total 8214took 0.11s

Identifying Mild Traumatic Brain Injury Patients From MR Images Using Bag of Visual WordsOct 18 2017Feb 14 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests are used to both assess the patient condition and to monitor the patient progress. This work aims ... More

The Constituents of Sets, Numbers, and Other Mathematical Objects, Part TwoMay 15 2019The arithmetic of natural numbers has a natural and simple encoding within sets, and the simplest set whose structure is not that of any natural number extends this set-theoretic representation to positive and negative integers. The operation that implements ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Apr 11 2018Mild traumatic brain injury is a growing public health problem with an estimated incidence of over 1.7 million people annually in US. Diagnosis is based on clinical history and symptoms, and accurate, concrete measures of injury are lacking. This work ... More

A Deep Unsupervised Learning Approach Toward MTBI Identification Using Diffusion MRIFeb 08 2018Mild traumatic brain injury (mTBI) is a growing public health problem with an estimated incidence of one million people annually in US. Neurocognitive tests have been used to both assess the patient condition and to monitor the patient progress. This ... More

A Machine Learning Approach For Identifying Patients with Mild Traumatic Brain Injury Using Diffusion MRI ModelingAug 27 2017While diffusion MRI has been extremely promising in the study of MTBI, identifying patients with recent MTBI remains a challenge. The literature is mixed with regard to localizing injury in these patients, however, gray matter such as the thalamus and ... More

MTBI Identification From Diffusion MR Images Using Bag of Adversarial Visual FeaturesJun 27 2018In this work, we propose bag of adversarial features (BAF) for identifying mild traumatic brain injury (MTBI) patients from their diffusion magnetic resonance images (MRI) (obtained within one month of injury) by incorporating unsupervised feature learning ... More

Flavour Democracy in Strong UnificationApr 29 1998We show that the fermion mass spectrum may naturally be understood in terms of flavour democratic fixed points in supersymmetric theories which have a large domain of attraction in the presence of "strong unification". Our approach provides an alternative ... More

Reliability of swarming algorithms for mobile sensor network applicationsSep 24 2012There are many well-studied swarming algorithms which are often suited to very specific purposes. As mobile sensor networks become increasingly complex, and are comprised of more and more agents, it makes sense to consider swarming algorithms for movement ... More

Supermatrix Representations of Semigroup BandsSep 19 1996Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups ... More

Using the D1D5 CFT to Understand Black HolesDec 01 2010In this dissertation, we review work presented in arXiv:0906.2015, arXiv:0907.1663, arXiv:1002.3132, arXiv:1003.2746, and arXiv:1007.2202 on the D1D5 system. We begin with some motivational material for black holes in string theory. In Chapter 2, we review ... More

Elementary development of the gravitational self-forceAug 31 2009The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$. One part is an ... More

ProofPeer - A Cloud-based Interactive Theorem Proving SystemJan 02 2012ProofPeer strives to be a system for cloud-based interactive theorem proving. After illustrating why such a system is needed, the paper presents some of the design challenges that ProofPeer needs to meet to succeed. Contexts are presented as a solution ... More

Idempotents and Nilpotents Modulo nMay 01 2006We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.

PhonologyApr 11 2002Phonology is the systematic study of the sounds used in language, their internal structure, and their composition into syllables, words and phrases. Computational phonology is the application of formal and computational techniques to the representation ... More

A Mass Partition Problem Related to Equivariant Sections of Stiefel BundlesNov 08 2010Jun 19 2012We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of m mass distributions on R^n, the existence of k linearly independent regular q-fans, each of which equipartitions ... More

Gauge theory of gravity and matterAug 08 2014It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the theory to spin-0, ... More

Necessary and Sufficient Condition on the Lindblad Equation to Prevent Entropy IncreaseNov 18 2015Nov 23 2015It is shown that in order for the solutions of the Lindblad equation never to give a decreasing von Neumann entropy, it is necessary and sufficient that the operators appearing in this equation should be unitary linear combinations of their adjoints. ... More

Philosophical Solution to P=?NP: P is Equal to NPMar 19 2016The P=?NP problem is philosophically solved by showing P is equal to NP in the random access with unit multiply (MRAM) model. It is shown that the MRAM model empirically best models computation hardness. The P=?NP problem is shown to be a scientific rather ... More

Measure Partitions via Fourier Analysis II: Center Transversality in the $L^2$-norm for Complex HyperplanesJun 22 2015Sep 13 2015Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms. Considering the ... More

A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3Sep 29 2010Sep 03 2011A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyperplane H and a corresponding tiling of H^n into |G| fundamental regions ... More

From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex MeasuresJun 23 2010Sep 03 2011A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, satisfying the condition that for each complex measure, the "Z_m rotational ... More

Neutrino Mass Ordering Studies with PINGU and IceCube/DeepCoreApr 29 2016The Precision IceCube Next Generation Upgrade (PINGU) is a proposed extension to the IceCube detector. The design of PINGU would augment the existing 86 strings with an additional 40 with the main goal of determining the neutrino mass ordering (NMO). ... More

Particle propagators on discrete spacetimeJun 19 2008Oct 01 2008A quantum mechanical description of particle propagation on the discrete spacetime of a causal set is presented. The model involves a discrete path integral in which trajectories within the causal set are summed over to obtain a particle propagator. The ... More

Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism groupOct 18 2010Mar 13 2012In this paper we give a number of explicit constructions for II$_1$ factors and II$_1$ equivalence relations that have prescribed fundamental group and outer automorphism group. We construct factors and relations that have uncountable fundamental group ... More

Stably Newton non-degenerate singularitiesJun 02 2014Jan 28 2015We discuss a problem of Arnold, whether every function is stably equivalent to one which is non-degenerate for its Newton diagram. The answer is negative. The easiest example can be given in characteristic $p$: the function $x^p$ is not stably equivalent ... More

On the Descending Central Series of Higher Commutators for Simple AlgebrasDec 12 2018This paper characterizes the potential behaviors of higher commutators in a simple algebra.

No Quantum Brooks' TheoremNov 27 2014First, I introduce quantum graph theory. I also discuss a known lower bound on the independence numbers and derive from it an upper bound on the chromatic numbers of quantum graphs. Then, I construct a family of quantum graphs that can be described as ... More

The 21 Centimeter ForestApr 10 2006We examine the prospects for studying the pre-reionization intergalactic medium (IGM) through the so-called 21 cm forest in spectra of bright high-redshift radio sources. We first compute the evolution of the mean optical depth for models that include ... More

Degenerations of elliptic curves and cusp singularitiesDec 21 1995We give more or less explicit equations for all two-dimensional cusp singularities of embedding dimension at least 4. They are closely related to Felix Klein's equations for universal curves with level n structure. The main technical result is a description ... More

Quartic and Octic Characters Modulo nJul 28 2009Mar 25 2016The average number of primitive quadratic Dirichlet characters of modulus n tends to a constant as n->infty. The same is true for primitive cubic characters. It is therefore surprising that, as n->infty, the average number of primitive quartic characters ... More

Idempotents and Nilpotents Modulo nMay 01 2006Nov 18 2017We study asymptotic properties of periods and transient phases associated with modular power sequences. The latter are simple; the former are vaguely related to the reciprocal sum of square-free integer kernels.

A review of Dan's reduction method for multiple polylogarithmsMar 11 2017In this paper we will give an account of Dan's reduction method for reducing the weight $ n $ multiple logarithm $ I_{1,1,\ldots,1}(x_1, x_2, \ldots, x_n) $ to an explicit sum of lower depth multiple polylogarithms in $ \leq n - 2 $ variables. We provide ... More

Non-embeddable 1-convex manifoldsSep 27 2012Nov 11 2013We show that every small resolution of a three-dimensional terminal hypersurface singularity can occur on a non-embeddable 1-convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve ... More

Donaldson invariants of symplectic manifoldsJan 03 2013Jan 07 2013We prove that symplectic 4-manifolds with $b_1 = 0$ and $b^+ > 1$ have nonvanishing Donaldson invariants, and that the canonical class is always a basic class. We also characterize in many situations the basic classes of a Lefschetz fibration over the ... More

The contact homology of Legendrian knots with maximal Thurston-Bennequin invariantDec 22 2010We show that there exists a Legendrian knot with maximal Thurston-Bennequin invariant whose contact homology is trivial. We also provide another Legendrian knot which has the same knot type and classical invariants but nonvanishing contact homology.

Topological complexity of n points on a treeJul 27 2016Jan 24 2018The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration ... More

Random Cyclic QuadrilateralsOct 03 2016The circumcircle of a planar convex polygon P is a circle C that passes through all vertices of P. If such a C exists, then P is said to be cyclic. Fix C to have unit radius. While any two angles of a uniform cyclic triangle are negatively correlated, ... More

Random Gaussian TetrahedraMay 06 2010Dec 17 2015Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The probability that the tetrahedron ABCD is acute remains intractible. We make ... More

Initial Blow-up of Solutions of Semilinear Parabolic InequalitiesNov 19 2009We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.

Lower Bounds for Cubical PseudomanifoldsSep 30 2009Apr 02 2011It is verified that the number of vertices in a $d$-dimensional cubical pseudomanifold is at least $2^{d+1}$. Using Adin's cubical $h$-vector, the generalized lower bound conjecture is established for all cubical 4-spheres, as well as for some special ... More

On Arthur's Φ-FunctionMar 24 2005Write $\Theta^E$ for the stable character associated to a finite dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's extension of $ |D_M^G(\gm)|^{\half} ... More

Cosmological Fluctuations of Short WavelengthJul 18 2002This paper presents a completely analytic treatment of cosmological fluctuations whose wavelength is small enough to come within the horizon well before the energy densities of matter and radiation become equal. This analysis yields a simple formula for ... More

On Alternative Supermatrix ReductionJun 02 1995Jun 16 1995We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible ... More

Six-dimensional Methods for Four-dimensional Conformal Field TheoriesJun 17 2010Aug 02 2010The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as projections of fields ... More

A No-Truncation Approach to Cosmic Microwave Background AnisotropiesJul 05 2006Sep 12 2006We offer a method of calculating the source term in the line-of-sight integral for cosmic microwave background anisotropies without using a truncated partial-wave expansion in the Boltzmann hierarchy.

Damping of Tensor Modes in CosmologyJun 16 2003Oct 05 2003An analytic formula is given for the traceless transverse part of the anisotropic stress tensor due to free streaming neutrinos, and used to derive an integro-differential equation for the propagation of cosmological gravitational waves. The solution ... More

The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000)May 12 2000The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help ... More

Must Cosmological Perturbations Remain Non-Adiabatic After Multi-Field Inflation?May 20 2004Jul 20 2004Even if non-adiabatic perturbations are generated in multi-field inflation, the perturbations will become adiabatic if the universe after inflation enters an era of local thermal equilibrium, with no non-zero conserved quantities, and will remain adiabatic ... More

The Making of the Standard ModelJan 03 2004This is the edited text of a talk given at CERN on Septembr 16, 2003, as part of a celebration of the 30th anniversary of the discovery of neutral currents and the 20th anniversary of the discovery of the W and Z particles.

Adiabatic Modes in CosmologyFeb 17 2003We show that the field equations for cosmological perturbations in Newtonian gauge always have an adiabatic solution, for which a quantity ${\cal R}$ is non-zero and constant in all eras in the limit of large wavelength, so that it can be used to connect ... More

Black Hole Thermodynamics and Statistical MechanicsJul 28 2008We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical ... More

Notes on the (2+1)-Dimensional Wheeler-DeWitt EquationSep 02 1993In contrast to other approaches to (2+1)-dimensional quantum gravity, the Wheeler-DeWitt equation appears to be too complicated to solve explicitly, even for simple spacetime topologies. Nevertheless, it is possible to obtain a good deal of information ... More

The Sum over Topologies in Three-Dimensional Euclidean Quantum GravityJun 26 1992In Hawking's Euclidean path integral approach to quantum gravity, the partition function is computed by summing contributions from all possible topologies. The behavior such a sum can be estimated in three spacetime dimensions in the limit of small cosmological ... More

Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave FunctionMay 11 1992In most attempts to compute the Hartle-Hawking ``wave function of the universe'' in Euclidean quantum gravity, two important approximations are made: the path integral is evaluated in a saddle point approximation, and only the leading (least action) extremum ... More

(2+1)-Dimensional Chern-Simons Gravity as a Dirac Square RootSep 04 1991Sep 16 1991For (2+1)-dimensional spacetimes with the spatial topology of a torus, the transformation between the Chern-Simons and ADM versions of quantum gravity is constructed explicitly, and the wave functions are compared. It is shown that Chern-Simons wave functions ... More

A lexical database tool for quantitative phonological researchJul 22 1997A lexical database tool tailored for phonological research is described. Database fields include transcriptions, glosses and hyperlinks to speech files. Database queries are expressed using HTML forms, and these permit regular expression search on any ... More

Topological quantum field theory and quantum gravityAug 07 2014This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same result as the ... More

Polyadic systems, representations and quantum groupsAug 19 2013Jun 08 2014Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic systems having ... More

Nonlocal invariants in index theoryJul 21 1997This article surveys the relations among local and nonlocal invariants in Atiyah-Singer index theory. We discuss the local invariants that arise from the heat equation approach to the index theorem for geometric operators, as well as the nonlocal invariants ... More

Deforming nonnormal isolated surface singularities and constructing 3-folds with $\mathbb{P}^1$ as exceptional setDec 11 2015Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as isolated, non ... More

Quasilinear reformulation of Lovelock gravityApr 30 2015Jun 04 2015Here we give an extended review of the quasilinear reformulation of the Lovelock gravitational field equations in harmonic gauge presented in 1409.6656 [gr-qc]. This is important in order to establish rigorously well-posedness of the theory perturbed ... More

Low Correlation Noise Stability of Symmetric SetsNov 02 2015Sep 02 2016We study the Gaussian noise stability of subsets A of Euclidean space satisfying A=-A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the real line of ... More

Lindblad Decoherence in Atomic ClocksOct 08 2016It is shown how possible corrections to ordinary quantum mechanics described by the Lindblad equation might be detected by exploiting the great precision of atomic clocks.

Topological complexity of n points on a treeJul 27 2016The topological complexity of a path-connected space $X,$ denoted $TC(X),$ can be thought of as the minimum number of continuous rules needed to describe how to move from one point in $X$ to another. The space $X$ is often interpreted as a configuration ... More

A Characterisation of Manhart's Relative Normal Vector FieldsDec 20 2009In this article a relation between curvature functionals for surfaces in the Euclidean space and area functionals in relative differential geometry will be given. Relative differential geometry can be described as the geometry of surfaces in the affine ... More

Average-Value Tverberg Partitions via Finite Fourier AnalysisJan 19 2015Jul 25 2016The long-standing topological Tverberg conjecture claimed, for any continuous map from the boundary of an $N(q,d):=(q-1)(d+1)$-simplex to $d$-dimensional Euclidian space, the existence of $q$ pairwise disjoint subfaces whose images have non-empty $q$-fold ... More

Hyperplane Equipartitions Plus ConstraintsAug 01 2017Jul 22 2018While equivariant methods have seen many fruitful applications in geometric combinatorics, their inability to answer the now settled Topological Tverberg Conjecture has made apparent the need to move beyond the use of Borsuk--Ulam type theorems alone. ... More

On the reductive Borel-Serre compactification, II: Excentric quotients and least common modificationsSep 14 2006Let X be a locally symmetric variety. Let EBS(X) and TorE(X) denote its excentric Borel-Serre and excentric toroidal compactifications, resp. We determine their least common modification and use it to prove a conjecture of Goresky and Tai concerning canonical ... More

Analogues of cyclic insertion type identities for multiple zeta star valuesJun 26 2018We prove an identity for multiple zeta star values, which generalises some identities due to Imatomi, Tanaka, Tasaka and Wakabayashi. This identity gives an analogue of cyclic insertion type identities, for multiple zeta star values, and connects the ... More

Dual Selection GamesSep 27 2018Often, a given selection game studied in the literature has a known dual game. In dual games, a winning strategy for a player in either game may be used to create a winning strategy for the opponent in the dual. For example, the Rothberger selection game ... More

Quasigeodesic flows and sphere-filling curvesOct 26 2012Given a closed hyperbolic 3-manifold M with a quasigeodesic flow we construct a \pi_1-equivariant sphere-filling curve in the boundary of hyperbolic space. Specifically, we show that any complete transversal P to the lifted flow on H^3 has a natural compactification ... More

Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamicsAug 05 2013Sep 07 2014A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number ... More

Poincare series and zeta function for an irreducible plane curve singularityOct 15 2003The Poincare series of an irreducible plane curve singularity equals the zeta function of its monodromy, by a result of Campillo, Delgado and Gusein-Zade. We derive this fact from a formula of Ebeling and Gusein-Zade relating the Poincare series of a ... More

Arithmetic universes and classifying toposesJan 17 2017Reasoning in the 2-category Con of contexts, certain sketches for arithmetic universes (i.e. list arithmetic pretoposes; AUs), is shown to give rise to base-independent results of Grothendieck toposes, provided the base elementary topos has a natural ... More

A Convex Maximization Problem: Continuous CaseDec 05 1999We study a specific convex maximization problem in the space of continuous functions defined on a semi-infinite interval. An unexplained connection to the discrete version of this problem is investigated.

M/M/$c$ Queues and the Poisson Clumping HeuristicApr 08 2019In continuous time, customers arrive at random. Each waits until one of $c$ servers is available; each thereafter departs at random. The distribution of maximum line length of idle customers was studied over 25 years ago. We revisit two good approximations ... More

Second N=1 Superanalog of Complex StructureOct 19 1995We found another N=1 odd superanalog of complex structure (the even one is widely used in the theory of super Riemann surfaces). New N=1 superconformal-like transformations are similar to anti-holomorphic ones of nonsupersymmetric complex function theory. ... More

Stochastic Attribute-Value GrammarsOct 23 1996Probabilistic analogues of regular and context-free grammars are well-known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: ... More

An Incidence Bound Over FieldsSep 20 2016We prove an upper bound on incidences between points and lines in the plane over a field $\mathbb{F}$. In particular, given $n$ points and $m$ lines in $\mathbb{F}^2$ (where $n\leq m$, and if $\text{char}(\mathbb{F})=p>0$, then $n\leq p^{4/3}$), we prove ... More

Tetraquark Mesons in Large $N$ Quantum ChromodynamicsMar 02 2013It is argued that exotic mesons consisting of two quarks and two antiquarks are not ruled out in quantum chromodynamics with a large number $N$ of colors, as generally thought. They can come in two varieties: short-lived tetraquarks with decay rates proportional ... More

Asymptotically Safe InflationNov 16 2009Mar 30 2010Inflation is studied in the context of asymptotically safe theories of gravitation. Conditions are explored under which it is possible to have a long period of nearly exponential expansion that eventually comes to an end.

Non-Gaussian Correlations Outside the Horizon II: The General CaseOct 16 2008The results of a recent paper [0808.2909] are generalized. A more detailed proof is presented that under essentially all conditions, the non-linear classical equations governing matter and gravitation in cosmology have ``adiabatic'' solutions in which, ... More

A Tree Theorem for InflationMay 24 2008Aug 13 2008It is shown that the generating function for tree graphs in the "in-in" formalism may be calculated by solving the classical equations of motion subject to certain constraints. This theorem is illustrated by application to the evolution of a single inflaton ... More

Living in the MultiverseNov 03 2005This is the written version of the opening talk at the symposium "Expectations of a Final Theory," at Trinity College, Cambridge, on September 2, 2005. It is to be published in Universe or Multiverse?, ed. B. Carr (Cambridge University Press).

What is Quantum Field Theory, and What Did We Think It Is?Feb 04 1997This is a talk presented at the conference ``Historical and Philosophical Reflections on the Foundations of Quantum Field Theory,'' at Boston University, March 1996. It will be published in the proceedings of this conference.

Effective Field Theory, Past and FutureAug 13 2009Sep 26 2009This is a written version of the opening talk at the 6th International Workshop on Chiral Dynamics, at the University of Bern, Switzerland, July 6, 2009, to be published in the proceedings of the Workshop. In it, I reminisce about the early development ... More

Can Non-Adiabatic Perturbations Arise After Single-Field Inflation?Jan 15 2004May 18 2004It is shown that non-adiabatic cosmological perturbations cannot arise during the period of reheating following inflation with a single scalar inflaton field.

Fluctuations in the Cosmic Microwave Background II: $C_\ell$ at Large and Small $\ell$Mar 19 2001Aug 16 2001General asymptotic formulas are given for the coefficient $C_\ell$ of the term of multipole number $\ell$ in the temperature correlation function of the cosmic microwave background, in terms of scalar and dipole form factors introduced in a companion ... More

Permutation Complexity Related to the Letter Doubling MapAug 18 2011Given a countable set X (usually taken to be the natural numbers or integers), an infinite permutation, \pi, of X is a linear ordering of X. This paper investigates the combinatorial complexity of infinite permutations on the natural numbers associated ... More

Permutation Complexity of the Thue-Morse WordMar 31 2010Apr 05 2010Given a countable set X (usually taken to be the natural numbers or the integers), an infinite permutation \pi of X is a linear ordering of X. This paper investigates the combinatorial complexity of the infinite permutation on the natural numbers associated ... More

Spontaneous Dimensional Reduction in Short-Distance Quantum Gravity?Sep 17 2009Several lines of evidence suggest that quantum gravity at very short distances may behave effectively as a two-dimensional theory. I summarize these hints, and offer an additional argument based on the strong-coupling limit of the Wheeler-DeWitt equation. ... More

The Statistical Mechanics of the Three-Dimensional Euclidean Black HoleJun 17 1996Oct 08 1996In its formulation as a Chern-Simons theory, three-dimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting ... More

Computational PhonologyApr 10 2002Phonology, as it is practiced, is deeply computational. Phonological analysis is data-intensive and the resulting models are nothing other than specialized data structures and algorithms. In the past, phonological computation - managing data and developing ... More

l --> l' gamma in the Lepton Number Violating MSSMOct 30 2006A minimal particle content supersymmetric model with a discrete Z_3 symmetry, allowing lepton number violating terms, is studied. Within this model, the neutrino masses and mixing can be generated by lepton number violating couplings. Choosing parameters ... More

On the classification of rational surface singularitiesApr 01 2012A general strategy is given for the classification of graphs of rational surface singularities. For each maximal rational double point configuration we investigate the possible multiplicities in the fundamental cycle. We classify completely certain types ... More

Partial Hamiltonian formalism, multi-time dynamics and singular theoriesJul 22 2013We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the initially reduced ... More

The localic compact interval is an Escardó-Simpson interval objectJun 26 2015The locale corresponding to the real interval [-1,1] is an interval object, in the sense of Escard\'o and Simpson, in the category of locales. The map c from 2^\omega to [-1,1], mapping a stream s of signs +1 or -1 to \Sum_{i=1}^\infty s_i 2^{-i}, is ... More

Hamiltonian analysis of self-dual gauge gravityApr 15 2015The Hamiltonian analysis of the self-dual gauge gravity theory is carried out. The resulting canonical structure is equivalent to that of self-dual gravity.

A semiclassical reversibility paradox in simple chaotic systemsSep 27 2015Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly chaotic, there ... More

Algebroids and Twistor SpacesDec 14 2015We introduce a plethora of skew algebroids on twistor spaces and describe the corresponding foliations. In a forthcoming paper, we use these algebroids to derive results about bihermitian manifolds, also known as generalized Kahler manifolds.