Публікації
GRAMMCell: Docking-based Cell Modeling Resource
J. Mol. Biology169085The environment inside biological cells is densely populated by macromolecules and other cellular components. The crowding has a significant impact on folding and stability of macromolecules, and on kinetics of molecular interactions. Computational approaches to cell modeling, such as molecular dynamics, provide details of macromolecular behavior in concentrated solutions. However, such simulations are either slow, when carried out at atomic resolution, or significantly coarse-grained. Protein docking has been widely used for predicting structures of protein complexes. Systematic docking approaches, such as those based on Fast Fourier Transform (FFT), map the entire intermolecular energy landscape by determining the position and depth of the energy minima. The GRAMMCell web server implements docking-based approach for simulating cell crowded environment by sampling the intermolecular energy landscape generated by GRAMM (Global RAnge Molecular Matching). GRAMM systematically maps the landscape by a spectrum of docking poses corresponding to stable (deep energy minima) and transient (shallow minima) protein interactions. The sampling of these energy landscapes of a large system of proteins is performed in GRAMMCell using highly optimized Markov Chain Monte Carlo protocol. The procedure allows simulation of extra-long trajectories of large, crowded protein systems with atomic resolution accuracy. GRAMMCell is available at https://grammcell.compbio.ku.eduScimago Journal & Country Rank Q12025Highly Optimized Simulation of Atomic Resolution Cell-Like Protein Environment
J. Phys. Chem.B 129 no. 12 3183–3190Computational approaches can provide details of molecular mechanisms in a crowded environment inside cells. Protein docking predicts stable configurations of molecular complexes, which correspond to deep energy minima. Systematic docking approaches, such as those based on fast Fourier transform (FFT), also map the entire intermolecular energy landscape by determining the position and depth of the full spectrum of the energy minima. Such mapping allows speeding up simulations by precalculating the intermolecular energy values. Our earlier study combined FFT docking with the Monte Carlo protocol, enabling simulation of cell-size, crowded protein systems with seconds, and longer trajectories at atomic resolution, several orders of magnitude longer than those achievable by alternative approaches. In this study, we present a further drastic extension of the modeling capabilities by parallelized implementation of the simulation protocol. The procedure was applied to a panel of Death Fold Domains that form nucleated polymers in human innate immune signaling, recapitulating their homooligomerization tendencies and providing insights into the molecular mechanisms of polymer nucleation. The parallelized protocol allows extension of the simulation trajectories by orders of magnitude beyond the previously reported implementation, reaching into the uncharted territory of atomic resolution simulation of cell-sized systems. Copyright © 2025 The Authors. Published by American Chemical SocietyScimago Journal & Country Rank Q22025Acute angle lemma for noncompact image sets
J. Fixed Point Theory Appl.27 no. 67This note establishes an extension of the acute angle lemma (also known as the Hairy Ball Theorem or the Hedgehog Theorem in the case of single-valued mappings) to multifunctions with noncompact image sets. The main result establishes the existence of solutions for operator inclusions involving upper semi-continuous multifunctions with convex values. By relaxing the coercivity assumptions typically required in such analyses, we extend the applicability to scenarios where standard dissipation conditions do not hold. The introduced framework leverages the concept of -inf-compact support to ensure the existence of zeroes for multifunctions under less restrictive conditions. Applications to hemivariational inequalities and related variational problems are discussed. The examples and counterexamples that demonstrate the obtained generalizations are provided.Scimago Journal & Country Rank Q12025Continuity of filters for discrete-time control problems defined by explicit equations
SIAM J. Control Optim.63 no. 3Discrete time control systems whose dynamics and observations are described by stochastic equations are common in engineering, operations research, health care, and economics. For example, stochastic filtering problems are usually defined via stochastic equations. These problems can be reduced to Markov decision processes (MDPs) whose states are posterior state distributions, and transition probabilities for such MDPs are sometimes called filters. This paper investigates sufficient conditions on transition and observation functions for the original problems to guarantee weak continuity of the filter. Under mild conditions on cost functions, weak continuity implies the existence of optimal policies minimizing the expected total costs, the validity of optimality equations, and convergence of value iterations to optimal values. This paper uses recent results on weak continuity of filters for partially observable MDPs defined by transition and observation probabilities. It develops a criterion of weak continuity of transition probabilities and a sufficient condition for continuity in total variation of transition probabilities. The results are illustrated with applications to filtering problems.Scimago Journal & Country Rank Q12025Sufficient conditions for solving statistical filtering problems by dynamic programming
Proc. IEEE Conf. Decision Control4052–4057The paper studies discrete-time statistical filtering problems with the goal to minimize expected total costs. Such problems are usually defined by pairs of stochastic equations and by one-step cost functions. Stochastic equations describe the state and observation processes, and these equations are defined by transition and observation functions. This paper provides sufficient conditions on observation, transition, and one-step cost functions for convergence of value-iteration algorithms for problems with finite and infinite horizons. It is well-known that nonlinear and linear filtering problems can be presented as Partially Observable Markov Decision Processes (POMDPs). The paper applies contemporary results on convergence of value iterations for Markov Decision Processes (MDPs) and for POMDPs to filtering problems. It formulates conditions on observation and transition functions which imply weak continuity of the filter. Weak continuity of the filter means weak continuity of transition probabilities between belief states. The sufficient condition on one-step functions is their K-inf-compactness. The described conditions hold for broad classes of nonlinear filters and for Kalman filters.2024Solutions for zero-sum two-player games with noncompact decision sets
Naval Res. Logist.70 no. 5, 493–506This article provides sufficient conditions for the existence of solutions for two-person zero-sum games with inf/sup-compact payoff functions and with possibly noncompact decision sets for both players. Payoff functions may be unbounded, and we do not assume any convexity/concavity-type conditions. For such games expected payoff may not exist for some pairs of strategies. The results of this article imply several classic facts. The article also provides sufficient conditions for the existence of a value and solutions for each player. The results of this article are illustrated with the number guessing game.Scimago Journal & Country Rank Q12023Equivalent conditions for weak continuity of nonlinear filters
Systems Control Lett.173, 105458This paper studies weak continuity of nonlinear filters. It is well-known that Borel measurability of transition probabilities for problems with incomplete state observations is preserved when the original discrete-time process is replaced with the process whose states are belief probabilities. It is also known that the similar preservation may not hold for weak continuity of transition probabilities. In this paper we show that the sufficient condition for weak continuity of transition probabilities for beliefs introduced by Kara et al. (2019) is a necessary and sufficient condition for semi-uniform Feller continuity of transition probabilities. The property of semi-uniform Feller continuity was introduced recently by Feinberg et al. (2022), and the original transition probability for a Markov decision processes with incomplete information has this property if and only if the transition probability of the process, whose state is a pair consisting of the belief probability and observation, also has this property. Thus, this property implies weak continuity of nonlinear filters. This paper also reviews several necessary and sufficient conditions for semi-uniform Feller continuity.Scimago Journal & Country Rank Q12023Epi-convergence of expectation functions under varying measures and integrands
J. Convex Anal.30 no. 3, 917–936For expectation functions on metric spaces, we provide sufficient conditions for epi-convergence under varying probability measures and integrands, and examine applications in the area of sieve estimators, mollifier smoothing, PDE-constrained optimization, and stochastic optimization with expectation constraints. As a stepping stone to epi-convergence of independent interest, we develop parametric Fatou's lemmas under mild integrability assumptions. In the setting of Suslin metric spaces, the assumptions are expressed in terms of Pasch-Hausdorff envelopes. For general metric spaces, the assumptions shift to semicontinuity of integrands also on the sample space, which then is assumed to be a metric space.2023Semi-uniform Feller stochastic kernels
J. Theoret. Probab.36, 2262–2283This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies the property of semi-uniform Feller continuity. This paper provides several equivalent definitions of semi-uniform Feller continuity and establishes its preservation under integration. The motivation for this study came from the theory of Markov decision processes with incomplete information, and this paper provides the fundamental results useful for this theory.Scimago Journal & Country Rank Q22023Formalization of methods for the development of autonomous artificial intelligence systems
Cybernet. Syst. Anal.59, 763–771This paper explores the problem of formalizing the development of autonomous artificial intelligence systems (AAISs) whose mathematical models may be complex or non-identifiable. Using the value-iterations method for Q-functions of rewards, a methodology for constructing ε-optimal strategies with a given accuracy was developed. The results allow us to outline classes (including dual-use), for which it is possible to rigorously justify the construction of optimal and ε-optimal strategies even in cases where the models are identifiable, but the computational complexity of standard dynamic programming algorithms may not be strictly polynomial.Scimago Journal & Country Rank Q32023