Normalization of Arabic Dialects into Modern Standard Arabic using BERT and GPT-2

We present an encoder-decored based model for normalization of Arabic dialects using both BERT and GPT-2 based models. Arabic is a language of many dialects that not only differ from the Modern Standard Arabic (MSA) in terms of pronunciation but also in terms of morphology, grammar and lexical choice. This diversity can be troublesome even to a native Arabic speaker let alone a computer. Several NLP tools work well for MSA and in some of the main dialects but fail to cover Arabic language as a whole. Based on our manual evaluation, our model normalizes sentences entirely correctly 46\% of the time and almost correctly 26\% of the time

Weighted norm inequalities for integral transforms with splitting kernels

We obtain necessary and sufficient conditions on weights for a wide class ofintegral transforms to be bounded between weighted $L^p-L^q$ spaces, with$1\leq p\leq q\leq \infty$. The kernels $K(x,y)$ of such transforms are onlyassumed to satisfy upper bounds given by products of two functions, one in eachvariable. The obtained results are applicable to a number of transforms, some of whichare included here as particular examples. Some of the new results derived hereare the characterization of weights for the boundedness of the$\mathscr{H}_\alpha$ (or Struve) transform in the case $\alpha>\frac{1}{2}$, orthe characterization of power weights for which the Laplace transform isbounded in the limiting cases $p=1$ or $q=\infty$

Interpolation and moduli spaces of vector bundles on very general blowups of the projective plane

In this paper, we study certain moduli spaces of vector bundles on the blowupof the projective plane in at least 10 very general points. Moduli spaces ofsheaves on general type surfaces may be nonreduced, reducible and evendisconnected. In contrast, moduli spaces of sheaves on minimal rationalsurfaces and certain del Pezzo surfaces are irreducible and smooth along thelocus of stable bundles. We find examples of moduli spaces of vector bundles onmore general blowups of the projective plane that are disconnected and havecomponents of different dimensions. In fact, assuming the SHGH Conjecture, wecan find moduli spaces with arbitrarily many components of arbitrarily largedimension

Cayley Linear-Time Computable Groups

This paper looks at the class of groups admitting normal forms for which theright multiplication by a group element is computed in linear time on amulti-tape Turing machine. We show that the groups $\mathbb{Z}_2 \wr\mathbb{Z}^2$, $\mathbb{Z}_2 \wr \mathbb{F}_2$ and Thompson's group $F$ havenormal forms for which the right multiplication by a group element is computedin linear time on a $2$-tape Turing machine. This refines the resultspreviously established by Elder and the authors that these groups are Cayleypolynomial-time computable.Comment: Published in journal of Groups, Complexity, Cryptolog

A new approach to integrals of discretizations by polarization

Recently, a family of unconventional integrators for ODEs with polynomialvector fields was proposed, based on the polarization of vector fields. Thesimplest instance is the by now famous Kahan discretization for quadraticvector fields. All these integrators seem to possess remarkable conservationproperties. In particular, it has been proved that, when the underlying ODE isHamiltonian, its polarization discretization possesses an integral of motionand an invariant volume form. In this note, we propose a new algebraic approachto derivation of the integrals of motion for polarization discretizations.Comment: v2 re-formatted for the journa

Representing polynomial of ST-CONNECTIVITY

We show that the coefficients of the representing polynomial of any monotoneBoolean function are the values of the M\"obius function of an atomisticlattice related to this function. Using this we determine the representingpolynomial of any Boolean function corresponding to a ST-CONNECTIVITY problemin acyclic quivers (directed acyclic multigraphs). Only monomials correspondingto unions of paths have non-zero coefficients which are $(-1)^D$ where $D$ isan easily computable function of the quiver corresponding to the monomial (itis the number of plane regions in the case of planar graphs). We determine thatthe number of monomials with non-zero coefficients for the two-dimensional $n\times n$ grid connectivity problem is $2^{\Omega(n^2)}$.Comment: 13 pages, 6 figure

DeepSec: Deciding Equivalence Properties for Security Protocols -- Improved theory and practice

Automated verification has become an essential part in the securityevaluation of cryptographic protocols. In this context privacy-type propertiesare often modelled by indistinguishability statements, expressed as behaviouralequivalences in a process calculus. In this paper we contribute both to thetheory and practice of this verification problem. We establish new complexityresults for static equivalence, trace equivalence and labelled bisimilarity andprovide a decision procedure for these equivalences in the case of a boundednumber of protocol sessions. Our procedure is the first to decide traceequivalence and labelled bisimilarity exactly for a large variety ofcryptographic primitives -- those that can be represented by a subtermconvergent destructor rewrite system. We also implemented the procedure in anew tool, DeepSec. We showed through extensive experiments that it issignificantly more efficient than other similar tools, while at the same timeraises the scope of the protocols that can be analysed.Comment: 136 page

Sharp Restriction Theory

These are detailed notes for a lecture on "Sharp restriction theory" which I presented as part of my "Agregação em Matemática" in Instituto Superior Técnico, Lisboa, Portugal (9-10 February, 2023)

Local properties and augmented Lagrangians in fully nonconvex composite optimization

A broad class of optimization problems can be cast in composite form, thatis, considering the minimization of the composition of a lower semicontinuousfunction with a differentiable mapping. This paper investigates the versatiletemplate of composite optimization without any convexity assumptions. First-and second-order optimality conditions are discussed. We highlight thedifficulties that stem from the lack of convexity when dealing with necessaryconditions in a Lagrangian framework and when considering error bounds.Building upon these characterizations, a local convergence analysis isdelineated for a recently developed augmented Lagrangian method, deriving ratesof convergence in the fully nonconvex setting.Comment: 36 page

Contribution à la définition de la notion de port territorial : l’approche juridique

From a legal point of view, a territorial port seems to be similar to a decentralised port. Unfortunately, the concept of local public interest, which justifies the exercise of port powers by local authorities, is difficult to define. We will therefore rely on the mirror concept of state port to try to identify the criteria for defining decentralised ports. This analysis will lead us to question the relevance of understanding territorial ports as ports of lesser importance in terms of economic development or territorial planning.Du point de vue juridique, la notion de port territorial semble s’assimiler à celle de port décentralisé. L’intérêt public local qui justifie l’exercice de compétences portuaires par les collectivités territoriales apparait toutefois difficile à conceptualiser, si bien que l’on préfèrera s’appuyer sur la notion miroir de port étatique pour tenter d’identifier, en négatif, les critères de définition des ports décentralisés. Cette analyse conduira à s’interroger sur la pertinence de l’appréhension des ports territoriaux comme des ports de moindre importance au regard des enjeux nationaux de développement économique ou d’aménagement du territoire