College of Sciences
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Browsing College of Sciences by Department "Mathematics"
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Item A Low Cost, Edge Computing, All-Sky Imager for Cloud Tracking and Intra-Hour Irradiance Forecasting(2017-03-23) Richardson, Walter; Krishnaswami, Hariharan; Vega, Rolando; Cervantes, MichaelWith increasing use of photovoltaic (PV) power generation by utilities and their residential customers, the need for accurate intra-hour and day-ahead solar irradiance forecasting has become critical. This paper details the development of a low cost all-sky imaging system and an intra-hour cloud motion prediction methodology that produces minutes-ahead irradiance forecasts. The SkyImager is designed around a Raspberry Pi single board computer (SBC) with a fully programmable, high resolution Pi Camera, housed in a durable all-weather enclosure. Our software is written in Python 2.7 and utilizes the open source computer vision package OpenCV. The SkyImager can be configured for different operational environments and network designs, from a standalone edge computing model to a fully integrated node in a distributed, cloud-computing based micro-grid. Preliminary results are presented using the imager on site at the National Renewable Energy Laboratory (NREL) in Golden, CO, USA during the fall of 2015 under a variety of cloud conditions.Item A Multimodal Appraisal of Zaha Hadid's Glasgow Riverside Museum—Criticism, Performance Evaluation, and Habitability(2023-01-09) Salama, Ashraf M.; Salingaros, Nikos A.; MacLean, LauraHigh-profile projects promoted by governments, local municipalities, and the media do not always meet program requirements or user expectations. The Riverside Museum in Glasgow by Zaha Hadid Architects, which has generated significant discussion in the media, is used to test this claim. A multimodal inquiry adopts three factors: criticism, performance evaluation, and habitability. Results from this method are then correlated with visual attention scans using software from 3M Corporation to map unconscious user engagement. A wide spectrum of tools is employed, including a walking tour assessment procedure, contemplation of selected settings, navigational mapping, and assessing user emotional experiences. Key aspects of the design and spatial qualities of this museum are compared with an analysis of critical writings on how the project was portrayed in the media. Further, we examine socio-spatial practices, selected behavioral phenomena, and the emotional experiences that ensue from users' interaction with the building and its immediate context. The findings suggest design shortcomings and, more worrisome, that spatial qualities relevant to users' experiences do not seem to have been met. In going beyond the usual method of analysis, we apply new techniques of eye-tracking simulations, which verify results obtained by more traditional means. An in-depth analysis suggests the need for better compatibility between the imagined design ideas and the actual spatial environments in use.Item Biometric Pilot-Studies Reveal the Arrangement and Shape of Windows on a Traditional Façade to be Implicitly "Engaging", Whereas Contemporary Façades Are Not(2020-05-18) Salingaros, Nikos A.; Sussman, AnnThe human brain evolved to implicitly approach or avoid objects in its surroundings. Requisite for survival, this behavior happens without conscious awareness or control, honed over 60 million years of primate evolution. Biometric technologies, including eye tracking, reveal these unconscious behaviors at work and allow us to predict the initial response of a design experience. This paper shows how a biometric tool, 3M-VAS (Visual Attention Software), can be effectively used in architecture. This tool aggregates 30 years of eye-tracking data, and is commonly applied in website and signage design. A pilot-study uses simplified drawings of building elevations to show 3M-VAS's predictive power in revealing implicit human responses of engagement and disengagement to buildings. The implications on the impact of a structure in creating the public realm suggest recommendations for approving new architecture.Item Boundary-Value Problem for Nonlinear Fractional Differential Equations of Variable Order with Finite Delay via Kuratowski Measure of Noncompactness(2023-01-12) Telli, Benoumran; Souid, Mohammed Said; Stamova, IvankaThis paper is devoted to boundary-value problems for Riemann–Liouville-type fractional differential equations of variable order involving finite delays. The existence of solutions is first studied using a Darbo's fixed-point theorem and the Kuratowski measure of noncompactness. Secondly, the Ulam–Hyers stability criteria are examined. All of the results in this study are established with the help of generalized intervals and piecewise constant functions. We convert the Riemann–Liouville fractional variable-order problem to equivalent standard Riemann–Liouville problems of fractional-constant orders. Finally, two examples are constructed to illustrate the validity of the observed results.Item Computational Mathematics and Neural Systems(2021-04-01) Tomasiello, Stefania; Pinto, Carla M.A.; Stamova, IvankaThis special issue was conceived to explore the latest advancements in the field of computational techniques for solving forward and inverse problems [...]Item Deep Learning to Forecast Solar Irradiance Using a Six-Month UTSA SkyImager Dataset(2018-07-31) Moncada, Ariana; Richardson, Walter; Vega-Avila, RolandoDistributed PV power generation necessitates both intra-hour and day-ahead forecasting of solar irradiance. The UTSA SkyImager is an inexpensive all-sky imaging system built using a Raspberry Pi computer with camera. Reconfigurable for different operational environments, it has been deployed at the National Renewable Energy Laboratory (NREL), Joint Base San Antonio, and two locations in the Canary Islands. The original design used optical flow to extrapolate cloud positions, followed by ray-tracing to predict shadow locations on solar panels. The latter problem is mathematically ill-posed. This paper details an alternative strategy that uses artificial intelligence (AI) to forecast irradiance directly from an extracted subimage surrounding the sun. Several different AI models are compared including Deep Learning and Gradient Boosted Trees. Results and error metrics are presented for a total of 147 days of NREL data collected during the period from October 2015 to May 2016.Item Defense against Adversarial Swarms with Parameter Uncertainty(2022-06-24) Walton, Claire; Kaminer, Isaac; Gong, Qi; Clark, Abram H.; Tsatsanifos, TheodorosThis paper addresses the problem of optimal defense of a high-value unit (HVU) against a large-scale swarm attack. We discuss multiple models for intra-swarm cooperation strategies and provide a framework for combining these cooperative models with HVU tracking and adversarial interaction forces. We show that the problem of defending against a swarm attack can be cast in the framework of uncertain parameter optimal control. We discuss numerical solution methods, then derive a consistency result for the dual problem of this framework, providing a tool for verifying computational results. We also show that the dual conditions can be computed numerically, providing further computational utility. Finally, we apply these numerical results to derive optimal defender strategies against a 100-agent swarm attack.Item Design and Practical Stability of a New Class of Impulsive Fractional-Like Neural Networks(2020-03-15) Stamov, Gani; Stamova, Ivanka; Martynyuk, Anatoliy; Stamov, TrayanIn this paper, a new class of impulsive neural networks with fractional-like derivatives is defined, and the practical stability properties of the solutions are investigated. The stability analysis exploits a new type of Lyapunov-like functions and their derivatives. Furthermore, the obtained results are applied to a bidirectional associative memory (BAM) neural network model with fractional-like derivatives. Some new results for the introduced neural network models with uncertain values of the parameters are also obtained.Item Experiences in Delivering Online CS Teacher Professional Development(Association for Computing Machinery, 2024-03-07) Wilde, Jina; Beltran, Emiliano; Zawatski, Michael J.; Fernandez, Amanda S.; Prasad, Priya V.; Yuen, Timothy T.This paper describes our team's experience in designing and delivering the online teacher professional development (PD) program, Computer Science for San Antonio (CS4SA), aimed at empowering educators with computer science (CS) knowledge to increase Latinx participation in CS and STEM education within a large, urban predominantly Latinx school district in South Texas. This paper highlights the successes, challenges, and lessons learned while facilitating two cohorts of the CS PD through online platforms during the COVID-19 pandemic. As a result of this program, participants recognized the importance of integrating CS into their classroom and becoming advocates for the discipline at the high school level. Additionally, teachers, investigators, and other personnel learned important lessons for enhancing the program's impact through collaboration with district administrators and refinement of the online learning experience.Item Extended Stability and Control Strategies for Impulsive and Fractional Neural Networks: A Review of the Recent Results(2023-03-27) Stamov, Gani; Stamova, IvankaIn recent years, cellular neural networks (CNNs) have become a popular apparatus for simulations in neuroscience, biology, medicine, computer sciences and engineering. In order to create more adequate models, researchers have considered memory effects, reaction–diffusion structures, impulsive perturbations, uncertain terms and fractional-order dynamics. The design, cellular aspects, functioning and behavioral aspects of such CNN models depend on efficient stability and control strategies. In many practical cases, the classical stability approaches are useless. Recently, in a series of papers, we have proposed several extended stability and control concepts that are more appropriate from the applied point of view. This paper is an overview of our main results and focuses on extended stability and control notions including practical stability, stability with respect to sets and manifolds and Lipschitz stability. We outline the recent progress in the stability and control methods and provide diverse mechanisms that can be used by the researchers in the field. The proposed stability techniques are presented through several types of impulsive and fractional-order CNN models. Examples are elaborated to demonstrate the feasibility of different technologies.Item Formulation of Impulsive Ecological Systems Using the Conformable Calculus Approach: Qualitative Analysis(2023-05-09) Martynyuk, Anatoliy; Stamov, Gani; Stamova, Ivanka; Gospodinova, EkaterinaIn this paper, an impulsive conformable fractional Lotka–Volterra model with dispersion is introduced. Since the concept of conformable derivatives avoids some limitations of the classical fractional-order derivatives, it is more suitable for applied problems. The impulsive control approach which is common for population dynamics' models is applied and fixed moments impulsive perturbations are considered. The combined concept of practical stability with respect to manifolds is adapted to the introduced model. Sufficient conditions for boundedness and generalized practical stability of the solutions are obtained by using an analogue of the Lyapunov function method. The uncertain case is also studied. Examples are given to demonstrate the effectiveness of the established results.Item Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior(2020-08-31) Tuladhar, Rohisha; Santamaria, Fidel; Stamova, IvankaWe present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n−species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.Item Fractional-Order Impulsive Delayed Reaction-Diffusion Gene Regulatory Networks: Almost Periodic Solutions(2023-05-03) Stamov, Trayan; Stamov, Gani; Stamova, IvankaThe paper is oriented on the existence of almost periodic solutions of factional-order impulsive delayed reaction-diffusion gene regulatory networks. Caputo type fractional-order derivatives and impulsive disturbances at not fixed instants of time are considered. New almost periodic and perfect Mittag–Leffler stability criteria are proposed. Lyapunov's like impulsive functions, the properties of the fractional derivatives and comparison principle are the main tools in the investigation. Illustrative examples are also presented to demonstrate the proposed criteria. Our results contribute to the development of qualitative the theory of fractional-order gene regulatory networks.Item Global Stability of Integral Manifolds for Reaction–Diffusion Delayed Neural Networks of Cohen–Grossberg-Type under Variable Impulsive Perturbations(2020-07-03) Stamov, Gani; Stamova, Ivanka; Venkov, George; Stamov, Trayan; Spirova, CvetelinaThe present paper introduces the concept of integral manifolds for a class of delayed impulsive neural networks of Cohen–Grossberg-type with reaction–diffusion terms. We establish new existence and boundedness results for general types of integral manifolds with respect to the system under consideration. Based on the Lyapunov functions technique and Poincare`-type inequality some new global stability criteria are also proposed in our research. In addition, we consider the case when the impulsive jumps are not realized at fixed instants. Instead, we investigate a system under variable impulsive perturbations. Finally, examples are given to demonstrate the efficiency and applicability of the obtained results.Item Homogenization of Boundary Layers in the Boltzmann--Poisson System(Society for Industrial and Applied Mathematics, 2021) Heitzinger, Clemens; Morales Escalante, José A.We homogenize the Boltzmann--Poisson system where the background medium is given by a periodic permittivity and a periodic charge concentration. The domain is the half-space with a periodic charge concentration on the boundary. Hence the domain consists of cells in R3 that are periodically repeated in two dimensions and unbounded in the third dimension. We obtain formal results for this homogenization problem. We prove the existence and uniqueness of the solution of the Laplace and Poisson problems in the fast variables with periodic and surface charge boundary conditions generating an electric field at infinity, obtaining formal solutions for the potential in terms of Magnus expansions for the case where the diagonal permittivity matrix depends on the vertical fast variable. Further on, splitting the potential into a stationary part and a self-consistent part, performing the two-scale homogenization expansions for the Poisson and the Boltzmann equations, and applying a solvability condition, we arrive at the drift-diffusion equations for the boundary-layer problem.Item Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds(2019-10-31) Stamov, Gani; Stamova, IvankaIn this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wide range of biological and chemical processes.Item Impulsive Fractional Cohen-Grossberg Neural Networks: Almost Periodicity Analysis(2021-07-27) Stamova, Ivanka; Sotirov, Sotir; Sotirova, Evdokia; Stamov, GaniIn this paper, a fractional-order Cohen–Grossberg-type neural network with Caputo fractional derivatives is investigated. The notion of almost periodicity is adapted to the impulsive generalization of the model. General types of impulsive perturbations not necessarily at fixed moments are considered. Criteria for the existence and uniqueness of almost periodic waves are proposed. Furthermore, the global perfect Mittag–Leffler stability notion for the almost periodic solution is defined and studied. In addition, a robust global perfect Mittag–Leffler stability analysis is proposed. Lyapunov-type functions and fractional inequalities are applied in the proof. Since the type of Cohen–Grossberg neural networks generalizes several basic neural network models, this research contributes to the development of the investigations on numerous fractional neural network models.Item Impulsive Fractional Differential Inclusions and Almost Periodic Waves(2021-06-18) Stamov, Gani; Stamova, IvankaIn the present paper, the concept of almost periodic waves is introduced to discontinuous impulsive fractional inclusions involving Caputo fractional derivative. New results on the existence and uniqueness are established by using the theory of operator semigroups, Hausdorff measure of noncompactness, fixed point theorems and fractional calculus techniques. Applications to a class of fractional-order impulsive gene regulatory network (GRN) models are proposed to illustrate the results.Item Impulsive Fractional-Like Differential Equations: Practical Stability and Boundedness with Respect to h-Manifolds(2019-11-07) Stamov, Gani; Martynyuk, Anatoliy; Stamova, IvankaIn this paper, an impulsive fractional-like system of differential equations is introduced. The notions of practical stability and boundedness with respect to h-manifolds for fractional-like differential equations are generalized to the impulsive case. For the first time in the literature, Lyapunov-like functions and their derivatives with respect to impulsive fractional-like systems are defined. As an application, an impulsive fractional-like system of Lotka–Volterra equations is considered and new criteria for practical exponential stability are proposed. In addition, the uncertain case is also investigated.Item Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach(2021-12-03) Stamov, Gani; Stamova, Ivanka; Spirova, CvetelinaIn this paper we study an impulsive delayed reaction-diffusion model applied in biology. The introduced model generalizes existing reaction-diffusion delayed epidemic models to the impulsive case. The integral manifolds notion has been introduced to the model under consideration. This notion extends the single state notion and has important applications in the study of multi-stable systems. By means of an extension of the Lyapunov method integral manifolds’ existence, results are established. Based on the Lyapunov functions technique combined with a Poincare`-type inequality qualitative criteria related to boundedness, permanence, and stability of the integral manifolds are also presented. The application of the proposed impulsive control model is closely related to a most important problems in the mathematical biology—the problem of optimal control of epidemic models. The considered impulsive effects can be used by epidemiologists as a very effective therapy control strategy. In addition, since the integral manifolds approach is relevant in various contexts, our results can be applied in the qualitative investigations of many problems in the epidemiology of diverse interest.