Deterministic Set Research Articles

A dynamical system to model land use interactions by using population dynamics: application on vulnerable grasslands

We introduce a deterministic set of equations, the Lotka–Volterra (LV) generalized equations, to explain or predict the temporal dynamics and competition between land use and land cover (LULC) classes. We evaluated this new approach in two regions of Uruguay where human activities have reduced natural grasslands. We infer the interaction coefficients from the LV model through the pairwise maximum entropy method using the spatial covariance matrices obtained from annual remote-sensing LULC maps. The model performed well in predicting short-term temporal changes, with errors similar to those obtained using traditional Markov chains. This model introduces a novel avenue for assisting LULC modelling in improving the temporal dynamics.

Safety-Based Speed Control of a Wheelchair Using Robust Adaptive Model Predictive Control.

Electric-powered wheelchairs play a vital role in ensuring accessibility for individuals with mobility impairments. The design of controllers for tracking tasks must prioritize the safety of wheelchair operation across various scenarios and for a diverse range of users. In this study, we propose a safety-oriented speed tracking control algorithm for wheelchair systems that accounts for external disturbances and uncertain parameters at the dynamic level. We employ a set-membership approach to estimate uncertain parameters online in deterministic sets. Additionally, we present a model predictive control scheme with real-time adaptation of the system model and controller parameters to ensure safety-related constraint satisfaction during the tracking process. This proposed controller effectively guides the wheelchair speed toward the desired reference while maintaining safety constraints. In cases where the reference is inadmissible and violates constraints, the controller can navigate the system to the vicinity of the nearest admissible reference. The efficiency of the proposed control scheme is demonstrated through high-fidelity speed tracking results from two tasks involving both admissible and inadmissible references.

The Nonsingular Estimator for Exoplanet Orbits: An Unscented Batch Estimation Method for Direct Imaging Measurements

We present a new method for fitting exoplanet orbits to direct astrometric measurements, using nonlinear batch estimation and nonsingular orbital elements. Our estimation technique is based on the unscented transform, which approximates probability distributions using finite, deterministic sets of weighted sample points. Furthermore, we use Gaussian mixtures to account for the strong nonlinearities in the measurement model. As a fitting basis, we use a set of orbital elements developed specifically for directly observed exoplanets, combining features of the Thiele–Innes constants and the Cohen–Hubbard nonsingular elements. We validate the new method using simulated exoplanet orbits, and we demonstrate its use with real exoplanet data. Compared to state-of-the-art Markov Chain Monte Carlo and Bayesian rejection sampling techniques, the new method is found to give orbit estimates of comparable or higher accuracy but with much faster execution.

Weak-Type (1,1) Inequality for Discrete Maximal Functions and Pointwise Ergodic Theorems Along Thin Arithmetic Sets

We establish weak-type (1, 1) bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets B. As a corollary we obtain the corresponding pointwise convergence result on L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document}. This contributes yet another counterexample for the conjecture of Rosenblatt and Wierdl from 1991 asserting the failure of pointwise convergence on L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^1$$\\end{document} of ergodic averages along arithmetic sets with zero Banach density. The second main result is a multiparameter pointwise ergodic theorem in the spirit of Dunford and Zygmund along B on Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document}, p>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p>1$$\\end{document}, which is derived by establishing uniform oscillation estimates and certain vector-valued maximal estimates.

Evaluation of technological tendencies in the carbon capture process: a review.

This paper evaluates the technological trends in the carbon sequestration process. For this purpose, these systems have been classified into two subsystems: conventional technologies subsystem and emerging technologies subsystem. Each is explored for its suitability for meeting a set of six attributes. A bibliometric analysis process was developed using the Scopus database and VOSviewer Software to present the potential of each subsystem evaluated, through an evaluation matrix. The analysis of the subsystems and attributes was performed through the formal concept analysis methodology (8FCA). To facilitate the processing of the information, the open access software concept Explorer was used. The analysis shows that conventional technologies, despite their cost, will be maintained and advance in their implementation process. The bibliometric analysis integrated with the applied FCA methodology has proven to be useful for the evaluation of technological typologies and serves as an alternative to develop theoretical studies that group and link different options as a model to evaluate a deterministic set of attributes.

Concentrating Solar Power Systems: a review of their applicability in Colombia

This paper evaluates the applicability of centralized concentrating solar power systems in Colombia. For this purpose, these systems have been classified into four subsystems: parabolic trough, linear Fresnel, parabolic dish and tower. Each is explored for its suitability by meeting a set of six attributes. A bibliometric analysis process was developed using the Scopus database and the VOSviewer software to present the potential of each subsystem evaluated through an evaluation matrix. The analysis of the subsystems and attributes was carried out through the formal concept analysis methodology 8FCA). To facilitate data processing, the open access software concept Explorer is implemented. The analysis shows that parabolic trough technology is more widely used worldwide than the other three technologies evaluated, and its maturity makes it possible to plan centralized and decentralized projects in developing countries. The bibliometric analysis integrated with the applied FCA methodology has proven to be useful for the evaluation of technological typologies and serves as an alternative to develop theoretical studies that group and link different options as a model to evaluate a deterministic set of attributes.

Evaluation of the anaerobic digestion process for low and micro-scale biogas production: a review

A theoretical analysis of biogas production technologies classified in two subgroups; low and micro scale, was carried out using the methodology of formal concept analysis (FCA) together with the VOSviewer and Conception Explorer tools for information processing, a series of attributes that each subsystem must comply with in terms of the sustainability of each technology were analyzed. The information selected for the development of the analysis required a quality study, based on the percentile of the journals in which the manuscript was published. The search for information was carried out in web sites such as: Scopus, Web Of Science, Dimensions and Lens among others. In total, 105 sources of academic information were analyzed, selecting 56 articles and 18 book chapters for the development of the work. In conclusion, it can be affirmed that low-scale biogas plants present more favorable characteristics than micro-scale plants; however, both technologies have a high potential for application worldwide in isolated or rural areas, supplying electric or thermal energy to less favored communities. Finally, it is important to point out that the methodology developed has proven to be a relevant tool for the classification of information and serves as a first step to group and relate search concepts by means of a deterministic set of attributes.

Grid entropy in last passage percolation — A superadditive critical exponent approach

Working in the setting of i.i.d. last-passage percolation on RD with no assumptions on the underlying edge-weight distribution, we arrive at the notion of grid entropy — a Subadditive Ergodic Theorem limit of the entropies of paths with empirical measures weakly converging to a given target, or equivalently a deterministic critical exponent of canonical order statistics associated with the Levy-Prokhorov metric. This provides a fresh approach to an entropy first developed by Rassoul-Agha and Seppäläinen as a large deviation rate function of empirical measures along paths. In their 2014 paper, variational formulas are developed for the point-to-point/point-to-level Gibbs Free Energies as the convex conjugates of this entropy. We rework these formulas in our new framework and explicitly link our descriptions of grid entropy to theirs. We also improve on a known bound for this entropy by introducing a relative entropy term in the inequality. Furthermore, we show that the set of measures with finite grid entropy coincides with the deterministic set of limit points of empirical measures studied in a 2020 paper by Bates. We partially answer a directed polymer version of a question of Hoffman which was previously tackled in the zero temperature case by Bates.

Effects of real random perturbations on Monod and Haldane consumption functions in the chemostat model

In this paper, we investigate the classical chemostat model where the consumption function of the species, in both cases Monod and Haldane, is perturbed by real random fluctuations. Once the existence and uniqueness of non-negative global solution of the corresponding random systems is ensured, we prove the existence of a deterministic compact attracting set, whence we are able to find conditions to guarantee either the extinction or the persistence of the species, the most important aim in real applications. In addition, we depict several numerical simulations to illustrate the theoretical framework, standing out our contributions, providing the biological interpretation of every result and comparing with similar works in the literature.

Existence and Internal Structure of the Deterministic Attracting Set for a Random Ant Colonies Model

This paper is concerned with the attracting set of an ant colonies model with bounded noisy perturbation. This perturbation is modeled by the well-known Ornstein–Uhlenbeck process and the arc tangent function. For the random model, we first verify the existence and uniqueness of the global positive solution, and then prove the existence of the deterministic attracting set. Furthermore, in order to reveal more detailed information about the long-time behavior of the ant colonies system, we analyze the internal structure of the attracting set and provide some conditions under which coexistence (or extinction) of the ant species exists in the ant colonies system.

A Comparative Analysis of the Response-Tracking Techniques in Aerospace Dynamic Systems Using Modal Participation Factors

Mechanical structural systems are subject to multiple dynamic disturbances during service. While several possible scenarios can be examined to determine their design loading conditions, only a relatively small set of such scenarios is considered critical. Therefore, only such particular deterministic set of critical load cases is commonly employed for the structural design and optimization. Nevertheless, during the design and optimization stages, the mass and stiffness distributions of such assemblies vary, and, in consequence, their dynamic response also varies. Thus, it is important to consider the variations in the dynamic loading conditions during the design-and-optimization cycles. This paper studies the modal participation factors at length and proposes an alternative to the current point-wise treatment of the dynamic equations of motion of flexible bodies during design optimization. First, the most relevant-to-structural-dynamics definitions available in the literature are reviewed in depth. Second, the analysis of those definitions that have the potential to be adopted as point-wise constraint equations during structural optimization is extended. Finally, a proof of concept is presented to demonstrate the usability of each definition, followed by a case study in which the potential advantages of the proposed extended analysis are shown.

From oracle generalization bound toward empirical inequality

Learning guarantees are tools for analyzing the performance of statistical learning problems. Most of the existing guarantees are oracle generalization bounds and are proper for theoretical analysis, and they cannot be used directly for various applications. The upper bound on the empirical excess risk is more useful in practice since it is obtained based on the observed data. Therefore, getting a learning guarantee on the empirical process is helpful in practice. In this paper, under the Bernstein condition, we propose a novel approach that uses any oracle generalization bound to calculate an upper bound on the empirical excess risk of the empirical risk minimization (ERM) predictor with the fast convergence rate (O(1n)). Using a tighter general bound, our approach obtains a tighter bound on the empirical excess risk. We show that the proposed empirical excess risk bound is tighter compared to the best in the literature. Using this upper bound, we get a deterministic and known set of predictors such that with a high probability contains the minimum risk predictor. This set can be used in the algorithm design.

Fast and deterministic (3+1)DOF point set registration with gravity prior

Point set registration is the technology used to estimate the spatial transformation between two LiDAR scans, which is challenging in the presence of outlier correspondences and noise. Our focus is on 4 degrees of freedom (DOF) point set registration, in which 1DOF rotation and 3DOF translation need to be estimated. It is commonly found in practical scenarios, such as arbitrarily mobile robots equipped with an inertial measurement unit (IMU), terrestrial LiDAR scanners, or planar moving vehicles in urban environments. Recently, many solutions have leveraged branch and bound (BnB) in global and deterministic approaches to solve the registration problem with performance guarantees. However, BnB-based methods are usually time-consuming since their convergence speed is exponential to the dimensionality of the solution domain, and existing methods estimate these 4DOF simultaneously. Our key idea is to speed up BnB-based methods by decoupling the joint pose into separate translation and rotation with the aid of known gravity directions. This effectively reduces the search domain to 3DOF+1DOF, thereby enhancing algorithm efficiency. Specifically, we propose a novel BnB-based consensus maximization method for a fast 3DOF translation search and derive the specific lower and upper bound functions. We then propose an efficient global voting method for estimating the rotation with 1DOF. To demonstrate the superiority of our proposed method, we conduct extensive experiments on both synthetic and real-world datasets. The experimental results show that (1) our proposed method is more robust against outliers and noise than several existing methods and far faster than the existing BnB-based 4DOF method by almost an order of magnitude, (2) our proposed method is robust against the biases in gravity directions, such that the general error of the IMU is acceptable, and (3) thanks to its significant robustness, our proposed method can solve the challenging problem of simultaneous pose and correspondence registration (SPCR). Moreover, the proposed approach is also more robust and accurate than several SPCR benchmark methods. Code is available at https://github.com/Xinyi-tum/Fast-and-Deterministic-Registration.

A New Static Compaction of Deterministic Test Sets

Test set compaction is one of the key steps of the postproduction test known to bring down test pattern counts. This, in turn, allows one to reduce the corresponding test data volume, test application time, and hence the cost of testing. This article presents a method that strives to reduce the number of automatic test pattern generation (ATPG)-produced deterministic test patterns to deliver compact test sets. In principle, the new scheme works with a meaningful representation of test patterns by using external and internal necessary assignments (NAs) to determine small groups of potentially compatible faults. These faults are subsequently retargeted by the robust satisfiability (SAT)-based ATPG that produces a single test pattern for the entire group, thus making the resultant test set smaller in size. Experimental results obtained for 12 large industrial cores and stuck-at faults confirm superiority of the proposed scheme over the state-of-the-art test set compaction techniques and are reported herein.

Strategy Adjustments for FMCG Supply Chains in Bangladesh to Counter Future Pandemic Disruptions

The Fast-Moving Consumer Goods (FMCG) industry in Bangladesh was not ready to resist the repercussions of the worldwide pandemic recently. The pandemic caused the supply chain to become disorganized. Companies must make both micro and macro adjustments to their strategy in order to adapt to the new norm and be ready for future occurrences of this nature. This research seeks to give a paradigm for creating new pandemic defense tactics. This study also examines the facets of imminent supply chain collapse and alters the existing characteristics to overcome the shortcomings. The objective is to build comprehensive guidelines that an FMCG can use to avoid the possibility of such a scenario. The study incorporates short and long-term supply chain restoration policies for material sourcing, manufacturing, and distribution. The process entails identifying the fundamental drivers that are typically affected by the disruption. The short-term proposals serve as corrective agents committed to fighting the interruption as soon as it arises. Long-term ideas, on the other hand, are a type of preventive measure that require more time to implement. However, they focus on building barriers around the brand so that external disruptions cannot impact it in the long run. Among other advantages, these recommendations will result in improved forecasting, responsiveness, real-time monitoring, and cost-effectiveness. In addition, the proposed philosophies were formulated into a Mixed-Integer Linear Programming (MILP) model. The focus of the paper is the formulation of supply chain equations involving ordering cost, holding cost, inbound and outbound transportation cost, downtime, inventory level, response time, and other pertinent aspects. It also houses pandemic and non-pandemic coordination initiatives across the organization. The incurred costs were determined using a formulated objective function and constraints. The presented model demonstrated a 36% cost reduction while maintaining supply chain integrity during disruptions using a deterministic data set. Finally, 25 industry experts were interviewed in two rounds utilizing both structured and unstructured patterns to determine the KPI scores achieved due to the execution of the proposals. The Key Performance Indicators (KPI) were evaluated following a comparison of the costs of conventional and proposed methods. According to the study, the KPI scores for procurement, manufacturing, and distribution were 90%, 86.67%, and 80.30% correspondingly. The models are 85.66% viable overall.

The relationship between the backward and forward equations of stochastic neutron transport and associated matters

The relationship between the forward and backward equations of probability balance for neutron transport are discussed and, in particular, we show the close relationship between the characteristics of the forward equation to the main equations of the backward approach. The well-known failure of the backward method to handle feedback is also noted and possible origins proposed, although this curious feature remains an open question. A comparison of the backward and forward approaches is gone into in some detail and their relative advantages and disadvantages highlighted. We illustrate the matter by the discussion of a problem of an energy burst due to a ramp insertion of reactivity. This problem leads to a transition from the stochastic region to the deterministic one and shows how the backward equation may be used in tandem with a deterministic set of equations without violating the restriction on the backward method. The problems arising from a spatially varying source are also discussed with reference to the backward equations and their undoubted superiority over the forward equations is stressed.

Robust domination in random graphs

In this paper, we study “robust” dominating sets of random graphs that retain the domination property even if a small deterministic set of edges are removed. We motivate our study by illustrating with examples from wireless networks in harsh environments. We then use the probabilistic method and martingale difference techniques to determine sufficient conditions for the asymptotic optimality of the robust domination number. We also discuss robust domination in sparse random graphs where the number of edges grows at most linearly in the number of vertices.

Optimal Design of Integrated Semi-Flexible Transit Services in Low-Demand Conditions

Semi-flexible transit (SFT) is commonly discussed as a cost-effective alternative to serving public transportation users in low-demand conditions. We hypothesize that joint optimization of service headway and slack time per trip for route deviation is essential for designing a schedule for the operation of an integrated SFT that can meet both fixed-route and paratransit demand. An integrated SFT has the potential to lower the cost of transportation for regular transit users (both operators and riders) while redirecting potential paratransit riders to less expensive transit modes; thus, reducing demand for overwhelmed paratransit services operating with limited resources. The optimization problem has three competing objectives: minimizing operator costs, minimizing user costs, and maximizing service benefits. Two state-of-the-art multi-objective evolutionary algorithms NSGA-II and SMPSO are compared to obtain the most representative deterministic Pareto optimal solution set. This study has three major contributions. First, quantile regression is used to suggest multiple slack time values for a given headway that transit planners can consider when generating a static schedule for SFT operation. Second, relationships derived to analyze cost trade-offs suggest that headway governs operator cost and is negatively correlated, user cost is positively and equally influenced by both variables, and slack time governs service benefit and is positively correlated. Third, sensitivity analysis for an integrated SFT operation reveals that low-capacity minivans and standard vans offer higher vehicle occupancy and cost efficiency, mostly economical for low to medium demand (5-20 pass/hr), low permissible deviation from the fixed route is desirable during peak hours to avoid delays for passengers on-board, and extreme weather conditions dramatically and negatively influence costs. Policy recommendations for integrated SFT implementation include a recommendation for fare structure design addressing service equity through surcharges/discounts, vehicle technology and service booking technology advancements for cost reduction, and fleet mix design through estimation of passenger loading profile. The application of the study methodology is demonstrated for a low-demand bus route in Regina, Canada.

Stochastic hydrodynamics and hydro-kinetics: Similarities and differences

The hydro-kinetic formalism has been used as a complementary approach to solving the Stochastic Differential Equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of 2-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuations in the Bjorken hydrodynamic model. For white noise, the two approaches agree. For colored Catteneo noise, which is causal, the two approaches diverge. This is because white noise only induces two-point correlations, while Catteneo noise also induces higher-order correlations. This difference is quantified from the effects of causal evolution and influence from higher-order correlations induced by the Catteneo noise.

Asymptotic Distributions of Covering and Separation Measures on the Hypersphere

We consider measures of covering and separation that are expressed through maxima and minima of distances between points of an hypersphere. We investigate the behavior of these measures when applied to a sample of independent and uniformly distributed points. In particular, we derive their asymptotic distributions when the number of points diverges. These results can be useful as a benchmark against which deterministic point sets can be evaluated. Whenever possible, we supplement the rigorous derivation of these limiting distributions with some heuristic reasonings based on extreme value theory. As a by-product, we provide a proof for a conjecture on the hole radius associated to a facet of the convex hull of points distributed on the hypersphere.