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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

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

Logic Column 16: Higher-Order Abstract Syntax: Setting the Record StraightJul 31 2006This article responds to a critique of higher-order abstract syntax appearing in Logic Column 14, ``Nominal Logic and Abstract Syntax'', cs.LO/0511025.

On Equivalence and Canonical Forms in the LF Type TheoryOct 11 2001Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of definitional equality are based on a confluent, strongly-normalizing notion ... 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 IV: Inductive TypesJan 04 2018Jul 18 2018This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of indexed cubical ... 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

Algebraic Foundations of Proof RefinementMar 15 2017We contribute a general apparatus for dependent tactic-based proof refinement in the LCF tradition, in which the statements of subgoals may express a dependency on the proofs of other subgoals; this form of dependency is extremely useful and can serve ... 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

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

A Monadic Formalization of ML5Sep 14 2010ML5 is a programming language for spatially distributed computing, based on a Curry-Howard correspondence with the modal logic S5. Despite being designed by a correspondence with S5 modal logic, the ML5 programming language differs from the logic in several ... More

Potential Impact of Global Navigation Satellite Services on Total Power HI Intensity Mapping SurveysMar 16 2018Mar 27 2019Future total-power single-dish HI intensity mapping (HI IM) surveys have the potential to provide unprecedented insight into late time ($z < 1$) cosmology that are competitive with Stage IV dark energy surveys. However, redshifts between $0 < z < 0.2$ ... More

Simulation of Systematics in Future Single-Dish HI Intensity Mapping ExperimentsMay 17 2018HI intensity mapping (IM) is an exciting new probe that could revolutionize the future of cosmology. However, the relative faintness of the HI signal when compared to foregrounds of astrophysical or terrestrial origin will make HI IM extremely challenging. ... More

Infinite $\frac{3}{2}$-generated groupsJul 11 2019Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be $\frac{3}{2}$-generated. Thompson's group ... 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.

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

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

On the partition function of the Riemann zeta function, and the Fyodorov--Hiary--Keating conjectureJun 13 2019We investigate the ``partition function'' integrals $\int_{-1/2}^{1/2} |\zeta(1/2 + it + ih)|^2 dh$ for the critical exponent 2, and the local maxima $\max_{|h| \leq 1/2} |\zeta(1/2 + it + ih)|$, as $T \leq t \leq 2T$ varies. In particular, we prove that ... 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

A Higher-Order Logic for Concurrent Termination-Preserving RefinementJan 20 2017Compiler correctness proofs for higher-order concurrent languages are difficult: they involve establishing a termination-preserving refinement between a concurrent high-level source language and an implementation that uses low-level shared memory primitives. ... More

Computational Higher Type Theory III: Univalent Universes and Exact EqualityDec 05 2017This is the third in a series of papers extending Martin-L\"of's meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higher-dimensional types. We extend this framework to include a cumulative ... More

Finite groups, 2-generation and the uniform domination numberOct 29 2018Let $G$ be a finite $2$-generated non-cyclic group. The spread of $G$ is the largest integer $k$ such that for any nontrivial elements $x_1, \ldots, x_k$, there exists $y \in G$ such that $G = \langle x_i, y\rangle$ for all $i$. The more restrictive notion ... More

On the uniform domination number of a finite simple groupOct 19 2017Apr 10 2018Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \in G$, there exists $y \in C$ with $G = \langle x,y\rangle$. Building on this deep result, we introduce ... 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

Early Lessons from a Voice-Only Interface for Finding MoviesAug 29 2018The current generation of streaming media players often allow users to speak commands (e.g., users can change the TV channel by pressing a button and saying "ESPN"). However, these devices typically support a narrow range of control- and search-oriented ... 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

Observations of Free-Free and Anomalous Microwave Emission from LDN 1622 with the 100 m Green Bank TelescopeJan 07 2015LDN 1622 has previously been identified as a possible strong source of dust-correlated Anomalous Microwave Emission (AME). Previous observations were limited by resolution meaning that the radio emission could not be compared with current generation high-resolution ... 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

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

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 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

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

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

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

Factorization for stacks and boundary complexesJun 24 2017We prove a weak factorization result on birational maps of Deligne-Mumford stacks, and deduce the following: Let $U \subset X$ be an open embedding of smooth Deligne-Mumford stacks such that $D = X-U$ is a normal crossings divisor, then the the simple ... 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.

Simulated Effects of 1/f Noise on an SKA Intensity Mapping SurveyJun 30 2016It has been proposed recently that the SKA1-MID could be used to conduct an HI intensity mapping survey that could rival upcoming Stage IV dark energy surveys. However, measuring the weak HI signal is expected to be very challenging due to contaminations ... 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

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

On the uniform spread of almost simple symplectic and orthogonal groupsMar 28 2017Jul 18 2017A group is $\frac{3}{2}$-generated if every non-identity element is contained in a generating pair. A conjecture of Breuer, Guralnick and Kantor from 2008 asserts that a finite group is $\frac{3}{2}$-generated if and only if every proper quotient of the ... More

Recognising and evaluating the effectiveness of extortion in the Iterated Prisoner's DilemmaApr 01 2019Since the introduction of zero-determinant strategies, extortionate strategies have received considerable interest. While an interesting class of strategies, the definitions of extortionate strategies are algebraically rigid, apply only to memory-one ... 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

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

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 Riemann zeta function in short intervals [after Najnudel, and Arguin, Belius, Bourgade, Radziwiłł, and Soundararajan]Apr 17 2019This is the text to accompany my Bourbaki seminar from 30th March 2019, on the maximum size of the Riemann zeta function in "almost all" intervals of length 1 on the critical line. It surveys the conjecture of Fyodorov--Hiary--Keating on the behaviour ... 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.

Floquet Topological Order in Interacting Systems of Bosons and FermionsSep 20 2016Mar 24 2017Periodically driven noninteracting systems may exhibit anomalous chiral edge modes, despite hosting bands with trivial topology. We find that these drives have surprising many-body analogs, corresponding to class A, which exhibit anomalous charge and ... 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

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

End-To-End Prediction of Emotion From Heartbeat Data Collected by a Consumer Fitness TrackerJul 16 2019Automatic detection of emotion has the potential to revolutionize mental health and wellbeing. Recent work has been successful in predicting affect from unimodal electrocardiogram (ECG) data. However, to be immediately relevant for real-world applications, ... 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

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

Moments of random multiplicative functions, I: Low moments, better than squareroot cancellation, and critical multiplicative chaosMar 20 2017We determine the order of magnitude of $\mathbb{E}|\sum_{n \leq x} f(n)|^{2q}$, where $f(n)$ is a Steinhaus or Rademacher random multiplicative function, and $0 \leq q \leq 1$. In the Steinhaus case, this is equivalent to determining the order of $\lim_{T ... 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.

Search for gas from the disintegrating rocky exoplanet K2-22bJun 20 2019Jul 09 2019[Abridged] Aims. We searched for circumplanetary sodium and ionized calcium gas around the disintegrating rocky exoplanet K2-22 b to constrain its gas-loss and sublimation processes. Methods. We observed four transits of K2-22 b with X-shooter on ESO's ... 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

Bit threads and holographic entanglement of purificationJun 14 2019Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite ... 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

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

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

Chromatic transit light curves of disintegrating rocky planetsJul 20 2018Context. Kepler observations have revealed a class of short period exoplanets, of which Kepler-1520 b is the prototype, which have comet-like dust tails thought to be the result of small, rocky planets losing mass. The shape and chromaticity of the transits ... More

Virtual knot groups and almost classical knotsJun 04 2015Dec 11 2016We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri. A virtual knot is called ... 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

Bit threads and holographic entanglement of purificationJun 14 2019Jul 09 2019Generalizing the bit thread formalism, we use convex duality to derive dual flow programs to the bipartite and multipartite holographic entanglement of purification proposals and then prove several inequalities using these constructions. In the multipartite ... 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.

Floquet topological phases with symmetry in all dimensionsOct 21 2016Dec 16 2016Dynamical systems may 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 several ... 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

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

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

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

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

Estimating the fidelity of T gates using standard interleaved randomized benchmarkingAug 09 2016Dec 20 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

Fault-Tolerant Logical Gates in the IBM Quantum ExperienceJun 06 2018Jan 30 2019Quantum computers will require encoding of quantum information to protect them from noise. Fault-tolerant quantum computing architectures illustrate how this might be done but have not yet shown a conclusive practical advantage. Here we demonstrate that ... More