Quantum and random walks as universal generators of probability distributions

Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a bell-shaped one in the second case. Here I show how one can impose any desired stochastic behavior (compatible with the continuity equation for the probability function) on both systems by the appropriate choice of time- and site-dependent coins. This implies, in particular, that one can devise quantum walks that show diffusive spreading without loosing coherence, as well as random walks that exhibit the characteristic fast propagation of a quantum particle driven by a Hadamard coin.Comment: 8 pages, 2 figures; revised and enlarged versio

Permissive Controller Synthesis for Probabilistic Systems

We propose novel controller synthesis techniques for probabilistic systems modelled using stochastic two-player games: one player acts as a controller, the second represents its environment, and probability is used to capture uncertainty arising due to, for example, unreliable sensors or faulty system components. Our aim is to generate robust controllers that are resilient to unexpected system changes at runtime, and flexible enough to be adapted if additional constraints need to be imposed. We develop a permissive controller synthesis framework, which generates multi-strategies for the controller, offering a choice of control actions to take at each time step. We formalise the notion of permissivity using penalties, which are incurred each time a possible control action is disallowed by a multi-strategy. Permissive controller synthesis aims to generate a multi-strategy that minimises these penalties, whilst guaranteeing the satisfaction of a specified system property. We establish several key results about the optimality of multi-strategies and the complexity of synthesising them. Then, we develop methods to perform permissive controller synthesis using mixed integer linear programming and illustrate their effectiveness on a selection of case studies

Efficient Emptiness Check for Timed B\"uchi Automata (Extended version)

The B\"uchi non-emptiness problem for timed automata refers to deciding if a given automaton has an infinite non-Zeno run satisfying the B\"uchi accepting condition. The standard solution to this problem involves adding an auxiliary clock to take care of the non-Zenoness. In this paper, it is shown that this simple transformation may sometimes result in an exponential blowup. A construction avoiding this blowup is proposed. It is also shown that in many cases, non-Zenoness can be ascertained without extra construction. An on-the-fly algorithm for the non-emptiness problem, using non-Zenoness construction only when required, is proposed. Experiments carried out with a prototype implementation of the algorithm are reported.Comment: Published in the Special Issue on Computer Aided Verification - CAV 2010; Formal Methods in System Design, 201

32. DATA REPORT: HYDRAULIC CONDUCTIVITY MEASUREMENTS ON DISCRETE SAMPLES COLLECTED FROM LEG 141, SITE 863

ABSTRACT Measurements made on samples collected across a prominent zone of cementation occurring at depths below ~400 mbsf at Site 863 suggest that this zone is associated with a 100 fold reduction in hydraulic conductivity. The cements are related to significant smectite and zeolite deposition and cause sharp changes in sonic velocity, porosity, and thermal conductivity. The current pore fluid chemistry profile suggests cementation is continuing in-situ at the present time

Neglect patients exhibit egocentric or allocentric neglect for the same stimulus contingent upon task demands

Hemispatial Neglect (HN) is a failure to allocate attention to a region of space opposite to where damage has occurred in the brain, usually the left side of space. It is widely documented that there are two types of neglect: egocentric neglect (neglect of information falling on the individual?s left side) and allocentric neglect (neglect of the left side of each object, regardless of the position of that object in relation to the individual). We set out to address whether neglect presentation could be modified from egocentric to allocentric through manipulating the task demands whilst keeping the physical stimulus constant by measuring the eye movement behaviour of a single group of neglect patients engaged in two different tasks (copying and tracing). Eye movements and behavioural data demonstrated that patients exhibited symptoms consistent with egocentric neglect in one task (tracing), and allocentric neglect in another task (copying), suggesting that task requirements may influence the nature of the neglect symptoms produced by the same individual. Different task demands may be able to explain differential neglect symptoms in some individuals