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A Monte-Carlo Simulation of Double Parton ScatteringJun 11 2019In this work, a new Monte-Carlo simulation of double parton scattering (DPS) at parton level is presented. The simulation is based on the QCD framework developed recently by M. Diehl, J. R. Gaunt and K. Sch\"{o}nwald. With this framework, the dynamics ... More

Using FLAME Toolkit for Agent-Based Simulation: Case Study Sugarscape ModelAug 14 2014Social scientists have used agent-based models to understand how individuals interact and behave in various political, ecological and economic scenarios. Agent-based models are ideal for understanding such models involving interacting individuals producing ... More

When actions of amenable groups can be lifted to the universal coverSep 23 2014Jul 17 2015In the first part of this paper, we let $G$ be a finitely-generated amenable group such that $G/[G, G]$ is torsion-free. We suppose that $G$ acts by homeomorphisms homotopic to the identity on a manifold $M$, and give conditions on $M$ which imply that ... More

Smooth gluing of group actions and applicationsOct 08 2012Oct 30 2012Let $M_1$ and $M_2$ be two $n$-dimensional smooth manifolds with boundary. Suppose we glue $M_1$ and $M_2$ along some boundary components (which are, therefore, diffeomorphic). Call the result $N.$ If we have a group $G$ acting continuously on $M_1,$ ... More

Smoothing nilpotent actions on 1-manifoldsMar 30 2014Sep 26 2014Let $M$ be a connected 1-manifold, i.e., $M = \R \cong (0, 1), [0, 1), [0, 1]$, or $S^1$, and let $\Homeo_+(M)$ (resp. $\Diff_+^1(M)$) be the group of orientation-preserving homeomorphisms (resp. $C^1$ diffeomorphisms) of $M$. It is a classical result ... More

Completed K-theory and Equivariant Elliptic CohomologyMar 29 2019Kitchloo and Morava give a strikingly simple picture of elliptic cohomology at the Tate curve by studying a completed version of $S^1$-equivariant $K$-theory for spaces. I present a $G$-equivariant version of their construction, which is a completed version ... More

Distortion for diffeomorphisms of surfaces with boundaryFeb 16 2012Mar 14 2012If $G$ is a finitely generated group with generators $\{g_1,..., g_s\}$, we say an infinite-order element $f \in G$ is a distortion element of $G$ provided that $\displaystyle \liminf_{n \to \infty} \frac{|f^n|}{n} = 0$, where $|f^n|$ is the word length ... More

One-parameter families of circle diffeomorphisms with strictly monotone rotation numberSep 14 2011We show that if $f \colon S^1 \times S^1 \to S^1 \times S^1$ is $C^2$, with $f(x, t) = (f_t(x), t)$, and the rotation number of $f_t$ is equal to $t$ for all $t \in S^1$, then $f$ is topologically conjugate to the linear Dehn twist of the torus $(1&1 ... More

Impact of Mobility On QoS of Mobile WiMax Network With CBR ApplicationJul 19 2011The issue of mobility is important in wireless network because internet connectivity can only be effective if it's available during the movement of node. To enhance mobility, wireless access systems are designed such as IEEE 802.16e to operate on the ... More

Quantum stabilizer codes and beyondOct 14 2008The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes. Firstly, it extends ... More

On the algebraicity of generalized power seriesAug 07 2015Mar 29 2016Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn-Mal'cev-Neumann generalized ... More

Slopes of indecomposable F-isocrystalsApr 03 2016Oct 06 2016We prove that for an indecomposable convergent or overconvergent F-isocrystal on a smooth irreducible variety over a perfect field of characteristic p, the gap between consecutive slopes at the generic point cannot exceed 1. (This may be thought of as ... More

Automorphisms of perfect power series ringsFeb 29 2016Let R be a perfect ring of characteristic p. We show that the group of continuous R-linear automorphisms of the perfect power series ring over R is generated by the automorphisms of the ordinary power series ring together with Frobenius; this answers ... More

On commutative nonarchimedean Banach fieldsFeb 29 2016Nov 20 2016We study the problem of whether a commutative nonarchimedean Banach ring which is algebraically a field can be topologized by a multiplicative norm. This can fail in general, but it holds for uniform Banach rings under some mild extra conditions. Notably, ... More

Some ring-theoretic properties of A_infFeb 29 2016The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism ... More

Physicists' approach to studying socio-economic inequalities: Can humans be modelled as atoms?Jun 20 2016A brief overview of the models and data analyses of income, wealth, consumption distributions by the physicists, are presented here. It has been found empirically that the distributions of income and wealth possess fairly robust features, like the bulk ... More

On the Effect of Suboptimal Estimation of Mutual Information in Feature Selection and ClassificationApr 30 2018This paper introduces a new property of estimators of the strength of statistical association, which helps characterize how well an estimator will perform in scenarios where dependencies between continuous and discrete random variables need to be rank ... More

Physicists' approach to studying socio-economic inequalities: Can humans be modelled as atoms?Jun 20 2016Aug 06 2018A brief overview of the models and data analyses of income, wealth, consumption distributions by the physicists, are presented here. It has been found empirically that the distributions of income and wealth possess fairly robust features, like the bulk ... More

Finite automata and algebraic extensions of function fieldsOct 17 2004May 04 2005We give an automata-theoretic description of the algebraic closure of the rational function field F_q(t) over a finite field, generalizing a result of Christol. The description takes place within the Hahn-Mal'cev-Neumann field of "generalized power series" ... More

The Algebraic Closure of the Power Series Field in Positive CharacteristicOct 23 1998Dec 16 1999We answer a question of Abhyankar by constructing an algebraic closure of the field of power series over a field of positive characteristic, using "generalized power series". (The corresponding construction in characteristic 0 dates back to Newton.)

Power series and p-adic algebraic closuresJun 04 1999Dec 16 1999In an earlier preprint (math.AG/9810142) we gave an explicit description of the algebraic closure of the field of power series over a field of characteristic p, in terms of "generalized power series". In this paper, we give an analogous description of ... More

Another Combinatorial DeterminantOct 20 1998May 18 1999We present a variation and generalization of a determinant evaluation of Wilf (math.CO/9809120). His result concerns a matrix whose entries are the coefficients of powers of a given power series; we replace the powers by repeated compositions and obtain ... More

Converting a Systems Dynamic Model to an Agent-based model for studying the Bicoid morphogen gradient in Drosophila embryoDec 17 2014The concentration gradient of the Bicoid morphogen, which is established during the early stages of a Drosophila melanogaster embryonic development, determines the differential spatial patterns of gene expression and subsequent cell fate determination. ... More

Etale covers of affine spaces in positive characteristicJul 18 2002We prove that every projective variety of dimension n over a field of positive characteristic admits a morphism to projective n-space, etale away from the hyperplane H at infinity, which maps a chosen divisor into H and a chosen smooth point not on the ... More

Quantum computation of zeta functions of curvesNov 28 2004Nov 30 2005We exhibit a quantum algorithm for determining the zeta function of a genus g curve over a finite field F_q, which is polynomial in g and log(q). This amounts to giving an algorithm to produce provably random elements of the class group of a curve, plus ... More

Finiteness of rigid cohomology with coefficientsAug 04 2002Nov 03 2005We prove that for any field k of characteristic p>0, any separated scheme X of finite type over k, and any overconvergent F-isocrystal E over X, the rigid cohomology H^i(X, E) and rigid cohomology with compact supports H^i_c(X,E) are finite dimensional ... More

Unipotency and semistability of overconvergent F-crystalsFeb 21 2001May 29 2001In this paper (part of the author's PhD thesis), we introduce the notions of semistability and potential semistability of overconvergent F-crystals over an equal characteristic local field. We establish their equivalence with the notions of unipotency ... More

Some new directions in p-adic Hodge theorySep 12 2007Feb 03 2009We recall some basic constructions from p-adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B-pairs, introduced recently by Berger, which provides a natural enlargement of the category of p-adic Galois ... More

Good formal structures for flat meromorphic connections, III: Irregularity is nefAug 23 2013Given a formal flat meromorphic connection over an excellent scheme over a field of characteristic zero, in a previous paper we established existence of good formal structures and a good Deligne-Malgrange lattice after suitably blowing up; however, no ... More

Notes on isocrystalsJun 04 2016Aug 18 2016For varieties over a perfect field of characteristic p, etale cohomology with Q_l-coefficients is a Weil cohomology theory only when l is not equal to p; the corresponding role for l = p is played by Berthelot's rigid cohomology. In that theory, the coefficient ... More

Convergence polygons for connections on nonarchimedean curvesMay 07 2015Jul 10 2015This is a survey article on ordinary differential equations over nonarchimedean fields based on the author's lecture at the 2015 Simons Symposium on nonarchimedean and tropical geometry. Topics include: the convergence polygon associated to a differential ... More

New methods for (phi, Gamma)-modulesJul 10 2013Jan 15 2015We provide new proofs of two key results of p-adic Hodge theory: the Fontaine-Wintenberger isomorphism between Galois groups in characteristic 0 and characteristic p, and the Cherbonnier-Colmez theorem on decompletion of (phi, Gamma)-modules. These proofs ... More

Time Resolved Measurement of Electron Cloud Densities from Dispersion of Transverse Electric PulsesNov 05 2015The measurement of electron cloud densities in particle accelerators using microwaves has proven to be an effective, non-invasive and inexpensive method. So far the experimental schemes have used continuous waves. This has either been in the form of travelling ... More

Basis discrepancies for extensions of valued fieldsApr 10 2006Let F be a field complete for a real valuation. It is a standard result in valuation theory that a finite extension of F admits a valuation basis if and only if it is without defect. We show that even otherwise, one can construct bases in which the discrepancy ... More

Counting Points on Hyperelliptic Curves using Monsky-Washnitzer CohomologyMay 03 2001Nov 20 2001We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, ... More

Semantic Web Approach towards Interoperability and Privacy issues in Social NetworksOct 08 2014The Social Web is a set of social relations that link people through World Wide Web. This Social Web encompasses how the websites and software are designed and developed to support social relations. The new paradigms, tools and web services introduced ... More

Experimental Report on Setting up a Cloud Computing Environment at the University of BradfordDec 15 2014Cloud computing is increasingly attracting large attention in computing both in academic research and in industrial initiatives. Emerging as a popular paradigm and an attractive model of providing computing, information technology (IT) infrastructure, ... More

Copula Index for Detecting Dependence and Monotonicity between Stochastic SignalsMar 20 2017Oct 06 2018This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula Index for Detecting ... More

The p-adic local monodromy theorem for fake annuliJul 24 2005Nov 11 2006We establish a generalization of the p-adic local monodromy theorem (of Andre, Mebkhout, and the author) in which differential equations on rigid analytic annuli are replaced by differential equations on so-called fake annuli. The latter correspond loosely ... More

Quasi-unipotence of overconvergent F-crystalsJun 22 2001Building on our previous papers (math.AG/0102173, math.AG/0105244, math.AG/0106192) we prove that every overconvergent F-isocrystal over k((t)) is quasi-unipotent (in the sense of Crew), for k a field of positive characteristic.

Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensionsMay 05 2004Jan 20 2007Let X be a smooth variety over a field of positive characteristic, and let E be an overconvergent isocrystal on X. We establish a criterion for the existence of a "canonical logarithmic extension" of E to a good compactification of X. In the process, ... More

Descent of morphisms of overconvergent F-crystalsMay 29 2001Tsuzuki has conjectured that for crystals with Frobenius and connection over a local field k((t)), the embedding of the category of overconvergent crystals into the category of convergent crystals is fully faithful. We prove Tsuzuki's conjecture restricted ... More

Hot Streaks on Social MediaApr 05 2019Measuring the impact and success of human performance is common in various disciplines, including art, science, and sports. Quantifying impact also plays a key role on social media, where impact is usually defined as the reach of a user's content as captured ... More

Understanding International Migration using Tensor FactorizationFeb 16 2017Understanding human migration is of great interest to demographers and social scientists. User generated digital data has made it easier to study such patterns at a global scale. Geo coded Twitter data, in particular, has been shown to be a promising ... More

Slopes of indecomposable F-isocrystalsApr 03 2016Sep 29 2018We prove that for an indecomposable convergent or overconvergent F-isocrystal on a smooth irreducible variety over a perfect field of characteristic p, the gap between consecutive slopes at the generic point cannot exceed 1. (This may be thought of as ... More

The Hochschild-Serre property for some p-adic analytic group actionsJun 06 2015Jun 11 2015Let $H \subseteq G$ be an inclusion of $p$-adic Lie groups. When $H$ is normal or even subnormal in $G$, the Hochschild-Serre spectral sequence implies that any continuous $G$-module whose $H$-cohomology vanishes in all degrees also has vanishing $G$-cohomology. ... More

Studies of fractal structures and processes using methods of fractional calculusNov 04 1998The thesis deals with applications of fractional calculus to fractals. It introduces the notion of local fractional derivative (LFD). Fractal and multifractal functions have been studied in the thesis using LFD. New kind of equations are introduced which ... More

On the algebraicity of generalized power seriesAug 07 2015Nov 24 2016Let K be an algebraically closed field of characteristic p. We exhibit a counterexample against a theorem asserted in one of our earlier papers, which claims to characterize the integral closure of K((t)) within the field of Hahn-Mal'cev-Neumann generalized ... More

Reified valuations and adic spectraSep 03 2013Aug 19 2015We revisit Huber's theory of continuous valuations, which give rise to the adic spectra used in his theory of adic spaces. We instead consider valuations which have been reified, i.e., whose value groups have been forced to contain the real numbers. This ... More

Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuationsSep 22 2006Jun 12 2008We resolve the local semistable reduction problem for overconvergent F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and residue transcendence degree 0). We first introduce a higher-dimensional analogue of the generic radius of ... More

Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approachAug 11 2005Sep 02 2007We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness of the Riemann-Zariski ... More

Fourier transforms and p-adic "Weil II"Oct 10 2002Jul 20 2005Building on work of Crew, we give a rigid cohomological analogue of the main result of Deligne's "Weil II"; this makes it possible to give a purely p-adic proof of the Weil conjectures. Ingredients include a p-adic analogue of Laumon's application of ... More

Full faithfulness for overconvergent F-isocrystalsOct 11 2001Jun 01 2003Let X be a smooth variety over a field of characteristic p>0. We prove that the forgetful functor from the category of overconvergent F-isocrystals on X to the category of convergent F-isocrystals is fully faithful. The argument uses the quasi-unipotence ... More

A p-adic local monodromy theoremOct 11 2001Jan 01 2003We produce a canonical filtration for locally free sheaves on an open p-adic annulus equipped with a Frobenius structure. Using this filtration, we deduce a conjecture of Crew on p-adic differential equations, analogous to Grothendieck's local monodromy ... More

Slope filtrations revisitedApr 10 2005Oct 25 2005We give a "second generation" exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which ... More

Good formal structures for flat meromorphic connections, III: Irregularity and turning lociAug 23 2013Mar 07 2019Given a formal flat meromorphic connection over an excellent scheme over a field of characteristic zero, in a previous paper we established existence of good formal structures and a good Deligne-Malgrange lattice after suitably blowing up. In this paper, ... More

Algebraic Generalized Power Series and AutomataOct 08 2001A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol's result, we prove that the same assertion holds for generalized ... More

Sato-Tate groups of genus 2 curvesAug 29 2014Dec 11 2014We describe the analogue of the Sato-Tate conjecture for an abelian variety over a number field; this predicts that the zeta functions of the reductions over various finite fields, when properly normalized, have a limiting distribution predicted by a ... More

Relative p-adic Hodge theory and Rapoport-Zink period domainsApr 06 2010As an example of relative p-adic Hodge theory, we sketch the construction of the universal admissible filtration of an isocrystal (\phi$-module) over the completion of the maximal unramified extension of Q_p, together with the associated universal crystalline ... More

Recursive Local Fractional DerivativeDec 30 2013The definition of the local fractional derivative has been generalised to the orders beyond the critical order. This makes it possible to retain more terms in the local fractional Taylor expansion leading to better approximation. This also extends the ... More

Good formal structures for flat meromorphic connections, III: Irregularity and turning lociAug 23 2013Sep 27 2018Given a formal flat meromorphic connection over an excellent scheme over a field of characteristic zero, in a previous paper we established existence of good formal structures and a good Deligne-Malgrange lattice after suitably blowing up. In this paper, ... More

Detecting gravitational decoherence with clocks: Limits on temporal resolution from a classical channel model of gravityNov 29 2016The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between ... More

A formulation of difference Galois theoryOct 19 2006As a simple corollary of a highly general framework for differential and difference Galois theory introduced by Y. Andre, we formulate a version of the Galois correspondence that applies over a difference field with arbitrary field of constants.

Local and global structure of connections on nonarchimedean curvesJan 27 2013Aug 29 2014Consider a vector bundle with connection on a p-adic analytic curve in the sense of Berkovich. We collect some improvements and refinements of recent results on the structure of such connections, and on the convergence of local horizontal sections. This ... More

Nonarchimedean geometry of Witt vectorsApr 03 2010Feb 15 2012Let R be a perfect F_p-algebra, equipped with the trivial norm. Let W(R) be the ring of p-typical Witt vectors over R, equipped with the p-adic norm. At the level of nonarchimedean analytic spaces (in the sense of Berkovich), we demonstrate a close analogy ... More

On Families of (Phi,Gamma)-modulesNov 29 2008Feb 06 2011Berger and Colmez introduced a theory of families of overconvergent \'etale (Phi,Gamma)-modules associated to families of p-adic Galois representations over p-adic Banach algebras. However, in contrast with the classical theory of (Phi,Gamma)-modules, ... More

More etale covers of affine spaces in positive characteristicMar 31 2003Jan 27 2004We prove that every geometrically reduced projective variety of pure dimension n over a field of positive characteristic admits a morphism to projective n-space, etale away from the hyperplane H at infinity, which maps a chosen divisor into H and some ... More

On the geometry of p-typical covers in characteristic pJan 30 2005Jan 16 2006A p-typical cover of a connected scheme on which p=0 is a finite etale cover whose monodromy group (i.e., the Galois group of its normal closure) is a p-group. The geometry of such covers exhibits some unexpectedly pleasant behaviors; building on work ... More

Computing zeta functions via p-adic cohomologyMar 15 2004We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.

Semistable reduction for overconvergent F-isocrystals on a curveFeb 23 2002May 24 2003Given a smooth affine curve X over a field k of positive characteristic, and an overconvergent F-isocrystal on X, we prove after replacing k by a finite purely inseparable extension, there exists a finite separable cover of X, the pullback of the isocrystal ... More

The Newton polygons of overconvergent F-crystalsJun 22 2001R. Crew conjectured that every overconvergent F-isocrystal over k((t)) (k a field of positive characteristic) is quasi-unipotent (equivalently, potentially semistable), and so has ``generic'' and ``special'' Newton polygons. It is easy to construct a ... More

Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuationsDec 20 2007Jul 22 2010We complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic singularities and ... More

Swan conductors for p-adic differential modules, I: A local constructionNov 27 2006Sep 18 2007We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over ... More

Frobenius modules and de Jong's theoremFeb 26 2004Dec 12 2004Let k be a field of characteristic p>0. A theorem of de Jong shows that morphisms of modules over W(k)[[t]] with Frobenius and connection structure descend from the completion of W(k)((t)). A careful reading of de Jong's proof suggests the possibility ... More

Good formal structures on flat meromorphic connections, I: SurfacesNov 02 2008Dec 08 2009We give a criterion under which one can obtain a good decomposition (in the sense of Malgrange) of a formal flat connection on a complex analytic or algebraic variety of arbitrary dimension. The criterion is stated in terms of the spectral behavior of ... More

A construction of polynomials with squarefree discriminantsMar 29 2011May 04 2011For any integer n >= 2 and any nonnegative integers r,s with r+2s = n, we give an unconditional construction of infinitely many monic irreducible polynomials of degree n with integer coefficients having squarefree discriminant and exactly r real roots. ... More

Local Fractional Calculus: a ReviewJul 02 2013The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local fractional Taylor ... More

Brownian motion of fractal particles: Levy flights from white noiseNov 14 2005We generalise the Langevin equation with Gaussian white noise by replacing the velocity term by a local fractional derivative. The solution of this equation is a Levy process. We further consider the Brownian motion of a fractal particle, for example, ... More

Separable local fractional differential equationsNov 15 2015The concept of local fractional derivative was introduced in order to be able to study the local scaling behavior of functions. However it has turned out to be much more useful. It was found that simple equations involving these operators naturally incorporate ... More

Slopes of indecomposable F-isocrystalsApr 03 2016Aug 26 2016We prove that for an indecomposable convergent or overconvergent F-isocrystal on a smooth irreducible variety over a perfect field of characteristic p, the gap between consecutive slopes at the generic point cannot exceed 1. (This may be thought of as ... More

FPGA Implementation of High Speed Baugh-Wooley Multiplier using Decomposition LogicSep 11 2015The Baugh-Wooley algorithm is a well-known iterative algorithm for performing multiplication in digital signal processing applications. Decomposition logic is used with Baugh-Wooley algorithm to enhance the speed and to reduce the critical path delay. ... More

Noetherian properties of Fargues-Fontaine curvesOct 20 2014Jul 06 2015We establish that the extended Robba rings associated to a perfect nonarchimedean field of characteristic p, which arise in p-adic Hodge theory as certain completed localizations of the ring of Witt vectors, are strongly noetherian Banach rings; that ... More

A Long-Term Analysis of Polarization on TwitterMar 08 2017Mar 17 2017Social media has played an important role in shaping political discourse over the last decade. At the same time, it is often perceived to have increased political polarization, thanks to the scale of discussions and their public nature. In this paper, ... More

Search techniques for root-unitary polynomialsAug 03 2006Sep 25 2007We give an anecdotal discussion of the problem of searching for polynomials with all roots on the unit circle, whose coefficients are rational numbers subject to certain congruence conditions. We illustrate with an example from a calculation in p-adic ... More

Crew's Euler characteristic formula fails for nonzero slopesMay 15 2001A result of Crew implies that for an etale Galois p-cover of smooth proper varieties over a field of characteristic p, the alternating sum of the p-ranks of the cohomology groups behave like Euler characteristics in characteristic 0. That is, the sum ... More

Evaluating the Utility of Anonymized Network Traces for Intrusion DetectionDec 07 2007Jun 27 2008Anonymization is the process of removing or hiding sensitive information in logs. Anonymization allows organizations to share network logs while not exposing sensitive information. However, there is an inherent trade off between the amount of information ... More

Good formal structures for flat meromorphic connections, II: Excellent schemesJan 04 2010Jul 30 2010Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for algebraic varieties. The argument combines a numerical ... More

Product-free subsets of groups, then and nowAug 16 2007Nov 07 2007A subset of a group is product-free if it does not contain elements a, b, c such that ab = c. We review progress on the problem of determining the size of the largest product-free subset of an arbitrary finite group, including a lower bound due to the ... More

Some slope theory for multivariate Robba ringsNov 29 2013We describe a class of multivariate series rings generalizing the usual Robba ring over a p-adic field, and develop a partial slope theory for Frobenius modules over such rings. This involves passage to certain perfect closures, invocation of results ... More

Swan conductors for p-adic differential modules, II: Global variationMay 01 2007Nov 24 2008Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an isocrystal on a variety over a perfect field of positive characteristic overconvergent along a boundary divisor; this leads to ... More

Slope filtrations for relative FrobeniusSep 10 2006Sep 06 2007The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over the Robba ring (the ring of germs of rigid analytic functions on an ... More

Local monodromy of p-adic differential equations: an overviewJan 22 2005May 23 2005This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda's classification of quasi-unipotent ... More

p-adic cohomologyJan 20 2006Apr 26 2008This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.

Unramified alternating extensions of quadratic fieldsMar 30 2001We exhibit, for n at least 5, infinitely many quadratic number fields admitting unramified degree n extensions with prescribed signature whose normal closures have Galois group A_n. This generalizes a result of Uchida and Yamamoto, which did not include ... More

Degenerate quantum codes and the quantum Hamming boundDec 14 2008Nov 21 2009The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether or not the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this ... More

Encoding Subsystem CodesJun 30 2008In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the known results ... More

Clifford Code Constructions of Operator Quantum Error Correcting CodesApr 21 2006Oct 18 2006Recently, operator quantum error-correcting codes have been proposed to unify and generalize decoherence free subspaces, noiseless subsystems, and quantum error-correcting codes. This note introduces a natural construction of such codes in terms of Clifford ... More

Endomorphism fields of abelian varietiesJun 09 2016We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrary number field; this refines a result of Silverberg. This follows from ... More

Dynamics of ten clusters of galaxies with substructuresApr 01 2014We present a detailed Chandra study of a sample of ten clusters of galaxies selected based on the presence of substructures in their optical images. The X-ray surface brightness maps of most of these clusters show anisotropic morphologies, especially ... More

Relative p-adic Hodge theory, II: (phi, Gamma)-modulesJan 04 2013Feb 18 2016Building on foundations introduced in a previous paper, we give several p-adic analytic descriptions of the categories of etale Zp-local systems and etale Qp-local systems on an affinoid algebra over a finite extension of Qp (or more generally, over the ... More