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Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multilateral systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multilateral topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped-clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ~89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases. [ABSTRACT FROM AUTHOR]

In mathematical physics, time-dependent Green’s functions (GFs) are the solutions of differential equations of the first and second time derivatives. Habitually, the time-dependent GFs are Fourier transformed into the frequency space. Then, analytical continuation of the frequency is extended to below or above the real axis. After inverse Fourier transformation, retarded and advanced GFs can be obtained, and there may be arbitrariness in such analytical continuation. In the present work, we establish the differential equations from which the retarded and advanced GFs are rigorously solved. The key point is that the derivative of the time step function is the Dirac δ function plus an infinitely small quantity, where the latter is not negligible because it embodies the meaning of time delay or time advance. The retarded and advanced GFs defined in this paper are the same as the one-body GFs defined with the help of the creation and destruction operators in many-body theory. There is no way to define the causal GF in mathematical physics, and the reason is given. This work puts the initial conditions into differential equations, thereby paving a way for solving the problem of why there are motions that are irreversible in time. [ABSTRACT FROM AUTHOR]

The deep neural network with step function activation (0/1 DNNs) is a fundamental composite model in deep learning which has high efficiency and robustness to outliers. However, due to the discontinuity and lacking subgradient information of the 0/1 DNNs model, prior researches are largely focused on designing continuous functions to approximate the step activation and developing continuous optimization methods. In this paper, by introducing two sets of network node variables into the 0/1 DNNs and by exploring the composite structure of the resulted model, the 0/1 DNNs is decomposed into a unary optimization model associated with the step function and three derivational optimization subproblems associated with the other variables. For the unary optimization model and two derivational optimization subproblems, we present a closed form solution, and for the third derivational optimization subproblem, we propose an efficient proximal method. Based on this, a globally convergent step function based recursion method for the 0/1 DNNs is developed. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples on classifying MNIST, FashionMNIST and Cifar10 datasets. • We analyse the relevant optimal conditions for 0/1 deep neural networks. • We develop a globally convergent step function based recurtion method for solving 0/1 deep neural networks. • We investigate the proposed method on three classifying datasets: MNIST, FashionMNIST and Cifar10. [ABSTRACT FROM AUTHOR]

Molecular dynamics characteristics have important significance in studying the interaction between biomolecules, such as drug screening, environmental monitoring and evaluation of virus infectivity. In this work, a simulation method based on step function is proposed to study the molecular binding and dissociation processes, which is further coupled with surface plasmon wave evanescent field. A complete simulation model is established from biomolecular reaction to surface plasmon resonance (SPR) optical detection, which is consistent with the experimental process. Furthermore, experimental verification studies were carried out on human serum albumin (HSA), a marker of the urinary protein disease. The effects of microchannel size, liquid flow rate, molecular concentration, complex samples and other conditions on the molecular dynamics binding characteristics were studied under the conditions of antibody fixation and antigen–antibody binding reaction. Optimized parameters are obtained such as microchannel size and liquid flow rate, which can save reaction reagents reduce the experimental process and improve the experimental detection accuracy. Therefore, the established simulation and experimental methods include a complete process from biological information to optical information, which is expected to be a powerful tool for molecular interaction analysis in the future. [ABSTRACT FROM AUTHOR]

Aiming at the problem of force transmission through wire-steel and pulley in previous cam lifting, a new type of negative cam shedding mechanism with spring return was designed and developed on the basis of plane bar group, gear drive, tension spring and disk-cam mechanism with swinging roller follower. The stiffness and initial tension of the spring for coarse cotton fabric were determined through mechanism analysis, derivation of mechanical model and warp tension calculation. Functional simulation prototype of the mechanism was established on ADAMS/View platform. In view of real work situation on the mechanism, dynamic warp tension simulated by Step function was loaded into the heald frame which effectively improved dynamic design accuracy and reliability for lifting process of the heald frame. Based on that, the feasibility of cam lifting and spring return were verified by kinematic and dynamic simulation analysis. The results indicate that in the process of opening and closing, the travel range of heald frame is about 14. 5 mm and angular range of swing bar on the cam is 12. 4°, which can meet the technological requirements of negative cam shedding. [ABSTRACT FROM AUTHOR]

Actuator rate limit phenomenon is ubiquitous in control systems, but it has always been neglected in practical engineering. Especially, few papers are published to investigate the system identification while considering the rate limit. Step function is commonly used in parameter estimation and its first‐order derivative at the step time goes to infinity, which is not affordable by real actuators. As a result, the rate limit slows down the system response speed, misleads the parameter identification, and subsequently affects the controller design and deteriorates the control performance. This study proposes both graphical method and curve fitting method to identify the first‐order plus time‐delay (FOPTD) systems with consideration of the actuator rate limit effect whose limit value is unknown. Quantitative analyses of the parameter mismatch in the traditional FOPTD model and parameter sensitivity analyses are also carried out. Both simulation results and experimental results have shown the necessity and feasibility of defining a new model structure which includes the rate limit value. [ABSTRACT FROM AUTHOR]

To enable targeted therapies and enhance medical decision-making, biomarkers are increasingly used as screening and diagnostic tests. When using quantitative biomarkers for classification purposes, this often implies that an appropriate cutoff for the biomarker has to be determined and its clinical utility must be assessed. In the context of drug development, it is of interest how the probability of response changes with increasing values of the biomarker. Unlike sensitivity and specificity, predictive values are functions of the accuracy of the test, depend on the prevalence of the disease and therefore are a useful tool in this setting. In this paper, we propose a Bayesian method to not only estimate the cutoff value using the negative and positive predictive values, but also estimate the uncertainty around this estimate. Using Bayesian inference allows us to incorporate prior information, and obtain posterior estimates and credible intervals for the cut-off and associated predictive values. The performance of the Bayesian approach is compared with alternative methods via simulation studies of bias, interval coverage and width and illustrations on real data with binary and time-to-event outcomes are provided. [ABSTRACT FROM AUTHOR]

In this note, we study a discontinuous three-term recurrence relation which arises from seeking the steady states of a cellular neural network with step control function. Several collections of periodic solutions are found. A necessary and sufficient condition for a solution to be periodic is stated and aperiodic solutions are found as consequences. We also show that any periodic solution can be derived from a primary periodic solution with least period not divisible by 5. Although the periodic or aperiodic solutions we found are not exhaustive, they are quite abundant and may reflect some of the rich physical phenomena in true biological systems. Our method in this note may also provide a general approach to analyze the periodicity of solutions of similar recurrence relations. [ABSTRACT FROM AUTHOR]

• Expand the application of singularity functions for cable configuration. • Provide the mathematical derivation defining the cable deflection and forces when subject to point loads. • Define the procedure to employ the developed method for determining cable configuration during varied construction stages. • Provide an example of determining cable configuration by using developed method when main span cable is subject to point loads from suspenders. This paper presents a solution procedure for cable configurations, such as the ones used for suspension and cable stayed bridges. It employs a semi analytical method with direct integration of singularity functions. The procedure is rigorous and more efficient than other solution techniques for this class of structures. It can include any number of discontinuous and continuous loads and can take into account the initial configuration of the cable. Because of its efficiency the solution process compared to other solution methods such as finite element analysis is suitable for parametric studies that are needed during the design and construction processes. The procedure may also be used for developing a macro element of cable and its suspenders for use in an efficient finite element solution. [ABSTRACT FROM AUTHOR]

Let G be an abelian ℓ-group with a strong order unit u > 0. We call G u-clean after Hager, Kimber, and McGovern if every element of G can be written as a sum of a strong order unit of G and a u-component of G. We prove that G is u-clean if and only if u-components of G can be lifted modulo any ℓ-ideal of G. Moreover, we introduce a notion of u-suitable ℓ-groups (as a natural analogue of the corresponding notion in Ring Theory) and we prove that the ℓ-group G is u-clean when and only when it is u-suitable. Also, we show that if E is a vector lattice, then E is u-clean if and only if the space of all u-step functions of E is u-uniformly dense in E. As applications, we will generalize a result by Banaschewski on maximal ℓ-ideals of an archimedean bounded f-algebras to the non-archimedean case. We also extend a result by Miers on polynomially ideal C (X)-type algebras to the more general setting of bounded f-algebras. [ABSTRACT FROM AUTHOR]

Aggregation prone Huntingtin (Htt) protein and its aberrations, causing protein misfolding, have been the prototype of intense research for several decades. Misfolded aggregates or oligomers of different sizes not only deregulate the homeostasis, cellular machinery also counterbalances the effects at least at the initial stages, till the balance tilts towards toxicity and degeneration. In this paper, we combine experimental approaches with system based computational modeling to decipher the molecular mechanisms as well as the hidden dynamics leading to neuronal death in HD. We built an abstracted Boolean gate based electronic circuit that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, at the initial stages of Htt aggregate formation, individual changes in different protein levels and their interactions in cascade constitute the Grb2-pERK-Foxd3 feedback loop that is sufficient to create Hill-like sensitivity and prevent aggregation to the extent till mutant Htt (mHtt) aggregates become predominant in the cell when they spatially isolate the homeostatic reaction mechanism. [ABSTRACT FROM AUTHOR]

In this paper, continuing the work of the first and third authors, we study the function spaces from coherent continuous domains to RB-domains. Firstly, we prove that the function spaces from coherent core compact spaces with compact open sets as a basis to bifinite domains (algebraic RB-domains) are algebraic. As an application, we give an example which shows that a function space from a coherent quasi-algebraic domain to a finite domain might not be coherent. Finally, we show that the function space from a coherent continuous domain to an RB-domain is an RB-domain. Particularly, a function space from an FS-domain (introduced by Achim Jung) to an RB-domain is an RB-domain. This addresses an old open problem of whether FS-domains are RB-domains. [ABSTRACT FROM AUTHOR]

We propose a system of first-order ordinary differential equations to describe and understand the physiological mechanisms of the interplay between plasma glucose and insulin and their behaviors in diabetes. The proposed model is based on Hill and step functions which are used to simulate the switch-like behavior that occurs in metabolic regulatory variables when some of the threshold parameters are approached. A simplified piecewise-linear system is also proposed to study the possible equilibria and solutions and used to introduce simple theoretical control mechanisms representing the action of an artificial pancreas and regulating exogenous insulin. [ABSTRACT FROM AUTHOR]

A new chaotic system is proposed to generate multiscroll chaotic attractors. The major method used is for the step function to act as a nonlinear function. To prove that the proposed system can generate multiscroll chaotic attractors, the equilibrium point, the time domain waveform and the phase diagram of the proposed system are calculated. Finally, the design of the hardware circuit produces experimental results at a maximum of 8-scroll hardware. Theoretical analysis, simulation and hardware experimental results are fully matched, which further proves the existence of the proposed system and the physical realization. This provides the possibility for future applications in engineering. [ABSTRACT FROM AUTHOR]

We study the uniform approximation of the sigmoid cut function by smooth sigmoid functions such as the logistic and the Gompertz functions. The limiting case of the interval-valued step function is discussed using Hausdorff metric. Various expressions for the error estimates of the corresponding uniform and Hausdorff approximations are obtained. Numerical examples are presented using CAS MATHEMATICA. [ABSTRACT FROM AUTHOR]

This paper proposed an approach of subgradient integrated into particle swarm optimizer (SGPSO) for globally optimizing continuous objective function. In minimization, itproposed a revision for the manner of velocity update with the direction of subgradient to search for the local minima of a given non-diiferentiable and non-convex objective function. Thus it combined with communications among particles, this revision would offer more chances to obtain the global minima. Furthermore, in the part of subgradient iteration, it suggested that the step function should be a lower order infinitesimal with respect to subgradient magnitude as well as be a decreasing function with respect to iteration time. In the end, experiments and comparisons of the proposed SGPSO on benchmark problems validate its performance with better effectivenees and efficiency. [ABSTRACT FROM AUTHOR]

Stiffeners are used to reduce the probability of local failures in structures. Local stiffening is a matter of interest in aerospace, civil, and mechanical engineering. In spite of the presence of local stiffeners in different structures, the analysis of stiffened frames is scarce in the literature. The effect of local stiffeners on the stability of frame structures is investigated in this paper using detailed modelling of columns. A stiffener reduces the flexibility of a stiffened column. It is a common practice to model a stiffened column by a system of springs in series. This system is not suitable for simulating stiffness in finite element models. Consequently, this has been replaced by an equivalent parallel spring system. The parallel system is used in studying the effects of stiffener on the stability of a structural frame. The exact formulation for simple system is mapped onto the real structure and the exact finite element formulation is derived. The effect of stiffeners on the stability analysis of structural frames is considered and the governing equations are derived. For simple members, a closed form solution and, for stiffened structural frames, the finite element formulation have been proposed. The formulation is implemented in a computer programme. The accuracy, efficiency, and robustness of the presented formulation work are verified using case studies. [ABSTRACT FROM AUTHOR]

Abstract: Non-Fourier heat conduction phenomenon in a finite slab with insulated boundaries is investigated in the present paper. Since solving the hyperbolic heat conduction equation analytically requires considerable effort, a new high-order numerical approach has been implemented to achieve comparable exactitude. This method solves the considered equation in Laplace space and numerical inversion is employed with the intention of transformation to temporal domain. In order to examine numerical accuracy of this method, Dirac delta heat flux is applied to the assumed medium and results were compared with those of the analytical solution. It was observed that numerical values follow exact ones, at least up to the seventh order of accuracy. In addition, Step and Triangular heat pulses in the medium were studied to reveal temporal and spatial non-Fourier heat conduction characteristics. It was found that in large values of Ve number, for various kinds of heat fluxes carrying the same amount of energy, temperature distribution varies conspicuously through the medium; nevertheless, at each pass of heat wave, a specific point experiences a definite rise of temperature regardless of the type of heat flux provided that the same conditions are present. [Copyright &y& Elsevier]

Given a real ∊ > 0, an integer g ≥ 0 and a set of points in the plane, we study the problem of computing a piecewise linear functional curve with minimum number of line segments to approximate all points after removing g outliers such that the approximation error is at most ∊. We give an improved algorithm over the previous work. The algorithm is based on two dynamic data structures developed in this paper for the simplicial thickness queries, which are of independent interest. For a set S of simplices in the d-dimensional space ℝd (d ≥ 2 is a constant), the simplicial thickness of a point p is defined as the number of simplices in S that contain p. Given a set P of n points in ℝd, we develop two dynamic data structures to support the following operations. (1) Simplex insertion: Insert a simplex into S. (2) Simplex deletion: Delete a simplex from S. (3) Simplicial thickness query: Given a query simplex σ, compute the minimum simplicial thickness among all points in σ∩P. The first data structure is constructed in O(n1+δ) time, for any constant δ > 0, and can support each operation in O(n1-1/d) time; the second one is con-structed in O(n n) time and can support each operation in O(n1-1/d ( n)O(1)) time. Both data structures use O(n). space. These data structures may find other applications as well. [ABSTRACT FROM AUTHOR]

logical Kronecker delta reformulation of the absolute value function and the related discrete problem of the optimal absolute deviation are studied as the basic step towards applications of first order norms in theoretical chemistry. Absolute value function derivatives appear in the present context related to unit step function, Dirac delta function and its derivatives. The absolute value of the difference of two Minkowski normalized Gaussian functions is analyzed as an example. The proposed logical Kronecker delta deconstruction manner to express the absolute value function is also applied to the absolute deviation from the median of a set of numerical values, which looks to be just the optimal first order norm. [ABSTRACT FROM AUTHOR]

Abstract: An analytic solution for an elastic layer under suddenly applied or pulse, torsional, ring-shaped, surface displacement is derived. The solution is based on application of double (Laplace–Hankel) integral transforms on governing equations and boundary conditions of elastic medium in the domain of time and space respectively. A transfer matrix is obtained correlating the Laplace–Hankel transformed displacements and stresses for two arbitrary planes of the elastic layer. Analytical inversion of Laplace transform is achieved leading to an exact solution for the displacements’ field on each plane. [Copyright &y& Elsevier]

Quasicontinuity with respect to one coordinate and symmetrical quasicontinuity strengthen the concept of classical quasicontinuity of a bivariate function f from a product space X x Y into a topological space Z. For certain spaces X, Y, we show that a function f from X x Y into a metric space Z is quasicontinuous with respect to the first coordinate if and only if it is the uniform limit of step functions quasicontinuous with respect to the first coordinate. This applies in particular to arbitrary X ⊆ ℝm, m ≥ 0, and every Y ⊆ ℝn , n ≥ 1, without isolated points. A second result concerns spaces X,Y such that every continuous f : X x Y → Z is the uniform limit of symmetrically quasicontinuous step functions. It comprises all X, Y ⊆ ℝ without isolated points. [ABSTRACT FROM AUTHOR]

In Predescu et al. 2002, the authors present a model for the interaction between the number of mosquito breeding sites in a community and that community's "level of consciousness" of the environmental problem. We build upon this concept here by generalizing the model and incorporating a threshold relationship between the environmental hazard, [image omitted] , and community response, [image omitted] ; the hazard must exceed a critical level ω before a community intervenes.[image omitted] The model exhibits three different regimes of behavior as a function of the parameters: a zero-consciousness equilibrium, a positive consciousness (and low hazard) regime, and an oscillatory intermediate regime. This paper establishes global and local stability results, characterizations of trajectories and invariant regions of phase space for each of the regimes, and presents a complete characterization of the behavior of the special case in which community awareness increases at a constant rate once the threshold is reached. [ABSTRACT FROM AUTHOR]

Abstract: The steep sigmoid framework developed by Plahte and Kjøglum [Plahte, E., Kjøglum, S., 2005. Analysis and generic properties of gene regulatory networks with graded response functions. Phys. D 201, 150–176, doi:10.1016/j.physd.2004.11.014] provides a uniform description of gene regulatory networks in which there may be both graded and binary transcriptional responses, as well as a method for analysing the models developed. Here we extend this framework. We show that there is a relation between the location of steady states and the feedback structure of a system, thus generalising existing results for Boolean type models. In addition, we justify underlying assumptions and generic features of the modelling framework in terms of biology and generalise the overall approach to take into account that each transcription factor only regulates one gene at a given threshold. By this assumption, the analysis of the models are greatly simplified. [Copyright &y& Elsevier]

The pressure-volume-temperature (pVT) relations for intermolecular interactions described by a repulsive step-function are obtained by molecular dynamics (MD) and Monte Carlo (MC) simulations. The system is modeled as a cubic unit cell with periodic boundary condition, where the unit cell contains 108 molecules. The pressure is obtained by the virial equation, and the phase diagram is estimated by Maxwell construction. The self-diffusion coefficients are calculated by MD simulation and used to assign phases as solid or fluid. High- and low-density solid and fluid phases are identified at low temperatures, and negative expansion is observed in the fluid phase near the low-density solid. [ABSTRACT FROM AUTHOR]

Given two topological spaces X and Y and a family 풪* of subsets of X, a function f : X → Y is called 풪*-continuous if f-1 (V ) ∈ 풪* for every open set V ⊆ Y . An 풪*-step function is meant to be a function 훗 : X → Y that is piecewise constant on a partition of X into sets from 풪*. Using some technical assumptions on X, Y , and 풪* we give representations of 풪*-continuous functions as uniform limits of 풪*-step functions. We deal in particular with α-continuous, nearly continuous, almost quasi-continuous, and somewhat continuous functions. The paper is motivated by a corresponding characterization of quasi-continuous functions. [ABSTRACT FROM AUTHOR]

In the modeling of modulated or composite structures, crenel functions proved to be very efficient on many occasions. After a brief summary on the theory and practice of crenel functions, illustrations are provided from both modulated and composite structures. An example is also given where the use of crenel function, although apparently applicable, is not appropriate. [ABSTRACT FROM AUTHOR]

In any X- or γ-ray spectrometry measurement, the approximation of the continuum background is important, because it influences strongly the net area values and the associated uncertainties of the total absorption peaks and consequently, the activity determination.Two mathematical methods to describe the background under the peaks have been tested: the first one uses a step function, and the second one—orthogonal polynomials. Both methods were applied to different spectral regions having multiple peaks. The results obtained from this work and the main conclusions are presented here. [Copyright &y& Elsevier]

We consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship, while the variance of the observations depends on their mean. This model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints. The basic statistical problem consists of identification of the number of changepoints, their locations and the levels the function assumes in between. We embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model; for the choice of the number of changepoints, we discuss a modified Schwarz criterion. A dynamic programming algorithm makes the segmentation feasible for sequences of moderate length. The performance of the segmentation method is demonstrated in an application to the segmentation of the Bacteriophage λ sequence. [ABSTRACT FROM PUBLISHER]

The function space plays an indispensable role in investigating the Cartesian closedness of categories of domains. This paper focuses on the quasicontinuity and topological properties of the function spaces associated with quasicontinuous domains. For any quasicontinuous domain P with property M ⁎ and bounded complete algebraic domain X , it is shown that: (i) the function space [ X → P ] is a quasicontinuous domain; especially, a counterexample is given to illustrate that property M ⁎ is necessary for the quasicontinuity of the function space; (ii) the Isbell topology and Scott topology are equal in the function space [ X → P ]. [ABSTRACT FROM AUTHOR]

Politeness, both as a form of respect and as a protocol, is as important in the virtual world as in the physical. [ABSTRACT FROM PUBLISHER]

Rapid change is dangerous socially and professionally. [ABSTRACT FROM PUBLISHER]