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Habitat‐selection analyses are often used to link environmental covariates, measured within some spatial domain of assumed availability, to animal location data that are assumed to be independent. Step‐selection functions (SSFs) relax this independence assumption, by using a conditional model that explicitly acknowledges the spatiotemporal dynamics of the availability domain and hence the temporal dependence among successive locations. However, it is not clear how to produce an SSF‐based map of the expected utilization distribution. Here, we used SSFs to analyze virtual animal movement data generated at a fine spatiotemporal scale and then rarefied to emulate realistic telemetry data. We then compared two different approaches for generating maps from the estimated regression coefficients. First, we considered a naïve approach that used the coefficients as if they were obtained by fitting an unconditional model. Second, we explored a simulation‐based approach, where maps were generated using stochastic simulations of the parameterized step‐selection process. We found that the simulation‐based approach always outperformed the naïve mapping approach and that the latter overestimated home‐range size and underestimated local space‐use variability. Differences between the approaches were greatest for complex landscapes and high sampling rates, suggesting that the simulation‐based approach, despite its added complexity, is likely to offer significant advantages when applying SSFs to real data.

Popular frameworks for studying habitat selection include resource‐selection functions (RSFs) and step‐selection functions (SSFs), estimated using logistic and conditional logistic regression, respectively. Both frameworks compare environmental covariates associated with locations animals visit with environmental covariates at a set of locations assumed available to the animals. Conceptually, slopes that vary by individual, that is, random coefficient models, could be used to accommodate inter‐individual heterogeneity with either approach. While fitting such models for RSFs is possible with standard software for generalized linear mixed‐effects models (GLMMs), straightforward and efficient one‐step procedures for fitting SSFs with random coefficients are currently lacking. To close this gap, we take advantage of the fact that the conditional logistic regression model (i.e. the SSF) is likelihood‐equivalent to a Poisson model with stratum‐specific fixed intercepts. By interpreting the intercepts as a random effect with a large (fixed) variance, inference for random‐slope models becomes feasible with standard Bayesian techniques, or with frequentist methods that allow one to fix the variance of a random effect. We compare this approach to other commonly applied alternatives, including models without random slopes and mixed conditional regression models fit using a two‐step algorithm. Using data from mountain goats (Oreamnos americanus) and Eurasian otters (Lutra lutra), we illustrate that our models lead to valid and feasible inference. In addition, we conduct a simulation study to compare different estimation approaches for SSFs and to demonstrate the importance of including individual‐specific slopes when estimating individual‐ and population‐level habitat‐selection parameters. By providing coded examples using integrated nested Laplace approximations (INLA) and Template Model Builder (TMB) for Bayesian and frequentist analysis via the R packages R‐INLA and glmmTMB, we hope to make efficient estimation of RSFs and SSFs with random effects accessible to anyone in the field. SSFs with individual‐specific coefficients are particularly attractive since they can provide insights into movement and habitat‐selection processes at fine‐spatial and temporal scales, but these models had previously been very challenging to fit. The authors provide a coherent framework for fitting resource‐selection functions (RSFs) and step‐selection functions (SSFs) with random effects. To allow fitting of SSFs, the authors reformulate the conditional logistic regression model as a (likelihood‐equivalent) Poisson model, where stratum‐specific intercepts are included as a random effect with a fixed large prior variance.

We present a methodology for multiple regression analysis that deals with categorical variables (possibly mixed with continuous ones), in combination with regularization, variable selection and high-dimensional data (𝑃 ≫ 𝑁). Regularization and optimal scaling (OS) are two important extensions of ordinary least squares regression (OLS) that will be combined in this paper. There are two data analytic situations for which optimal scaling was developed. One is the analysis of categorical data, and the other the need for transformations because of nonlinear relationships between predictors and outcome. Optimal scaling of categorical data finds quantifications for the categories, both for the predictors and for the outcome variables, that are optimal for the regression model in the sense that they maximize the multiple correlation. When nonlinear relationships exist, nonlinear transformation of predictors and outcome maximize the multiple correlation in the same way. We will consider a variety of transformation types; typically we use step functions for categorical variables, and smooth (spline) functions for continuous variables. Both types of functions can be restricted to be monotonic, preserving the ordinal information in the data. In combination with optimal scaling, three popular regularization methods will be considered: Ridge regression, the Lasso and the Elastic Net. The resulting method will be called ROS Regression (Regularized Optimal Scaling Regression). The OS algorithm provides straightforward and efficient estimation of the regularized regression coefficients, automatically gives the Group Lasso and Blockwise Sparse Regression, and extends them by the possibility to maintain ordinal properties in the data. Extended examples are provided.

The energy charging of quantum battery is analysed by open quantum approach. The modelled of the charger and battery are described by harmonic oscillator model. We choose this model because the harmonic oscillator battery gives the largest maximum energy albeit having the longest maximum time. In this paper, the interaction as actual quantum system whose dynamic is determined by Lindblad Master Equation in terms of constant is a step function to set the time when energy flow and what time that energy stop to flow or the interaction between charger and battery has stopped. The energy equation was determined by solving the master equation with second order differential equation to find the first momenta from charger and battery. Based on the equation, the energy of charger will not be zero which mean after interaction in several times, the charger will not one hundred percent lose its energy when the energy storage in battery already done.

In this paper, the author obtains an analytical exact form of the Unit Step Function (or Heaviside Step Function) which evidently constitutes a fundamental concept of Operational Calculus. This important function is also involved in many other fields of applied and engineering mathematics. Heaviside step function is performed here in a very simple manner, using a finite number of standard operations. In particular it is expressed as the summation of six inverse tangent functions. The novelty of this work when compared with other analytical representations, is that the proposed exact formula contains two arbitrary single-valued continuous functions which satisfy only one restriction. In addition, the proposed explicit representation is not exhibited in terms of miscellaneous special functions, e.g. Bessel functions, Error function, Beta function etc. and also are neither the limit of a function, nor the limit of a sequence of functions with point-wise or uniform convergence. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into Operational Calculus techniques and other engineering practices.

Workflows orchestrate a collection of computing tasks to form a complex workflow logic. Different from the traditional monolithic workflow management systems, modern workflow systems often manifest high throughput, concurrency and scalability. As service-based systems, execution time monitoring is an important part of maintaining the performance for those systems. We developed a trace profiling approach that leverages quantitative verification (also known as probabilistic model checking) to analyse complex time metrics for workflow traces. The strength of probabilistic model checking lies in the ability of expressing various temporal properties for a stochastic system model and performing automated quantitative verification. We employ semi-Makrov chains (SMCs) as the formal model and consider the first passage times (FPT) measures in the SMCs. Our approach maintains simple mergeable data summaries of the workflow executions and computes the moment parameters for FPT efficiently. We describe an application of our approach to AWS Step Functions, a notable workflow web service. An empirical evaluation shows that our approach is efficient for computer high-order FPT moments for sizeable workflows in practice. It can compute up to the fourth moment for a large workflow model with 10,000 states within 70 s.

Advances in tracking technology have led to an exponential increase in animal location data, greatly enhancing our ability to address interesting questions in movement ecology, but also presenting new challenges related to data management and analysis. Step‐selection functions (SSFs) are commonly used to link environmental covariates to animal location data collected at fine temporal resolution. SSFs are estimated by comparing observed steps connecting successive animal locations to random steps, using a likelihood equivalent of a Cox proportional hazards model. By using common statistical distributions to model step length and turn angle distributions, and including habitat‐ and movement‐related covariates (functions of distances between points, angular deviations), it is possible to make inference regarding habitat selection and movement processes or to control one process while investigating the other. The fitted model can also be used to estimate utilization distributions and mechanistic home ranges. Here, we present the R package amt (animal movement tools) that allows users to fit SSFs to data and to simulate space use of animals from fitted models. The amt package also provides tools for managing telemetry data. Using fisher (Pekania pennanti) data as a case study, we illustrate a four‐step approach to the analysis of animal movement data, consisting of data management, exploratory data analysis, fitting of models, and simulating from fitted models. New tracking technologies allow users to collect large amount of data and address entirely new questions. The amt (animal movement tools) R package provides tools to manage telemetry data and to fit step‐selection functions and resource‐selection functions.

An analytical solution has been developed developed in this research for electro-mechanical flexural response of smart laminated piezoelectric composite rectangular plates encompassing flexible-spring boundary conditions at two opposite edges. Flexible-spring boundary structure is introduced to the system by inclusion of rotational springs of adjustable stiffness which can vary depending on changes in the rotational fixity factor of the springs. To add to the case study complexity, the two other edges are kept free. Three advantages of employing the proposed analytical method include: (1) the electro-mechanical flexural coupling between the piezoelectric actuators and the plate’s rotational springs of adjustable stiffness is addressed; (2) there is no need for trial deformation and characteristic function—therefore, it has higher accuracy than conventional semi-inverse methods; (3) there is no restriction imposed to the position, type, and number of applied loads. The Linear Theory of Piezoelectricity and Classical Plate Theory are adopted to derive the exact elasticity equation. The higher-order Fourier integral and higher-order unit step function differential equations are combined to derive the analytical equations. The analytical results are validated against those obtained from Abaqus Finite Element (FE) package. The results comparison showed good agreement. The proposed smart plates can potentially be applied to real-life structural systems such as smart floors and bridges and the proposed analytical solution can be used to analyze the flexural deformation response.

A numerical collocation method is developed for solving nonlinear Volterra integro-differential equations (VIDBs) of the neutral type, as well as other non-standard and classical VIDEs. A sigmoidal functions approximation is used to suitably represent the solutions. Special computational advantages are obtained using unit step functions, and important applications can also be obtained by using other sigmoidal functions, such as logistic and Gompertz functions. The method allows one to obtain a simultaneous approximation of the solution to a given VIDE and its first derivative, by means of an explicit formula. A priori as well as a posteriori estimates are derived for the numerical errors, and numerical examples are given for the purpose of illustration. A comparison is made with the classical piecewise polynomial collocation method as for accuracy and CPU time.

The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics.