Human Posterior Parietal Cortex Plans Where to Reach and What to Avoid

In this time-resolved functional magnetic resonance imaging (fMRI) study, we aimed to trace the neuronal correlates of covert planning processes that precede visually guided motor behavior. Specifically, we asked whether human posterior parietal cortex has prospective planning activity that can be distinguished from activity related to retrospective visual memory and attention. Although various electrophysiological studies in monkeys have demonstrated such motor planning at the level of parietal neurons, comparatively little support is provided by recent human imaging experiments. Rather, a majority of experiments highlights a role of human posterior parietal cortex in visual working memory and attention. We thus sought to establish a clear separation of visual memory and attention from processes related to the planning of goal-directed motor behaviors. To this end, we compared delayed-response tasks with identical mnemonic and attentional demands but varying degrees of motor planning. Subjects memorized multiple target locations, and in a random subset of trials targets additionally instructed (1) desired goals or (2) undesired goals for upcoming finger reaches. Compared with the memory/attention-only conditions, both latter situations led to a specific increase of preparatory fMRI activity in posterior parietal and dorsal premotor cortex. Thus, posterior parietal cortex has prospective plans for upcoming behaviors while considering both types of targets relevant for action: those to be acquired and those to be avoided

Tractable Pathfinding for the Stochastic On-Time Arrival Problem

We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution is a pathfinding algorithm that uses the solution to the policy-based SOTA problem---which is of pseudo-polynomial-time complexity in the time budget of the journey---as a search heuristic for the optimal path. In particular, we show that this heuristic can be exceptionally efficient in practice, effectively making it possible to solve the path-based SOTA problem as quickly as the policy-based SOTA problem. Our secondary contribution is the extension of policy-based preprocessing to path-based preprocessing for the SOTA problem. In the process, we also introduce Arc-Potentials, a more efficient generalization of Stochastic Arc-Flags that can be used for both policy- and path-based SOTA. After developing the pathfinding and preprocessing algorithms, we evaluate their performance on two different real-world networks. To the best of our knowledge, these techniques provide the most efficient computation strategy for the path-based SOTA problem for general probability distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental Algorithms 2016 and published by Springer in the Lecture Notes in Computer Science series on June 1, 2016. Includes typographical corrections and modifications to pre-processing made after the initial submission to SODA'15 (July 7, 2014

Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Constraint-Based Qualitative Simulation

We consider qualitative simulation involving a finite set of qualitative relations in presence of complete knowledge about their interrelationship. We show how it can be naturally captured by means of constraints expressed in temporal logic and constraint satisfaction problems. The constraints relate at each stage the 'past' of a simulation with its 'future'. The benefit of this approach is that it readily leads to an implementation based on constraint technology that can be used to generate simulations and to answer queries about them.Comment: 10 pages, to appear at the conference TIME 200