Some New Light-cone Time Dependent Solutions in Deformed pp-wave Backgrounds

Brane solutions in time \ light-cone time dependent backgrounds are of interest in order to gain a deeper understanding of the physics associated with cosmological and null singularities. In this paper, we report both brane solutions and their bound states in light-cone time dependent pp wave-like backgrounds. We show that the backgrounds our solutions live in are all cosmologically singular (lightlike) at the classical level. A spacetime supersymmetry analysis of the backgrounds reveals that they retain 1/8 of the full type IIB supersymmetry

Empirical Bounds on Linear Regions of Deep Rectifier Networks

We can compare the expressiveness of neural networks that use rectified linear units (ReLUs) by the number of linear regions, which reflect the number of pieces of the piecewise linear functions modeled by such networks. However, enumerating these regions is prohibitive and the known analytical bounds are identical for networks with same dimensions. In this work, we approximate the number of linear regions through empirical bounds based on features of the trained network and probabilistic inference. Our first contribution is a method to sample the activation patterns defined by ReLUs using universal hash functions. This method is based on a Mixed-Integer Linear Programming (MILP) formulation of the network and an algorithm for probabilistic lower bounds of MILP solution sets that we call MIPBound, which is considerably faster than exact counting and reaches values in similar orders of magnitude. Our second contribution is a tighter activation-based bound for the maximum number of linear regions, which is particularly stronger in networks with narrow layers. Combined, these bounds yield a fast proxy for the number of linear regions of a deep neural network.Comment: AAAI 202

An Inventory of Preposition Relations

We describe an inventory of semantic relations that are expressed by prepositions. We define these relations by building on the word sense disambiguation task for prepositions and propose a mapping from preposition senses to the relation labels by collapsing semantically related senses across prepositions.Comment: Supplementary material for Srikumar and Roth, 2013. Modeling Semantic Relations Expressed by Prepositions, TAC

A Taxonomy of Data Grids for Distributed Data Sharing, Management and Processing

Data Grids have been adopted as the platform for scientific communities that need to share, access, transport, process and manage large data collections distributed worldwide. They combine high-end computing technologies with high-performance networking and wide-area storage management techniques. In this paper, we discuss the key concepts behind Data Grids and compare them with other data sharing and distribution paradigms such as content delivery networks, peer-to-peer networks and distributed databases. We then provide comprehensive taxonomies that cover various aspects of architecture, data transportation, data replication and resource allocation and scheduling. Finally, we map the proposed taxonomy to various Data Grid systems not only to validate the taxonomy but also to identify areas for future exploration. Through this taxonomy, we aim to categorise existing systems to better understand their goals and their methodology. This would help evaluate their applicability for solving similar problems. This taxonomy also provides a "gap analysis" of this area through which researchers can potentially identify new issues for investigation. Finally, we hope that the proposed taxonomy and mapping also helps to provide an easy way for new practitioners to understand this complex area of research.Comment: 46 pages, 16 figures, Technical Repor