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This article discusses the use of error bars in psychological research papers and raises questions about the differences between error bars using the Standard Deviation (SD), the Standard Error (SE), and the Confidence Interval (CI). The paper aims to clarify misconceptions and confusions in error bar applications through mathematical theory analyses. The article acknowledges that controversies over error bar applications have been an unsettled issue in the psychological field and other scientific domains. However, it is important to note that this preprint has not been peer-reviewed. [Extracted from the article]

Purpose: As a powerful mathematical analysis tool, the local fractional calculus has attracted wide attention in the field of fractal circuits. The purpose of this paper is to derive a new ℑ -order non-differentiable (ND) R-C zero state-response circuit (ZSRC) by using the local fractional derivative on the Cantor set for the first time. Design/methodology/approach: A new ℑ -order ND R-C ZSRC within the local fractional derivative on the Cantor set is derived for the first time in this work. By defining the ND lumped elements via the local fractional derivative, the ℑ -order Kirchhoff voltage laws equation is established, and the corresponding solutions in the form of the Mittag-Leffler decay defined on the Cantor sets are derived by applying the local fractional Laplace transform and inverse local fractional Laplace transform. Findings: The characteristics of the ℑ -order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the ℑ -order R-C ZSRC becomes the classic one when ℑ = 1. The comparative results between the ℑ -order R-C ZSRC and the classic one show that the proposed method is correct and effective and is expected to shed light on the theory study of the fractal electrical systems. Originality/value: To the best of the authors' knowledge, this paper, for the first time ever, proposes the ℑ -order ND R-C ZSRC within the local fractional derivative on the Cantor sets. The results of this paper are expected to give some new enlightenment to the development of the fractal circuits. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce a notion of a t-filter on residuated lattices which is a generalization of several special types of filters. We provide some basic properties of t-filters and show how particular results about special types of filters (e.g. Extension property, Triple of equivalent characteristics, and Quotient characteristics) are uniformly covered by this simple general framework. [Copyright &y& Elsevier]

In this paper we provide a new parametrization of the characteristic curve (I - V curve) associated to the photovoltaic (PV) single-diode model (SDM), which is the most common model in the literature to analyze the behavior of a PV panel. The SDM relates the voltage with the current, through a transcendental equation with five parameters to be determined. There are many methodologies to extract the SDM parameters and some of them are based on obtaining the best fit of the SDM model on a voltage–current dataset through the ordinary least squares method. However, the fact that errors affect not only the current but also the voltage indicates that the maximum likelihood estimation (MLE) of the parameters is obtained by the total least squares method, also called orthogonal distance regression (ODR). The main difficulty in performing ODR lies in obtaining the Euclidean distance from a point to the SDM I - V curve which is in general a hard mathematical problem; in our particular case it is noticeably more difficult due to the implicit nature of the SDM equation and the fact that solution candidates might not be unique. This paper proposes a new parametrization that allows reduction of the calculus of the Euclidean distance from any point to the I - V curve to solving a single-variable equation. An in-depth mathematical analysis determines the number of possible candidates where the Euclidean distance can be attained. Moreover, a full casuistry alongside a geometrical study based on the curvature of the I - V curve and the Maximum Curvature Point, permits identification and classification of all these candidates. This enables for the first time a complete algorithm to compute the Euclidean distance from a point to an I - V curve at any condition and, thus, to perform a reliable ODR to obtain the MLE of the SDM parameters. Using the obtained theoretical background, it is demonstrated that two existing methodologies to compute the Euclidean distance fail in some cases, whereas the proposed algorithm is execution-proof and runs faster. • A parametrization of the photovoltaic single-diode model. • Calculus of the Euclidean distance (ED) to an I - V curve. • The point of maximum curvature and the evolute of an I - V curve. • Fast and fail-safe algorithm to compute the ED to an I - V curve. • The ED algorithm to perform a robust orthogonal distance regression. [ABSTRACT FROM AUTHOR]

Suppose that your house needs some restoration, and that you call a master mason asking for an estimate. If the mason replies at once that he will quote 1000 € for himself, plus 500 € for each helper apprentice, you will likely be puzzled, if not annoyed. Surely you have good reasons to complain, reasoning that the job you ask for should be remunerated with a fixed amount, irrespective of the number of labourers involved. Yet, this is not a criterion that we usually apply when evaluating the CV of an applicant for an academic position or for a grant. [ABSTRACT FROM AUTHOR]

The presence of nonlinearities in a fractional-N frequency synthesizer leads to the generation of an additional component of noise that appears in the output phase noise spectrum. This nonlinearity-induced noise component manifests itself as spurious tones and an elevated noise floor, also known as folded noise. This paper presents a mathematical analysis of the folded noise generated in fractional-N phase locked loops (PLL) by the interaction between the quantization noise introduced by the divider controller and a nonlinearity. The analysis is performed for different digital $\Delta \Sigma $ modulators (DDSM) and nonlinearities, providing expressions that allow one to predict the folded noise. These are compared with state-of-the-art predictions and simulation results. [ABSTRACT FROM AUTHOR]

We study in this paper, a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk management. The linear constraint on both the control and state variables considered in our model destroys the elegant structure of the conventional LQ formulation and has blocked the derivation of an explicit control policy so far in the literature. We successfully derive in this paper, the analytical control policy for such a class of problems by utilizing the state separation property induced from its structure. We reveal that the optimal control policy is a piecewise affine function of the state and can be computed offline efficiently by solving two coupled Riccati equations. Under some mild conditions, we also obtain the stationary control policy for an infinite time horizon. We demonstrate the implementation of our method via some illustrative examples and show how to calibrate our model to solve dynamic constrained portfolio optimization problems. [ABSTRACT FROM AUTHOR]

The paper describes a scheme for symbolic manipulation of index expressions which arise as a by-product of the symbolic manipulation of expressions in the matrix calculi described by the authors in a previous paper. This scheme attempts program optimization by transforming the original algorithm rather than the machine code. The goal is to automatically generate code for handling the tedious address calculations necessitated by complicated data structures. The paper is therefore preoccupied with "indexing by position." The relationship of "indexing by name" and "indexing by position" is discussed. [ABSTRACT FROM AUTHOR]

In this paper, a new filtering power divider topology is presented. The divider is distinguished from traditional power dividers as it is capable of having a predefined transmission response, an improved isolation performance between the two output ports over a wide frequency range, and reflectionless responses at all three ports. Since the proposed divider topology is based on complete closed-form design equations derived through a rigorous mathematical analysis, it make it possible to design reflectionless filtering power dividers with any prespecified requirements without using time-consuming parametric optimizations. For verifying the proposed divider topology, we have designed, fabricated, and measured a microstrip Butterworth filtering power divider. The proposed design approach can also be applied to the design of filtering power dividers with other transmission responses such as Chebyshev and inverse-Chebyshev responses. [ABSTRACT FROM AUTHOR]

Provides instructions and guidelines to prospective authors who wish to submit manuscripts. [ABSTRACT FROM AUTHOR]

Abstract: In reply to Péter Majlender, the connection between the (maximum spread) equidifferent OWA operator weights and the analytical method for the minimum variance OWA operator problem [R. Fullér, P. Majlender, On obtaining minimal variability OWA operator weights, Fuzzy Sets and Systems 136 (2003) 203–215] is pointed out and the differences between them are clarified. [Copyright &y& Elsevier]

Purpose This paper aims to study the heat transfer phenomenon occurring between heated walls and impinging fuel, showing the strict relationship between cooling effect after impingement and enhancing of wallfilm formation. The study focuses on a fundamental task in terms of pollutant emissions in internal combustion engines, aiming at giving a major contribution to the optimization of energy conversion systems in terms of environmental impact.Design/methodology/approach The paper is based on experimental campaigns relevant at taking measurements of an impinging spray over a heated wall in a confined vessel. The results, in both qualitative and quantitative terms (measurements of liquid and vapour radial penetration and thickness), are numerically reproduced by a computational model based on a Reynolds Averaged Navier Stokes approach, properly validated through customized sub-models.Findings The paper provides quantitative results about the agreement between radial penetration and vapour thickness between measurements and simulation, achieved by taking into account the cooling effect determined by the fuel impingement. This validation of the numerical model allows the author to give more considerations about the link between wall temperature and wallfilm formation.Originality/value This paper presents an original approach for the simulation of wall heat transfer, by imposing a boundary condition at the wall that may consider the heat conduction and temperature cooling given by fuel impingement in both lateral and normal directions. The classical Dirichlet boundary condition, characterized by imposing a fixed temperature value, is, instead, replaced by an approach based on calculating the unsteady process that couples the heat fluxes between the fluid and the solid material and within the solid itself. [ABSTRACT FROM AUTHOR]

This paper aims to study an HIV model with age structure and latently in a spatially homogeneous environment. By applying the fixed point theorem, we obtain the existence of the global solution and the global attractor for the model. We also identify the explicit formula of the basic reproduction number by the mean of the Laplace transformation, and confirm that this number predicts whether the infection occurs or not. Through analyzing the root distribution of the characteristic equation, the local stability of the equilibrium is obtained. By appealing to the appropriate Lyapunov functionals, we further study the global stability of the equilibrium. Numerical simulations also validate our theoretical results. [ABSTRACT FROM AUTHOR]

Purpose - The objective of this paper is two-fold: to share information about color and to solicit information about sound, with the ultimate goal of producing a simple formula for generating a cybernetic mixed reality environment; and to serve as a vehicle for inviting conversation at the "Cybernetics: Art, Design and Mathematics 2010" Conference. Design/methodology/approach - The majority of research in color focuses on the perceptual, experiential, phenomenon. Conceptual color is a perceptual and non-experiential. It is color observed as a thought. By engaging in study, from this methodological approach, color can be modeled as a simple computational system of inter-related abstract elements. This makes the complexity of the perceptual environment understandable and translatable to abstract data, but also makes the transition from the abstract back to actual possible. Findings - The conceptual model approach has yielded a number of features for future study, not least of which is color, as a true mathematical system. This is very different from a simple color-coding system. Practical implications - With more development, the new system may prove to be of significance to future digital design applications. Given that music is also a spatial pattern system, revisiting the age-old belief that there must be a correlation between color and music may now be productive. Originality/value - This paper presents a puzzle with thought-provoking questions, designed to solicit the information needed, in order to determine if a spatial correlation between color and sound is identifiable. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of factor prime factorizations for n-D polynomial matrices and presents a criterion for the existence of factor prime factorizations for an important class of n-D polynomial matrices. As a by-product, we also obtain an algebraic algorithm to check n-D factor primeness in some important cases which partially solves the long-standing open problem of recognizing n-D factor prime matrices. Some problems related to the factorization methods are also studied. Several exam- pies are given to illustrate the results. The results presented in this paper are true over any coefficient field. [ABSTRACT FROM AUTHOR]

In this paper, the sensitivity of the neural network (NN) outputs to device parameter uncertainties (non-idealities) in inverter-based memristor (IM) crossbar neuromorphic circuits is mathematically modeled and verified using exhaustive circuit and system-level simulations. The NN sensitivity is obtained by modeling the sensitivity of the IM neuron output to the non-idealities of its circuit elements. The analysis reveals a higher sensitivity of the output voltage of the IM neuron to the non-idealities of the inverters compared to the conductance variation of the memristors. Among the inverter non-idealities, horizontal shift of the inverters voltage transfer characteristic (VTC) shows the highest impact on the output voltage of the neuron. To reduce the accuracy loss due to the variations, a training approach which includes a sensitivity term in the cost function of the training phase, is suggested. The achievable improvements through the said NN training approach are evaluated. In the evaluation, the California Housing, MNIST, and Fashion MNIST datasets are employed. The results show up to 50% reduction in the NN output variations in the presence of circuit elements’ non-idealities. [ABSTRACT FROM AUTHOR]

This paper investigates an ultra-broadband sampling technique based on charge sampling using an Integrate-and-Hold Circuit (IHC) and ultra-short integration times. The charge sampling technique is mathematically analyzed in detail and compared to conventional switched-capacitor sampling. The mathematical analysis allows to predict the sampler bandwidth as well as the degradation of sampling precision due to analog circuit impairments such as integrator gain error, integration capacitor leakage, hold-mode droop, thermal noise, and clock jitter. Furthermore, design, simulation, and measurement results of an ultra-broadband charge sampler IC in SiGe BiCMOS technology are presented. The charge sampler IC achieves a 1dB bandwidth of 70 GHz. A resolution of better than 5.9 effective number of bits (ENOB) is measured from 0 to 70 GHz at a sampling rate of 5 GS/s. The results suggest that charge sampling using an IHC is a viable concept for ultra-broadband sampling. [ABSTRACT FROM AUTHOR]

This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma _1 \subset \Gamma _2 \subset \mathbb {R}^n$ , with $\Gamma _1$ compact, the theorems presented in this paper give conditions under which a qualitative property of $\Gamma _1$ that holds relative to $\Gamma _2$ (stability, attractivity, or asymptotic stability) can be guaranteed to also hold relative to the state space of the hybrid system. As a consequence of these results, sufficient conditions are presented for the stability of compact sets in cascade-connected hybrid systems. We also present a result for hybrid systems with outputs that converge to zero along solutions. If such a system enjoys a detectability property with respect to a set $\Gamma _1$ , then $\Gamma _1$ is globally attractive. The theory of this paper is used to develop a hybrid estimator for the period of oscillation of a sinusoidal signal. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed computation of the well-known linear matrix equation in the form of ${{AXB}} = F$ , with the matrices $A$ , $B$ , $X$ , and $F$ of appropriate dimensions, over multiagent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multiagent network has access to one of the subblock matrices of $A$ , $B$ , and $F$. To be specific, we first propose different decomposition methods to reformulate the matrix equations in standard structures as distributed constrained optimization problems by introducing substitutional variables; we show that the solutions of the reformulated distributed optimization problems are equivalent to least squares solutions to original matrix equations; and we design distributed continuous-time algorithms for the constrained optimization problems, even by using augmented matrices and a derivative feedback technique. Moreover, we prove the exponential convergence of the algorithms to a least squares solution to the matrix equation for any initial condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the identification of matrix state-space models (MSSM) of the following form: \begin{align*} \mathbf {X}(k+1) &= \mathbf {A}_2 \mathbf {X}(k) \mathbf {A}_1^T + \mathbf {B}_2 \mathbf {U}(k) \mathbf {B}_1^T \\ \mathbf {Y}(k) &= \mathbf {C}_2 \mathbf {X}(k) \mathbf {C}_1^T + \mathbf {E}(k) \end{align*} for all time dependent quantities and matrices of appropriate dimensions. Due to the large size of these matrices, vectorization does not allow the use of standard multivariable subspace methods such as N4SID or MOESP. In this paper, the resulting Kronecker structure that appears in the system matrices due to vectorization is exploited for developing a scalable subspace-like identification approach. This approach consists of first estimating the Markov parameters associated to the MSSM via the solution of a regularized bilinear least-squares problem that is solved in a globally convergent manner. Second, a bilinear low-rank minimization problem is tackled which allows to write a three-dimensional low-rank tensor and consequently to estimate the state sequence and the lower-dimensional matrices $\mathbf {A}_1,\mathbf {A}_2,\mathbf {B}_1,\mathbf {B}_2,\mathbf {C}_1,\mathbf {C}_2$. A numerical example on a large-scale adaptive optics system demonstrates the ability of the algorithm to handle the identification of state-space models within the class of Kronecker structured matrices in a scalable manner which results in more compact models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new state observer design technique for nonlinear systems. It combines the well-known Kazantzis–Kravaris–Luenberger observer and the recently introduced parameter estimation-based observer, which become special cases of it—extending the realm of applicability of both methods. A second contribution of this paper is the proof that these designs can be recast as particular cases of immersion and invariance observers—providing in this way a unified framework for their analysis and design. Simulation results of a physical system that illustrates the superior performance of the proposed observer compared to other existing observers are presented. [ABSTRACT FROM AUTHOR]

This paper considers chaos synchronization and chaos-based secure communication problems based on high-gain sliding mode unknown input observers when the observer matching condition is not satisfied to the drive signal. An auxiliary drive signal vector which satisfies the observer matching condition is introduced and an adaptive and robust observer is developed by using the auxiliary drive signal directly to not only estimate the states but also adjust adaptively the unknown parameters and the Lipschitz constants of the nonlinear terms. A high-gain sliding mode observer is considered to exactly estimate both the auxiliary drive signals and their derivatives in a finite time only based on the original drive signal. The combination of the adaptive and robust observer and the high-gain sliding mode observer becomes the receiver in chaos-based secure communication discussion. A kind of information signal recovering method is developed based on both the state synchronization and exact estimates of the derivatives of the auxiliary drive signals. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM PUBLISHER]

This paper presents a systematic framework to analyze the global pinning-controllability of general complex networks with or without time-delay based on the properties of M-matrices and directed spanning trees. Some stability criteria are established to guarantee that a network can be globally asymptotically pinned to a homogenous state. By partitioning the interaction diagraph into a minimum number of components, a selective pinning scheme for a complex network with arbitrary topology is proposed to determine the number and the locations of the pinned nodes. In particular, this paper deeply investigates the roles of network nodes in the pinning control, including what kind of nodes should be pinned and what kind of nodes may be left unpinned. Numerical simulations are given to verify the theoretical analysis. [ABSTRACT FROM PUBLISHER]

S-type locally-active memristor (LAM) has a great potential for brain- inspired neuromorphic computing, where the S-type LAM-based oscillator is a fundamental building block. Concerning the S-type LAM, this paper constructs a material-independent model in simple mathematical expression, which can be relatively easily analyzed. By biasing the memristor into the locally- active region, and connecting it with a capacitor, a second-order oscillator can be built. The small-signal equivalent circuit of the memristor and its frequency response are applied to determine the period oscillation frequency range and compensation capacitance. Hopf bifurcation theory is used to analyze oscillation mechanism of the second-order circuit and appropriate capacitance. By adding an extra inductor into the second-order oscillator, a novel third-order chaotic circuit is developed, where a saddle-focus is derived to create chaos. Its dynamic characteristics are investigated via Lyapunov exponents, bifurcation diagrams, dynamic route map, and so on. The local activities of the single memristor, second-order oscillator, and third-order chaotic circuit are verified through the mathematical analysis. Finally, physical circuit realizations of the S- type LAM-based oscillators, including the memristor emulator, are presented. Both simulation and experimental results demonstrate the practicability of the proposed mathematical model and the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, an epidemic model with homogeneous Dirichlet boundary condition is formulated to study the joint impact of spatial diffusion, infection age and treatment adherence on the HIV/AIDS transmission among humans. It is an interesting problem to understand the threshold dynamics of HIV/AIDS model with the above three factors. Since the complexity of the model and specificity of the boundary condition, there are two main mathematical challenges: i). the compactness of the solution map is not guaranteed; ii). the explicit expression of the basic reproduction cannot be given even if the parameters are spatially independent. We first discuss the well-posedness of the system, then we identify the basic reproduction number R 0 as the spectral radius of the next generation operator, followed by the global attractivity of disease-free steady state when R 0 < 1 , the uniform persistence of the disease and the existence of the endemic steady state when R 0 > 1. Numerical simulations are carried out to illustrate our theoretical results, which suggest that the diffusion of individuals has an opposite effect on the disease outbreaks, and improving the treatment compliance of HIV infected individuals can control HIV transmission among the population effectively. [ABSTRACT FROM AUTHOR]

Emerging advanced System-on-Chip (SoC) designs contain more and more complicated functions to be accelerated. This presents a challenge to conventional design approaches which use different hardware architectures or separate hardware accelerators to implement the various functions. To tackle this challenge, for the first time, we propose a generalized hardware accelerator called “Huicore” to speed up diverse functions on the same substrate. Through the analysis and transformation of mathematical characteristics, we reveal the commonality of many complicated functions using the CORDIC algorithm. Then we explore a reconfigurable architecture to implement them. The proposed reconfigurable accelerator can not only accelerate the implementation of many complicated functions, but also has small area, low power consumption and high precision. It is very suitable for integration in a SoC system to accelerate the implementation of various applications. [ABSTRACT FROM AUTHOR]

Most wireless battery-operated devices spend more energy receiving than transmitting. Hence, minimizing the power dissipation in the receiver front end, which, in many cases, is the prominent power consuming part of the receiver, is an important challenge. This paper addresses this challenge by solving two closely related optimization problems. Firstly, we optimize the overall power dissipation in an RF front end consisting of a chain of building blocks to satisfy required overall specifications in gain, linearity and noise figure. We extend this into a second optimization problem, namely to maximize the transmission rate that the receiver can accommodate for a given available receiver battery power budget. In fact, the ratio of this transmission rate vs the available receiver power budget serves as the figure-of-merit that allows a formal optimization where, in particular, the (adjacent channel) interference is a critical factor. Our results include closed-form analytical solutions for certain cases. For high signal power, where the noise is limited by interference, the largest bit/s/Hz per nJ drawn from receiver is reached for a transmission rate of 2.3 bits/s/Hz, irrespective of interference power. Numerical results using practical circuit blocks with 90 nm and 65 nm technologies are in close agreement with the analytical results. [ABSTRACT FROM AUTHOR]

This work deals with the analysis and the design of minimum-time control laws for a class of nonlinear discrete-time dynamical systems characterized by \cal K-continuous transition maps and bounded control inputs. In the paper, it is shown that the reachability properties of the target set, even if not robust positively controllable in one state transition, can be exploited to assess the existence of a robust positively controllable set including the target in its interior. This result allows the formulation of a robustified minimum-time control policy, based on iterated online optimizations and guaranteeing the ultimate boundedness of the state-trajectories in the presence of bounded uncertainties, even if the target set is not robust positively controllable. [ABSTRACT FROM PUBLISHER]

This paper presents a numerical procedure for the reachability analysis of systems with nonlinear, semi-explicit, index-1 differential-algebraic equations. The procedure computes reachable sets for uncertain initial states and inputs in an overapproximative way, i.e. it is guaranteed that all possible trajectories of the system are enclosed. Thus, the result can be used for formal verification of system properties that can be specified in the state space as unsafe or goal regions. Due to the representation of reachable sets by zonotopes and the use of highly scalable operations on them, the presented approach scales favorably with the number of state variables. This makes it possible to solve problems of industry-relevant size, as demonstrated by a transient stability analysis of the IEEE 14-bus benchmark problem for power systems. [ABSTRACT FROM AUTHOR]

Stefan melting problems involve the tracking of a sharp melt front during the heat conduction controlled melting of a solid. A feature of this problem is a jump discontinuity in the heat flux across the melt interface. Time fractional versions of this problem introduce fractional time derivatives into the governing equations. Starting from an appropriate thermodynamic balance statement, this paper develops a new sharp interface time fractional Stefan melting problem, the memory-enthalpy formulation. A mathematical analysis reveals that this formulation exhibits a natural regularization in that, unlike the classic Stefan problem, the flux is continuous across the melt interface. It is also shown how the memory-enthalpy formulation, along with previously reported time fractional Stefan problems based on a memory-flux, can be derived by starting from a generic continuity equation and melt front condition. The paper closes by mathematically proving that the memory-enthalpy fractional Stefan formulation is equivalent to the previous memory-flux formulations. A result that provides a thermodynamic consistent basis for a widely used and investigated class of time fractional (memory) Stefan problems. • A new time fractional Stefan problem is presented, the memory-enthalpy formulation. • The problem is obtained from an appropriate thermodynamic balance statement. • We prove that this formulation exhibits a natural regularization of the problem. • A comparison with the previous memory-flux formulation is made. • We prove that the memory-enthalpy formulation is equivalent to the memory-flux one. [ABSTRACT FROM AUTHOR]

The paper presents a study of issues related to the identification of a non-linear mathematical model describing dynamics of the temporomandibular joint (TMJ) disc. Based on the tests of real disks, a non-linear model was built and verified, and then numerical simulations were carried out, the purpose of which was to analyze the behavior of the model for various excitation conditions. They include, among others, plotting a multi-colored map of distribution of the largest Lyapunov exponent based on which the areas of occurrence of periodic and chaotic motion zones are identified. Bifurcation diagrams of steady states for sample sections of the Lyapunov map and phase flows of periodic and chaotic solutions are generated. For the same sections, numerical simulations are performed to identify coexisting solutions. These studies are carried out using diagrams showing the number of coexisting solutions and their periodicity. The research presented in the paper shows a very good match between the results of computer simulations and the data recorded in the laboratory experiment. Due to the very strong damping occurring in the system, the chaotic attractors resemble quasi-periodic solutions with their geometric shape. Strong damping also significantly affects multiple solutions, which are relatively rare in the analyzed model. Most of the chaotic responses and multiple solutions occur in the range of low amplitude values of the dynamic load affecting the tissues of the articular disc. The obtained results of numerical experiments clearly indicate that in the range of low frequency values of the external load acting on the system, single periodic solutions with a periodicity of 1 T dominate. With the increase of the load amplitude, the area of occurrence of such solutions increases. [Display omitted] • A novel non-linear mathematical model of the TMJ disk has been proposed. • The model was very well adjusted to the results of experimental studies. • The behavior of the model for chaotic and periodic motion zones was tested. • The presence of coexisting solutions was confirmed. [ABSTRACT FROM AUTHOR]

Direct-conversion transceivers are the predominating architecture in current mobile communication systems. Despite many advantages, this topology suffers from unavoidable mismatches in the analog part, which causes imbalance between the in-phase and quadrature (I/Q) component. In this paper, we present a novel fully digital, blind I/Q imbalance compensation algorithm that features extremely low computational complexity and high compensation performance for a wide range of input signal types. Different to many state-of-the-art compensation schemes, the approach is not based on a gradient descent optimization and does not require any global feedback. This simplifies the implementation at high data rates and reduces the configuration effort to a minimum. For comparison, we examine an existing method of moment-based estimator with similar properties, for which we also provide the detailed insights beyond available literature. For both algorithms, we provide a rigorous mathematical analysis, which is supported by simulations with a focus on various long-term evolution (LTE) signal types. In addition, hardware architectures, including field-programmable gate array (FPGA) verification, are presented for both algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the optimization problem for partially observable Markov decision processes (POMDPs) with the continuous state, observation, and action spaces. POMDPs with the discrete spaces have emerged as a promising approach to the decision systems with imperfect state information. However, in recent applications of POMDPs, there are many problems that have continuous states, observations, and actions. For such problems, due to the infinite dimensionality of the belief space, the existing studies usually discretize the continuous spaces with the sufficient or nonsufficient statistics, which may cause the curse of dimensionality and performance degradation. In this paper, based on the sensitivity analysis of the performance criteria, we have developed a simulation-based policy iteration algorithm to find the local optimal observation-based policy for POMDPs with the continuous spaces. The proposed algorithm needs none of the specific assumptions and prior information, and has a low computational complexity. One numerical example of the complicated multiple-input multiple-output beamforming problem shows that the algorithm has a significant performance improvement. [ABSTRACT FROM AUTHOR]

This paper proposes a new optimal control synthesis algorithm for multirobot systems under global temporal logic tasks. Existing planning approaches under global temporal goals rely on graph search techniques applied to a product automaton constructed among the robots. In this paper, we propose a new sampling-based algorithm that builds incrementally trees that approximate the state space and transitions of the synchronous product automaton. By approximating the product automaton by a tree rather than representing it explicitly, we require much fewer memory resources to store it and motion plans can be found by tracing sequences of parent nodes without the need for sophisticated graph search methods. This significantly increases the scalability of our algorithm compared to existing optimal control synthesis methods. We also show that the proposed algorithm is probabilistically complete and asymptotically optimal. Finally, we present numerical experiments showing that our approach can synthesize optimal plans from product automata with billions of states, which is not possible using standard optimal control synthesis algorithms or model checkers. [ABSTRACT FROM AUTHOR]

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a “global solution” of the scenario problem (SP), we resort to multiple interconnected processors that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual subgradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum _{t=1}^k\zeta ^t))$ , where $\lbrace \zeta ^t\rbrace$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms. [ABSTRACT FROM AUTHOR]

The goal of this paper is to explore the relationship between the network graph of a state-space representation of an observed process and the causal relations among the components of that process. We will show that the existence of a linear time-invariant state-space representation, with its network graph being the star graph, is equivalent to (conditional) Granger noncausal relations among the components of the output process. Granger noncausality is a statistical concept, which applies to arbitrary processes and does not depend on the representation of the process. That is, we relate intrinsic properties of a process with the network graph of its state-space representations. [ABSTRACT FROM AUTHOR]

This paper will investigate the stabilization and optimal linear quadratic (LQ) control problems for infinite horizon discrete-time mean-field systems. Unlike the previous works, for the first time, the necessary and sufficient stabilization conditions are explored under mild conditions, and the optimal LQ controller for infinite horizon is designed with a coupled algebraic Riccati equation (ARE). More specifically, we show that under the exact detectability (exact observability) assumption, the mean-field system is stabilizable in the mean square sense with the optimal controller if and only if a coupled ARE has a unique positive semidefinite (positive definite) solution. The presented results are parallel to the classical results for the standard LQ control. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of computing the distance between a given singular descriptor system $ (E,A)$ , and a nearest descriptor system that has impulsive initial conditions. The link between existence of impulsive initial conditions and zeros at infinity for the associated matrix pencil $sE - A$ is well-known. Much of the literature focusses on the case when only one of $E$ and $A$ is perturbed. We give a closed form expression of the distance to a nearest descriptor system having impulsive solutions via rank-1 perturbations when both $E$ and $A$ are perturbed. Next, for the case of perturbations without rank restrictions, we propose and evaluate the bounds for the distance. In the context of structured perturbations, we formulate and obtain an explicit expression for the distance, when $E$ and $A$ are Hermitian and are perturbed by Hermitian matrices. For a suitable class of systems, we also show that upper and lower bounds are within a factor of $\sqrt{2}$. We finally construct examples and compare the bounds obtained from our results with those from the literature as well as with computed values of the distance obtained via three numerical optimization techniques such as the structured low rank approximation, the Broyden–Fletcher–Goldfarb–Shanno algorithm, and direct optimization tools like globalsearch. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to identify faults in distribution systems which are unavoidable because of adverse weather conditions and unexpected accidents. Hence, quick fault location is vital for continuous power supply. However, most fault location methods depend on the stored database for locating fault. The database is created by simulation, which is time consuming. Therefore, in this work, a comprehensive fault location method to detect faulty section and fault distance from one-ended bus using limited simulated data is proposed.Design/methodology/approach The work uses voltage sag data measured at a primary substation. Support vector machine estimates the data which are not simulated. The possible faulty section is determined using matching approach and fault distance using mathematical analysis.Findings This work proposed a ranking analysis for multiple possible faulty sections, and the fault distance is calculated using Euclidean distance approach.Practical implications The research work uses Malaysian distribution system as it represents a practical distribution system with multiple branches and limited measurement at primary substation. The work requires only metering devices to identify fault which is cost effective. In addition, the distribution system is simulated using real-time PSCAD by which the capability of proposed method can be fully tested.Originality/value The paper presents a new method for fault analysis. It reduces simulation time and storage space of database. The work identifies faulty section and ranks the prior faulty section. It also identifies fault distance using a mathematical approach. [ABSTRACT FROM AUTHOR]

Purpose - The purpose of this paper is to explore new mathematical results to advance the understanding of the picture of a chaotic unimodal map. Design/methodology/approach - Ever since Poicare, deterministic chaos is ultimately connected with exponential divergence of nearby trajectories, unpredictability and erratic behaviour. Here, the authors propose an alternative approach in terms of complexity theory and transcendence. Findings - In this paper, the authors were able to reproduce previous results easily, due to new theorems. Originality/value - The paper updates previous results and proposes a more complete understanding of the phenomenon of deterministic chaos, also making possible connections with number theory, combinatorics and possibly quantum mechanics, as in quantum mechanics there does not exist the notion on nearby trajectories. [ABSTRACT FROM AUTHOR]

Switched dynamical systems can be found in many practical electronic circuits, such as various kinds of power converters, chaos generators, etc. This paper is concerned with the filter design problem for a class of switched system with average dwell time switching. Mode-dependent full-order filters are designed taking a more practical phenomenon, the asynchronous switching into account, where “asynchronous” means that the switching of the filters to be designed has a lag to the switching of the system modes. New results on the stability and l2-gain analyses for the systems are first given where the Lyapunov-like functions during the running time of subsystems are allowed to increase. In light of the proposed Lyapunov-like functions, the desired mode-dependent filters can be designed in that the unmatched filters are allowed to perform in the interval of the asynchronous switching before the matched ones are applied. In H\infty sense, the problem of asynchronous filtering for the underlying systems in linear cases is formulated and the conditions of the existence of admissible asynchronous filters are obtained. Two examples are provided to show the potential of the developed results. [ABSTRACT FROM PUBLISHER]

The volume, moments of inertia, and similar properties of solids are defined by triple (volumetric) integrals over subsets of three-dimensional Euclidean space. The automatic computation of such integral properties for geometrically complex solids is important in CAD/CAM, robotics, and other fields and raises interesting mathematical and computational problems that have received little attention from numerical analysts and computer scientists. This paper summarizes the known methods for calculating integral properties of solids that may be geometrically complex and identifies some significant gaps in our current knowledge. [ABSTRACT FROM AUTHOR]

The combinatorial complexity of most floor plan design problems makes it practically impossible to obtain a systematic knowledge of possible solutions using pencil and paper. The objective of this paper is to contribute to the development of computer methods providing such knowledge for the designer. The paper describes an algorithm which generates all possible rectangular plans on modular grids with congruent cells, subject to constraints on total area, room areas, wall lengths, room adjacencies, and room orientations. To make room sizes regular and limit the solution set only such grids are used which minimize the number of cells in the smallest room. The description is sufficiently detailed to serve as a basis for programming. Test results for a Pascal implementation of the algorithm are reported. Realistic problems of up to ten rooms have been solved in modest lengths of computer time The results indicate that the approach of exhaustive generation may prove to be more fruitful than generally assumed. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical analysis of the power spectral density of the output of a nonlinear block driven by a digital delta–sigma modulator. The nonlinearity is a memoryless third-order polynomial with real coefficients. The analysis yields expressions that predict the noise floor caused by the nonlinearity when the input is constant. [ABSTRACT FROM PUBLISHER]

The focal point of this paper is the well known problem of polynomial positivity over a given domain. More specifically, we consider a multivariate polynomial ƒ(x) with parameter vector x restricted to a hypercube X C Rn. The objective is to determine if ƒ(x) > 0 for all x E X. Motivated by NP-Hardness considerations, we introduce the so-called dilation integral method. Using this method, a "softening" of this problem is described. That is, rather than insisting that ƒ(x) be positive for all x ϵ X, we consider the notions of practical positivity and practical non-positivisy. As explained in the paper, these notions involve the calculation of a quantity e > 0 which serves as an upper bound on the percentage volume of violation in parameter space where ƒ(x) ≤ 0. Whereas checking the polynomial positivity requirement may be computationally prohibitive, using our ϵ-softening and associated dilation integrals, computations are typically straightforward. One highlight of this paper is that we obtain a sequence of upper bounds ϵk which are shown to be "sharp" in the sense that they converge to zero whenever the positivity requirement is satisfied. Since for fixed n, computational difficulties generally increase with k, this paper also focuses on results which reduce the size of the required k in order to achieve an acceptable percentage volume certification level. For large classes of problems, as the dimension of parameter space n grows, the required k value for acceptable percentage volume violation may be quite low. In fact, it is often the case that low volumes of violation can be achieved with values as low as k = 2. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust H∞ estimation for uncertain systems subject to limited communication capacity. The parameter uncertainty belongs to a given convex polytope and the communication limitations include measurement quantization, signal transmission delay, and data packet dropout, which appear typically in a network environment. The problem of H∞ filter design is first solved for a nominal system subject to the aforementioned information limitations, which is then extended to the uncertain case based on the notion of quadratic stability. To further reduce the overdesign in the quadratic framework, this paper also proposes a parameter-dependent filter design procedure, which is much less conservative than the quadratic approach. The quadratic and parameter-dependent approaches provide alternatives for designing robust H∞ filters with different degrees of conservativeness and computational complexity. Two examples, including a mass-spring system, are utilized to illustrate the design procedures proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. [ABSTRACT FROM AUTHOR]

In this paper, a family of nonlinear congruential generators (NLCGs) based on the digitized Rényi map is considered for the definition of hardware-efficient pseudorandom number generators (PRNGs), and a theoretical framework for their study is presented. The authors investigate how the nonlinear structure o these systems eliminates some of the statistical regularities spoiling the randomness of sequences generated with linear techniques. In detail, in this paper, a necessary condition that the considered NLCGs must satisfy to have maximum period length is given, and a list of such maximum period PRNGs. for period lengths up to 231 - 1 is provided. Referring to the NIST800-22 statistical test suite, two PRNG examples are presented and compared to well-known PRNGs based on linear recurrencies requiring a similar amount of resources for their implementation. [ABSTRACT FROM AUTHOR]