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Results for "Max N. Markmeyer"

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Formation of Acetaldehyde on CO-rich IcesApr 12 2019The radicals HCO and CH$_3$ on carbon monoxide ice surfaces were simulated using density functional theory. Their binding energy on amorphous CO ice shows broad distributions, with approximative average values of 500 K for HCO and 200 K for CH$_3$. If ... More
A componentwise version of Terao's conjectureJan 22 2009Aug 25 2009This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.
A Newton conditional gradient method for constrained nonlinear systemsAug 24 2016In this paper, we consider the problem of solving a constrained system of nonlinear equations. We propose an algorithm based on a combination of the Newton and conditional gradient methods, and establish its local convergence analysis. Our analysis is ... More
Convergence of the Gauss-Newton method for a special class of systems of equations under a majorant conditionJun 19 2012Jun 20 2012In this paper, we study the Gauss-Newton method for a special class of systems of nonlinear equation. Under the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. ... More
Pointwise and ergodic convergence rates of a variable metric proximal ADMMFeb 22 2017May 04 2017In this paper, we obtain global $\mathcal{O} (1/ \sqrt{k})$ pointwise and $\mathcal{O} (1/ {k})$ ergodic convergence rates for a variable metric proximal alternating direction method of multipliers(VM-PADMM) for solving linearly constrained convex optimization ... More
The thermal Hall effect of spin excitations in a Kagome magnetFeb 19 2015At low temperatures, the thermal conductivity of spin excitations in a magnetic insulator can exceed that of phonons. However, because they are charge neutral, the spin waves are not expected to display a thermal Hall effect in a magnetic field. Recently, ... More
Paramagnetic to ferromagnetic phase transition in lightly Fe-doped Cr$_2$BJun 17 2014Cr$_2$B displays temperature independent paramagnetism. We induce ferromagnetism by replacing less than $3\,\%$ of the Cr atoms by Fe. By the lowest Fe doping level made, Curie-Weiss behavior is observed; $\Theta_{CW}$ changes from $-20\,$K for $0.5\,\%$ ... More
Geometric Cycles in Floer TheorySep 03 2014We construct a version of Hamiltonian Floer Homology based on the notion of a semi-infinite cycle. As an application, we provide a new proof for the existence of critical points of the action functional.
Geometric HomologySep 03 2014The purpose of this paper is to introduce a version of singular homology based on smooth mappings of manifolds with corners. Although variants of such a theory exists in the literature, we felt that certain points were not adequately addressed. In particular, ... More
Asymptotic Symmetry Algebras in Non-Anti-de-Sitter Higher-Spin Gauge TheoriesOct 24 2012We analyze asymptotic symmetry algebras in (2+1)-dimensional non-AdS higher-spin gravity with a focus on AdS$_2\times\mathbb{R}$ and $\mathbb{H}_2\times\mathbb{R}$. We find a consistent set of boundary conditions for spin-3 gravity in the non-principal ... More
On the Choice of Regions for Generalized Belief PropagationJul 11 2012Generalized belief propagation (GBP) has proven to be a promising technique for approximate inference tasks in AI and machine learning. However, the choice of a good set of clusters to be used in GBP has remained more of an art then a science until this ... More
Limit theorems for projections of random walk on a hypersphereAug 25 2009We show that almost any one-dimensional projection of a suitably scaled random walk on a hypercube, inscribed in a hypersphere, converges weakly to an Ornstein-Uhlenbeck process as the dimension of the sphere tends to infinity. We also observe that the ... More
Umbral Moonshine and String DualityMar 20 2018By studying 2d string compactifications with half-maximal supersymmetry in a variety of duality frames, we find a natural physical setting for understanding Umbral moonshine. Near points in moduli space with enhanced gauge symmetry, we find that the Umbral ... More
TikZ-FeynHand: Basic User GuideJan 31 2018This is a userguide for the LaTex package Tikz-FeynHand at https://ctan.org/pkg/tikz-feynhand which let's you draw Feynman diagrams using TikZ. It contains many examples and a 5-minute introduction to TikZ. The package is a low-end modification of the ... More
Coplanar Low-Thrust Transfer with Eclipses Using Analytical Costate GuessFeb 17 2018Low-thrust orbital transfers are difficult to optimize by indirect methods. The main issues come from the costate guess and from the numerical propagation accuracy required by the shooting method. In the case of a coplanar minimum-time low-thrust transfer ... More
Why do launch trajectories end downwardsJun 04 2017The problem of finding the optimal thrust profile of a launcher upper stage is analyzed. The engine is assumed to be continuously thrusting, following either a linear or a bilevel parametric profile, until reaching the targeted coplanar orbit. The minimum-fuel ... More
How General Is Holography?Sep 09 2016In this thesis I explore the generality of the holographic principle in 2+1 (bulk) dimensions by looking at the possibility of having holographic correspondences for non-AdS (higher-spin) spacetimes. The first part focuses on Lobachevsky spacetimes with ... More
Cloud Security Architecture and Implementation - A practical approachAug 12 2018Sep 23 2018While cloud computing provides lower Infrastructure cost, higher agility and faster delivery, it also presents higher operational and security risks for business critical assets, but a well-designed solution and security architecture will keep businesses ... More
On the Randomized Complexity of Minimizing a Convex Quadratic FunctionJul 24 2018Sep 23 2018Minimizing a convex, quadratic objective is a fundamental problem in machine learning and optimization. In this work, we study prove information-theoretic, gradient query complexity lower bounds for minimizing convex quadratic functions, which, unlike ... More
Projective Decomposition and Matrix Equivalence up to ScaleJan 04 2019A data matrix may be seen simply as a means of organizing observations into rows ( e.g., by measured object) and into columns ( e.g., by measured variable) so that the observations can be analyzed with mathematical tools. As a mathematical object, a matrix ... More
Fibre bundles, connections and cyclic homologyOct 04 2005This is a survey paper, starting from the general notion of coordinate bundle taken from Steenrod. Its aim is to provide a motivation for the introduction of cyclic homology (and the closely related noncommutative de Rham cohomology) by Connes, Tsygan ... More
Futility Analysis in the Cross-Validation of Machine Learning ModelsMay 27 2014Many machine learning models have important structural tuning parameters that cannot be directly estimated from the data. The common tactic for setting these parameters is to use resampling methods, such as cross--validation or the bootstrap, to evaluate ... More
Taking Inspiration from Quantum-Wave Analogies --- Recent Results for Photonic CrystalsApr 04 2018Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This proceeding ... More
Hamilton cycles in infinite cubic graphsMay 19 2017Investigating a problem of B. Mohar, we show that every one-ended Hamiltonian cubic graph with end degree 3 contains a second Hamilton cycle. We also construct two examples showing that this result does not extend to give a third Hamilton cycle, nor that ... More
Thermal elastic-wave attenuation in low-dimensional SiN$_{x}$ bars at low temperaturesMay 26 2017At low temperatures, < 200 mK, the thermal flux through low-dimensional amorphous dielectric bars, < 2 $\mu$m wide and 200 nm thick, is transported by a small number of low-order elastic modes. For long bars, L > 400 $\mu$m, it is known that the conductance ... More
Are Bitcoin Bubbles Predictable? Combining a Generalized Metcalfe's Law and the LPPLS ModelMar 15 2018We develop a strong diagnostic for bubbles and crashes in bitcoin, by analyzing the coincidence (and its absence) of fundamental and technical indicators. Using a generalized Metcalfe's law based on network properties, a fundamental value is quantified ... More
Simulating Linear Logic in 1-Only Linear LogicSep 09 2017Linear Logic was introduced by Girard as a resource-sensitive refinement of classical logic. It turned out that full propositional Linear Logic is undecidable (Lincoln, Mitchell, Scedrov, and Shankar) and, hence, it is more expressive than (modalized) ... More
A sharp symmetrized form of Talagrand's transport-entropy inequality for the Gaussian measureJun 17 2018This note presents a sharp transport-entropy inequality that improves on Talagrand's inequality for the Gaussian measure, arising as a dual formulation of the functional Santal\'o inequality. We also discuss some extensions and connections with concentration ... More
Stein kernels and moment mapsApr 12 2018Jun 16 2018We describe a construction of Stein kernels using moment maps, which are solutions to a variant of the Monge-Amp\`ere equation. As a consequence, we show how regularity bounds on these maps control the rate of convergence in the classical central limit ... More
The Nonexistence of Noncompact Type-I Ancient 3-d $κ$-Solutions of Ricci Flow with Positive CurvatureJan 26 2018In this short paper, we show there do not exist three-dimensional noncompact $\kappa$-solutions of Ricci flow that have positive curvature and satisfy a Type-I bound. This represents progress towards the proof of Perelman's conjecture that the only complete ... More
Inflaton vacuum fluctuations as dark matter and the potential V(phi) as dark energyDec 13 2017Jan 21 2019It is shown, using quantum field theory in curved spacetime, how the expansion of the universe during inflation produces an aggregate of particles and inflaton vacuum fluctuations at a temperature of 5x10^17GeV and dense enough to make reheating unnecessary. ... More
A Free Boundary Problem for the Parabolic Poisson KernelOct 19 2015We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystr\"om, and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson kernel ... More
Two-parameter Asymptotics in Magnetic Weyl CalculusSep 18 2008May 28 2010This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter \eps, the case of small coupling $\lambda$ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl ... More
Splittings of generalized Baumslag-Solitar groupsFeb 02 2005Mar 11 2006We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity ... More
Error estimates for the finite element approximation of bilinear boundary control problemsJan 11 2019In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin coefficient from ... More
Deformation and rigidity of simplicial group actions on treesJul 02 2001May 08 2002We study a notion of deformation for simplicial trees with group actions (G-trees). Here G is a fixed, arbitrary group. Two G-trees are related by a deformation if there is a finite sequence of collapse and expansion moves joining them. We show that this ... More
On uniqueness of JSJ decompositions of finitely generated groupsOct 17 2001May 22 2003We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the ... More
Return Probabilities of Random WalksDec 14 2015Associated to a random walk on $\mathbb{Z}$ and a positive integer $n$, there is a return probability of the random walk returning to the origin after $n$ steps. An interesting question is when the set of return probabilities uniquely determines the random ... More
Partial flag incidence algebrasMay 05 2016The $n^{th}$ partial flag incidence algebra of a poset $P$ is the set of functions from $P^n$ to some ring which are zero on non-partial flag vectors. These partial flag incidence algebras for $n>2$ are not commutative, not unitary, and not associative. ... More
Genealogical distance under selectionApr 21 2018We study the genealogical distance of two randomly chosen individuals in a population that evolves according to a two type Moran model with mutation and selection. We prove that this distance is stochastically smaller than the corresponding distance in ... More
Numerical Solution of the Simple Monge-Ampère Equation with Non-convex Dirichlet Data on Non-convex DomainsMay 12 2017Jun 01 2017The existence of a unique numerical solution of the semi-Lagrangian method for the simple Monge-Amp\`ere equation is known independently of the convexity of the domain or Dirichlet boundary data -- when the Monge-Amp\`ere equation is posed as Bellman ... More
Stabilization of the Witt groupSep 27 2005Using an idea due to R.Thomason, we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find P. Balmer's higher Witt groups. ... More
Family size decomposition of genealogical treesMar 07 2019We study the path of family size decompositions of varying depth of genealogical trees. We prove that this decomposition as a function on (equivalence classes of) ultra-metric measure spaces to the Skorohod space describing the family sizes at different ... More
Evidence for massive bulk Dirac Fermions in Pb$_{1-x}$Sn$_x$Se from Nernst and thermopower experimentsJul 15 2013Sep 10 2013The lead chalcogenides (Pb,Sn)Te and (Pb,Sn)Se are the first examples of topological crystalline insulators (TCI) predicted \cite{Fu,Hsieh} (and confirmed \cite{Hasan,Story,Takahashi}) to display topological surface Dirac states (SDS) that are protected ... More
Integrated-optics heralded controlled-NOT gate for polarization-encoded qubitsAug 22 2017Feb 21 2018Recent progress in integrated-optics technology has made photonics a promising platform for quantum networks and quantum computation protocols. Integrated optical circuits are characterized by small device footprints and unrivalled intrinsic interferometric ... More
Correlation of Crystal Quality and Extreme Magnetoresistance of WTe$_2$Jun 16 2015High quality single crystals of WTe$_2$ were grown using a Te flux followed by a cleaning step involving self-vapor transport. The method is reproducible and yields consistently higher quality single crystals than are typically obtained via halide assisted ... More
A zero point energy explanation of a peak in liquid helium's dynamic structure factorMay 27 1997Recent high resolution experiments show a strong peak at Q = 1.9 Ang^{-1} in liquid helium's dynamic structure factor that exhibits a singular dependence on temperature. The theoretical situation is briefly reviewed, and the comment is made that the simplest ... More
The Large Hadron Electron Collider ProjectAug 20 2009A Conceptual Design Report (CDR) for the Large Hadron Electron Collider, the LHeC, is being prepared, to which an introduction was given for the plenary panel discussion on the future of deep inelastic scattering held at DIS09. This is briefly summarised ... More
The pentagram map and Y-patternsMay 04 2010Apr 15 2011The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its "shortest" diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain ... More
Characterizations of countably $n$-rectifiable Radon measures by higher-dimensional Menger curvaturesApr 07 2018May 05 2018In the late `90s there was a flurry of activity relating $1$-rectifiable sets, boundedness of singular integral operators, the analytic capacity of a set, and the integral Menger curvature in the plane. In `99 Leger extended the results for Menger curvature ... More
Twisted sheaves and the period-index problemNov 09 2005May 25 2007We use twisted sheaves and their moduli spaces to study the Brauer group of a scheme. In particular, we (1) show how twisted methods can be efficiently used to re-prove the basic facts about the Brauer group and cohomological Brauer group (including Gabber's ... More
Derivation degree sequences of non-free arrangementsJul 19 2018In this note we study the logarithmic derivation module of a non-free arrangement. We prove a generalized addition theorem for all arrangements. This addition theorem allows us to find various relationships between non-free arrangements, free arrangements ... More
Semiclassical Dynamics and Magnetic Weyl CalculusFeb 20 2012Aug 16 2015Weyl quantization and related semiclassical techniques can be used to study conduction properties of crystalline solids subjected to slowly-varying, external electromagnetic fields. The case where the external magnetic field is constant, is not covered ... More
Classical Klein-Gordon solutions, symplectic structures and isometry actions on AdS spacetimesDec 12 2012Dec 21 2012We study classical, real Klein-Gordon theory on Lorentzian Anti de Sitter (AdS_{1,d}) spacetimes with spatial dimension d. We give a complete list of well defined and bounded Klein-Gordon solutions for three types of regions on AdS: slice (time interval ... More
Equivariant K-theory of real vector spaces and real vector bundlesSep 21 2005Jan 05 2007Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V), using previous ... More
$L^2(H^1_γ)$ Finite Element Convergence for Degenerate Isotropic Hamilton-Jacobi-Bellman EquationsJul 01 2015In this paper we study the convergence of monotone $P1$ finite element methods for fully nonlinear Hamilton-Jacobi-Bellman equations with degenerate, isotropic diffusions. The main result is strong convergence of the numerical solutions in a weighted ... More
The Least-Perimeter Partition of a Sphere into Four Equal AreasMar 24 2009Jun 19 2009We prove that the least-perimeter partition of the sphere into four regions of equal area is a tetrahedral partition.
Constructing Superelliptic Curves with non-trivial rational Torsion on their JacobiansJul 13 2017In this paper, we describe the construction of superelliptic curves with a rational point of prescribed order on their jacobians. The construction is based on Hensel's Lemma and produces for a given integer $N$ a superelliptic curve of genus linear in ... More
The Devron propertyDec 24 2013Jul 17 2014We introduce a criterion called the Devron property that a discrete dynamical system can possess. The Devron property is said to occur when a class of highly singular inputs of a mapping F are carried by some iterate of $F^{-1}$ to a class of highly singular ... More
A Equação de Euler e a Análise Assintótica de GevreyApr 09 2014In this work, we introduce the notion of Gevrey asymptotic expansion and we show how the classical concept of a convergent power series can be generalized to include the case in which the radius of convergence is zero. This technique can be useful in ... More
Extended Dependency Structures and their Formal InterpretationApr 29 1996May 09 1996We describe two ``semantically-oriented'' dependency-structure formalisms, U-forms and S-forms. U-forms have been previously used in machine translation as interlingual representations, but without being provided with a formal interpretation. S-forms, ... More
A unified treatment of cubic invariants at fixed and arbitrary energyNov 09 1998Dec 20 1999Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the invariant ... More
Spatial Fluid Limits for Stochastic Mobile NetworksJul 17 2013Apr 26 2016We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial differential equations ... More
On partitions into squares of distinct integers whose reciprocals sum to 1Jan 18 2018Apr 23 2018In 1963, Graham proved that all integers greater than 77 (but not 77 itself) can be partitioned into distinct positive integers whose reciprocals sum to 1. He further conjectured that for any sufficiently large integer, it can be partitioned into squares ... More
E-Embargoes: Discouraging the Deployment of Traffic Manipulating Boxes With Economic IncentivesJun 28 2016An increasing number of systems have been proposed or deployed to the transit core of the Internet with the goal of observing and manipulating traffic in flight, systems we term Traffic Manipulating Boxes. Examples of these include: decoy routing systems, ... More
Recurrent Inference Machines for Solving Inverse ProblemsJun 13 2017Much of the recent research on solving iterative inference problems focuses on moving away from hand-chosen inference algorithms and towards learned inference. In the latter, the inference process is unrolled in time and interpreted as a recurrent neural ... More
Quantitative stratification for some free-boundary problemsFeb 14 2017Sep 16 2017In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli. Our main tools are the Quantitative Stratification and Rectifiable-Reifenberg framework ... More
Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome latticeOct 28 2016We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, ... More
Simplified D=11 Pure Spinor b GhostMar 15 2017May 12 2017A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor superparticle by requiring that $\{Q , b\} = T$ where $Q = \Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ is the usual non-minimal pure spinor BRST operator. As was done for ... More
Efficient Search-Based Inference for Noisy-OR Belief Networks: TopEpsilonFeb 13 2013Inference algorithms for arbitrary belief networks are impractical for large, complex belief networks. Inference algorithms for specialized classes of belief networks have been shown to be more efficient. In this paper, we present a search-based algorithm ... More
A note on privacy preserving iteratively reweighted least squaresMay 24 2016Iteratively reweighted least squares (IRLS) is a widely-used method in machine learning to estimate the parameters in the generalised linear models. In particular, IRLS for L1 minimisation under the linear model provides a closed-form solution in each ... More
Metric Learning on ManifoldsFeb 05 2019Recent literature has shown that symbolic data, such as text and graphs, is often better represented by points on a curved manifold, rather than in Euclidean space. However, geometrical operations on manifolds are generally more complicated than in Euclidean ... More
Graph rules for the linked cluster expansion of the Legendre effective actionDec 17 2018Graph rules for the linked cluster expansion of the Legendre effective action $\Gamma[\phi]$ are derived and proven in $D\geq 2$ Euclidean dimensions. A key aspect is the weight assigned to articulation vertices which is itself shown to be computable ... More
Over Saturation in SiPMs: The Difference Between Signal Charge and Signal AmplitudeJul 03 2015A recent report on the over saturation in SiPMs is puzzling. The measurements, using a variety of SiPMs, show an excess in signal far beyond the physical limit of the number of SiPM microcells without indication of an ultimate saturation. In this work ... More
Length functions of 2-dimensional right-angled Artin groupsMar 28 2011Apr 08 2011Morgan and Culler proved that a minimal action of a free group on a tree is determined by its translation length function. We prove an analogue of this theorem for 2-dimensional right-angled Artin groups acting on CAT(0) rectangle complexes.
First-principle study of the melting temperature of MgOFeb 21 2019Apr 04 2019Using first-principles only, we calculate the melting point of MgO, also called periclase or magnesia. The random phase approximation (RPA) is used to include the exact exchange as well as local and non-local many-body correlation terms, in order to provide ... More
On the large N expansion in hyperbolic sigma-modelsNov 23 2007Jun 27 2008Invariant correlation functions for ${\rm SO}(1,N)$ hyperbolic sigma-models are investigated. The existence of a large $N$ asymptotic expansion is proven on finite lattices of dimension $d \geq 2$. The unique saddle point configuration is characterized ... More
A reconstruction theorem for varietiesFeb 12 2019We show that varieties of dimension at least 2 over infinite fields are determined as abstract schemes by their Zariski topological spaces together with the rational equivalence relation on the set of effective divisors. This gives a universal Torelli ... More
Diagrams and the second homotopy groupJun 05 2003Oct 18 2004We use Klyachko's methods [A funny property of sphere and equations over groups, Comm. in Alg. 21 (1993) 2555--2575] (see also Fenn-Rourke, L'Enseignment Math. 42 (1996) 49--74 and math.GR/9810184 and Cohen-Rourke, math.GR/0009101) to prove that, if a ... More
The Large Hadron Electron ColliderMay 09 2013An overview is given on key physics, detector and accelerator aspects of the LHeC, including its further development, with emphasis to its role as the cleanest microscope of parton dynamics and a precision Higgs facility.
A note on the cone conjecture for K3 surfaces in positive characteristicFeb 16 2011Mar 13 2019We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative integer g, there ... More
The Krein-Schrödinger Formalism of Bosonic BdG and Certain Classical Systems and Their Topological ClassificationMar 15 2019To understand recent works on classical and quantum spin equations and their topological classification, we develop a unified mathematical framework for bosonic BdG systems and associated classical wave equations; it applies not just to equations that ... More
Inference for Empirical Wasserstein Distances on Finite SpacesOct 11 2016Apr 26 2017The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive the asymptotic ... More
A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSbDec 31 2018A recurring theme in topological matter is the protection of unusual electronic states by symmetry, for example, protection of the surface states in Z2 topological insulators by time reversal symmetry [1-3]. Recently interest has turned to unusual surface ... More
Multiplicative Normalizing Flows for Variational Bayesian Neural NetworksMar 06 2017Jun 12 2017We reinterpret multiplicative noise in neural networks as auxiliary random variables that augment the approximate posterior in a variational setting for Bayesian neural networks. We show that through this interpretation it is both efficient and straightforward ... More
Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modelingNov 02 2016Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design process, a stochastic ... More
Structured and Efficient Variational Deep Learning with Matrix Gaussian PosteriorsMar 15 2016Jun 23 2016We introduce a variational Bayesian neural network where the parameters are governed via a probability distribution on random matrices. Specifically, we employ a matrix variate Gaussian \cite{gupta1999matrix} parameter posterior distribution where we ... More
Transmuting CHY formulaeAug 22 2018The various formulations of scattering amplitudes presented in recent years have underlined a hidden unity among very different theories. The KLT and BCJ relations, together with the CHY formulation, connect the S-matrices of a wide range of theories: ... More
Stratification Trees for Adaptive Randomization in Randomized Controlled TrialsJun 13 2018Nov 01 2018This paper proposes an adaptive randomization procedure for two-stage randomized controlled trials. The method uses data from a first-wave experiment in order to determine how to stratify in a second wave of the experiment, where the objective is to minimize ... More
Higher Spins Without (Anti-)de SitterOct 30 2017Jan 28 2018Can the holographic principle be extended beyond the well known AdS/CFT correspondence? During the last couple of years there has been a substantial amount of research trying to find answers for this question. In this work we provide a review of recent ... More
Most general AdS_3 boundary conditionsAug 03 2016Sep 21 2017We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical ... More
Giant Lyman-Alpha Nebulae in the Illustris SimulationMay 11 2016Dec 19 2016Several `giant' Lyman-$\alpha$ (Ly$\alpha$) nebulae with extent $\gtrsim 300\,$kpc and observed Ly$\alpha$ luminosity of $\gtrsim 10^{44}\,{\rm erg}\,{\rm s}^{-1}\,{\rm cm}^{-2}\,{\rm arcsec}^{-2}$ have recently been detected, and it has been speculated ... More
Introduction to Cluster AlgebrasMar 23 2018These are notes for a series of lectures presented at the ASIDE conference 2016. The definition of a cluster algebra is motivated through several examples, namely Markov triples, the Grassmannians $Gr_2(\mathbb{C})$, and the appearance of double Bruhat ... More
Herding as a Learning System with Edge-of-Chaos DynamicsFeb 09 2016Mar 01 2016Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted as "samples" ... More
A stronger derived Torelli theorem for K3 surfacesDec 20 2015In an earlier paper the notion of a filtered derived equivalence was introduced, and it was shown that if two K3 surfaces admit such an equivalence then they are isomorphic. In this paper we study more refined aspects of filtered derived equivalences ... More
$S$-duality of $u(1)$ gauge theory with $θ=π$ on non-orientable manifolds: Applications to topological insulators and superconductorsOct 19 2015Electric-magnetic duality ($S$-duality) is a well-known property of pure $u(1)$ gauge theory in 3+1 dimensions. In this paper, we investigate the compatibility of this duality with time-reversal symmetry. We consider two theories obtained by coupling ... More
Splitting Brauer classes using the universal AlbaneseMay 31 2018Nov 12 2018We prove that every Brauer class over a field splits over a torsor under an abelian variety. If the index of the class is not congruent to 2 modulo 4, we show that the Albanese variety of any smooth curve of positive genus that splits the class also splits ... More
Density of isoperimetric spectraDec 04 2008We show that the set of k-dimensional isoperimetric exponents of finitely presented groups is dense in the interval [1, \infty) for k > 1. Hence there is no higher-dimensional analogue of Gromov's gap (1,2) in the isoperimetric spectrum.
Poincaré, modified logarithmic Sobolev and isoperimetric inequalities for Markov chains with non-negative Ricci curvatureDec 01 2016We study functional inequalities for Markov chains on discrete spaces with entropic Ricci curvature bounded from below. Our main results are that when curvature is non-negative, but not necessarily positive, the spectral gap, the Cheeger isoperimetric ... More
Whitehead moves for G-treesOct 10 2007Aug 29 2008We generalize the familiar notion of a Whitehead move from Culler and Vogtmann's Outer space to the setting of deformation spaces of G-trees. Specifically, we show that there are two moves, each of which transforms a reduced G-tree into another reduced ... More