Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD

We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N flavors, and exhibit an enhancement of supersymmetry for the reduced moduli space associated with broken flavor symmetries. We provide an explicit construction of the worldvolume superalgebra which corresponds to an N=2 Kahler sigma model in 2+1D deformed by a potential, given by the norm squared of a U(1) Killing vector, resulting from the flavor symmetries broken by unequal quark masses. This framework leads to a worldvolume description of novel two-wall junction configurations, which are 1/4-BPS objects, but nonetheless preserve two supercharges when viewed as kinks on the wall worldvolume.Comment: 35 pages, 3 figures; v2: minor corrections and a reference added, to appear in Phys. Rev.

Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Two remarks on generalized entropy power inequalities

This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed log-concave random variables. We also present a complex analogue of a recent dependent entropy power inequality of Hao and Jog, and give a very simple proof.Comment: arXiv:1811.00345 is split into 2 papers, with this being on

Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type

International audienceThis study addresses the problem of delay compensation via a predictor-based output feedback for a class of linear systems subject to input delay which itself depends on the input. The equation defining the delay is implicit and involves past values of the input through an integral relation, the kernel of which is a polynomial function of the input. This modeling represents systems where transport phenomena take place at the inlet of a system involving a nonlinearity, which frequently occurs in the processing industry. The conditions of asymptotic stabilization require the magnitude of the feedback gain to comply with the initial conditions. Arguments for the proof of this novel result include general Halanay inequalities for delay differential equations and take advantage of recent advances in backstepping techniques for uncertain or varying delay systems

Counting Domain Walls in N=1 Super Yang-Mills Theory

We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced worldvolume theory, which is invariant under the deformation to the Higgs phase. The worldvolume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in IIA string theory.Comment: 28 pages, RevTeX, 3 figures; v2: discussion of the index slightly expanded, using an alternative regulator, and references added; v3: typos corrected, to appear in Phys. Rev.

Basic notions of information structure

This article takes stock of the basic notions of Information Structure (IS). It first provides a general characterization of IS — following Chafe (1976) — within a communicative model of Common Ground(CG), which distinguishes between CG content and CG management. IS is concerned with those features of language that concern the local CG. Second, this paper defines and discusses the notions of Focus (as indicating alternatives) and its various uses, Givenness (as indicating that a denotation is already present in the CG), and Topic (as specifying what a statement is about). It also proposes a new notion, Delimitation, which comprises contrastive topics and frame setters, and indicates that the current conversational move does not entirely satisfy the local communicative needs. It also points out that rhetorical structuring partly belongs to IS.Peer Reviewe

KneeTex: an ontology–driven system for information extraction from MRI reports

Background. In the realm of knee pathology, magnetic resonance imaging (MRI) has the advantage of visualising all structures within the knee joint, which makes it a valuable tool for increasing diagnostic accuracy and planning surgical treatments. Therefore, clinical narratives found in MRI reports convey valuable diagnostic information. A range of studies have proven the feasibility of natural language processing for information extraction from clinical narratives. However, no study focused specifically on MRI reports in relation to knee pathology, possibly due to the complexity of knee anatomy and a wide range of conditions that may be associated with different anatomical entities. In this paper we describe KneeTex, an information extraction system that operates in this domain. Methods. As an ontology–driven information extraction system, KneeTex makes active use of an ontology to strongly guide and constrain text analysis. We used automatic term recognition to facilitate the development of a domain–specific ontology with sufficient detail and coverage for text mining applications. In combination with the ontology, high regularity of the sublanguage used in knee MRI reports allowed us to model its processing by a set of sophisticated lexico–semantic rules with minimal syntactic analysis. The main processing steps involve named entity recognition combined with coordination, enumeration, ambiguity and co–reference resolution, followed by text segmentation. Ontology–based semantic typing is then used to drive the template filling process. Results. We adopted an existing ontology, TRAK (Taxonomy for RehAbilitation of Knee conditions), for use within KneeTex. The original TRAK ontology expanded from 1,292 concepts, 1,720 synonyms and 518 relationship instances to 1,621 concepts, 2,550 synonyms and 560 relationship instances. This provided KneeTex with a very fine–grained lexico–semantic knowledge base, which is highly attuned to the given sublanguage. Information extraction results were evaluated on a test set of 100 MRI reports. A gold standard consisted of 1,259 filled template records with the following slots: finding, finding qualifier, negation, certainty, anatomy and anatomy qualifier. KneeTex extracted information with precision of 98.00%, recall of 97.63% and F–measure of 97.81%, the values of which are in line with human–like performance. Conclusions. KneeTex is an open–source, stand–alone application for information extraction from narrative reports that describe an MRI scan of the knee. Given an MRI report as input, the system outputs the corresponding clinical findings in the form of JavaScript Object Notation objects. The extracted information is mapped onto TRAK, an ontology that formally models knowledge relevant for the rehabilitation of knee conditions. As a result, formally structured and coded information allows for complex searches to be conducted efficiently over the original MRI reports, thereby effectively supporting epidemiologic studies of knee conditions