A non-ambiguous decomposition of regular languages and factorizing codes

AbstractGiven languages Z,L⊆Σ∗,Z is L-decomposable (finitely L-decomposable, resp.) if there exists a non-trivial pair of languages (finite languages, resp.) (A,B), such that Z=AL+B and the operations are non-ambiguous. We show that it is decidable whether Z is L-decomposable and whether Z is finitely L-decomposable, in the case Z and L are regular languages. The result in the case Z=L allows one to decide whether, given a finite language S⊆Σ∗, there exist finite languages C,P such that SC∗P=Σ∗ with non-ambiguous operations. This problem is related to Schützenberger's Factorization Conjecture on codes. We also construct an infinite family of factorizing codes

Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term

We study the asymptotic behaviour of the perturbative series in the heavy quark effective theory (HQET) using the $1/N_f$ expansion. We find that this theory suffers from an {\it ultraviolet} renormalon problem, corresponding to a non-Borel-summable behaviour of perturbation series in large orders, and leading to a principal nonperturbative ambiguity in its definition. This ambiguity is related to an {\it infrared} renormalon in the pole mass and can be understood as the necessity to include the residual mass term $\delta m$ in the definition of HQET, which must be considered as ambiguous (and possibly complex), and is required to cancel the ultraviolet renormalon singularity generated by the perturbative expansion. The formal status of $\delta m$ is thus identical to that of condensates in the conventional short-distance expansion of correlation functions in QCD. The status of the pole mass of a heavy quark, the operator product expansion for inclusive decays, and QCD sum rules in the HQET are discussed in this context.Comment: LATEX, 43 pages, 6 figures appended as uu-encoded file, MPI-PhT/94-9, (Text as to appear in NPB, typing errors corrected [Eq.(3.24),(3.26)], some statements in Sect.5 more precise

Direction of Arrival with One Microphone, a few LEGOs, and Non-Negative Matrix Factorization

Conventional approaches to sound source localization require at least two microphones. It is known, however, that people with unilateral hearing loss can also localize sounds. Monaural localization is possible thanks to the scattering by the head, though it hinges on learning the spectra of the various sources. We take inspiration from this human ability to propose algorithms for accurate sound source localization using a single microphone embedded in an arbitrary scattering structure. The structure modifies the frequency response of the microphone in a direction-dependent way giving each direction a signature. While knowing those signatures is sufficient to localize sources of white noise, localizing speech is much more challenging: it is an ill-posed inverse problem which we regularize by prior knowledge in the form of learned non-negative dictionaries. We demonstrate a monaural speech localization algorithm based on non-negative matrix factorization that does not depend on sophisticated, designed scatterers. In fact, we show experimental results with ad hoc scatterers made of LEGO bricks. Even with these rudimentary structures we can accurately localize arbitrary speakers; that is, we do not need to learn the dictionary for the particular speaker to be localized. Finally, we discuss multi-source localization and the related limitations of our approach.Comment: This article has been accepted for publication in IEEE/ACM Transactions on Audio, Speech, and Language processing (TASLP

Tachyon Condensation on the Elliptic Curve

We use the framework of matrix factorizations to study topological B-type D-branes on the cubic curve. Specifically, we elucidate how the brane RR charges are encoded in the matrix factors, by analyzing their structure in terms of sections of vector bundles in conjunction with equivariant R-symmetry. One particular advantage of matrix factorizations is that explicit moduli dependence is built in, thus giving us full control over the open-string moduli space. It allows one to study phenomena like discontinuous jumps of the cohomology over the moduli space, as well as formation of bound states at threshold. One interesting aspect is that certain gauge symmetries inherent to the matrix formulation lead to a non-trivial global structure of the moduli space. We also investigate topological tachyon condensation, which enables us to construct, in a systematic fashion, higher-dimensional matrix factorizations out of smaller ones; this amounts to obtaining branes with higher RR charges as composites of ones with minimal charges. As an application, we explicitly construct all rank-two matrix factorizations.Comment: 69p, 6 figs, harvmac; v2: minor change

Matrix Factorizations, D-Branes and their Deformations

We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.Comment: 20p, 5 figs, Proceedings of Cargese school on string theory, 200

Fitting DVCS at NLO and beyond

We outline the twist-two analysis of deeply virtual Compton scattering (DVCS)within the conformal partial wave expansion of the amplitude, represented as a Mellin--Barnes integral. The complete next-to-leading order results, including evolution, are obtained in the MS and a conformal factorization scheme. Within the latter, exploiting conformal symmetry, the radiative corrections are evaluated up to next-to-next-to-leading order. Using a new proposed parameterization for GPDs, we study the convergence of perturbation theory and demonstrate for H1 and ZEUS measurements that our formalism is suitable for a fitting procedure of DVCS observables. We comment on a recent claim of a breakdown of collinear factorization and show that a Regge-inspired Q^2 scaling law is ruled out by small x_Bj DVCS data.Comment: 15 pages, 4 figure

CESI: Canonicalizing Open Knowledge Bases using Embeddings and Side Information

Open Information Extraction (OpenIE) methods extract (noun phrase, relation phrase, noun phrase) triples from text, resulting in the construction of large Open Knowledge Bases (Open KBs). The noun phrases (NPs) and relation phrases in such Open KBs are not canonicalized, leading to the storage of redundant and ambiguous facts. Recent research has posed canonicalization of Open KBs as clustering over manuallydefined feature spaces. Manual feature engineering is expensive and often sub-optimal. In order to overcome this challenge, we propose Canonicalization using Embeddings and Side Information (CESI) - a novel approach which performs canonicalization over learned embeddings of Open KBs. CESI extends recent advances in KB embedding by incorporating relevant NP and relation phrase side information in a principled manner. Through extensive experiments on multiple real-world datasets, we demonstrate CESI's effectiveness.Comment: Accepted at WWW 201