Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Mathematica--A System for Doing Mathematics by Computer.

In the last decade, the research topic of automatic analysis of facial expressions has become a central topic in machine vision research. Nonetheless, there is a glaring lack of a comprehensive, readily accessible reference set of face images that could be used as a basis for benchmarks for efforts in the field. This lack of easily accessible, suitable, common testing resource forms the major impediment to comparing and extending the issues concerned with automatic facial expression analysis. In this paper, we discuss a number of issues that make the problem of creating a benchmark facial expression database difficult. We then present the MMI facial expression database, which includes more than 1500 samples of both static images and image sequences of faces in frontal and in profile view displaying various expressions of emotion, single and multiple facial muscle activation. It has been built as a Web-based direct-manipulation application, allowing easy access and easy search of the available images. This database represents the most comprehensive reference set of images for studies on facial expression analysis to date.

https://ibug.doc.ic.ac.uk/media/uploads/documents/PanticEtAl-ICME2005-final.pdf

Web-based database for facial expression analysis

Autoencoders play a fundamental role in unsupervised learning and in deep architectures for transfer learning and other tasks. In spite of their fundamental role, only linear autoencoders over the real numbers have been solved analytically. Here we present a general mathematical framework for the study of both linear and non-linear autoencoders. The framework allows one to derive an analytical treatment for the most non-linear autoencoder, the Boolean autoencoder. Learning in the Boolean autoencoder is equivalent to a clustering problem that can be solved in polynomial time when the number of clusters is small and becomes NP complete when the number of clusters is large. The framework sheds light on the different kinds of autoencoders, their learning complexity, their horizontal and vertical composability in deep architectures, their critical points, and their fundamental connections to clustering, Hebbian learning, and information theory.

/pdf/autoencoders-unsupervised-learning-and-deep-architectures-1pv6obbygf.pdf

Autoencoders, unsupervised learning and deep architectures

This paper surveys and compares various strategies for processing logic queries in relational databases. The survey and comparison is limited to the case of Horn Clauses with evaluable predicates but without function symbols. The paper is organized in three parts. In the first part, we introduce the main concepts and definitions. In the second, we describe the various strategies. For each strategy, we give its main characteristics, its application range and a detailed description. We also give an example of a query evaluation. The third part of the paper compares the strategies on performance grounds. We first present a set of sample rules and queries which are used for the performance comparisons, and then we characterize the data. Finally, we give an analytical solution for each query/rule system. Cost curves are plotted for specific configurations of the data.

/pdf/an-amateur-s-introduction-to-recursive-query-processing-4akrykp5r2.pdf

An amateur's introduction to recursive query processing strategies

Le probleme du reparateur itinerant consiste en la donnee d'un ensemble fini de points, et des temps de parcours entre ces points. Le but est de trouver une trajectoire qui passe par tous ces points et qui minimise la duree totale du trajet. On etudie ce probleme dans le cas ou tous les points sont alignes, et on presente une solution polynomiale. Si le retard maximum pour chaque point est borne, le probleme devient NP-complet, mais il peut etre resolu avec un algorithme pseudo-polynome

http://www.numdam.org/item/ITA_1986__20_1_79_0.pdf

The complexity of the travelling repairman problem

Runge–Kutta methods for fuzzy differential equations

We study the relative merits of the phase-lag property of Runge-Kutta pairs and we propose new explicit embedded pairs for the numerical solution of first order differential systems with periodical solution. We analyze two families of 5(4) paris and one family of 6(5) pairs with respect to the attainable phase-lag order. From each family we choose a pair with the highest achievable phase-lag order, optimized with respect to a measure of the magnitude of its truncation error coefficients. The new 5(4) algebraic order pairs are of phase-lag order 8(4) and 8(6) and they are both non-dissipative, while the 6(5) pair is dissipative and of phase-lag order 10(6). The new pairs exhibit an improved performance, in comparison with other currently known general and special purpose methods, when they are applied to semidiscretized hyperbolic equations and problems describing free and weakly forced oscillations.

Runge-Kutta pairs for periodic initial value problems

A five-stage fifth-order singly diagonally implicit Runge–Kutta–Nystrom method for the integration of second order differential equations possessing an oscillatory solution, is presented in this article This method is P-stable, which is recommended for problems with a theoretical solution consisting of a periodic part of moderate frequency with a high frequency oscillation with small amplitude superimposed It also attains an order which is one higher than existing methods of this type Numerical comparisons with existing methods of this type show its clear advantage

A P-stable singly diagonally implicit Runge–Kutta–Nyström method

Explicit Runge–Kutta formula pairs of different orders of accuracy form a class of efficient algorithms for treating nonstiff ordinary differential equations. So far, several Runge–Kutta pairs of order 6(5) have appeared in the literature. These pairs use 8 function evaluations per step and belong to certain families of solutions of a set of 54 nonlinear algebraic equations in 44 or 45 coefficients, depending on the use of the FSAL (first stage as last) device. These equations form a set of necessary and sufficient conditions that a 6(5) Runge–Kutta pair must satisfy. The solution of the latter is achieved by employing various types of simplifying assumptions. In this paper we make use of the fact that all these families of pairs satisfy a common set of simplifying assumptions. Using only these simplifying assumptions we define a new family of 6(5) Runge–Kutta pairs. Its main characteristic, which is also a property that no other known family shares, is that all of its nodes (except the last one, which eq...

G. Papageorgiou

Papers

The complexity of the travelling repairman problem

Runge–Kutta methods for fuzzy differential equations

Runge-Kutta pairs for periodic initial value problems

A P-stable singly diagonally implicit Runge–Kutta–Nyström method

A general family of explicit Runge-Kutta pairs of orders 6(5)