative recognition, our analysis sheds light on the event-related potential components implicated in the study of recognition memory. (PsycINFO Database Record

This paper presents a new methodology for hyperspectral image classification based on the definition of typical sets from the Asymptotic Equipartition Property, an important tool in the field of information theory. The Endmembers (EM) are decomposed in orthogonal functions by a discrete wavelet transform and are modeled as a HMM (Hidden Markov Model). Based on this model, for each EM, a Typical Sequence set is established. One spectrum is classified as a member of a specific EM if belongs to its typical set. It is considered the case in which a class in the hyperspectral image can be represented by several subclasses and also the original spectra can be decimated and be used with less bands in the classification processes. The proposed method is tested with a set of AVIRIS data and is compared with the classification performed by Euclidian Distance, Spectral Angle Mapper (SAM) and Spectral Information Divergence (SID). It is shown that the proposed classification can be used with a reduced number of bands and achieves results comparable with other methods using all bands.

The main aim of this paper is to present results of a full-scale pushover test of a 40 meter telecommunication tower under breaking load. A detailed description of the studied tower has been presented with emphasis on the geometrical imperfections of the selected members of the structure. The results of the experiment consisting of the axial forces in the tower's members, as well as the displacements of the observed nodes as a function of external load have been presented. A comparison of a wind load based on the current standards with the load based on the experimental breaking force has been discussed for a typical set of telecommunication equipment. The main conclusion was that the structure's overall carrying capacity depended on the buckling resistance of the legs. Additionally, theoretical buckling resistances (based on standards) of the tower's legs made with round solid bars were smaller than the experimental axial forces in compression.

The system of axioms for probability theory laid in 1933 by Andrey Nikolaevich Kolmogorov can be extended to encompass the imaginary set of numbers and this by adding to his original five axioms an additional three axioms. Therefore, we create the complex probability set , which is the sum of the real set with its corresponding real probability, and the imaginary set with its corresponding imaginary probability. Hence, all stochastic experiments are performed now in the complex set instead of the real set . The objective is then to evaluate the complex probabilities by considering supplementary new imaginary dimensions to the event occurring in the ‘real’ laboratory. Consequently, the corresponding probability in the whole set is always equal to one and the outcome of the random experiments that follow any probability distribution in is now predicted totally in . Subsequently, it follows that, chance and luck in is replaced by total determinism in . Consequently, by subtracting the chaotic factor ...

In this paper, a new and efficient hybrid AC/DC solar powered Homegrid model is proposed based on the load characteristics of a typical set of home appliances working on a 220 V, 50 Hz system. The load characteristics of home appliances are represented by a static ZIP (constant impedance (Z), constant current (I) and constant power (P)) coefficient model, a useful load model in power flow studies. A Homegrid system is formed by analysing the distortion produced by modern household equipment, and a K-factor with a significant role in the overheating of residential/distribution transformers is determined. Further, the ZIP load model is validated by a simulation and the results are compared with experimental data. To improve the efficiency and quality of the traditional Homegrid system, a solar powered hybrid AC/DC supply network model is proposed. This system eliminates redundant power conversion stages and mitigates the loss due to the harmonics by a shift of harmonic intensive loads to the Direct Current (DC) network side. Its effectiveness has been investigated with a simulation in MATLAB as well as with hardware implementation. This proposed energy efficient Homegrid model could be quite helpful in fulfilling the idea of net zero or surplus energy buildings.

Dynamics of non-stationary nonlinear processes that follow the maximum entropy principle (MaxEnt) for continuous probability distributions is considered. A set of equations describing the dynamics of probability density function (pdf) under the mass conservation and the energy conservation constraints is derived. The asymptotic convergence of evolving pdf and convergence of differential entropy are examined. It is shown that for pdfs with compact carrier the limit pdf is unique and coincides with the pdf obtained from Jaynes’s MaxEnt principle.

Each solar powered device that is based on solar cells requires energy system, which contains typical set of subsystems which should be implemented in software and hardware to achieve efficient power management. This paper will structure general design of solar power system that could be modular and applied to many different types of devices and applications.

k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes, which is known as the node fault model. In this paper, we investigate k-connectivity of random graphs in the node fault model by evaluating the network breakdown probability, i.e., the disconnectivity probability of random graphs after stochastic node removals. Using the notion of a strongly typical set, we obtain universal asymptotic upper and lower bounds of the network breakdown probability. The bounds are applicable both to random graphs and to random geometric graphs. We then consider three representative random graph ensembles: the Erdos-Renyi random graph as the simplest case, the random intersection graph for WSNs with random key predistribution schemes, and the random geometric graph as a model of WSNs generated by random sensor node deployment. The bounds unveil the existence of the phase transition of the network breakdown probability for those ensembles., 6 pages

Redox-based resistive random access memories (ReRAM) are promising candidates for the use in ‘beyond-von Neumann’ architectures. One key issue for utilizing ReRAM for e.g. neuromorphic applications is a gradual SET and RESET behavior, allowing to write various resistance states emulating synaptic weights. However, a typical SET event for filamentary-like valence change mechanism devices is happening abrupt due to its physical principle. In this work we demonstrate a gradual SET behavior for $\text{HfO}_{2}/\text{TiO}_{\mathrm{x}}$ ReRAM cells in pulse mode. The results are discussed in view of the inherent properties of the particular bilayer structure.

Macroscopic properties of reacting mixtures are necessary to design synthetic strategies, determine yield, and improve the energy and atom efficiency of many chemical processes. The set of time-ordered sequences of chemical species are one representation of the evolution from reactants to products. However, only a fraction of the possible sequences is typical, having the majority of the joint probability and characterizing the succession of chemical nonequilibrium states. Here, we extend a variational measure of typicality and apply it to atomistic simulations of a model for hydrogen oxidation over a range of temperatures. We demonstrate an information-theoretic methodology to identify typical sequences under the constraints of mass conservation. Including these constraints leads to an improved ability to learn the chemical sequence mechanism from experimentally accessible data. From these typical sequences, we show that two quantities defining the variational typical set of sequences-the joint entropy rate and the topological entropy rate-increase linearly with temperature. These results suggest that, away from explosion limits, data over a narrow range of thermodynamic parameters could be sufficient to extrapolate these typical features of combustion chemistry to other conditions.

According to the asymptotic equipartition property, sufficiently long sequences of random variables converge to a set that is typical. While the size and probability of this set are central to information theory and statistical mechanics, they can often only be estimated accurately in the asymptotic limit due to the exponential growth in possible sequences. Here we derive a time-inhomogeneous dynamics that constructs the properties of the typical set for all finite length sequences of independent and identically distributed random variables. These dynamics link the finite properties of the typical set to asymptotic results and allow the typical set to be applied to small and transient systems. The main result is a geometric mapping-the triangle map-relating sequences of random variables of length n to those of length n+1. We show that the number of points in this map needed to quantify the properties of the typical set grows linearly with sequence length, despite the exponential growth in the number of typical sequences. We illustrate the framework for the Bernoulli process and the Schlögl model for autocatalytic chemical reactions and demonstrate both the convergence to asymptotic limits and the ability to reproduce exact calculations.

The overall intention of chaotic control is to eliminate chaos, and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes, and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision, and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems, or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

We suggest a transformation to obtain the negation of a probability distribution. We investigate the properties of this negation. Using the Dempster–Shafer theory of evidence, we show of all the possible negations our proposed negation is one having a maximal type entropy.

Purpose – Value-at-risk (VaR) is a risk measure of potential loss on a specific portfolio. The main uses of VaR are in risk management and financial reporting. Researchers are continuously looking for new and efficient ways to evaluate VaR, and the 2008 financial crisis has given further impetus to finding new and reliable ways of evaluating and using VaR. In this study, the authors use genetic algorithm (GA) to evaluate VaR and compare the results with conventional VaR techniques. Design/methodology/approach – In essence, the authors propose two modifications to the standard GA: normalized population selection and strict population selection. For a typical set of simulation, eight chromosomes were used each with eight stored values, and the authors get eight values for VaR. Findings – The experiments using data from four different market indices show that by adjusting the volatility, the VaR computed using GA is more conservative as compared to those computed using Monte Carlo simulation. Research limitations/implications – The proposed methodology is designed for VaR computation only. This could be generalized for other applications. Practical implications – This is achieved with much less cost of computation, and hence, the proposed methodology could be a viable practical approach for computing VaR. Originality/value – The proposed methodology is simple and, at the same time, novel that could have far-reaching impact on practitioners.

We calculate the next-to-leading order electroweak corrections to the production of a photon pair in association with zero, one and two jets at the LHC. We use GoSam and Sherpa to obtain the results in a fully automated way. For a typical set of fiducial cuts the electroweak corrections lead to a modification of the total cross section of up to 3 per cent, depending on the jet multiplicity. We find substantial contributions in differential distributions, leading to tens of per cent corrections for phase space regions within the reach of the LHC. Furthermore we investigate the importance of photon induced processes as well as subleading contributions. Photon induced processes are found to be negligible, subleading contributions can have a sizeable impact however they can be removed by appropriate phase space cuts., 19 pages, 11 figure, 1 table

Cell detection is the essential step for various analyses in biological fields. One of the conventional approach is to construct a specialized method for every specified task, but it is not efficient in the meaning of the coding workload. Another approach is based on some machine learning technique, but it is difficult to prepare many training data. To solve these problems, we propose a balanced system by combining image processing and machine learning. The system is universally applicable to any image, because it only consists of basic methods of image processing. The code of the system does not need to be modified, because its behavior is adaptively tuned by machine learning. Users are free from excessive request of training data, because only a few desirable data is specifically requested by the system. The system consists of three units to achieve functionalities for avoiding parameter collision, compensating lack of training data, and reducing complexity of feature space. The effectiveness of the system is evaluated with a typical set of cell images, and the result is sufficient. The proposed system provides a reasonable way of preparing a tuned cell detection method for arbitrary sets of images in this field.

We study the entropy production of systems out of equilibrium using random networks. We focus on systems with a finite number of states described by a master equation close to equilibrium. The dynamics are mapped into a network of states (nodes) connected by transition rates (links). Using this framework, we analyze the entropy production of ensembles of randomly generated networks owing to specific constraints (e.g., size or symmetries) and identify the most important parameters that determine its value. This analysis gives a null-model estimation for the entropy production that can be used for comparison with specific systems.

Similar to fuzzy set on a possibility space, uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Entropy provides a quantitative measurement of the uncertainty associated with an uncertain set. This paper presents a formula for calculating the entropy of an uncertain set via its inverse membership function. Based on the formula, the entropy operator is shown to satisfy positive linearity property. In addition, this paper proposes a concept of relative entropy to describe the divergence between the membership functions of two uncertain sets.

Entropy is used as a quantitative measurement of the information deficiency. In uncertain set theory, logarithm entropy for uncertain set has been proposed. However, it fails to measure the degree of uncertainty associated with some uncertain sets. Thus this paper will propose sine entropy for uncertain set as a supplement, and investigate its properties such as translation invariance and positive linearity. Besides, it proposes sine relative entropy for uncertain set, and gives its applications in portfolio selection and clustering.

Machining using industrial robots is currently limited to applications with low geometrical accuracies and soft materials. This paper analyzes the sources of errors in robotic machining and characterizes them in amplitude and frequency. Experiments under different conditions represent a typical set of industrial applications and allow a qualified evaluation. Based on this analysis, a modular approach is proposed to overcome these obstacles, applied both during program generation (offline) and execution (online). Predictive offline compensation of machining errors is achieved by means of an innovative programming system, based on kinematic and dynamic robot models. Real-time adaptive machining error compensation is also provided by sensing the real robot positions with an innovative tracking system and corrective feedback to both the robot and an additional high-dynamic compensation mechanism on piezo-actuator basis.

Safety factors proposed in codes CEB, B.A.E.L 91 and EUROCODE 1 cover a great number of uncertainties; making them inadequate for the assessment of existing structures. Suitable safety factors are established using a probabilistic assessment, once real dimensions, materials strength and existing structures deterioration mechanisms are taken into account. This paper presents a calibration method for safety factors using a typical set of RC bridges in France. It considers the principal stages of corrosion provoked by CO2 and Cl− penetration and threshold indexes (B0) for existing structures. Reliability indexes are determined by the FORM method in the calibration method.

This paper studies several properties of channel codes that approach the fundamental limits of a given (discrete or Gaussian) memoryless channel with a nonvanishing probability of error. The output distribution induced by an ϵ-capacity-achieving code is shown to be close in a strong sense to the capacity achieving output distribution. Relying on the concentration of measure (isoperimetry) property enjoyed by the latter, it is shown that regular (Lipschitz) functions of channel outputs can be precisely estimated and turn out to be essentially nonrandom and independent of the actual code. It is also shown that the output distribution of a good code and the capacity achieving one cannot be distinguished with exponential reliability. The random process produced at the output of the channel is shown to satisfy the asymptotic equipartition property.

We show that the derivative of the relative entropy with respect to its parameters is lower and upper bounded. We characterize the conditions under which this derivative can reach zero. We use these results to explain when the minimum relative entropy and the maximum log likelihood approaches can be valid. We show that these approaches naturally activate in the presence of large data sets and that they are inherent properties of any density estimation process involving large numbers of random variables.