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We propose a time-fractional compartmental model (SEI A I S HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the COVID-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.

8 Páginas.-- 4 Figuras.-- 3 Tablas, Sensory quality, assessed following a standardized method, is one of the parameters defining the commercial category of virgin olive oil. Considering the difficulties linked to the organoleptic evaluation, especially the high number of samples to be assessed, setting up instrumental methods to support sensory panels becomes a need for the olive oil sector. Volatile fingerprint by Headspace Solid Phase Microextraction-Gas Chromatography-Mass Spectrometry can be an excellent fit-for-purpose tool as the volatile fraction is responsible for virgin olive oil sensory attributes. A fingerprinting approach was applied to the volatile profile of 176 virgin olive oils previously graded by six official sensory panels. The classification strategy consisted in two sequential Partial Least Square-Discriminant Analysis models built with the aligned chromatograms: the first discriminated extra virgin and non-extra virgin samples; the second classified the latter into virgin or lampante categories. Results were satisfactory in the cross-validation by leave 10%-out (97% of correct classification). For external validation, an uncertainty range was set for the prediction models to detect boundary samples, which would be further assessed by the sensory panels. By doing this, a considerable decrease of the panel workload (around 80%) was achieved, while maintaining a highly reliable classification of samples (error rate, This work was developed in the context of the project OLEUM “Advanced solutions for assuring authenticity and quality of olive oil at global scale”, funded by the European Commission within the Horizon 2020 Program (2014–2020, grant agreement no. 635690). The information and views set out in this article are those of the author(s) and do not necessarily reflect the official opinion of the European Union. Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible for the use which may be made of the information contained therein. B. Quintanilla-Casas thanks the Spanish Ministry of Science, Innovation and Universities predoctoral fellowship FPU16/01744. A. Tres thanks the Spanish Ministry of Economy, Industry and Competitivity “Juan de la Cierva” postdoctoral fellowship (JCI-2012_13412) and the Ministry of Science, Innovation and Universities “Ramón y Cajal” postdoctoral fellowship (RYC-2017-23601).

This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.

It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991) [2], employed by Arslan, without the use of the Kolmogorov Consistency Theorem.

An integrated model for ranking scientific publications together with authors and journals recently presented in [Bini, Del Corso, Romani, ETNA 2008] is closely analyzed. The model, which relies on certain adjacency matrices H,K and F obtained from the relations of citation, authorship and publication, provides the ranking by means of the Perron vector of a stochastic matrix obtained by combining H,K and F. Some perturbation theorems concerning the Perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented. The theoretical results confirm the consistency and effectiveness of our model. Some paradigmatic examples are reported together with some results obtained on a real set of data.

This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs., 21 pages

The input parameters for the hardening law for the elasto-plastic constitutive model of unsaturated soils are generally fitting parameters that control the degree of hardening response and cannot easily be determined without the results of experimental tests in which the changes in suction, water content, and volume are measured or controlled. However, it is next to impossible to complete such precise experimental tests on all the geomaterials comprising the earth structure to be analysed, such as an embankment. It is important, therefore, to establish a method for determining these parameters from more easily attainable data on the material. This paper presents a practical method for estimating the input parameters related to hardening/softening due to desaturation/saturation in the elasto-plastic constitutive model proposed by Ohno et al. (2007a) from a compaction curve, which is frequently obtained and widely used in engineering practice. In the proposed method, the input parameters are estimated by simultaneously solving three theoretical equations, each of which holds for a different point, indicating the statically compacted state on the dry side of the compaction curve, while the approximately represented compaction curve is used instead of a hand-drawn one. The paper demonstrates that the proposed method enables the estimation of the input parameter values within a range small enough so as not to affect the results of the simulation, irrespective of the way in which the points on the represented compaction curve are selected. The validity of the estimated parameters is verified and then discussed through a series of static compaction test simulations.

The Hartshorne–Hirschowitz theorem says that a generic union of lines in P n , ( n ≥ 3 ) , has good postulation. The proof of Hartshorne and Hirschowitz in the initial case P 3 is handled by a method of specialization via a smooth quadric surface with the property of having two rulings of skew lines. We provide a proof in the case P 3 based on a new degeneration of disjoint lines via a plane H ≅ P 2 , which we call ( 2 , s ) -cone configuration, that is a schematic union of s intersecting lines passing through a single point P together with the trace of an s-multiple point supported at P on the double plane 2H. In the first part of this paper, we discuss our degeneration inductive approach. We prove that a ( 2 , s ) -cone configuration is a degeneration of s disjoint lines in P 3 , or more generally in P n . In the second part of the paper, we use this degeneration in an effective method to show that a generic union of lines in P 3 imposes independent conditions on the linear system | O P 3 ( d ) | of surfaces of given degree d. The basic motivation behind our degeneration approach is that it looks more systematic that gives some hope of extensions to the analogous problem in higher dimensional spaces, that is the postulation problem for m-dimensional planes in P 2 m + 1 .

*Maldar, Samet ( Aksaray, Yazar ) *Atalan, Yunus ( Aksaray, Yazar ), In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods.

The paper is devoted to construction of solutions in dynamic bimatrix games. In the model, the payoffs are presented by discounted integrals on the infinite time horizon. The dynamics of the game is subject to the system of the A.N. Kolmogorov type differential equations. The problem of construction of equilibrium trajectories is analyzed in the framework of the minimax approach proposed by N.N. Krasovskii and A.I. Subbotin in the differential games theory. The concept of dynamic Nash equilibrium developed by A.F. Kleimenov is applied to design the structure of the game solution. For obtaining constructive control strategies of players, the maximum principle of L.S. Pontryagin is used in conjunction with the generalized method of characteristics for Hamilton-Jacobi equations. The impact of the discount index is indicated for equilibrium strategies of the game and demand functions in the dynamic bimatrix game are constructed. © 2018 The paper is supported by Russin Foundation for Basic Reseaarch (Project No. 18-01-0264a).

We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was proposed in Guo and Jung (2017) [12,13]. We present also some numerical examples that confirm the theoretical approximation orders derived in the paper.

The paper deals with a two-person zero-sum differential game for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional of this game, we derive the Hamilton-Jacobi type equation with coinvariant derivatives. It is proved that, if the solution of this equation satisfies certain smoothness conditions, then it coincides with the value functional. On the other hand, it is proved that, at the points of coinvariant differentiability, the value functional satisfies the derived Hamilton-Jacobi equation. Therefore, this equation can be called the Hamilton-Jacobi-Bellman-Isaacs equation for time-delay systems. © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

We consider the Euclidean Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). For the long time, approximability of this well-known problem in the class of algorithms with theoretical guarantees was poorly studied. This year, for the case of a single depot, we proposed two approximation algorithms, which are the Efficient Polynomial Time Approximation Schemes (EPTAS) for any fixed given capacity q and the number p of mutually disjunctive time windows. The former scheme extends the celebrated approach proposed by M. Haimovich and A. Rinnooy Kan and allows the evident parallelization, while the latter one has an improved time complexity bound and the enlarged domain in terms q = q(n) and p = p(n), where it retains polynomial time complexity. In this paper, we announce an extension of these results to the case of multiple depots. So, the first scheme is also EPTAS for any fixed parameters q, p, and m, where m is the number of depots, and remains PTAS for q = o(log log n) and mp = o(log log n). In other turn, the second one is a PTAS for p3q4 = O(log n) and (pq)2 log m = O(log n). © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Russian Foundation for Basic Research, RFBR: 17-08-01385, 19-07-01243 Michaeffi Khachay was supported by the Russian Foundation for Basic Research, grants no. 17-08-01385 and 19-07-01243.

In this paper we consider some recent properties defined by relative versions of star-covering properties and note that some of them are in fact characterizations of the original property or, surprisingly, of known properties. We study “non absurd” properties and their behaviour with respect to related properties. Also we answer some questions posed in [4] and [17] .

In the analysis of the fluid queues, it is necessary to obtain the nonnegative solution of a nonsymmetric algebraic Riccati matrix equation. Under suitable conditions, this solution can be obtained transforming algebraic Riccati equations into unilateral quadratic matrix equations. In this paper, we use an efficient iterative scheme to approximate a solution of this quadratic matrix equation. We improve the efficiency and the accuracy of Newton’s method, widely used in the literature. Moreover, a local convergence result is proved. Finally, we apply this efficient method to approximate the solution of a particular noisy Wiener–Hopf problem and we compare it with Newton’s method. Moreover, a predictor–corrector iterative scheme is constructed that improve the accessibility of the aforesaid method.

In this paper, we explore a set of new heuristic strategies integrated within the column generation algorithm to solve the Capacitated Vehicle Routing Problem with 2-Dimensional Loading constraints. These heuristics rely on constructive procedures that iteratively build a solution using the solutions of a mixed integer linear programming model. The pricing subproblem is also heuristically solved, using strategies relying on variable neighborhood search algorithms proposed in literature. Column generation approaches for the 2L-CVRP are not quite explored. This paper aims to contribute with new strategies to tackle this problem. All the approaches were implemented and an exhaustive computational study is performed., This work has been supported by FEDER funding through the Programa Operacional Factores de Competitividade COMPETE and through the Portuguese Science and Technology Foundation (FCT): project UID/CEC/00319/2013 and grant SFRH/BD/73584/2010.

The paper is concerned with a nonlinear impulsive control system with trajectories of bounded variation. Necessary conditions of optimality in a form of the Maximum Principle are derived for a class of infinite horizon impulsive optimal control problems. For the overtaking optimality criterion under the assumption that all gradients of the payoff function are bounded, we construct a transversality condition for the adjoint variable in terms of limit points of the gradient of the payoff function. In the case when this limit point is unique, this condition supplements the system of the Maximum Principle and determines a unique solution of the adjoint system. This solution can be written explicitly with the use of the (Cauchy type) formula proposed earlier by S.M. Aseev and A.V. Kryazhimskii. The key idea of the proof is the application of the convergence of subdifferentials within Halkin’s scheme.

For a Tychonoff space X, we denote by C p ( X ) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we continue to study different selectors for sequences of dense sets of C p ( X ) started to study in the paper [14] . A set A ⊆ C p ( X ) will be called 1-dense in C p ( X ) , if for each x ∈ X and an open set W in R there is f ∈ A such that f ( x ) ∈ W . We give the characterizations of selection principles S 1 ( A , A ) , S f i n ( A , A ) and S 1 ( S , A ) where • A — the family of 1-dense subsets of C p ( X ) ; • S — the family of sequentially dense subsets of C p ( X ) , through the selection principles of a space X. In particular, we give the functional characterizations of the Rothberger and Menger properties.

In this paper, we introduce a numerical scheme for fractional differential equations with feedback control. Due to the possibility of dealing with a feedback control as a functional delay, we construct a numerical method based on Euler method accompanied with piecewise constant interpolation. The method is based on the idea of separating the current state and the prehistory function. The convergence of the method is stated and proved. Numerical experiments are given to clarify the good agreement between numerical and theoretical results.

The paper deals with the Cauchy problem for Hamilton—Jacobi equation with discontinuous w.r.t. state variable Hamiltonian. In this case we use the notion of M-solution proposed by Subbotin. We consider the sequence of auxiliary Cauchy problems for Hamilton— Jacobi equations with Lipschitz continuous w.r.t. phase variable Hamiltonians. We show that the sequence of distances between of graphs of solutions for auxiliary Cauchy problems and graph of M-solution tends to zero in metrics L1.

In this paper we establish a construction of Euclidean 9-designs (i.e., the fourth order rotatable designs) on the unit ball. A classical, popular approach for this is to use the corner vectors of the hyperoctahedron such as the vertices, the midpoints of the edges, the barycentres of the faces and so on. As an improvement of this, we propose to use the corner vectors of the hyperoctahedral group, plus their “internally dividing points”. We give a classification of Euclidean 9-designs on two spheres, and several examples of the fourth order optimal rotatable designs in low dimensions.

Matsubara–Usuba [13] introduced the notion of skinniness and its variants for subsets of P κ λ and showed that the existence of skinny stationary subsets of P κ λ is related to large cardinal properties of ideals over P κ λ and to Jensen's diamond principle on λ. In this paper, we study the existence of skinny stationary sets in more detail.

Based on recent developments in joint regression models for quantile and expected shortfall, this paper seeks to develop models to analyse the risk in the right tail of the distribution of non-negative dependent random variables. We propose an algorithm to estimate conditional tail expectation regressions, introducing generalized risk regression models with link functions that are similar to those in generalized linear models. To preserve the natural ordering of risk measures conditional on a set of covariates, we add extra non-negative terms to the quantile regression. A case using telematics data in motor insurance illustrates the practical implementation of predictive risk models and their potential usefulness in actuarial analysis.

Made available in DSpace on 2021-06-25T15:07:00Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribu-tion ( J). An approach based on the sup -J extension principle, which is a generalization of Zadeh & rsquo;s extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup -J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh & rsquo;s extension. (c) 2021 Elsevier Inc. All rights reserved. Univ Austral Chile, Ctr Basic Sci Teaching Engn, Valdivia, Chile Sao Paulo State Univ, Dept Math, Rio Claro, Brazil Univ Austral Chile, Inst Acoust, Valdivia, Chile Univ Estadual Campinas, Dept Appl Math, Campinas, Brazil Natl Ctr Res Energy & Mat, Dept Integrated Sci Teaching Ctr, Campinas, Brazil Sao Paulo State Univ, Dept Math, Rio Claro, Brazil CNPq: 142414/20174 CNPq: 306546/20175 FAPESP: 2016/260407 CAPES: 001

In this paper, for a significant class of uncertain MIMO systems, in particular for robots, new fundamental results are stated. These allow to design robust control laws without chattering, of pseudo-PID type, in order to track sufficiently regular trajectories with a preassigned maximum error. The proposed pseudo-PID controllers are easy to design and implement because these laws can also be decentralized and they are based on two design parameters. The first parameter is related to the minimum eigenvalue of a suitable matrix, depending on the inertia matrix in the case of a mechanical system, from which the practical stability depends on, and the second parameter is related to the practical region of asymptotic stability, to the precision of the tracking error and to the time constant of an appropriate linearized majorant system of the closed-loop control system. The utility and the efficiency of the main results proposed in this paper are illustrated with a significant example.

In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamiltonian system. The knowledge of this Taylor expansion of the period function for this system is one of the key points to study the number of zeroes of an Abelian integral that controls the number of limit cycles bifurcating from the periodic orbits of a planar Hamiltonian system that is inspired by a physical model on capillarity. Several other classical tools, like for instance Chebyshev systems are applied to study this number of zeroes. The approach introduced can also be applied in other situations., 23 pages

Made available in DSpace on 2021-06-25T12:39:00Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-03-15 In this paper we study topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. We show that the stability and the asymptotical stability of a compact set is characterized by the stability and the asymptotical stability of its components, respectively. We also present a characterization of the stability of a compact set by means of omega-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of invariant neighborhoods of it. (c) 2021 Elsevier B.V. All rights reserved. Univ Estadual Paulista, Dept Matemat & Comp, R Roberto Simonsen 305, BR-19060080 Presidente Prudente, SP, Brazil Univ Estadual Paulista, Dept Matemat & Comp, R Roberto Simonsen 305, BR-19060080 Presidente Prudente, SP, Brazil

金沢大学理工研究域機械工学系, In this paper, the basic characteristics of the differential evolution (DE) are examined. Thus, one is the meta-heuristics, and the other is the global optimization technique. It is said that DE is the global optimization technique, and also belongs to the meta-heuristics. Indeed, DE can find the global minimum through numerical experiments. However, there are no proofs and useful investigations with regard to such comments. In this paper, the DE is compared with the generalized random tunneling algorithm (GRTA) and the particle swarm optimization (PSO) that are the global optimization techniques for continuous design variables. Through the examinations, some common characteristics as the global optimization technique are clarified in this paper. Through benchmark test problems including structural optimization problems, the search ability of DE as the global optimization technique is examined. © 2011 Elsevier B.V. All rights reserved.

A proper coloring of a given graph is an assignment of a positive integer number (color) to each vertex such that two adjacent vertices receive different colors. This paper studies the Minimum Sum Coloring Problem (MSCP), which asks for finding a proper coloring while minimizing the sum of the colors assigned to the vertices. We propose the first branch-and-price algorithm to solve the MSCP to proven optimality. The newly developed exact approach is based on an Integer Programming (IP) formulation with an exponential number of variables which is tackled by column generation. We present extensive computational experiments, on synthetic and benchmark DIMACS graphs from the literature, to compare the performance of our newly developed branch-and-price algorithm against three compact IP formulations. On synthetic graphs, our algorithm outperforms the compact formulations in terms of: ( i ) number of solved instances, ( i i ) running times and ( i i i ) exit gaps obtained when optimality is not achieved. For the DIMACS instances, our algorithm is competitive with the best compact formulation and provides very strong dual bounds.

In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential., 14 pages

The Lyndon factorization of a word has been largely studied and recently variants of it have been introduced and investigated with different motivations. In particular, the canonical inverse Lyndon factorization ICFL ( w ) of a word w, introduced in [1] , maintains the main properties of the Lyndon factorization since it can be computed in linear time and it is uniquely determined. In this paper we investigate new properties of this factorization with the aim of exploring their use in some classical queries on w. The main property we prove is related to a classical query on words. We prove that there are relations between the length of the longest common prefix (or longest common extension) lcp ( x , y ) of two different suffixes x , y of a word w and the maximum length M of two consecutive factors of ICFL ( w ) . More precisely, M is an upper bound on the length of lcp ( x , y ) . A main tool used in the proof of the above result is a property that we state for factors m i with nonempty borders in ICFL ( w ) : a nonempty border of m i cannot be a prefix of the next factor m i + 1 . Another interesting result relates sorting of global suffixes, i.e., suffixes of a word w, and sorting of local suffixes, i.e., suffixes of products of factors in ICFL ( w ) . This is the counterpart for ICFL ( w ) of the compatibility property, proved in [2] , [3] for the Lyndon factorization. Roughly, the compatibility property allows us to extend the mutual order between suffixes of products of the (inverse) Lyndon factors to the suffixes of the whole word. The last property we prove focuses on the Lyndon factorizations of a word and its factors. It suggests that the Lyndon factorizations of two words sharing a common overlap could be used to capture the common overlap of these two words.

This paper presents a fast approximate rank-1 L1-norm Principal Component Analysis (L1-PCA) estimator implemented in the Fourier domain. Specifically, we first rephrase the problem of rank-1 L1-PCA estimation as a cyclic shift parameter estimation and then we present an algorithm for estimating the first L1-norm Principal Component (L1-PC) in the Fourier domain, practically using FFT. The proposed method is shown to be asymptotically efficient and our numerical studies corroborate its performance merits.

The aim of this work consists of finding a suitable numerical method for the solution of the mathematical model describing the prostate tumor growth, formulated as a system of time-dependent partial differential equations (PDEs), which plays a key role in the field of mathematical oncology. In the literature on the subject, there are a few numerical methods for solving the proposed mathematical model. Localized prostate cancer growth is known as a moving interface problem, which must be solved in a suitable stable way. The mathematical model considered in this paper is a system of time-dependent nonlinear PDEs that describes the interaction between cancer cells, nutrients, and prostate-specific antigen (PSA). Here, we first derive a non-dimensional form of the studied mathematical model using the well-known non-dimensionalization technique, which makes it easier to implement different numerical techniques. Afterward, the analysis of the numerical method describing the two-dimensional prostate tumor growth problem, based on radial basis function-generated finite difference (RBF-FD) scheme, in combination with a first-order time discretization has been done. The numerical technique we use, does not need the use of any adaptivity techniques to capture the features in the interface. The discretization leads to solving a linear system of algebraic equations solved via the biconjugate gradient stabilized (BiCGSTAB) algorithm with zero-fill incomplete lower–upper (ILU) preconditioner. Comparing the results obtained in this investigation with those reported in the recent literature, the proposed approach confirms the ability of the developed numerical scheme. Besides, the effect of choosing constant parameters in the mathematical model is verified by many simulations on rectangular and circular domains.

In this paper we study associative unitary superalgebras with graded involution or superinvolution having polynomial growth of the codimension sequence. The first goal is to prove that, for this kind of algebras, the codimension sequence is a polynomial with rational coefficients. Then we shall construct several superalgebras with graded involution or superinvolution realizing the smallest and the largest value of the leading term of such a polynomial.

We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equations on the iterated tangent group. We also present in detail the 2nd order Lagrangian dynamics on the 2nd order tangent group of a double cross product group., Comment: Revisions has been made to shorten the text... the discussion on discrete dynamics has been spared for a separate paper

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R 0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to estimate R 0 . I examine the performance of these methods using Monte Carlo studies and demonstrate that they yield fairly accurate estimates of R 0 . Next, I apply these methods to estimate R 0 for the US, California, and Japan, and document heterogeneity in the value of R 0 across regions. My estimation approach accounts for possible underreporting of the number of cases. I demonstrate that if one fails to take underreporting into account and estimates R 0 from the reported cases data, the resulting estimate of R 0 may be biased downward and the resulting forecasts may exaggerate the long run number of deaths. Finally, I discuss how auxiliary information from random tests can be used to calibrate the initial parameters of the model and narrow down the range of possible forecasts of the future number of deaths.

The Shapley value (Shapley, 1953) has been axiomatically characterized from different points of view. van den Brink (2001) proposes a characterization by means of efficiency, fairness and the null player property. In this paper, we characterize the family of single-valued solutions obtained by relaxing fairness into weak fairness. To point out the Shapley value, we impose the additional axiom of weak self consistency and strengthen the null player property into the dummy player property. Remarkably, impossibility results emerge when replacing self consistency by a large set of consistency properties.

In the present paper, dwell time stability conditions of the switched delay systems are derived using scheduled Lyapunov-Krasovskii functions. The derivative of the Lyapunov functions are guaranteed to be negative semidefinite using free weighting matrices method. After representing the dwell time in terms of linear matrix inequalities, the upper bound of the dwell time is minimized using a bisection algorithm. Some numerical examples are given to illustrate effectiveness of the proposed method, and its performance is compared with the existing approaches. The yielding values of dwell time via the proposed technique show that the novel approach outperforms the previous ones.

In this paper, we study partial traces on additive categories. Haghverdi and Scott introduced partially traced symmetric monoidal categories generalizing traced symmetric monoidal categories given by Joyal, Street and Verity. The original example of a partial trace is given in terms of the execution formula on the category of vector spaces and linear functions. Malherbe, Scott and Selinger gave another example of a partial trace on the category of vector spaces, and they observed that we can define these two partial traces on arbitrary additive categories. A natural question is: what kind of partial traces does the category of vector spaces have? We give a (partial) answer to this question. Our main result is: every abelian category has a largest partial trace. Here, “largest” means that every partial trace on the abelian category is obtained by restricting the domain of the largest partial trace. As a corollary, we show that the partial trace given by Malherbe, Scott and Selinger is the largest partial trace on the category of vector spaces., Proceedings of the Thirty-Fourth Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXIV). The conference was held in Halifax, Nova Scotia, Canada, June 6–9 2018.

In a twin support vector machine (TSVM), the separating hyperplane associated with one class is determined such that the hyperplane is near to the data belonging to the class and that it is away from the other class. A data sample is classified into the class with the nearer hyperplane. In this paper we discuss whether the twin hyperplanes are necessary for the TSVM. By theoretical analysis we first show the equivalence conditions that one of the two decision boundaries of the TSVM coincides with the decision boundary of the SVM. Then for the least squares (LS) version of the TSVM, we clarify the equivalence conditions with the LS SVM or that with two hyperparameters for imbalanced data (one for each class). A comparison of the LS TSVM with the LS SVMs, by computer experiments, shows that the generalization abilities of the LS TSVM are comparable but not superior for 13 two-class problems and an imbalanced two-class problem.

We developed unconstrained large margin distribution machines (ULDMs) for pattern classification.The ULDM maximizes the margin mean and minimizes the margin variance.The ULDM can be trained by solving a set of linear equations.We clarify the characteristics of ULDMs.Performance of the ULDM is compared with that of the L1 SVM, LS SVM, and the LDM. Large margin distribution machines (LDMs) maximize the margin mean and minimize the margin variance, and show good generalization performance compared to support vector machines (SVMs). But because two additional hyperparameters are necessary, model selection needs more time. In this paper we propose unconstrained large margin distribution machines (ULDMs). In the ULDM, the objective function is the sum of the margin mean (a linear term), the margin variance (a quadratic term), and the weighted regularization term (a quadratic term), and constraints are not included. Therefore, the solution is expressed by a set of linear equations with one hyperparameter for the regularization term. Theoretical analysis proves that the decision boundary between two classes passes through the mean of all mapped training data if the numbers of training data of both classes are the same. The case where the numbers are different is analyzed for a one-dimensional input and how the decision boundary is determined is clarified. Using benchmark data sets, we show that the generalization performance of ULDMs is comparable to or better than that of SVMs.

The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese 3-fold projections. More precisely, for any integer d ≥ 4 and any d -th root e of 1 we denote by X d the toric variety defined as the image of the morphism φ T d : P 3 ⟶ P μ ( T d ) − 1 where T d are all monomials of degree d in k [ x , y , z , t ] invariant under the action of the diagonal matrix M ( 1 , e , e 2 , e 3 ) . In this work, we describe a Z -basis of the lattice L η associated to I ( X d ) as well as a minimal binomial set of generators of the lattice ideal I ( X d ) = I + ( η ) .

The article is devoted to the analysis of optimal control problems with infinite time horizon. These problems arise in economic growth models and in stabilization problems for dynamic systems. The problem peculiarity is a quality functional with an unbounded integrand which is discounted by an exponential index. The problem is reduced to an equivalent optimal control problem with the stationary value function. It is shown that the value function is the generalized minimax solution of the corresponding Hamilton-Jacobi equation. The boundary condition for the stationary value function is replaced by the property of the Hölder continuity and the sublinear growth condition. A backward procedure on infinite time horizon is proposed for construction of the value function. This procedure approximates the value function as the generalized minimax solution of the stationary Hamilton-Jacobi equation. Its convergence is based on the contraction mapping method defined on the family of uniformly bounded and Hölder continuous functions. After the special change of variables the procedure is realized in numerical finite difference schemes on strongly invariant compact sets for optimal control problems and differential games. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license

This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.

The minimum tracking set problem is an optimization problem that deals with monitoring communication paths that can be used for exchanging point-to-point messages using as few tracking devices as possible. More precisely, a tracking set of a given graph G and a set of source-destination pairs of vertices, is a subset T of vertices of G such that the vertices in T traversed by any source-destination shortest path P uniquely identify P. The minimum tracking set problem has been introduced in [Banik et al., CIAC 2017] for the case of a single source-destination pair. There, the authors show that the problem is APX-hard and that it can be 2-approximated for the class of planar graphs, even though no hardness result is known for this case. In this paper we focus on the case of multiple source-destination pairs and we present the first \(\widetilde{O}(\sqrt{n})\)-approximation algorithm for general graphs. Moreover, we prove that the problem remains NP-hard even for cubic planar graphs and all pairs \(S \times D\), where S and D are the sets of sources and destinations, respectively. Finally, for the case of a single source-destination pair, we design an (exact) FPT algorithm w.r.t. the maximum number of vertices at the same distance from the source.

For a topological flow $(V,\phi)$ - i.e., $V$ is a linearly compact vector space and $\phi$ a continuous endomorphism of $V$ - we gain a deep understanding of the relationship between $(V,\phi)$ and the Bernoulli shift: a topological flow $(V,\phi)$ is essentially a product of one-dimensional left Bernoulli shifts as many as $\mathrm{ent}^*(V,\phi)$ counts. This novel comprehension brings us to introduce a notion of corank for topological flows designed for coinciding with the value of the topological entropy of $(V,\phi)$. As an application, we provide an alternative proof of the so-called Bridge Theorem for locally linearly compact vector spaces connecting the topological entropy to the algebraic entropy by means of Lefschetz duality., Comment: the organisation of the paper has been substantially changed

In 3-axis milling operations the surface error caused by the tool/workpiece static deflection assumes a certain shape along the axial depth of cut. The error shape changes considerably according to the cutting strategy, tool geometry and cutting parameters. This paper presents a comprehensive method to identify all the types of surface error profile in down-milling, proposing dedicated analytical equations. This approach has been experimentally validated to assess its accuracy and limits. The results of this approach are meant to ease the surface error prediction and measurement by reducing the number of points to consider along the axial depth of cut.

The Equivalent Material Concept is a tool that allows the fracture behavior of notched components in elastoplastic materials to be analyzed by transforming them into fictitious linear elastic ones, defining a fictitious failure stress. The combination of a failure criterion with this approach offers a methodology for predicting the maximum load of notched solids with elastoplastic behavior.The validity limits have been established experimentally by a logistic regression using fracture data of linear elastic, small scale yielding and fully plastic material. This paper also proposes an extension of the Equivalent Material Concept, applying the fictitious transformation in a more complete form to tensile, toughness and notch tests. New magnitudes as the fictitious stress, the fictitious toughness and the fictitious notch stress intensity factors have been defined. The final proposal is a partial application of the fictitious transformation that incorporates all of the experimental data gathered. The authors wish to express their gratitude to the European Union’s H2020 research and innovation program for their financial support under the LightCoce project (No 814632).

A longstanding open problem in mathematical physics has been that of finding an action principle for the Einstein-Weyl (EW) equations. In this paper, we present for the first time such an action principle in three dimensions in which the Weyl vector is not exact. More precisely, our model contains, in addition to the Weyl nonmetricity, a traceless part. If the latter is (consistently) set to zero, the equations of motion boil down to the EW equations. In particular, we consider a metric affine $f(R)$ gravity action plus additional terms involving Lagrange multipliers and gravitational Chern-Simons contributions. In our framework, the metric and the connection are considered as independent objects, and no a priori assumptions on the nonmetricity and the torsion of the connection are made. The dynamics of the Weyl vector turns out to be governed by a special case of the generalized monopole equation, which represents a conformal self-duality condition in three dimensions., Comment: 14 pages