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Classifying Camina groups: a theorem of Dark and ScoppolaJul 01 2008Sep 28 2011Recall that a group $G$ is a Camina group if every nonlinear irreducible character of $G$ vanishes on $G \setminus G'$. Dark and Scoppola classified the Camina groups that can occur. We present a different proof of this classification using Theorem 2, ... More

Groups where all the irreducible characters are super-monomialDec 11 2008Isaacs has defined a character to be super monomial if every primitive character inducing it is linear. Isaacs has conjectured that if $G$ is an $M$-group with odd order, then every irreducible character is super monomial. We prove that the conjecture ... More

Variations on average character degrees and $p$-nilpotenceJul 01 2015We prove that if $p$ is an odd prime, $G$ is a solvable group, and the average value of the irreducible characters of $G$ whose degrees are not divisible by $p$ is strictly less than $2(p+1)/(p+3)$, then $G$ is $p$-nilpotent. We show that there are examples ... More

Landau's theorem, fields of values for characters, and solvable groupsJun 26 2015When $G$ is solvable group, we prove that the number of conjugacy classes of elements of prime power order is less than or equal to the number of irreducible characters with values in fields where $\mathbb {Q}$ is extended by prime power roots of unity. ... More

Fitting heights of solvable groups with no nontrivial prime power character degreesJun 23 2015We construct solvable groups where the only degree of an irreducible character that is a prime power is $1$ and that have arbitrarily large Fitting heights. We will show that we can construct such groups that also have a Sylow tower. We also will show ... More

p-Group Camina pairsJan 18 2012Let $(G,Z(G))$ be a Camina pair. We prove that $G$ must be a $p$-group for some prime $p$. We also prove that $|Z(G)| < |G:Z(G)|^{3/4}$. Also, we discuss how one might build examples with $|Z(G)| > |G:Z(G)|^{1/2}$, although we are not able to prove the ... More

Semi-extraspecial groups with an abelian subgroup of maximal possible orderOct 27 2017Let $p$ be a prime. A $p$-group $G$ is defined to be semi-extraspecial if for every maximal subgroup $N$ in $Z(G)$ the quotient $G/N$ is a an extraspecial group. In addition, we say that $G$ is ultraspecial if $G$ is semi-extraspecial and $|G:G'| = |G'|^2$. ... More

${\rm B}_π$-characters and quotientsSep 07 2016Sep 11 2016Let $\pi$ be a set of primes, and let $G$ be a finite $\pi$-separable group. We consider the Isaacs ${\rm B}_\pi$-characters. We show that if $N$ is a normal subgroup of $G$, then ${\rm B}_\pi (G/N) = {\rm Irr} (G/N) \cap {\rm B}_\pi (G)$.

Constructing solvable groups with derived length four and four character degreesMar 01 2018In this paper, we present a new method to construct solvable groups with derived length four and four character degrees. We then use this method to present a number of new families of groups with derived length four and four character degrees.

Lifts of partial characters with respect to a chain of normal subgroupsDec 11 2008In this paper, we consider lifts of $\pi$-partial characters with the property that the irreducible constituents of their restrictions to certain normal subgroups are also lifts. We will show that such a lift must be induced from what we call an inductive ... More

Bounding group orders by large character degrees: A question of SnyderJun 19 2012Oct 08 2012Let $G$ be a nonabelian finite group and let $d$ be an irreducible character degree of $G$. Then there is a positive integer $e$ so that $|G| = d(d+e)$. Snyder has shown that if $e > 1$, then $|G|$ is bounded by a function of $e$. This bound has been ... More

The vanishing-off subgroupJun 12 2008Jun 21 2008In this paper, we define the vanishing-off subgroup of a nonabelian group. We study the structure of the quotient of this subgroup and a central series obtained from this subgroup.

Brauer pairs of Camina p-groups of nilpotence class 2Sep 26 2008In this paper, we find a condition that characterizes when two Camina $p$-groups of nilpotence class 2 form a Brauer pair.

Groups where the centers of the irreducible characters form a chainFeb 27 2019We consider groups where the centers of the irreducible characters form a chain. We obtain two alternate characterizations of these groups, and we obtain some information regarding the structure of these groups. Using our results, we are able to classify ... More

Inducing $π$-partial characters with a given vertexAug 10 2010Let $G$ be a solvable group. Let $p$ be a prime and let $Q$ be a $p$-subgroup of a subgroup $V$. Suppose $\phi \in \ibr G$. If either $|G|$ is odd or $p = 2$, we prove that the number of Brauer characters of $H$ inducing $\phi$ with vertex $Q$ is at most ... More

Bounding an index by the largest character degree of a solvable groupSep 28 2010Nov 15 2011In this paper, we show that if $p$ is a prime and $G$ is a $p$-solvable group, then $| G:O_p (G) |_p \le (b(G)^p/p)^{1/(p-1)}$ where $b(G)$ is the largest character degree of $G$. If $p$ is an odd prime that is not a Mersenne prime or if the nilpotence ... More

A group with three real irreducible characters: answering a question of Moreto and NavarroOct 07 2008In this paper, we construct a group with three real irreducible characters whose Sylow 2-subgroup is an iterated central extension of a Suzuki 2-group. This answers a question raised by Moreto and Navarro who asked whether such a group exists.

Camina pairs that are not $p$-closedAug 28 2013We show for every prime $p$ that there exists a Camina pair $(G,N)$ where $N$ is a $p$-group and $G$ is not $p$-closed.

Centralizers of Camina $p$-groups of nilpotence class $3$Oct 21 2015Nov 23 2015Let $G$ be a Camina $p$-group of nilpotence class $3$. We prove that if $G' < C_G (G')$, then $|Z(G)| \le |G':G_3|^{1/2}$. We also prove that if $G/G_3$ has only one or two abelian subgroups of order $|G:G'|$, then $G' < C_G (G')$. If $G/G_3$ has $p^a ... More

Semi-extraspecial GroupsSep 12 2017We survey the results regarding semi-extraspecial $p$-groups. Semi-extraspecial groups can be viewed as generalizations of extraspecial groups. We present the connections between semi-extraspecial groups and Camina groups and VZ-groups, and give upper ... More

Preliminary Results on a Generalization of the Hughes SubgroupSep 20 2018Let $G$ be a finite group, $\pi$ be a set of primes, and define $H_{\pi}(G)$ to be the subgroup generated by all elements of $G$ which do not have prime order for every prime in $\pi$. In this paper, we investigate some basic properties of $H_{\pi}(G)$ ... More

Enumerating isoclinism classes of semi-extraspecial groupsJun 27 2018Sep 12 2018We enumerate the number of isoclinism classes of semi-extraspecial $p$-groups with derived subgroup of order $p^2$. To do this, we enumerate $\text{GL}(2, p)$-orbits of sets of irreducible, monic polynomials in $\mathbb{F}_p[x]$. Along the way, we also ... More

A Generalization of the Hughes SubgroupSep 20 2018Mar 02 2019Let $G$ be a finite group, $\pi$ be a set of primes, and define $H_{\pi}(G)$ to be the subgroup generated by all elements of $G$ which do not have prime order for every prime in $\pi$. In this paper, we investigate some basic properties of $H_{\pi}(G)$ ... More

$p$-groups with $p^2$ as a codegreeNov 07 2018Let $G$ be a $p$-group and let $\chi$ be an irreducible character of $G$. The codegree of $\chi$ is given by $|G:\text{ker}(\chi)|/\chi(1)$. This paper investigates the relationship between the nilpotence class of a group and the inclusion of $p^2$ as ... More

Square character degree graphs yield direct productsMay 13 2011If $G$ is a solvable group, we take $\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\Delta (G)$ is a square, then $G$ must be a direct product.

Solvable groups satisfying the two-prime hypothesis IIOct 19 2010In this paper, we consider solvable groups that satisfy the two-prime hypothesis. We prove that if $G$ is such a group and $G$ has no nonabelian nilpotent quotients, then $|\cd G| \le 462,515$. Combining this result with the result from part I, we deduce ... More

$p$-groups with exactly four codegreesJan 22 2019Let $G$ be a $p$-group and let $\chi$ be an irreducible character of $G$. The codegree of $\chi$ is given by $|G:\text{ker}(\chi)|/\chi(1)$. Du and Lewis have shown that a $p$-group with exactly three codegrees has nilpotence class at most 2. Here we ... More

Itô's theorem and monomial Brauer charactersMar 07 2017Let $G$ be a finite solvable group, and let $p$ be a prime. In this note, we prove that $p$ does not divide $\varphi(1)$ for every irreducible monomial $p$-Brauer character $\varphi$ of $G$ if and only if $G$ has a normal Sylow $p$-subgroup.

Groups with one or two super-Brauer character theoriesFeb 28 2017A super-Brauer character theory of a group $G$ and a prime $p$ is a pair consisting of a partition of the irreducible $p$-Brauer characters and a partition of the $p$-regular elements of $G$ that satisfy certain properties. We classify the groups and ... More

Character codegrees of maximal class p-groupsSep 20 2018Let $G$ be a $p$-group and let $\chi$ be an irreducible character of $G$. The codegree of $\chi$ is given by $|G:\text{ker}(\chi)|/\chi(1)$. If $G$ is a maximal class $p$-group that is normally monomial or has at most three character degrees then the ... More

A family of graphs that cannot occur as character degree graphs of solvable groupsJul 10 2017We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur as solvable groups. Finally, we show a specific family of graphs cannot occur as a character ... More

Counting characters in blocks of solvable groups with abelian defect groupDec 16 2011If $G$ is a solvable group and $p$ is a prime, then the Fong-Swan theorem shows that given any irreducible Brauer character $\phi$ of $G$, there exists a character $\chi \in \irrg$ such that $\chi^o = \phi$, where $^o$ denotes the restriction of $\chi$ ... More

Isomorphism in expanding families of indistinguishable groupsOct 26 2010Oct 13 2011For every odd prime $p$ and every integer $n\geq 12$ there is a Heisenberg group of order $p^{5n/4+O(1)}$ that has $p^{n^2/24+O(n)}$ pairwise nonisomorphic quotients of order $p^{n}$. Yet, these quotients are virtually indistinguishable. They have isomorphic ... More

Camina $p$-groups that are generalized Frobenius complementsNov 12 2014Let $P$ be a Camina $p$-group that acts on a group $Q$ in such a way that $C_P (x) \subseteq P'$ for all nonidentity elements $x \in Q$. We show that $P$ must be isomorphic to the quaternion group $Q_8$. If $P$ has class $2$, this is a known result, and ... More

Counting lifts of Brauer charactersJul 18 2010In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if \phi \in IBrp(G) is a Brauer character of a solvable group such that \phi has an abelian vertex subgroup ... More

Brauer characters of $q^\prime$- degreeJan 20 2016Jun 30 2016We show that if $p$ is a prime and $G$ is a finite $p$-solvable group satisfying the condition that a prime $q$ divides the degree of no irreducible $p$-Brauer character of $G$, then the normalizer of some Sylow $q$-subgroup of $G$ meets all the conjugacy ... More

The character degree ratio and composition factors of a finite groupFeb 25 2015For a finite non-abelian group $G$ let $\rat(G)$ denote the largest ratio of degrees of two nonlinear irreducible characters of $G$. We prove that the number of non-abelian composition factors of $G$ is bounded above by $1.8\ln(\rat(G))+1.3$.

Lifts and vertex pairs in solvable groupsOct 12 2010Suppose $G$ is a $p$-solvable group, where $p$ is odd. We explore the connection between lifts of Brauer characters of $G$ and certain local objects in $G$, called vertex pairs. We show that if $\chi$ is a lift, then the vertex pairs of $\chi$ form a ... More

Characterizations of nested GVZ-groups by central seriesJul 10 2019Many properties of groups can be defined by the existence of a particular normal series. The classic examples being solvability, supersolvability and nilpotence. Among the nilpotent groups are the so-called nested GVZ-groups --- groups where the centers ... More

Vanishing-off subgroups and supercharacter theory productsApr 26 2019In this paper, we study the vanishing-off subgroups of supercharacters, and use these to determine several new characterizations of supercharacter theory products. In particular, we give a character theoretic characterization that allows us to conclude ... More

Using a Galois connection to compute character degreesMar 31 2014Given a Mersenne prime $q$ and a positive even integer $e$, let $F$ and $E$ be the fields of orders $q$ and $q^e$ respectively. Let $C$ be a cyclic subgroup of $E^\times$ whose index in $E^\times$ is divisible only by primes dividing $q - 1$. We compute ... More

Classifying Character Degree Graphs With 6 VerticesSep 26 2017Aug 11 2018We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve non-isomorphic connected graphs with six vertices, of which all except nine are classified in this paper. We also completely classify ... More

Groups with exactly two supercharacter theoriesMay 29 2015Oct 12 2015In this paper, we classify those finite groups with exactly two supercharacter theories. We show that the solvable groups with two supercharacter theories are $\mathbb{Z}_3$ and $S_3$. We also show that the only nonsolvable group with two supercharacter ... More

Upper and lower bounds on Chillag table sumsFeb 09 2017Chillag has showed that there is a single generalization showing that the sums of ordinary character tables, Brauer character, and projective indecomposable characters are positive integers. We show that Chillag's construction also applies to Isaacs' ... More

A nonlocal continuum model for biological aggregationApr 01 2005We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist ... More

Finite groups with an irreducible character of large degreeMay 19 2015Let $G$ be a finite group and $d$ the degree of a complex irreducible character of $G$, then write $|G|=d(d+e)$ where $e$ is a nonnegative integer. We prove that $|G|\leq e^4-e^3$ whenever $e>1$. This bound is best possible and improves on several earlier ... More

Groups satisfying the two-prime hypothesis with a composition factor isomorphic to ${\rm PSL}_2(q)$ for $q\geq 7$Jan 19 2017Let $G$ be a finite group, and write ${\rm cd}(G)$ for the degree set of the complex irreducible characters of $G$. The group $G$ is said to satisfy the {\it two-prime hypothesis} if, for any distinct degrees $a, b \in {\rm cd}(G)$, the total number of ... More

Subgroups of Division RingsJun 25 2018We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.

Multi-boson spectrum of the SU(2)-Higgs modelOct 03 2013Lattice simulations are used to compute the spectrum of energy levels for all angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-W boson sector of the standard model. ... More

Higgs and W boson spectrum from lattice simulationsJul 04 2013Oct 01 2013The spectrum of energy levels is computed for all available angular momentum and parity quantum numbers in the SU(2)-Higgs model, with parameters chosen to match experimental data from the Higgs-W boson sector of the standard model. Several multi-boson ... More

Expansion under climate change: the genetic consequencesSep 27 2016Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population ... More

Climate change and integrodifference equations in a stochastic environmentMay 12 2016Climate change impacts population distributions, forcing some species to migrate poleward if they are to survive and keep up with the suitable habitat that is shifting with the temperature isoclines. Previous studies have analyzed whether populations ... More

Simple Groups Whose Prime Graph or Solvable Graph is SplitSep 26 2018A graph is split if there is a partition of its vertex set into a clique and an independent set. The present paper is devoted to the splitness of some graphs related to finite simple groups, namely, prime graphs and solvable graphs, and their compact ... More

Predicting local and non-local effects of resources on animal space use using a mechanistic step selection modelJan 22 20151. Predicting space use patterns of animals from their interactions with the environment is fundamental for understanding the effect of habitat changes on ecosystem functioning. Recent attempts to address this problem have sought to unify resource selection ... More

Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary DistributionSep 23 2018May 25 2019We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact ... More

Exact Solutions for a GBM-type Stochastic Volatility Model having a Stationary DistributionSep 23 2018We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact ... More

Explicit gauge covariant Euler-Lagrange equationJul 14 2009Jul 14 2009The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic part of the ... More

An analytic investigation of the scatter in the integrated X-ray properties of galaxy groups and clustersNov 28 2005Jan 03 2006(Abridged) We revisit the scaling relationships between the dark matter mass and observed X-ray luminosity and temperature of galaxy clusters and groups in the local Universe. Specifically, we compare recent observations with analytic models of the intracluster ... More

Territorial pattern formation in the absence of an attractive potentialMar 23 2015Territoriality is a phenomenon exhibited throughout nature. On the individual level, it is the processes by which organisms exclude others of the same species from certain parts of space. On the population level, it is the segregation of space into separate ... More

Exploring free-form smearing for bottomonium and B meson spectroscopyOct 19 2015Free-form smearing was designed as a way to implement source operators of any desired shape. A variation of the method is introduced that reduces the computational cost by reducing the number of link multiplications to its absolute minimum. Practical ... More

Spatial memory and taxis-driven pattern formation in model ecosystemsMar 13 2019Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births ... More

On impulsive reaction-diffusion models in higher dimensionsNov 02 2015Nov 17 2016Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$ \begin{eqnarray*}\label{} \ \ ... More

A mathematical approach to territorial pattern formationApr 17 2014Jan 23 2015Territorial behaviour is widespread in the animal kingdom, with creatures seeking to gain parts of space for their exclusive use. It arises through a complicated interplay of many different behavioural features. Extracting and quantifying the processes ... More

Nanolensing of gamma-ray burstsDec 16 2002Feb 10 2003All quasars vary in their optical flux on a time-scale of years, and it has been proposed that these variations are principally due to gravitational lensing by a cosmologically distributed population of planetary mass objects. This interpretation has ... More

Free-form Smeared Bottomonium Correlation FunctionsSep 24 2014Gauge-invariant sources with a hydrogen wave function shape are constructed for bottomonium two-point correlation functions using the free-form smearing technique. The bottomonium spectrum, including a first lattice result for the D-wave first-excited ... More

Free-form smearing for bottomonium and B meson spectroscopyMay 17 2015Sep 24 2015To obtain high-quality results from lattice QCD, it is important to use operators that produce good signals for the quantities of interest. Free-form smearing is a powerful tool that helps to accomplish that goal. The present work introduces a new implementation ... More

Robustness of movement models: can models bridge the gap between temporal scales of data sets and behavioural processes?Aug 26 2015Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale of the biological ... More

Effect of Multiple Higgs Fields on the Phase Structure of the SU(2)-Higgs ModelFeb 06 2009Jul 29 2009The SU(2)-Higgs model, with a single Higgs field in the fundamental representation and a quartic self-interaction, has a Higgs region and a confinement region which are analytically connected in the parameter space of the theory; these regions thus represent ... More

Dynamic Service Rate Control for a Single Server Queue with Markov Modulated ArrivalsJul 09 2013We consider the problem of service rate control of a single server queueing system with a finite-state Markov-modulated Poisson arrival process. We show that the optimal service rate is non-decreasing in the number of customers in the system; higher congestion ... More

On impulsive reaction-diffusion models in higher dimensionsNov 02 2015Assume that $N_m(x)$ denotes the density of the population at a point $x$ at the beginning of the reproductive season in the $m$th year. We study the following impulsive reaction-diffusion model for any $m\in \mathbb Z^+$ \begin{eqnarray*}\label{} \left\{ ... More

On the Convergence of Optimal Actions for Markov Decision Processes and the Optimality of $(s,S)$ Policies for Inventory ControlJul 17 2015Nov 25 2016This paper describes results on the existence of optimal policies and convergence properties of optimal actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities. It is possible that cost ... More

On the Convergence of Optimal Actions for Markov Decision Processes and the Optimality of $(s,S)$ Policies for Inventory ControlJul 17 2015May 24 2016This paper describes results on the existence of optimal policies and convergence properties of optimal actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities. It is possible that cost ... More

Robust Optimization of Unconstrained Binary Quadratic ProblemsSep 21 2017In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are motivated to find ... More

On the Convergence of Optimal Actions for Markov Decision Processes and the Optimality of $(s,S)$ Inventory PoliciesJul 17 2015Mar 20 2017This paper studies convergence properties of optimal values and actions for discounted and average-cost Markov Decision Processes (MDPs) with weakly continuous transition probabilities and applies these properties to the stochastic periodic-review inventory ... More

Spatial memory and taxis-driven pattern formation in model ecosystemsMar 13 2019May 28 2019Mathematical models of spatial population dynamics typically focus on the interplay between dispersal events and birth/death processes. However, for many animal communities, significant arrangement in space can occur on shorter timescales, where births ... More

Logical and Inequality Implications for Reducing the Size and Complexity of Quadratic Unconstrained Binary Optimization ProblemsMay 26 2017The quadratic unconstrained binary optimization (QUBO) problem arises in diverse optimization applications ranging from Ising spin problems to classical problems in graph theory and binary discrete optimization. The use of preprocessing to transform the ... More

Stacking-fault energies for Ag, Cu, and Ni from empirical tight-binding potentialsJul 12 2002The intrinsic stacking-fault energies and free energies for Ag, Cu, and Ni are derived from molecular-dynamics simulations using the empirical tight-binding potentials of Cleri and Rosato [Phys. Rev. B 48, 22 (1993)]. While the results show significant ... More

Stability of strained heteroepitaxial systems in (1+1) dimensionsDec 17 2003We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1+1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are adjusted to an atomistic ... More

Gradient bounds for p-harmonic systems with vanishing neumann data in a convex domainMay 01 2013Let $ \ti \Om $ be a bounded convex domain in Euclidean $ n $ space, $ \hat x \in \ar \ti \Om, $ and $ r > 0. $ Let $ \ti u = (\ti u^1, \ti u^2, \dots, \ti u^N) $ be a weak solution to \[\nabla \cdot \left (|\nabla \ti u |^{p-2} \nabla \ti u \right) = ... More

Quantum Dots and Etch-Induced Depletion of a Silicon 2DEGMar 31 2005The controlled depletion of electrons in semiconductors is the basis for numerous devices. Reactive-ion etching provides an effective technique for fabricating both classical and quantum devices. However, Fermi level pinning can occur, and must be carefully ... More

The Giant Proto-Galaxy cB58; an Artifact of Gravitational Lensing?May 13 1996The proto-galaxy, cB58, was discovered in the CNOC survey of cluster redshifts. Absorption features reveal that this system is at a redshift of $z=2.72$, implying an absolute magnitude of ${\rm M_v \sim -26}$, and a star-formation rate of $4700 {\rm M_{\odot} ... More

A unifying framework for quantifying the nature of animal interactionsFeb 08 2014Mar 18 2016Collective phenomena, whereby agent-agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite ... More

Synchronization of electrically coupled resonate-and-fire neuronsJan 17 2018Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical ... More

Measuring transverse velocities in gravitationally lensed extragalactic systems using an annual parallax effectApr 07 2004Jul 16 2004A parallax method to determine transverse velocity in a gravitationally lensed system is described. Using the annual motion of the Earth around the Sun allows us to probe the local structure of the magnification map that, under certain assumptions, can ... More

A Characterization of the Prime Graphs of Solvable GroupsMay 10 2013Let \pi(G) denote the set of prime divisors of the order of a finite group G. The prime graph of G is the graph with vertex set \pi(G) with edges {p,q} if and only if there exists an element of order pq in G. In this paper, we prove that a graph is isomorphic ... More

Liquid marbles as thermally robust droplets: coating-assisted Leidenfrost-like effectJul 03 2012The Leidenfrost effect-prolonged evaporation of droplets on a superheated surface-happens only when the surface temperature is above a certain transitional value. Here, we show that specially engineered droplets - liquid marbles - can exhibit similar ... More

The Wavefront Control System for the National Ignition FacilityNov 12 2001The National Ignition Facility (NIF) requires that pulses from each of the 192 laser beams be positioned on target with an accuracy of 50 um rms. Beam quality must be sufficient to focus a total of 1.8 MJ of 0.351-um light into a 600-um-diameter volume. ... More

On the interaction of massive spinor particles with external electromagnetic and torsion fieldsMay 21 1998We explore the Dirac equation in external electromagnetic and torsion fields. Motivated by the previous study of quantum field theory in an external torsion field, we include a nonminimal interaction of the spinor field with torsion. As a consequence, ... More

Partial smoothness of the numerical radius at matrices whose fields of values are disksDec 31 2018Solutions to optimization problems involving the numerical radius often belong to a special class: the set of matrices having field of values a disk centered at the origin. After illustrating this phenomenon with some examples, we illuminate it by studying ... More

A First Option Calibration of the GARCH Diffusion Model by a PDE MethodJan 18 2018Time-series calibrations often suggest that the GARCH diffusion model could also be a suitable candidate for option (risk-neutral) calibration. But unlike the popular Heston model, it lacks a fast, semi-analytic solution for the pricing of vanilla options, ... More

Equivariant Universal Coefficient and Kunneth Spectral SequencesOct 06 2004We construct hyper-homology spectral sequences of Z-graded and ROG-graded Mackey functors for Ext and Tor over G-equivariant S-algebras (A-infty ring spectra) for finite groups G. These specialize to universal coefficient and Kunneth spectral sequences. ... More

Variance-Based Rewards for Approximate Bayesian Reinforcement LearningMar 15 2012The explore{exploit dilemma is one of the central challenges in Reinforcement Learning (RL). Bayesian RL solves the dilemma by providing the agent with information in the form of a prior distribution over environments; however, full Bayesian planning ... More

On the Identifiability of the Influence Model for Stochastic Spatiotemporal Spread ProcessesOct 26 2018Nov 06 2018The influence model is a discrete-time stochastic model that succinctly captures the interactions of a network of Markov chains. The model produces a reduced-order representation of the stochastic network, and can be used to describe and tractably analyze ... More

Undistorted Lensed Images in Galaxy ClustersOct 03 1997To date, the study of high-magnification gravitational lensing effects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a different type ... More

Relaxation kinetics in two-dimensional structuresJun 16 2003We have studied the approach to equilibrium of islands and pores in two dimensions. The two-regime scenario observed when islands evolve according to a set of particular rules, namely relaxation by steps at low temperature and smooth at high temperature, ... More

New model for surface fracture induced by dynamical stressJun 16 1997We introduce a model where an isotropic, dynamically-imposed stress induces fracture in a thin film. Using molecular dynamics simulations, we study how the integrated fragment distribution function depends on the rate of change and magnitude of the imposed ... More

Improved models of upper-level wind for several astronomical observatoriesSep 20 2010An understanding of wind speed and direction as a function of height are critical to the proper modeling of atmospheric turbulence. We have used radiosonde data from launch sites near significant astronomical observatories and created mean profiles of ... More

Modules in Monoidal Model CategoriesJun 12 2006This paper studies the existence of and compatibility between derived change of ring, balanced product, and function module derived functors on module categories in monoidal model categories.

Integrated step selection analysis: bridging the gap between resource selection and animal movementDec 05 2015A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability? Step-selection analysis deals with this problem at the scale ... More

Quantum dots in Si/SiGe 2DEGs with Schottky top-gated leadsAug 03 2005Aug 16 2005We report on the fabrication and characterization of quantum dot devices in a Schottky-gated silicon/silicon-germanium two-dimensional electron gas (2DEG). The dots are confined laterally inside an etch-defined channel, while their potential is modulated ... More