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Parallel implementation of high-fidelity multi-qubit gates with neutral atomsAug 16 2019We report the implementation of universal two- and three-qubit entangling gates on neutral atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states, and are implemented in parallel ... More

High-fidelity control and entanglement of Rydberg atom qubitsJun 12 2018Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities ... More

Probing many-body dynamics on a 51-atom quantum simulatorJul 13 2017Nov 30 2017Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on ... More

A comparison of motivic and classical homotopy theoriesDec 31 2011Mar 07 2013Let k be an algebraically closed field of characteristic zero. Let SH(k) denote the motivic stable homotopy category of T-spectra over k and SH the classical stable homotopy category. Let c:SH -> SH(k) be the functor induced by sending a space to the ... More

Slices and TransfersMar 09 2010We study the slice filtration for S^1-spectra over a field k, and raise a number of questions regardings its properties. We show that the slices, except for the 0th slice, admit a further filtration whose layers are in a natural way the Eilenberg-Maclane ... More

The slice filtration and Grothendieck-Witt groupsDec 27 2010Let k be a perfect field of characteristic different from two. We show that the filtration on the Grothendieck-Witt group GW(k) induced by the slice filtration for the sphere spectrum in the motivic stable homotopy category is the I-adic filtration, where ... More

The homotopy coniveau towerOct 16 2005We examine the "homotopy coniveau tower" for a general cohomology theory on smooth k-schemes and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. In addition, the homotopy coniveau tower agrees with Voevodsky's ... More

Algebraic cobordismApr 15 2003Together with F. Morel, we have constructed in \cite{CR, Cobord1, Cobord2} a theory of {\em algebraic cobordism}, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey of the construction and main ... More

Sandpile groups and spanning trees of directed line graphsJun 15 2009Apr 06 2010We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted ... More

Linear and nonlinear susceptibilities of a decoherent two-level systemFeb 19 2000The linear and nonlinear dynamical susceptibilities of a two level system are calculated as it undergoes a transition to a decoherent state. Analogously to the Glover-Tinkham-Ferrell sum rule of superconductivity, spectral weight in the linear susceptibility ... More

Smooth motivesJul 14 2008Following ideas of Bondarko, we construct a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme $S$ generated by the motives of smooth projective $S$-schemes, assuming that $S$ is itself smooth over ... More

Motivic Euler characteristics and Witt-valued characteristic classesJun 26 2018This paper examines a number of related questions about Euler characteristics and characteristic classes with values in Witt cohomology. We establish a motivic version of the Becker-Gottllieb transfer, generalizing a construction of Hoyois. Ananyevskiy's ... More

Motivic Tubular NeighborhoodsSep 21 2005Oct 25 2005We construct motivic versions of the classical tubular neighborhood and the punctured tubular neighborhood, and give applications to the construction of tangential base-points for mixed Tate motives, algebraic gluing of curves with boundary components, ... More

Motivic Landweber exact theories and their effective coversJan 01 2014Jan 01 2015Let $k$ be a field of characteristic zero and let $(F,R)$ be a Landweber exact formal group law. We consider a Landweber exact $T$-spectrum $\mathcal{E}:=R\otimes_{\mathbb{L}}\text{MGL}$ and its effective cover $f_0\mathcal{E}\to \mathcal{E}$ with respect ... More

Comparison of cobordism theoriesJul 14 2008Relying on results of Hopkins-Morel, we show that, for $X$ a quasi-projective variety over a field of characteristic zero, the canonical map $\Omega_n(X)\to MGL_{2n,n}'(X)$ is an isomorphism. Here $\Omega_*(X)$ is the theory of algebraic cobordism defined ... More

A Giambelli formula for classical $G/P$ spacesAug 25 2009Mar 30 2014Let $G$ be a classical complex Lie group, $P$ any parabolic subgroup of $G$, and $G/P$ the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in the cohomology ring of $G/P$ ... More

A la Carte of Correlation Models: Which One to Choose?Oct 19 2010In this paper we propose a copula contagion mixture model for correlated default times. The model includes the well known factor, copula, and contagion models as its special cases. The key advantage of such a model is that we can study the interaction ... More

L-series and isomorphisms of number fieldsJan 18 2019Apr 18 2019Two number fields with equal Dedekind zeta function are not necessarily isomorphic. However, if the number fields have equal sets of Dirichlet $L$-series then they \emph{are} isomorphic. We extend this result by showing that the isomorphisms between the ... More

Rigidification and the Coherent Nerve for Enriched QuasicategoriesOct 23 2018We introduce, for \(\C\) a regular Cartesian Reedy category a model category whose fibrant objects are an analogue of quasicategories enriched in simplicial presheaves on \(C\). We then develop a coherent realization and nerve for this model structure ... More

Entanglement entropy in a boundary impurity modelAug 16 2004Nov 30 2004Boundary impurities are known to dramatically alter certain bulk properties of 1+1 dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite ... More

A Factorization of the Conway PolynomialNov 08 1997A string link S can be closed in a canonical way to produce an ordinary closed link L. We also consider a twisted closing which produces a knot K. We give a formula for the Conway polynomial of L as a product of the Conway polynomial of K times a power ... More

Eshel Ben-Jacob: A unique individual in the science of collective phenomenaMar 18 2018Eshel Ben-Jacob, one of the co-organizers of this meeting on collective behavior and one of the pioneers in the field of collective behavior in biology, passed away suddenly just before we convened. This article presents a brief glimpse of Eshel's life-long ... More

Robust functional estimation in the multivariate partial linear modelDec 25 2017We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional component is ... More

Toward an enumerative geometry with quadratic formsMar 08 2017Oct 18 2018We develop various aspects of classical enumerative geometry, including Euler characteristics and formulas for counting degenerate fibres in a pencil, with the classical numerical formulas being replaced by identitites in the Grothendieck-Witt group of ... More

Arithmetic Intersection Theory on Flag VarietiesNov 06 1996Let F be the complete flag variety over Spec(Z) with the tautological filtration 0 \subset E_1 \subset E_2 \subset ... \subset E_n=E of the trivial bundle E over F. The trivial hermitian metric on E(\C) induces metrics on the quotient line bundles L_i(\C). ... More

L-series and isomorphisms of number fieldsJan 18 2019Feb 02 2019Two number fields with equal Dedekind zeta function are not necessarily isomorphic. However, if the number fields have equal sets of Dirichlet $L$-series then they \emph{are} isomorphic. We extend this result by showing that the isomorphisms between the ... More

Integer Complexity and Well-OrderingOct 10 2013Aug 26 2015Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed that $\|n\| \ge 3\log_3 n$ for all $n$. Define the defect of $n$, denoted ... More

Theta and eta polynomials in geometry, Lie theory, and combinatoricsJul 27 2018The classical Schur polynomials form a natural basis for the ring of symmetric polynomials, and have geometric significance since they represent the Schubert classes in the cohomology ring of Grassmannians. Moreover, these polynomials enjoy rich combinatorial ... More

The Injective Spectrum of a Right Noetherian Ring II: Sheaves and Torsion TheoriesAug 16 2019This is the second of two papers on the injective spectrum of a right noetherian ring. In the prequel, we considered the injective spectrum as a topological space associated to a ring (or, more generally, a Grothendieck category), which generalises the ... More

On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functionsJul 14 2018Jun 30 2019This paper deals with the equation $-\Delta u+\mu u=f$, $\mu$ a positive constant, on high-dimensional spaces $\mathbb{R}^m$. If the right-hand side $f$ is a rapidly converging series of separable functions, the solution $u$ can be represented in the ... More

Integer Complexity: Representing Numbers of Bounded DefectMar 19 2016Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed that $\|n\|\ge 3\log_3 n$ for all $n$. Based on this, this author and Zelinsky ... More

Tiling with punctured intervalsMay 08 2018It was shown by Gruslys, Leader and Tan that any finite subset of $\mathbb{Z}^n$ tiles $\mathbb{Z}^d$ for some $d$. The first non-trivial case is the punctured interval, which consists of the interval $\{-k,\ldots,k\} \subset \mathbb{Z}$ with its middle ... More

Schubert polynomials and Arakelov theory of orthogonal flag varietiesJul 19 2009Sep 06 2013We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of orthogonal flag varieties. We use these polynomials to describe the arithmetic Schubert calculus ... More

Schubert polynomials and Arakelov theory of symplectic flag varietiesAug 09 2008Sep 06 2013Let X be the flag variety of the symplectic group. We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the cohomology ring of X. We use these polynomials to describe the ... More

Einstein's aborted attempt at a dynamic steady-state universeFeb 14 2014Feb 24 2014In June 1930 Einstein visited Cambridge where he stayed with Eddington who had just shown that Einstein's supposedly static universe of 1917 was not stable. This forced Einstein to rethink his cosmology. He spent January and February 1931 at Pasadena. ... More

Einstein's conversion from his static to an expanding universeNov 12 2013Mar 24 2014In 1917 Einstein initiated modern cosmology by postulating, based on general relativity, a homogeneous, static, spatially curved universe. To counteract gravitational contraction he introduced the cosmological constant. In 1922 Alexander Friedman showed ... More

Schubert polynomials, theta and eta polynomials, and Weyl group invariantsJun 07 2017Jul 27 2018We examine the relationship between the (double) Schubert polynomials of Billey-Haiman and Ikeda-Mihalcea-Naruse and the (double) theta and eta polynomials of Buch-Kresch-Tamvakis and Wilson from the perspective of Weyl group invariants. We obtain generators ... More

Schubert polynomials and degeneracy locus formulasFeb 18 2016Sep 02 2017In our previous work arXiv:1305.3543, we employed the approach to Schubert polynomials by Fomin, Stanley, and Kirillov to obtain simple, uniform proofs that the double Schubert polynomials of Lascoux and Schutzenberger and Ikeda, Mihalcea, and Naruse ... More

The connection between representation theory and Schubert calculusJun 29 2003Sep 06 2013We describe a direct connection between the representation theory of the general linear group and classical Schubert calculus on the Grassmannian, which goes via the Chern-Weil theory of characteristic classes. We also explain why the analogous constructions ... More

A Note on Approximate Inverse IterationNov 13 2016Different variants of approximate inverse iteration like the locally optimal block preconditioned conjugate gradient method became in recent years increasingly popular for the solution of the large matrix eigenvalue problems arising from the discretization ... More

L-series and isogenies of abelian varietiesJan 21 2019Apr 18 2019Faltings's isogeny theorem states that two abelian varieties are isogenous over a number field precisely when the characteristic polynomials of the reductions at almost all prime ideals of the number field agree. This implies that two abelian varieties ... More

The Injective Spectrum of a Right Noetherian Ring I: Injective Spectra and Krull DimensionAug 16 2019The injective spectrum is a topological space associated to a ring $R$, which agrees with the Zariski spectrum when $R$ is commutative noetherian. We consider injective spectra of right noetherian rings (and locally noetherian Grothendieck categories) ... More

Integer complexity: algorithms and computational resultsJun 11 2016Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. Define $n$ to be stable if for all $k\ge 0$, we have $\|3^k n\|=\|n\|+3k$. In [7], this author and ... More

Intermediate arithmetic operations on ordinal numbersJan 23 2015Apr 21 2016There are two well-known ways of doing arithmetic with ordinal numbers: the "ordinary" addition, multiplication, and exponentiation, which are defined by transfinite iteration; and the "natural" (or Hessenberg) addition and multiplication (denoted $\oplus$ ... More

Integer complexity: The integer defectApr 20 2018Aug 03 2018Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. John Selfridge showed that $\|n\|\ge 3\log_3 n$ for all $n$, leading this author and Zelinsky to ... More

Integer complexity: algorithms and computational resultsJun 11 2016Dec 21 2017Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. Define $n$ to be stable if for all $k\ge 0$, we have $\|3^k n\|=\|n\|+3k$. In [7], this author and ... More

On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functionsJul 14 2018Sep 17 2018This paper deals with the equation $-\Delta u+\mu u=f$, $\mu$ a positive constant, on high-dimensional spaces $\mathbb{R}^m$. If the right-hand side $f$ is a rapidly converging series of separable functions, the solution $u$ can be represented in the ... More

microRNAs may sharpen spatial expression patternsFeb 22 2007Jun 08 2007The precise layout of gene expression patterns is a crucial step in development. Formation of a sharp boundary between high and low expression domains requires a genetic mechanism which is both sensitive and robust to fluctuations, a demand that may not ... More

Unicellular algal growth: A biomechanical approach to cell wall dynamicsMay 07 1997We present a model for unicellular algal growth as motivated by several experiments implicating the importance of calcium ions and ``loosening'' enzymes in morphogenesis. A growing cell at rest in a diffusive calcium solution is viewed as an elastic shell ... More

(CAD)$^2$RL: Real Single-Image Flight without a Single Real ImageNov 13 2016We propose (CAD)$^2$RL, a flight controller for Collision Avoidance via Deep Reinforcement Learning that can be used to perform collision-free flight in the real world although it is trained entirely in a 3D CAD model simulator. Our method uses only single ... More

Dynamic instabilities of fracture under biaxial strain using a phase field modelFeb 23 2004Jun 11 2004We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and ... More

Scaling Limits for Internal Aggregation Models with Multiple SourcesDec 20 2007May 02 2009We study the scaling limits of three different aggregation models on Z^d: internal DLA, in which particles perform random walks until reaching an unoccupied site; the rotor-router model, in which particles perform deterministic analogues of random walks; ... More

On a spectral sequence for equivariant K-theoryNov 15 2005Nov 19 2005We apply the machinery developed by the first-named author to the K-theory of coherent G-sheaves on a finite type G-scheme X over a field, where G is a finite group. This leads to a definition of G-equivariant higher Chow groups (different from the Chow ... More

Resampling Method For Unsupervised Estimation Of Cluster ValidityMay 18 2000We introduce a method for validation of results obtained by clustering analysis of data. The method is based on resampling the available data. A figure of merit that measures the stability of clustering solutions against resampling is introduced. Clusters ... More

A Thermodynamic Model for Receptor ClusteringAug 06 1999Intracellular signaling often arises from ligand-induced oligomerization of cell surface receptors. This oligomerization or clustering process is fundamentally a cooperative behavior between near-neighbor receptor molecules; the properties of this cooperative ... More

Spherical Asymptotics for the Rotor-Router Model in Z^dMar 14 2005The rotor-router model is a deterministic analogue of random walk invented by Jim Propp. It can be used to define a deterministic aggregation model analogous to internal diffusion limited aggregation. We prove an isoperimetric inequality for the exit ... More

Thousands of DebitCredit Transactions-Per-Second: Easy and InexpensiveJan 25 2007A $2k computer can execute about 8k transactions per second. This is 80x more than one of the largest US bank's 1970's traffic - it approximates the total US 1970's financial transaction volume. Very modest modern computers can easily solve yesterday's ... More

CoEulerian graphsFeb 16 2015Sep 11 2015We suggest a measure of "Eulerianness" of a finite directed graph and define a class of "coEulerian" graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we address a question in chip-firing posed by Bjorner, ... More

A Phase-Field Model of Spiral Dendritic GrowthMay 16 1996Domains of condensed-phase monolayers of chiral molecules exhibit a variety of interesting nonequilibrium structures when formed via pressurization. To model these domain patterns, we add a complex field describing the tilt degree of freedom to an (anisotropic) ... More

Computing Knot Floer Homology in Cyclic Branched CoversSep 10 2007Dec 09 2007We use grid diagrams to give a combinatorial algorithm for computing the knot Floer homology of the pullback of a knot K in its m-fold cyclic branched cover Sigma^m(K), and we give computations when m=2 for over fifty three-bridge knots with up to eleven ... More

Slicing mixed Bing-Whitehead doublesDec 28 2009Aug 20 2010We show that if K is any knot whose Ozsvath-Szabo concordance invariant tau(K) is positive, the all-positive Whitehead double of any iterated Bing double of K is topologically but not smoothly slice. We also show that the all-positive Whitehead double ... More

Deep Visual Foresight for Planning Robot MotionOct 03 2016Mar 13 2017A key challenge in scaling up robot learning to many skills and environments is removing the need for human supervision, so that robots can collect their own data and improve their own performance without being limited by the cost of requesting human ... More

Stochastic fluctuations in metabolic pathwaysApr 13 2007Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of downstream targets ... More

Tate motives and the fundamental groupAug 29 2007Let k be a number field, and let S be a finite set of k-rational points of P^1. We relate the Deligne-Goncharov contruction of the motivic fundamental group of X:=P^1_k- S to the Tannaka group scheme of the category of mixed Tate motives over X.

Interfacial Velocity Corrections due to Multiplicative NoiseNov 02 1998The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading edge which perforce ... More

Activity-dependent stochastic resonance in recurrent neuronal networksJun 10 2008We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. Addition of an additional ... More

Wave nucleation rate in excitable systems in the low noise limitJan 08 2003Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential ... More

Strong Spherical Asymptotics for Rotor-Router Aggregation and the Divisible SandpileApr 05 2007Oct 14 2008The rotor-router model is a deterministic analogue of random walk. It can be used to define a deterministic growth model analogous to internal DLA. We prove that the asymptotic shape of this model is a Euclidean ball, in a sense which is stronger than ... More

Abelian networks III. The critical groupAug 30 2014Oct 31 2015The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical group of an irreducible abelian network acts freely and ... More

Connective algebraic K-theoryDec 02 2012We examine the theory of connective algebraic K-theory, CK, defined by taking the -1 connective cover of algebraic K-theory with respect to Voevodsky's slice tower in the motivic stable homotopy category. We extend CK to a bi-graded oriented duality theory ... More

Motives of Azumaya algebrasOct 08 2007Feb 17 2008We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson-Lichtenbaum conjecture, ... More

Partitioning a reflecting stationary setJul 19 2019We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer that it is ... More

Relatively exchangeable structuresSep 22 2015Oct 01 2015We study random relational structures that are \emph{relatively exchangeable}---that is, whose distributions are invariant under the automorphisms of a reference structure $\mathfrak{M}$. When $\mathfrak{M}$ has {\em trivial definable closure}, every ... More

A Monopole MetricOct 18 1996We calculate explicitly in terms of complete elliptic integrals the metric on the moduli space of tetrahedrally-symmetric, charge four, SU(2) monopoles. Using this we verify that in the asymptotic regime the metric of Gibbons and Manton is exact up to ... More

Quantum Verification of Matrix ProductsSep 06 2004Jul 06 2005We present a quantum algorithm that verifies a product of two n*n matrices over any field with bounded error in worst-case time n^{5/3} and expected time n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This improves the previous ... More

An analysis of a class of variational multiscale methods based on subspace decompositionAug 14 2016Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods that are very ... More

Pattern Avoidance for Random PermutationsSep 26 2015We use techniques from Poisson approximation to prove explicit error bounds on the number of permutations that avoid any pattern. Most generally, we bound the total variation distance between the Poisson distribution and the distribution of the number ... More

A phase transition in a model for the spread of an infectionOct 17 2004We show that a certain model for the spread of an infection has a phase transition in the recuperation rate. The model is as follows: There are particles or individuals of type A and type B, interpreted as healthy and infected, respectively. All particles ... More

Quantum Pascal's Triangle and Sierpinski's carpetAug 24 2017In this paper we consider a quantum version of Pascal's triangle. Pascal's triangle is a well-known triangular array of numbers and when these numbers are plotted modulo 2, a fractal known as the Sierpinski triangle appears. We first prove the appearance ... More

The Levi Problem in $\mathbb C^n$: A SurveyNov 03 2014We discuss domains of holomorphy and several notions of pseudoconvexity (drawing parallels with the corresponding notions from geometric convexity), and present a mostly self-contained solution to the Levi problem. We restrict our attention to domains ... More

Double theta polynomials and equivariant Giambelli formulasOct 30 2014Feb 13 2016We use Young's raising operators to introduce and study double theta polynomials, which specialize to both the theta polynomials of Buch, Kresch, and Tamvakis, and to double (or factorial) Schur S-polynomials and Q-polynomials. These double theta polynomials ... More

The Hodge star operator on Schubert formsJun 29 2003Let X=G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this ... More

Lower Bound Approximation to Basket Option Values for Local Volatility Jump-Diffusion ModelsDec 13 2012Oct 12 2013In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. ... More

Constrained NonSmooth Utility Maximization on the Positive Real LineOct 19 2010We maximize the expected utility of terminal wealth in an incomplete market where there are cone constraints on the investor's portfolio process and the utility function is not assumed to be strictly concave or differentiable. We establish the existence ... More

Turnpike Property and Convergence Rate for an Investment and Consumption ModelAug 13 2018We discuss the turnpike property for optimal investment and consumption problems. We find there exists a threshold value that determines the turnpike property for investment policy. The threshold value only depends on the Sharpe ratio, the riskless interest ... More

Tree-level invariants of three-manifolds, Massey products and the Johnson homomorphismApr 20 1999Oct 14 2003Two references added and the introduction slightly expanded. We show that the tree-level part of a recent theory of invariants of 3-manifolds (due, independently, to Goussarov and Habiro) is essentially given by classical algebraic topology in terms of ... More

On Finite Type 3-manifold invariants IV: Comparison of DefinitionsSep 27 1995Sep 27 1995This paper compares the definitions of finite-type invariants due to Ohtsuki and to Garoufalidis, showing that, residually, type 3m of the former equals type m of the latter. It also shows that type 2m Ohtsuki invariants define knot invariants of type ... More

Noise, diffusion, and hyperuniformityNov 08 2016We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles interact, ... More

Correlation length for amorphous systemsApr 30 2009Crystals and quasicrystals can be characterized by an order that is a purely geometric property of an instantaneous configuration, independent of particle dynamics or interactions. Glasses, on the other hand, are ostensibly amorphous arrangements of particles. ... More

Finite type invariants, the mapping class group and blinksDec 17 1997Dec 18 1997The goal of the present paper is to find higher genus surgery formulae for the set of finite-type invariants of homology spheres, and to develop a companion theory of finite-type invariants to be applied, in a subsequent publication, to the study of subgroups ... More

Multi-Eulerian tours of directed graphsSep 21 2015Not every graph has an Eulerian tour. But every finite, strongly connected graph has a multi-Eulerian tour, which we define as a closed path that uses each directed edge at least once, and uses edges e and f the same number of times whenever tail(e)=tail(f). ... More

Realistic Interaction-Free Detection of Objects in a ResonatorJun 27 1999Sep 12 1999We propose a realistic device for detecting objects almost without transferring a single quantum of energy to them. The device can work with an efficiency close to 100% and relies on two detectors counting both presence and absence of the objects. Its ... More

Directed Spontaneous Emission from $N$-atom Extended EnsembleFeb 15 2012Coherence and interference play crucial roles in emission and absorption of photons to and from large systems with many atoms. Confusion has arisen because nuclear X-ray physicists and atomic quantum-optics physicists do not understand one another's individual ... More

Difficulties in using the sharp neutrino spectrum at short timesApr 30 2009Final states produced by a decay have a much broader energy spectrum than the natural line width at times much shorter than the decay lifetime. This tends to render impossible the use for neutrino detection of the high value of the resonance absorption ... More

New systematics in charmless strange $B^+ \to VP$ decaysMay 17 2007Latest data on charmless strange vector-pseudoscalar $B^+$ decays now including $B^+\to \rho^+ K^o$ confirm a simple penguin model in which the gluon $G$ in an initial $\bar s u G$ state fragments equally into $u \bar u$, $d \bar d$ and $s \bar s$ and ... More

Physics of Debye-Waller FactorsMay 03 2004This note has no new results and is therefore not intended to be submitted to a "research" journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. The Debye-Waller factor is the ratio of the ... More

Experimental Challenges for QCD - The past and the futureDec 31 2002Jan 02 2003The past leaves the surprising experimental successes of the simple constituent quark model to be expained by QCD. Surprising agreement with experiment from simple Sakharov-Zeldovich model (1966) having quarks with effective masses and hyperfine interaction. ... More

Systematics of Large Axial Vector Meson Production in Heavy Flavor Weak DecaysNov 18 2000Jun 05 2001Branching ratios observed for $D$ and B decays to final states $a_1(1260)^{\pm} X$ are comparable to those for corresponding decays to $\pi^{\pm} X$ and $\rho^{\pm} X$ and much larger than those for all other decays. Implications are discussed of a "vector-dominance ... More

CP violation difference in $B^o$ and $B^\pm$ decays explained No tree-penguin interference in $B^+ \to K^+π^o$Aug 25 2006Sep 25 2006A new experimental analysis of $B\to K\pi$ decays provides finite experimental values for the contributions from interference terms between the dominant penguin amplitude and the color-favored and color-suppressed tree amplitudes. These results can explain ... More

Why pentaquarks are seen in some experiments and not in othersJan 23 2005The $\Theta^+$ Pentaquark is a Very narrow $\Gamma \approx 1$ MeV KN Resonance. Why do some experiments see it and others do not? The lowest quark configuration that can describe it is exotic $uudd \bar s$. Why have no exotics been seen before? Is this ... More