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Computational Higher Type Theory II: Dependent Cubical RealizabilityJun 30 2016This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I, and extend ... More

A Separation Logic for Concurrent Randomized ProgramsFeb 08 2018Nov 21 2018We present Polaris, a concurrent separation logic with support for probabilistic reasoning. As part of our logic, we extend the idea of coupling, which underlies recent work on probabilistic relational logics, to the setting of programs with both probabilistic ... More

Computational Higher Type Theory II: Dependent Cubical RealizabilityJun 30 2016Apr 26 2017This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I, and extend ... More

Parametric Cubical Type TheoryJan 02 2019We exhibit a computational type theory which combines the higher-dimensional structure of cartesian cubical type theory with the internal parametricity primitives of parametric type theory, drawing out the similarities and distinctions between the two ... More

Computational Higher Type Theory II: Dependent Cubical RealizabilityJun 30 2016Oct 04 2016This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I, and extend ... More

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

Guarded Computational Type TheoryApr 24 2018Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until now, it has been ... More

Entropy Rates of the Multidimensional Moran Processes and GeneralizationsJan 13 2014The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The entropy rate ... More

A Population-centric Approach to the Beauty Contest GameMay 07 2010Dec 13 2014An population-centric analysis for a version of the p-beauty contest game is given for the two-player, finite population, and infinite population cases. Winning strategies are characterized in terms of iterative thinking relative to the population. To ... More

The Inherent Randomness of Evolving PopulationsMar 08 2013Mar 27 2013The entropy rates of the Wright-Fisher process, the Moran process, and generalizations are computed and used to compare these processes and their dependence on standard evolutionary parameters. Entropy rates are measures of the variation dependent on ... More

Escort Evolutionary Game TheoryNov 09 2009Feb 24 2012A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations ... More

A Note on the Uniform Kan Condition in Nominal Cubical SetsJan 23 2015Bezem, Coquand, and Huber have recently given a constructively valid model of higher type theory in a category of nominal cubical sets satisfying a novel condition, called the uniform Kan condition (UKC), which generalizes the standard cubical Kan condition ... More

The scissors mode from a different perspectiveJan 05 2015Apr 09 2015The scissors mode, a magnetic dipole excitation-mainly orbital is usually discussed in terms of a transition from a J=0^{+} ground state to a J=1^{+} excited state. This is understandable because it follows from the way the experiment is performed-e.g. ... More

Wave functions of the Q.Q interaction in terms of unitary 9-j coefficientsJun 19 2013Mar 20 2015We obtain wave functions for 2 protons and 2 neutrons in the g_{9/2} shell expressed as column vectors with amplitudes D(J_{p},J_{n}). When we use a quadrupole-quadrupole interaction (Q.Q) we get, in many cases, a very strong overlap with wave functions ... More

Computational Higher Type Theory I: Abstract Cubical RealizabilityApr 29 2016Jun 14 2016Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in terms of computation. ... More

Stability of Anomalous Floquet Edge UnitariesSep 20 2016It has recently been shown that periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We obtain many-body versions of such drives, corresponding to class A, which exhibit anomalous ... More

Competitive Parallelism: Getting Your Priorities RightJul 10 2018Multi-threaded programs have traditionally fallen into one of two domains: cooperative and competitive. These two domains have traditionally remained mostly disjoint, with cooperative threading used for increasing throughput in compute-intensive applications ... More

Selective MemoizationJun 02 2011This paper presents language techniques for applying memoization selectively. The techniques provide programmer control over equality, space usage, and identification of precise dependences so that memoization can be applied according to the needs of ... More

MUSE CSP: An Extension to the Constraint Satisfaction ProblemNov 01 1996This paper describes an extension to the constraint satisfaction problem (CSP) called MUSE CSP (MUltiply SEgmented Constraint Satisfaction Problem). This extension is especially useful for those problems which segment into multiple sets of partially shared ... More

The RedPRL Proof Assistant (Invited Paper)Jul 05 2018RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish behavioral ... More

Inferring the time-varying functional connectivity of large-scale computer networks from emitted eventsFeb 12 2018We consider the problem of inferring the functional connectivity of a large-scale computer network from sparse time series of events emitted by its nodes. We do so under the following three domain-specific constraints: (a) non-stationarity of the functional ... More

Discovery Potential for GMSB Supersymmetry in ATLAS using the $Zγ+ \not E_T$ Final State at a center of mass energy of $\sqrt{s}$=10 \TeVOct 21 2009We have studied the sensitivity of the ATLAS detector for supersymmetric neutralino signals in the $Z\gamma +\notE_{T}$ final state in a GMSB model in which the Higgsino-like neutralino is NLSP. This study considers the reaction of $pp \ra \tilde{\chi}^{0}_{1} ... More

Quadratic invariants for discrete clusters of weakly interacting wavesDec 13 2012May 13 2013We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic ... More

Morse Matchings on a HypersimplexNov 07 2012We present a family of complete acyclic Morse matchings on the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. In a future paper we will utilize these matchings to ... More

Information Geometry and Evolutionary Game TheoryNov 09 2009The Shahshahani geometry of evolutionary game theory is realized as the information geometry of the simplex, deriving from the Fisher information metric of the manifold of categorical probability distributions. Some essential concepts in evolutionary ... More

The Replicator Equation as an Inference DynamicNov 09 2009May 03 2010The replicator equation is interpreted as a continuous inference equation and a formal similarity between the discrete replicator equation and Bayesian inference is described. Further connections between inference and the replicator equation are given ... More

On instanton homology of corks W_nApr 18 2013We consider a family of corks, denoted $W_n$, constructed by Akbulut and Yasui. Each cork gives rise to an exotic structure on a smooth 4-manifold via a twist $\tau$ on its boundary $\Sigma_n = \partial W_n$. We compute the instanton Floer homology of ... More

PDEs and hypercomplex analytic functionsSep 07 2016Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.

Astro2020: Molecular Masers as Probes of the Dynamic Atmospheres of Dying StarsMar 13 2019More than half of the dust and heavy element enrichment in galaxies originates from the winds and outflows of evolved, low-to-intermediate mass stars on the asymptotic giant branch (AGB). However, numerous details of the physics of late-stage stellar ... More

Inferring Fitness in Finite Populations with Moran-like dynamicsMar 19 2013Oct 23 2013Biological fitness is not an observable quantity and must be inferred from population dynamics. Bayesian inference applied to the Moran process and variants yields a robust inference method that can infer fitness in populations evolving via a Moran dynamic ... More

Explaining quantum correlations through evolution of causal modelsAug 10 2016May 01 2017We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables ... More

Explaining quantum correlations through evolution of causal modelsAug 10 2016We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multi-objective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables ... More

Minor arcs, mean values, and restriction theory for exponential sums over smooth numbersAug 07 2014We investigate exponential sums over those numbers $\leq x$ all of whose prime factors are $\leq y$. We prove fairly good minor arc estimates, valid whenever $\log^{3}x \leq y \leq x^{1/3}$. Then we prove sharp upper bounds for the $p$-th moment of (possibly ... More

A note on the maximum of the Riemann zeta function, and log-correlated random variablesApr 02 2013In recent work, Fyodorov and Keating conjectured the maximum size of $|\zeta(1/2+it)|$ in a typical interval of length O(1) on the critical line. They did this by modelling the zeta function by the characteristic polynomial of a random matrix; relating ... More

Converting Basic D3 Charts into Reusable Style TemplatesSep 17 2016Sep 20 2016We present a technique for converting a basic D3 chart into a reusable style template. Then, given a new data source we can apply the style template to generate a chart that depicts the new data, but in the style of the template. To construct the style ... More

Homology Representations Arising from a HypersimplexAug 30 2011We present a complete acyclic matching of the Hasse diagram associated with the face lattice of a hypersimplex. Since a hypersimplex is a convex polytope, there is a natural way to form a CW complex from its faces. We will then utilize this matching along ... More

Bar constructions and Quillen homology of modules over operadsFeb 16 2008Sep 27 2009We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing ... More

Stationary Stability for Evolutionary Dynamics in Finite PopulationsNov 05 2013Feb 17 2015We demonstrate a vast expansion of the theory of evolutionary stability to finite populations with mutation, connecting the theory of the stationary distribution of the Moran process with the Lyapunov theory of evolutionary stability. We define the notion ... More

A Casson-Lin type invariant for linksJul 06 2009Nov 23 2009We define an integer valued invariant for two-component links in S^3 by counting projective SU(2) representations of the link group having non-trivial second Stiefel-Whitney class. We show that our invariant is, up to sign, the linking number of the link. ... More

Homotopy theory of modules over operads in symmetric spectraDec 31 2007May 15 2014We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.

Science with an ngVLA: Stellar Activity on Red Giant and Supergiant Stars: Mass Loss and the Evolution of the Stellar DynamoOct 22 2018In this Chapter we examine the role of the ngVLA to further our understanding of the different manifestations of convective or turbulence-driven stellar activity on red giant and supergiant stars. The combination of high spatial resolution and high sensitivity ... More

Pickands' constant $H_α$ does not equal $1/Γ(1/α)$, for small $α$Apr 22 2014Pickands' constants $H_{\alpha}$ appear in various classical limit results about tail probabilities of suprema of Gaussian processes. It is an often quoted conjecture that perhaps $H_{\alpha} = 1/\Gamma(1/\alpha)$ for all $0 < \alpha \leq 2$, but it is ... More

Sharp conditional bounds for moments of the Riemann zeta functionMay 20 2013We prove, assuming the Riemann Hypothesis, that \int_{T}^{2T} |\zeta(1/2+it)|^{2k} dt \ll_{k} T log^{k^{2}} T for any fixed k \geq 0 and all large T. This is sharp up to the value of the implicit constant. Our proof builds on well known work of Soundararajan, ... More

Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbersAug 29 2012We prove Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for the y-smooth numbers less than x, on the range log^{K}x \leq y \leq x. This improves on the range \exp{log^{2/3 + \epsilon}x} \leq y \leq x that was previously available. ... More

Can the Sierpinski graph be embedded in the Hamming graph?Sep 21 2016The (generalized & expanded) Sierpinski graph, S(n,m), and the Hamming graph have the same set of vertices (n-tuples from the set {0,1,...,m-1}. The edges of both are (unordered) pairs of vertices. Each set of edges is defined by a different property ... More

Instanton Floer homology for two-component linksJan 22 2010Sep 25 2011For any link of two components in an integral homology sphere, we define an instanton Floer homology whose Euler characteristic is the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka instanton ... More

The edge-isorperimetric problem on Sierpinski graphsOct 06 2016Some families of graphs, such as the n-cubes and Sierpinski gaskets, are self-similar. In this paper we show how such recursive structure can be used systematically to prove isoperimetric theorems.

Periodic Table for Floquet Topological InsulatorsMar 22 2016Aug 16 2016Dynamical phases with novel topological properties are known to arise in driven systems of free fermions. In this paper, we obtain a `periodic table' to describe the phases of such time-dependent systems, generalizing the periodic table for static topological ... More

Floquet topological phases with symmetry in all dimensionsOct 21 2016Dynamical systems are known to host a number of remarkable symmetry-protected phases that are qualitatively different from their static analogs. In this work, we consider the phase space of symmetry-respecting unitary evolutions in detail and identify ... More

Abelian Floquet symmetry-protected topological phases in one dimensionFeb 25 2016Sep 06 2016Time-dependent systems have recently been shown to support novel types of topological order that cannot be realised in static systems. In this paper, we consider a range of time-dependent, interacting systems in one dimension that are protected by an ... More

Entropic Equilibria Selection of Stationary Extrema in Finite PopulationsMay 08 2015We propose the entropy of random Markov trajectories originating and terminating at a state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov ... More

The Edge-Isoperimetric Problem on Sierpinski Graphs: Final ResolutionFeb 23 2018This paper completes the project started in [10]; to solve the edge-isoperimetric problem on the (generalized and extended) Sierpinski graph, S(n,m). We prove that initial segments of lexicographic order are solutions of the EIP for all n,m.

Astro2020: Unlocking the Secrets of Late-Stage Stellar Evolution and Mass Loss through Radio Wavelength ImagingMar 13 2019During the late phases of evolution, low-to-intermediate mass stars like our Sun undergo periods of extensive mass loss, returning up to 80% of their initial mass to the interstellar medium. This mass loss profoundly affects the stellar evolutionary history, ... More

Incentive Processes in Finite PopulationsJun 11 2013Dec 03 2013We define the incentive process, a natural generalization of the Moran process incorporating evolutionary updating mechanisms corresponding to well-known evolutionary dynamics, such as the logit, projection, and best-reply dynamics. Fixation probabilities ... More

J=0 T=1 Pairing Interaction Selection RulesAug 18 2014May 10 2015Wave functions arising form a pairing Hamiltonian E(0) i,e, one in which the interaction is only between J=0^{+}T=1 pairs, lead to magnetic dipole and Gamow-Teller transition rates that are much larger than those from an interaction E(J_{max}) in which ... More

On finding many solutions to S-unit equations by solving linear equations on averageAug 18 2011We give improved lower bounds for the number of solutions of some $S$-unit equations over the integers, by counting the solutions of some associated linear equations as the coefficients in those equations vary over sparse sets. This method is quite conceptually ... More

Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative functionDec 01 2010Feb 22 2013We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We present an extended ... More

On a paper of K. Soundararajan on smooth numbers in arithmetic progressionsMar 10 2011In a recent paper, K. Soundararajan showed, roughly speaking, that the integers smaller than x whose prime factors are less than y are asymptotically equidistributed in arithmetic progressions to modulus q, provided that y^{4\sqrt{e}-\delta} \geq q and ... More

On the limit distributions of some sums of a random multiplicative functionDec 01 2010We study sums of a random multiplicative function; this is an example, of number-theoretic interest, of sums of products of independent random variables (chaoses). Using martingale methods, we establish a normal approximation for the sum over those n ... More

A Bayesian Deep Learning Framework for End-To-End Prediction of Emotion from HeartbeatFeb 08 2019Automatic prediction of emotion promises to revolutionise human-computer interaction. Recent trends involve fusion of multiple modalities - audio, visual, and physiological - to classify emotional state. However, practical considerations 'in the wild' ... More

The Range of a Steiner OperationAug 27 2016This paper answers a fundamental question in the theory of Steiner operations (StOps) as defined and studied in the monograph, "Global Methods for Combinatorial Isoperimetric Problems" (GMCIP). StOps are morphisms for combinatorial isoperimetric problems, ... More

Homotopy theory of modules over operads and non-Sigma operads in monoidal model categoriesDec 31 2007Jun 03 2009This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.

Alexander invariants for virtual knotsSep 04 2014Apr 09 2015Given a virtual knot $K$, we construct a group $VG_K$ called the virtual knot group, and we use the elementary ideals of $VG_K$ to define invariants of $K$ called the virtual Alexander invariants. For instance, associated to the $k=0$ ideal is a polynomial ... More

The star formation histories of low surface brightness galaxiesSep 23 1999We have performed deep imaging of a diverse sample of 26 low surface brightness galaxies (LSBGs) in the optical and the near-infrared. Using stellar population synthesis models, we find that it is possible to place constraints on the ratio of young to ... More

CARMA CO(J = 2 - 1) Observations of the Circumstellar Envelope of BetelgeuseJun 19 2012We report radio interferometric observations of the 12C16O 1.3 mm J = 2-1 emission line in the circumstellar envelope of the M supergiant Alpha Ori and have detected and separated both the S1 and S2 flow components for the first time. Observations were ... More

Holographic Renormalization for Asymptotically Lifshitz SpacetimesJul 28 2011Sep 07 2011A variational formulation is given for a theory of gravity coupled to a massive vector in four dimensions, with Asymptotically Lifshitz boundary conditions on the fields. For theories with critical exponent z=2 we obtain a well-defined variational principle ... More

Conditions for the importance of inelastic losses in photoemissionDec 04 2001It is shown that for materials near the metal insulator transition, inelastic losses can give rise to substantial changes on a scale of 10-100 meV in the observed lineshape compared to the intrinsic spectral function of an electron photoemitted from a ... More

Additive decompositions of sets with restricted prime factorsSep 03 2013We investigate sumset decompositions of quite general sets with restricted prime factors. We manage to handle certain sets, such as the smooth numbers, even though they have little sieve amenability, and conclude that these sets cannot be written as a ... More

One Dimensional Dynamical Models of the Carina Nebula BubbleDec 16 2008We have tested the two main theoretical models of bubbles around massive star clusters, Castor et al. and Chevalier & Clegg, against observations of the well studied Carina Nebula. The Castor et al. theory over-predicts the X-ray luminosity in the Carina ... More

Lower bounds for the variance of sequences in arithmetic progressions: primes and divisor functionsFeb 05 2016We develop a general method for lower bounding the variance of sequences in arithmetic progressions mod $q$, summed over all $q \leq Q$, building on previous work of Liu, Perelli, Hooley, and others. The proofs lower bound the variance by the minor arc ... More

Estimating the fidelity of T gates using standard interleaved randomized benchmarkingAug 09 2016Randomized benchmarking (RB) is an important protocol for robustly characterizing the error rates of quantum gates. The technique is typically applied to the Clifford gates since they form a group that satisfies a convenient technical condition of forming ... More

Homotopy completion and topological Quillen homology of structured ring spectraFeb 07 2011Feb 06 2013Working in the context of symmetric spectra, we describe and study a homotopy completion tower for algebras and left modules over operads in the category of modules over a commutative ring spectrum (e.g., structured ring spectra). We prove a strong convergence ... More

A nilpotent Whitehead theorem for TQ-homology of structured ring spectraJun 26 2018Oct 12 2018The aim of this short paper is to prove a TQ-Whitehead theorem for nilpotent structured ring spectra. We work in the framework of symmetric spectra and algebras over operads in modules over a commutative ring spectrum. Our main result can be thought of ... More

TEXES Observations of M Supergiants: Dynamics and Thermodynamics of Wind AccelerationJun 25 2009We have detected [Fe II] 17.94 um and 24.52 um emission from a sample of M supergiants using TEXES on the IRTF. These low opacity emission lines are resolved at R = 50, 000 and provide new diagnostics of the dynamics and thermodynamics of the stellar ... More

Topological Quillen localization of structured ring spectraNov 15 2018Jan 23 2019The aim of this short paper is to construct a TQ-localization functor on algebras over a spectral operad O, in the general case where no connectivity assumptions are made on the O-algebras, and to establish the associated TQ-local homotopy theory as a ... More

Higher homotopy excision and Blakers-Massey theorems for structured ring spectraFeb 19 2014May 05 2016Working in the context of symmetric spectra, we prove higher homotopy excision and higher Blakers-Massey theorems, and their duals, for algebras and left modules over operads in the category of modules over a commutative ring spectrum (e.g., structured ... More

The SU(N) Casson-Lin invariants for linksJun 11 2015Dec 03 2015We introduce the $SU(N)$ Casson-Lin invariants for links $L$ in $S^3$ with more than one component. Writing $L = \ell_1 \cup \cdots \cup \ell_n$, we require as input an $n$-tuple $(a_1,\ldots, a_n) \in {\mathbb Z}^n$ of labels, where $a_j$ is associated ... More

Obstacle Tower: A Generalization Challenge in Vision, Control, and PlanningFeb 04 2019The rapid pace of research in Deep Reinforcement Learning has been driven by the presence of fast and challenging simulation environments. These environments often take the form of games; with tasks ranging from simple board games, to classic home console ... More

Small-N collisional dynamics III: The battle for the realm of not-so-small-NJul 06 2017In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that produce direct ... More

Ohmic Losses in Valence-band Photoemission ExperimentsAug 14 2000Photoemission experiments involve the motion of an electron near a conducting surface. This necessarily generates heat by ohmic losses from eddy currents. This inelastic scattering of the electrons will result in a downward shift in observed spectra. ... More

Theory of Percolative Conduction in Polycrystaline High-temperature SuperconductorsNov 17 1998Jul 01 1999Conduction in bulk polycrystalline high-T$_c$ superconductors with relatively high critical currents has been shown to be percolative. This phenomenon is due to weak links at grain boundaries. These weak links are the major limiting factor for technological ... More

The Chern-Simons state for the non-diagonal Bianchi IX modelFeb 03 1998The Bianchi IX mixmaster model is quantized in its non-diagonal form, imposing spatial diffeomorphism, time reparametrization and Lorentz invariance as constraints on physical state vectors before gauge-fixing. The result turns out to be different from ... More

Exact quantum states for the diagonal Bianchi type IX model with negative cosmological constantMay 17 1996Quantum states of the diagonal Bianchi type IX model with negative cosmological constant $\Lambda$ are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed earlier for $\Lambda>0$ ... More

Triad representation of the Chern-Simons state in quantum gravityMar 30 2000We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed ... More

c-axis Josephson Tunneling in Twinned YBCO CrystalsJul 02 1999Jan 13 2000Josephson tunneling between YBCO and Pb with the current flowing along the c-axis of the YBCO is persumed to come from an s-wave component of the superconductivity of the YBCO. Experiments on multi-twin samples are not entirely consistent with this hypothesis. ... More

Theory of Josephson tunneling along the c-axis of YBCOMar 10 1998The existence of Josephson tunneling has been demonstrated between YBa$_2$Cu$_3$O$_{7-\delta}$ and Pb with the current flowing along the c-axis of YBa$_2$Cu$_3$O$_{7-\delta}$. This is presumed to come from an s-wave component of the superconductivity ... More

Physical states of Bianchi type IX quantum cosmologies described by the Chern-Simons functionalMar 18 1996A class of exact solutions of the Wheeler-DeWitt equation for diagonal Bianchi type IX cosmologies with cosmological constant is derived in the metric representation. This class consists of all the ``topological solutions'' which are associated with the ... More

Detecting Concepts Crucial for Success in Mathematics Courses from Knowledge State-based Placement DataDec 02 2013We show that individual topics and skills can have a dramatic effect on the outcomes of students in various mathematics courses at the University of Illinois. Data from the placement program at Illinois associates a knowledge state, a subset of 182 items ... More

Orderings of weakly correlated random variables, and prime number races with many contestantsSep 24 2015We investigate the race between prime numbers in many residue classes modulo $q$, assuming the standard conjectures GRH and LI. Among our results we exhibit, for the first time, prime races modulo $q$ with $n$ competitor classes where the biases do not ... More

On H-Spaces and a Congruence of Catalan NumbersDec 12 2016Jul 09 2017For $p$ an odd prime and $F$ the cyclic group of order $p$, we show that the number of conjugacy classes of embeddings of $F$ in $SU(p)$ such that no element of $F$ has 1 as an eigenvalue is $(1+C_{p-1})/p$, where $C_{p-1}$ is a Catalan number. We prove ... More

Derived Koszul duality and TQ-homology completion of structured ring spectraFeb 24 2015Jul 23 2015Working in the context of symmetric spectra, we consider any higher algebraic structures that can be described as algebras over an operad O. We prove that the fundamental adjunction comparing O-algebra spectra with coalgebra spectra over the associated ... More

Basic Experiment Planning via Information Metrics: the RoboMendel ProblemOct 17 2012In this paper we outline some mathematical questions that emerge from trying to "turn the scientific method into math". Specifically, we consider the problem of experiment planning (choosing the best experiment to do next) in explicit probabilistic and ... More

Effective Lifetimes of $B_s$ Decays and their Constraints on the $B_s^0$-$\bar B_s^0$ Mixing ParametersSep 23 2011Measurements of the effective lifetimes of $B_s$-meson decays, which only require untagged rate analyses, allow us to probe the width difference $\Delta\Gamma_s$ and the CP-violating phase $\phi_s$ of $B^0_s$-$\bar B^0_s$ mixing. We point out that the ... More

A Fresh Look at B_{s,d} -> pi pi, pi K, K K DecaysDec 03 2010Using updated measurements and SU(3)-breaking form factors, we have a detailed look at the B_d -> pi^+ pi^-, B_s -> K^+ K^- and B_d -> pi^\mp K^\pm, B_s -> pi^\pm K^\mp systems. The corresponding decays are related to each other by the U-spin symmetry ... More

A Flow-aware MAC Protocol for a Passive Optical Metropolitan Area NetworkFeb 17 2011The paper introduces an original MAC protocol for a passive optical metropolitan area network using time-domain wavelength interleaved networking (TWIN)% as proposed recently by Bell Labs . Optical channels are shared under the distributed control of ... More

From Regular to Context Free to Mildly Context Sensitive Tree Rewriting Systems: The Path of Child Language AcquisitionNov 04 1994Current syntactic theory limits the range of grammatical variation so severely that the logical problem of grammar learning is trivial. Yet, children exhibit characteristic stages in syntactic development at least through their sixth year. Rather than ... More

Photonics Explorer - An European program to foster science education with hands-on experimentsMay 04 2012The Photonics Explorer program aims to equip science teachers at Europe's secondary schools free-of-charge with up-to-date educational material to really engage, excite and educate students about the fascination of working with light.

Vector bundles and $SO(3)$ invariants for elliptic surfaces IJul 14 1993This paper is the first in a series of three devoted to the smooth classification of simply connected elliptic surfaces. The method is to compute some coefficients of Donaldson polynomials of $SO(3)$ invariants whose second Stiefel-Whitney class is transverse ... More

A Robust Approximation to a Lambert-Type FunctionApr 08 2015The function $y = g(x) = \mathrm{log}\big(W(e^x)\big)$, where $W()$ denotes the Lambert W function, is the solution to the equation $y + e^y = x$. It appears in various problem situations, for instance the calculation of current-voltage curves for solar ... More

FC-families, and improved bounds for Frankl's ConjectureFeb 13 2007A family of sets F is said to be union-closed if A \cup B is in F for every A and B in F. Frankl's conjecture states that given any finite union-closed family of sets, not all empty, there exists an element contained in at least half of the sets. Here ... More