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Comparison of an artificial neural network and Gompertz model for predicting the dynamics of deaths from COVID-19 in Mexico

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NONLINEAR DYNAMICS 2021年第4期104卷 4655-4669页

作者： Conde-Gutierrez, R. A. Colorado, D. Hernandez-Bautista, S. L. Univ Veracruzana Ctr Invest Recursos Energet & Sustentables Av Univ Km 7-5 Coatzacoalcos Sp 96535 Veracruz Mexico Univ Veracruzana Ctr Invest Recursos Energet & Sustentables Fac Ciencias Quim Campus CoatzacoalcosAv Univ Km 7-5 Coatzacoalcos Sp 96535 Veracruz Mexico

The present work is focused on modeling and predicting the cumulative number of deaths from COVID-19 in Mexico by comparing an artificial neural network (ANN) with a Gompertz model applying multiple optimization algorithms for the estimation of coefficients and parameters, respectively. For the modeling process, the data published by the daily technical report COVID-19 in Mexico from March 19th to September 30th were used. The data published in the month of October were included to carry out the prediction. The results show a satisfactory comparison between the real data and those obtained by both models with a R-2 > 0.999. The Levenberg-Marquardt and BFGS quasi-Newton optimization algorithm were favorable for fitting the coefficients during learning in the ANN model due to their fast and precision, respectively. On the other hand, the Nelder-Mead simplex algorithm fitted the parameters of the Gompertz model faster by minimizing the sum of squares. Therefore, the ANN model better fits the real data using ten coefficients. However, the Gompertz model using three parameters converges in less computational time. In the prediction, the inverse ANN model was solved by a genetic algorithm obtaining the best precision with a maximum error of 2.22% per day, as opposed to the 5.48% of the Gompertz model with respect to the real data reported from November 1st to 15th. Finally, according to the coefficients and parameters obtained from both models with recent data, a total of 109,724 cumulative deaths for the inverse ANN model and 100,482 cumulative deaths for the Gompertz model were predicted for the end of 2020.

关键词： COVID-19 Dynamic models Artificial neural network model Gompertz model optimal algorithms

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Deterministic Quadrature Formulas for SDEs Based on Simplified Weak It-Taylor Steps

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2016年第5期16卷 1325-1366页

作者： Mueller-Gronbach, Thomas Yaroslavtseva, Larisa Univ Passau Fak Informat & Math Innstr 33 D-94032 Passau Germany

We study the problem of approximating the expected value of a function f of the solution X of a d-dimensional system of stochastic differential equations (SDE) at time point 1 based on finitely many evaluations of the coefficients of the SDE, the integrand f and their derivatives. We present a deterministic algorithm, which produces a quadrature rule by iteratively applying a Markov transition based on the distribution of a simplified weak It-Taylor step together with strategies to reduce the diameter and the size of the support of a discrete measure. We essentially assume that the coefficients of the SDE are s-times continuously differentiable and the diffusion coefficient satisfies a uniform non-degeneracy condition and that the integrand f is r-times continuously differentiable. In the case , we almost achieve an error of order in terms of the computational cost, which is optimal in a worst-case sense.

关键词： Quadrature of SDEs Simplified weak Ito-Taylor step Lower bounds optimal algorithms

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Randomized and quantum complexity of nonlinear two-point BVPs

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APPLIED MATHEMATICS AND COMPUTATION 2014年第0期245卷 357-371页

作者： Gocwin, Maciej AGH Univ Sci & Technol Fac Appl Math PL-30059 Krakow Poland

We deal with the complexity of nonlinear BVPs with nonlinear two-point boundary conditions. We consider the randomized and quantum models of computation. We assume that the right-hand side function is r times differentiable with all derivatives bounded by a constant. We show that the epsilon-complexity is roughly of order epsilon(-1/(r+1/2)) in the randomized setting, and epsilon(-1/(r+1)) in the quantum setting. We compare our results with known results in the deterministic setting. The speed-up of the randomized computations with respect to the deterministic computations is by 1/(r(2r + 1)) in the exponent of 1/epsilon, and the speed-up of the quantum computations by 1/(r(r +1)) in the exponent. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Boundary value problems Complexity optimal algorithms Randomized computing Quantum computing

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WHAT IS THE COMPLEXITY OF ILL-POSED PROBLEMS

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 1987年第9-10期9卷 945-967页

作者： WERSCHULZ, AG FORDHAM UNIV DIV SCI & MATHNEW YORKNY 10023 COLUMBIA UNIV DEPT COMP SCINEW YORKNY 10027

This paper deals with the optimal solution of ill-posed linear problems, i.e..linear problems for which the solution operator is unbounded. We consider worst-case ar,and averagecase settings. Our main result is that algorithms having finite error (for a given setting) exist if and only if the solution operator is bounded (in that setting). In the worst-case setting, this means that there is no algorithm for solving ill-posed problems having finite error. In the average-case setting, this means that algorithms having finite error exist if and only lf the solution operator is bounded on the average. If the solution operator is bounded on the average, we find average-case optimal information of cardinality n and optimal algorithms using this information, and show that the average error of these algorithms tends to zero as n→∞. These results are then used to determine the [euro]-complexity, i.e., the minimal costof finding an [euro]-accurate approximation. In the worst-case setting, the [euro]comp1exity of an illposed problem is infinite for all [euro]>0; that is, we cannot find an approximation having finite error and finite cost. In the average-case setting, the [euro]-complexity of an ill-posed problem is infinite for all [euro]>0 iff the solution operator is not bounded on the average, moreover, if the the solutionoperator is bounded on the average, then the [euro]-complexity is finite for all [euro]>0.

关键词： Ill-posed problems integral equations Fredholm problem of the first kind optimal algorithms computational complexity. 1980 Mathematics subject classifications: Primary: 65R20 68C05 68C25. Secondary: 28C20 35R25 44A10 45L10 47B05 60B11.

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LINEAR-TIME OPTIMIZATION algorithms FOR P-4-SPARSE GRAPHS

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DISCRETE APPLIED MATHEMATICS 1995年第2期61卷 155-175页

作者： JAMISON, B OLARIU, S OLD DOMINION UNIV DEPT COMP SCINORFOLKVA 23529 MARYMOUNT UNIV DEPT COMP SCIARLINGTONVA 22347

Quite often, real-life applications suggest the study of graphs that feature some local density properties. In particular, graphs that are unlikely to have more than a few chordless paths of length three appear in a number of contexts. A graph G is P-4-sparse if no set of five vertices in G induces more than one chordless path of length three. P-4-sparse graphs generalize both the class of cographs and the class of P-4-reducible graphs. It has been shown that P-4-sparse graphs can be recognized in time linear in the size of the graph. The main contribution of this paper is to show that once the data structures returned by the recognition algorithm are in place, a number of NP-hard problems on general graphs can be solved in linear time for P-4-sparse graphs. Specifically with an n-vertex P-4-sparse graph as input the problems of finding a maximum size clique, maximum size stable set, a minimum coloring, a minimum covering by clique, and the size of the minimum fill-in can be solved in O(n) time, independent of the number of edges in the graph.

关键词： OPTIMIZATION NP-HARD PROBLEMS RESOURCE ALLOCATION LOCAL DENSITY LINEAR algorithms optimal algorithms

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Distributed algorithms for barrier coverage using relocatable sensors

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DISTRIBUTED COMPUTING 2016年第5期29卷 361-376页

作者： Eftekhari, Mohsen Kranakis, Evangelos Krizanc, Danny Morales-Ponce, Oscar Narayanan, Lata Opatrny, Jaroslav Shende, Sunil Concordia Univ Dept Comp Sci & Software Engn Montreal PQ Canada Carleton Univ Sch Comp Sci Ottawa ON Canada Wesleyan Univ Dept Math & Comp Sci Middletown CT 06459 USA Chalmers Univ Technol Dept Comp Sci Gothenburg Sweden Rutgers State Univ Dept Comp Sci Camden NJ USA

We study the barrier coverage problem using relocatable sensor nodes. We assume each sensor can sense an intruder or event inside its sensing range. Sensors are initially located at arbitrary positions on the barrier and can move along the barrier. The goal is to find final positions for sensors so that the entire barrier is covered. In recent years, the problem has been studied extensively in the centralized setting. In this paper, we study a barrier coverage problem in the distributed and discrete setting. We assume that we have n identical sensors located at grid positions on the barrier, and that each sensor repeatedly executes a Look-Compute-Move cycle: based on what it sees in its vicinity, it makes a decision on where to move, and moves to its next position. We make two strong but realistic restrictions on the capabilities of sensors: they have a constant visibility range and can move only a constant distance in every cycle. In this model, we give the first two distributed algorithms that achieve barrier coverage for a line segment barrier when there are enough nodes in the network to cover the entire barrier. Our algorithms are synchronous, and local in the sense that sensors make their decisions independently based only on what they see within their constant visibility range. One of our algorithms is oblivious whereas the other uses two bits of memory at each sensor to store the type of move made in the previous step. We show that our oblivious algorithm terminates within steps with the barrier fully covered, while the constant-memory algorithm is shown to take steps to terminate in the worst case. Since any algorithm in which a sensor can only move a constant distance in one step requires steps on some inputs, our second algorithm is asymptotically optimal.

关键词： Barrier coverage Wireless relocatable sensors Autonomous mobile robots optimal algorithms Distributed algorithms

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PIECEWISE POLYNOMIAL algorithms FOR THE ANALYSIS OF PROCESSES IN INHOMOGENEOUS MEDIA

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CYBERNETICS AND SYSTEMS ANALYSIS 2018年第4期54卷 636-642页

作者： Bilenko, V., I Bozhonok, K., V Dzyadyk, S. Yu Stelya, O. B. Natl Pedag Dragomanov Univ Kiev Ukraine State Univ Telecommun Kiev Ukraine Taras Shevchenko Natl Univ Kyiv Kiev Ukraine

The authors propose, theoretically substantiate, and programmatically implement high-precision numerical-analytical algorithms for approximation of problems solutions in inhomogeneous media on the basis of linear poly... 详细信息

关键词： piecewise polynomial approximation inhomogeneous medium unsaturation best approximation algebraic-nonlinear equations optimal algorithms computational optimization parabolic splines of special kind

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USING RESERVES FOR COMPUTATION OPTIMIZATION TO IMPROVE THE INTEGRATION OF RAPIDLY OSCILLATING FUNCTIONS

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CYBERNETICS AND SYSTEMS ANALYSIS 2011年第4期47卷 613-630页

作者： Zadiraka, V. K. Lnikova, S. S. Me. Lutsatt, L. V. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

We present a theory of evaluating integrals of rapidly oscillating functions in various classes of subintegral functions with the use of a mesh information operator on subintegral functions. The theory allows us to derive and prove optimal (with respect to accuracy and (or) performance) and nearly optimal quadrature formulas and to test their quality against well-known and proposed numerical integration algorithms and to determine their efficiency domains. A technique is proposed to determine the optimal parameters of computational algorithms that obtain the epsilon-solution of the problem.

关键词： integrals of rapidly oscillating functions quadrature formulas optimal algorithms quality characteristic testing epsilon-solution of a problem

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WHAT IS THE COMPLEXITY OF RELATED ELLIPTIC, PARABOLIC, AND HYPERBOLIC PROBLEMS

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MATHEMATICS OF COMPUTATION 1986年第176期47卷 461-472页

作者： WERSCHULZ, AG COLUMBIA UNIV DEPT COMP SCINEW YORKNY 10027

Abstract: Traub and Woźniakowski have dealt with the complexity of some simple partial differential equations. They chose three model problems and showed that the parabolic problem considered had significantly lower complexity than the elliptic problem, which in turn had significantly lower complexity than the hyperbolic problem considered. They asked whether this is true in general. We show that this is not the case by proving that if L is a reasonably well-behaved elliptic operator, then the steady-state heat equation $Lu = f$, the heat equation ${\partial _t}u + Lu = f$, and the wave equation ${\partial _{tt}}u + Lu = f$ all have roughly the same worst-case complexity for f in the unit ball of a certain Sobolev space of smoothness r.

关键词： optimal solution of partial differential equations elliptic problems parabolic problems hyperbolic problems computational complexity information-based complexity optimal algorithms

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Surface approximation is sometimes easier than surface integration

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CONSTRUCTIVE APPROXIMATION 2004年第2期20卷 267-302页

作者： Werschulz, AG Wozniakowski, H Fordham Univ Dept Comp & Informat Sci New York NY 10023 USA Columbia Univ Dept Comp Sci New York NY 10027 USA Univ Warsaw Inst Appl Math PL-00325 Warsaw Poland

The approximation and integration problems consist of finding an approximation to a function f or its integral over some fixed domain Sigma. For the classical version of these problems, we have partial information about the functions f and complete information about the domain Sigma;for example, Sigma might be a cube or ball in R-d. When this holds, it is generally the case that integration is not harder than approximation;moreover, integration can be much easier than approximation. What happens if we have partial information about Sigma? This paper studies the surface approximation and surface integration problems, in which Sigma = Sigma(g) for functions g. More specifically, the functions f are r times continuously differentiable scalar functions of l variables, and the functions g are s times continuously differentiable injective functions of d variables with l components. The class of surfaces considered is generated as images of cubes or balls, or as oriented cellulated regions. Error for the surface approximation problem is measured in the L-q-sense. These problems are well defined, provided that dless than or equal tol, rgreater than or equal to0, and sgreater than or equal to1. Information consists of function evaluations of f and g. We show that the epsilon-complexity of surface approximation is proportional to (1/epsilon)(1/mu) with mu = min{r,s}/d. We also show that if s greater than or equal to 2, then the epsilon-complexity of surface integration is proportional to (1/epsilon)(1/nu) with nu = min{r/d, s-delta(s,1)(1-delta(d,l))/min{d,l-1}}}. (This bound holds as well for several subcases of s=1;we conjecture that it holds for all rgreater than or equal to0, sgreater than or equal to1, and dless than or equal tol.) Using these results, we determine when surface approximation is easier than, as easy as, or harder than, surface integration;all three possibilities can occur. In particular, we find that if r=s=1 and d

关键词： surface approximation surface integration complexity optimal algorithms

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