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A Separation Logic for Concurrent Randomized ProgramsFeb 08 2018We present a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs with both probabilistic ... More

Augur: a Modeling Language for Data-Parallel Probabilistic InferenceDec 12 2013Jun 10 2014It is time-consuming and error-prone to implement inference procedures for each new probabilistic model. Probabilistic programming addresses this problem by allowing a user to specify the model and having a compiler automatically generate an inference ... More

Diophantine properties of continued fractions on the Heisenberg groupSep 20 2013Aug 11 2014We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem and that convergents ... More

Authentication Based Solutions to Counterfeiting of Manufactured GoodsNov 27 2015May 21 2016Counterfeiting of manufactured goods is presented as the theft of intellectual property, patents, copyright etc. accompanied by identity theft. The purpose of the identity theft is to facilitate the intellectual property theft. Without it the intellectual ... More

The Game of PhishingNov 12 2015Aug 04 2016Phishing attacks occur because of a failure of computer users to authenticate Bob. The computer user's role, her job, is to authenticate Bob. Nobody else can carry out this task. I researched the ability of browsers to counterfeit the behaviour of installed ... More

The normality of digits in almost constant additive functionsJun 06 2012We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last \lceil y \frac{\log \log \log n}{\log b} \rceil digits of each f(n) ... More

On multiplicativity of Fourier coefficients at cusps other than infinityFeb 11 2011This paper treats the problem of determining conditions for the Fourier coefficients of a Maass-Hecke newform at cusps other than infinity to be multiplicative. To be precise, the Fourier coefficients are defined using a choice of matrix in SL(2, Z) which ... More

On On_pAug 03 2011Feb 17 2015Generalizing John Conway's construction of the Field On_2, we give the "minimal" definitions of addition and multiplication that turn the ordinals into a Field of characteristic p, for any prime p. We then analyze the structure of the resulting Field, ... More

Cover times and generic chainingJul 04 2012Jul 10 2012A recent result of Ding, Lee and Peres expresses the cover time of the random walk on a graph in terms of generic chaining for the commute distance. Their proof is very involved and the purpose of this article is to present a simpler approach to this ... More

Generically large nongaussianity in small multifield inflationFeb 09 2015Jul 14 2015If forthcoming measurements of cosmic photon polarization restrict the primordial tensor-to-scalar ratio to $r < 0.01$, small field inflation will be a principal candidate for the origin of the universe. Here we show that small multifield inflation, without ... More

A preparation theorem for the kashiwara $b(\infty)$ crystalOct 21 2015The Kashiwara $B(\infty)$ crystal pertains to a Verma module for a Kac- Moody Lie algebra. Ostensibly it provides only a parametrisation of the global/canonical basis for the latter. Yet it is much more having a rich combinatorial structure from which ... More

Particle phenomenology on noncommutative spacetimeNov 24 2008May 12 2009We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spcetime noncommutativity is constrained from the CPT violation measurements in $K^{0}-\bar{K}^{0}$ system and $g-2$ difference ... More

Blackbody Friction: Analytic expressions for velocity and positionNov 08 2012The equations of motion are solved analytically for speed and position for the case of blackbody friction on objects traveling at relativistic speeds with respect to observers fixed in the frame of the blackbody radiation. Two model cases are considered, ... More

Intersections via resolutionsApr 08 2014We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a certain structure ... More

The $R_{\mathrm{h}}=ct$ universe and quintessenceJan 20 2016Over the last few years the $R_{\mathrm{h}}=ct$ universe has received a lot of attention, particularly when observational evidence seems to favor this over the standard $\Lambda$ cold dark matter ($\Lambda CDM$) universe. Like the $\Lambda CDM$, the $R_{\mathrm{h}}=ct$ ... More

Dileptons and Photons from Coarse-Grained Microscopic Dynamics and Hydrodynamics Compared to Experimental DataOct 09 2002We compute the radiation of dileptons and photons using relativistic hydrodynamics and a coarse-grained version of the microscopic event generator UrQMD, both of which provide a good description of the hadron spectra. The currently most accurate dilepton ... More

Variable Selection in High Dimensions with Random Designs and Orthogonal Matching PursuitSep 04 2011The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the design matrix, ... More

Midy's Theorem for Periodic DecimalsMay 07 2006The decimal expansion of 1/7 is 0.142857142857..., the block 142857 repeating forever. We call 142857 the period and its length is 6 = 2x3. If the period is broken into 2 pieces each of length 3 which are then added, the result is 142 + 857 = 999; similarly ... More

Wave approach for the resonances of rectangular and triangular membranesJun 09 2011This study develops a ray technique for determining the resonance frequencies of triangular membranes. The technique is demonstrated for homogenous rectangular and triangular membranes with fixed boundaries. Where possible, the results are compared with ... More

Relativity and Aether Theory, a Crucial DistinctionOct 10 2006Dec 14 2008We study the case of two rockets which meet at a point O of an inertial co-ordinate system S, and are scheduled to move at constant speed, in opposite directions, toward two targets placed at equal distances from point O. At the instant they meet, the ... More

On Multiplicative Functions with Bounded Partial SumsAug 06 2011Consider a multiplicative function f(n) taking values on the unit circle. Is it possible that the partial sums of this function are bounded? We show that if we weaken the notion of multiplicativity so that f(pn)=f(p)f(n) for all primes p in some finite ... More

On diagonal lower bound of Markov kernel from $L^2$ analyticityAug 10 2015Let $\Gamma$ be a graph and $P$ be a reversible random walk on $\Gamma$. From the $L^2$ analyticity of the Markov operator $P$, we deduce an on-diagonal lower bound of an iterate of odd number of $P$. The proof does not require the doubling property on ... More

Riesz transform on graphs under subgaussian estimatesMay 26 2015Jan 14 2016Let $\Gamma$ be a doubling graph satisfying some pointwise subgaussian estimates of the Markov kernel. We introduce a space $H^1(\Gamma)$ of functions and a space $H^1(T_\Gamma)$ of 1-forms and give various characterizations of them. We prove the $H^1$-boundedness ... More

Cosmic ConundrumsApr 10 2014What do we do when cosmology raises questions it cannot answer? These include the existence of a multiverse and the universality of the laws of physics. We cannot settle any of these issues by experiment, and this is where philosophers enter the debate. ... More

Feedback in Galaxy FormationFeb 01 2011I review the outstanding problems in galaxy formation theory, and the role of feedback in resolving them. I address the efficiency of star formation, the galactic star formation rate, and the roles of supernovae and supermassive black holes.

Failure of the parametric h-principle for maps with prescribed jacobianDec 06 2005Let M and N be closed n-dimensional manifolds, and equip N with a volume form \sigma. Let \mu be an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*\sigma=\mu. In 1973 Eliashberg and Gromov showed that this ... More

Symplectomorphism groups and isotropic skeletonsApr 27 2004Jun 17 2005The symplectomorphism group of a 2-dimensional surface is homotopy equivalent to the orbit of a filling system of curves. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of the symplectic ... More

Derived autoequivalences from periodic algebrasJun 14 2011Feb 18 2013We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by Rouquier-Zimmermann and ... More

Random Heegaard splittingsSep 29 2008Nov 16 2010A random Heegaard splitting is a 3-manifold obtained by using a random walk of length n on the mapping class group as the gluing map between two handlebodies. We show that the joint distribution of random walks of length n and their inverses is asymptotically ... More

Regularization in $L_1$ for the Ornstein--Uhlenbeck semigroupMay 15 2015Let $\gamma_n$ be the standard Gaussian measure on $\mathbb R^n$ and let $(Q_t)$ be the Ornstein--Ulhenbeck semigroup. Eldan and Lee recently established that for every non--negative function $f$ of integral $1$ and any time $t$ the following tail inequality ... More

Functional calculus and joint torsion of pairs of almost commuting operatorsSep 22 2014This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely summable Fredholm ... More

Stacks in Representation Theory. What is a continuous representation of an algebraic group ?Oct 02 2014May 12 2016In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack). This point of view necessarily ... More

Prequantization of logsymplectic structuresJan 12 2010In this paper, we study quatization condition of logsymplectic struc- ture using integrality of such structue on the complement of associated divisor D.

Self-Organized Criticality on Quasiperiodic GraphsApr 16 1999Jul 26 1999Self-organized critical models are used to describe the 1/f-spectra of rather different physical situations like snow avalanches, noise of electric currents, luminosities of stars or topologies of landscapes. The prototype of the SOC-models is the sandpile ... More

On the Existence of an Orthogonal Factorization System on 1-Cob and 2-CobJun 09 2015We define the category 2-Cob combinatorially and use this definition to prove the existence of an orthogonal factorization system. In the second half of the paper, we define oriented 1-Cob similarly and define a functor from oriented 1-Cob to 2-Cob. After ... More

General bound of overfitting for MLP regression modelsJan 03 2012Multilayer perceptrons (MLP) with one hidden layer have been used for a long time to deal with non-linear regression. However, in some task, MLP's are too powerful models and a small mean square error (MSE) may be more due to overfitting than to actual ... More

Testing the number of parameters with multidimensional MLPFeb 21 2008This work concerns testing the number of parameters in one hidden layer multilayer perceptron (MLP). For this purpose we assume that we have identifiable models, up to a finite group of transformations on the weights, this is for example the case when ... More

Pénalisations of Walsh's Brownian motionJun 16 2005In this paper, we construct a family of probability measures, by penalizations of a Walsh's Brownian motion with a weight dependent on its value and its local time at a time t. We prove that this family converges to a probability measure as t tends to ... More

Containment in (s,t)-core PartitionsSep 12 2008We introduce the idea of (s,t)-closure and delta-sets and show that (s,t)-closed beta-sets which are contained set-wise in (s,t)-closed delta-sets are also contained partition-wise. This implies the maximal (s,t)-core partition theorem of Olsson and Stanton. ... More

On the Yao-Yao partition theoremNov 09 2010The Yao-Yao partition theorem states that given a probability measure on an affine space of dimension n having a density which is continuous and bounded away from 0, it is possible to partition the space into 2^n regions of equal measure in such a way ... More

Period three actions on lens spacesNov 02 2003Feb 04 2008We show that a free period three action on a lens space is standard, i.e. the quotient is homeomorphic to a lens space. This is an extension of the result for period three actions on the three-sphere, arXiv:math.GT/0204077, by the author and J. Hyam Rubinstein. ... More

The Specification of SugarscapeMay 22 2015Jul 01 2016Sugarscape is a well known and influential Agent Based Social Simulation (ABSS). Various parts of Sugarscape are supplied as examples in almost all Agent Based Model (ABM) toolkits. It has been used for demonstrating the applicability of different approaches ... More

Category of fuzzy hyper BCK-algebrasJan 13 2011In this paper we ?rst de?ne the category of fuzzy hyper BCK- algebras. After that we show that the category of hyper BCK-algebras has equalizers, coequalizers, products. It is a consequence that this category is complete and hence has pullbacks.

Siegel zeros of Eisenstein seriesDec 05 2005If E(z,s) is the nonholomorphic Eisenstein series on the upper half plane, then for all y sufficiently large, E(z,s) has a "Siegel zero." That is E(z,\beta)=0 for a real number \beta just to the left of one. We give a generalization of this result to ... More

Tropical analytic geometry, Newton polygons, and tropical intersectionsJul 15 2010In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: ... More

The Case for Massive, Evolving Winds in Black Hole X-ray BinariesApr 22 2013In the last decade, high-resolution X-ray spectroscopy has revolutionized our understanding of the role of accretion disk winds in black hole X-ray binaries. Here I present a brief review of the state of wind studies in black hole X-ray binaries, focusing ... More

An Ansatz for Hyperkähler $8$-Manifolds with two Commuting Rotating Killing FieldsSep 27 2014We consider a hyperk\"{a}hler $8$-manifold admitting either a $U(1) \times \mathbb{R}$, or a $U(1) \times U(1)$ action, where the first factor preserves $g$ and $I$, and acts on $\omega_2+i\omega_3$ by multiplying it by itself, while the second factor ... More

New normality constructions for continued fraction expansionsJul 01 2015Adler, Keane, and Smorodinsky showed that if one concatenates the finite continued fraction expansions of the sequence of rationals \[ \frac{1}{2}, \frac{1}{3}, \frac{2}{3}, \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{1}{5}, \cdots \] into an infinite ... More

Dark matter ignition of type Ia supernovaeMay 27 2015Sep 25 2015Recent studies of low redshift type Ia supernovae (SNIa) indicate that half explode from less than Chandrasekhar mass white dwarfs, implying ignition must proceed from something besides the canonical criticality of Chandrasekhar mass SNIa progenitors. ... More

Borell's formula for a Riemannian manifold and applicationsDec 18 2015Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a convolution ... More

The class number formula for imaginary quadratic fieldsFeb 17 2015It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain information about ... More

Optical conductivity of a superfluid density waveJan 04 2002We present a calculation of the low frequency optical conductivity of a superconductor in the presence of quenched inhomogeneity in both the superfluid and normal fluid densities. We find that inhomogeneity in the superfluid density displaces spectral ... More

Kondo lattice on the edge of a two-dimensional topological insulatorMar 30 2012Jun 13 2012We revisit the problem of a single quantum impurity on the edge of a two-dimensional time-reversal invariant topological insulator and show that the zero temperature phase diagram contains a large local moment region for antiferromagnetic Kondo coupling ... More

Algebra properties for Besov spaces on unimodular Lie groupsMay 26 2015We consider the Besov space $B^{p,q}_\alpha(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property ... More

Relative decidability and definability in henselian valued fieldsOct 14 2009Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. Two applications ... More

Albedo heterogeneity on the surface of (1943) AnterosDec 28 2009We have investigated the effect of rotation on the polarization of scattered light for the near-Earth asteroid (1943) Anteros using the Dual Beam Imaging Polarimeter on the University of Hawaii's 2.2 m telescope. Anteros is an L-type asteroid that has ... More

Wave propagation on microstate geometriesSep 06 2016Supersymmetric microstate geometries were recently conjectured to be nonlinearly unstable due to numerical and heuristic evidence, based on the existence of very slowly decaying solutions to the linear wave equation on these backgrounds. In this paper, ... More

5D Maximally Supersymmetric Yang-Mills on the LatticeOct 11 2016We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting ... More

A Euclidean Lattice Formulation of D=5 Maximally Supersymmetric Yang-Mills TheoryApr 10 2016Jun 13 2016We construct lattice action for five-dimensional maximally supersymmetric Yang-Mills theory. This supersymmetric lattice formulation can be used to explore the non-perturbative regime of the continuum target theory, which has a known gravitational dual. ... More

Distances and Absolute Magnitudes of Dwarf Novae: Murmurs of Period BounceMar 05 2009Oct 23 2010We redetermine the relationship between absolute magnitude and orbital period for dwarf novae, based on 46 stars with good distance estimates. This improves upon Warner's previous relation, building upon today's improved estimates of distance and binary ... More

Accelerators Beyond The Tevatron?Jun 30 2010Following the successful operation of the Fermilab superconducting accelerator three new higher energy accelerators were planned. They were the UNK in the Soviet Union, the LHC in Europe, and the SSC in the United States. All were expected to start producing ... More

The Hilbert-Chow morphism and the incidence divisorSep 29 2010For a smooth projective variety $P$, we construct a Cartier divisor supported on the incidence locus in $\mathscr{C}_a (P) \times \mathscr{C}_{\dim(P)-a-1}(P)$. There is a natural definition of the corresponding line bundle on a product of Hilbert schemes, ... More

Indicators of Bismash Products from Exact Symmetric Group FactorizationsDec 15 2014Jul 22 2015We prove that all irreducible representations of the bismash product $H = \mathbb{k} ^G \# \mathbb{k} S_{n-k}$ have Frobenius-Schur indicators +1 or 0 where $\mathbb{k}$ is an algebraically closed field and $S_n = S_{n-k}\cdot G$ is an exact factorization. ... More

On Bass' question for finitely generated algebras over large fieldsMar 11 2008Aug 25 2008Recently Cortinas-Haesemayer-Walker-Weibel gave affirmative answer to Bass' 1972 question on NK-groups for algebras of essentially finite type over large fields of characteristic 0. Here we give an alternative short proof of this result for algebras of ... More

Explicit filtering for large eddy simulation as use of a spectral bufferOct 06 2016The explicit filtering method for large eddy simulation (LES,) which comprises integration of the governing equations without any added terms for sub-grid-scale modeling and the application of a low-pass filter to transported fields, is discussed. The ... More

Is the aether entrained by the motion of celestial bodies? What do the experiments tell us?Mar 20 2012Dec 17 2013Even though the concept has evolved and if the designation as aether is improperly regarded as outdated, nobody today considers that the vacuum is empty. However, the nature and the properties of the substratum, which permeates the entire universe, remain ... More

Statistical Mechanics of Amplifying ApparatusFeb 08 2005We implement Feynman's suggestion that the only missing notion needed for the puzzle of Quantum Measurement is the statistical mechanics of amplifying apparatus. We define a thermodynamic limit of quantum amplifiers which is a classically describable ... More

Partitions and functional Santalo inequalitiesNov 09 2010We give a direct proof of a functional Santalo inequality due to Fradelizi and Meyer. This provides a new proof of the Blaschke-Santalo inequality. The argument combines a logarithmic form of the Prekopa-Leindler inequality and a partition theorem of ... More

Higher-level canonical subgroups for p-divisible groupsOct 17 2009Mar 16 2011Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a K-subgroup of G\tensor_R ... More

Feedback and the Initial Mass functionOct 04 2004I describe a turbulence-inspired model for the stellar initial mass function which includes feedback and self-regulation via protostellar outflows. A new aspect of the model provides predictions of the star formation rate in molecular clouds and gas complexes. ... More

Supermassive Black Holes and Galaxy FormationSep 19 2001The formation of supermassive black holes (SMBH) is intimately related to galaxy formation, although precisely how remains a mystery. I speculate that formation of, and feedback from, SMBH may alleviate problems that have arisen in our understanding of ... More

Maps with symplectic graphsJul 13 2004Oct 22 2004We consider the homotopy type of maps between symplectic surface whose graphs form symplectic submanifolds of the product. We give a purely topological model for this space in terms of maps with constrained numbers of pre-images. We use this to show that ... More

String theory to the rescueDec 08 2015Dec 16 2015The search for a theory of quantum gravity faces two great challenges: the incredibly small scales of the Planck length and time, and the possibility that the observed constants of nature are in part the result of random processes. A priori, one might ... More

Comment on [arXiv:1106.1417] "Small Lorentz violations in quantum gravity: do they lead to unacceptably large effects?"Jun 30 2011Sep 02 2011A recent paper by Gambini, Rastgoo and Pullin [arXiv:1106.1417 investigates the important issue of constraints from Lorentz invariance on Planck scale physics, arguing that the classic analysis of Collins, Perez, Sudarsky, Urrutia and Vucetich \cite{cpsuv} ... More

Cosmic Superstrings RevisitedOct 08 2004Dec 21 2004It is possible that superstrings, as well as other one-dimensional branes, could have been produced in the early universe and then expanded to cosmic size today. I discuss the conditions under which this will occur, and the signatures of these strings. ... More

Brane/antibrane dynamics and KKLT stabilitySep 18 2015Sep 25 2015String theory has few or no stable nonsupersymmetric or de Sitter vacua, only metastable ones. Antibranes are a simple source of supersymmetry breaking, as in the KKLT model, but various arguments have been given that these fail to produce the desired ... More

What is String Theory?Nov 04 1994The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: 1. Conformal Field Theory 2. String Theory 3. Vacua and ... More

The Specification of SugarscapeMay 22 2015Nov 07 2016Sugarscape is a well known and influential Agent Based Social Simulation (ABSS). Various parts of Sugarscape are supplied as examples in almost all Agent Based Model (ABM) toolkits. It has been used for demonstrating the applicability of different approaches ... More

On the Atiyah problem on hyperbolic configurations of four pointsFeb 04 2015Aug 06 2015Given a configuration $\mathbf{x}$ of $n$ distinct points in hyperbolic $3$-space $H^3$, Michael Atiyah associated $n$ polynomials $p_1,\ldots,p_n$ of a variable $t \in \mathbb{C}P^1$, of degree $n-1$, and conjectured that they are linearly independent ... More

Hardy and BMO spaces on graphs, application to Riesz transformOct 24 2014Let $\Gamma$ be a graph with the doubling property for the volume of balls and $P$ a reversible random walk on $\Gamma$. We introduce $H^1$ Hardy spaces of functions and $1$-forms adapted to $P$ and prove various characterizations of these spaces. We ... More

The nilpotence conjecture in K-theory of toric varietiesSep 11 2002Oct 07 2004It is shown that all nontrivial elements in higher $K$-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine ... More

Moduli spaces of semitoric systemsFeb 25 2015Recently Pelayo-V\~{u} Ngoc classified semitoric integrable systems in terms of five symplectic invariants. Using this classification we define a family of metrics on the space of semitoric integrable systems. The family is parameterized by two choices. ... More

Angle Bisectors of a Triangle in Lorentzian PlaneApr 24 2014In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates ... More

Estimation and Test for Multidimensional Regression ModelsFeb 19 2008This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to get an optimal ... More

Affine-compact functorsAug 15 2016Several well known polytopal constuctions are examined from the functorial point of view. A naive analogy between the Billera-Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A correct functorial ... More

Logarithmic Poisson cohomology: example of calculation and application to prequantizationDec 21 2010Jan 19 2011In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, ... More

A simpler normal number construction for simple Luroth seriesNov 19 2013Champernowne famously proved that the number $0.(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)...$ formed by concatenating all the integers one after another is normal base 10. We give a generalization of Champernowne's construction to various other digit systems, ... More

A Generative Bayesian Model for Aggregating Experts' ProbabilitiesJul 11 2012In order to improve forecasts, a decisionmaker often combines probabilities given by various sources, such as human experts and machine learning classifiers. When few training data are available, aggregation can be improved by incorporating prior knowledge ... More

Introduction to effective Lagrangians for QCDDec 14 2001A brief introduction to the effective Lagrangian treatment of QCD (in the sense of using fields representing physical particles rather than quarks and gluons) will be given. The historical evolution of the subject will be discussed. Some background material ... More

Heegaard gradient and virtual fibersNov 10 2004Dec 13 2005We show that if a closed hyperbolic 3-manifold has infinitely many finite covers of bounded Heegaard genus, then it is virtually fibered. This generalizes a theorem of Lackenby, removing restrictions needed about the regularity of the covers. Furthermore, ... More

Virtually embedded boundary slopesJan 09 1999We show that for certain hyperbolic 3-manifolds, all boundary slopes are slopes of immersed incompressible surfaces, covered by incompressible embeddings in some finite cover. The manifolds include hyperbolic punctured torus bundles and hyperbolic two-bridge ... More

Variant vector-tensor multiplets in supergravity: Classification and component reductionOct 31 2012Mar 11 2013The recent paper arXiv:1205.6881 has developed superform formulations for two versions of the vector-tensor multiplet and their Chern-Simons couplings in four-dimensional N = 2 conformal supergravity. One of them is the standard vector-tensor multiplet ... More

Differencing Methods for Korobov-type exponential sumsJun 25 2016We study exponential sums of the form $\sum_{n=1}^N e^{2\pi i a b^n/m}$ for non-zero integers $a,b,m$. Classically, non-trivial bounds were known for $N\ge \sqrt{m}$ by Korobov, and this range has been extended significantly by Bourgain as a result of ... More

Absolutely abnormal, continued fraction normal numbersDec 01 2015In this short note, we give a proof, conditional on the Generalized Riemann Hypothesis, that there exist numbers x which are normal with respect to the continued fraction expansion but not to any base b expansion. This partially answers a question of ... More

Authentication Based Solutions to Counterfeiting of Manufactured GoodsNov 27 2015Oct 03 2016Counterfeiting of manufactured goods is presented as the theft of intellectual property, patents, copyright etc. accompanied by identity theft. The purpose of the identity theft is to facilitate the intellectual property theft. Without it the intellectual ... More

On an incomplete argument of Erdos on the irrationality of Lambert seriesJun 02 2012We show that the Lambert series $f(x)=\sum d(n) x^n$ is irrational at $x=1/b$ for negative integers $b < -1$ using an elementary proof that finishes an incomplete proof of Erdos.

Upper Triangular Forms and Spectral Orderings in a II_1-factorJun 11 2014Nov 21 2015Dykema, Sukochev and Zanin used a Peano curve covering the support of the Brown measure of an operator T in a diffuse, finite von Neumann algebra to give an ordering to the support of the Brown measure, and create a decomposition T = N + Q, where N is ... More

The Steinberg group of a monoid ring, nilpotence, and algorithmsJan 17 2006Mar 07 2006For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M]. This strengthens the K_2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any ... More

Slowly Decaying Waves on Spherically Symmetric Spacetimes and an Instability of Ultracompact Neutron StarsApr 28 2014Sep 07 2016We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, ... More

Adjoint associativity: an invitation to algebra in infinity-categoriesDec 17 2013There appeared not long ago a Reduction Formula for derived Hochschild cohomology, that has been useful e.g., in the study of Gorenstein maps and of rigidity w.r.t. semidualizing complexes. The formula involves the relative dualizing complex of a ring ... More