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Results for "Alex McDonald"

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Congruence classes of large configurations in vector spaces over finite fieldsJan 28 2019Bennett, Hart, Iosevich, Pakianathan, and Rudnev found an exponent $s<d$ such that any set $E\subset \mathbb{F}_q^d$ with $|E|\gtrsim q^s$ determines $\gtrsim q^{\binom{k+1}{2}}$ congruence classes of $(k+1)$-point configurations for $k\leq d$. Because ... More
Areas of triangles and SL_2 actions in finite ringsJun 11 2019In Euclidean space, one can use the dot product to give a formula for the area of a triangle in terms of the coordinates of each vertex. Since this formula involves only addition, subtraction, and multiplication, it can be used as a definition of area ... More
Doubly slice odd pretzel knotsApr 29 2019Jun 07 2019We prove that an odd pretzel knot is doubly slice if it has $2n+1$ twist parameters consisting of $n+1$ copies of $a$ and $n$ copies of $-a$ for some odd integer $a$. Combined with the work of Issa and McCoy, it follows that these are the only doubly ... More
Band Number and the Double Slice GenusJan 22 2019We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound is based on ... More
Stability of Non-Linear Filters and Observability of Stochastic Dynamical SystemsDec 05 2018Jan 08 2019Filter stability is a classical problem for partially observed Markov processes (POMP). For a POMP, an incorrectly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. ... More
Singer invariants and strongly curvature homogeneous manifolds of type (1,3)Sep 04 2013We extend the definition of curvature homogeneity of type (1,3) to include the possibility that there is a homothety between any two points of a manifold preserving the first r covariant derivatives of the curvature operator simultaneously; we call this ... More
List rankings and on-line list rankings of graphsJan 15 2014A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number of $G$, also ... More
A combinatorial proof on partition function parityJan 12 2014One of the most basic results concerning the number-theoretic properties of the partition function $p(n)$ is that $p(n)$ takes each value of parity infinitely often. This statement was first proved by Kolberg in 1959, and it was strengthened by Subbarao ... More
The onset of the AGB wind tied to a transition between sequences in the period-luminosity diagramJan 18 2019We link the onset of pulsation-enhanced, dust-driven winds from asymptotic giant branch (AGB) stars in the Magellanic Clouds to the star's transition between period--luminosity sequences (from B to C'). This transition occurs at ~60 days for solar-mass ... More
On-line vertex ranking of treesJan 12 2014A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number of $G$, also ... More
Coulomb drag at zero temperatureOct 08 2007We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet ... More
Keldysh Ginzburg-Landau action of fluctuating superconductorsJun 19 2007Sep 24 2007We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent ... More
Coulomb drag in quantum circuitsSep 09 2008Oct 22 2008We study drag effect in a system of two electrically isolated quantum point contacts (QPC), coupled by Coulomb interactions. Drag current exhibits maxima as a function of QPC gate voltages when the latter are tuned to the transitions between quantized ... More
Keldysh technique and non-linear sigma-model: basic principles and applicationsJan 23 2009Apr 27 2009The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic ... More
Matrix roots of imprimitive irreducible nonnegative matricesJul 16 2014Jun 03 2015Using matrix function theory, Perron-Frobenius theory, combinatorial matrix theory, and elementary number theory, we characterize, classify, and describe in terms of the Jordan canonical form the matrix pth-roots of imprimitive irreducible nonnegative ... More
Mean field convergence of a model of multiple TCP connections through a buffer implementing REDMar 14 2006RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows by dropping or marking packets with a probability that increases with ... More
$t$-cores for $(Δ+t)$-edge-colouringOct 24 2017Jul 31 2018We extend the edge-coloring notion of core (subgraph induced by the vertices of maximum degree) to $t$-core (subgraph induced by the vertices $v$ with $d(v)+\mu(v)> \Delta+t$), and find a sufficient condition for $(\Delta+t)$-edge-coloring. In particular, ... More
Jordan chains of $h$-cyclic matricesJul 16 2014Feb 24 2015Arising from the classification of the matrix-roots of a nonnegative imprimitive irreducible matrix, we present results concerning the Jordan chains of an $h$-cyclic matrix. We also present ancillary results applicable to nonnegative imprimitive irreducible ... More
ALMA observations of the nearby AGB star L$_{\rm 2}$ Puppis. II. Gas disk properties derived from $^{\rm 12}$CO and $^{\rm13}$CO $J=$3$-$2 emissionMar 14 2018The circumstellar environment of the AGB star L$_{\rm 2}$ Puppis was observed with ALMA in cycle 3, with a resolution of $15 \times 18 \rm\ mas$. The molecular emission shows a differentially rotating disk, inclined to a nearly edge-on position. In the ... More
Velocity Segregation and Systematic Biases In Velocity Dispersion Estimates With the SPT-GMOS Spectroscopic SurveyDec 08 2016Feb 08 2017The velocity distribution of galaxies in clusters is not universal; rather, galaxies are segregated according to their spectral type and relative luminosity. We examine the velocity distributions of different populations of galaxies within 89 Sunyaev ... More
X-ray Properties of SPT Selected Galaxy Clusters at 0.2<z<1.5 Observed with XMM-NewtonJul 06 2018Nov 29 2018We present measurements of the X-ray observables of the intra-cluster medium (ICM), including luminosity $L_X$, ICM mass $M_{ICM}$, emission-weighted mean temperature $T_X$, and integrated pressure $Y_X$, that are derived from XMM-Newton X-ray observations ... More
Long-time existence for Yang-Mills flowOct 11 2016We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region. ... More
Generating Sequences With Recurrent Neural NetworksAug 04 2013Jun 05 2014This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data are discrete) ... More
Characteristic Formulas 50 Years Later (An Algebraic Account)Jul 22 2014The Jankov (characteristic) formulas were introduced by V.Jankov fifty tears ago in 1963. Nowadays the Jankov (or frame) formulas are used in virtually every branch of propositional logic: intermediate, modal, fuzzy, relevant, many-valued, etc. All these ... More
New Algorithms for Solving Tropical Linear SystemsSep 20 2013The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although ... More
The X-ray Power Spectral Density Function of the Seyfert Active Galactic Nucleus NGC 7469Oct 15 2010We present the broadband X-ray power spectral density function (PSD) of the X-ray-luminous Seyfert 1.2 NGC 7469, measured from Rossi X-ray Timing Explorer monitoring data and two XMM-Newton observations. We find significant evidence for a turnover in ... More
Black hole spectra in holography: consequences for equilibration of dual gauge theoriesJan 19 2015May 07 2015For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented ... More
Higgs PhysicsDec 14 2014With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings, discussing the ... More
Boson Sampling is Robust to Small Errors in the Network MatrixDec 08 2014We demonstrate the robustness of BosonSampling to imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ ... More
1D accretion discs around eccentric planets: observable near-infrared variabilityNov 04 2014Dec 29 2014I present the results of 1D models of circumplanetary discs around planets on eccentric orbits. I use a classical viscous heating model to calculate emission fluxes at the wavelengths targeted by the NIRCam instrument on JWST, and compare the variability ... More
AdS boson stars in string theoryOct 28 2015Boson stars are stationary soliton-like gravitational configurations supported by a complex scalar field charged under the global $U(1)$ symmetry. We discuss properties of boson stars in type IIB supergravity approximation to string theory. A notable ... More
On Factoring an Operator Using Elements of its KernelNov 25 2015A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the derivation $\partial$ ... More
From rational billiards to dynamics on moduli spacesApr 30 2015Jul 26 2015This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, ... More
Schwarz triangle mappings and Teichmüller curves: the Veech-Ward-Bouw-Möller curvesMar 13 2012Jan 24 2013We study a family of Teichm\"uller curves T(n,m) constructed by Bouw and M\"oller, and previously by Veech and Ward in the cases n=2,3. We simplify the proof that T(n,m) is a Teichm\"uller curve, avoiding the use M\"oller's characterization of Teichm\"uller ... More
Gromov's measure equivalence and rigidity of higher rank latticesNov 01 1999In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the ... More
Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquidsDec 20 2014We discuss the violation of spin-charge separation in generic nonlinear Luttinger liquids and investigate its effect on the relaxation and thermal transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We identify basic scattering ... More
Transport theory of superconductors with singular interaction correctionsMay 01 2010We study effects of strong fluctuations on the transport properties of superconductors near the classical critical point. In this regime conductivity is set by the delicate interplay of two competing effects. The first is that strong electron-electron ... More
Interaction corrections to tunneling conductance in ballistic superconductorsApr 19 2009Feb 08 2010It is known that in the two-dimensional disordered superconductors electron-electron interactions in the Cooper channel lead to the negative logarithmic in temperature correction to the tunneling conductance above the critical temperature. Physically ... More
On (Non)Supermodularity of Average Control EnergySep 27 2016Oct 05 2016Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims ... More
Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over pathsNov 14 2014Jun 11 2015Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the ... More
Interpolation and embeddings of weighted tent spacesSep 18 2015Feb 09 2016Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on $X$ we identify ... More
Fell bundles over groupoidsJul 21 1996The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and C^*-algebra bundles ... More
Lines in supersingular quarticsApr 20 2016We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the ... More
Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part II: The Degenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More
Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part I: The Nondegenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More
Generators for Coulomb branches of quiver gauge theoriesMar 18 2019We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation ... More
Fundamental groups of symmetric sextics. IIMay 15 2008We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of and not of ... More
On the Picard group of a Delsarte surfaceJul 01 2013We suggest an algorithm computing, in some cases, an explicit generating set for the N\'eron--Severi lattice of a Delsarte surface.
Regulator constants of integral representations of finite groupsMar 30 2017Dec 22 2018Let G be a finite group and p be a prime. We investigate isomorphism invariants of $\mathbb{Z}_{p}[G]$-lattices whose extension of scalars to $\mathbb{Q}_p$ is self-dual, called regulator constants. These were originally introduced by Dokchitser--Dokchitser ... More
Factor equivalence of Galois modules and regulator constantsSep 17 2012Jun 21 2013We compare two approaches to the study of Galois module structures: on the one hand factor equivalence, a technique that has been used by Fr\"ohlich and others to investigate the Galois module structure of rings of integers of number fields and of their ... More
The Reasonable Effectiveness of Mathematics in the Physical SciencesDec 24 2012Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism ... More
Genus From Sandpile Torsor AlgorithmApr 20 2018Previous work by Chan-Church-Grochow and Baker-Wang showed that the structure of the output of the rotor routing or Bernardi process can be used to distinguish a planar ribbon graph from a nonplanar ribbon graph. Here, we show that the structure of the ... More
On the unit distance problemSep 23 2017The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known bound is $Cn^{\frac{4}{3}}$. ... More
Regression adjustments for estimating the global treatment effect in experiments with interferenceAug 27 2018Mar 05 2019Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model ... More
Multilinear Superhedging of Lookback OptionsOct 04 2018In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their ... More
Reflection identities of harmonic sums of weight fourSep 12 2018We consider the reflection identities for harmonic sums at weight four. We decompose a product of two harmonic sums with mixed pole structure into a linear combination of terms each having a pole at either negative or positive values of the argument. ... More
Linear Flows on $κ$-SolenoidsJun 24 1999Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.
A volume-based approach to the multiplicative ergodic theorem on Banach spacesFeb 23 2015Dec 07 2015A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the Lyapunov exponents ... More
Tent spaces over metric measure spaces under doubling and related assumptionsMay 10 2013Sep 25 2013In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, ... More
Duality symmetry in high energy scatteringAug 17 2009Dec 15 2009We discuss the duality symmetry of the linear(BFKL) and the non-linear(BK) high energy evolutions in the multicolor limit. We show that the usual color dipole picture is dual to the forward reggeized gluon formulation. The presented analysis is also generalized ... More
Fast Algorithms for Distributed Optimization and Hypothesis Testing: A TutorialSep 13 2016Oct 06 2016We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent linear-time algorithm ... More
Can Turing machine be curious about its Turing test results? Three informal lectures on physics of intelligenceJun 27 2016What is the nature of curiosity? Is there any scientific way to understand the origin of this mysterious force that drives the behavior of even the stupidest naturally intelligent systems and is completely absent in their smartest artificial analogs? ... More
Diffusion Processes in Turbulent Magnetic FieldsJul 04 2007Jul 05 2007We study of the effect of turbulence on diffusion processes within magnetized medium. While we exemplify our treatment with heat transfer processes, our results are quite general and are applicable to different processes, e.g. diffusion of heavy elements. ... More
Lattice games without rational strategiesJun 09 2011We show that the lattice games of Guo and Miller support universal computation, disproving their conjecture that all lattice games have rational strategies. We also state an explicit counterexample to that conjecture: a three dimensional lattice game ... More
Monte Carlo Renormalization Group calculation in $λφ^4_3$Sep 23 1997We start by discussing some theoretical issues of renormalization group transformations and Monte Carlo renormalization group technique. A method to compute the anomalous dimension is proposed and investigated. As an application, we find excellent values ... More
Optimal phase measurements with pure Gaussian statesSep 02 2005Feb 08 2006We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive ... More
Fast Algorithms for Distributed Optimization and Hypothesis Testing: A TutorialSep 13 2016We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent linear-time algorithm ... More
Introduction into "Local Correlation Modelling"Sep 18 2009Sep 22 2009In this paper we provide evidence that financial option markets for equity indices give rise to non-trivial dependency structures between its constituents. Thus, if the individual constituent distributions of an equity index are inferred from the single-stock ... More
On Eling-Oz formula for the holographic bulk viscosityMar 19 2011May 09 2011Recently Eling and Oz [1] proposed a simple formula for the bulk viscosity of holographic plasma. They argued that the formula is valid in the high temperature (near-conformal) regime, but is expected to break down at low temperatures. We point out that ... More
Hydrodynamics of the cascading plasmaMar 20 2009Jun 03 2009The cascading gauge theory of Klebanov et.al realizes a soluble example of gauge/string correspondence in a non-conformal setting. Such a gauge theory has a strong coupling scale Lambda, below which it confines with a chiral symmetry breaking. A holographic ... More
Shear viscosity of boost invariant plasma at finite couplingJan 29 2008Mar 04 2008We discuss string theory alpha' corrections in the dual description of the expanding boost invariant N=4 supersymmetric Yang-Mills plasma at strong coupling. We compute finite 't Hooft coupling corrections to the shear viscosity and find that it disagrees ... More
A holographic perspective on Gubser-Mitra conjectureJul 28 2005Oct 17 2005We point out an elementary thermodynamics fact that whenever the specific heat of a system is negative, the speed of sound in such a media is imaginary. The latter observation presents a proof of Gubser-Mitra conjecture on the relation between dynamical ... More
Comments on fractional instantons in N=2 gauge theoriesJan 10 2001Jun 18 2001N=1^* gauge theories are believed to have fractional instanton contributions in the confining vacua. D3 brane probe computations in gravitation dual of large-N N=2^* gauge theories point to the absence of such contributions in the low energy gauge dynamics. ... More
Relaxation time of non-conformal plasmaAug 03 2009Nov 27 2009We study effective relaxation time of viscous hydrodynamics of strongly coupled non-conformal gauge theory plasma using gauge theory/string theory correspondence. We compute leading corrections to the conformal plasma relaxation time from the relevant ... More
Computable randomness and monotonicitySep 25 2015We show that $z\in\R^n$ is computably random if and only if every computable monotone function on $\R^n$ is differentiable at $z$.
Translation surfaces and their orbit closures: An introduction for a broad audienceNov 07 2014Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces called strata ... More
Cylinder deformations in orbit closures of translation surfacesFeb 17 2013Mar 05 2013Let M be a translation surface. We show that certain deformations of M supported on the set of all cylinders in a given direction remain in the GL(2,R)-orbit closure of M. Applications are given concerning complete periodicity, field of definition, and ... More
Recent Advances in Charm PhysicsSep 16 2002New results from charm experiments have led to renewed interest in this physics. The charm sector is now seen as a powerful tool to search for new physics and to advance our understanding of the standard model. We owe much of this progress to the combination ... More
Inelastic quantum tunneling through disordered potential barrierJul 19 2004Jul 20 2004The effect of inelastic scattering on quantum tunneling through a rectangular potential barrier, of length $L$, containing randomly distributed impurities, is considered. It is shown that, despite the fact that the inelastic transition probability $\mathcal{T}_{\mathrm{inelastic}}$ ... More
Magnetoconductivity of low-dimensional disordered conductors at the onset of the superconducting transitionMar 13 2009Jun 24 2009Magnetoconductivity of the disordered two- and three-dimensional superconductors is addressed at the onset of superconducting transition. In this regime transport is dominated by the fluctuation effects and we account for the interaction corrections coming ... More
Efficient subgraph-based sampling of Ising-type models with frustrationSep 13 2014Here is proposed a general subgraph-based method for efficiently sampling certain graphical models, typically using subgraphs of a fixed treewidth, and also a related method for finding minimum energy (ground) states. In the case of models with frustration, ... More
On the theoretical RF field limits of multilayer coating structures of superconducting resonator cavitiesSep 22 2013This Comment addresses theoretical field limits for superconducting-insulating (S-I) thin films multilayers discussed by S. Posen, G. Catelani, M. Liepe, J. Sethna, and M. Transtrum [1]. It is shown that their criticism of the SIS multilayer approach ... More
Regression Adjustments for Estimating the Global Treatment Effect in Experiments with InterferenceAug 27 2018Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model ... More
Exact Replication of the Best Rebalancing Rule in HindsightOct 05 2018This paper prices and replicates the financial derivative whose payoff at $T$ is the wealth that would have accrued to a $\$1$ deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the ... More
Gaussian elimination corrects pivoting mistakesFeb 21 2016Gaussian elimination (GE) is the archetypal direct algorithm for solving linear systems of equations and this has been its primary application for thousands of years. In the last decade, GE has found another major use as an iterative algorithm for low ... More
Extremal Problems on Generalized Directed HypergraphsJul 18 2016In this paper we define a class of combinatorial structures the instances of which can each be thought of as a model of directed hypergraphs in some way. Each of these models is uniform in that all edges have the same internal structure, and each is simple ... More
A new measure of asymmetry of binary wordsApr 08 2010A binary word is symmetric if it is a palindrome or an antipalindrome. We define a new measure of asymmetry of a binary word equal to the minimal number of letters of the word whose deleting from the word yields a symmetric word and obtain upper and lower ... More
Long-time existence for Yang-Mills flowOct 11 2016Mar 22 2019We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region. ... More
Unstable Adams operations acting on $p$-local compact groups and fixed pointsApr 20 2011Jan 16 2012We prove in this paper that every $p$-local compact group is approximated by transporter systems over finite $p$-groups. To do so, we use unstable Adams operations acting on a given $p$-local compact group and study the structure of resulting fixed points. ... More
Central limit theorems via Stein's method for randomized experiments under interferenceApr 09 2018Mar 06 2019We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson estimator is ... More
A Simple Continuous Parametrization of the Kasner IndicesDec 12 2012A parametrization of the Kasner indices in terms of a continuous parameter is constructed by exploiting their representation as trilinear coordinates. This provides a clear picture of their variation through their entire range vis a vis each other. The ... More
On the palindromic decomposition of binary wordsApr 08 2010We prove a precise formula for the minimal number K(n) such that every binary word of length $n$ can be divided into K(n) palindromes. Also we estimate the average number $\ol K(n)$ of palindromes composing a random binary word of the length n.
Three-dimensional flow in cavity with elevated helicity driven by parallel wallsApr 02 2017Jul 13 2018The proposed flow in a 3-D cubic cavity is driven by its parallel walls moving in perpendicular directions to create a genuinely three-dimensional highly separated vortical flow yet having simple single-block cubical geometry of computational domain. ... More
Lines on smooth polarized $K3$-surfacesJun 18 2017Aug 17 2017For each integer $D\ge3$, we give a sharp bound on the number of lines contained in a smooth complex $2D$-polarized $K3$-surface in $\mathbb{P}^{D+1}$. In the two most interesting cases of sextics in $\mathbb{P}^4$ and octics in $\mathbb{P}^5$, the bounds ... More
Exponents and Almost Periodic OrbitsAug 01 1999We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Cech cohomology group of the closure of the image of the map. We show that this group generalizes the subgroup ... More
On the half-space theorem for minimal surfaces in Heisenberg spaceJun 18 2012Nov 02 2015We propose a simple proof of the vertical half-space theorem for Heisenberg space.
Type Ia Supernova Intrinsic Magnitude Dispersion and the Fitting of Cosmological ParametersJan 18 2011I present an analysis for fitting cosmological parameters from a Hubble Diagram of a standard candle with unknown intrinsic magnitude dispersion. The dispersion is determined from the data themselves, simultaneously with the cosmological parameters. This ... More
On Setting of Heat-and-Mass Transfer Problems under Directed CrystallizationAug 11 2011So far the problem of interface behavior upon phase transition has not yet acquired a satisfactory mathematical formulation due to a variety of the physical phenomena involved. Analytical solutions exist only for elementary problems describing the free ... More
Numerical homotopy continuation for control and online identification of nonlinear systems: the survey of selected resultsJan 26 2013The article gives an overview of the parameter numerical continuation methodology applied to setpoint control and parameter identification of nonlinear systems. The control problems for affine systems as well as general (nonaffine) nonlinear systems are ... More
The Negative Cycle Vectors of Signed Complete GraphsDec 30 2015A signed graph is a graph where the edges are assigned labels of either "$+$" or "$-$". The sign of a cycle in the graph is the product of the signs of its edges. We equip each signed complete graph with a vector whose entries are the number of negative ... More