Limit Synchronization in Markov Decision Processes

Markov decision processes (MDP) are finite-state systems with both strategic and probabilistic choices. After fixing a strategy, an MDP produces a sequence of probability distributions over states. The sequence is eventually synchronizing if the probability mass accumulates in a single state, possibly in the limit. Precisely, for 0 <= p <= 1 the sequence is p-synchronizing if a probability distribution in the sequence assigns probability at least p to some state, and we distinguish three synchronization modes: (i) sure winning if there exists a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there exists a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there exists a strategy that produces a (1-epsilon)-synchronizing sequence. We consider the problem of deciding whether an MDP is sure, almost-sure, limit-sure winning, and we establish the decidability and optimal complexity for all modes, as well as the memory requirements for winning strategies. Our main contributions are as follows: (a) for each winning modes we present characterizations that give a PSPACE complexity for the decision problems, and we establish matching PSPACE lower bounds; (b) we show that for sure winning strategies, exponential memory is sufficient and may be necessary, and that in general infinite memory is necessary for almost-sure winning, and unbounded memory is necessary for limit-sure winning; (c) along with our results, we establish new complexity results for alternating finite automata over a one-letter alphabet

Leader Election in Anonymous Rings: Franklin Goes Probabilistic

We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size

An Event Structure Model for Probabilistic Concurrent Kleene Algebra

We give a new true-concurrent model for probabilistic concurrent Kleene algebra. The model is based on probabilistic event structures, which combines ideas from Katoen's work on probabilistic concurrency and Varacca's probabilistic prime event structures. The event structures are compared with a true-concurrent version of Segala's probabilistic simulation. Finally, the algebraic properties of the model are summarised to the extent that they can be used to derive techniques such as probabilistic rely/guarantee inference rules.Comment: Submitted and accepted for LPAR19 (2013

Geometry-dependent electrostatics near contact lines

Long-ranged electrostatic interactions in electrolytes modify their contact angles on charged substrates in a scale and geometry dependent manner. For angles measured at scales smaller than the typical Debye screening length, the wetting geometry near the contact line must be explicitly considered. Using variational and asymptotic methods, we derive new transcendental equations for the contact angle that depend on the electrostatic potential only at the three phase contact line. Analytic expressions are found in certain limits and compared with predictions for contact angles measured with lower resolution. An estimate for electrostatic contributions to {\it line} tension is also given.Comment: 3 .eps figures, 5p

Population Pharmacokinetic Modelling of Intravenous Immunoglobulin Treatment in Patients with Guillain–Barré Syndrome

BACKGROUND AND OBJECTIVE: Intravenous immunoglobulin (IVIg) at a standard dosage is the treatment of choice for Guillain–Barré syndrome. The pharmacokinetics, however, is highly variable between patients, and a rapid clearance of IVIg is associated with poor recovery. We aimed to develop a model to predict the pharmacokinetics of a standard 5-day IVIg course (0.4 g/kg/day) in patients with Guillain–Barré syndrome. METHODS: Non-linear mixed-effects modelling software (NONMEM(®)) was used to construct a pharmacokinetic model based on a model-building cohort of 177 patients with Guillain–Barré syndrome, with a total of 589 sequential serum samples tested for total immunoglobulin G (IgG) levels, and evaluated on an independent validation cohort that consisted of 177 patients with Guillain–Barré syndrome with 689 sequential serum samples. RESULTS: The final two-compartment model accurately described the daily increment in serum IgG levels during a standard IVIg course; the initial rapid fall and then a gradual decline to steady-state levels thereafter. The covariates that increased IgG clearance were a more severe disease (as indicated by the Guillain–Barré syndrome disability score) and concomitant methylprednisolone treatment. When the current dosing regimen was simulated, the percentage of patients who reached a target ∆IgG > 7.3 g/L at 2 weeks decreased from 74% in mildly affected patients to only 33% in the most severely affected and mechanically ventilated patients (Guillain–Barré syndrome disability score of 5). CONCLUSIONS: This is the first population-pharmacokinetic model for standard IVIg treatment in Guillain–Barré syndrome. The model provides a new tool to predict the pharmacokinetics of alternative regimens of IVIg in Guillain–Barré syndrome to design future trials and personalise treatment. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s40262-022-01136-z