We give an effective sufficient condition for a variational problem with infinite horizon on a Riemannian manifold M to admit a smooth optimal synthesis, i. e. a smooth dynamical system on M whose positive semi-trajectories are solutions to the problem. To realize the synthesis we construct a well-projected to M invariant Lagrange submanifold of the extremals’ flow in the cotangent bundle T ∗M ...

We study some percolation problems on the complete graph over N. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the probability, such as independency, is made. The main tools are a topological version of Ramsey theory, exchangeability theory and elementary ergodic theory.

A nondeterministic automaton is called unambiguous if it has at most one accepting run on every input. A regular language is called unambiguous if there exists an unambiguous automaton recognizing this language. Currently, the class of unambiguous languages of infinite trees is not well-understood. In particular, there is no known decision procedure verifying if a given regular tree language is...

Allowing templates with infinite domains greatly expands the range of problems that can be formulated as a non-uniform constraint satisfaction problem. It turns out that many CSPs over infinite templates can be formulated with templates that are ω-categorical. We survey examples of such problems in temporal and spatial reasoning, infinite-dimensional algebra, acyclic colorings in graph theory, ...

In this paper we derive new properties of extreme inequalities for infinite group problems. We develop tools to prove that given valid inequalities for the infinite group problem are extreme. These results show that integer infinite group problems have discontinuous extreme inequalities. These inequalities are strong when compared to related classes of continuous extreme inequalities. This give...

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon meshrefinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and t...