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Bayesian Layers: A Module for Neural Network UncertaintyDec 10 2018Dec 11 2018We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with layers capturing uncertainty over weights (Bayesian neural nets), pre-activation units (dropout), activations ... More

Graph Convolutional Transformer: Learning the Graphical Structure of Electronic Health RecordsJun 11 2019Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that utilizing the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) ... More

Bayesian Layers: A Module for Neural Network UncertaintyDec 10 2018Mar 05 2019We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction over deterministic ... More

Graph Convolutional Transformer: Learning the Graphical Structure of Electronic Health RecordsJun 11 2019Jun 28 2019Effective modeling of electronic health records (EHR) is rapidly becoming an important topic in both academia and industry. A recent study showed that utilizing the graphical structure underlying EHR data (e.g. relationship between diagnoses and treatments) ... More

Analyzing the Role of Model Uncertainty for Electronic Health RecordsJun 10 2019In medicine, both ethical and monetary costs of incorrect predictions can be significant, and the complexity of the problems often necessitates increasingly complex models. Recent work has shown that changing just the random seed is enough for otherwise ... More

Deep Learning with Apache SystemMLFeb 08 2018Enterprises operate large data lakes using Hadoop and Spark frameworks that (1) run a plethora of tools to automate powerful data preparation/transformation pipelines, (2) run on shared, large clusters to (3) perform many different analytics tasks ranging ... More

Measuring Calibration in Deep LearningApr 02 2019The reliability of a machine learning model's confidence in its predictions is critical for highrisk applications. Calibration-the idea that a model's predicted probabilities of outcomes reflect true probabilities of those outcomes-formalizes this notion. ... More

Lecture Notes on Randomized Linear AlgebraAug 16 2016These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.

Complexity in the Immune SystemOct 15 2003The immune system is a real-time example of an evolving system that navigates the essentially infinite complexity of protein sequence space. How this system responds to disease and vaccination is discussed. Of particular focus is the case when vaccination ... More

Comment on ``Diffusion of Ionic Particles in Charged Disordered Media''Feb 13 1999Jul 06 1999This comment points out that simulation results of Mehrabi and Sahimi [Phys. Rev. Lett. 82, 735 (1999)] are iconsistent with exact bounds, renormalization group calculations, and previous numerical simulations.

Disclination Asymmetry in Two-Dimensional Nematic Liquid Crystals with Unequal Frank ConstantsJun 19 1996The behavior of a thin film of nematic liquid crystal with unequal Frank constants is discussed. Distinct Frank constants are found to imply unequal core energies for $+1/2$ and $-1/2$ disclinations. Even so, a topological constraint is shown to ensure ... More

San Pedro Meeting on Wide Field Variability Surveys: Some Concluding CommentsFeb 23 2017This is a written version of the closing talk at the 22nd Los Alamos Stellar pulsation conference on wide field variability surveys. It comments on some of the issues which arise from the meeting. These include the need for attention to photometric standardization ... More

Metrology with entangled coherent states - a quantum scaling paradoxJul 10 2013There has been much interest in developing phase estimation schemes which beat the so-called Heisenberg limit, i.e., for which the phase resolution scales better than 1/n, where n is a measure of resources such as the average photon number or the number ... More

Comment on "An Arrow of Time Operator for Standard Quantum Mechanics" - a sign of the time!Feb 19 2008Feb 20 2008It is shown that the `arrow of time' operator, M_F, recently suggested by Strauss et al., in arXiv:0802.2448v1 [quant-ph], is simply related to the sign of the canonical `time' observable, T (apparently first introduced by Holevo). In particular, the ... More

Prior information: how to circumvent the standard joint-measurement uncertainty relationSep 10 2003Mar 30 2004The principle of complementarity is quantified in two ways: by a universal uncertainty relation valid for arbitrary joint estimates of any two observables from a given measurement setup, and by a general uncertainty relation valid for the_optimal_ estimates ... More

Correlation Distance and Bounds for Mutual InformationJul 10 2013The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information between pairs ... More

Complementary contributions of indeterminism and signalling to quantum correlationsJun 18 2010Dec 21 2010Simple quantitative measures of indeterminism and signalling, $I$ and $S$, are defined for models of statistical correlations. It is shown that any such model satisfies a generalised Bell-type inequality, with tight upper bound B(I,S). This upper bound ... More

Reply to Comment by Galapon on 'Almost-periodic time observables for bound quantum systems'Nov 20 2008In a recent paper [1] (also at http://lanl.arxiv.org/abs/0803.3721), I made several critical remarks on a 'Hermitian time operator' proposed by Galapon [2] (also at http://lanl.arxiv.org/abs/quant-ph/0111061). Galapon has correctly pointed out that remarks ... More

Random quantum correlations and density operator distributionsFeb 19 1998Jul 24 1998Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique unitarily-invariant ... More

Decoherence due to three-body loss and its effect on the state of a Bose-Einstein condensateAug 16 2002A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large number limit only coherent states remain pure for times longer than the decoherence ... More

When are two Coxeter orbifolds diffeomorphic?Jun 25 2013Nov 15 2013One can define what it means for a compact manifold with corners to be a "contractible manifold with contractible faces." Two combinatorially equivalent, contractible manifolds with contractible faces are diffeomorphic if and only if their 4-dimensional ... More

The Nebulosity and Distance of the Cepheid RS PuppisApr 01 2008Adopting a distance for RS Pup derived from a period-luminosity relation based on Cepheid parallaxes, it is shown that the phase-lag observations of the surrounding nebulosity by Kervella et al. are well fitted by a model of an equatorial disc at an angle ... More

Comment on "Gleason-Type Theorem for Projective Measurements, Including Qubits" by F. De ZelaNov 02 2016Nov 07 2016It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions related to continuity and the existence of 'eigenstates'. This amounts to ... More

Exact uncertainty relations: technical detailsMar 14 2001Jul 30 2001The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The significance of this "exact" uncertainty relation ... More

Comment on "Gleason-Type Theorem for Projective Measurements, Including Qubits" by F. De ZelaNov 02 2016Nov 30 2016It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions related to continuity and the existence of 'eigenstates'. This amounts to ... More

Galactic and Extragalactic Distance Scales: The Variable Star ProjectJun 18 2008This paper summaries the status of a large project to improve distance scales of various classes of variable stars. This is being carried out by a large group in Cape Town, Japan, England and the USA. The results are illustrated by giving the distances ... More

BVRI Photometry of SN 2013ej in M74May 20 2014Jun 23 2014I present BVRI photometry of the type IIP supernova 2013ej in M74 from 3 to 182 days after the explosion. These photometric measurements and spectroscopic data from the literature are combined via the expanding photosphere method to estimate the distance ... More

A Search for Eclipsing Binary Lightcurve Variations among MACHO Project Lightcurves of 3256 Fundamental-Mode RR Lyrae Variables in the Galactic BulgeJun 03 2011The MACHO Project collected photometry of many RR Lyrae stars from its observations of the Milky Way's bulge. We examined the lightcurves of 3256 stars identified as RRab Lyr variables by \cite{Kund2008}, subtracting an empirical model of the pulsation ... More

High Resolution X-ray Spectroscopy of Galaxies and Clusters with AXAFOct 21 1998We review the high resolution X-ray spectroscopy capabilities of the AXAF observatory focusing on the High Energy Transmission Grating (HETG). As part of the Guaranteed Time Observation (GTO) program, the HETG science team will observe both elliptical ... More

Trust-free verification of steering: why you can't cheat a quantum refereeJun 01 2016It was believed until recently that the verification of quantum entanglement and quantum steering, between two parties, required trust in at least one of the parties and their devices, in contrast to the verification of Bell nonseparability. It has since ... More

Optimal estimates and joint measurement uncertainty relationsFeb 05 2005Often, one would like to determine some observable A, but can only measure some (hopefully related) observable M. This can arise, for example, in quantum eavesdropping, or when the research lab budget isn't large enough for that 100% efficient photodetector. ... More

Universal geometric approach to uncertainty, entropy and informationMar 30 1999Mar 20 2000It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a preferred and ... More

Comment on "Conceptual Inadequacy of Shannon Information ..." by C. Brukner and A. ZeilingerJul 31 2000It is pointed out that the case for Shannon entropy and von Neumann entropy, as measures of uncertainty in quantum mechanics, is not as bleak as suggested in quant-ph/0006087. The main argument of the latter is based on one particular interpretation of ... More

Right-angularity, flag complexes, asphericity. \ Criteria for asphericity: corrigenda for "Right-angularity, flag complexes, asphericity"Feb 23 2011Jan 22 2015The "polyhedral product functor" produces a space from a simplicial complex L and a collection of pairs of spaces, {(A(i),B(i))}, where i ranges over the vertex set of L. We give necessary and sufficient conditions for the resulting space to be aspherical. ... More

A Statistical Mechanical Approach to Combinatorial ChemistrySep 16 2000An analogy between combinatorial chemistry and Monte Carlo computer simulation is pursued. Examples of how to design libraries for both materials discovery and protein molecular evolution are given. For materials discovery, the concept of library redesign, ... More

Comment on 'Non-realism: deep thought or soft option?', by N. GisinSep 01 2009Nov 01 2009It is briefly demonstrated that Gisin's so-called 'locality' assumption [arXiv:0901.4255] is in fact equivalent to the existence of a local deterministic model. Thus, despite Gisin's suggestions to the contrary, 'local realism' in the sense of Bell is ... More

Almost-periodic time observables for bound quantum systemsMar 26 2008Apr 22 2008It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the harmonic oscillator). ... More

Superselection from canonical constraintsApr 21 2004Jun 23 2004The evolution of both quantum and classical ensembles may be described via the probability density P on configuration space, its canonical conjugate S, and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is, of course, equivalent ... More

Algebra for generalised quantum observablesFeb 02 2003Sep 16 2003Generalised observables (POM observables) are necessary for representing all possible measurements on a quantum system. Useful algebraic operations such as addition and multiplication are defined for these observables, recovering many advantages of the ... More

Exact uncertainty relations: physical significanceJul 30 2001The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary observables are thus ... More

Entropic Heisenberg limits and uncertainty relations from the Holevo information boundApr 04 2018Jun 29 2018Strong and general entropic and geometric Heisenberg limits are obtained, for estimates of multiparameter unitary displacements in quantum metrology, such as the estimation of a magnetic field from the induced rotation of a probe state in three dimensions. ... More

Generalisations of the recent Pusey-Barrett-Rudolph theorem for statistical models of quantum phenomenaNov 27 2011Pusey, Barrett and Rudolph (PBR) have recently given a completely novel argument that restricts the class of possible models for quantum phenomena (arXiv:1111.3328). In these notes the assumptions used by PBR are considerably weakened, to further restrict ... More

Relaxed Bell inequalities and Kochen-Specker theoremsFeb 22 2011Jul 16 2011The combination of various physically plausible properties, such as no signaling, determinism, and experimental free will, is known to be incompatible with quantum correlations. Hence, these properties must be individually or jointly relaxed in any model ... More

Consistent classical and quantum mixed dynamicsApr 16 2008Sep 18 2008A recent proposal for mixed dynamics of classical and quantum ensembles is shown, in contrast to other proposals, to satisfy the minimal algebraic requirements proposed by Salcedo for any consistent formulation of such dynamics. Generalised Ehrenfest ... More

Exact uncertainty approach in quantum mechanics and quantum gravityAug 31 2004The assumption that an ensemble of classical particles is subject to nonclassical momentum fluctuations, with the fluctuation uncertainty fully determined by the position uncertainty, has been shown to lead from the classical equations of motion to the ... More

Volume of classical and quantum ensembles: geometric approach to entropy and informationJun 04 1998It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It further provides ... More

The Difficulties of Addressing Interdisciplinary Challenges at the Foundations of Data ScienceSep 04 2019The National Science Foundation's Transdisciplinary Research in Principles of Data Science (TRIPODS) program aims to integrate three areas central to the foundations of data by uniting the statistics, mathematics, and theoretical computer science research ... More

Maximizing the Probability of Detecting an Electromagnetic Counterpart of Gravitational-wave EventsApr 18 2016Compact binary coalescences are a promising source of gravitational waves for second-generation interferometric gravitational-wave detectors such as advanced LIGO and advanced Virgo. These are among the most promising sources for joint detection of electromagnetic ... More

The Efficiency of Stellar Reionization: Effects of Rotation, Metallicity, and Initial Mass FunctionJan 08 2015We compute the production rate of photons in the ionizing Lyman continua (LyC) of H I (lambda < 912 A), He I (lambda < 504 A), and He II (lambda < 228 A) using recent stellar evolutionary tracks coupled to a grid of non-LTE, line-blanketed (WM-basic) ... More

Deflating Quantum Mysteries via the Relational BlockworldMar 07 2005Oct 28 2005We present a spacetime setting for non-relativistic quantum mechanics that deflates "quantum mysteries" and relates non-relativistic quantum mechanics to special relativity. This is achieved by assuming spacetime symmetries are fundamental in a blockworld ... More

Reconciling Spacetime and the Quantum: Relational Blockworld and the Quantum Liar ParadoxOct 12 2005Dec 31 2007The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal ... More

Comment on "Gleason-Type Theorem for Projective Measurements, Including Qubits" by F. De ZelaNov 02 2016It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding an assumption of continuity. This amounts to a claim of the derivation of Born's rule ... More

Lecture Notes on Spectral Graph MethodsAug 17 2016These are lecture notes that are based on the lectures from a class I taught on the topic of Spectral Graph Methods at UC Berkeley during the Spring 2015 semester.

Evolution: Life has Evolved to EvolveJan 30 2014Jim Shapiro synthesizes a great many observations about the mechanisms of evolution to reach the remarkable conclusion that large-scale modification, exchange, and rearrangement of the genome are common and should be viewed as fundamental features of ... More

Incompleteness of trajectory-based interpretations of quantum mechanicsJun 09 2004Aug 29 2004Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schroedinger ... More

The significance of measurement independence for Bell inequalities and localityNov 02 2015Nov 15 2015A local and deterministic model of quantum correlations is always possible, as shown explicitly by Brans in 1988: one simply needs the physical systems being measured to have a suitable statistical correlation with the physical systems performing the ... More

Local deterministic model of singlet state correlations based on relaxing measurement independenceJul 30 2010Dec 21 2010The derivation of Bell inequalities requires an assumption of measurement independence, related to the amount of free will experimenters have in choosing measurement settings. Violation of these inequalities by singlet state correlations, as has been ... More

Complete positivity for time-dependent qubit master equationsFeb 05 2008Mar 29 2008It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the full decoherence matrix is block-diagonal, ... More

Quantum properties of classical Fisher informationDec 13 1999The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian diffusion, thus ... More

Examples of buildings constructed via covering spacesSep 30 2008Covering space theory is used to construct new examples of buildings.

Algebraic Models: Coordinates, Scales, and Dynamical SymmetriesMay 15 2000We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle Schr\"odinger hamiltonian ... More

A Hybrid Algebraic/Schrödinger Approach to the 2D Franck-Condon ProblemMay 15 2000We use recent results regarding the geometry of the U(3) bosonic algebraic model to motivate a hybrid algebraic-Schr\"odinger approach to the 2D Franck-Condon problem analogous to 1D approaches. This approach allows one to analyze bent to linear Franck-Condon ... More

The Euler characteristic of a polyhedral productMar 15 2011Given a finite simplicial complex L and a collection of pairs of spaces indexed by its vertex set, one can define their polyhedral product. We record a simple formula for its Euler characteristic. In special cases the formula simplifies further to one ... More

Domains and Random VariablesJul 18 2016Aug 27 2016The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the mainstay of probability ... More

Complements of hyperplane arrangements as posets of spacesFeb 12 2015Feb 24 2016The complement of an arrangement A of a finite number of affine hyperplanes in complex n-space has the structure of a poset of spaces indexed by the intersection poset, L(A). The space corresponding to G in L(A) is homotopy equivalent to the complement ... More

A Bijection on Classes Enumerated by the Schröder NumbersOct 31 2015Sep 16 2016We consider a sorting machine consisting of two stacks in series where the first stack has the added restriction that entries in the stack must be in decreasing order from top to bottom. The class of permutations sortable by this machine are known to ... More

All-Orders Resummation of Leading Logarithmic Contributions to Heavy Quark Production in Polarized γγCollisionsJul 10 1998The measurements of the $\gamma\gamma$ and $b \bar b$ partial decay widths of an intermediate-mass Standard Model Higgs boson are among the most important goals of a future photon linear collider. While in an initially polarized $J_z=0$ state the background ... More

A Shifted View of Fundamental PhysicsSep 16 2010We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as shifted equations. ... More

Development of modularity in the neural activity of children's brainsJan 28 2015We study how modularity of the human brain changes as children develop into adults. Theory suggests that modularity can enhance the response function of a networked system subject to changing external stimuli. Thus, greater cognitive performance might ... More

Hierarchy of Gene Expression Data is Predictive of Future Breast Cancer OutcomeJan 20 2014We calculate measures of hierarchy in gene and tissue networks of breast cancer patients. We find that the likelihood of metastasis in the future is correlated with increased values of network hierarchy for expression networks of cancer-associated genes, ... More

Reaction, Levy Flights, and Quenched DisorderJul 07 2001Aug 13 2002We consider the A + A --> emptyset reaction, where the transport of the particles is given by Levy flights in a quenched random potential. With a common literature model of the disorder, the random potential can only increase the rate of reaction. With ... More

First-principles prediction of potentials and space-charge layers in all-solid-state batteriesFeb 28 2019Apr 02 2019As all-solid-state batteries (SSBs) develop as an alternative to traditional cells, a thorough theoretical understanding of driving forces behind battery operation is needed. We present a fully first-principles-informed model of potential profiles in ... More

Direct Numerical Observation of Anomalous Diffusion in Random MediaMar 20 1998Aug 03 1998We present computer simulations of anomalous diffusion, $< r^2(t) > \sim a t^{1-\delta}$, in two dimensions. The Monte Carlo calculations are in excellent agreement with previous renormalization group calculations. Interestingly, use of a high quality ... More

Hierarchy in Gene Expression is Predictive for Adult Acute Myeloid LeukemiaJan 28 2015Cancer progresses with a change in the structure of the gene network in normal cells. We define a measure of organizational hierarchy in gene networks of affected cells in adult acute myeloid leukemia (AML) patients. With a retrospective cohort analysis ... More

Uniform Spaces in the Pregeometric Modeling of Quantum Non-SeparabilityMar 28 2000Apr 16 2001We introduce a pregeometry employing uniform spaces over the denumerable set X of spacetime events. The discrete uniformity D_X over X is used to obtain a pregeometric model of macroscopic spacetime neighborhoods. We then use a uniformity base generated ... More

Cohomology computations for Artin groups, Bestvina-Brady groups, and graph productsFeb 12 2010We compute: * the cohomology with group ring coefficients of Artin groups (or actually, of their associated Salvetti complexes), Bestvina-Brady groups, and graph products of groups, * the L^2-Betti numbers of Bestvina-Brady groups and of graph products ... More

Quantum to Classical Transition per the Relational BlockworldMay 11 2006May 22 2006The transition from the quantum realm to the classical realm is described in the context of the Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics. We first introduce RBW, discuss its philosophical implications and provide ... More

Brownian motion of finite-inertia particles in a simple shear flowJan 25 2005Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The classical fluctuation ... More

Quantum Mechanics and the Consistency of Conscious ExperienceJan 28 2019We discuss the implications for the determinateness and intersubjective consistency of conscious experience in two gedanken experiments from quantum mechanics (QM). In particular, we discuss Wigner's friend and the delayed choice quantum eraser experiment ... More

Two-Dimensional Diffusion in the Presence of Topological DisorderAug 29 2003How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder leads to a finite ... More

Low-dimensional clustering detects incipient dominant influenza strain clustersApr 27 2012Influenza has been circulating in the human population and has caused three pandemics in the last century (1918 H1N1, 1957 H2N2, 1968 H3N2). The 2009 A(H1N1) was classified by the World Health Organization (WHO) as the fourth pandemic. Influenza has a ... More

A Configurational Bias Monte Carlo Method for Linear and Cyclic PeptidesSep 30 1997In this manuscript, we describe a new configurational bias Monte Carlo technique for the simulation of peptides. We focus on the biologically relevant cases of linear and cyclic peptides. Our approach leads to an efficient, Boltzmann-weighted sampling ... More

A three-dimensional approach to Visual Speech Recognition using Discrete Cosine TransformsSep 07 2016Visual speech recognition aims to identify the sequence of phonemes from continuous speech. Unlike the traditional approach of using 2D image feature extraction methods to derive features of each video frame separately, this paper proposes a new approach ... More

Low-distortion Subspace Embeddings in Input-sparsity Time and Applications to Robust Linear RegressionOct 11 2012Mar 21 2013Low-distortion embeddings are critical building blocks for developing random sampling and random projection algorithms for linear algebra problems. We show that, given a matrix $A \in \R^{n \times d}$ with $n \gg d$ and a $p \in [1, 2)$, with a constant ... More

Bose-Hubbard model with attractive interactionsJan 19 2005We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction ... More

A Bijection on Classes Enumerated by the Schröder NumbersOct 31 2015Jul 08 2017We consider a sorting machine consisting of two stacks in series where the first stack has the added restriction that entries in the stack must be in decreasing order from top to bottom. The class of permutations sortable by this machine are known to ... More

Quantum Mechanics and the Consistency of Conscious ExperienceJan 28 2019Apr 24 2019We discuss the implications for the determinateness and intersubjective consistency of conscious experience in two gedanken experiments from quantum mechanics (QM). In particular, we discuss Wigner's friend and the delayed choice quantum eraser experiment ... More

Renormalization Group Improved Heavy Quark Production in Polarized γγCollisionsMar 28 1999The experimental determination of the partial width $\Gamma (H \longrightarrow \gamma \gamma)$ of an intermediate mass Higgs is among the most important measurements at a future photon photon collider. Recently it was shown that large non-Sudakov as well ... More

Heavy Quark Production at a $γγ$ Collider: the Effect of Large Logarithmic Perturbative CorrectionsOct 21 1998We present quantitative results on the cross section for $\gamma + \gamma (J_z=0) \to b \bar{b}\to two b$-jets based on the recently achieved all orders resummation of large soft (Sudakov) and hard (non-Sudakov) double logarithms. The next-to-leading ... More

Learning with Spectral Kernels and Heavy-Tailed DataJun 24 2009May 10 2010Two ubiquitous aspects of large-scale data analysis are that the data often have heavy-tailed properties and that diffusion-based or spectral-based methods are often used to identify and extract structure of interest. Perhaps surprisingly, popular distribution-independent ... More

Loewy lengths of blocks with abelian defect groupsJul 29 2016We consider $p$-blocks with abelian defect groups and in the first part prove a relationship between its Loewy length and that for blocks of normal subgroups of index $p$. Using this, we show that if $B$ is a $2$-block of a finite group with abelian defect ... More

Observational Quantification of the Energy Dissipated by Alfvén Waves in a Polar Coronal Hole: Evidence that Waves Drive the Fast Solar WindFeb 21 2013Aug 29 2013We present a measurement of the energy carried and dissipated by Alfv\'en waves in a polar coronal hole. Alfv\'en waves have been proposed as the energy source that heats the corona and drives the solar wind. Previous work has shown that line widths decrease ... More

Influenza Evolution and H3N2 Vaccine Effectiveness, with Application to the 2014/2015 SeasonOct 02 2015Mar 18 2016Influenza A is a serious disease that causes significant morbidity and mortality, and vaccines against the seasonal influenza disease are of variable effectiveness. In this paper, we discuss use of the $p_{\rm epitope}$ method to predict the dominant ... More

Modular knowledge systems accelerate human migration in asymmetric random environmentsDec 06 2016Migration is a key mechanism for expansion of communities. In spatially heterogeneous environments, rapidly gaining knowledge about the local environment is key to the evolutionary success of a migrating population. For historical human migration, environmental ... More

Quantifying Selection and Diversity in Viruses by Entropy Methods, with Application to the Hemagglutinin of H3N2 InfluenzaApr 26 2012Many viruses evolve rapidly. For example, hemagglutinin of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly ... More

A Multi-Scale Model for Correlation in B Cell VDJ Usage of ZebrafishApr 26 2012The zebrafish (\emph{Danio rerio}) is one of the model animals for study of immunology because the dynamics in the adaptive immune system of zebrafish are similar to that in higher animals. In this work, we built a multi-scale model to simulate the dynamics ... More

Structure and Response in the World Trade NetworkOct 03 2010We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40 years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive ... More

Heterogeneous diversity of spacers within CRISPRAug 16 2010Clustered regularly interspaced short palindromic repeats (CRISPR) in bacterial and archaeal DNA have recently been shown to be a new type of anti-viral immune system in these organisms. We here study the diversity of spacers in CRISPR under selective ... More

A Physical Theory of the Competition that Allows HIV to Escape from the Immune SystemOct 08 2006Oct 16 2006Competition within the immune system may degrade immune control of viral infections. We formalize the evolution that occurs in both HIV-1 and the immune system quasispecies. Inclusion of competition in the immune system leads to a novel balance between ... More

Reducing theoretical uncertainties in mb and lambda1May 06 2002We calculate general moments of the lepton energy spectrum in inclusive semileptonic B -> X_c l \nu decay. Moments which allow the determination of mb^{1S} and lambda1 with theoretical uncertainties Delta(mb^{1S}) ~ 0.04 GeV and Delta(lambda1) ~ 0.05 ... More