We investigate the Semidefinite Programming based Sums of squares (SOS) decomposition method, designed for global optimization of polynomials, in the context of the (Maximum) Satisfiability problem. To be specific, we examine the potential of this theory for providing tests for unsatisfiability and providing MAX-SAT upper bounds. We compare the SOS approach with existing upper bound and roundin...

The study of the piecewise linear differential systems goes back to Andronov, Vitt and Khaikin in 1920’s, nowadays such still continue receive attention many researchers mainly due their applications. We discontinuous formed by two centers separated a nonregular straight line. provide upper bounds for maximum number limit cycles that these can exhibit we show are reached. Hence, solve extended ...

The INFORM Lab testbed allows experimenting with high-level distributed information fusion, dynamic resource management and configuration management, given multiple constraints on the resources and their communications networks. The paper describes the architecture, the concepts of goals and situation evidence, algorithms for distributed information and dynamic resource management, and auto-con...

We study the problem of placing effective upper bounds for the number of zeros of solutions of Fuchsian systems on the Riemann sphere. The principal result is an explicit (non-uniform) upper bound, polynomially growing on the frontier of the class of Fuchsian systems of a given dimension n having m singular points. As a function of n, m, this bound turns out to be double exponential in the prec...

We consider the number of zeros of the integral $I(h) = oint_{Gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $Gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. We prove that the number of zeros of $I(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

These highly informal lecture notes aim at introducing and explaining several closely related problems on zeros of analytic functions defined by ordinary differential equations and systems of such equations. The main incentive for this study was its potential application to the tangential Hilbert 16th problem on zeros of complete Abelian integrals. The exposition consists mostly of examples ill...

The limit cycle bifurcations of a Z2 equivariant planar Hamiltonian vector field of degree 7 under Z2 equivariant degree 7 perturbation is studied. We prove that the given system can have at least 53 limit cycles. This is an improved lower bound for the weak formulation of Hilbert’s 16th problem for degree 7, i.e., on the possible number of limit cycles that can bifurcate from a degree 7 planar...

The bodies of the founders and representatives many prominent Orthodox families from Grand Duchy Lithuania were buried in catacombs Suprasl monastery 16th century. Some people transferred to altar part Church Annunciation Blessed Virgin Mary 1644. Currently, an important problem is protection reconstruction catacombs.

In these notes we describe heuristics to predict computational-tostatistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances. The methods we describe here are based on mature, albeit non-rigorous, tools...