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Measuring Electromagnetic and Gravitational Responses of Photonic Landau LevelsFeb 13 2018The topology of an object describes global properties that are insensitive to local perturbations. Classic examples include string knots and the genus (number of handles) of a surface: no manipulation of a closed string short of cutting it changes its ... More

Detecting essential surfaces as intersections in the character varietySep 15 2016We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In particular, these ... More

F-polynomial formula from continued fractionsDec 20 2016For cluster algebras from surfaces, there is a known formula for cluster variables and F-polynomials in terms of the perfect matchings of snake graphs. If the cluster algebra has trivial coefficients, there is also a known formula for cluster variables ... More

Moduli spaces for families of rational maps on P^1Feb 11 2009Feb 15 2009Let phi: P^1 --> P^1 be a rational map defined over a field K. We construct the moduli space M_d(N) parameterizing conjugacy classes of degree-d maps with a point of formal period N and present an algebraic proof that M_2(N) is geometrically irreducible ... More

Difference modules and difference cohomologyDec 21 2016Jun 27 2018We give some basics about homological algebra of difference representations. We consider both the difference-discrete and the difference-rational case. We define the corresponding cohomology theories and show the existence of spectral sequences relating ... More

Detecting essential surfaces as intersections in the character varietySep 15 2016Jul 22 2017We describe a family of hyperbolic knots whose character variety contain exactly two distinct components of characters of irreducible representations. The intersection points between the components carry rich topological information. In particular, these ... More

Dynamics on the PSL(2,C)-character variety of a compression bodyJul 02 2013Let M be a nontrivial compression body without toroidal boundary components. We study the dynamics of the group of outer automorphisms of the fundamental group of M on the PSL(2,C)-character variety of M.

Dynamics on the PSL(2,C)-character variety of a twisted I-bundleMar 17 2011Let M be a twisted interval bundle over a nonorientable hyperbolizable surface. Let X(M) be the PSL(2,C)-character variety of \pi_1(M). We examine the dynamics of the action of Out(\pi_1(M)) on X(M), and in particular, we find an open set on which the ... More

Special subgroups of Bianchi groupsSep 29 2017We determine C-special subgroups of the Bianchi groups of index bounded above by 120 by effectivising the arguments of Agol-Long-Reid. These subgroups are congruence of level 2 or 4 and retract to the free group on two generators. As a consequence, we ... More

On Adaptation Cost and Tractability in Robust Adaptive Radiation Therapy OptimizationMay 14 2019A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii) address adaptation ... More

Finding New Order in Biological Functions from the Network Structure of Gene AnnotationsSep 28 2012May 03 2013The Gene Ontology (GO) provides biologists with a controlled terminology that describes how genes are associated with functions and how functional terms are related to each other. These term-term relationships encode how scientists conceive the organization ... More

Network Coding: Is zero error always possible?Feb 15 2011Oct 02 2011In this work we study zero vs. epsilon-error capacity in network coding instances. For multicast network coding it is well known that all rates that can be delivered with arbitrarily small error probability can also be delivered with zero error probability; ... More

Milnor-Wood inequalities for manifolds locally isometric to a product of hyperbolic planesApr 12 2008This note describes sharp Milnor--Wood inequalities for the Euler number of flat oriented vector bundles over closed Riemannian manifolds locally isometric to products of hyperbolic planes. One consequence is that such manifolds do not admit an affine ... More

The generalized Chern conjecture for manifolds that are locally a product of surfacesFeb 09 2009May 23 2009We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old conjecture proved ... More

The field of definition for dynamical systems on P^NSep 26 2013Let Hom^N_d be the set of morphisms of degree d from P^N to itself. For f an element of PGL_{N+1}, let phi^f represent the conjugation action f^{-1} phi f. Let M^N_d = Hom_d^N/PGL_{N+1} be the moduli space of degree d morphisms of P^N. A field of definition ... More

An Experimental View of Herman Rings for Dianalytic Maps of $\mathbb{RP}^2$Jun 29 2017We provide an experimental study of the existence of Herman rings in a parametrized family of rational maps preserving antipodal points, and a discussion of their properties on $\mathbb{RP}^2$. We study analytic maps of the sphere that project to dianalytic ... More

Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristicMay 10 2016Jan 24 2019We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely ... More

Explicit Descriptions of Quadratic Maps on $\pp^1$ defined over a field $K$Apr 15 2010Jul 30 2010We describe an explicit parameter space for the set of all quadratic rational maps on $\pp^1$ defined over a field $K$, up to conjugacy over $K$.

Annotation Enrichment Analysis: An Alternative Method for Evaluating the Functional Properties of Gene SetsAug 20 2012May 03 2013Gene annotation databases (compendiums maintained by the scientific community that describe the biological functions performed by individual genes) are commonly used to evaluate the functional properties of experimentally derived gene sets. Overlap statistics, ... More

The norm of the Euler classSep 13 2010We prove that the norm of the Euler class E for flat vector bundles is $2^{-n}$ (in even dimension $n$, since it vanishes in odd dimension). This shows that the Sullivan--Smillie bound considered by Gromov and Ivanov--Turaev is sharp. We construct a new ... More

The absence of phase transition for the classical XY-model on Sierpinski pyramid with fractal dimension D=2Aug 27 2010For the spin models with continuous symmetry on regular lattices and finite range of interactions the lower critical dimension is d=2. In two dimensions the classical XY-model displays Berezinskii-Kosterlitz-Thouless transition associated with unbinding ... More

Tailoring Native Defects in LiFePO4: Insights from First-Principles CalculationsMay 17 2011We report first-principles density-functional theory studies of native point defects and defect complexes in olivine-type LiFePO4, a promising candidate for rechargeable Li-ion battery electrodes. The defects are characterized by their formation energies ... More

Milnor-Wood inequalities for productsJan 01 2012We prove Milnor-Wood inequalities for local products of manifolds. As a consequence, we establish the generalized Chern Conjecture for products $M\times \Sigma^k$ for any product of a manifold $M$ with a product of $k$ copies of a surface $\Sigma$ for ... More

Dynamical Tides in Highly Eccentric Binaries: Chaos, Dissipation and Quasi-Steady StateAug 30 2017Feb 01 2018Highly eccentric binary systems appear in many astrophysical contexts, ranging from tidal capture in dense star clusters, precursors of stellar disruption by massive black holes, to high-eccentricity migration of giant planets. In a highly eccentric binary, ... More

Sum list coloring, the sum choice number, and sc-greedy graphsMay 08 2013Let G=(V,E) be a graph and let f be a function that assigns list sizes to the vertices of G. It is said that G is f-choosable if for every assignment of lists of colors to the vertices of G for which the list sizes agree with f, there exists a proper ... More

Separable-stable representations of a compression bodyNov 06 2013Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The set of separable-stable ... More

On a recursive construction of circular paths and the search for $π$ on the integer lattice $\mathbb{Z}^2$Feb 04 2016Digital circles not only play an important role in various technological settings, but also provide a lively playground for more fundamental number-theoretical questions. In this paper, we present a new recursive algorithm for the construction of digital ... More

Optical Spectroscopy of GX 339-4 - Paper I: Orbital ModulationFeb 12 2003Optical spectroscopic observations of GX 339-4 were carried out between 1998 May (X-ray high state) and 1999 May (X-ray low state) over 7 epochs. The equivalent width of Halpha increased during the high state then decreased during the low state. The equivalent ... More

How quantum bound states bounce and the structure it revealsAug 30 2010Mar 01 2011We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic ... More

Separation of source-network coding and channel coding in wireline networksOct 17 2011Dec 18 2012In this paper we prove the separation of source-network coding and channel coding in wireline networks. For the purposes of this work, a wireline network is any network of independent, memoryless, point-to-point, finite-alphabet channels used to transmit ... More

Bringing the Internet to Schools: US and EU policiesSep 24 2001The Internet is changing rapidly the way people around the world communicate, learn, and work. Yet the tremendous benefits of the Internet are not shared equally by all. One way to close the gap of the "digital divide" is to ensure Internet access to ... More

A Survey of the Trends in Facial and Expression Recognition Databases and MethodsNov 07 2015Dec 05 2015Automated facial identification and facial expression recognition have been topics of active research over the past few decades. Facial and expression recognition find applications in human-computer interfaces, subject tracking, real-time security surveillance ... More

Random 4-regular graphs have claw-decompositions asymptotically almost surelyOct 04 2016In 2006, Barat and Thomassen conjectured that the edges of every planar 4-regular 4-edge connected graph can be decomposed into claws. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method ... More

Statistical Implications of the Revenue Transfer Methodology in the Affordable Care ActMar 03 2017Jun 07 2018The Affordable Care Act (ACA) includes a permanent revenue transfer methodology which provides financial incentives to health insurance plans that have higher than average actuarial risk. In this paper, we derive some statistical implications of the revenue ... More

A numerical scheme for impact problemsOct 04 1999We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the boundary of K is ... More

A hyperbolic counterpart to Rokhlin's cobordism theoremMay 12 2019The purpose of the present note is to prove existence of super-exponentially many compact orientable hyperbolic arithmetic $n$-manifolds that are geometric boundaries of compact orientable hyperbolic $(n+1)$-manifolds, for each $2 \leq n \leq 8$, thereby ... More

Virtual Windshields: Merging Reality and Digital Content to Improve the Driving ExperienceMay 05 2014In recent years, the use of the automobile as the primary mode of transportation has been increasing and driving has become an important part of daily life. Driving is a multi-sensory experience as drivers rely on their senses to provide them with important ... More

On anti-Ramsey numbers for complete bipartite graphs and the Turan functionAug 25 2011Nov 18 2015Given two graphs $G$ and $H$ with $H\subseteq G$ we consider the anti-Ramsey function $AR(G,H)$ which is the maximum number of colors in any edge-coloring of $G$ so that every copy of $H$ receives the same color on at least one pair of edges. The classical ... More

On a Conjecture of ThomassenOct 18 2014Jun 10 2015In 1989, Thomassen asked whether there is an integer-valued function f(k) such that every f(k)-connected graph admits a spanning, bipartite $k$-connected subgraph. In this paper we take a first, humble approach, showing the conjecture is true up to a ... More

Obstructions to ShellabilityJul 07 1997We consider a simplicial complex generaliztion of a result of Billera and Meyers that every nonshellable poset contains the smallest nonshellable poset as an induced subposet. We prove that every nonshellable $2$-dimensional simplicial complex contains ... More

Surface bundles over surfaces: new inequalities between signature, simplicial volume and Euler characteristicMay 10 2016We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, namely ... More

On the Capacity Advantage of a Single BitJul 24 2016In this work we study the capacity advantage achieved by adding a single bit of communication -- not a link of capacity 1 but a single bit over all time -- to a memoryless network. Specifically, we present a memoryless network in which adding a single ... More

On Zero-Error Source Coding with FeedbackJan 14 2010We consider the problem of zero error source coding with limited feedback when side information is present at the receiver. First, we derive an achievable rate region for arbitrary joint distributions on the source and the side information. When all source ... More

The bounded cohomology of SL_2 over local fields and S-integersSep 16 2016It is proved that the continuous bounded cohomology of SL_2(k) vanishes in all positive degrees whenever k is a non-Archimedean local field. This holds more generally for boundary-transitive groups of tree automorphisms and implies low degree vanishing ... More

On the Separation of Lossy Source-Network Coding and Channel Coding in Wireline NetworksMay 02 2010This paper proves the separation between source-network coding and channel coding in networks of noisy, discrete, memoryless channels. We show that the set of achievable distortion matrices in delivering a family of dependent sources across such a network ... More

A Flexible Mixed Integer Programming framework for Nurse SchedulingOct 12 2012In this paper, a nurse-scheduling model is developed using mixed integer programming model. It is deployed to a general care ward to replace and automate the current manual approach for scheduling. The developed model differs from other similar studies ... More

Intelligent Search Heuristics for Cost Based SchedulingOct 04 2012Nurse scheduling is a difficult optimization problem with multiple constraints. There is extensive research in the literature solving the problem using meta-heuristics approaches. In this paper, we will investigate an intelligent search heuristics that ... More

Periodic points in towers of finite fields for polynomials associated to algebraic groupsJan 25 2013We find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps z^d and Chebyshev polynomials.

Multicut decomposition methods with cut selection for multistage stochastic programsMay 24 2017Mar 15 2018We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates strategies to select the most relevant cuts of ... More

Single cut and multicut SDDP with cut selection for multistage stochastic linear programs: convergence proof and numerical experimentsFeb 14 2019We introduce a variant of Multicut Decomposition Algorithms (MuDA), called CuSMuDA (Cut Selection for Multicut Decomposition Algorithms), for solving multistage stochastic linear programs that incorporates a class of cut selection strategies to choose ... More

On the Product Representation of Number Sequences, with Application to the Fibonacci FamilyAug 25 2015We investigate general properties of number sequences which allow explicit representation in terms of products. We find that such sequences form whole families of number sequences sharing similar recursive identities. Restricting to the cosine of fractional ... More

Poset Topology: Tools and ApplicationsFeb 10 2006Feb 11 2006These lecture notes for the IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004) provide an overview of poset topology. These notes include introductory material, as well as recent developments and open problems. Some of the topics ... More

Minimal exponential growth rates of metabelian Baumslag-Solitar groups and lamplighter groupsJun 11 2015We prove that for any prime $p\geq 3$ the minimal exponential growth rate of the Baumslag-Solitar group $BS(1,p)$ and the lamplighter group $\mathcal{L}_p=(\mathbb{Z}/p\mathbb{Z})\wr \mathbb{Z}$ are equal. We also show that for $p=2$ this claim is not ... More

Reflections on trisection genusSep 13 2018The Heegaard genus of a 3-manifold, as well as the growth of Heegaard genus in its finite sheeted cover spaces, has extensively been studied in terms of algebraic, geometric and topological properties of the 3-manifold. This note shows that analogous ... More

Penalty approximation for non smooth constraints in vibroimpactApr 10 2000We examine the penalty approximation of the free motion of a material point in an angular domain; we choose an over-damped penalty, and we prove that if the first impact point is not at the vertex, then, the limit of the approximation exists and is described ... More

On the use of analytic expressions for the voltage distribution to analyze intracellular recordingsFeb 09 2006Different analytic expressions for the membrane potential distribution of membranes subject to synaptic noise have been proposed, and can be very helpful to analyze experimental data. However, all of these expressions are either approximations or limit ... More

Cyclic sieving and rational Catalan theoryOct 28 2015Let $a < b$ be coprime positive integers. Armstrong, Rhoades, and Williams defined a set $\mathsf{NC}(a,b)$ of `rational noncrossing partitions', which form a subset of the ordinary noncrossing partitions of $\{1, 2, \dots, b-1\}$. Confirming a conjecture ... More

Effective Field Theory for Bound State ReflectionJun 27 2012Jan 17 2013Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory for elastic ... More

Small generators of cocompact arithmetic Fuchsian groupsMar 02 2016In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which we determine ... More

A Greedy Double Swap Heuristic for Nurse SchedulingMay 10 2012One of the key challenges of nurse scheduling problem (NSP) is the number of constraints placed on preparing the timetable, both from the regulatory requirements as well as the patients' demand for the appropriate nursing care specialists. In addition, ... More

Small generators of cocompact arithmetic Fuchsian groupsMar 02 2016Jul 22 2017In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in $\mathbf{SL}_2(\mathbb{R})$ from which we determine ... More

Universality under conditions of self-tuningFeb 11 2009Aug 09 2010We study systems with a continuous phase transition that tune their parameters to maximize a quantity that diverges solely at a unique critical point. Varying the size of these systems with dynamically adjusting parameters, the same finite-size scaling ... More

Galois theory of quadratic rational functionsJan 23 2011May 04 2012For a number field K with absolute Galois group G_K, we consider the action of G_K on the infinite tree of preimages of a point in K under a degree-two rational function phi, with particular attention to the case when phi commutes with a non-trivial Mobius ... More

Continued fractions and orderings on the Markov numbersJan 22 2018Markov numbers are integers that appear in the solution triples of the Diophantine equation, $x^2+y^2+z^2=3xyz$, called the Markov equation. A classical topic in number theory, these numbers are related to many areas of mathematics such as combinatorics, ... More

On Macroscopic dimension of non-spin 4-manifoldsApr 01 2019We prove that for 4-manifolds $M$ with residually finite fundamental group and non-spin universal covering $\Wi M$, the inequality $\dim_{mc}\Wi M\le 3$ implies the inequality $\dim_{mc}\Wi M\le 2$.

The simplicial volume of closed manifolds covered by H^2 x H^2Mar 20 2007Sep 13 2007We compute the value of the simplicial volume for closed, oriented Riemannian manifolds covered by $\mathbb{H}^{2}\times\mathbb{H}^{2}$ explicitly, thus in particular for products of closed hyperbolic surfaces. This gives the first exact value of a nonvanishing ... More

A tree metric using structure and length to capture distinct phylogenetic signalsJul 18 2015Sep 11 2015Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources (e.g. several ... More

Exponential growth rates of free and amalgamated productsSep 18 2012We prove that there is a gap between $\sqrt{2}$ and $(1+\sqrt{5})/2$ for the exponential growth rate of free products $G=A*B$ not isomorphic to the infinite dihedral group. For amalgamated products $G=A*_C B$ with $([A:C]-1)([B:C]-1)\geq2$, we show that ... More

Pi Visits ManhattanJul 31 2017Is it possible to draw a circle in Manhattan, using only its discrete network of streets and boulevards? In this study, we will explore the construction and properties of circular paths on an integer lattice, a discrete space where the distance between ... More

Defect chemistry in layered transition-metal oxides from screened hybrid density functional calculationsDec 16 2014We report a comprehensive first-principles study of the thermodynamics and transport of intrinsic point defects in layered oxide cathode materials LiMO$_2$ (M=Co, Ni), using density-functional theory and the Heyd-Scuseria-Ernzerhof screened hybrid functional. ... More

q-Eulerian Polynomials: Excedance Number and Major indexAug 11 2006In this research announcement we present a new q-analog of a classical formula for the exponential generating function of the Eulerian polynomials. The Eulerian polynomials enumerate permutations according to their number of descents or their number of ... More

Superfluid Friction and Late-time Thermal Evolution of Neutron StarsOct 27 1998The recent temperature measurements of the two older isolated neutron stars PSR 1929+10 and PSR 0950+08 (ages of $3\times 10^6$ and $2\times 10^7$ yr, respectively) indicate that these objects are heated. A promising candidate heat source is friction ... More

Persistent Homology of Geospatial Data: A Case Study with VotingJan 29 2019A crucial step in the analysis of persistent homology is transformation of data into a simplicial complex. Modern packages for persistent homology often construct Vietoris--Rips or other distance-based simplicial complexes on point clouds because they ... More

On enumerators of Smirnov words by descents and cyclic descentsJan 06 2019Apr 26 2019A Smirnov word is a word over the positive integers in which adjacent letters must be different. A symmetric function enumerating these words by descent number arose in the work of Shareshian and the second named author on $q$-Eulerian polynomials, where ... More

From Poset Topology to $q$-Eulerian Polynomials to Stanley's Chromatic Symmetric FunctionsMay 13 2015In recent years we have worked on a project involving poset topology, various analogues of Eulerian polynomials, and a refinement of Richard Stanley's chromatic symmetric function. Here we discuss how Stanley's ideas and results have influenced and inspired ... More

A Harris process to model stochastic volatilityMay 17 2016We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions, properties, ... More

A classification of degree $2$ semi-stable rational maps $\mathbb{P}^2\to\mathbb{P}^2$ with large finite dynamical automorphism groupJul 19 2016Aug 25 2017Let $K$ be an algebraically closed field of characteristic $0$. In this paper we classify the $\text{PGL}_3(K)$-conjugacy classes of semi-stable dominant degree $2$ rational maps $f:{\mathbb P}^2_K\dashrightarrow{\mathbb P}^2_K$ whose automorphism group ... More

Simulations of Glitches in Isolated PulsarsMay 25 2001Many radio pulsars exhibit glitches wherein the star's spin rate increases fractionally by $\sim 10^{-10} - 10^{-6}$. Glitches are ascribed to variable coupling between the neutron star crust and its superfluid interior. With the aim of distinguishing ... More

Top homology of hypergraph matching complexes, $p$-cycle complexes and Quillen complexes of symmetric groupsAug 22 2008We investigate the representation of a symmetric group $S_n$ on the homology of its Quillen complex at a prime $p$. For homology groups in small codimension, we derive an explicit formula for this representation in terms of the representations of symmetric ... More

Eulerian quasisymmetric functions and poset topologyMay 15 2008We introduce a family of quasisymmetric functions called {\em Eulerian quasisymmetric functions}, which have the property of specializing to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations ... More

Eulerian quasisymmetric functionsDec 03 2008Aug 21 2010We introduce a family of quasisymmetric functions called {\em Eulerian quasisymmetric functions}, which specialize to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle ... More

On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi NumbersNov 16 2018May 11 2019Hetyei recently introduced a hyperplane arrangement (called the homogenized Linial arrangement) and used the finite field method of Athanasiadis to show that its number of regions is a median Genocchi number. These numbers count a class of permutations ... More

A finite mixture model approach to regression under covariate misclassificationNov 28 2016Apr 26 2017This paper considers the problem of mismeasured categorical covariates in the context of regression modeling; if unaccounted for, such misclassification is known to result in misestimation of model parameters. Here, we exploit the fact that explicitly ... More

Pruning Bayesian Networks for Efficient ComputationMar 27 2013This paper analyzes the circumstances under which Bayesian networks can be pruned in order to reduce computational complexity without altering the computation for variables of interest. Given a problem instance which consists of a query and evidence for ... More

Machine Learning Applied to the Reionization History of the UniverseOct 18 2018The Epoch of Reionization (EoR) features a rich interplay between the first luminous sources and the low-density gas of the intergalactic medium (IGM), where photons from these sources ionize the IGM. There are currently few observational constraints ... More

Unimodality of Eulerian quasisymmetric functionsJan 24 2011We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and polynomials. The first states that the cycle type Eulerian quasisymmetric function $Q_{\lambda,j}$ is Schur-positive, and moreover that the sequence $Q_{\lambda,j}$ ... More

Chromatic quasisymmetric functionsMay 19 2014Mar 29 2016We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric ... More

Torsion in the Matching Complex and Chessboard ComplexSep 03 2004Topological properties of the matching complex were first studied by Bouc in connection with Quillen complexes, and topological properties of the chessboard complex were first studied by Garst in connection with Tits coset complexes. Bj\"orner, Lov\'asz, ... More

The Thual-Fauve pulse: skew stabilizationSep 15 1999It is possible to choose the parameters of a real quintic Ginzburg-Landau equation so that it possesses localized pulse-like solutions; Thual and Fauve have observed numerically that these pulses are stabilized by perturbations destroying the gradient ... More

Counterexamples Related to Rotations of Shadows of Convex BodiesMay 21 2015We construct examples of two convex bodies $K,L$ in $\mathbb{R}^n$, such that every projection of $K$ onto a $(n-1)$-dimensional subspace can be rotated to be contained in the corresponding projection of $L$, but $K$ itself cannot be rotated to be contained ... More

Electromechanical control of quantum emitters in nanophotonic devicesJan 25 2019Photon-mediated coupling between distant matter qubits may enable secure communication over long distances, the implementation of distributed quantum computing schemes, and the exploration of new regimes of many-body quantum dynamics. Nanophotonic devices ... More

Quantum interference of electromechanically stabilized emitters in nanophotonic devicesJan 25 2019Feb 22 2019Photon-mediated coupling between distant matter qubits may enable secure communication over long distances, the implementation of distributed quantum computing schemes, and the exploration of new regimes of many-body quantum dynamics. Nanophotonic devices ... More

Chromatic quasisymmetric functions and Hessenberg varietiesJun 21 2011Jul 06 2012We discuss three distinct topics of independent interest; one in enumerative combinatorics, one in symmetric function theory, and one in algebraic geometry. The topic in enumerative combinatorics concerns a q-analog of a generalization of the Eulerian ... More

Solitary waves and conservation laws for highly nonlinear wave equations modeling granular chainsJul 16 2015Jan 11 2016Nonlinear fourth-order wave equations modeling the long wavelength behavior of compression pulses in one-dimensional homogeneous granular chains with weak and strong initial pre-compression are considered. As a main result, the exact solitary wave solution ... More

First-principles studies of the effects of impurities on the ionic and electronic conduction in LiFePO$_{4}$Jan 19 2012Olivine-type LiFePO$_{4}$ is widely considered as a candidate for Li-ion battery electrodes, yet its applicability in the pristine state is limited due to poor ionic and electronic conduction. Doping can be employed to enhance the material's electrical ... More

A finite mixture model approach to regression under covariate misclassificationNov 28 2016This paper considers the problem of mismeasured categorical covariates in the context of regression modeling; if unaccounted for, such misclassification is known to result in misestimation of model parameters. Here, we exploit the fact that explicitly ... More

On the thermal expansion in MgSiN$_{2}$Oct 19 2017The thermal expansion of the wide band gap semiconductor MgSiN$_{2}$ has been determined using density functional calculations in combination with the quasi-harmonic approximation. We find that the thermal expansion is rather small in good agreement with ... More

Electronic structure of the high and low pressure polymorphs of MgSiN$_{2}$May 02 2016We have performed density functional calculations on the group II-IV nitride MgSiN$_{2}$. At a pressure of about 20~GPa the ground state wurtzite derived MgSiN$_{2}$ structure (LP-MgSiN$_{2}$) transforms into a rock-salt derived structure (HP-MgSiN$_{2}$) ... More

On the Homogenized Linial Arrangement: Intersection Lattice and Genocchi NumbersNov 16 2018Hetyei recently introduced the homogenized Linial arrangement and showed that its number of regions is equal to a median Genocchi number, which enumerates a class of permutations called Dumont derangements. Hetyei makes use of a a well-known formula of ... More

A classification of degree $2$ semi-stable rational maps $\mathbb{P}^2\to\mathbb{P}^2$ with large finite dynamical automorphism groupJul 19 2016Let $K$ be an algebraically closed field of characteristic $0$. In this paper we classify the $\text{PGL}_3(K)$-conjugacy classes of semi-stable dominant degree $2$ rational maps $f:{\mathbb P}^2_K\dashrightarrow{\mathbb P}^2_K$ whose automorphism group ... More