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.

Experimental analysis of soil and dust stabilizers for controlling displacement of contaminated soils by wind tunnel experiments

During the remediation of burial grounds at the US Department of Energy's (DOE's) Hanford Site in Washington State, the dispersion of contaminated soil particles and dust is an issue that is faced by site workers on a daily basis. This contamination problem is even more of a concern when one takes into account the semi-arid characteristics of the region where the site is located. To mitigate this problem, workers at the site use a variety of engineered methods to minimize the dispersion of contaminated soil and dust (i.e. use of water and/or suppression agents that stabilizes the soil prior to soil excavation, segregation, and removal activities). A primary contributor to the dispersion of contaminated soil and dust is wind soil erosion. The erosion process occurs when the wind speed exceeds a certain threshold value which depends on a number of factors including wind force loading, particle size, surface soil moisture, and the geometry of the soil. Thus under these circumstances, the mobility of contaminated soil and generation and dispersion of particulate matter are significantly influenced by these parameters. This dependence of soil and dust movement on threshold shear velocity, fixative dilution and/or application rates, soil moisture content, and soil geometry were studied for Hanford's sandy soil through a series of wind tunnel experiments, laboratory experiments and theoretical analysis. In addition, the behavior of plutonium (Pu) powder contamination in the soil was studied by introducing a Pu simulant (cerium oxide). The results showed that soil dispersion and PM10 concentrations decreased with increasing soil moisture. Also, it was shown that the mobility of the soil was affected by increasing wind velocity. It was demonstrated that the use of fixative products greatly decreased the amount of soil and PM10 concentrations when exposed to varying wind conditions. In addition, it was shown that geometry of the soil sample affected the velocity profile and calculation of roughness surface coefficient when comparing round and flat soil samples. Finally, threshold shear velocities were calculated for soil with flat surface and their dependency on surface soil moisture was demonstrated. A theoretical framework was developed to explain these dependencies.

Chemical characterization of soil organic matter in an oligotrophic, subtropical, freshwater wetland system: Sources, diagenesis and preservation

Freshwater wetland soils of the Everglades were studied in order to assess present environmental conditions and paleo-environmental changes using organic geochemistry techniques. Organic matter in dominant vegetation, peat and marl soils was characterized by geochemical means. Samples were selected along nutrient and hydrology gradients with the objective to determine the historical sources of organic matter as well as the extent of its preservation. Effective molecular proxies were developed to differentiate the relative input of organic matter from different biological sources to wetland soils. Thus historical vegetation shifts and hydroperiods were reconstructed using those proxies. The data show good correlations with historical water management practices starting at the turn of the century and during the mid 1900's. Overall, significant shortening of hydroperiods during this period was observed. The soil organic matter (SOM) preservation was assessed through elemental analysis and molecular characterizations of bulk 13C stable isotopes, solid state 13C NMR spectroscopy, UV-Vis spectroscopy, and tetramethyl ammonium hydroxide (TMAH) thermochemolysis-GC/MS. The relationship of the environmental conditions and degradation status of the soil organic matter (SOM) among the sites suggested that both high nutrient levels and long hydroperiod favor organic matter degradation in the soils. This is probably the result of an increase in the microbial activity in the soils which have higher nutrient levels, while longer hydroperiods may enhance physical/chemical degradation processes. The most significant transformations of biomass litter in this environment are controlled by very early physical/chemical processes and once the OM is incorporated into surface soils, the diagenetic change, even over extended periods of time is comparatively minimal, and SOM is relatively well preserved regardless of hydroperiod or nutrient levels. SOM accumulated in peat soils is more prone to continued degradation than the SOM in the marl soils. The latter is presumably stabilized early on through direct air exposure (oxidation) and thus, it is more refractory to further diagenetic transformations such as humification and aromatization reactions.