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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

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

Ground state solutions for a nonlinear Choquard equationJan 09 2017Sep 30 2017We discuss the existence of ground state solutions for the Choquard equation $$-\Delta u=(I_\alpha*F(u))F'(u)\quad\quad\quad\text{in }\mathbb R^N.$$ We prove the existence of solutions under general hypotheses, investigating in particular the case of ... More

B2 and G2 Toda systems on compact surfaces: a variational approachDec 23 2015Jan 22 2017We consider the B2 and G2 Toda systems on compact surfaces. We attack the problem using variational techniques. We get existence and multiplicity of solutions under a topological assumption on the surface and some generic conditions on the parameters. ... More

Improving Constraints on Fundamental Physics Parameters with the Clustering of Sunyaev-Zeldovich Selected Galaxy ClustersMar 03 2019Upcoming millimeter experiments that probe the cosmic microwave background (CMB) will observe tens of thousands of galaxy clusters through the thermal Sunyaev-Zeldovich (tSZ) effect. tSZ selected clusters are powerful probes of cosmological models, as ... More

Improving Constraints on Fundamental Physics Parameters with the Clustering of Sunyaev-Zeldovich Selected Galaxy ClustersMar 03 2019Mar 30 2019Upcoming millimeter experiments that probe the cosmic microwave background (CMB) will observe tens of thousands of galaxy clusters through the thermal Sunyaev-Zeldovich (tSZ) effect. tSZ selected clusters are powerful probes of cosmological models, as ... More

Testing Gravity with Gravitational Wave Source CountsFeb 11 2016Jun 23 2016We show that the gravitational wave source counts distribution can test how gravitational radiation propagates on cosmological scales. This test does not require obtaining redshifts for the sources. If the signal-to-noise ratio (SNR, $\rho$) from a gravitational ... More

Existence and non-existence results for the SU(3) singular Toda system on compact surfacesAug 04 2015Jan 27 2016We consider the SU(3) Toda system on a compact surface. We give both existence and non-existence results under some conditions on the parameters. Existence results are obtained using variational methods, which involve a geometric inequality of new type; ... More

A Moser-Trudinger inequality for the singular Toda systemJul 15 2013Oct 07 2013In this paper we prove a sharp version of the Moser-Trudinger inequality for the Euler-Lagrange functional of a singular Toda system, motivated by the study of models in Chern-Simons theory. Our result extends those for the scalar case, as well as for ... More

Systematic errors in the measurement of neutrino masses due to baryonic feedback processes: Prospects for stage IV lensing surveysMay 23 2014Sep 04 2014We examine the importance of baryonic feedback effects on the matter power spectrum on small scales, and the implications for the precise measurement of neutrino masses through gravitational weak lensing. Planned large galaxy surveys such as the Large ... More

Weak lensing calibration of mass bias in the REFLEX+BCS X-ray galaxy cluster catalogueFeb 03 2015Apr 03 2017The use of large, X-ray selected galaxy cluster catalogues for cosmological analyses requires a thorough understanding of the X-ray mass estimates. Weak gravitational lensing is an ideal method to shed light on such issues, due to its insensitivity to ... More

Precision Studies of the Higgs Boson Profile at the e+e- Linear ColliderJan 15 2001This paper reviews the potential of a high luminosity e+e- linear collider (LC) in the precision study of the Higgs boson profile. The complementarity of the linear collider data with that from the LHC is also discussed together with a comparison with ... More

Weak lensing calibration of mass bias in the REFLEX+BCS X-ray galaxy cluster catalogueFeb 03 2015Nov 28 2015The use of large, X-ray selected galaxy cluster catalogues for cosmological analyses requires a thorough understanding of the X-ray mass estimates.%, including the possibility of biases due to the assumption of hydrostatic equilibrium. Weak gravitational ... More

Neutrino Mass from Cosmology: Probing Physics Beyond the Standard ModelMar 08 2019Recent advances in cosmic observations have brought us to the verge of discovery of the absolute scale of neutrino masses. Nonzero neutrino masses are known evidence of new physics beyond the Standard Model. Our understanding of the clustering of matter ... More

Beyond CMB cosmic variance limits on reionization with the polarized SZ effectOct 04 2017May 31 2018Upcoming cosmic microwave background (CMB) surveys will soon make the first detection of the polarized Sunyaev-Zel'dovich effect, the linear polarization generated by the scattering of CMB photons on the free electrons present in collapsed objects. Measurement ... More

Future constraints on halo thermodynamics from combined Sunyaev-Zel'dovich measurementsMay 16 2017Oct 13 2017The improving sensitivity of measurements of the kinetic Sunyaev-Zel'dovich (SZ) effect opens a new window into the thermodynamic properties of the baryons in halos. We propose a methodology to constrain these thermodynamic properties by combining the ... More

Groundstates of the Choquard equations with a sign-changing self-interaction potentialOct 12 2017May 17 2018We consider a nonlinear Choquard equation $$ -\Delta u+u= (V * |u|^p )|u|^{p-2}u \qquad \text{in }\mathbb{R}^N, $$ when the self-interaction potential $V$ is unbounded from below. Under some assumptions on $V$ and on $p$, covering $p =2$ and $V$ being ... More

Electron Distribution Functions in Solar Flares from combined X-ray and EUV ObservationsOct 15 2013Simultaneous solar flare observations with SDO and RHESSI provide spatially resolved information about hot plasma and energetic particles in flares. RHESSI allows the properties of both hot (> 8 MK) thermal plasma and nonthermal electron distributions ... More

RHESSI and SDO/AIA observations of the chromospheric and coronal plasma parameters during a solar flareOct 11 2012X-ray and EUV observations are an important diagnostic of various plasma parameters of the solar atmosphere during solar flares. Soft X-ray and EUV observations often show coronal sources near the top of flaring loops, while hard X-ray emission is mostly ... More

Testing the Large-Scale Environments of Cool-core and Noncool-core Clusters with Clustering BiasOct 05 2016There is a well observed bimodality in X-ray astronomy between cool-core (CC) and non-cool-core (NCC) clusters, but the origin of this distinction is still largely unknown. Competing theories can be divided into internal (inside-out), in which internal ... More

The BlueTides Simulation: First Galaxies and ReionizationApr 24 2015We introduce the BlueTides simulation and report initial results for the luminosity functions of the first galaxies and AGN, and their contribution to reionization. BlueTides was run on the BlueWaters cluster at NCSA from $z=99$ to $z=8.0$ and includes ... More

Visual Interaction NetworksJun 05 2017From just a glance, humans can make rich predictions about the future state of a wide range of physical systems. On the other hand, modern approaches from engineering, robotics, and graphics are often restricted to narrow domains and require direct measurements ... More

Testing the Large-Scale Environments of Cool-core and Noncool-core Clusters with Clustering BiasOct 05 2016Feb 16 2017There are well-observed differences between cool-core (CC) and non-cool-core (NCC) clusters, but the origin of this distinction is still largely unknown. Competing theories can be divided into internal (inside-out), in which internal physical processes ... More

Reionization on Large Scales IV: Predictions for the 21 cm signal incorporating the light cone effectSep 26 2013Aug 01 2014We present predictions for the 21 cm brightness temperature power spectrum during the Epoch of Reionization (EoR). We discuss the implications of the "light cone" effect, which incorporates evolution of the neutral hydrogen fraction and 21 cm brightness ... More

A Machine Learning Approach for Dynamical Mass Measurements of Galaxy ClustersOct 02 2014Apr 27 2015We present a modern machine learning approach for cluster dynamical mass measurements that is a factor of two improvement over using a conventional scaling relation. Different methods are tested against a mock cluster catalog constructed using halos with ... More

Constraining primordial magnetic fields through large scale structureNov 12 2012Apr 15 2013We study primordial magnetic field effects on the matter perturbations in the Universe. We assume magnetic field generation prior to the big bang nucleosynthesis (BBN), i.e. during the radiation dominated epoch of the Universe expansion, but do not limit ... More

Measuring the Thermal Sunyaev-Zel'dovich Effect Through the Cross Correlation of Planck and WMAP Maps with ROSAT Galaxy Cluster CatalogsSep 12 2013We measure a significant correlation between the thermal Sunyaev-Zel'dovich effect in the Planck and WMAP maps and an X-ray cluster map based on ROSAT. We use the 100, 143 and 343 GHz Planck maps and the WMAP 94 GHz map to obtain this cluster cross spectrum. ... More

On the Assembly Bias of Cool Core Clusters Traced by H$α$ NebulaeMar 12 2019Do cool-core (CC) and noncool-core (NCC) clusters live in different environments? We make novel use of H$\alpha$ emission lines in the central galaxies of redMaPPer clusters as proxies to construct large (1,000's) samples of CC and NCC clusters, and measure ... More

The Stacked Thermal SZ Signal of Locally Brightest Galaxies in Planck Full Mission Data: Evidence for Galaxy Feedback?Sep 23 2014Jul 31 2015We use the Planck full mission temperature maps to examine the stacked thermal Sunyaev-Zel'dovich (tSZ) signal of 188042 "locally brightest galaxies'" (LBGs) selected from the Sloan Digital Sky Survey Data Release 7. Our LBG sample closely matches that ... More

The formation of Milky Way-mass disk galaxies in the first 500 million years of a cold dark matter universeApr 24 2015Jun 15 2015Whether among the myriad tiny proto-galaxies there exists a population with similarities to present day galaxies is an open question. We show, using BlueTides, the first hydrodynamic simulation large enough to resolve the relevant scales, that the first ... More

Cosmology with kSZ: breaking the optical depth degeneracy with Fast Radio BurstsJan 08 2019The small-scale cosmic microwave background (CMB) is dominated by anisotropies from the kinematic Sunyaev-Zeldovich (kSZ) effect, and upcoming experiments will measure it very precisely, but the optical depth degeneracy limits the cosmological information ... More

Nonradial entire solutions for Liouville systemsJan 11 2017Jun 13 2017We consider the following system of Liouville equations: $$\left\{\begin{array}{ll}-\Delta u_1=2e^{u_1}+\mu e^{u_2}&\text{in }\mathbb R^2\\-\Delta u_2=\mu e^{u_1}+2e^{u_2}&\text{in }\mathbb R^2\\\int_{\mathbb R^2}e^{u_1}<+\infty,\int_{\mathbb R^2}e^{u_2}<+\infty\end{array}\right.$$ ... More

An efficient relativistic density-matrix renormalization group implementation in a matrix-product formulationOct 23 2017We present an implementation of the relativistic quantum-chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions including a variational ... More

Monojet Searches for MSSM Simplified ModelsJun 06 2015Sep 19 2016We explore the implications of monojet searches at hadron colliders in the minimal supersymmetric extension of the Standard Model (MSSM). To quantify the impact of monojet searches, we consider simplified MSSM scenarios with neutralino dark matter. The ... More

Supersymmetry with Light Dark Matter confronting the recent CDMS and LHC ResultsAug 09 2013Oct 18 2013We revisit MSSM scenarios with light neutralino as a dark matter candidate in view of the latest LHC and dark matter direct and indirect detection experiments. We show that scenarios with a very light neutralino (~ 10 GeV) and a scalar bottom quark close ... More

Implications of LHC Searches on SUSY Particle Spectra: The pMSSM Parameter Space with Neutralino Dark MatterOct 17 2011Dec 14 2011We study the implications of LHC searches on SUSY particle spectra using flat scans of the 19-parameter pMSSM phase space. We apply constraints from flavour physics, g_mu-2, dark matter and earlier LEP and Tevatron searches. The sensitivity of the LHC ... 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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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

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

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

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

The Simons Observatory: Project OverviewOct 05 2018The Simons Observatory (SO) will make precision temperature and polarization measurements of the cosmic microwave background (CMB) over angular scales between 1 arcminute and tens of degrees using over 60,000 detectors and sampling frequencies between ... 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

A Construction of the Quantum Steenrod Squares and Their Algebraic RelationsMay 07 2018We construct a quantum deformation of the Steenrod square construction on closed monotone symplectic manifolds, based on the work of Fukaya, Betz and Cohen. We prove quantum versions of the Cartan and Adem relations. We compute the quantum Steenrod squares ... 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

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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

Some Structure Properties of Finite Normal-Form GamesMay 02 2019Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic structure of ... 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

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

Optical Design of PICO, a Concept for a Space Mission to Probe Inflation and Cosmic OriginsAug 03 2018The Probe of Inflation and Cosmic Origins (PICO) is a probe-class mission concept currently under study by NASA. PICO will probe the physics of the Big Bang and the energy scale of inflation, constrain the sum of neutrino masses, measure the growth of ... More

Coevolutionary Genetic Algorithms for Establishing Nash Equilibrium in Symmetric Cournot GamesMay 22 2009We use co-evolutionary genetic algorithms to model the players' learning process in several Cournot models, and evaluate them in terms of their convergence to the Nash Equilibrium. The "social-learning" versions of the two co-evolutionary algorithms we ... More

Complex quotients by nonclosed groups and their stratificationsApr 20 2007Mar 01 2008We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural generalization to the nonrational ... More

A general existence result for stationary solutions to the Keller-Segel systemFeb 07 2018Dec 09 2018We consider a Liouville-type PDE on a smooth bounded planar domain, which is related to stationary solutions of the Keller-Segel's model for chemotaxis. We prove existence of solutions under some algebraic conditions on the parameters. In particular, ... More

Uniform bounds for solutions to elliptic problems on simply connected planar domainsSep 15 2018Dec 09 2018We consider the singular Liouville equation and the Henon-Lane-Emden problem on simply connected planar domains. We show that any solution to each problem must satisfy a uniform bound on the mass. The same results applies to some systems and more general ... More