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Generative Hybrid Representations for Activity Forecasting with No-Regret LearningApr 12 2019Automatically reasoning about future human behaviors is a difficult problem with significant practical applications to assistive systems. Part of this difficulty stems from learning systems' inability to represent all kinds of behaviors. Some behaviors, ... More

Visual Chunking: A List Prediction Framework for Region-Based Object DetectionOct 27 2014Mar 16 2015We consider detecting objects in an image by iteratively selecting from a set of arbitrarily shaped candidate regions. Our generic approach, which we term visual chunking, reasons about the locations of multiple object instances in an image while expressively ... More

First-Person Activity Forecasting with Online Inverse Reinforcement LearningDec 22 2016Aug 06 2017We address the problem of incrementally modeling and forecasting long-term goals of a first-person camera wearer: what the user will do, where they will go, and what goal they seek. In contrast to prior work in trajectory forecasting, our algorithm, DARKO, ... More

Learning Action Maps of Large Environments via First-Person VisionMay 05 2016When people observe and interact with physical spaces, they are able to associate functionality to regions in the environment. Our goal is to automate dense functional understanding of large spaces by leveraging sparse activity demonstrations recorded ... More

N2N Learning: Network to Network Compression via Policy Gradient Reinforcement LearningSep 18 2017Dec 17 2017While bigger and deeper neural network architectures continue to advance the state-of-the-art for many computer vision tasks, real-world adoption of these networks is impeded by hardware and speed constraints. Conventional model compression methods attempt ... More

Directed-Info GAIL: Learning Hierarchical Policies from Unsegmented Demonstrations using Directed InformationSep 29 2018Mar 12 2019The use of imitation learning to learn a single policy for a complex task that has multiple modes or hierarchical structure can be challenging. In fact, previous work has shown that when the modes are known, learning separate policies for each mode or ... More

Directed-Info GAIL: Learning Hierarchical Policies from Unsegmented Demonstrations using Directed InformationSep 29 2018The use of imitation learning to learn a single policy for a complex task that has multiple modes or hierarchical structure can be challenging. In fact, previous work has shown that when the modes are known, learning separate policies for each mode or ... More

Learning Neural Parsers with Deterministic Differentiable Imitation LearningJun 20 2018Sep 19 2018We explore the problem of learning to decompose spatial tasks into segments, as exemplified by the problem of a painting robot covering a large object. Inspired by the ability of classical decision tree algorithms to construct structured partitions of ... More

Human-Interactive Subgoal Supervision for Efficient Inverse Reinforcement LearningJun 22 2018Humans are able to understand and perform complex tasks by strategically structuring the tasks into incremental steps or subgoals. For a robot attempting to learn to perform a sequential task with critical subgoal states, such states can provide a natural ... More

Predictive-State Decoders: Encoding the Future into Recurrent NetworksSep 25 2017Recurrent neural networks (RNNs) are a vital modeling technique that rely on internal states learned indirectly by optimization of a supervised, unsupervised, or reinforcement training loss. RNNs are used to model dynamic processes that are characterized ... More

Random Field Induced Order in Low DimensionMar 26 2012Oct 22 2012Consider the behavior of a classical O(n) model in a weak random external field acting along some $k$-dimensional subspace in $\R^n$ with $k<n$. We show rigorously that if $k=n-1$, for the model defined on $\Z^d$, $d ={2, 3}$ there is residual magnetic ... More

Excited Random Walk in a Markovian EnvironmentNov 05 2016One dimensional excited random walk has been extensively studied for bounded, i.i.d. cookie environments. In this case, many important properties of the walk including transience or recurrence, positivity or non-positivity of the speed, and the limiting ... More

Modernizing Quantum Annealing II: Genetic Algorithms and InferenceSep 19 2016Sep 23 2016I discuss how a quantum annealer may be employed for an inference task of finding the likely lowest energy state for a system of qubits with uncertainty values for the state of individual qubits and clusters of qubits depending on the structure of the ... More

Quantum Multiplicative Hypertoric Varieties and LocalizationFeb 02 2016We consider q-deformations of multiplicative hypertoric varieties, for q a non-zero element of an algebraically closed field of characteristic 0. We construct an algebra Dq of q-difference operators as a Heisenberg double in a braided monoidal category. ... More

Value Function Approximation for Direct Control of Switched Power ConvertersJan 19 2016We consider the problem of controlling switched-mode power converters using model predictive control. Model predictive control requires solving optimization problems in real time, limiting its application to systems with small numbers of switches and ... More

The Hypercube of Resistors, Asymptotic Expansions, and Preferential ArrangementsApr 10 2009Motivated by the problem of finding resistances among vertices in a hypercube, we derive exact expressions, generating functions, and asymptotic expansions for these resistances, then study the combinatorial interpretations of the coefficients arising ... More

Invariants Related to the Tree PropertyNov 19 2015May 25 2018We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the relations that obtain ... More

Domain wall encoding of integer variables for quantum annealing and QAOAMar 12 2019In this paper I propose a new method of encoding integer variables into Ising model qubits for quantum optimization. The new method is based on the physics of domain walls in one dimensional Ising spin chains. I find that these encodings and the encoding ... More

Van den Essen's theorem on the de Rham cohomology of a holonomic D-module over a formal power series ringMay 07 2015Aug 21 2016In this expository paper, we give a complete proof of van den Essen's theorem that the de Rham cohomology spaces of a holonomic D-module are finite-dimensional in the case of a formal power series ring over a field of characteristic zero. This proof requires ... More

Infinitary propositional Gödel logics with rational constants embed realsAug 25 2017Sep 23 2017It is shown that in infinitary propositional standard G\"odel logics, enhanced with constant value formulas corresponding to the rational values contained in the unit interval, it is possible to define formulas over these constants using said infinitary ... More

Bridge spectra of cables of 2-bridge knotsJun 12 2017We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

A note on strong axiomatization of Gödel-Justification LogicSep 25 2018Oct 26 2018Justification Logics are special kinds of modal logics which provide a framework for reasoning about epistemic justification. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators "$t:$", indexed over ... More

On the one-endedness of graphs of groupsMar 25 2014Mar 25 2015We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group is not one-ended, ... More

The algebraic geometry of Kazhdan-Lusztig-Stanley polynomialsDec 04 2017Jun 13 2018Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, ... More

The Local Joyal Model StructureJul 31 2015Jul 18 2016It is shown that the Joyal quasi-category model structure for simplicial sets extends to a model structure on simplicial presheaves, for which the weak equivalences are local (or stalkwise) Joyal equivalences.

Combinatorially two-orbit convex polytopesNov 06 2014Feb 19 2015Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group coincide.) Hence, ... More

The Birth of Calculus: Towards a More Leibnizian ViewDec 11 2012We re-evaluate the great Leibniz-Newton calculus debate, exactly three hundred years after it culminated, in 1712. We reflect upon the concept of invention, and to what extent there were indeed two independent inventors of this new mathematical method. ... More

United States v. Microsoft: A Failure of Antitrust in the New EconomySep 24 2001This paper analyzes the law and economics of United States v. Microsoft, a landmark case of antitrust intervention in network industries. [abridged]

Using invariants for phylogenetic tree constructionSep 18 2007Jan 21 2008Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical interest--they ... More

Toric ideals of homogeneous phylogenetic modelsJan 15 2004We consider the phylogenetic tree model in which every node of the tree is observed and binary and the transitions are given by the same matrix on each edge of the tree. We are able to compute the Grobner basis and Markov basis of the toric ideal of invariants ... More

Generalization of Doob decomposition TheoremJan 14 2016In the paper, we introduce the notion of a local regular supermartingale relative to a convex set of equivalent measures and prove for it an optional Doob decomposition in the discrete case. This Theorem is a generalization of the famous Doob decomposition ... More

Modernizing Quantum Annealing using Local SearchesJun 22 2016Jun 22 2017I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have numerous advantages ... More

Modernizing Quantum Annealing II: Genetic algorithms with the Inference Primitive FormalismSep 19 2016Nov 28 2017Quantum annealing allows for quantum fluctuations to be used used to assist in finding the solution to some of the worlds most challenging computational problems. Recently, this field has attracted much interest because of the construction of large-scale ... More

Random cyclationsAug 03 2004Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and we investigate ... More

The Linking Probability of Deep Spider-Web NetworksFeb 14 2005We consider crossbar switching networks with base $b$ (that is, constructed from $b\times b$ crossbar switches), scale $k$ (that is, with $b^k$ inputs, $b^k$ outputs and $b^k$ links between each consecutive pair of stages) and depth $l$ (that is, with ... More

Straight knotsJan 31 2018Apr 13 2018Jablan and Radovi\'c originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, ... More

On nonlinear polynomial selection for the number field sieveSep 29 2011Jun 28 2013Nonlinear polynomial selection algorithms for the number field sieve address the problem of constructing polynomials with small coefficients by reducing to instances of the well-studied problem of finding short vectors in lattices. The reduction rests ... More

Explicit Infinity-Harmonic Maps whose Interfaces have Junctions and CornersMar 07 2013Given a map $u : \Om \sub \R^n \larrow \R^N$, the $\infty$-Laplacian is the system \[ \label{1} \De_\infty u \, :=\, \Big(Du \ot Du + |Du|^2 [Du]^\bot \ \ot I \Big) : D^2 u\, = \, 0 \tag{1} \] and arises as the "Euler-Lagrange PDE" of the supremal functional ... More

Extensions of racks and quandlesAug 03 2004Jun 22 2005New definitions of rack and quandle modules are introduced, and shown to generalise the definitions previously studied by Andruskiewitsch, Etingof and Grana. This new construct is shown to coincide with Beck's general definition of a module in an arbitrary ... More

Local Complete Segal SpacesJul 20 2016Sep 02 2018We show that the complete Segal model structure extends to a model structure on bimplicial presheaves on a small site $\mathscr{C}$, for which the weak equivalences are local (or stalkwise) weak equivalences. This model structure can be realized as a ... More

The Planar Modular Partition MonoidAug 21 2018The primary contribution of this thesis is to introduce and examine the planar modular partition monoid for parameters $m, k \in \mathbb{Z}_{>0}$, which has simultaneously and independently generated interest from other researchers as outlined within. ... More

Divisibility of great webs and reducible Dehn surgeryOct 13 2014We use the combinatorial techniques of graphs of intersection to study reducible Dehn surgeries on knots in the three-sphere. In particular, in the event that a reducible surgery on a knot K in the three-sphere of slope r produces a manifold with more ... More

On Random Field Induced Ordering in the Classical XY ModelSep 26 2010Consider the classical XY model in a weak random external field pointing along the $Y$ axis with strength $\epsilon$. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension $d \geq 2$ and for all ... More

The Star Formation History of the Solar Neighbourhood from the White Dwarf Luminosity FunctionJun 18 2013The termination in the white dwarf luminosity function is a standard diagnostic tool for measuring the total age of nearby stellar populations. In this paper, an algorithm is presented for inverting the full white dwarf luminosity function to obtain a ... More

Inverting the White Dwarf Luminosity Function: the Star Formation History of the Solar NeighbourhoodSep 25 2012I present an algorithm for inverting the luminosity function for white dwarfs to obtain a maximum likelihood estimate of the star formation rate of the host stellar population. The algorithm is of the general class of Expectation Maximization, and involves ... More

The Tau of Galaxy ClustersJul 08 2016Nov 21 2016The recent emergence of detections of the kinetic Sunyaev-Zel'dovich (kSZ) effect through cross-correlation techniques is encouraging for the prospects of future cosmic microwave background (CMB) experiments. Extracting information on the large-scale ... More

Modernizing Quantum Annealing using Local SearchesJun 22 2016Sep 27 2016I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have numerous advantages ... More

A Simple Guide to S3 MethodsAug 23 2016Writing functions in R is an important skill for anyone using R. S3 methods allow for functions to be generalised across different classes and are easy to implement. Whilst many R users are be adept at creating their own functions, it seems that there ... More

Cohomology of Polychromatic Configuration Spaces of Euclidean SpaceDec 08 2016Recently, the homology and cohomology of non-k-overlapping discs, or, equivalently, no k-equal subspaces of Euclidean space, were calculated by Dobrinskaya and Turchin. We calculate the homology and cohomology of two classes of more general spaces: decreasing ... More

Non-Commutative Integrability of the Grassmann Pentagram MapOct 28 2018Feb 01 2019The pentagram map is a discrete integrable system first introduced by Schwartz in 1992. It was proved to be intregable by Schwartz, Ovsienko, and Tabachnikov in 2010. Gekhtman, Shapiro, and Vainshtein studied Poisson geometry associated to certain networks ... More

Equivariant Kazhdan-Lusztig polynomials of $q$-niform matroidsAug 23 2018Sep 01 2018We introduce $q$-analogues of uniform matroids, which we call $q$-niform matroids. While uniform matroids admit actions of symmetric groups, $q$-niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan-Lusztig ... More

Cocycles in Local Higher Category TheoryFeb 19 2018We develop a model structure on presheaves of small simplicially enriched categories on a site $\mathscr{C}$, for which the weak equivalences are 'stalkwise' weak equivalences for the Bergner model structure. This model structure is right proper, and ... More

Invariants Related to the Tree PropertyNov 19 2015Mar 31 2019We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the relations that obtain ... More

L^2 stability estimates for shock solutions of scalar conservation laws using the relative entropy methodNov 20 2009We consider scalar nonviscous conservation laws with strictly convex flux in one spatial dimension, and we investigate the behavior of bounded L^2 perturbations of shock wave solutions to the Riemann problem using the relative entropy method. We show ... More

Modification of Bayesian Updating where Continuous Parameters have Differing Relationships with New and Existing DataAug 13 2013Bayesian analyses are often performed using so-called noninformative priors, with a view to achieving objective inference about unknown parameters on which available data depends. Noninformative priors depend on the relationship of the data to the parameters ... More

Digital Arroyos: An Examination of State Policy and Regulated Market Boundaries in Constructing Rural Internet AccessSep 25 2001This focused study on state-level policy and access patterns contributes to a fuller understanding of how these invisible barriers work to structure access and define rural communities. Combining both quantitative and qualitative data, this study examines ... More

The Tau of Galaxy ClustersJul 08 2016The recent emergence of detections of the kinetic Sunyeav-Zel'dovich (kSZ) effect through cross-correlation techniques is encouraging for the prospects of future cosmic microwave background (CMB) experiments. Extracting information on the large-scale ... More

Microscopic dissipation in a cohesionless granular jet impactMar 29 2012Sufficiently fine granular systems appear to exhibit continuum properties, though the precise continuum limit obtained can be vastly different depending on the particular system. We investigate the continuum limit of an unconfined, dense granular flow. ... More

Invariants Related to the Tree PropertyNov 19 2015We consider global analogues of model-theoretic tree properties. The main objects of study are the invariants related to Shelah's tree property $\kappa_{\text{cdt}}(T)$, $\kappa_{\text{sct}}(T)$, and $\kappa_{\text{inp}}(T)$ and the relations that obtain ... More

Arithmetic Progressions in the Primitive Length SpectrumFeb 04 2016In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in its primitive length spectrum. Moreover, we show the stronger property that ... More

Low-Lying Cosmic String Spectrum and Background Fields in Effective String TheoryDec 10 2015We present a detailed analysis of the cosmic string spectrum. Explicit solutions are numerically found using Mathematica and presented here for the lowest-lying supported modes. Most of the emphasis is on the Nambu-Goldstone modes and the least massive ... More

An Overview of Approaches to Modernize Quantum Annealing Using Local SearchesJun 22 2016I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. The quantum annealing algorithm is an analogue ... More

Per-event significance indicator to visualise significant eventsFeb 22 2019In this note, an alternative for presenting the distribution of `significant' events in searches for new phenomena is described. The alternative is based on probability density functions used in the evaluation of the `significance' of an observation, ... More

Fast and Fuzzy Private Set IntersectionMay 13 2014May 21 2014Private Set Intersection (PSI) is usually implemented as a sequence of encryption rounds between pairs of users, whereas the present work implements PSI in a simpler fashion: each set only needs to be encrypted once, after which each pair of users need ... More

A Secure and Comparable Text Encryption AlgorithmAug 15 2013This paper discloses a simple algorithm for encrypting text messages, based on the NP-completeness of the subset sum problem, such that the similarity between encryptions is roughly proportional to the semantic similarity between their generating messages. ... More

A Krull-Schmidt Theorem for One-dimensional Rings of Finite Cohen-Macaulay TypeOct 27 2004We determine, up to isomorphism, the indecomposable maximal Cohen-Macaulay modules over certain complete one-dimensional local rings of finite Cohen-Macaulay type. We then investigate the direct sum relations of maximal Cohen-Macaulay modules over non-complete ... More

Constant Mean Curvature TrinoidsMar 02 2004This paper constructs a family of constant mean curvature immersions of the thrice-punctured Riemann sphere into Euclidean 3-space with asymptotically Delaunay ends via loop group methods.

On the structure of $\infty$-Harmonic mapsApr 24 2012Jan 07 2014Let $H \in C^2(\mathbb{R}^{N \times n})$, $H\geq 0$. The PDE system \[ \label{1} A_\infty u \, :=\, \Big(H_P \otimes H_P + H [H_P]^\bot H_{PP} \Big)(Du) : D^2 u\, = \, 0 \tag{1} \] arises as the ``Euler-Lagrange PDE" of vectorial variational problems ... More

The Subelliptic $\infty$-Laplace System on Carnot-Carathéodory SpacesMar 01 2013Apr 11 2013Given a Carnot-Carath\'eodory space $\Om \sub \R^n$ with associated vector fields $X=\{X_1,...,X_m\}$, we derive the subelliptic $\infty$-Laplace system for mappings $u : \Om \larrow \R^N$, which reads \[ \label{1} \De^X_\infty u \, :=\, \Big(Xu \ot Xu ... More

Stair-step bridge spectra does not imply high distanceOct 28 2015Tomova, along with results of Bachman and Schleimer, showed that any high distance knot has a stair-step bridge spectrum. In this paper, we compute the bridge spectra and distance of generalized Montesinos knots. In particular, we produce the first example ... More

Descent Theory and Mapping SpacesSep 03 2018Nov 02 2018The purpose of this paper is to develop a theory of $(\infty, 2)$-stacks, in the sense of Hirschowitz-Simpson's `Descent Pour Les n-Champs', using the language of quasi-category theory and the author's local Joyal model structure. The main result is a ... More

Do We Need a Scientific Revolution?Mar 10 2011Many see modern science as having serious defects, intellectual, social, moral. Few see this as having anything to do with the philosophy of science. I argue that many diverse ills of modern science are a consequence of the fact that the scientific community ... More

Divided Difference Operator for the Highest root Hessenberg varietyApr 30 2013May 01 2013We construct a divided difference operator using GKM theory. This generalizes the classical divided difference operator for the cohomology of the complete flag variety. This construction proves a special case of a recent conjecture of Shareshian and Wachs. ... More

On the de Rham homology and cohomology of a complete local ring in equicharacteristic zeroMar 31 2016Let $A$ be a complete local ring with a coefficient field $k$ of characteristic zero, and let $Y$ be its spectrum. The de Rham homology and cohomology of $Y$ have been defined by R. Hartshorne using a choice of surjection $R \rightarrow A$ where $R$ is ... More

Classifications of Symmetric Normal Form GamesNov 18 2013In this paper we survey various classifications of symmetric games and their characterisations under the theme of fairness; show that game bijections and game isomorphisms form groupoids; introduce matchings as a convenient characterisation of strategy ... More

Generating the support with extreme value lossesFeb 08 2019When optimizing against the mean loss over a distribution of predictions in the context of a regression task, then even if there is a distribution of targets the optimal prediction distribution is always a delta function at a single value. Methods of ... More

Counting Counterfeit Coins: A New Coin Weighing ProblemJun 13 2016In 2007, a new variety of the well-known problem of identifying a counterfeit coin using a balance scale was introduced in the sixth International Kolmogorov Math Tournament. This paper offers a comprehensive overview of this new problem by presenting ... More

On fuzzyfied public announcement operators in Gödel-Dummett logicJul 18 2017In this paper, we consider the expansion of basic modal G\"odel logic with the notions of public announcements. Additionally, the public announcement operators are itself fuzzyfied, allowing statements about relations between the truth-value of a formula ... More

The Interaction Between Multi-Overlaps in the High Temperature Phase of the Sherrington-Kirkpatrick Spin GlassNov 26 2007Apr 10 2008We explore the joint behavior of a finite number of multi-overlaps in the high temperature phase of the SK model. Extending work by M. Talagrand, we show that, when these objects are scaled to have non-trivial limiting distributions, the joint behavior ... More

On the de Rham homology and cohomology of a complete local ring in equicharacteristic zeroMar 31 2016Apr 25 2017Let $A$ be a complete local ring with a coefficient field $k$ of characteristic zero, and let $Y$ be its spectrum. The de Rham homology and cohomology of $Y$ have been defined by R. Hartshorne using a choice of surjection $R \rightarrow A$ where $R$ is ... More

Lyubeznik numbers for nonsingular projective varietiesMar 23 2014Oct 15 2014In this paper, we determine completely the Lyubeznik numbers $\lambda_{i,j}(A)$ of the local ring $A$ at the vertex of the affine cone over a nonsingular projective variety $V$, where $V$ is defined over a field of characteristic zero, in terms of the ... More

Dynamic extensions for the logic of knowing why with public announcements of formulasJul 18 2017Sep 20 2018In this paper, we address the logic of knowing why, an example of a non-standard epistemic logic dealing with justified knowledge via a new epistemic operator, under the extensions with ideas from dynamic epistemic logic, namely public announcements. ... More

Random Field Induced Order in Low Dimension IAug 15 2012Aug 16 2012Consider the classical XY model in a weak random external field pointing along the Y axis with strength $\epsilon$. We prove that the model defined on $\Z^3$ with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for ... More

The average amount of information lost in multiplicationAug 03 2004We show that if X and Y are integers independently and uniformly distributed in the set {1, ..., N}, then the information lost in forming their product (which is given by the equivocation H(X,Y | XY)), is of order log log N. We also prove two extremal ... More

Elementary Proofs of the Main Limit Theorems of ProbabilityJul 25 2012We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most basic notions ... More

Families of not perfectly straight knotsApr 13 2018May 17 2018We present two families of knots which have straight number higher than crossing number. In the case of the second family, we have computed the straight number explicitly. We also give a general theorem about alternating knots that states adding an even ... More

Rack and quandle homologyNov 02 2004The theory of rack and quandle modules is developed - in particular a tensor product is defined, and shown to satisfy an appropriate adjointness condition. Notions of free rack and quandle modules are introduced, and used to define an enveloping object ... More

Two-orbit convex polytopes and tilingsMar 10 2014We classify the convex polytopes whose symmetry groups have two orbits on the flags. These exist only in two or three dimensions, and the only ones whose combinatorial automorphism group is also two-orbit are the cuboctahedron, the icosidodecahedron, ... More

Quantum Steenrod Squares and the Equivariant Pair-of-Pants in Symplectic CohomologyOct 05 2018We relate the quantum Steenrod square to Seidel's equivariant pair-of-pants product for open convex weakly monotone symplectic manifolds, using an equivariant version of the PSS isomorphism. We proceed similarly for $\mathbb{Z}/2$-equivariant symplectic ... More

On geodesic ray bundles in hyperbolic groupsJun 06 2017We construct a Cayley graph $\mathbf{Cay}_S(\Gamma)$ of a hyperbolic group $\Gamma$ such that there are elements $g,h\in\Gamma$ and a point $\gamma \in \partial_\infty\Gamma = \partial_\infty\mathbf{Cay}_S(\Gamma)$ such that the sets $\mathcal{RB}(g,\gamma)$ ... More

On model-theoretic tree propertiesMay 03 2015We study model theoretic tree properties ($\text{TP}, \text{TP}_1, \text{TP}_2$) and their associated cardinal invariants ($\kappa_{\text{cdt}}, \kappa_{\text{sct}}, \kappa_{\text{inp}}$, respectively). In particular, we obtain a quantitative refinement ... More

Sequences of stable bundles over a compact complex surfaceMay 05 1995When identified with sequences of irreducible Hermitian-Einstein connections, sequences of stable holomorphic bundles of fixed topological type and bounded degree on a compact complex surface equipped with a Gauduchon metric are shown to have strongly ... More

The Reflectivity of Mars at 1064 nm: Derivation from Mars Orbiter Laser Altimeter Data and Application to Climatology and MeteorologyMay 31 2016The Mars Orbiter Laser Altimeter (MOLA) on board Mars Global Surveyor (MGS) made $\gg 10^{8}$ measurements of the reflectivity of Mars at 1064 nm ($R_{1064}$) by both active sounding and passive radiometry. Past studies of $R_{1064}$ neglected the effects ... More

Fault Tolerance in Cellular Automata at High Fault RatesSep 06 2007A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the case we treat ... More

Holographic Renormalization Group Flows: The View from Ten DimensionsNov 22 2000The holographic description of supersymmetric RG flows in supergravity is considered from both the five-dimensional and ten-dimensional perspectives. An N=1* flow of N=4 super-Yang Mills is considered in detail, and the infra-red limit is studied in terms ... More

A note on the discrepancy of matrices with bounded row and column sumsJul 08 2013Jul 19 2013A folklore result uses the Lovasz local lemma to analyze the discrepancy of hypergraphs with bounded degree and edge size. We generalize this result to the context of real matrices with bounded row and column sums.

M-decomposability, elliptical unimodal densities, and applications to clustering and kernel density estimationFeb 12 2008Apr 21 2010Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also ... More

r-modes in the Tolman VII solutionJun 18 2001Aug 31 2001The r-mode frequencies of the Tolman VII solution for the slowly rotating non-barotropic approximation within the low frequency regime are estimated. The relativistic correction to Newtonian r-mode calculations is shown as function of the tenuity $\frac{R}{M}$ ... More

Improving the Calibration of Type Ia Supernovae Using Late-time LightcurvesNov 11 2007Jun 20 2008The use of Type Ia supernovae (SNe Ia) as cosmological standard candles is a key to solving the mystery of dark energy. Improving the calibration of SNe Ia increases their power as cosmological standard candles. We find tentative evidence for a correlation ... More

Ray Transforms on a Conformal Class of CurvesNov 01 2010Nov 11 2010We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields defining the initial ... More