Related papers: Extended Differential Aggregations in Process Alge…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
Four adaptations of the smoothed aggregation algebraic multigrid (SA-AMG) method are proposed with an eye towards improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak…
Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first…
We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and…
With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and…
We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…
We consider the problem of evaluating certain types of functional aggregation queries on relational data subject to additive inequalities. Such aggregation queries, with a smallish number of additive inequalities, arise naturally/commonly…
We consider a linear integro-differential equation which arises to describe both aggregation-fragmentation processes and cell division. We prove the existence of a solution $(\lb,\U,\phi)$ to the related eigenproblem. Such eigenelements are…
Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption…
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…
We introduce a method for obtaining analytic approximations to the evolution of Markovian open quantum systems. It is based on resumming a generalized Dyson series in a way that ensures optimal convergence even in the absence of a small…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…
Kinetics of collision processes with linear mixing rules are investigated analytically. The velocity distribution becomes self-similar in the long time limit and the similarity functions have algebraic or stretched exponential tails. The…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…
In this work we have obtained Maxwell-type equations for a compressible fluid which sources are functions of velocity and vorticity. A correlation function and the dispersion relation were analyzed as function of the Reynolds number. A…
Most real-world problems have huge state and/or action spaces. Therefore, a naive application of existing tabular solution methods is not tractable on such problems. Nonetheless, these solution methods are quite useful if an agent has…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the…