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Vectorization of Multibyte Floating Point Data FormatsJan 26 2016Jul 22 2016We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and data transfer ... More

A Taxonomy of Channel Pruning Signals in CNNsJun 11 2019Convolutional neural networks (CNNs) are widely used for classification problems. However, they often require large amounts of computation and memory which are not readily available in resource constrained systems. Pruning unimportant parameters from ... More

How the Experts Do It: Assessing and Explaining Agent Behaviors in Real-Time Strategy GamesNov 19 2017How should an AI-based explanation system explain an agent's complex behavior to ordinary end users who have no background in AI? Answering this question is an active research area, for if an AI-based explanation system could effectively explain intelligent ... More

Low-memory GEMM-based convolution algorithms for deep neural networksSep 08 2017Deep neural networks (DNNs) require very large amounts of computation both for training and for inference when deployed in the field. A common approach to implementing DNNs is to recast the most computationally expensive operations as general matrix multiplication ... More

Constraining the Initial-Final Mass Relation with Wide Double White DwarfsOct 24 2014In wide double white dwarf (DWD) binaries, in which the co-eval WDs evolve independently, the more massive, faster-evolving WD can be used to obtain a main-sequence lifetime for the less-massive WD. By converting this lifetime into an initial mass for ... More

Laser powder-bed fusion additive manufacturing: physics of complex melt flow and formation mechanisms of pores, spatter and denudation zonesDec 08 2015Jan 05 2016This study demonstrates the significant effect of the recoil pressure and Marangoni convection in laser powder bed fusion (L-PBF) of 316L stainless steel. A three-dimensional high fidelity powder-scale model reveals how the strong dynamical melt flow ... More

Scalar Arithmetic Multiple Data: Customizable Precision for Deep Neural NetworksSep 27 2018Quantization of weights and activations in Deep Neural Networks (DNNs) is a powerful technique for network compression, and has enjoyed significant attention and success. However, much of the inference-time benefit of quantization is accessible only through ... More

The Romulus Cosmological Simulations: A Physical Approach to the Formation, Dynamics and Accretion Models of SMBHsJul 07 2016We present a novel implementation of supermassive black hole (SMBH) formation, dynamics, and accretion in the massively parallel tree+SPH code, ChaNGa. This approach improves the modeling of SMBHs in fully cosmological simulations, allowing for a more ... More

Toward Foraging for Understanding of StarCraft Agents: An Empirical StudyNov 21 2017Dec 26 2017Assessing and understanding intelligent agents is a difficult task for users that lack an AI background. A relatively new area, called "Explainable AI," is emerging to help address this problem, but little is known about how users would forage through ... More

Constraints on the Initial-Final Mass Relation from Wide Double White DwarfsOct 21 2015We present observational constraints on the initial-final mass relation (IFMR) using wide double white dwarfs (DWDs). We identify 65 new candidate wide DWDs within the Sloan Digital Sky Survey, bringing the number of candidate wide DWDs to 142. We then ... More

Candidate Identification and Interference Removal in SETI@homeSep 07 2011SETI@home, a search for signals from extraterrestrial intelligence, has been recording data at the Arecibo radio telescope since 1999. These data are sent via the Internet to the personal computers of volunteers who have donated their computers' idle ... More

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group AveragingMay 15 2019Jun 09 2019In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables level treatment. ... More

Positivity in the cohomology of flag bundles (after Graham)Nov 06 2007We give a short, geometric proof of Graham's theorem on positivity in the equivariant cohomology of a flag variety, based on a transversality argument.

A survey of food recommendersSep 08 2018Sep 15 2018Everyone eats. However, people do not always know what to eat. They need a little help and inspiration. Consequently, a number of apps, services, and programs have developed recommenders around food. These cover food, meal, recipe, and restaurant recommendations, ... More

An elegant solution of the n-body Toda problemJul 19 1995The solution of the classical open-chain n-body Toda problem is derived from an ansatz and is found to have a highly symmetric form. The proof requires an unusual identity involving Vandermonde determinants. The explicit transformation to action-angle ... More

The use of exp(iS[x]) in the sum over historiesAug 17 1993The use of $\sum \exp(iS[x])$ as the generic form for a sum over histories in configuration space is discussed critically and placed in its proper context. The standard derivation of the sum over paths by discretizing the paths is reviewed, and it is ... More

Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the TorusOct 13 1992Dec 31 1992Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of 2+1-dimensional quantum gravity on the torus. A non-polynomial factor ordering ... More

Quantum Backreaction on ``Classical'' VariablesJun 28 1994Nov 17 1994A mathematically consistent procedure for coupling quasiclassical and quantum variables through coupled Hamilton-Heisenberg equations of motion is derived from a variational principle. During evolution, the quasiclassical variables become entangled with ... More

Special functions from quantum canonical transformationsOct 26 1993Jun 01 1994Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation ... More

Quantum Canonical Transformations and Integrability: Beyond Unitary TransformationsFeb 15 1993Sep 06 1993Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A definition of ... More

Evolving Constants of MotionJul 18 1995A critical presentation of Rovelli's ``evolving constants of motion'' is given. Previous criticisms by Kucha\v{r} concerning the role of factor ordering and the non-existence of observables are dealt with and shown to be unfounded. Kucha\v{r}'s criticisms ... More

A Local Resolution of the Problem of Time. III. The other classical facets piecemealMay 15 2019We introduce seven further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two articles having covered one further facet-and-aspect each for a total of nine. I.e. Constraint Closure, Assignment ... More

A Local Resolution of the Problem of Time. II. Configurational Relationalism via a generalization of Group AveragingMay 15 2019In this article, we consider a second Problem of Time Facet. This started life as Wheeler's Thin Sandwich Problem, within the narrow context of 1) GR-as-Geometrodynamics, in particular its momentum constraint. 2) A Lagrangian variables level treatment. ... More

Two new versions of Heron's FormulaDec 05 2017Recollect that Heron's formula for the area of a triangle given its sides has a counterpart given the medians instead, which carries an extra factor of $\frac{4}{3}$. On the one hand, we formulate the pair of these in Linear Algebra terms, showing that ... More

A Local Resolution of the Problem of Time. I. Introduction and Temporal RelationalismMay 15 2019This Series of Articles provides a local resolution of this major longstanding foundational problem between QM and GR, or, more generally, between Background Dependent and Background Independent Physics. We focus on the classical version; the concepts ... More

How to prolong network life-span in wireless networksSep 27 2011One of the most important problems in wireless sensor network is to develop a routing protocol that has energy efficiency. Since the power of the sensor Nodes are limited, conserving energy and network life is a critical issue in wireless sensor network. ... More

Johnson-Levine Homomorphisms and the tree reduction of the LMO functorNov 30 2017Let M denote the mapping class group of S, a compact connected oriented surface with one boundary component. The action of M on the nilpotent quotients of the fundamental group of S allows to define the so-called Johnson filtration and the Johnson homomorphisms. ... More

Homotopy sphere representations for matroidsMar 16 2009For any rank $r$ oriented matroid $M$, a construction is given of a "topological representation" of $M$ by an arrangement of homotopy spheres in a simplicial complex which is homotopy equivalent to $S^{r-1}$. The construction is completely explicit and ... More

Dimming the Internet: Detecting Throttling as a Mechanism of Censorship in IranJun 18 2013In the days immediately following the contested June 2009 Presidential election, Iranians attempting to reach news content and social media platforms were subject to unprecedented levels of the degradation, blocking and jamming of communications channels. ... More

Okounkov bodies and toric degenerationsJan 25 2010Oct 30 2012Let \Delta be the Okounkov body of a divisor D on a projective variety X. We describe a geometric criterion for \Delta to be a lattice polytope, and show that in this situation X admits a flat degeneration to the corresponding toric variety. This degeneration ... More

A Local Resolution of the Problem of Time. V. Combining Temporal and Configurational Relationalism for Finite TheoriesJun 09 2019As we have known comprehensively since the early 1990's works of Isham and Kucha\v{r}, The Problem of Time mostly concerns interferences between its many facets. Having introduced the local facets in Articles I to IV, we now show how Article I's approach ... More

Curvature-based Gauge-Invariant Perturbation Theory for Gravity: A New ParadigmJan 20 1998A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In the Minkowski ... More

Colors of c-type RR Lyrae Stars and Interstellar ReddeningOct 02 2013RR Lyrae stars pulsating in the fundamental mode have long been used to measure interstellar reddening, based on their observed uniformity of $B-V$ color at minimum light after small corrections for metallicity and period are applied. However, little ... More

Learning to Navigate in Cities Without a MapMar 31 2018Jan 10 2019Navigating through unstructured environments is a basic capability of intelligent creatures, and thus is of fundamental interest in the study and development of artificial intelligence. Long-range navigation is a complex cognitive task that relies on ... More

On the Co-existence of TD-LTE and Radar over 3.5 GHz Band: An Experimental StudyMay 03 2016This paper presents a pioneering study based on a series of experiments on the operation of commercial Time-Division Long-Term Evolution (TD-LTE) systems in the presence of pulsed interfering signals in the 3550-3650 MHz band. TD-LTE operations were carried ... More

Excited quark production at a 100 TeV VLHCSep 03 2013Sep 05 2013I look for a dijet resonance produced by an excited quark q* in a simulated sample corresponding to 3 ab^{-1} of pp collisions at $\sqrt{s} = 100$ TeV. Using a cut and count analysis approach I demonstrate the potential to explore q* masses up to 50 TeV, ... More

A Local Resolution of the Problem of Time. IX. Spacetime ConstructabilityJun 09 2019Assuming Temporal and Configurational Relationalism, GR as Geometrodynamic's DeWitt supermetric alongside local Lorentzian Relativity with its universal finite maximum propagation speed arises as one of very few options from Feeding Families through a ... More

A Local Resolution of the Problem of Time. III. The other classical facets piecemealMay 15 2019Jun 09 2019We introduce seven further local facets of the classical Problem of Time, and underlying Background Independence aspects, the previous two articles having covered one further facet-and-aspect each for a total of nine. I.e. Constraint Closure, Assignment ... More

The Hidden Internet of Iran: Private Address Allocations on a National NetworkSep 28 2012While funding agencies have provided substantial support for the developers and vendors of services that facilitate the unfettered flow of information through the Internet, little consolidated knowledge exists on the basic communications network infrastructure ... More

Parallel Multi Channel Convolution using General Matrix MultiplicationApr 06 2017Jul 03 2017Convolutional neural networks (CNNs) have emerged as one of the most successful machine learning technologies for image and video processing. The most computationally intensive parts of CNNs are the convolutional layers, which convolve multi-channel images ... More

Developing Knowledge States: Technology and the Enhancement of National Statistical CapacityFeb 26 2015National statistical systems are the enterprises tasked with collecting, validating and reporting societal attributes. These data serve many purposes - they allow governments to improve services, economic actors to traverse markets, and academics to assess ... More

The StreetLearn Environment and DatasetMar 04 2019Navigation is a rich and well-grounded problem domain that drives progress in many different areas of research: perception, planning, memory, exploration, and optimisation in particular. Historically these challenges have been separately considered and ... More

ASKAP Detection of Periodic and Elliptically Polarized Radio Pulses from UV CetiJun 15 2019Active M-dwarfs are known to produce bursty radio emission, and multi-wavelength studies have shown that Solar-like magnetic activity occurs in these stars. However, coherent bursts from active M-dwarfs have often been difficult to interpret in the Solar ... More

Power dissipation in fractal AC circuitsMay 12 2016Feb 12 2017We extend Feynman's analysis of an infinite ladder circuit to fractal circuits, providing examples in which fractal circuits constructed with purely imaginary impedances can have characteristic impedances with positive real part. Using (weak) self-similarity ... More

A Local Resolution of the Problem of Time. VI. Combining Temporal and Configurational Relationalism for Field Theories and GRJun 09 2019We next combine Temporal and Configurational Relationalism's resolution for Field Theory, including in particular for GR. The current Article also provides the finite-and-field theory portmanteau notation, by which the rest of this series' reworking of ... More

Properties of Norms on SetsNov 06 2018We investigate the norms appearing in the forcing from combinatorial point of view. We make first steps towards building a catalog of the norms appearing in multiple settings and sources, reviewing four norms from Bartoszy\'nski and Judah [1], Ros{\l}anowski ... More

Quantum computing by color-code lattice surgeryJul 18 2014We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same ... More

Understanding Electron Transfer on the Single-Molecule LevelDec 18 2018Electron-transfer reactions are ubiquitous in chemistry, however, there are still gaps in the fundamental understanding of electron transfer at the molecular level, particularly the degree to which the nuclear dynamics that accompany the process straddle ... More

Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural NetworksMar 29 2018Sep 22 2018Modern deep neural networks (DNNs) spend a large amount of their execution time computing convolutions. Winograd's minimal algorithm for small convolutions can greatly reduce the number of arithmetic operations. However, a large reduction in floating ... More

New SETI Sky Surveys for Radio PulsesNov 19 2008Jan 27 2010Berkeley conducts 7 SETI programs at IR, visible and radio wavelengths. Here we review two of the newest efforts, Astropulse and Fly's Eye. A variety of possible sources of microsecond to millisecond radio pulses have been suggested in the last several ... More

Optical charge state control of spin defects in 4H-SiCMay 26 2017Defects in silicon carbide (SiC) have emerged as a favorable platform for optically-active spin-based quantum technologies. Spin qubits exist in specific charge states of these defects, where the ability to control these states can provide enhanced spin-dependent ... More

D4M 2.0 Schema: A General Purpose High Performance Schema for the Accumulo DatabaseJul 15 2014Non-traditional, relaxed consistency, triple store databases are the backbone of many web companies (e.g., Google Big Table, Amazon Dynamo, and Facebook Cassandra). The Apache Accumulo database is a high performance open source relaxed consistency database ... More

Probing spin-phonon interactions in silicon carbide with Gaussian acousticsApr 29 2018Aug 04 2018Hybrid spin-mechanical systems provide a platform for integrating quantum registers and transducers. Efficient creation and control of such systems require a comprehensive understanding of the individual spin and mechanical components as well as their ... More

HALO7D II: The Halo Velocity Ellipsoid and Velocity Anisotropy with Distant Main Sequence StarsOct 29 2018The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D) dataset consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope-measured proper motions of Milky Way (MW) halo main sequence turnoff stars in the CANDELS fields. In this ... More

Hamiltonian dynamics of two same-sign point vorticesDec 09 2015Apr 14 2016We have studied numerically the Hamiltonian dynamics of two same-sign point vortices in an effectively two-dimensional, harmonically trapped Bose-Einstein condensate. We have found in the phase space of the system an impenetrable wall that divides the ... More

Limitless HTTP in an HTTPS World: Inferring the Semantics of the HTTPS Protocol without DecryptionMay 29 2018We present new analytic techniques for inferring HTTP semantics from passive observations of HTTPS that can infer the value of important fields including the status-code, Content-Type, and Server, and the presence or absence of several additional HTTP ... More

Fault-tolerant quantum computing with color codesAug 29 2011We present and analyze protocols for fault-tolerant quantum computing using color codes. We present circuit-level schemes for extracting the error syndrome of these codes fault-tolerantly. We further present an integer-program-based decoding algorithm ... More

Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural NetworksMar 29 2018May 01 2019Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, ... More

Commensurability and locally free Kleinian groupsMar 23 1999We show that there exist infinitely many commensurability classes of finite volume hyperbolic 3-manifolds whose fundamental group contains a subgroup which is locally free but not free. The main technical tool is the fact that a collection of hyperbolic ... More

Spectral Theory for Second-Order Vector Equations on Finite Time-Varying DomainsJan 22 2010In this study, we are concerned with spectral problems of second-order vector dynamic equations with two-point boundary value conditions and mixed derivatives, where the matrix-valued coefficient of the leading term may be singular, and the domain is ... More

Rank 2 distributions of Monge equations: symmetries, equivalences, extensionsOct 30 2009By developing the Tanaka theory for rank 2 distributions, we completely classify classical Monge equations having maximal finite-dimensional symmetry algebras with fixed (albeit arbitrary) pair of its orders. Investigation of the corresponding Tanaka ... More

A Mathematical Model for Simulating Meteor ShowersMay 23 2019This paper presents a mathematical model to simulate the trajectory of a meteor as seen by a single observer located anywhere on Earth. Our strategy is to define a new coordinate system, called Radiant Coordinate System, which is centered on the observer ... More

Scalar Charges and Scaling Relations in Massless Scalar-Tensor TheoriesJan 03 2019The timing of binary pulsars allows us to place some of the tightest constraints on modified theories of gravity. Perhaps some of the most interesting and well-motivated extensions to General Relativity are scalar-tensor theories, in which gravity is ... More

Preservation of algebraicity in free probabilityJun 25 2014Aug 14 2014We show that any matrix-polynomial combination of free noncommutative random variables each having an algebraic law has again an algebraic law. Our result answers a question raised by a recent paper of Shlyakhtenko and Skoufranis. The result belongs to ... More

Prising apart geodesics by length in hyperbolic 3-manifoldsFeb 04 2012Feb 13 2015In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely determines the ... More

We have time because we shall never knowJun 26 2015We argue against current proposals concerning the non-existence of time. We point out that a large number of these proposals rely, at least implicitly, on the assumption of `closure' (or `partial closure') of the laws of Physics. I.e. the assumption that ... More

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov ChainsSep 13 2011May 11 2012We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed and nominal ... More

Efficient Threshold Aggregation of Moving ObjectsNov 07 2006May 01 2007Calculating aggregation operators of moving point objects, using time as a continuous variable, presents unique problems when querying for congestion in a moving and changing (or dynamic) query space. We present a set of congestion query operators, based ... More

Specialists and Generalists: Equilibrium Skill Acquisition Decisions in Problem-solving PopulationsAug 22 2011Jul 26 2016Many organizations rely on the skills of innovative individuals to create value, including academic and government institutions, think tanks, and knowledge-based firms. Roughly speaking, workers in these fields can be divided into two categories: specialists, ... More

An arbitrary order scheme on generic meshes for miscible displacements in porous mediaJul 13 2017Jan 14 2019We design, analyse and implement an arbitrary order scheme applicable to generic meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in porous media. The discretisation is based on several adaptations of the Hybrid-High-Order ... More

Global asymptotic stability for a class of nonlinear chemical equationsAug 02 2007Nov 15 2007We consider a class of nonlinear differential equations that arises in the study of chemical reaction systems that are known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable. More specifically, we will ... More

A cusp singularity with no Galois cover by a complete intersectionSep 18 2001Jul 16 2002With an explicit example, we confirm a conjecture by Neumann and Wahl that there exist cusps with no Galois cover by a complete intersection. Some computational techniques are reviewed, and a method for deciding whether a given cusp has a complete intersection ... More

Hyers-Ulam stability of higher-order Cauchy-Euler dynamic equations on time scalesDec 17 2012We establish the stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales in the sense of Hyers and Ulam. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact ... More

Equivariant quantum Schubert polynomialsOct 26 2011Feb 18 2012We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum ... More

Self-organisation of random oscillators with Lévy stable distributionsJul 10 2017A novel possibility of self-organized behaviour of stochastically driven oscillators is presented. It is shown that synchronization by L\'evy stable processes is significantly more efficient than that by oscillators with Gaussian statistics. The impact ... More

Taylor's formula and integral inequalities for conformable fractional derivativesSep 20 2014We derive Taylor's Formula for conformable fractional derivatives. This is then employed to extend some recent and classical integral inequalities to the conformable fractional calculus, including the inequalities of Steffensen, Chebychev, Hermite-Hadamard, ... More

Positive Green's functions for some fractional-order boundary value problemsNov 20 2014We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate, right-focal, and Lidstone ... More

Limit set intersection theorems for Kleinian groups and a conjecture of SusskindOct 01 2013We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, and the intersection of the limit sets of the subgroups. Of specific interest ... More

A meta analysis of core-collapse supernova $^{56}$Ni massesMay 27 2019A fundamental property determining the transient behaviour of core-collapse supernovae (CCSNe) is the amount of radioactive $^{56}$Ni synthesised in the explosion. Using established methods, this is a relatively easy parameter to extract from observations. ... More

MWStat: A Modulated Web-Based Statistical SystemApr 29 2016In this paper we present the development of a modulated web based statistical system, hereafter MWStat, which shifts the statistical paradigm of analyzing data into a real time structure. The MWStat system is useful for both online storage data and questionnaires ... More

Region of Attraction Estimation Using Invariant Sets and Rational Lyapunov FunctionsApr 04 2016This work addresses the problem of estimating the region of attraction (RA) of equilibrium points of nonlinear dynamical systems. The estimates we provide are given by positively invariant sets which are not necessarily defined by level sets of a Lyapunov ... More

Type II supernova diversityOct 15 2015It is now firmly established that at a significant fraction of hydrogen-rich type II supernovae (SNe II) arise from red supergiant progenitors. However, a large diversity of SN properties exist, and it is presently unclear how this can be understood in ... More

Boundedness of trajectories for weakly reversible, single linkage class reaction systemsApr 26 2011Jun 16 2011This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems biology. A ... More

Schubert varieties are log Fano over the integersMar 29 2012Given a Schubert variety X_w, we exhibit a divisor \Delta, defined over the integers, such that the pair (X_w,\Delta) is log Fano in all characteristics.

Hyers-Ulam stability of second-order linear dynamic equations on time scalesAug 22 2010We establish the stability of second-order linear dynamic equations on time scales in the sense of Hyers and Ulam. To wit, if an approximate solution of the second-order linear equation exists, then there exists an exact solution to the dynamic equation ... More

Digit patterns and Coleman power seriesOct 17 2005Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics of base $p$ ... More

Operational K-theoryJan 03 2013Jun 08 2015We study the operational bivariant theory associated to the covariant theory of Grothendieck groups of coherent sheaves, and prove that it has many geometric properties analogous to those of operational Chow theory. This operational K-theory agrees with ... More

Titchmarsh-Sims-Weyl theory for complex Hamiltonian systems on Sturmian time scalesJan 22 2010We study non-self-adjoint Hamiltonian systems on Sturmian time scales, defining Weyl-Sims sets, which replace the classical Weyl circles, and a matrix-valued $M-$function on suitable cone-shaped domains in the complex plane. Furthermore, we characterize ... More

Hyers--Ulam Stability for Discrete Time Scale with Two Step SizesJul 10 2018We clarify the Hyers--Ulam stability (HUS) of certain first-order linear constant coefficient dynamic equations on time scales, in the case of a specific time scale with two alternating step sizes, where the exponential function changes sign. In particular, ... More

Interpolation of numbers of Catalan type in a local field of positive characteristicJan 19 2006Jun 21 2006Let $k$ be a local field of positive characteristic. Let $L$ be a cocompact discrete subgroup of $k$. Let $U$ be an open compact subgroup of $k$. Let $\ell$, $u$ and $a$ be elements of $k$, with $a$ nonzero. We study the behavior of the product $\prod_{0\neq ... More

A local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matricesAug 21 2013Aug 28 2013Our main result is a local limit law for the empirical spectral distribution of the anticommutator of independent Wigner matrices, modeled on the local semicircle law. Our approach is to adapt some techniques from one of the recent papers of Erd\"os-Yau-Yin. ... More

A brief survey of the deformation theory of Kleinian groupsOct 23 1998We give a brief overview of the current state of the study of the deformation theory of Kleinian groups. The topics covered include the definition of the deformation space of a Kleinian group and of several important subspaces; a discussion of the parametrization ... More

Second-Order Self-Adjoint Differential Equations Using a Conformable Proportional DerivativeJul 25 2016In this study, linear second-order conformable differential equations using a proportional derivative are shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. Defining ... More

Logical Modelling of Physarum PolycephalumMay 20 2011We propose a novel model of unconventional computing where a structural part of computation is presented by dynamics of plasmodium of Physarum polycephalum, a large single cell. We sketch a new logical approach combining conventional logic with process ... More

Non-Abelian Cut Constructions and Hyperkähler ModificationsFeb 09 2010We discuss a general framework for cutting constructions and reinterpret in this setting the work on non-Abelian symplectic cuts by Weitsman. We then introduce two analogous non-Abelian modification constructions for hyperk\"ahler manifolds: one modifies ... More

On Creativity of Elementary Cellular AutomataMay 11 2013We map cell-state transition rules of elementary cellular automata (ECA) onto the cognitive control versus schizotypy spectrum phase space and interpret cellular automaton behaviour in terms of creativity. To implement the mapping we draw analogies between ... More

Modifying hyperkaehler manifolds with circle symmetryOct 24 2005Oct 25 2005A construction is introduced for modifying hyperkaehler manifolds with tri-Hamiltonian circle action, that in favourable situations increases the second Betti number by one. This is based on the symplectic cut construction of Lerman. In 4 or 8 dimensions ... More

Bigness in compatible systemsAug 13 2009Apr 21 2010Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if rho is an l-adic representation of the absolute Galois group of a number field for which the residual representation rho-bar comes from a modular ... More

Toric Hypersymplectic QuotientsApr 30 2004May 06 2004We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space R^{4d} by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The image of the hypersymplectic moment ... More

Hypertoric manifolds and hyperKähler moment mapsJul 14 2016We discuss various aspects of moment map geometry in symplectic and hyperK\"ahler geometry. In particular, we classify complete hyperK\"ahler manifolds of dimension $4n$ with a tri-Hamiltonian action of a torus of dimension $n$, without any assumption ... More