Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio

Extending Finite Memory Determinacy to Multiplayer Games

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. For most of our conditions we provide counterexamples showing that they cannot be dispensed with. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant winning strategies.Comment: In Proceedings SR 2016, arXiv:1607.0269

This Time the Robot Settles for a Cost: A Quantitative Approach to Temporal Logic Planning with Partial Satisfaction

The specification of complex motion goals through temporal logics is increasingly favored in robotics to narrow the gap between task and motion planning. A major limiting factor of such logics, however, is their Boolean satisfaction condition. To relax this limitation, we introduce a method for quantifying the satisfaction of co-safe linear temporal logic specifications, and propose a planner that uses this method to synthesize robot trajectories with the optimal satisfaction value. The method assigns costs to violations of specifications from user-defined proposition costs. These violation costs define a distance to satisfaction and can be computed algorithmically using a weighted automaton. The planner utilizes this automaton and an abstraction of the robotic system to construct a product graph that captures all possible robot trajectories and their distances to satisfaction. Then, a plan with the minimum distance to satisfaction is generated by employing this graph as the high-level planner in a synergistic planning framework. The efficacy of the method is illustrated on a robot with unsatisfiable specifications in an office environment

Asymmetric Preorganization of Inverted Pair Residues in the Sodium-Calcium Exchanger

International audienceIn analogy with many other proteins, Na(+)/Ca(2+) exchangers (NCX) adapt an inverted twofold symmetry of repeated structural elements, while exhibiting a functional asymmetry by stabilizing an outward-facing conformation. Here, structure-based mutant analyses of the Methanococcus jannaschii Na(+)/Ca(2+) exchanger (NCX_Mj) were performed in conjunction with HDX-MS (hydrogen/deuterium exchange mass spectrometry) to identify the structure-dynamic determinants of functional asymmetry. HDX-MS identified hallmark differences in backbone dynamics at ion-coordinating residues of apo-NCX_Mj, whereas Na(+)or Ca(2+) binding to the respective sites induced relatively small, but specific, changes in backbone dynamics. Mutant analysis identified ion-coordinating residues affecting the catalytic capacity (kcat/Km), but not the stability of the outward-facing conformation. In contrast, distinct "noncatalytic" residues (adjacent to the ion-coordinating residues) control the stability of the outward-facing conformation, but not the catalytic capacity. The helix-breaking signature sequences (GTSLPE) on the α1 and α2 repeats (at the ion-binding core) differ in their folding/unfolding dynamics, while providing asymmetric contributions to transport activities. The present data strongly support the idea that asymmetric preorganization of the ligand-free ion-pocket predefines catalytic reorganization of ion-bound residues, where secondary interactions with adjacent residues couple the alternating access. These findings provide a structure-dynamic basis for ion-coupled alternating access in NCX and similar proteins

Dynamic distinctions in the Na + /Ca 2+ exchanger adopting the inward- and outward-facing conformational states

International audienceNa(+)/Ca(2+) exchanger (NCX) proteins operate through the alternating access mechanism, where the ion-binding pocket is exposed in succession either to the extracellular or the intracellular face of the membrane. The archaeal NCX_Mj (Methanococcus jannaschii NCX) system was used to resolve the backbone dynamics in the inward-facing (IF) and outward-facing (OF) states by analyzing purified preparations of apo- and ion-bound forms of NCX_Mj-WT and its mutant, NCX_Mj-5L6-8. First, the exposure of extracellular and cytosolic vestibules to the bulk phase was evaluated as the reactivity of single cysteine mutants to a fluorescent probe, verifying that NCX_Mj-WT and NCX_Mj-5L6-8 preferentially adopt the OF and IF states, respectively. Next, hydrogen-deuterium exchange-mass spectrometry (HDX-MS) was employed to analyze the backbone dynamics profiles in proteins, preferentially adopting the OF (WT) and IF (5L6-8) states either in the presence or absence of ions. Characteristic differences in the backbone dynamics were identified between apo NCX_Mj-WT and NCX_Mj-5L6-8, thereby underscoring specific conformational patterns owned by the OF and IF states. Saturating concentrations of Na(+) or Ca(2+) specifically modify HDX patterns, revealing that the ion-bound/occluded states are much more stable (rigid) in the OF than in the IF state. Conformational differences observed in the ion-occluded OF and IF states can account for diversifying the ion-release dynamics and apparent affinity (Km ) at opposite sides of the membrane, where specific structure-dynamic elements can effectively match the rates of bidirectional ion movements at physiological ion concentrations