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Training Multi-organ Segmentation Networks with Sample Selection by Relaxed Upper Confident BoundApr 07 2018Deep convolutional neural networks (CNNs), especially fully convolutional networks, have been widely applied to automatic medical image segmentation problems, e.g., multi-organ segmentation. Existing CNN-based segmentation methods mainly focus on looking ... More

Recurrent Saliency Transformation Network: Incorporating Multi-Stage Visual Cues for Small Organ SegmentationSep 13 2017Apr 08 2018We aim at segmenting small organs (e.g., the pancreas) from abdominal CT scans. As the target often occupies a relatively small region in the input image, deep neural networks can be easily confused by the complex and variable background. To alleviate ... More

Schmidt's game, Badly Approximable Linear Forms and FractalsSep 11 2008We prove that for every two natural numbers M and N, if Tau is a Borel, finite, absolutely friendly measure on a compact set K of R^MN, then the intersection of K and BA(M,N) is a winning set in Schmidt's game sense played on K, where BA(M,N) is the set ... More

Schmidt's Game on Certain FractalsJun 13 2006Nov 10 2010We construct (\alpha ,\beta) and \alpha -winning sets in the sense of Schmidt's game, played on the support of certain measures (very friendly and awfully friendly measures) and show how to derive the Hausdorff dimension for some. In particular we prove ... More

Deep Supervision for Pancreatic Cyst Segmentation in Abdominal CT ScansJun 22 2017Automatic segmentation of an organ and its cystic region is a prerequisite of computer-aided diagnosis. In this paper, we focus on pancreatic cyst segmentation in abdominal CT scan. This task is important and very useful in clinical practice yet challenging ... More

Unexpected equality of the quark and gluon Belinfante angular momentum and Canonical angular momentum in the light-cone gauge $A^+=0$, in a spin 1/2 nucleonDec 11 2012Jan 26 2016A controversy is raging concerning the most physically meaningful definition of quark and gluon angular momentum, a question of importance in understanding the internal structure of the nucleon. There are, in my, opinion, two principal candidates: the ... More

Vizing's conjecture for cographsSep 27 2016Oct 03 2016We show that if $G$ is a cograph, that is $P_4$-free, then for any graph $H$, $\gamma(G\square H)\geq \gamma(G)\gamma(H)$. By the characterization of cographs as a finite sequence of unions and joins of $K_1$, this result easily follows from that of Bartsalkin ... More

Distributional Lattices on Riemannian symmetric spacesJul 02 2017Jul 04 2017A Riemannian symmetric space is a Riemannian manifold in which it is possible to reflect all geodesics through a point by an isometry of the space. On such spaces, we introduce the notion of a distributional lattice, generalizing the notion of lattice. ... More

Phase transitions of an anisotropic N=4 super Yang-Mills plasma via holographyApr 12 2016Black hole solutions of type IIB supergravity were previously found that are dual to N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. In the zero temperature limit, these black holes approach a Liftshitz like scaling solution ... More

Resolution of a conflict between Laser and Elementary Particle PhysicsOct 12 2015The claim some years ago, contrary to all textbooks, that the angular momentum of a photon (and gluon) can be split in a gauge-invariant way into an orbital and spin term, sparked a major controversy in the Particle Physics community. A further cause ... More

New relation between transverse angular momentum and generalized parton distributionsSep 06 2011Nov 04 2011I derive a rigorous relation between the expectation value of the transverse component of the angular momentum <J_T> of a quark in a transversely polarized nucleon in terms of the Generalized Parton Distributions H and E, namely <J_T(quark)> = 1/2M [P_0 ... More

On the controversy concerning the definition of quark and gluon angular momentumJan 31 2011Mar 21 2011A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge invariant way, into a spin and orbital part. ... More

A critical assessment of the angular momentum sum rulesNov 16 2012Sep 14 2013There are now five angular momentum relations or sum rules in the literature: the Jaffe, Manohar relation for a longitudinally polarized nucleon, and the Bakker, Leader, Trueman result for the case of transverse polarization; the Ji relation for longitudinal ... More

WW and WZ Production at the TevatronJan 19 2007This report summarizes recent measurements of the production properties of WW and WZ pairs of bosons at the Tevatron. This includes measurements of the cross-section and triple gauge couplings in the WW process and the first evidence for WZ production. ... More

Vizing's conjecture for cographsSep 27 2016Sep 28 2016We show that if $G$ is a cograph, that is $P_4$-free, then for any graph $H$, $\gamma(G\square H)\geq \gamma(G)\gamma(H)$.

A new bound for Vizing's conjectureAug 06 2016For any graph $G$, we define the power $\pi(G)$ as the minimum of the largest number of neighbors in a $\gamma$-set of $G$, of any vertex, taken over all $\gamma$-sets of $G$. We show that $\gamma(G\square H)\geq \frac{\pi(G)}{2\pi(G) -1}\gamma(G)\gamma(H)$. ... More

Lobsters with an almost perfect matching are gracefulFeb 17 2014Let $T$ be a lobster with a matching that covers all but one vertex. We show that in this case, $T$ is graceful.

The end of WHAT nucleon-spin crisis?Apr 01 2016Apr 05 2016Povh and Walcher have written a paper entitled "The end of the nucleon-spin crisis" [arXiv:1603.05884]. But there is no such crisis. What appeared to be a spin crisis in the parton model, 28 years ago, was a consequence of a misinterpretation of the results ... More

Reply to the comment of Huey-Wen Lin and Keh-Fei Liu on "Controversy concerning the definition of quark and gluon angular momentum" by E. Leader (arXiv:1111.0678, PRD 83, 096012 (2011))Nov 24 2011Lin and Liu evaluate the nucleon expectation value of the non gauge-invariant canonical quark momentum operator on a lattice, and obtain zero. They conclude that my argument that, despite the non gauge-invariance of the operator, its physical matrix elements ... More

Alexander Polynomials of Periodic Knots: A Homological Proof and Twisted ExtensionNov 12 2009Nov 17 2009In 1971, Kunio Murasugi proved a necessary condition on a knot's Alexander polynomial for that knot to be periodic of prime power order. In this paper I present an alternate proof of Murasugi's condition which is subsequently used to extend his result ... More

Computing the Canonical Height of a Point in Projective SpaceFeb 16 2016We give an algorithm which requires no integer factorization for computing the canonical height of a point in $\mathbb{P}^1(\mathbb{Q})$ relative to a morphism $\phi: \mathbb{P}_{\mathbb{Q}}^1 \rightarrow \mathbb{P}_{\mathbb{Q}}^1$ of degree $d \geq 2$. ... More

Quantum Decoherence During Inflation from Gravitational NonlinearitiesJan 14 2016We study the inflationary quantum-to-classical transition for the adiabatic curvature perturbation $\zeta$ due to quantum decoherence, focusing on the role played by squeezed-limit mode couplings. We evolve the quantum state $\Psi$ in the Schr\"odinger ... More

The transverse angular momentum sum ruleJun 30 2008We explain the origin of the controversy about the existence of a transverse angular momentum sum rule, and show that it stems from utilizing an incorrect result in the literature, concerning the expression for the expectation values of the angular momentum ... More

Vizing's conjecture: a two-thirds bound for claw-free graphsJul 23 2016We show that for any claw-free graph $G$ and any graph $H$, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where $\gamma(G)$ is the domination number of $G$.

A brief, simple proof of Vizing's conjectureSep 04 2011Sep 16 2011For any graph $G=(V,E)$, a subset $S\subseteq V$ \emph{dominates} $G$ if all vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The minimum cardinality over all such $S$ is called the domination number, written $\gamma(G)$. In ... More

Vizing's conjecture: a two-thirds bound for claw-free graphsJul 23 2016Jun 29 2017We show that for any claw-free graph $G$ and any graph $H$, $\gamma(G\square H)\geq \frac{2}{3}\gamma(G)\gamma(H)$, where $\gamma(G)$ is the domination number of $G$.

Relaxation and Diffusion for the Kicked RotorOct 28 1999The dynamics of the kicked-rotor, that is a paradigm for a mixed system, where the motion in some parts of phase space is chaotic and in other parts is regular is studied statistically. The evolution (Frobenius-Perron) operator of phase space densities ... More

Is transport in time-dependent random potentials universal ?Mar 30 2012The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small velocities uniform ... More

Effective noise theory for the Nonlinear Schrödinger Equation with disorderAug 30 2011Feb 07 2012For the Nonlinear Shr\"odinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as ... More

Scaling Properties of Weak Chaos in Nonlinear Disordered LatticesJul 23 2010Sep 16 2010The Discrete Nonlinear Schroedinger Equation with a random potential in one dimension is studied as a dynamical system. It is characterized by the length, the strength of the random potential and by the field density that determines the effect of nonlinearity. ... More

Dynamics of an ion chain in a harmonic potentialJul 26 2004Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, thus the eigenmodes are not phononic-like waves. We study chains of N>>1 ions and evaluate analytically the long wavelength modes ... More

Variations on Dirichlet's theoremMar 07 2015We give a necessary and sufficient condition for the following property of an integer $d\in\mathbb N$ and a pair $(a,A)\in\mathbb R^2$: There exist $\kappa > 0$ and $Q_0\in\mathbb N$ such that for all $\mathbf x\in \mathbb R^d$ and $Q\geq Q_0$, there ... More

Intrinsic approximation for fractals defined by rational iterated function systems - Mahler's research suggestionAug 10 2012Jul 26 2014Following K. Mahler's suggestion for further research on intrinsic approximation on the Cantor ternary set, we obtain a Dirichlet type theorem for the limit sets of rational iterated function systems. We further investigate the behavior of these approximation ... More

Slowly changing potential problems in Quantum Mechanics: Adiabatic Theorems, Ergodic Theorems, and ScatteringJan 06 2015We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the Adiabatic ... More

Localized Perturbations of Integrable SystemsNov 28 2001The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a typical position. Different results are found for these ... More

Diffusion For Ensembles of Standard MapsSep 17 2014Aug 18 2015Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian distribution ... More

Collapses and revivals of matter wavesAug 27 2014Jan 27 2015Quantum collapses and revivals are fascinating manifestations of interference. Of particular interest in recent years are macroscopic quantum interference effects in Bose-Einstein condensates. In this letter such effects will be studied for the two site ... More

Statistical Properties of the one dimensional Anderson model relevant for the Nonlinear Schrödinger Equation in a random potentialJun 05 2012The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as expected from ... More

Effects of interactions on the dynamics of driven cold atomsApr 10 2014Aug 27 2014The quantum fidelity was introduced by Peres to study some fingerprints of classically chaotic behavior in the quantum dynamics of the corresponding systems. In the present paper the signatures of classical dynamics near elliptic points and of interactions ... More

Multiscale time averaging, ReloadedJul 04 2012Aug 15 2013We develop a rigorously controlled multi-time scale averaging technique; the averaging is done on a finite time interval, properly chosen, and then, via iterations and normal form transformations, the time intervals are scaled to arbitrary order. Here, ... More

Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potentialFeb 18 2004The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phonons. We calculate the long wavelength modes in the continuum limit, and evaluate the density of states in the short wavelength ... More

Relaxation and Noise in Chaotic SystemsApr 29 2002For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems, that are studied ... More

Spectral Statistics of Rectangular Billiards with Localized PerturbationsNov 28 2001Oct 02 2002The form factor $K(\tau)$ is calculated analytically to the order $\tau^3$ as well as numerically for a rectangular billiard perturbed by a $\delta$-like scatterer with an angle independent diffraction constant, $D$. The cases where the scatterer is at ... More

The possibility of a metal insulator transition in antidot arrays induced by an external drivingAug 13 1999It is shown that a family of models associated with the kicked Harper model is relevant for cyclotron resonance experiments in an antidot array. For this purpose a simplified model for electronic motion in a related model system in presence of a magnetic ... More

Semiclassical analysis of Bose-Hubbard dynamicsSep 17 2014In this work the two site Bose-Hubbard model is studied analytically in the limit of weak coupling u and large number of particles N . The semiclassical approximation where \frac{1}{N} plays the role of Planck's constant was used and perturbation theory ... More

Excitation of Small Quantum Systems by High-Frequency FieldsMay 20 1996The excitation by a high frequency field of multi--level quantum systems with a slowly varying density of states is investigated. A general approach to study such systems is presented. The Floquet eigenstates are characterized on several energy scales. ... More

Abdominal multi-organ segmentation with organ-attention networks and statistical fusionApr 23 2018Accurate and robust segmentation of abdominal organs on CT is essential for many clinical applications such as computer-aided diagnosis and computer-aided surgery. But this task is challenging due to the weak boundaries of organs, the complexity of the ... More

Multi-Scale Coarse-to-Fine Segmentation for Screening Pancreatic Ductal AdenocarcinomaJul 09 2018This paper proposes an intuitive approach to finding pancreatic ductal adenocarcinoma (PDAC), the most common type of pancreatic cancer, by checking abdominal CT scans. Our idea is named segmentation-for-classification (S4C), which classifies a volume ... More

Joint Shape Representation and Classification for Detecting PDACApr 27 2018We aim to detect pancreatic ductal adenocarcinoma (PDAC) in abdominal CT scans, which sheds light on early diagnosis of pancreatic cancer. This is a 3D volume classification task with little training data. We propose a two-stage framework, which first ... More

Bridging the Gap Between 2D and 3D Organ Segmentation with Volumetric Fusion NetApr 02 2018Jun 09 2018There has been a debate on whether to use 2D or 3D deep neural networks for volumetric organ segmentation. Both 2D and 3D models have their advantages and disadvantages. In this paper, we present an alternative framework, which trains 2D networks on different ... More

Elastic Boundary Projection for 3D Medical Imaging SegmentationDec 03 2018We focus on an important yet challenging problem: using a 2D deep network to deal with 3D segmentation for medical imaging analysis. Existing approaches either applied multi-view planar (2D) networks or directly used volumetric (3D) networks for this ... More

Prior-aware Neural Network for Partially-Supervised Multi-Organ SegmentationApr 12 2019Accurate multi-organ abdominal CT segmentation is essential to many clinical applications such as computer-aided intervention. As data annotation requires massive human labor from experienced radiologists, it is common that training data are partially ... More

A 3D Coarse-to-Fine Framework for Volumetric Medical Image SegmentationDec 01 2017Aug 02 2018In this paper, we adopt 3D Convolutional Neural Networks to segment volumetric medical images. Although deep neural networks have been proven to be very effective on many 2D vision tasks, it is still challenging to apply them to 3D tasks due to the limited ... More

Thickened 2D Networks for 3D Medical Image SegmentationApr 02 2019There has been a debate in medical image segmentation on whether to use 2D or 3D networks, where both pipelines have advantages and disadvantages. This paper presents a novel approach which thickens the input of a 2D network, so that the model is expected ... More

A Fixed-Point Model for Pancreas Segmentation in Abdominal CT ScansDec 25 2016Jun 21 2017Deep neural networks have been widely adopted for automatic organ segmentation from abdominal CT scans. However, the segmentation accuracy of some small organs (e.g., the pancreas) is sometimes below satisfaction, arguably because deep networks are easily ... More

Semi-Supervised Multi-Organ Segmentation via Deep Multi-Planar Co-TrainingApr 07 2018Nov 19 2018In multi-organ segmentation of abdominal CT scans, most existing fully supervised deep learning algorithms require lots of voxel-wise annotations, which are usually difficult, expensive, and slow to obtain. In comparison, massive unlabeled 3D CT volumes ... More

Birkhoff sum fluctuations in substitution dynamical systemsMay 06 2015We consider the deviation of Birkhoff sums along fixed orbits of substitution dynamical systems. We show distributional convergence for the Birkhoff sums of eigenfunctions of the substitution matrix. For noncoboundary eigenfunctions with eigenvalue of ... More

Price Doubling and Item Halving: Robust Revenue Guarantees for Item PricingNov 08 2016Nov 13 2016We study approximation algorithms for revenue maximization based on static item pricing, where a seller chooses prices for various goods in the market, and then the buyers purchase utility-maximizing bundles at these given prices. We formulate two somewhat ... More

Price Competition in Networked Markets: How do monopolies impact social welfare?Oct 05 2014Oct 05 2015We study the efficiency of allocations in large markets with a network structure where every seller owns an edge in a graph and every buyer desires a path connecting some nodes. While it is known that stable allocations in such settings can be very inefficient, ... More

Approximate Equilibrium and Incentivizing Social CoordinationApr 18 2014We study techniques to incentivize self-interested agents to form socially desirable solutions in scenarios where they benefit from mutual coordination. Towards this end, we consider coordination games where agents have different intrinsic preferences ... More

The law of large numbers for the maximum of almost Gaussian log-correlated fields coming from random matricesNov 27 2016We compute the leading asymptotics as $N\to\infty$ of the maximum of the field $Q_N(q)= \log\det|q- A_N|$, $q\in \mathbb{C}$, for any unitarily invariant Hermitian random matrix $A_N$ associated to a non-critical real-analytic potential. Hence, we verify ... More

The Daniell IntegralJan 01 2014Mar 17 2016The basic properties of the Daniell integral are presented. We do not use the standard approach of introducing auxiliary spaces of the "over-functions" and "under-functions." Instead, we use a simple and direct approach based on approximating integrable ... More

Improved Bounds for Relaxed Graceful TreesFeb 02 2014Nov 24 2016We introduce left and right-layered trees as trees with a specific representation and define the excess of a tree. Applying these ideas, we show a range-relaxed graceful labeling which improves on the upper bound for maximum vertex label given by Van ... More

Anisotropic Challenges in Pedestrian Flow ModelingJun 19 2017Apr 05 2018Macroscopic models of crowd flow incorporating individual pedestrian choices present many analytic and computational challenges. Anisotropic interactions are particularly subtle, both in terms of describing the correct "optimal" direction field for the ... More

Generic derivations on o-minimal structuresMay 17 2019May 26 2019Let $T$ be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language $L$. We study derivations $\delta$ on models $\mathcal{M}\models T$. We introduce the notion of a $T$-derivation: ... More

On Non-singlets in Kaon Production in Semi-inclusive DIS reactionsMar 12 2007We consider semi-inclusive unpolarized DIS for the production of charged kaons and the different possibilities, both in LO and NLO, to test the conventionally used assumptions $s-\bar s=0$ and $D_d^{K^+-K^-}=0$. The considered tests have the advantage ... More

Non-singlets in Semi-inclusive DIS and inclusive e+e- annihilationDec 06 2005We show that non-singlets in semi-inclusive DIS with pi^\pm determine without assumptions Delta u_V, Delta d_V and D_u^{\pi+ - pi-}. Non-singlets in SIDIS and inclusive e+e- -annihilation with K^\pm determine (s-bar s) and (Delta s-Delta bar s), but an ... More

Blind, Greedy, and Random: Ordinal Approximation Algorithms for Matching and ClusteringDec 17 2015Aug 01 2016We study Matching and other related problems in a partial information setting where the agents' utilities for being matched to other agents are hidden and the mechanism only has access to ordinal preference information. Our model is motivated by the fact ... More

The maximum of the CUE fieldFeb 29 2016Let $U_N$ denote a Haar Unitary matrix of dimension N, and consider the field \[ {\bf U}(z) = \log |\det(1-zU_N)| \] for z in the unit disk. Then, \[ \frac{\max_{|z|=1} {\bf U}(z) -\log N + \frac{3}{4} \log\log N} {\log\log N} \to 0 \] in probability. ... More

On the Edge-balanced Index Sets of Complete Bipartite GraphsJun 06 2011Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, and $f$ be a 0-1 labeling of $E(G)$ so that the absolute difference in the number of edges labeled 1 and 0 is no more than one. Call such a labeling $f$ \emph{edge-friendly}. The \emph{edge-balanced ... More

Some work on a problem of Marco BurattiJun 03 2011Nov 18 2015Marco Buratti's conjecture states that if $p$ is a prime and $L$ a multiset containing $p-1$ non-zero elements from the integers modulo $p$, then there exists a Hamiltonian path in the complete graph of order $p$ with edge lengths in $L$. Say that a multiset ... More

Truthful Mechanisms for Matching and Clustering in an Ordinal WorldOct 13 2016We study truthful mechanisms for matching and related problems in a partial information setting, where the agents' true utilities are hidden, and the algorithm only has access to ordinal preference information. Our model is motivated by the fact that ... More

A note on the implications of gauge invariance in QCDJan 18 2011We compare and contrast the implications of gauge invariance for the structure of scattering amplitudes in QED and QCD. We derive the most general analogue for QCD of the famous QED rule that the scattering amplitude must be invariant if the polarization ... More

Improved Bounds for Relaxed Graceful TreesFeb 02 2014Feb 18 2014We introduce left and right-layered trees as trees with a specific representation and define the excess of a tree. Applying these ideas, we show a range-relaxed graceful labeling which improves on the upper bound for maximum vertex label given by Van ... More

Automatic Full Compilation of Julia Programs and ML Models to Cloud TPUsOct 23 2018Google's Cloud TPUs are a promising new hardware architecture for machine learning workloads. They have powered many of Google's milestone machine learning achievements in recent years. Google has now made TPUs available for general use on their cloud ... More

The power of 2 choices over preferential attachmentNov 05 2013Feb 15 2014We introduce a new type of preferential attachment tree that includes choices in its evolution, like with Achlioptas processes. At each step in the growth of the graph, a new vertex is introduced. Two possible neighbor vertices are selected independently ... More

The maximum deviation of the Sine$_β$ counting processJan 26 2018Jun 23 2018In this paper, we consider the maximum of the $\text{Sine}_\beta$ counting process from its expectation. We show the leading order behavior is consistent with the predictions of log-correlated Gaussian fields, also consistent with work on the imaginary ... More

Randomized Social Choice Functions Under Metric PreferencesDec 23 2015Sep 26 2016We determine the quality of randomized social choice mechanisms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to the mechanisms ... More

Contribution Games in Social NetworksApr 11 2010Apr 20 2011We consider network contribution games, where each agent in a social network has a budget of effort that he can contribute to different collaborative projects or relationships. Depending on the contribution of the involved agents a relationship will flourish ... More

The index of a vector field on an orbifold with boundaryJun 12 2008A Poincar\'{e}-Hopf theorem in the spirit of Pugh is proven for compact orbifolds with boundary. The theorem relates the index sum of a smooth vector field in generic contact with the boundary orbifold to the Euler-Satake characteristic of the orbifold ... More

A class of graphs approaching Vizing's conjectureDec 03 2015Apr 04 2016For any graph $G=(V,E)$, a subset $S\subseteq V$ \emph{dominates} $G$ if all vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The minimum cardinality over all such $S$ is called the domination number, written $\gamma(G)$. In ... More

Generic derivations on o-minimal structuresMay 17 2019Let $T$ be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language $L$. We study derivations $\delta$ on models $\mathcal{M}\models T$. We introduce the notion of a $T$-derivation: ... More

Price Doubling and Item Halving: Robust Revenue Guarantees for Item PricingNov 08 2016We study approximation algorithms for revenue maximization based on static item pricing, where a seller chooses prices for various goods in the market, and then the buyers purchase utility-maximizing bundles at these given prices. We formulate two somewhat ... More

Comment on "Proton Spin Structure from Measurable Parton Distributions" by Ji, Xiong and Yuan (PRL109, 152005 (2012))Nov 20 2012We show that the recent claim that the expression 1/2 \int x dx [ H_q (x,0,0) + E_q(x,0,0)], involving the generalized parton distributions H and E, measures the transverse angular momentum of quarks in a transversely polarized nucleon, is incorrect.

Extremal eigenvalue fluctuations in the GUE minor process and the law of fractional logarithmMay 21 2015Jun 09 2015We consider the GUE minor process, where a sequence of GUE matrices is drawn from the corner of a doubly infinite array of i.i.d. standard normal variables subject to the symmetry constraint. From each matrix, we take its largest eigenvalue, appropriately ... More

Choices and intervalsFeb 17 2014We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals goes to infinity. ... More

On Kaon production in e+e- and Semi-inclusive DIS reactionsDec 05 2006Jun 04 2007We consider semi-inclusive unpolarized DIS for the production of charged kaons and the different possibilities to test the conventionally used assumptions s-\bar=0 and D_d^{K^+-K^-}=0. The considered tests have the advantage that they do not require any ... More

Characteristic time scales for diffusion processes through layers and across interfacesJan 16 2018Apr 12 2018This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, ... More

Calculating how long it takes for a diffusion process to effectively reach steady state without computing the transient solutionApr 21 2017Jul 11 2017Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient solution to ... More

Tridiagonal Models for Dyson Brownian MotionJul 10 2017In this paper, we consider tridiagonal matrices the eigenvalues of which evolve according to $\beta$-Dyson Brownian motion. This is the stochastic gradient flow on $\mathbb{R}^n$ given by, for all $1 \leq i \leq n,$ \[ d\lambda_{i,t} = \sqrt{\frac{2}{\beta}}dZ_{i,t} ... More

The power of choice combined with preferential attachmentMar 17 2014We prove almost sure convergence of the maximum degree in an evolving tree model combining local choice and preferential attachment. At each step in the growth of the graph, a new vertex is introduced. A fixed, finite number of possible neighbors are ... More

Quantitative Small Subgraph ConditioningJul 18 2013May 22 2015We revisit the method of small subgraph conditioning, used to establish that random regular graphs are Hamiltonian a.a.s. We refine this method using new technical machinery for random $d$-regular graphs on $n$ vertices that hold not just asymptotically, ... More

Number Systems with Simplicity Hierarchies IIDec 13 2015In [15], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway's ordered field No of surreal numbers was brought to the fore and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to ... 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

Nonmedian Direct Products of Graphs with LoopsFeb 22 2011A \emph{median graph} is a connected graph in which, for every three vertices, there exists a unique vertex $m$ lying on the geodesic between any two of the given vertices. We show that the only median graphs of the direct product $G\times H$ are formed ... More

The problem of kinematic mass corrections for unpolarized semi-inclusive deep inelastic scatteringSep 19 2016Miraculously, target mass corrections for inclusive deep inelastic scattering can be calculated exactly. On the contrary, there does not exist a consistent derivation of kinematic hadron mass corrections for semi-inclusive deep inelastic scattering (SIDIS). ... More

Tests of the extraction of the Sivers, Boer-Mulders and transversity distributions in SIDIS reactionsJul 06 2015Nov 05 2015A major experimental program is presently underway worldwide to determine the fundamental non-perturbative functions, the Sivers, Boer-Mulders and transversity distributions, which are vital for an understanding of the internal structure of the nucleon. ... More

A Model Independent Approach to Semi-Inclusive Deep Inelastic ScatteringDec 11 2004We present a method for extraction of detailed information on polarized quark densities from semi-inclusive deep inelastic scattering l+N -> l+h+X, in both LO and NLO QCD without any assumptions about fragmentation functions and polarized sea densities. ... More

Vizing's Conjecture for Almost All Pairs of GraphsFeb 03 2015For any graph $G=(V,E)$, a subset $S\subseteq V$ $dominates$ $G$ if all vertices are contained in the closed neighborhood of $S$, that is $N[S]=V$. The minimum cardinality over all such $S$ is called the domination number, written $\gamma(G)$. In 1963, ... More

The integer homology threshold in $Y_d(n, p)$Aug 31 2018We prove that in the $d$-dimensional Linial--Meshulam stochastic process the $(d - 1)$st homology group with integer coefficients vanishes exactly when the final isolated $(d - 1)$-dimensional face is covered by a top-dimensional face. This generalizes ... More