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Big but Imperceptible Adversarial Perturbations via Semantic ManipulationApr 12 2019Machine learning, especially deep learning, is widely applied to a range of applications including computer vision, robotics and natural language processing. However, it has been shown that machine learning models are vulnerable to adversarial examples, ... More

Detecting Anomalous Faces with 'No Peeking' AutoencodersFeb 15 2018Detecting anomalous faces has important applications. For example, a system might tell when a train driver is incapacitated by a medical event, and assist in adopting a safe recovery strategy. These applications are demanding, because they require accurate ... More

Quantitative Evaluation of Style TransferMar 31 2018Style transfer methods produce a transferred image which is a rendering of a content image in the manner of a style image. There is a rich literature of variant methods. However, evaluation procedures are qualitative, mostly involving user studies. We ... More

Syzygy divisors on Hurwitz spacesMay 02 2018We describe a sequence of effective divisors on the Hurwitz space $H_{d,g}$ for $d$ dividing $g-1$ and compute their cycle classes on a partial compactification. These divisors arise from vector bundles of syzygies canonically associated to a branched ... More

Vector bundles and finite coversAug 04 2016We prove that, up to twist, every vector bundle on a smooth projective curve arises from the direct image of the structure sheaf of a smooth, connected branched cover.

The Picard rank conjecture for the Hurwitz spaces of degree up to fiveFeb 06 2014Jun 09 2014We prove that the rational Picard group of the simple Hurwitz space ${\mathcal H}_{d,g}$ is trivial for $d$ up to five. We also relate the rational Picard groups of the Hurwitz spaces to the rational Picard groups of the Severi varieties of nodal curves ... More

Sharp slope bounds for sweeping families of trigonal curvesNov 12 2012We establish sharp bounds for the slopes of curves in $\bar{M}_g$ that sweep the locus of trigonal curves, proving Stankova-Frenkel's conjectured bound of $7+6/g$ for even $g$ and obtaining the bound $7+20/(3g+1)$ for odd $g$. For even $g$, we find an ... More

Vector bundles and finite coversAug 04 2016Jan 06 2019Motivated by the problem of finding algebraic constructions of finite coverings in commutative algebra, the Steinitz realization problem in number theory, and the study of Hurwitz spaces in algebraic geometry, we investigate the vector bundles underlying ... More

Comment on Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanicsJul 02 2015Jul 04 2015This is a comment to the paper, Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics by C Cisneros et al 1998 Eur. J. Phys. 19 237. doi:10.1088/0143-0807/19/3/005. The proof that the authors construct ... More

On a Conjecture on Linear SystemsApr 08 2015Apr 12 2016In a remark to Green's conjecture, Paranjape and Ramanan analyzed the vector bundle $E$ which is the pullback by the canonical map of the universal quotient bundle $T_{\Pp^{g-1}}(-1)$ on $\Pp^{g-1}$ and stated a more general conjecture and proved it for ... More

On the topology of scalar-flat manifoldsJun 20 2000Jun 21 2000Let $M$ be a simply-connected closed manifold of dimension $\geq 5$ which does not admit a metric with positive scalar curvature. We give necessary conditions for $M$ to admit a scalar-flat metric. These conditions involve the first Pontrjagin class and ... More

A statistical model for word discovery in child directed speechOct 13 1999A statistical model for segmentation and word discovery in child directed speech is presented. An incremental unsupervised learning algorithm to infer word boundaries based on this model is described and results of empirical tests showing that the algorithm ... More

Bordism-finiteness and semi-simple group actionsMar 27 2000May 01 2001We give bordism-finiteness results for manifolds with semi-simple group action. Consider the class of oriented manifolds which admit a circle action with isolated fixed points such that the action extends to an $S^3$-action with fixed point. We exhibit ... More

Special codimension one loci in Hurwitz spacesAug 25 2015We investigate two families of divisors which we expect to play a distinguished role in the global geometry of Hurwitz space. In particular, we show that they are extremal and rigid in the small degree regime $d \leq 5$. We further show their significance ... More

Covers of stacky curves and limits of plane quinticsJul 12 2015Aug 20 2018We construct a well-behaved compactification of finite covers of a stacky curve using admissible cover degenerations. Using our construction, we compactify the space of tetragonal curves on Hirzebruch surfaces. As an application, we explicitly describe ... More

Stability and GrothendieckMar 14 2017Mar 27 2017This note is a commentary on the model-theoretic interpretation of Grothendieck's double limit characterization of weak relative compactness.

Moduli of Linear Sections of a General HypersurfaceMay 05 2016We investigate the global variation of moduli of linear sections of a general hypersurface. We prove a "generic Torelli" result for a large proportion of cases, and we obtain a complete picture of the global variation of moduli of line slices of a general ... More

Homotopy complex projective spaces with Pin(2)-actionFeb 07 2001Let $M$ be a manifold homotopy equivalent to the complex projective space $\C P^m$. Petrie conjectured that $M$ has standard total Pontrjagin class if $M$ admits a non-trivial action by $S^1$. We prove the conjecture for $m<12$ under the assumption that ... More

Domination and regularityJun 22 2018We discuss the close relationship between structural theorems in generalized stability theory and graph regularity theorems.

Hypergraph Markov Operators, Eigenvalues and Approximation AlgorithmsAug 11 2014Oct 30 2014The celebrated Cheeger's Inequality \cite{am85,a86} establishes a bound on the expansion of a graph via its spectrum. This inequality is central to a rich spectral theory of graphs, based on studying the eigenvalues and eigenvectors of the adjacency matrix ... More

Cut-Matching Games on Directed GraphsOct 06 2010We give O(log^2 n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for computing the sparsest cut on directed graphs. Our algorithm uses only O(log^2 n) single commodity max-flow computations and thus breaks the multicommodity-flow ... More

Covers of stacky curves and limits of plane quinticsJul 12 2015We construct a well-behaved compactification of finite covers of a stacky curve using admissible cover degenerations. Using our construction, we compactify the space of tetragonal curves on Hirzebruch surfaces. As an application, we explicitly describe ... More

Torus Actions, Fixed-Point Formulas, Elliptic Genera and positive curvatureMay 18 2016Aug 18 2016We study fixed points of smooth torus actions on closed manifolds using fixed point formulas and equivariant elliptic genera. We also give applications to positively curved Riemannian manifolds with symmetry.

A procedure for unsupervised lexicon learningNov 30 2001We describe an incremental unsupervised procedure to learn words from transcribed continuous speech. The algorithm is based on a conservative and traditional statistical model, and results of empirical tests show that it is competitive with other algorithms ... More

Modular compactifications of the space of marked trigonal curvesJun 20 2012We construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent. Beginning with the standard admissible cover compactification, the sequence first proceeds through ... More

On genericity and weight in the free groupDec 09 2008I prove that the generic type of the free nonabelian group has infinite weight (strengthening non superstability of the free group).

Strongly minimal pseudofinite structuresNov 18 2014Nov 24 2014We observe that the nonstandard finite cardinality of a definable set in a strongly minimal pseudofinite structure D is a polynomial over the integers in the nonstandard finite cardinality of D. We conclude that D is unimodular, hence also locally modular. ... More

A Statistical Model for Word Discovery in Transcribed SpeechNov 30 2001A statistical model for segmentation and word discovery in continuous speech is presented. An incremental unsupervised learning algorithm to infer word boundaries based on this model is described. Results of empirical tests showing that the algorithm ... More

Obstructions to positive curvature and symmetryApr 26 2001Apr 29 2002We show that the indices of certain twisted Dirac operators vanish on a $Spin$-manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\geq 2$ or if the symmetry rank is one and $M$ is two connected. We also give examples of simply ... More

On the moduli space of nonnegatively curved metrics on Milnor spheresDec 23 2017Jan 21 2018Let $M$ be a Milnor sphere or, more generally, the total space of a linear $S^3$-bundle over $S^4$ with $H^4(M;\mathbb{Q})=0$. We show that the moduli space of metrics of nonnegative sectional curvature on $M$ has infinitely many path components. The ... More

Naive vs. genuine A^1-connectednessMar 17 2017We show that the triviality of sections of the sheaf of A^1-chain connected components of a space over finitely generated separable field extensions of the base field is not sufficient to ensure the triviality of the sheaf of its A^1-chain connected components, ... More

Remarks on compactifications of pseudofinite groupsSep 09 2015We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out (i) the Bohr compactification of an ultraproduct of finite simple groups is trivial, and ... More

Forking in the free groupFeb 06 2007We study model-theoretic and stability-theoretic properies of the nonabelian free group in the light of Sela's recent result on stability and results announced by Bestvina and Feighn. We point out analogies between the free group and so-called bad groups ... More

A Fourier continuation framework for high-order approximationsJul 15 2018Jul 21 2018It is well known that approximation of functions on $[0,1]$ whose periodic extension is not continuous fail to converge uniformly due to rapid Gibbs oscillations near the boundary. Among several approaches that have been proposed toward the resolution ... More

Bernoulli Runs: Using "Book Cricket" to Evaluate CricketersJul 15 2011This paper proposes a simple method to evaluate batsmen and bowlers in cricket. The idea in this paper refines "book cricket" and evaluates a batsman by answering the question: How many runs a team consisting of same player replicated eleven times will ... More

The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groupsOct 29 2016We prove that a differential field K is algebraically closed and Picard-Vessiot closed if and only if the differential Galois cohomology group H^1_\partial(K,G) is trivial for any linear differential algebraic group G over K. We give an application to ... More

Groups definable in o-minimal structures: structure theorem, G^000, definable amenability and bounded orbitsDec 21 2010Jan 10 2011We settle some open problems in the special case of groups in o-minimal structures, such as the equality of G^00 and G^000 and the equivalence of definable amenability and existence of a type with bounded orbit. We prove almost exactness of the G to G^00 ... More

Stable embeddedness and NIPJan 04 2010We give sufficient conditions for a predicate P in a complete theory T to be stably embedded: P with its induced 0-definable structure has "finite rank", P has NIP in T and P is 1-stably embedded. This generalizes recent work by Hasson and Onshuus in ... More

MAP Lexicon is useful for segmentation and word discovery in child-directed speechJul 06 1999Oct 14 1999Because of rather fundamental changes to the underlying model proposed in the paper, it has been withdrawn from the archive.

Cyclic actions and elliptic generaApr 26 2001Mar 20 2002Let $M$ be a $Spin$-manifold with $S^1$-action and let $\sigma \in S^1$ be of finite order. We show that the indices of certain twisted Dirac operators vanish if the action of $\sigma $ has sufficiently large fixed point codimension. These indices occur ... More

Strong dependence, weight, and measureMay 01 2010I give an account of Shelah's notion of strong dependence, or strong NIP, in terms of suitable generically stable measures, forking, and weight.

Topological dynamics and definable groupsJan 11 2012Following the works of Newelski we continue the study of the relations between abstract topological dynamics and generalized stable group theory. We show that the Ellis theory, applied to the action of G(M) on its type space, for G an fsg group in a NIP ... More

Ward's solitionsJul 14 1997Using the `Riemann Problem with zeros' method, Ward has constructed exact solutions to a (2+1)-dimensional integrable Chiral Model, which exhibit solitons with nontrivial scattering. We give a correspondence between what we conjecture to be all pure soliton ... More

Compactifications of Hurwitz spacesJun 20 2012We construct several modular compactifications of the Hurwitz space $H^d_{g/h}$ of genus $g$ curves expressed as $d$-sheeted, simply branched covers of genus $h$ curves. These compactifications are obtained by allowing the branch points of the covers ... More

An MSE Based Ttransfer Chart to Analyze Iterative Decoding SchemesJun 14 2005An alternative to extrinsic information transfer (EXIT) charts called mean squared error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and minimum mean squared ... More

Ramification divisors of general projectionsJan 06 2019We study the ramification divisors of projections of a smooth projective variety onto a linear subspace of the same dimension. We prove that the ramification divisors vary in a maximal dimensional family for a large class of varieties. Going further, ... More

Decision Feedback Based Scheme for Slepian-Wolf Coding of sources with Hidden Markov CorrelationJun 12 2005We consider the problem of compression of two memoryless binary sources, the correlation between which is defined by a Hidden Markov Model (HMM). We propose a Decision Feedback (DF) based scheme which when used with low density parity check codes results ... More

How much is Wikipedia Lagging Behind News?Mar 30 2017Wikipedia, rich in entities and events, is an invaluable resource for various knowledge harvesting, extraction and mining tasks. Numerous resources like DBpedia, YAGO and other knowledge bases are based on extracting entity and event based knowledge from ... More

Contrastive Entropy: A new evaluation metric for unnormalized language modelsJan 03 2016Mar 31 2016Perplexity (per word) is the most widely used metric for evaluating language models. Despite this, there has been no dearth of criticism for this metric. Most of these criticisms center around lack of correlation with extrinsic metrics like word error ... More

Saturated free algebras revisitedSep 30 2014We give an exposition of results of Baldwin-Shelah on saturated free algebras, at the level of generality of complete first order theories $T$ with a saturated model $M$ which is in the algebraic closure of an indiscernible set. We then make some new ... More

A note on the $\hat A$-genus for $π_2$-finite manifolds with $S^1$-symmetryNov 05 2008We construct examples of $S^1$-manifolds with finite second homotopy group and non-vanishing $\hat A$-genus. This is related to the classification of positive quaternionic Kaehler manifolds.

Fault Localization in a Software Project using Back-Tracking Principles of Matrix DependencyMay 05 2014Fault identification and testing has always been the most specific concern in the field of software development. To identify and testify the bug we should be aware of the source of the failure or any unwanted issue. In this paper, we are trying to extract ... More

A^1-connectedness in reductive algebraic groupsMay 15 2016Oct 06 2016Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be A^1-local if the group does not satisfy suitable isotropy hypotheses. As a consequence, we show the failure of ... More

Robust self-testing of many-qubit statesOct 12 2016We introduce a simple two-player test which certifies that the players apply tensor products of Pauli $\sigma_X$ and $\sigma_Z$ observables on the tensor product of $n$ EPR pairs. The test has constant robustness: any strategy achieving success probability ... More

Interpolation Problems: Del Pezzo SurfacesJan 21 2016We consider the problem of interpolating projective varieties through points and linear spaces. After proving general facts about interpolation, we show that del Pezzo surfaces satisfy weak interpolation.

Efficient local search limitation strategy for single machine total weighted tardiness scheduling with sequence-dependent setup timesJan 23 2015Nov 30 2015This paper concerns the single machine total weighted tardiness scheduling with sequence-dependent setup times, usually referred as $1|s_{ij}|\sum w_jT_j$. In this $\mathcal{NP}$-hard problem, each job has an associated processing time, due date and a ... More

Two presumptions in Goedel's interpretation of his own, formal, reasoning that are classically objectionableMar 24 2007Standard expositions of Goedel's 1931 paper on undecidable arithmetical propositions are based on two presumptions in Goedel's 1931 interpretation of his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which do not meet Goedel's, explicitly ... More

The formal roots of PlatonismMay 02 2003May 17 2003We present some arguments for the thesis that a set-theoretic inspired faith, in the ability of intuitive truth to faithfully reflect relationships between elements of a Platonic universe, may be as misplaced as an assumption that such truth cannot be ... More

Some consequences of a recursive number-theoretic relation that is not the standard interpretation of any of its formal representationsOct 05 2002May 11 2003We give a precise definition of a formal mathematical object as any symbol for an individual constant, predicate letter, or a function letter that can be introduced through definition into a formal mathematical language without inviting inconsistency. ... More

Naive Philosophical FoundationsDec 15 2005This soliloquy outlines some naive philosophical arguments underlying the thesis that mathematics ought to be viewed simply as a universal set of languages, some of precise expression, and some of effective communication.

Do Goedel's incompleteness theorems set absolute limits on the ability of the brain to express and communicate mental concepts verifiably?Jul 30 2004Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general, scientific, discourse ... More

Is a deterministic universe logically consistent with a probabilistic Quantum Theory?Dec 31 2002Jan 02 2003If we assume the Thesis that any classical Turing machine T, which halts on every n-ary sequence of natural numbers as input, determines a PA-provable formula, whose standard interpretation is an n-ary arithmetical relation f(x1, >..., xn) that holds ... More

Are there parts of our arithmetical competence that no sound formal system can duplicate?Oct 30 2002May 19 2003In 1995, David Chalmers opined as implausible that there may be parts of our arithmetical competence that no sound formal system could ever duplicate. We prove that the recursive number-theoretic relation x=Sb(y 19|Z(y)) - which is algorithmically verifiable ... More

Remarks on unimodularityDec 05 2010We clarify the relationship between unimodulariy in the sense of Hrushovski and measurability in the sense of Macpherson and Steinhorn, correcting some statements in the literature. In particular we point out that the notions coincide for strongly minimal ... More

Extremal effective divisors of Brill-Noether and Gieseker-Petri type in $\overline{\mathcal M}_{1,n}$Jul 18 2014We show that certain divisors of Brill-Noether and Gieseker-Petri type span extremal rays of the effective cone in the moduli space of stable genus one curves with $n$ ordered marked points. In particular, they are different from the infinitely many extremal ... More

Inflectionary Invariants for Isolated Complete Intersection Curve SingularitiesMay 24 2017Feb 19 2019We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let $N \geq 2$, and consider an isolated complete intersection curve singularity germ $f \colon (\mathbb{C}^N,0) ... More

Stable log surfaces, admissible covers, and canonical curves of genus 4Jul 23 2018We describe a compactification of the moduli space of pairs $(S, C)$ where $S$ is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^1$ and $C \subset S$ is a genus 4 curve of class $(3,3)$. We show that the compactified moduli space is a smooth Deligne-Mumford ... More

Interpolation Problems: Del Pezzo SurfacesJan 21 2016Dec 09 2016We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.

Posthoc Interpretability of Learning to Rank Models using Secondary Training DataJun 29 2018Predictive models are omnipresent in automated and assisted decision making scenarios. But for the most part they are used as black boxes which output a prediction without understanding partially or even completely how different features influence the ... More

A Decision Feedback Based Scheme for Slepian-Wolf Coding of sources with Hidden Markov CorrelationJun 13 2005We consider the problem of compression of two memoryless binary sources, the correlation between which is defined by a Hidden Markov Model (HMM). We propose a Decision Feedback (DF) based scheme which when used with low density parity check codes results ... More

A^1-connectedness in reductive algebraic groupsMay 15 2016Using sheaves of A^1-connected components, we prove that the Morel-Voevodsky singular construction on a reductive algebraic group fails to be A^1-local if the group does not satisfy suitable isotropy hypotheses. As a consequence, we show the failure of ... More

Constant-Soundness Interactive Proofs for Local HamiltoniansDec 07 2015$ \newcommand{\Xlin}{\mathcal{X}} \newcommand{\Zlin}{\mathcal{Z}} \newcommand{\C}{\mathbb{C}} $We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers, questions are classical ... More

A Compositional Approach to Language ModelingApr 01 2016Traditional language models treat language as a finite state automaton on a probability space over words. This is a very strong assumption when modeling something inherently complex such as language. In this paper, we challenge this by showing how the ... More

Some model theory of fibrations and algebraic reductionsOct 10 2012Dec 18 2013Let p=tp(a/A) be a stationary type in an arbitrary finite rank stable theory, and P an A-invariant family of partial types. The following property is introduced and characterised: whenever c is definable over (A,a) and a is not algebraic over (A,c) then ... More

Jump relations for magnetrohydrodynamic shock waves in a dusty gas atmosphereJun 07 2014In this paper, jump relations for one dimensional magnetohydrodynamic (MHD) shock waves propagating in a dusty gas environment are expressed in a simple form in terms of dimensionless variables. The dusty gas is assumed to be a mixture of a perfect gas ... More

Fast Computation of Isomorphisms Between Finite Fields Using Elliptic CurvesApr 11 2016Jul 11 2016We propose a randomized algorithm to compute isomorphisms between finite fields using elliptic curves. To compute an isomorphism between two fields of cardinality $q^n$, our algorithm takes $\widetilde{O}\left(n \log^2 q + \max_{\ell} (\ell^{n_\ell + ... More

Stable groups and expansions of $(\mathbb{Z},+,0)$Jan 21 2016Jan 27 2016We show that if $G$ is a stable group of finite weight with no infinite, infinite-index, chains of definable subgroups, then $G$ is superstable of finite $U$-rank. Combined with recent work of Palacin and Sklinos, we conclude that $(\mathbb{Z},+,0)$ has ... More

Inflectionary Invariants for Isolated Complete Intersection Curve SingularitiesMay 24 2017Jan 09 2019In this article, we investigate the role played by germs of curve singularities in the enumeration of inflection points in families of curves acquiring singular members. More precisely, let $k$ be an algebraically closed field of characteristic $0$, let ... More

R-equivalence and A^1-connectedness in anisotropic groupsAug 28 2014We show that if G is an anisotropic, semisimple, absolutely almost simple, simply connected group over a field k, then two elements of G over any field extension of k are R-equivalent if and only if they are A^1-equivalent. As a consequence, we see that ... More

Complete Intersections with S^1-actionAug 26 2011Feb 07 2017We give the diffeomorphism classification of complete intersections with S^1-symmetry in dimension less than or equal to 6. In particular, we show that a 6-dimensional complete intersection admits a smooth non-trivial S^1-action if and only if it is diffeomorphic ... More

Some consequences of interpreting the associated logic of the first-order Peano Arithmetic PA finitarilyAug 20 2011Sep 23 2012We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two essentially ... More

Why Brouwer was right in suggesting that Hilbert's Law of the Excluded Middle needed qualificationMar 26 2006We reproduce Hilbert's axiomatic formalisation of Number Theory, and argue that his enunciation of the Law of the Excluded Middle is inconsistent with a Turing-verifiable model of the axioms under the standard interpretation.

Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?Jun 07 2005We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show that, classically, ... More

An arguable addition to the standard Deduction Theorems of first order theoriesFeb 23 2005We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

The Goebbellian SyndromeJul 03 2005Can we really falsify truth by dictat? A critical note on J. R. Lucas' 1996 remarks concerning non-standard models of first-order Peano Arithmetic.

Three beliefs that lend illusory legitimacy to Cantor's diagonal argumentApr 21 2003May 17 2003Whatever other beliefs there may remain for considering Cantor's diagonal argument as mathematically legitimate, there are three that, prima facie, lend it an illusory legitimacy; they need to be explicitly discounted appropriately. The first, Cantor's ... More

Beyond Goedel : Simply consistent constructive systems of first order Peano's Arithmetic that do not yield undecidable propositions by Goedel's reasoningJan 08 2002Jan 29 2002In this paper, we argue that formal systems of first order Arithmetic that admit Goedelian undecidable propositions validly are abnormally non-constructive. We argue that, in such systems, the strong representation of primitive recursive predicates admits ... More

Combinatorial Polytope EnumerationAug 12 2009We describe a provably complete algorithm for the generation of a tight, possibly exact superset of all combinatorially distinct simple n-facet polytopes in R^d, along with their graphs, f-vectors, and face lattices. The technique applies repeated cutting ... More

Affine Nash groups over real closed fieldsMay 13 2011We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-points of some algebraic group H defined over R. In the case when R is the field ... More

A new Bound for the Maker-Breaker Triangle GameDec 04 2018The triangle game introduced by Chv\'{a}tal and Erd\H{o}s (1978) is one of the most famous combinatorial games. For $n,q\in\mathbb{N}$, the $(n,q)$-triangle game is played by two players, called Maker and Breaker, on the complete graph $K_n$. Alternately ... More

On canonical bases and internality criteriaMay 28 2007A criterion is given for a type in a finite rank stable theory to be (almost) internal to a given nonmodular minimal type. The motivation comes from results of Campana which give criteria for compact complex analytic spaces to be algebraic (namely Moishezon), ... More

In-focus wavefront sensing using non-redundant mask-induced pupil diversityJul 06 2016Wavefront estimation using in-focus image data is critical to many applications. This data is invariant to a sign flip with complex conjugation of the complex amplitude in the pupil, making for a non-unique solution. Information from an in-focus image ... More

Rost nilpotence and étale motivic cohomologyJun 20 2017Mar 22 2018A smooth projective scheme $X$ over a field $k$ is said to satisfy the Rost nilpotence principle if any endomorphism of $X$ in the category of Chow motives that vanishes on an extension of the base field $k$ is nilpotent. We show that an \'etale motivic ... More

EXS: Explainable Search Using Local Model Agnostic InterpretabilitySep 11 2018Retrieval models in information retrieval are used to rank documents for typically under-specified queries. Today machine learning is used to learn retrieval models from click logs and/or relevance judgments that maximizes an objective correlated with ... More

Tempas: Temporal Archive Search Based on TagsFeb 03 2017Limited search and access patterns over Web archives have been well documented. One of the key reasons is the lack of understanding of the user access patterns over such collections, which in turn is attributed to the lack of effective search interfaces. ... More

Module tensor product of subnormal modules need not be subnormalAug 29 2016Let $\kappa : \mathbb D \times \mathbb D \to \mathbb C$ be a diagonal positive definite kernel and let $\mathscr H_{\kappa}$ denote the associated reproducing kernel Hilbert space of holomorphic functions on the open unit disc $\mathbb D$. Assume that ... More

Inferring disease correlation from healthcare dataOct 11 2015Electronic Health Records maintained in health care settings are a potential source of substantial clinical knowledge. The massive volume of data, unstructured nature of records and obligatory requirement of domain acquaintance together pose a challenge ... More

The stable regularity lemma revisitedApr 23 2015May 12 2015We prove a regularity lemma with respect to arbitrary Keisler measures mu on V, nu on W where the bipartite graph (V,W,R) is definable in a saturated structure M and the formula R(x,y) is stable. The proof is rather quick and uses local stability theory. ... More

The free group has the dimensional order propertyApr 24 2016We prove that the common theory of nonabelian free groups has the dimensional order property, or DOP, implying, for example, that there is no reasonable structure theorem for $\aleph_1$-saturated models of this theory.

Complete Intersections with S^1-actionAug 26 2011Aug 16 2016We give the diffeomorphism classification of complete intersections with S^1-symmetry in dimension less than or equal to 6. In particular, we show that a 6-dimensional complete intersection admits a smooth non-trivial S^1-action if and only if it is diffeomorphic ... More