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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

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

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

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

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

Degree Optimization and Stability Condition for the Min-Sum DecoderMay 09 2007The min-sum (MS) algorithm is arguably the second most fundamental algorithm in the realm of message passing due to its optimality (for a tree code) with respect to the {\em block error} probability \cite{Wiberg}. There also seems to be a fundamental ... More

On the Distortion SNR Exponent of Some Layered Transmission SchemesMar 08 2007Apr 20 2007We consider the problem of joint source-channel coding for transmitting K samples of a complex Gaussian source over T = bK uses of a block-fading multiple input multiple output (MIMO) channel with M transmit and N receive antennas. We consider the case ... More

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

Minimal Network Coding for MulticastJun 12 2005We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of ... 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

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

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.

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

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

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

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

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

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

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

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

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

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

A note on the effective listing of complete typesApr 22 2019We use the "geometric axioms" point of view to give an effective listing of the complete types of the theory $DCF_{0}$ of differentially closed fields of characteristic $0$. This gives another account of observations made in earlier papers.

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

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

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

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

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

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

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

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

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).

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.

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

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

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

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

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.

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

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.

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

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

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

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^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.

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

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

Gibbs entropy of networks ensembles by cavity methodsJan 26 2010May 25 2010The Gibbs entropy of a microcanonical network ensemble is the logarithm of the number of network configurations compatible with a set of hard constraints. This quantity characterizes the level of order and randomness encoded in features of a given real ... 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.

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

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

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

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.

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

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

The Goldstone Equivalence Theorem and AdS/CFTFeb 11 2015The Goldstone equivalence theorem allows one to relate scattering amplitudes of massive gauge fields to those of scalar fields in the limit of large scattering energies. We generalize this theorem under the framework of the AdS/CFT correspondence. First, ... More

Shock dynamics of strong imploding cylindrical and spherical shock waves with non-ideal gas effectsJun 04 2013In this paper, the generalized analytical solution for one dimensional adiabatic flow behind the strong imploding shock waves propagating in a non-ideal gas is obtained by using the geometrical shock dynamics theory. The equation of state for non-ideal ... More

Meromorphic GroupsMay 02 2000May 16 2000We introduce the notion of a meromorphic group, weakening somewhat Fujiki's definition We prove that a meromorphic group is meromorphically an extension of a complex torus by a linear algebraic group, generalizing results in [Fujiki, 1978]. A special ... More

PoreNet: CNN-based Pore Descriptor for High-resolution Fingerprint RecognitionMay 16 2019With the development of high-resolution fingerprint scanners, high-resolution fingerprint-based biometric recognition has received increasing attention in recent years. This letter presents a pore feature-based approach for biometric recognition. Our ... More

Artificial Neural Networks for Detection of Malaria in RBCsAug 23 2016Malaria is one of the most common diseases caused by mosquitoes and is a great public health problem worldwide. Currently, for malaria diagnosis the standard technique is microscopic examination of a stained blood film. We propose use of Artificial Neural ... More

No information can be conveyed by certain events: The case of the clever widows of Fornicalia and the Stobon OracleJul 08 1999In this short article, we look at an old logical puzzle, its solution and proof and discuss some interesting aspects concerning its representation in a logic programming language like Prolog. We also discuss an intriguing information theoretic aspect ... More

Connected components of definable groups, and o-minimality IIJun 17 2011We study the connected components G^00, G^000 and their quotients for a group G definable in a saturated o-minimal expansion of a real closed field. We show that G^00/G^000 is naturally the quotient of a connected compact commutative Lie group by a dense ... More

Polynomial Factorization over Finite Fields By Computing Euler-Poincare Characteristics of Drinfeld ModulesApr 29 2015Jul 11 2016We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank $2$ Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from Euler-Poincare characteristics ... More

NEEXP in MIP*Apr 11 2019We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), ... More

Entropy measures for complex networks: Toward an information theory of complex topologiesJul 09 2009Oct 16 2009The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how ... More

Connected components of definable groups and o-minimality IJan 29 2011We give examples of groups G such that G^00 is different from G^000. We also prove that for groups G definable in an o-minimal structure, G has a "bounded orbit" iff G is definably amenable. These results answer questions of Gismatullin, Newelski, Petrykovski. ... More

An arguable inconsistency in ZFFeb 23 2005Feb 26 2005Classical theory proves that every primitive recursive function is strongly representable in PA; that formal Peano Arithmetic, PA, and formal primitive recursive arithmetic, PRA, can both be interpreted in Zermelo-Fraenkel Set Theory, ZF; and that if ... More

Reviewing Goedel's and Rosser's meta-reasoning of undecidabilityApr 16 2002May 11 2003I review the classical conclusions drawn from Goedel's meta-reasoning establishing an undecidable proposition GUS in standard PA. I argue that, for any given set of numerical values of its free variables, every recursive arithmetical relation can be expressed ... More

A case for weakening the Church-Turing ThesisAug 20 2011We conclude from Goedel's Theorem VII of his seminal 1931 paper that every recursive function f(x_{1}, x_{2}) is representable in the first-order Peano Arithmetic PA by a formula [F(x_{1}, x_{2}, x_{3})] which is algorithmically verifiable, but not algorithmically ... More

An elementary proof that P =/= NPMar 26 2006Feb 27 2007We show that, if PA has no non-standard models, then P=/=NP. We then give an elementary proof that PA has no non-standard models.

PA is instantiationally complete, but algorithmically incomplete: An alternative interpretation of Goedelian incompleteness under Church's Thesis that links formal logic and computabilityJul 03 2005We define instantiational and algorithmic completeness for a formal language. We show that, in the presence of Church's Thesis, an alternative interpretation of Goedelian incompleteness is that Peano Arithmetic is instantiationally complete, but algorithmically ... More

Is the Halting probability a Dedekind real number?Jun 01 2003In a recent historical overview, Cristian S. Calude, Elena Calude, and Solomon Marcus identify eight stages in the development of the concept of a mathematical proof in support of an ambitious conjecture: we can express classical mathematical concepts ... More

Can we express every transfinite concept constructively?May 17 2003In a forthcoming book, professional computer scientist and physicist Paul Budnik presents an exposition of classical mathematical theory as the backdrop to an elegant thesis: we can interpret any model of a formal system of Peano Arithmetic in an appropriate, ... More

Representation learning of drug and disease terms for drug repositioningMay 15 2017May 20 2017Drug repositioning (DR) refers to identification of novel indications for the approved drugs. The requirement of huge investment of time as well as money and risk of failure in clinical trials have led to surge in interest in drug repositioning. DR exploits ... More

On stable fields and weightSep 30 2009We prove that if K is an infinite stable field whose generic type has weight 1 then K is separably closed. We also obtain partial results when the generic of K has finite weight and when K is strongly stable.

Generalized Picard-Vessiot extensions and differential Galois cohomologyFeb 07 2017Sep 11 2017In an earlier paper it was proved that if a differential field $(K,\delta)$ is algebraically closed and closed under Picard-Vessiot extensions then every differential algebraic principal homogeneous space over K for a linear differential algebraic group ... More

On minimal flows. definably amenable groups, and o-minimalityApr 03 2015We study definably amenable groups in NIP theories, and answer a question of Newelski (and also of Chernikov-Simon), by giving an example in the o-minimal context where weak generic types do not coincide with almost periodic types, equivalently where ... More

Model theory and Kaehler geometryFeb 15 2007We survey and explain some recent work at the intersection of model theory and bimeromorphic geometry (classification of compact complex manifolds). Included here are the essential saturation of the many sorted structure $\mathcal{C}$ of compact Kaehler ... More

On the Chow ring of the Hurwitz space of degree three covers of ${\bf P}^{1}$May 16 2015We determine the Chow ring (with ${\bf Q}$-coefficients) of the Hurwitz space parametrizing degree three covers of ${\bf P}^{1}$. We also compute the rational Picard groups of auxiliary spaces of degree three maps with special marked points. In particular, ... More

Galois theory, functional Lindemann-Weierstrass, and Manin mapsFeb 06 2015We prove several new results of Ax-Lindemann type for semiabelian varieties over the algebraic closure K of C(t), making heavy use of the Galois theory of logarithmic differential equations. Using related techniques, we also give a generalization of the ... More

Multilogarithmic velocity renormalization in grapheneMar 03 2016Jun 20 2016We reexamine the effect of long-range Coulomb interactions on the quasiparticle velocity in graphene. Using a nonperturbative functional renormalization group approach with partial bosonization in the forward scattering channel and momentum transfer cutoff ... More