Different approaches have been taken to defining randomness for non-computable probability measures. We will explain the approach of Reimann and Slaman, along with the uniform test approach first introduced by Levin and also used by Gács, Hoyrup and Rojas. We will show that these approaches are fundamentally equivalent. Having clarified what it means to be random for a non-computable probabilit...

Spatial interaction between two or more classes or species has important implications in various fields and causes multivariate patterns such as segregation or association. Segregation occurs when members of a class or species are more likely to be found near members of the same class or conspecifics; while association occurs when members of a class or species are more likely to be found near m...

1. Why were you initially drawn to the study of computation and randomness? 2 1.1. Physical randomness (classical) 2 1.2. Physical randomness (quantum) 2 1.3. Algorithmic randomness 3 1.4. Computer science randomness 3 1.5. Biology 4 2. What have we learned? 4 2.1. Physical randomness (classical) 5 2.2. Physical randomness (quantum) 5 2.3. Algorithmic randomness 5 2.4. Randomness in computer sc...

1. Why were you initially drawn to the study of computation and randomness? 2 1.1. Physical randomness (classical) 2 1.2. Physical randomness (quantum) 2 1.3. Algorithmic randomness 3 1.4. Computer science randomness 3 1.5. Biology 4 2. What have we learned? 4 2.1. Physical randomness (classical) 5 2.2. Physical randomness (quantum) 5 2.3. Algorithmic randomness 5 2.4. Randomness in computer sc...

We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The result...

A prospective randomized, placebo-controlled trial comparing mifepristone and vaginal misoprostol to vaginal misoprostol alone for elective termination of early pregnancy. Author: Dr Roopa Malik, Assistant Professor, Obstetrics and gynaecology department Pt BDS PGIMS Rohtak. Background: Vaginal misoprostol has been shown to be an effective single agent for medical agent for medical abortion. Th...

Planning with incomplete information may mean a number of diierent things; that certain facts of the initial state are not known, that operators can have random or nondeterministic eeects, or that the plans created contain sensing operations and are branching. Study of the complexity of incomplete information planning has so far been concentrated on probabilistic domains, where a number of resu...

We analyze a model of fault-tolerant systems in a probabilistic setting. The model has been introduced under the name of “sabotage games”. A reachability problem over graphs is considered, where a “Runner” starts from a vertex u and seeks to reach some vertex in a target set F while, after each move, the adversary “Blocker” deletes one edge. Extending work by Löding and Rohde (who showed PSpace...

We study the problem of finding robust equilibria in multiplayer concurrent games with mean payoff objectives. A (k, t)-robust equilibrium is a strategy profile such that no coalition of size k can improve the payoff of one its member by deviating, and no coalition of size t can decrease the payoff of other players. We are interested in pure equilibria, that is, solutions that can be implemente...

We formalize and analyze a new automata-theoretic problem termed control improvisation. Given an automaton, the problem is to produce an improviser, a probabilistic algorithm that randomly generates words in its language, subject to two additional constraints: the satisfaction of an admissibility predicate, and the exhibition of a specified amount of randomness. Control improvisation has multip...