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On the strange duality conjecture for abelian surfacesJul 23 2012We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ... More

GL Verlinde numbers and the Grassmann TQFTFeb 12 2010We give a brief exposition of the 2d TQFT that captures the structure of the GL Verlinde numbers, following Witten.

Sheaves on abelian surfaces and Strange DualityOct 03 2007We formulate three versions of a strange duality conjecture for sections of the Theta bundles on the moduli spaces of sheaves on abelian surfaces. As supporting evidence, we check the equality of dimensions on dual moduli spaces, answering a question ... More

On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisorsDec 28 2012We extend results on generic strange duality for K3 surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized K3s. We interpret the statement globally as an isomorphism of sheaves ... More

On the strange duality conjecture for elliptic K3 surfacesFeb 18 2009Apr 30 2010The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.

A tour of theta dualities on moduli spaces of sheavesOct 16 2007Feb 26 2008The purpose of this paper is twofold. First, we survey known results about theta dualities on moduli spaces of sheaves on curves and surfaces. Secondly, we establish new such dualities in the surface case. Among others, the case of elliptic K3 surfaces ... More

On the intersection theory of the moduli space of rank two bundlesMay 19 2005May 31 2005We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we obtain the intersections ... More

The rank-level duality for non-abelian theta functionsMay 03 2006We prove that the strange duality conjecture of Beauville-Donagi-Tu holds for all curves. We establish first a more extended rank-level duality, interesting in its own right, from which the standard rank-level duality follows by restriction.

Higher rank Segre integrals over the Hilbert scheme of pointsDec 06 2017Jun 09 2019Let S be a nonsingular projective surface. Each vector bundle V on S of rank s induces a tautological vector bundle over the Hilbert scheme of n points of S. When s=1, the top Segre classes of the tautological bundles are given by a recently proven formula ... More

On the strange duality conjecture for abelian surfaces IIFeb 26 2014In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves with fixed ... More

Playing Adaptively Against Stealthy Opponents: A Reinforcement Learning Strategy for the FlipIt Security GameJun 27 2019A rise in Advanced Persistant Threats (APTs) has introduced a need for robustness against long-running, stealthy attacks which circumvent existing cryptographic security guarantees. FlipIt is a security game that models the attacker-defender interactions ... More

Counts of maps to Grassmannians and intersections on the moduli space of bundlesFeb 15 2006Feb 27 2006We show that intersection numbers on the moduli space of stable bundles of coprime rank and degree over a smooth complex curve can be recovered as highest-degree asymptotics in formulas of Vafa-Intriligator type. In particular, we explicitly evaluate ... More

Virtual intersections on the Quot-scheme and Vafa-Intriligator formulasMay 31 2005Sep 09 2006We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the Vafa-Intriligator ... More

On the Intriguing Connections of Regularization, Input Gradients and Transferability of Evasion and Poisoning AttacksSep 08 2018Transferability captures the ability of an attack against a machine-learning model to be effective against a different, potentially unknown, model. Studying transferability of attacks has gained interest in the last years due to the deployment of cyber-attack ... More

Higher rank Segre integrals over the Hilbert scheme of pointsDec 06 2017Dec 19 2018Let S be a nonsingular projective K-trivial surface, and let V be a vector bundle on S of rank s. We calculate the top Segre class of the tautological bundle over the Hilbert scheme of points of S associated to V. In the rank s=1 case, our result specializes ... More

On a geometric inequalityNov 03 2005As we showed in [3], a geometric inequality can be regarded as an optimization problem. In this paper we find another proof for a Chen's inequality,regarding the Ricci curvature [2] and we improve this inequality in the Lagrangian case.

The combinatorics of Lehn's conjectureAug 27 2017Apr 12 2018Let S be a smooth projective surface equipped with a line bundle H. Lehn's conjecture is a formula for the top Segre class of the tautological bundle associated to H on the Hilbert scheme of points of S. Voisin has recently reduced Lehn's conjecture to ... More

Segre classes and Hilbert schemes of pointsJul 02 2015Apr 03 2016We prove a closed formula for the integrals of the top Segre classes of tautological bundles over the Hilbert schemes of points of a K3 surface X. We derive relations among the Segre classes via equivariant localization of the virtual fundamental classes ... More

Generic strange duality for $K3$ surfacesMay 01 2010May 07 2010Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier-Mukai techniques. Applications to Brill-Noether theory for sheaves on $K3$s are also obtained. ... More

On a Riemannian invariant of Chen typeMay 12 2006In [6] we proved Chen's inequality regarded as a problem of constrained maximum. In this paper we introduce a Riemannian invariant obtained from Chen's invariant, replacing the sectional curvature by the Ricci curvature of k-order. This invariant can ... More

The Chern classes of the Verlinde bundlesAug 20 2013Oct 01 2016A formula for the first Chern class of the Verlinde bundle over the moduli space of smooth genus g curves is given. A finite-dimensional argument is presented in rank 2 using geometric symmetries obtained from strange duality, relative Serre duality, ... More

Robust High-Dimensional Linear RegressionAug 07 2016Aug 09 2016The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the most important ... More

Higher topological complexity of aspherical spacesFeb 26 2019In this article we study the higher topological complexity ${\sf TC}_r(X)$ in the case when $X$ is an aspherical space, $X=K(\pi, 1)$ and $r\ge 2$. We give a characterisation of ${\sf TC}_r(K(\pi, 1))$ in terms of classifying spaces for equivariant Bredon ... More

A neutron transmission study of environmental GdJun 02 2014A new method for the determination of environmental Gd by neutron transmission (NT) experiments is proposed. The NT method is based on the measurements of neutron spectra passing through a target. From the attenuation neutron spectra new data as concentration, ... More

Privacy-Preserving Hierarchical Clustering: Formal Security and Efficient ApproximationApr 09 2019Machine Learning (ML) is widely used for predictive tasks in a number of critical applications. Recently, collaborative or federated learning is a new paradigm that enables multiple parties to jointly learn ML models on their combined datasets. Yet, in ... More

Are Self-Driving Cars Secure? Evasion Attacks against Deep Neural Networks for Steering Angle PredictionApr 15 2019Deep Neural Networks (DNNs) have tremendous potential in advancing the vision for self-driving cars. However, the security of DNN models in this context leads to major safety implications and needs to be better understood. We consider the case study of ... More

Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristicsMar 21 2019We compute tautological integrals over Quot schemes on curves and surfaces. After obtaining several explicit formulas over Quot schemes of dimension 0 quotients on curves (and finding a new symmetry), we apply the results to tautological integrals against ... More

Detecting Elements and Lusternik--Schnirelmann Category of 3-ManifoldsNov 15 2001In this paper, we give a new simplified calculation of the Lusternik-Schnirelmann category of closed 3-manifolds. We also describe when 3-manifolds have detecting elements and prove that 3-manifolds satisfy the equality of the Ganea conjecture.

On the structure of co-Kähler manifoldsSep 15 2012Apr 24 2013By the work of Li, a compact co-K\"ahler manifold $M$ is a mapping torus $K_\varphi$, where $K$ is a K\"ahler manifold and $\varphi$ is a Hermitian isometry. We show here that there is always a finite cyclic cover $\bar M$ of the form $\bar M \cong K ... More

On the Lusternik-Schnirelmann category of symplectic manifolds and the Arnold conjectureAug 11 1997We prove that the Lusternik-Schnirelmann category $cat(M)$ of a closed symplectic manifold $(M, \omega)$ equals the dimension $dim(M)$ provided that the symplectic cohomology class vanishes on the image of the Hurewicz homomorphism. This holds, in particular, ... More

Consequences of conformal anomaly on fluid dynamicsNov 28 2018We review a recent progress on fluid dynamics applied to strongly interacting nuclear matter. The efforts are made to highlight consequences of scale invariance breaking on the hydrodynamic description of a nuclear medium. Both phenomenological and analytical ... More

Can Multisensory Cues in VR Help Train Pattern Recognition to Citizen Scientists?Apr 01 2018As the internet of things (IoT) has integrated physical and digital technologies, designing for multiple sensory media (mulsemedia) has become more attainable. Designing technology for multiple senses has the capacity to improve virtual realism, extend ... More

Quantum Query Algorithm Constructions for Computing AND, OR and MAJORITY Boolean FunctionsOct 30 2007Apr 23 2009Quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given in a black box and the aim is to compute function value for arbitrary input using as few queries as possible. We concentrate on quantum query algorithm ... More

On roots of unity in orbits of rational functionsMar 13 2016Apr 30 2016In this paper we characterise univariate rational functions over a number field $\K$ having infinitely many points in the cyclotomic closure $\K^c$ for which the orbit contains a root of unity. Our results are similar to previous results of Dvornicich ... More

On the extension of the Reverse Hölder Inequality for power functions on the real axisOct 12 2018We consider the class of all non-negative on $\mathbb{R_+}$ functions such that each of them satisfies the Reverse H\"older Inequality uniformly over all intervals with some constant the minimum value of which can be regarded as the corresponding "norm" ... More

Universality class of the critical point in the restricted primitive model of ionic systemsJan 03 2006A coarse-grained description of the restricted primitive model is considered in terms of the local charge- and number-density fields. Exact reduction to a one-field theory is derived, and exact expressions for the number-density correlation functions ... More

Gorenstein flat dimension of complexesFeb 09 2010We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for complexes; we also define a generalized Tate cohomology for complexes over Gorenstein ... More

A note on Bourgain-Milman's universal constantApr 30 2014May 31 2014The present note is a result of an on-going investigation into the logarithmic Brunn-Minkowski inequality. We obtain lower estimates on the volume product for convex bodies in $\mathbb{R}^n$ not necessarily symmetric with respect to the origin from a ... More

Differentially Private Fair LearningDec 06 2018Feb 05 2019Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study of fair learning ... More

On Designing Machine Learning Models for Malicious Network Traffic ClassificationJul 10 2019Machine learning (ML) started to become widely deployed in cyber security settings for shortening the detection cycle of cyber attacks. To date, most ML-based systems are either proprietary or make specific choices of feature representations and machine ... More

Storing cycles in Hopfield-type networks with pseudoinverse learning rule: admissibility and network topologyNov 19 2012Apr 28 2013Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the network connectivities ... More

New lower bounds for the topological complexity of aspherical spacesSep 17 2013We show that the topological complexity of an aspherical space $X$ is bounded below by the cohomological dimension of the direct product $A\times B$, whenever $A$ and $B$ are subgroups of $\pi_1(X)$ whose conjugates intersect trivially. For instance, ... More

Detection of Early-Stage Enterprise Infection by Mining Large-Scale Log DataNov 18 2014Nov 24 2014Recent years have seen the rise of more sophisticated attacks including advanced persistent threats (APTs) which pose severe risks to organizations and governments by targeting confidential proprietary information. Additionally, new malware strains are ... More

Differentially Private Fair LearningDec 06 2018May 31 2019Motivated by settings in which predictive models may be required to be non-discriminatory with respect to certain attributes (such as race), but even collecting the sensitive attribute may be forbidden or restricted, we initiate the study of fair learning ... More

Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression LearningApr 01 2018As machine learning becomes widely used for automated decisions, attackers have strong incentives to manipulate the results and models generated by machine learning algorithms. In this paper, we perform the first systematic study of poisoning attacks ... More

Multivariate Permutation Polynomial Systems and Nonlinear Pseudorandom Number GeneratorsJun 21 2009Jan 10 2010In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques studied previously ... More

On the number of optimal surfacesApr 12 2009Let X be a closed oriented Riemann surface of genus > 1 of constant negative curvature -1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus > 3 up to orientation-preserving ... More

Yes and...? Using Improv to Design for Narrative in Lights OutApr 23 2018Mixed reality experiences often require detailed narrative that can be used to craft physical and virtual design components. This work elaborates on a mentoring experience at the Carnegie Mellon's ETC to consider how improv games may be used ideate and ... More

Rational approximations to algebraic Laurent series with coefficients in a finite fieldFeb 28 2011In this paper we give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of ... More

Groups, periodic planes and hyperbolic buildingsJul 30 2003We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular, we construct ... More

Polyhedra with specified linksFeb 25 2003We construct compact polyhedra with $m$-gonal faces whose links are generalized 3-gons. It gives examples of cocompact hyperbolic bildings of type $P(m,3)$. For $m=3$ we get compact spaces covered by Euclidean buildings of type $A_2$.

Gorenstein injective envelopes and covers over two sided noetherian ringsJan 18 2016We prove that the class of Gorenstein injective modules is both enveloping and covering over a two sided noetherian ring such that the character modules of Gorenstein injective modules are Gorenstein flat. In the second part of the paper we consider the ... More

Some Affine Invariants RevisitedAug 03 2012We present several sharp inequalities for the SL(n) invariant $\Omega_{2,n}(K)$ introduced in our earlier work on centro-affine invariants for smooth convex bodies containing the origin. A connection arose with the Paouris-Werner invariant $\Omega_K$ ... More

Sur le développement en fraction continue d'une généralisation de la cubique de Baum et SweetJan 18 2010In 1976, Baum and Sweet gave the first example of a power series that is algebraic over the field $\mathbb F_2(T)$ and whose continued fraction expansion has partial quotients with bounded degree. This power series is the unique solution of the equation ... More

Subword complexity and Laurent series with coefficients in a finite fieldJan 14 2010Decimal expansions of classical constants such as $\sqrt2$, $\pi$ and $\zeta(3)$ have long been a source of difficult questions. In the case of Laurent series with coefficients in a finite field, where no carry-over difficulties appear, the situation ... More

On the number of extremal surfacesNov 28 2003Let $X$ be a compact Riemann surface of genus $\geq 2$ of constant negative curvature -1. An extremal disk is an embedded (resp. covering) disk of maximal (resp. minimal) radius. A surface containing an extremal disk is an {\em extremal surface}. This ... More

Supersymmetric plasma systems and their nonsupersymmetric counterpartsJan 29 2016In this thesis a systematic comparison of supersymmetric plasma systems and their nonsupersymmetric counterparts is presented. The work is motivated by the AdS/CFT correspondence and the main aim is to check how much the plasma governed by the N=4 super ... More

Centro-Affine Invariants for Smooth Convex BodiesNov 23 2010Employing a centro-affine flow on smooth convex bodies, we generate new centro-affine differential invariants. One class of the newly defined invariants is the object of a sharp isoperimetric inequality, while other new inequalities on known centro-affine ... More

E-books and Graphics with LaTeXMLApr 25 2014Marked by the highlights of native generation of EPUB E-books and TikZ support for creating SVG images, we present an annual report of LaTeXML development in 2013. LaTeXML provides a reimplementation of the $\TeX$ parser, geared towards preserving macro ... More

Parallel forms, co-Kähler Manifolds and their ModelsSep 26 2016We show how certain topological properties of co-K\"ahler manifolds derive from those of the K\"ahler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-K\"ahler manifold reduces the computation of cohomology ... More

A Mapping Theorem for Topological ComplexityDec 27 2013We give new lower bounds for the (higher) topological complexity of a space, in terms of the Lusternik-Schnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally ... More

Subdivision of Maps of Digital ImagesJun 07 2019With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as the fundamental ... More

Homotopy Theory in Digital TopologyMay 19 2019Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the most ... More

Homotopy Invariants and Almost Non-Negative CurvatureMar 01 2019This paper explores the relation between the structure of fibre bundles akin to those associated to a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.

A Fundamental Group for Digital ImagesJun 14 2019We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways from previously ... More

Why Do Adversarial Attacks Transfer? Explaining Transferability of Evasion and Poisoning AttacksSep 08 2018Feb 18 2019Transferability captures the ability of an attack against a machine-learning model to be effective against a different, potentially unknown, model. Empirical evidence for transferability has been shown in previous work, but the underlying reasons why ... More

Trace element distribution in human teeth by x-ray fluorescence spectrometry and multivariate statistical analysisJun 14 2014X-ray fluorescence spectrometry (XRFS) was used as a multielement method of evaluation of individual whole human tooth or tooth tissues for their amounts of trace elements. Measurements were carried out on human enamel, dentine, and dental cementum, and ... More

Why Do Adversarial Attacks Transfer? Explaining Transferability of Evasion and Poisoning AttacksSep 08 2018Jun 13 2019Transferability captures the ability of an attack against a machine-learning model to be effective against a different, potentially unknown, model. Empirical evidence for transferability has been shown in previous work, but the underlying reasons why ... More

Search of parity violation effects in neutron reaction on natural LeadJun 02 2014Parity violation effects (PV) in nuclear reaction were discovered in the 60 years of the last century in the capture of thermal transversal polarized neutrons by 113Cd nucleus. In this reaction experimentally was measured a non zero asymmetry of emitted ... More

The shear and bulk relaxation times from the general correlation functionsMay 22 2017In this paper we present two quantum field theoretical analyses on the shear and bulk relaxation times. First, we discuss how to find Kubo formulas for the shear and the bulk relaxation times. Next, we provide results on the shear viscosity relaxation ... More

A Combinatorial Proof of the Enumeration of Alternating Permutations with Given Peak SetApr 05 2012Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.

Effect of mesoscopic fluctuations on equation of state in cluster-forming systemsJan 02 2012Jul 12 2012Equation of state for systems with particles self-assembling into aggregates is derived within a mesoscopic theory combining density functional and field-theoretic approaches. We focus on the effect of mesoscopic fluctuations in the disordered phase. ... More

Orientational ordering of lamellar structures on closed surfacesApr 11 2018Self-assembly of particles with short-range attraction and long-range repulsion (SALR) interactions on a flat and on a spherical surface is compared. Molecular dynamics (MD) simulations are performed for the two systems having the same area and the density ... More

Instance Influence Estimation for Hyperspectral Target Signature Characterization using Extended Functions of Multiple InstancesMar 21 2016The Extended Functions of Multiple Instances (eFUMI) algorithm is a generalization of Multiple Instance Learning (MIL). In eFUMI, only bag level (i.e. set level) labels are needed to estimate target signatures from mixed data. The training bags in eFUMI ... More

On Approximating Maximum Independent Set of RectanglesJul 31 2016We study the Maximum Independent Set of Rectangles (MISR) problem: given a set of $n$ axis-parallel rectangles, find a largest-cardinality subset of the rectangles, such that no two of them overlap. MISR is a basic geometric optimization problem with ... More

A Local-Global Approach to Semantic Segmentation in Aerial ImagesJul 19 2016Aerial images are often taken under poor lighting conditions and contain low resolution objects, many times occluded by other objects. In this domain, visual context could be of great help, but there are still very few papers that consider context in ... More

Initialization of ReLUs for Dynamical IsometryJun 17 2018Jun 06 2019Deep learning relies on good initialization schemes and hyperparameter choices prior to training a neural network. Random weight initializations induce random network ensembles, which give rise to the trainability, training speed, and sometimes also generalization ... More

E-learning and use of computer in forensic fieldFeb 28 2012In the Romanian penitentiary establishments and those of other European countries one talks about the formal and informal education. Since the correspondence education system, important steps have been made towards the e-learning didactics which are reflected ... More

A Phase Transition in a Quantum Crystal with Asymmetric PotentialsNov 08 2006A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. ... More

Triangular hyperbolic buildingsJun 30 2005We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$. Moreover, the ... More

Second order q-difference equations solvable by factorization methodDec 22 2003By solving an infinite nonlinear system of $q$-difference equations one constructs a chain of $q$-difference operators. The eigenproblems for the chain are solved and some applications, including the one related to $q$-Hahn orthogonal polynomials, are ... More

Counting 1-vertex Triangulations Of Oriented SurfacesOct 02 2001A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus $g$ is an embedded graph $T\subset S$ with a unique vertex such that all connected components of $S\setminus T$ are triangles (adjacent to exactly 3 edges of $T$). This paper ... More

Improved Convergence for $\ell_\infty$ and $\ell_1$ Regression via Iteratively Reweighted Least SquaresFeb 18 2019The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good practical performance. ... More

On the group of zero-cycles of holomorphic symplectic varietiesNov 27 2017Nov 29 2017For a moduli space of Bridgeland-stable objects on a K3 surface, we show that the Chow class of a point is determined by the Chern class of the corresponding object on the surface. This establishes a conjecture of Junliang Shen, Qizheng Yin, and the second ... More

Multi-Resolution Multi-Modal Sensor Fusion For Remote Sensing Data With Label UncertaintyMay 02 2018In remote sensing, each sensor can provide complementary or reinforcing information. It is valuable to fuse outputs from multiple sensors to boost overall performance. Previous supervised fusion methods often require accurate labels for each pixel in ... More

Map-guided Hyperspectral Image Superpixel Segmentation Using Proportion MapsJan 06 2017A map-guided superpixel segmentation method for hyperspectral imagery is developed and introduced. The proposed approach develops a hyperspectral-appropriate version of the SLIC superpixel segmentation algorithm, leverages map information to guide segmentation, ... More

Pattern Count on Multiply Restricted PermutationsFeb 17 2013Previous work has studied the pattern count on singly restricted permutations. In this work, we focus on patterns of length 3 in multiply restricted permutations, especially for double and triple pattern-avoiding permutations. We derive explicit formulae ... More

Cayley Graph Expanders and Groups of Finite WidthSep 09 2008We present new infinite families of expander graphs of vertex degree 4, which is the minimal possible degree for Cayley graph expanders. Our first family defines a tower of coverings (with covering indices equals 2) and our second family is given as Cayley ... More

Series of $p$-groups with Beauville structureMay 15 2014Jul 19 2015For every $p\geq 2$ we show that each finite $p$-group with an unmixed Beauville structure is part of a surjective infinite projective system of finite $p$-groups with compatible unmixed Beauville structures. This leads to the new notion of an unmixed ... More

Chen's inequality in Lagrangian caseNov 03 2005In the theory of submanifolds, the following problem is fundamental: to establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of the submanifolds.The basic relationships discovered until now [1, 2, 3, 4] ... More

A new obstruction to minimal isometric immersions into a real space formNov 03 2005In the theory of minimal submanifold, the following problem is fundamental: when does a given Riemannian manifold admit (or does not admit) a minimal isometric immersion into an Euclidean space form of arbitrary dimension? A partial solution of this problem ... More

Multiple Instance Choquet Integral Classifier Fusion and Regression for Remote Sensing ApplicationsMar 11 2018In classifier (or regression) fusion the aim is to combine the outputs of several algorithms to boost overall performance. Standard supervised fusion algorithms often require accurate and precise training labels. However, accurate labels may be difficult ... More

Beyond Serre's "Trees" in two directions: $Λ$--trees and products of treesOct 27 2017Serre in "Trees" laid down the fundamentals of the theory of groups acting on simplicial trees. In particular, Bass-Serre theory makes it possible to extract information about the structure of a group from its action on a simplicial tree. Serre's original ... More

Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical SystemsSep 02 2011We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of trajectories generated ... More

Low complexity algorithms in knot theoryMar 13 2018Mar 27 2018We show that the genus problem for alternating knots with $n$ crossings has linear time complexity and is in Logspace$(n)$. Almost all alternating knots of given genus possess additional combinatorial structure, we call them standard. We show that the ... More

Predicting System-level Power for a Hybrid SupercomputerMay 31 2016For current High Performance Computing systems to scale towards the holy grail of ExaFLOP performance, their power consumption has to be reduced by at least one order of magnitude. This goal can be achieved only through a combination of hardware and software ... More

Statistics of Local Seismic Emission from the Solar GranulationJul 04 2013We apply computational seismic holography to high-frequency helioseismic observations of the quiet Sun from SDO/HMI to locate predominant sources of seismic emission with respect to the structure of the solar granulation. The regions of greatest seismic ... More

On Successive Refinement for the Kaspi/Heegard-Berger ProblemDec 17 2008Consider a source that produces independent copies of a triplet of jointly distributed random variables, $\{X_{i},Y_{i},Z_{i}\}_{i=1}^{\infty}$. The process $\{X_{i}\}$ is observed at the encoder, and is supposed to be reproduced at two decoders, where ... More

Towards Operator-less Data Centers Through Data-Driven, Predictive, Proactive AutonomicsJun 14 2016Continued reliance on human operators for managing data centers is a major impediment for them from ever reaching extreme dimensions. Large computer systems in general, and data centers in particular, will ultimately be managed using predictive computational ... More

The formation of low-mass helium white dwarfs in close binariesOct 21 2014Recently, a large number of low-mass (<0.30 M_sun) helium white dwarfs (He WDs) have been discovered as a result of several surveys campaigns such as WASP, ELM, Kepler or SDSS. The far majority of them have as companion another compact object. There appears ... More