Multipartite Moore digraphs

We derive some Moore-like bounds for multipartite digraphs, which extend those of bipartite digraphs, under the assumption that every vertex of a given partite set is adjacent to the same number $\delta$ of vertices in each of the other independent sets. We determine when a Moore multipartite digraph is weakly distance-regular. Within this framework, some necessary conditions for the existence of a Moore $r$-partite digraph with interpartite outdegree $\delta>1$ and diameter $k=2m$ are obtained. In the case $\delta=1$, which corresponds to almost Moore digraphs, a necessary condition in terms of the permutation cycle structure is derived. Additionally, we present some constructions of dense multipartite digraphs of diameter two that are vertex-transitive

Optimal Strategies in Infinite-state Stochastic Reachability Games

We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from this subclass, and second, these games are strongly determined. The subclass is defined by the property that the set of all values can only have one accumulation point -- 0. Our results nicely mirror recent results for finitely-branching games, where, on the contrary, Player Min always has optimal strategies. However, our proof methods are substantially different, because the roles of the players are not symmetric. We also do not restrict the branching of the games. Finally, we apply our results in the context of recently studied One-Counter stochastic games

Computer aided synthesis: a game theoretic approach

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Distributed Synthesis in Continuous Time

We introduce a formalism modelling communication of distributed agents strictly in continuous-time. Within this framework, we study the problem of synthesising local strategies for individual agents such that a specified set of goal states is reached, or reached with at least a given probability. The flow of time is modelled explicitly based on continuous-time randomness, with two natural implications: First, the non-determinism stemming from interleaving disappears. Second, when we restrict to a subclass of non-urgent models, the quantitative value problem for two players can be solved in EXPTIME. Indeed, the explicit continuous time enables players to communicate their states by delaying synchronisation (which is unrestricted for non-urgent models). In general, the problems are undecidable already for two players in the quantitative case and three players in the qualitative case. The qualitative undecidability is shown by a reduction to decentralized POMDPs for which we provide the strongest (and rather surprising) undecidability result so far

Research Letter

Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited.Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited. Here we demonstrate that detailed analysis of seismic ground motion caused by subglacial water flow at Mendenhall Glacier (Alaska) allows for continuous measurement of daily to subseasonal changes in basal water pressure gradient, channel size, and sediment transport. We observe intermittent subglacial water pressure gradient changes during the melt season, at odds with common assumptions of slowly varying, low-pressure channels. These observations indicate that changes in channel size do not keep pace with changes in discharge. This behavior strongly affects glacier dynamics and subglacial channel erosion at Mendenhall Glacier, where episodic periods of high water pressure gradients enhance glacier surface velocity and channel sediment transport by up to 30% and 50%, respectively. We expect the application of this framework to future seismic observations acquired at glaciers worldwide to improve our understanding of subglacial processes.This study was funded by NSF grant EAR-1453263. We thank Flavien Beaud and an anonymous reviewer for thorough reviews that improved the manuscript. We also thank Michael Lamb, Olivier Gagliardini, Jean-Philippe Avouac, Gael Durand and Adrien Gilbert for fruitful discussions.Ye

Subseasonal changes observed in subglacial channel pressure, size, and sediment transport

Water that pressurizes the base of glaciers and ice sheets enhances glacier velocities and modulates glacial erosion. Predicting ice flow and erosion therefore requires knowledge of subglacial channel evolution, which remains observationally limited. Here we demonstrate that detailed analysis of seismic ground motion caused by subglacial water flow at Mendenhall Glacier (Alaska) allows for continuous measurement of daily to subseasonal changes in basal water pressure gradient, channel size, and sediment transport. We observe intermittent subglacial water pressure gradient changes during the melt season, at odds with common assumptions of slowly varying, low-pressure channels. These observations indicate that changes in channel size do not keep pace with changes in discharge. This behavior strongly affects glacier dynamics and subglacial channel erosion at Mendenhall Glacier, where episodic periods of high water pressure gradients enhance glacier surface velocity and channel sediment transport by up to 30% and 50%, respectively. We expect the application of this framework to future seismic observations acquired at glaciers worldwide to improve our understanding of subglacial processes

Seismic Mapping of Subglacial Hydrology Reveals Previously Undetected Pressurization Event

Understanding the dynamic response of glaciers to climate change is vital for assessing water resources and hazards, and subglacial hydrology is a key player in glacier systems. Traditional observations of subglacial hydrology are spatially and temporally limited, but recent seismic deployments on and around glaciers show the potential for comprehensive observation of glacial hydrologic systems. We present results from a high-density seismic deployment spanning the surface of Lemon Creek Glacier, Alaska. Our study coincided with a marginal lake drainage event, which served as a natural experiment for seismic detection of changes in subglacial hydrology. We observed glaciohydraulic tremor across the surface of the glacier that was generated by the subglacial hydrologic system. During the lake drainage, the relative changes in seismic tremor power and water flux are consistent with pressurization of the subglacial system of only the upper part of the glacier. This event was not accompanied by a significant increase in glacier velocity; either some threshold necessary for rapid basal motion was not attained, or, plausibly, the geometry of Lemon Creek Glacier inhibited speedup. This pressurization event would have likely gone undetected without seismic observations, demonstrating the power of cryoseismology in testing assumptions about and mapping the spatial extent of subglacial pressurization.This work was made possible in part by hard work in the field by Margot Vore, Daniel Bowden, Galen Kaip, and the students and staff of the 2017 Juneau Icefield Research Program. We especially thank Matt Beedle for provision of the photogrammetrically-produced DEM of Lake Linda, following lake drainage. This work was also aided by the advice of Mike Gurnis and Rob Clayton. We thank Paul Winberry and two anonymous reviewers for their helpful feedback, which improved this paper greatly. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. This work was made possible in part by a University of Idaho seed grant, #FY18-01. DEM provided by the Polar Geospatial Center under NSF-OPP awards 1043681, 1559691, and 1542736.Ye