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In this article, a photovoltaic system is modeled and simulated in order to compare two different approaches of maximum power point tracking control structures. First, the system uses a Perturb & Observe maximum power point tracking control directly applied to the duty cycle, and its simulations results are compared with the experimental ones obtaining a good agreement. Then, an average current-mode control structure is coupled to the maximum power point tracking controller and simulations are performed for both systems. The system that incorporates current-mode control exhibits better response when perturbations are present, improving the settling time and reducing the steady-state oscillations. [ABSTRACT FROM AUTHOR]

The development of advanced metering technologies makes demand response (DR) able to provide fast response services, e.g., primary frequency control. It is recognized that DR can contribute to the primary frequency control like thermal generators. This paper proposes a day-ahead scheduling method that considers DR as a frequency control resource, so that the DR resources can be dispatched properly with other resources. In the proposed method, the objective of frequency control is realized by defining a frequency limit equation under a supposed contingency. The frequency response model is used to model the dynamics of system frequency. The nonlinear frequency limit equation is transformed to a linear arithmetic equation by piecewise linearization, so that the problem can be solved by mixed integer linear programming (MILP). Finally, the proposed method is verified on numerical examples. [ABSTRACT FROM AUTHOR]

A high speed high resolution direct digital frequency synthesizer (DDFS) architecture is presented. The proposed architecture combines the advantage of ROM-based DDFS and nonlinear DAC (NLDAC) based DDFS. The phase-to-amplitude mapping is implemented with NLDAC coarse quantization and further increase its resolution by adding a ROM-based piecewise linear interpolation. ROM size is reduced by using coarse-fine decomposition. A ROM compression ratio of 32 is achieved by further combing the adjacent lines in the same segment into one straight line. A 4-GHz 32-bit DDFS is implemented based on the proposed architecture. The prototype DDFS is fabricated in 0.25 μm SiGe HBT process. The DDFS with 9-bit amplitude resolution are capable of producing a minimum spurious-free dynamic range (SFDR) of 46 dBc up to Nyquist frequency at the clock frequency of 4.0 GHz. Compared with state-of-the-art DDFSs the proposed DDFS demonstrates excellent performance. [ABSTRACT FROM AUTHOR]

Nowadays, chaos generators are an attractive field for research and the challenge is their realization for the development of engineering applications. From more than three decades ago, chaotic oscillators have been designed using discrete electronic devices, very few with integrated circuit technology, and in this work we propose the use of field-programmable gate arrays (FPGAs) for fast prototyping. FPGA-based applications require that one be expert on programming with very-high-speed integrated circuits hardware description language (VHDL). In this manner, we detail the VHDL descriptions of chaos generators for fast prototyping from high-level programming using Python. The cases of study are three kinds of chaos generators based on piecewise-linear (PWL) functions that can be systematically augmented to generate even and odd number of scrolls. We introduce new algorithms for the VHDL description of PWL functions like saturated functions series, negative slopes and sawtooth. The generated VHDL-code is portable, reusable and open source to be synthesized in an FPGA. Finally, we show experimental results for observing 2, 10 and 30-scroll attractors. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of flux controlled memristive circuits with a piecewise linear memristor (i.e. the characteristic curve of the memristor is given by a piecewise linear function). The mathematical model is described by a discontinuous planar piecewise smooth differential system, which is defined on three zones separated by two parallel straight lines (called as discontinuity lines in discontinuous differential systems). We first investigate the stability of equilibrium points and the existence and uniqueness of a crossing limit cycle for the memristor-based circuit under self-excited oscillation. We then analyze the existence of periodic orbits of forced nonlinear oscillation for the memristive circuit with an external exciting source. Finally, we give numerical simulations to show good matches between our theoretical and simulation results. [ABSTRACT FROM AUTHOR]

This paper proposes two algorithms (ATIRMM and ALPM) for estimating the time-varying behavior of single input single output (SISO) switching piecewise linear systems. Walsh basis functions are used to capture the non-smooth fast varying dynamics. The piecewise time-varying frequency response function (TV-FRF) is approximated by the sum of a series of LTI FRFs multiplied with a set of Walsh functions. The best linear time invariant approximation (BLTIA) of the TV-FRF is estimated with small uncertainty. Besides the BLTIA, the two methods are capable of estimating the noise power spectrum and the TV-FRF. The error analysis shows that ATIRMM delivers more accurate TV-FRF and BLTIA estimations, while ALPM has better performance in noise power spectrum estimation. The conclusions are illustrated by simulations. [ABSTRACT FROM AUTHOR]

In this paper, a stabilized finite element method for optimal control problems governed by a convection dominated diffusion equation is investigated. The state and the adjoint variables are approximated by piecewise linear continuous functions with bubble functions. The control variable either is approximated by piecewise linear functions (called the standard method) or is not discretized directly (called the variational discretization method). The stabilization term only depends on bubble functions, and the projection operator can be replaced by the difference of two local Gauss integrations. A priori error estimates for both methods are given and numerical examples are presented to illustrate the theoretical results. [ABSTRACT FROM PUBLISHER]

Numerous chaotic systems have been studied in order to understand the phenomena of chaos. This paper introduces a novel three-dimensional chaotic system with the presence of infinite equilibria, that located on a piecewise linear curve. From a computational point of view, such system belongs to a class of nonlinear system with hidden attractor. Dynamics properties of this system are studied by means of phase portraits, bifurcation diagram, Lyapunov exponents and Kaplan–Yorke fractional dimension. Furthermore, experimental results show the feasibility of the theoretical system. [ABSTRACT FROM AUTHOR]

We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order μ ∈ (0, 1) with variable coefficients. For the spatial discretization, we apply the standard continuous Galerkin method of total degree ≤ 1 on each spatial mesh elements. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval (0, T) and a spatial domain Ω, our analysis suggest that the error in $L^{2}\left ((0,T),L^{2}({\Omega })\right )$ -norm is $O(k^{2-\frac {\mu }{2}}+h^{2})$ (that is, short by order $\frac {\mu }{2}$ from being optimal in time) where k denotes the maximum time step, and h is the maximum diameter of the elements of the (quasi-uniform) spatial mesh. However, our numerical experiments indicate optimal O( k + h ) error bound in the stronger $L^{\infty }\left ((0,T),L^{2}({\Omega })\right )$ -norm. Variable time steps are used to compensate the singularity of the continuous solution near t = 0. [ABSTRACT FROM AUTHOR]

We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar function as it is common in level set based methods. Hence, the interface is not aligned with the mesh. An unfitted finite element discretization based on a Taylor-Hood velocity-pressure pair and an XFEM (or CutFEM) modification is used for the approximation of the solution. This allows for the accurate approximation of solutions which have strong or weak discontinuities across interfaces which are not aligned with the mesh. To arrive at a consistent, stable and accurate formulation we require several additional techniques. First, a Nitsche-type formulation is used to implement interface conditions in a weak sense. Secondly, we use the ghost penalty stabilization to obtain an inf-sup stable variational formulation. Finally, for the highly accurate approximation of the implicitly described geometry, we use a combination of a piecewise linear interface reconstruction and a parametric mapping of the underlying mesh. We introduce the method and discuss results of numerical examples. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Reconstructing the as-built architectural shape of building interiors has emerged in recent years as an important and challenging research problem. An effective approach must be able to faithfully capture the architectural structures and separate permanent components from clutter (e.g. furniture), while at the same time dealing with defects in the input data. For many applications, higher-level information on the environment is also required, in particular the shape of individual rooms. To solve this ill-posed problem, state-of-the-art methods assume constrained input environments with a 2.5D or, more restrictively, a Manhattan-world structure, which significantly restricts their applicability in real-world settings. We present a novel pipeline that allows to reconstruct general 3D interior architectures, significantly increasing the range of real-world architectures that can be reconstructed and labeled by any interior reconstruction method to date. Our method finds candidate permanent components by reasoning on a graph-based scene representation, then uses them to build a 3D linear cell complex that is partitioned into separate rooms through a multi-label energy minimization formulation. We demonstrate the effectiveness of our method by applying it to a variety of real-world and synthetic datasets and by comparing it to more specialized state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

This paper presents a composite color-characterization model for Liquid Crystal Displays (LCDs), considering channel dependence and poor chromaticity constancy of primaries. The proposed model consists of two parts, that is, the Piecewise Linear assuming Variation in Chromaticity (PLVC) model and a partition compensation error model. PLVC model can accurately predict CIEXYZ for primaries and calculate the CIEXYZ of any digital input values ( d r, d g, d b) based on the channel independence assumption. In addition, the prediction error of PLVC model is compensated in RGB subspace using the partition compensation error model. The color difference Δ [ABSTRACT FROM AUTHOR]

A Segment-based Tensor Voting (SBTV) algorithm is presented for planar surface detection and reconstruction of man-made objects. Our work is inspired by piecewise planar stereo reconstruction. During the vital procedure to detect and label the planar surface, the two main contributions are: first, tensor voting is used for obtaining the geometry attribute of the 3D points cloud. The candidate planar patches are generated through scene image segment of low variation of color and intensity. Second, we over-segment the scene image into the segment and the candidate 3D planar patch is generated. The SBTV algorithm is used on 3D points cloud sets to identify the co-plane on the candidate patch. After detecting every planar patch, the geometry architecture of object is obtained. The experiments demonstrate the effectiveness of our proposed approach on either outdoor or indoor datasets. [ABSTRACT FROM AUTHOR]

A smoothed representation (based on natural exponential and logarithmic functions) for the canonical piecewise-linear model, is presented. The result is a completely differentiable formulation that exhibits interesting properties, like preserving the parameters of the original piecewise-linear model in such a way that they can be directly inherited to the smooth model in order to determine their parameters, the capability of controlling not only the smoothness grade, but also the approximation accuracy at specific breakpoint locations, a lower or equal overshooting for high order derivatives in comparison with other approaches, and the additional advantage of being expressed in a reduced mathematical form with only two types of inverse functions (logarithmic and exponential). By numerical simulation examples, this proposal is verified and well-illustrated. [ABSTRACT FROM AUTHOR]

We introduce a canonical method for transforming a discrete sequential data set into an associated rough path made up of lead–lag increments. In particular, by sampling a d -dimensional continuous semimartingale X : [ 0 , 1 ] → R d at a set of times D = { t i } , we construct a piecewise linear, axis-directed process X D : [ 0 , 1 ] → R 2 d comprised of a past and a future component. We call such an object the Hoff process associated with the discrete data { X t } t i ∈ D . The Hoff process can be lifted to its natural rough path enhancement and we consider the question of convergence as the sampling frequency increases. We prove that the Itô integral can be recovered from a sequence of random ODEs driven by the components of X D . This is in contrast to the usual Stratonovich integral limit suggested by the classical Wong–Zakai Theorem (Wong and Zakai, 1965). Such random ODEs have a natural interpretation in the context of mathematical finance. [ABSTRACT FROM AUTHOR]

Tropical Nevanlinna theory studies value distribution of continuous piecewise linear functions of a real variable. In this paper, we use the reasoning from tropical Nevanlinna theory to present tropical counterparts of some classical complex results related to Format type equations, Hayman conjecture and Brück conjecture. [ABSTRACT FROM AUTHOR]

We define piecewise linear and continuous finite element methods for a class of interface problems in two dimensions. Correction terms are added to the right-hand side of the natural method to render it second-order accurate. We prove that the method is second-order accurate on general quasiuniform meshes at the nodal points. Finally, we show that the natural method, although non-optimal near the interface, is optimal for points ... away from the interface. [ABSTRACT FROM AUTHOR]

Albeit simple and easy to interpret, a piecewise representation of time series comes with discontinuities that inevitably lead to substantial representation (approximation) error. In this study, we present models of time series with time granulation that reduce representation errors and subsequently give rise to the better approximation abilities and classification rates of classifiers of time series. The jumps (discontinuities) occurring because of the local piecewise representation of time series over disjoint time windows are eliminated due to the use of fuzzy sets describing overlapping time segments (temporal windows). We engage particle swarm optimization (PSO) as an optimization vehicle to minimize the representation error based on the adjustments of the length of the segments and the degree of overlap among membership functions of the temporal windows. We also consider PSO to minimize the classification error of classifiers of time series. In a series of experiments, we consider two commonly used piecewise techniques of approximation of time series such as piecewise aggregate approximation (PAA) and piecewise linear representation (PLR). The results demonstrate that PLR models produce lower approximation errors in comparison with those obtained for the PAA representation and quantify an impact of fuzzy temporal segmentation on the overall quality of the model. Results of comprehensive comparative studies are provided as well. [ABSTRACT FROM AUTHOR]

An efficient computational technique for solving linear delay differential equations with a piecewise constant delay function is presented. The new approach is based on a hybrid of block-pulse functions and Legendre polynomials. A key feature of the proposed framework is the excellent representation of smooth and especially piecewise smooth functions. The operational matrices of delay, derivative, and product corresponding to the mentioned hybrid functions are implemented to transform the original problem into a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

Tropical Nevanlinna theory, introduced by Halburd and Southall as a tool to analyze integrability of ultra-discrete equations, studies the growth and complexity of continuous piecewise linear real functions. The purpose of this paper is to extend tropical Nevanlinna theory to n -dimensional tropical projective spaces by introducing a natural characteristic function for tropical holomorphic curves, and by proving a tropical analogue of Cartan's second main theorem. It is also shown that in the 1-dimensional case this result implies a known tropical second main theorem due to Laine and Tohge. [ABSTRACT FROM AUTHOR]

In this paper a digital architecture for generating piecewise-linear arbitrary waveforms is presented. The proposed design is able to generate a piecewise-linear periodic signal by only using a minimum number of input data (breakpoints). The generator circuit implements a hybrid scheme which takes advantage of two methods: the purely piecewise-linear interpolation and the lookup-table structure. From the piecewise-linear method exploits the characteristic of a reduced memory requirement as well as the capability of automatically construct a waveform by repetitive (iterative) function evaluations. From lookup-table makes use of the simplicity in hardware implementation and the higher processing speed. In order to verify the performance of this proposal, three piecewise-linear waveforms have been successfully implemented in a ATMEGA32 microcontroller. Experimental results show a fast execution speed and a reduced memory demand in the proposed circuit realization. [ABSTRACT FROM AUTHOR]

For the analysis of dynamic characteristics of fluid-conveying pipes with piecewise linear support, a fluid-structure coupling dynamic model based on the finite element method is proposed. A user-defined pipe element based on Euler-Bernoulli beam is developed for modeling the pipes, considering the dynamic flow conditions. A nonlinear spring element is utilized to model the clamp between the pipe and the base. The dynamic responses of the system are obtained through the direct time integration. The stiffness of the clamp support is investigated by the analytical method and the experimental method, in which it is found that the clamp stiffness is piecewise linear. For different pipe geometries the user-defined element model, analytical model and measurement data are compared. The results show high quality of the element developed in this paper. Finally, the dynamic characteristics of the pipe system with piecewise linear support subjected to base harmonic excitation are calculated and the effects of the system parameters on pipe behaviors have also been studied. As a consequence, the model proposed in this paper can represent the piecewise linear nonlinearity of the clamp support and be used conveniently to investigate the effects of the fluid-structure coupling on the system behaviors. [ABSTRACT FROM AUTHOR]

We report simulation of nanostructured memristor device using piecewise linear and nonlinear window functions for RRAM and neuromorphic applications. The linear drift model of memristor has been exploited for the simulation purpose with the linear and non-linear window function as the mathematical and scripting basis. The results evidences that the piecewise linear window function can aptly simulate the memristor characteristics pertaining to RRAM application. However, the nonlinear window function could exhibit the nonlinear phenomenon in simulation only at the lower magnitude of control parameter. This has motivated us to propose a new nonlinear window function for emulating the simulation model of the memristor. Interestingly, the proposed window function is scalable up to f( x) = 1 and exhibits the nonlinear behavior at higher magnitude of control parameter. Moreover, the simulation results of proposed nonlinear window function are encouraging and reveals the smooth nonlinear change from LRS to HRS and vice versa and therefore useful for the neuromorphic applications. [ABSTRACT FROM AUTHOR]

The analysis and detection of edges is a central problem in applied mathematics and image processing. A number of results in recent years have shown that directional multiscale methods such as continuous curvelet and shearlet transforms offer a powerful theoretical framework to capture the geometry of edge singularities, going far beyond the capabilities of the conventional wavelet transform. The continuous shearlet transform, in particular, provides a precise geometric characterization of edges in piecewise constant functions in R 2 and R 3 , including corner points. However, a question has been raised frequently: What happens if the function is piecewise smooth and not just piecewise constant? Clearly, a piecewise smooth function is a much more realistic model of images with edges. In this paper, we extend the characterization results previously known and show that, also in the case of piecewise smooth functions, the continuous shearlet transform can detect the location and orientation of edge points, including corner points, through its asymptotic decay at fine scales. The new proof introduces innovative technical constructions to deal with the more challenging problem. The new results set the theoretical groundwork for the application of the shearlet framework to a wider class of problems from image processing. [ABSTRACT FROM AUTHOR]

Light stripe centerline extraction is the basic and key procedure in line-structured laser three-dimensional (3D) scanner. Based on the fact that light stripe׳s contour is approximately parallel to its centerline, a novel contour polygon segmentation method is proposed for extracting and optimizing centerline. Different light stripe segments are identified in images by contour tracking, and then each of them is segmented into several parts using contour polygonization. Interior angle is defined to trim open light stripe polygon and contour to make sure that centerlines extracted from open light stripes do not include superfluous points. Taking advantage of polygon segmentation, piecewise polynomial fitting method and self-adaptive interpolating strategy are adopted to acquire smoother and evenly spaced centerline points. Simulated experiments show that the proposed method can calculate centerlines from images robustly with a 0.309 pixel average accuracy. Point clouds and surface models of different objects acquired by a line-structured laser scanner demonstrate that the proposed method can produce more complete and smoother 3D models compared to other classical methods. Processing time for the proposed method is approximately positive proportional to the number of pixels in image. Quantitative analysis of time used for each sub-procedure puts forward an improvement direction for the proposed method. [ABSTRACT FROM AUTHOR]

This paper develops new refinement rules for non-uniform Catmull-Clark surfaces that produce G1 extraordinary points whose blending functions have a single local maximum. The method consists of designing an "eigen polyhedron" in R2 for each extraordinary point, and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules, when applied to a non-uniform Catmull-Clark control mesh in R3, yield a G1 extraordinary point. [ABSTRACT FROM AUTHOR]

Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise to a piecewise linear (PL) approximant. This is extended to isotopic convergence, with that discovery aided by computational experiments. Sufficient conditions to attain isotopic equivalence can be determined a priori . These sufficient conditions need not be tight bounds, providing opportunities for further optimizations. The results presented will facilitate further computational experiments on the theory of PL knots (also known as stick knots), where this theory is less mature than for smooth knots. [ABSTRACT FROM AUTHOR]

We consider a single-server polling system consisting of two queues of fluid with arrival process generated by a big number of heavy-tailed On/Off sources, and application in road traffic and communication systems. Class- j fluid is assigned to queue j, $$j=1,2$$ . Server 2 visits both queues to process or let pass the corresponding fluid class. If there is class-2 fluid in the system, it is processed by server 2 until the queue is empty, and only then server 2 visits queue 1, revisiting queue 2 and restarting the cycle as soon as new class-2 fluid arrives, with zero switchover times. Server 1 is an 'extra' server which continuously processes class-1 fluid (if there is any). During the visits of server 2 to queue 1, class-1 fluid is simultaneously processed by both servers (possibly at different speeds). We prove a heavy-traffic limit theorem for a suitable workload process associated with this model. Our limit process is a two-dimensional reflected fractional Brownian motion living in a convex polyhedron. A key ingredient in the proof is a version of the Invariance Principle of Semimartingale reflecting Brownian motions which, in turn, is also proved. [ABSTRACT FROM AUTHOR]

The generalized type neural networks have always been a hotspot of research in recent years. This paper concerns the stabilization control of generalized type neural networks with piecewise constant argument. Through three types of stabilization control rules (single state stabilization control rule, multiple state stabilization control rule and output stabilization control rule), together with the estimate of the state vector with piecewise constant argument, several succinct criteria of stabilization are derived. The obtained results improve and extend some existing results. Two numerical examples are proposed to substantiate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Molecular Spring Isolator (MSI) is a novel passive vibration isolation technique, providing High-Static-Low-Dynamic (HSLD) stiffness based on the use of molecular spring material. The molecular spring material is a solid-liquid mixture consisting of water and hydrophobic nanoporous materials. Under a certain level of external pressure, water molecules can intrude into the hydrophobic pores of nanoporous materials, developing an additional solid-liquid interface. Such interfaces are able to store, release, and transform mechanical energy, providing properties like mechanical spring. Having been only recently developed, the basic mechanic properties of a MSI have not been studied in depth. This paper focuses on the stiffness influence factors, the dynamic frequency response, and the vibration isolation performance of a MSI; these properties help engineers to design MSIs for different engineering applications. First, the working mechanism of a MSI is introduced from a three-dimensional general view of the water infiltration massive hydrophobic nanoporous pores. Next, a wide range of influence factors on the stiffness properties of MSI are studied. In addition, the frequency response functions (FRFs) of the MSI vibration isolation system are studied utilizing the matching method based on equivalent piecewise linear (EPL) system. Finally, the vibration isolation properties of MSI are evaluated by force transmissibility. [ABSTRACT FROM AUTHOR]

Let S be a real n × n matrix, z , c ˆ ∈ R n , and | z | the componentwise modulus of z . Then the piecewise linear equation system z − S | z | = c ˆ is called an absolute value equation (AVE). It has been proven to be equivalent to the general linear complementarity problem , which means that it is NP-hard in general. We will show that for several system classes (in the sense of structural impositions on S ) the AVE essentially retains the good-natured solvability properties of regular linear systems. I.e., it can be solved directly by a slightly modified Gaussian elimination that we call the signed Gaussian elimination. For dense matrices S this algorithm has, up to a term in O ( n ) , the same operations count as the classical Gaussian elimination with column pivoting. For tridiagonal systems in n variables its computational cost is roughly that of sorting n floating point numbers. The sharpness of the proposed restrictions on S will be established. [ABSTRACT FROM AUTHOR]

A model of asymptotically stationary piecewise-linear random processes based on homogeneous Poisson flows is considered in the paper. Exact expressions for the mathematical expectation and variance as functions of a continuous argument are presented. A model of asymptotically periodically correlated piecewise-constant non-Gaussian random processes is also presented. This model is based on inhomogeneous Poisson flows of special form. [ABSTRACT FROM AUTHOR]

ABSTRACT A novel approach utilizing one-dimensional (1D) wave equation based finite difference time domain (FDTD) formulations for Lorentz-type Epsilon-Negative (ENG) medium is developed. To demonstrate the validity and accuracy of the formulation, reflection of a plane wave normally incident at free space-ENG interface is compared with the analytical solution. Moreover, propagation characteristics of Lorentz-type ENG medium is investigated using the FDTD formulations both for wave equation and Maxwell's curl equations in 1D case. Comparisons of memory and computational time requirements of both formulations are given. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:304-310, 2016. [ABSTRACT FROM AUTHOR]

We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space. [ABSTRACT FROM PUBLISHER]

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation of the state and the control is done by using piecewise linear functions. With this choice, a superlinear order of convergence for the control is obtained in the $$L^2$$ -norm; moreover, under a further assumption on the regularity structure of the optimal control this error estimate can be improved to $$h^{3/2}$$ , extending the results in Rösch (Optim. Methods Softw. 21(1): 121-134, ). The theoretical findings are tested experimentally by means of numerical examples. [ABSTRACT FROM AUTHOR]

In the real world, decision making processes must be able to integrate non-stationary information that changes systematically while the decision is in progress. Although theories of decision making have traditionally been applied to paradigms with stationary information, non-stationary stimuli are now of increasing theoretical interest. We use a random-dot motion paradigm along with cognitive modeling to investigate how the decision process is updated when a stimulus changes. Participants viewed a cloud of moving dots, where the motion switched directions midway through some trials, and were asked to determine the direction of motion. Behavioral results revealed a strong delay effect: after presentation of the initial motion direction there is a substantial time delay before the changed motion information is integrated into the decision process. To further investigate the underlying changes in the decision process, we developed a Piecewise Linear Ballistic Accumulator model (PLBA). The PLBA is efficient to simulate, enabling it to be fit to participant choice and response-time distribution data in a hierarchal modeling framework using a non-parametric approximate Bayesian algorithm. Consistent with behavioral results, PLBA fits confirmed the presence of a long delay between presentation and integration of new stimulus information, but did not support increased response caution in reaction to the change. We also found the decision process was not veridical, as symmetric stimulus change had an asymmetric effect on the rate of evidence accumulation. Thus, the perceptual decision process was slow to react to, and underestimated, new contrary motion information. [ABSTRACT FROM AUTHOR]

In 1965, E. C. Zeeman proved that the (±1)-twist spin of any knotted sphere in (n−1)-space is unknotted in the n-sphere. In 1991, Y. Marumoto and Y. Nakanishi gave an alternate proof of Zeeman's theorem by using the moving picture method. In this paper, we define a knotted 2-dimensional foam which is a generalization of a knotted sphere and prove that a (±1)-twist spin of a knotted trivalent graph may be knotted. We then construct some families of knotted graphs for which the (±1)-twist spins are always unknotted. [ABSTRACT FROM AUTHOR]

Given a finite simplicial complex, a unimodular representation of its fundamental group, and a closed twisted cochain of odd degree, we define a twisted version of the Reidemeister torsion, extending a previous definition of V. Mathai and S. Wu. The main tool is a complex of piecewise smooth currents introduced by J. Dupont in 1986. [ABSTRACT FROM AUTHOR]

Intrinsic location functional is a large class of random locations closely related to stationary processes. In this paper the author firstly identifies a subclass of intrinsic location functional and proves that it characterizes stationary increment processes. Then a generalization of intrinsic location functional is introduced and its relationship with intrinsic location functional is discussed. Finally we develop representation results using ordered random sets and piecewise linear functions. It is proved that each random location corresponds to the maximal element in a random set according to certain order, and the locations change in a specific way when the path is translated. [ABSTRACT FROM AUTHOR]

Avian lungs are remarkably different from mammalian lungs in that air flows unidirectionally through rigid tubes in which gas exchange occurs. Experimental observations have been able to determine the pattern of gas flow in the respiratory system, but understanding how the flow pattern is generated and determining the factors contributing to the observed dynamics remains elusive. It has been hypothesized that the unidirectional flow is due to aerodynamic valving during inspiration and expiration, resulting from the anatomical structure and the fluid dynamics involved, however, theoretical studies to back up this hypothesis are lacking. We have constructed a novel mathematical model of the airflow in the avian respiratory system that can produce unidirectional flow which is robust to changes in model parameters, breathing frequency and breathing amplitude. The model consists of two piecewise linear ordinary differential equations with lumped parameters and discontinuous, flow-dependent resistances that mimic the experimental observations. Using dynamical systems techniques and numerical analysis, we show that unidirectional flow can be produced by either effective inspiratory or effective expiratory valving, but that both inspiratory and expiratory valving are required to produce the high efficiencies of flows observed in avian lungs. We further show that the efficacy of the inspiratory and expiratory valving depends on airsac compliances and airflow resistances that may not be located in the immediate area of the valving. Our model provides additional novel insights; for example, we show that physiologically realistic resistance values lead to efficiencies that are close to maximum, and that when the relative lumped compliances of the caudal and cranial airsacs vary, it affects the timing of the airflow across the gas exchange area. These and other insights obtained by our study significantly enhance our understanding of the operation of the avian respiratory system. [ABSTRACT FROM AUTHOR]

In this article, we consider the inclusion of random effects in both the survival function for at-risk subjects and the cure probability assuming a bivariate normal distribution for those effects in each cluster. For parameter estimation, we implemented the restricted maximum likelihood (REML) approach. We consider Weibull and Piecewise Exponential distributions to model the survival function for non-cured individuals. Simulation studies are performed, and based on a real database we evaluate the performance of our proposed model. Effect of different follow-up times and the effect of considering independent random effects instead of bivariate random effects are also studied. [ABSTRACT FROM PUBLISHER]

A ring of N = 2 M identical neuron cells with piecewise linear and saturated bidirectional coupling nonlinearities is considered. The rotating wave under investigation exists for ‘most’ values of the coupling parameters α > 0 and | β | ≤ α . The dominant Floquet multiplier is unstable and converges exponentially to 1 in the number of cells. The remaining 2 M − 2 nontrivial Floquet multipliers converge exponentially to 0. A heteroclinic bifurcation curve and also the heteroclinic orbit connections are described by explicit formulas. The entire work was motivated by electrical circuit experiments. [ABSTRACT FROM AUTHOR]

Voltage deviation and stability constrained VAr planning or reactive power planning (RPP) is an important challenging issue in power systems. This paper presents a new hybrid technique for modeling and solving RPP problem taking into account the static voltage stability constraint. First, the uncertain fuzzy clustering theory is employed to select new candidate VAr source locations. Then, modified gray code is applied and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Based on the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability and new VAr capacity is derived and applied as static voltage stability constraint in RPP problem. Last, the RPP optimization problem is solved by a self adaptive fuzzy chaotic interactive honey bee mating optimization (FCIHBMO) technique taking advantage of the modified gray code. In the FCIHBMO algorithm, a modified definition of the updating factors on generation solution is proposed. In the case study, uncertain fuzzy clustering mechanism, the modified gray code, and the modified HBMO are applied to the IEEE 118-bus and IEEE 300-bus systems. Test results conclude that the proposed hybrid technique is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered. [ABSTRACT FROM AUTHOR]

In many applications, sequences generated by chaotic maps have been considered as pseudo-random sequences. This paper deals with the correlation between chaotic sequences generated by a given piecewise linear map; we have based the measure of the correlation on the statistics of the Kendall tau, which is usually used in the field of statistics. We considered three piecewise linear maps to generate chaotic sequences and computed the statistics of the Kendall tau of couples of sequences obtained from randomly chosen couples of initial conditions. We essentially found that the results depend on the considered chaotic map and that it is possible to approach the uncorrelated case. [ABSTRACT FROM AUTHOR]

This paper presents a skip entry guidance algorithm that uses a numerical predictor–corrector and a patched corridor for low-lifting capsules returning from the Moon. The longitudinal and lateral channels are assumed to be decoupled. The bank angle magnitude profile is parameterized using piecewise linear segments with respect to a normalized energy. The shape of the bank-vs-energy profile is determined using a single piecewise-defined variable. The predicted longitudinal bias is nullified using a false position method. The adverse effects of aerodynamic and atmospheric uncertainties are mitigated using an on-board estimating strategy during the trajectory prediction. A patched corridor is devised to manage the lateral state based on analytical derivations and reasonable approximations. The sign of the bank angle is reversed when the boundary of the patched corridor is violated. Dispersed simulations are implemented in a three-degree-of-freedom dynamical context, and the results demonstrate the high performance of the proposed guidance algorithm under stressful testing conditions. [ABSTRACT FROM AUTHOR]