Search results for: dynamical heterogeneity

Authors: Sasan Talebnezhad, Parviz Hamidia

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GPC and RMS analysis showed no distinct difference between PE 100 On, Off, and Reference grade. But FTIR spectra and multiple endothermic peaks obtained from SSA analysis, attributed to heterogeneity of ethylene sequence length, lamellar thickness and also the non-uniformity of short chain branching, showed sharp discrepancy and proposed a blend structure of high-density polyethylenes in PE 100 grade. Catalysis along with process parameters dictates poly blend PE 100 structure. This in-reactor blend is a mixture of compatible co-crystallized phases with different crystalinity, forming a physical semi hard and soft segment network responsible for improved impact properties in PE 100 pipe grade. We propose a new approach for PE100 evaluation that is more efficient than normal microstructure characterization.

Keywords: HDPE, pipe grade, in-reactor blend, hard and soft segments

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Authors: Nini Johana Marín Rodríguez, William Fernando Oquendo Patino

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In this work, we model a coupled system where we explore the effects of steady and random behavior on a linear system like an extension of the classic Strogatz model. This is exemplified by modeling a couple love dynamics as a linear system of two coupled differential equations and studying its stability for four types of lovers chosen as CC='Cautious- Cautious', OO='Only other feelings', OP='Opposites' and RR='Romeo the Robot'. We explore the effects of, first, introducing saturation, and second, adding a random variation to one of the CC-type lover, which will shape his character by trying to model how its variability influences the dynamics between love and hate in couple in a long run relationship. This work could also be useful to model other kind of systems where interactions can be modeled as linear systems with external or internal random influence. We found the final results are not easy to predict and a strong dependence on initial conditions appear, which a signature of chaos.

Keywords: differential equations, dynamical systems, linear system, love dynamics

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Authors: Zhenqiu Liu

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Visualizing the heterogeneity within cell-populations for single-cell RNA-seq data is crucial for studying the functional diversity of a cell. However, because of the high level of noises, outlier, and dropouts, it is very challenging to measure the cell-to-cell similarity (distance), visualize and cluster the data in a low-dimension. Minimum volume embedding (MVE) projects the data into a lower-dimensional space and is a promising tool for data visualization. However, it is computationally inefficient to solve a semi-definite programming (SDP) when the sample size is large. Therefore, it is not applicable to single-cell RNA-seq data with thousands of samples. In this paper, we develop an efficient algorithm with an accelerated proximal gradient method and visualize the single-cell RNA-seq data efficiently. We demonstrate that the proposed approach separates known subpopulations more accurately in single-cell data sets than other existing dimension reduction methods.

Keywords: single-cell RNA-seq, minimum volume embedding, visualization, accelerated proximal gradient method

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Authors: Justin Reverdi, Sixin Zhang, Serge Gratton, Said Aoues, Thomas Pellegrini

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In Vapor Cycle Systems, the flow sensor plays a key role in different monitoring and control purposes. However, physical sensors can be expensive, inaccurate, heavy, cumbersome, or highly sensitive to vibrations, which is especially problematic when embedded into an aircraft. The conception of a virtual sensor based on other standard sensors is a good alternative. In this paper, a data-driven model using a Convolutional Neural Network is proposed to estimate the flow of the compressor. To fit the model to our dataset, we tested different loss functions. We show in our application that a Dynamic Time Warping based loss function called DILATE leads to better dynamical performance than the vanilla mean squared error (MSE) loss function. DILATE allows choosing a trade-off between static and dynamic performance.

Keywords: deep learning, dynamic time warping, vapor cycle system, virtual sensor

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Authors: Alma Sobrevilla

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Using panel data from Mexico, this paper studies the determinants of women’s intrahousehold decision-making power using a generalised ordered logit model. Fixed effects estimations are also carried out to solve potential endogeneity coming from unobservable time-invariant factors. Finally, the paper analyses quadratic and community divergence effects of education on power. Results show heterogeneity in the effect of each of the determinants across different levels of decision-making power and suggest the presence of a significant quadratic effect of education. Having more education than the community average has a negative effect on power, supporting the notion that women tend to compensate their success outside the household with submissive attitudes at home.

Keywords: women, decision-making power, intrahousehold, Mexico

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Authors: Luis Andrey Fajardo Fajardo

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We are immersed in complex systems. The human brain, the galaxies, the snowflakes are examples of complex systems. An area of interest in Complex systems is the chaos theory. This revolutionary field of science presents different ways of study than determinism and reductionism. Here is where in junction with the Nonlinear DSP, chaos theory offer valuable techniques that establish a link between time series and complex theory in terms of complex networks, so that, the study of signals can be explored from the graph theory. Recently, some people had purposed a method to transform time series in graphs, but no one had developed a suitable implementation in Python with signals extracted from Chaotic Systems or Complex systems. That’s why the implementation in Python of an existing method to transform one dimensional chaotic signals from time domain to graph domain and some measures that may reveal information not extracted in the time domain is proposed.

Keywords: Python, complex systems, graph theory, dynamical systems

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Authors: Avan Al-Saffar, Eun-Jin Kim

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Both the logistic growth model and the gompertz growth model are used to describe growth processes. Both models driven by perturbations in different cases are investigated using information theory as a useful measure of sustainability and the variability. Specifically, we study the effect of different oscillatory modulations in the system's parameters on the evolution of the system and Probability Density Function (PDF). We show the maintenance of the initial conditions for a long time. We offer Fisher information analysis in positive and/or negative feedback and explain its implications for the sustainability of population dynamics. We also display a finite amplitude solution due to the purely fluctuating growth rate whereas the periodic fluctuations in negative feedback can lead to break down the system's self-regulation with an exponentially growing solution. In the cases tested, the gompertz and logistic systems show similar behaviour in terms of information and sustainability although they develop differently in time.

Keywords: dynamical systems, fisher information, probability density function (pdf), sustainability

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Authors: Ding Jue, Li Jiahua, Lei Zhidi, Weng Peifen, Li Xiaowei

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With the rapid development of national modern industry, people begin to pay attention to environmental pollution and harm caused by industrial dust. Based on above, a numerical study on the dedusting technology of industrial environment was conducted. The dynamic models of multicomponent particles collision and coagulation, breakage and deposition are developed, and the interaction of water droplet and aerosol particle in 2-Dimension flow field was researched by Eulerian-Lagrangian method and Multi-Monte Carlo method. The effects of the droplet scale, movement speed of droplet and the flow field structure on scavenging efficiency were analyzed. The results show that under the certain condition, 30μm of droplet has the best scavenging efficiency. At the initial speed 1m/s of droplets, droplets and aerosol particles have more time to interact, so it has a better scavenging efficiency for the particle.

Keywords: water droplet, aerosol particle, collision and coagulation, multi-monte carlo method

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Authors: Haowei Chen, Kaiqi Xiong

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This paper aims to answer how malware will propagate in Wireless Mesh Networks (WMNs) and how communication radius and distributed density of nodes affects the process of spreading. The above analysis is essential for devising network-wide strategies to counter malware. We answer these questions by developing an improved dynamical system that models malware propagation in the area where nodes were uniformly distributed. The proposed model captures both the spatial and temporal dynamics regarding the malware spreading process. Equilibrium and stability are also discussed based on the threshold of the system. If the threshold is less than one, the infected nodes disappear, and if the threshold is greater than one, the infected nodes asymptotically stabilize at the endemic equilibrium. Numerical simulations are investigated about communication radius and distributed density of nodes in WMNs, which allows us to draw various insights that can be used to guide security defense.

Keywords: Bluetooth security, malware propagation, wireless mesh networks, stability analysis

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Authors: Sanjay Kumar Behera, Kanhu Charan Patra

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A GIS-based method has been applied for the determination of soil erosion and sediment yield in a small watershed in Ong River basin, Odisha, India. The method involves spatial disintegration of the catchment into homogenous grid cells to capture the catchment heterogeneity. The gross soil erosion in each cell was calculated using Universal Soil Loss Equation (USLE) by carefully determining its various parameters. The concept of sediment delivery ratio is used to route surface erosion from each of the discretized cells to the catchment outlet. The process of sediment delivery from grid cells to the catchment outlet is represented by the topographical characteristics of the cells. The effect of DEM resolution on sediment yield is analyzed using two different resolutions of DEM. The spatial discretization of the catchment and derivation of the physical parameters related to erosion in the cell are performed through GIS techniques.

Keywords: DEM, GIS, sediment delivery ratio, sediment yield, soil erosion

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Authors: Wael M. Elawady, Mohamed F. Asar, Amany M. Sarhan

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This paper adopts a continuous sliding mode control scheme for trajectory tracking control of robot manipulators with structured and unstructured uncertain dynamics and external disturbances. In this algorithm, the equivalent control in the conventional sliding mode control is replaced by a PID control action. Moreover, the discontinuous switching control signal is replaced by a continuous proportional-integral (PI) control term such that the implementation of the proposed control algorithm does not require the prior knowledge of the bounds of unknown uncertainties and external disturbances and completely eliminates the chattering phenomenon of the conventional sliding mode control approach. The closed-loop system with the adopted control algorithm has been proved to be globally stable by using Lyapunov stability theory. Numerical simulations using the dynamical model of robot manipulators with modeling uncertainties demonstrate the superiority and effectiveness of the proposed approach in high speed trajectory tracking problems.

Keywords: PID, robot, sliding mode control, uncertainties

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Authors: Shuting Ji, Yueming Zhang, Jing Zhao

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The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of the output error (including the transmission error and the displacement error along the output axis) by considering different manufacture and assembly errors. The effects of the center distance error, the perpendicular error between input and output axes and the rotational angle error of the globoidal cam on the output error are systematically analyzed. A globoidal cam mechanism which is widely used in automatic tool changer of CNC machines is applied for illustration. Our results show that the perpendicular error and the rotational angle error have little effects on the transmission error but have great effects on the displacement error along the output axis. This study plays an important role in the design, manufacture and assembly of the globoidal cam mechanism.

Keywords: globoidal cam mechanism, manufacture error, transmission error, automatic tool changer

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Authors: Tomas Menard

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The design of control-law for engineering systems has been investigated for many decades. While many results are concerned with continuous systems with continuous output, nowadays, many controlled systems have to transmit their output measurements through network, hence making it discrete-time. But it is well known that the sampling of a system whose control-law is based on the continuous output may render the system unstable, especially when this sampling period is long compared to the system dynamics. The control design then has to be adapted in order to cope with this issue. In this paper, we consider systems which can be modeled as double integrator with uncertainty on the input since many mechanical systems can be put under such form. We present a control scheme based on an observer using only discrete time measurement and which provides continuous time estimation of the state, combined with a continuous control law, which stabilized a system with second-order dynamics even in the presence of uncertainty. It is further shown that arbitrarily long sampling periods can be dealt with properly setting the control scheme parameters.

Keywords: dynamical system, control law design, sampled output, observer design

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Authors: Amadou Banda Ndione, Charles Awono Onana

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In this paper the compartmental approach is applied to build a macroeconomic model characterized by countries. We consider a total of N countries that are subdivided into three compartments according to their economic status: D(t) denotes the compartment of developing countries at time t, E(t) stands for the compartment of emerging countries at time t while A(t) represents advanced countries at time t. The model describes the process of economic development and includes the notion of openness through collaborations between countries. Two delays appear in this model to describe the average time necessary for collaborations between countries to become efficient for their development process. Our model represents the different stages of development. It further gives the conditions under which a country can change its economic status and demonstrates the short-term positive effect of openness on economic growth. In addition, we investigate bifurcation by considering the delay as a bifurcation parameter and examine the onset and termination of Hopf bifurcations from a positive equilibrium. Numerical simulations are provided in order to illustrate the theoretical part and to support discussion.

Keywords: compartmental systems, delayed dynamical system, economic development, fiscal policy, hopf bifurcation

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Authors: Alica Miller

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A semiflow is a triple consisting of a Hausdorff topological space $X$, a commutative topological monoid $T$ and a continuous monoid action of $T$ on $X$. The acting monoid $T$ is usually either the discrete monoid $\N_0$ of nonnegative integers (in which case the semiflow can be defined as a pair $(X,f)$ consisting of a phase space $X$ and a continuous function $f:X\to X$), or the monoid $\R_+$ of nonnegative real numbers (the so-called one-parameter monoid). However, it turns out that there are real-life situations where it is useful to consider the acting monoids that are a combination of discrete and continuous monoids. That, for example, happens, when we are observing certain dynamical system at discrete moments, but after some time realize that it would be beneficial to continue our observations in real time. The acting monoid in that case would be $T=\{0, t_0, 2t_0, \dots, (n-1)t_0\} \cup [nt_0,\infty)$ with the operation and topology induced from real numbers. This partly explains the motivation for the level of generality which is pursued in our research. We introduce the PSP monoids, which include all but ``pathological'' monoids, and most of our statements hold for them. The topic of our presentation are some recent results about chaos-related properties in semiflows, indecomposability and sensitivity of semiflows in the described general context.

Keywords: chaos, indecomposability, PSP monoids, semiflow, sensitivity

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Authors: A. Sengouga, Y. Imessaoudene, A. Semar, B. Mouhouche, M. Kadir

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Biskra or Zibans, is located in a structural transition zone between the chain of the Saharan Atlas Mountains and the Sahara. It is an arid region where the superficial water resource is the mild, hence the importance of the lithological description and the evaluation of aquifers rock’s volumes, which are highly dependent on the mobilized water contained in the various reservoirs (Quaternary, Mio-Pliocene, Eocene and Continental intercalary). Through a data synthesis which is particularly based on stratigraphic logs of drilling, the description of aquifers heterogeneity and the determining of the spatial variability of aquifer appearance became possible, by using geostatistical analysis, which allowed the representation of the aquifer thicknesses mapping and their space variation. The different thematic maps realized focus on drilling position, the substratum shape and finally the aquifers thicknesses of the region. It is found that the high density of water points especially these of drilling points are superposed on the hydrologic reservoirs with significant thicknesses.

Keywords: log stratigraphic ArcGIS 10, geometry of aquifers, rocks reservoir volume, Biskra

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Authors: Owolabi Kolade Matthew

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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

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Authors: Leo Nnamdi Ozurumba-Dwight

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Single-cell genomic analytical systems have proved to be a platform to isolate bulk cells into selected single cells for genomic, proteomic, and related metabolomic studies. This is enabling systematic investigations of the level of heterogeneity in a diverse and wide pool of cell populations. Single cell technologies, embracing techniques such as high parameter flow cytometry, single-cell sequencing, and high-resolution images are playing vital roles in these investigations on messenger ribonucleic acid (mRNA) molecules and related gene expressions in tracking the nature and course of disease conditions. This entails targeted molecular investigations on unit cells that help us understand cell behavoiur and expressions, which can be examined for their health implications on the health state of patients. One of the vital good sides of single-cell RNA sequencing (scRNA seq) is its probing capacity to detect deranged or abnormal cell populations present within homogenously perceived pooled cells, which would have evaded cursory screening on the pooled cell populations of biological samples obtained as part of diagnostic procedures. Despite conduction of just single-cell transcriptome analysis, scRNAseq now permits comparison of the transcriptome of the individual cells, which can be evaluated for gene expressional patterns that depict areas of heterogeneity with pharmaceutical drug discovery and clinical treatment applications. It is vital to strictly work through the tools of investigations from wet lab to bioinformatics and computational tooled analyses. In the precise steps for scRNAseq, it is critical to do thorough and effective isolation of viable single cells from the tissues of interest using dependable techniques (such as FACS) before proceeding to lysis, as this enhances the appropriate picking of quality mRNA molecules for subsequent sequencing (such as by the use of Polymerase Chain Reaction machine). Interestingly, scRNAseq can be deployed to analyze various types of biological samples such as embryos, nervous systems, tumour cells, stem cells, lymphocytes, and haematopoietic cells. In haematopoietic cells, it can be used to stratify acute myeloid leukemia patterns in patients, sorting them out into cohorts that enable re-modeling of treatment regimens based on stratified presentations. In immunotherapy, it can furnish specialist clinician-immunologist with tools to re-model treatment for each patient, an attribute of precision medicine. Finally, the good predictive attribute of scRNAseq can help reduce the cost of treatment for patients, thus attracting more patients who would have otherwise been discouraged from seeking quality clinical consultation help due to perceived high cost. This is a positive paradigm shift for patients’ attitudes primed towards seeking treatment.

Keywords: immunotherapy, transcriptome, re-modeling, mRNA, scRNA-seq

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Authors: Federico Capra, Emanuele Martelli, Matteo Gazzani, Marco Mazzotti, Maurizio Notaro

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Natural gas is a major energy source in the current global economy, contributing to roughly 21% of the total primary energy consumption. Production of natural gas starting from renewable energy sources is key to limit the related CO2 emissions, especially for those sectors that heavily rely on natural gas use. In this context, biomethane produced via biogas upgrading represents a good candidate for partial substitution of fossil natural gas. The upgrading process of biogas to biomethane consists in (i) the removal of pollutants and impurities (e.g. H2S, siloxanes, ammonia, water), and (ii) the separation of carbon dioxide from methane. Focusing on the CO2 removal process, several technologies can be considered: chemical or physical absorption with solvents (e.g. water, amines), membranes, adsorption-based systems (PSA). However, none emerged as the leading technology, because of (i) the heterogeneity in plant size, ii) the heterogeneity in biogas composition, which is strongly related to the feedstock type (animal manure, sewage treatment, landfill products), (iii) the case-sensitive optimal tradeoff between purity and recovery of biomethane, and iv) the destination of the produced biomethane (grid injection, CHP applications, transportation sector). With this contribution, we explore the use of a technology for biogas upgrading and we compare the resulting performance with benchmark technologies. The proposed technology makes use of a chemical sorbent, which is engineered by RSE and consists of Di-Ethanol-Amine deposited on a solid support made of γ-Alumina, to chemically adsorb the CO2 contained in the gas. The material is packed into fixed beds that cyclically undergo adsorption and regeneration steps. CO2 is adsorbed at low temperature and ambient pressure (or slightly above) while the regeneration is carried out by pulling vacuum and increasing the temperature of the bed (vacuum-temperature swing adsorption - VTSA). Dynamic adsorption tests were performed by RSE and were used to tune the mathematical model of the process, including material and transport parameters (i.e. Langmuir isotherms data and heat and mass transport). Based on this set of data, an optimal VTSA cycle was designed. The results enabled a better understanding of the interplay between material and cycle tuning. As exemplary application, the upgrading of biogas for grid injection, produced by an anaerobic digester (60-70% CO2, 30-40% CH4), for an equivalent size of 1 MWel was selected. A plant configuration is proposed to maximize heat recovery and minimize the energy consumption of the process. The resulting performances are very promising compared to benchmark solutions, which make the VTSA configuration a valuable alternative for biomethane production starting from biogas.

Keywords: biogas upgrading, biogas upgrading energetic cost, CO2 adsorption, VTSA process modelling

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Authors: Wided Bakari, Patrce Bellot, Mahmoud Neji

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With the development of electronic media and the heterogeneity of Arabic data on the Web, the idea of building a clean corpus for certain applications of natural language processing, including machine translation, information retrieval, question answer, become more and more pressing. In this manuscript, we seek to create and develop our own corpus of pair’s questions-texts. This constitution then will provide a better base for our experimentation step. Thus, we try to model this constitution by a method for Arabic insofar as it recovers texts from the web that could prove to be answers to our factual questions. To do this, we had to develop a java script that can extract from a given query a list of html pages. Then clean these pages to the extent of having a database of texts and a corpus of pair’s question-texts. In addition, we give preliminary results of our proposal method. Some investigations for the construction of Arabic corpus are also presented in this document.

Keywords: Arabic, web, corpus, search engine, URL, question, corpus building, script, Google, html, txt

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Authors: Anusha De, Bjorn Van Campenhout

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Faced with imperfect information, economic actors use judgment and perceptions in decision-making. Inaccurate perceptions or false beliefs may result in inefficient value chains, and systematic bias in perceptions may affect inclusiveness. In this paper, perceptions in Ugandan maize supply chains are studied. A random sample of maize farmers where they were asked to rate other value chain actors—agro-input dealers, assembly traders and maize millers—on a set of important attributes such as service quality, price competitiveness, ease of access, and overall reputation. These other value chain actors are tracked and asked to assess themselves on the same attributes. It is observed that input dealers, traders and millers assess themselves more favorably than farmers do. Zooming in on heterogeneity in perceptions related to gender, it is evident that women rate higher than men. The sex of the actor being rated does not affect the rating.

Keywords: gender, input dealers, maize supply chain, perceptions, processors

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Authors: DRIS Mohammed El-Amine, BOUNIF Abdelhamid

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This paper considers an experimental and numerical investigation of variable density in axisymmetric turbulent free jets. Special attention is paid to the study of the scalar dissipation rate. In this case, dynamic field equations are coupled to scalar field equations by the density which can vary by the thermal effect (jet heating). The numerical investigation is based on the first and second order turbulence models. For the discretization of the equations system characterizing the flow, the finite volume method described by Patankar (1980) was used. The experimental study was conducted in order to evaluate dynamical characteristics of a heated axisymmetric air flow using the Laser Doppler Anemometer (LDA) which is a very accurate optical measurement method. Experimental and numerical results are compared and discussed. This comparison do not show large difference and the results obtained are in general satisfactory.

Keywords: Scalar dissipation rate, thermal effects, turbulent axisymmetric jets, second order modelling, Velocimetry Laser Doppler.

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Authors: N. Fusun Oyman Serteller

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In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: Sarra Khelifi, Youcef Guerabli, Ahcene Boumaiza

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Advances in techniques for measuring individual crystallographic orientations have made it possible to investigate the role of local crystallography during the plastic deformation of materials. In this study, the change in crystallographic orientation distribution during deformation by deep drawing in carbon steel has been investigated in order to understand their role in propagation and arrest of crack. The results show that the change of grain orientation from initial recrystallization texture components of {111}<112> to deformation orientation {111}<110> incites the initiation and propagation of cracks in the region of {111}<112> small grains. Moreover, the misorientation profile and local orientation are analyzed in detail to discuss the change from {111}<112> to {111}<110>. The deformation of the grain with {111}<110> orientation is discussed in terms of stops of the crack in carbon steel during drawing. The SEM-EBSD technique was used to reveal the change of orientation; XRD was performed for the characterization of the global evolution of texture for deformed samples.

Keywords: fracture, heterogeneity, misorientation profile, stored energy

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Authors: Aliasghar Arab

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Autonomous robots interacting with humans, as safety-critical nonlinear control systems, are complex closed-loop cyber-physical dynamical machines. Keeping these intelligent yet complicated systems safe and smooth during their operations is challenging. The aim of the safe predictive output feedback linearization control synthesis is to design a novel controller for smooth trajectory following while unsafe situations must be avoided. The controller design should obtain a linearized output for smoothness and invariance to a safety subset. Inspired by finite-horizon nonlinear model predictive control, the problem is formulated as constrained nonlinear dynamic programming. The safety constraints can be defined as control barrier functions. Avoiding unsafe maneuvers and performing smooth motions increases the predictability of the robot’s movement for humans when robots and people are working together. Our results demonstrate the proposed output linearization method obeys the safety constraints and, compared to existing safety-guaranteed methods, is smoother and performs better.

Keywords: robotics, collaborative robots, safety, autonomous robots

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Authors: Shelby Simpson, William Stanley, Namir Naba, Xiaodi Wang

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Both t-SNE and UMAP are brand new state of art tools to predominantly preserve the local structure that is to group neighboring data points together, which indeed provides a very informative visualization of heterogeneity in our data. In this research, we develop a t-SNE and UMAP base neural network image classification algorithm to embed the original dataset to a corresponding low dimensional dataset as a preprocessing step, then use this embedded database as input to our specially designed neural network classifier for image classification. We use the fashion MNIST data set, which is a labeled data set of images of clothing objects in our experiments. t-SNE and UMAP are used for dimensionality reduction of the data set and thus produce low dimensional embeddings. Furthermore, we use the embeddings from t-SNE and UMAP to feed into two neural networks. The accuracy of the models from the two neural networks is then compared to a dense neural network that does not use embedding as an input to show which model can classify the images of clothing objects more accurately.

Keywords: t-SNE, UMAP, fashion MNIST, neural networks

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Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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