Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments

* This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Adaptive Control and Multi-agent Interface for Infotelecommunication Systems of New Generation

Problems for intellectualisation for man-machine interface and methods of self-organization for network control in multi-agent infotelecommunication systems have been discussed. Architecture and principles for construction of network and neural agents for telecommunication systems of new generation have been suggested. Methods for adaptive and multi-agent routing for information flows by requests of external agents- users of global telecommunication systems and computer networks have been described.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.

Asymptotic Expansion of Solution for Almost Regular and Weakly Perturbed Systems of Ordinary Differential Equations

Л. И. Каранджулов, Н. Д. Сиракова - В работата се прилага методът на Поанкаре за решаване на почти регулярни нелинейни гранични задачи при общи гранични условия. Предполага се, че диференциалната система съдържа сингулярна функция по отношение на малкия параметър. При определени условия се доказва асимптотичност на решението на поставената задача.

A general Approach to Methods with a Sparse Jacobian for Solving Nonlinear Systems of Equations

2000 Mathematics Subject Classification: 65H10.

Revisiting goal-oriented models for self-aware systems-of-systems

Systems-of-systems (SoS) are systems resulted from the interaction among other independent constituent systems that collaborate to offer new functionalities towards accomplishing global missions. Each of these constituent systems accomplishes its individual missions and is able to contribute to the achievement of the global missions of the SoS, both being viewed as a set of associated goals. In the perspective of self-aware systems, SoS need to exhibit goal-awareness, i.e., They need to be aware of their own goals and of how their constituent systems contribute to their accomplishment. In this paper, we revisit goal-oriented concepts aiming at identifying and modeling goals at both SoS level and the constituent systems level. Moreover, we take advantage of such goal-oriented models to express the relationship among goals at these levels as well as to define how each constituent system can contribute to the accomplishment of global goals of an SoS. In addition, we shed light on important issues related to goal modeling in self-aware SoS to be addressed in future research.