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Probing weakly hybridized magnetic molecules by spin-polarized tunnelingJun 11 2019Advances in molecular spintronics rely on the in-depth characterization of the molecular building blocks in terms of their electronic and, more importantly, magnetic properties. For this purpose, inert substrates that interact only weakly with adsorbed ... More

Non-local Field Theories and the Non-commutative TorusFeb 12 1998We argue that by taking a limit of SYM on a non-commutative torus one can obtain a theory on non-compact space with a finite non-locality scale. We also suggest that one can also obtain a similar generalization of the (2,0) field theory in 5+1 dimensions, ... More

From SYM Perturbation Theory to Closed Strings in Matrix TheoryDec 23 1999For the purpose of better understanding the AdS/CFT correspondence it is useful to have a description of the theory for all values of the 't Hooft coupling, and for all $N$. We discuss such a description in the framework of Matrix theory for SYM on D4-branes, ... More

Limit theorems for random walks with absorptionNov 28 2018We introduce a class of absorption mechanisms and study the behavior of real-valued centered random walks with finite variance that do not get absorbed. In particular, we prove persistence and scaling limit results, which, in many cases of interests, ... More

Nonparametric estimation of a distribution function under biased sampling and censoringAug 08 2007This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the algorithm ... More

A Supergravity Dual of a (1,0) Field Theory in Six DimensionsFeb 26 1998Mar 02 1998We suggest a supergravity dual for the $(1,0)$ superconformal field theory in six dimensions which has $E_8$ global symmetry. Compared to the description of the (2,0) field theory, the 4-sphere is replaced by a 4-hemisphere, or by orbifolding the 4-sphere. ... More

Double Trace Deformations, Infinite Extra Dimensions and Supersymmetry BreakingSep 29 2002It was recently shown how to break supersymmetry in certain $AdS_3$ spaces, without destabilizing the background, by using a ``double trace'' deformation which localizes on the boundary of space-time. By viewing spatial sections of $AdS_3$ as a compactification ... More

String Dualities from Matrix Theory: A SummaryNov 30 1997I review the appearance, within Matrix theory, of the $SL(5,Z)$ U-duality group of M-theory on $T^4$, and the duality between M-theory on K3 and the Heterotic string on $T^3$. In both cases the duality is geometrical and manifest.

Holographic backgrounds from D-brane probesSep 02 2014Jan 09 2015This thesis focuses on the derivation of holographic backgrounds from the field theory side, without using any supergravity equations of motion. Instead, we rely on the addition of probe D-branes to the stack of D-branes generating the background. From ... More

A Proposal on Some Microscopic Aspects of the AdS/CFT DualityJul 30 1998We suggest a model of the large N limit ${\cal N}=4$ D=4 SU(N) SYM as a gas of 3-branes in a 10 dimensional space. Field theory analysis suggests that this 10 dimensional space does not carry the usual gravity dynamics but rather a contraction of it. ... More

Light-like (2,0) Noncommutativity and Light-Cone Rigid Open Membrane TheoryOct 18 2000The six-dimensional (2,0) field theory admits a generalized ``noncommutative'' deformation associated with turning on a large null 3-form field strength. This theory is studied using its discrete light-cone formulation as quantum mechanics on a blow-up ... More

5D Black Holes and Non-linear Sigma ModelsFeb 12 2008Feb 19 2009Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric non-linear sigma model. We generalize this procedure to 5D gauged ... More

IR Dynamics of d=2, N=(4,4) Gauge Theories and DLCQ of "Little String Theories"Sep 14 1999Oct 04 1999We analyze the superconformal theories (SCFTs) which arise in the low-energy limit of N=(4,4) supersymmetric gauge theories in two dimensions, primarily the Higgs branch SCFT. By a direct field theory analysis we find a continuum of "throat"-like states ... More

Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distancesOct 05 2016We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools ... More

Near Hagedorn Dynamics of NS Fivebranes, or A New Universality Class of Coiled StringsMay 04 2000May 12 2000We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to ... More

Incidences in Three Dimensions and Distinct Distances in the PlaneMay 06 2010We first describe a reduction from the problem of lower-bounding the number of distinct distances determined by a set $S$ of $s$ points in the plane to an incidence problem between points and a certain class of helices (or parabolas) in three dimensions. ... More

An Improved Bound on the Number of Unit Area TrianglesJan 26 2010We show that the number of unit-area triangles determined by a set of $n$ points in the plane is $O(n^{9/4+\epsilon})$, for any $\epsilon>0$, improving the recent bound $O(n^{44/19})$ of Dumitrescu et al.

Semi-algebraic Range Reporting and Emptiness Searching with ApplicationsAug 27 2009Aug 31 2009In a typical range emptiness searching (resp., reporting) problem, we are given a set $P$ of $n$ points in $\reals^d$, and wish to preprocess it into a data structure that supports efficient range emptiness (resp., reporting) queries, in which we specify ... More

Homotheties and incidencesSep 09 2017We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R^3, we are able ... More

Delaunay Triangulations of Degenerate Point SetsOct 15 2015The Delaunay triangulation (DT) is one of the most common and useful triangulations of point sets $P$ in the plane. DT is not unique when $P$ is degenerate, specifically when it contains quadruples of co-circular points. One way to achieve uniqueness ... More

Output-Sensitive Tools for Range Searching in Higher DimensionsDec 21 2013Let $P$ be a set of $n$ points in ${\mathbb R}^{d}$. A point $p \in P$ is $k$\emph{-shallow} if it lies in a halfspace which contains at most $k$ points of $P$ (including $p$). We show that if all points of $P$ are $k$-shallow, then $P$ can be partitioned ... More

Finding the Largest Disk Containing a Query Point in Logarithmic Time with Linear StorageOct 12 2013Let D be a set of n disks in the plane. We present a data structure of size O(n) that can compute, for any query point q, the largest disk in D that contains q, in O(log n) time. The structure can be constructed in O(n log^3 n) time. The optimal storage ... More

Counting Triangulations of Planar Point SetsNov 17 2009Jan 03 2010We study the maximal number of triangulations that a planar set of $n$ points can have, and show that it is at most $30^n$. This new bound is achieved by a careful optimization of the charging scheme of Sharir and Welzl (2006), which has led to the previous ... More

Ruin probabilities in the Cramér-Lundberg model with temporarily negative capitalApr 25 2019We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive due to certain ... More

The One-Sided Isometric Extension ProblemOct 01 2014Aug 22 2016Let $\Sigma$ be a codimension one submanifold of an $n$-dimensional Riemannian manifold $M$, $n\geqslant 2$. We give a necessary condition for an isometric immersion of $\Sigma$ into $\mathbb R^q$ equipped with the standard Euclidean metric, $q\geqslant ... More

An integral that counts the zeros of a functionAug 29 2018Feb 17 2019Given a real function $f$ on an interval $[a,b]$ satisfying mild regularity conditions, we determine the number of zeros of $f$ by evaluating a certain integral. The integrand depends on $f, f'$ and $f''$. In particular, by approximating the integral ... More

Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distancesOct 05 2016Apr 28 2017We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools ... More

Weakly Renormalized Near 1/16 SUSY Fermi Liquid Operators in N = 4 SYMJul 03 2008Sep 26 2008We discuss a class of Fermi Liquid Operators in N = 4 SYM. We show that these operators are eigenstates of the full quantum dilatation operator. We compute their 1 and 2 loop anomalous dimensions, and show that, similar to Fermi liquids in condensed matter ... More

D-instanton probe and the enhançon mechanism from a quiver gauge theoryDec 02 2013May 06 2014We study the $\mathcal N=2$ field theory realized by D3-branes on the ${\mathbb C}^2/{\mathbb Z}_2$ orbifold. The dual supergravity solution exhibits a repulson singularity cured by the enhancon mechanism. By comparing the open and closed string descriptions ... More

The Decision Tree Complexity for $k$-SUM is at most Nearly QuadraticJul 14 2016Following a recent improvement of Cardinal et al. on the complexity of a linear decision tree for $k$-SUM, resulting in $O(n^3 \log^3{n})$ linear queries, we present a further improvement to $O(n^2 \log^2{n})$ such queries.

Distinct and repeated distances on a surface and incidences between points and spheresApr 06 2016In this paper we show that the number of distinct distances determined by a set of $n$ points on a constant-degree two-dimensional algebraic variety $V$ (i.e., a surface) in $\mathbb R^3$ is at least $\Omega\left(n^{7/9}/{\rm polylog} \,n\right)$. This ... More

Incidences between points on a variety and planes in R^3Mar 15 2016May 30 2017In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic variety $V$ of constant ... More

Almost Tight Bounds for Eliminating Depth Cycles in Three DimensionsDec 01 2015Jun 08 2016Given $n$ non-vertical lines in 3-space, their vertical depth (above/below) relation can contain cycles. We show that the lines can be cut into $O(n^{3/2}\mathop{\mathrm{polylog}} n)$ pieces, such that the depth relation among these pieces is now a proper ... More

Improved Bounds for 3SUM, $k$-SUM, and Linear DegeneracyDec 16 2015Mar 05 2017Given a set of $n$ real numbers, the 3SUM problem is to decide whether there are three of them that sum to zero. Until a recent breakthrough by Gr{\o}nlund and Pettie [FOCS'14], a simple $\Theta(n^2)$-time deterministic algorithm for this problem was ... More

Incidences between points and lines on two- and three-dimensional varietiesSep 28 2016Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in $\mathbb R^4$, such that the points of $P$ lie on an algebraic three-dimensional surface of degree $D$ that does not contain hyperplane or quadric components, and no 2-flat contains more than ... More

Splitting the Wino Multiplet by Higher-Dimensional Operators in Anomaly MediationSep 28 2008Feb 25 2009In a class of AMSB models, the splitting in the Wino multiplet turns out to be very small, such as the often-quoted 170 MeV in minimal AMSB, which originates from MSSM loops. Such a small mass gap is potentially a window into higher scale physics, as ... More

Dynamic Time Warping: Breaking the Quadratic BarrierJul 20 2016Aug 15 2016Dynamic Time Warping (DTW) is one of the basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequence of points in some metric space $(X, \operatorname{dist})$. The DTW measure is massively ... More

Cutting Algebraic Curves into Pseudo-segments and ApplicationsApr 26 2016We show that a set of $n$ algebraic plane curves of constant maximum degree can be cut into $O(n^{3/2}\operatorname{polylog} n)$ Jordan arcs, so that each pair of arcs intersect at most once, i.e., they form a collection of pseudo-segments. This extends ... More

Incidences between points and lines on a two-dimensional varietyJan 13 2015We present a direct and fairly simple proof of the following incidence bound: Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in ${\mathbb R}^d$, for $d\ge 3$, which lie in a common algebraic two-dimensional surface of degree $D$ that does not ... More

Eppstein's bound on intersecting triangles revisitedApr 28 2008Jul 27 2008Let S be a set of n points in the plane, and let T be a set of m triangles with vertices in S. Then there exists a point in the plane contained in Omega(m^3 / (n^6 log^2 n)) triangles of T. Eppstein (1993) gave a proof of this claim, but there is a problem ... More

Incidences between points on a variety and planes in R^3Mar 15 2016In this paper we establish an improved bound for the number of incidences between a set $P$ of $m$ points and a set $H$ of $n$ planes in $\mathbb R^3$, provided that the points lie on a two-dimensional nonlinear irreducible algebraic variety $V$ of constant ... More

A Short Review of Time Dependent Solutions and Space-like Singularities in String TheoryMay 15 2007These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such ... More

Membrane Dynamics in M(atrix) TheoryNov 25 1996We analyze some of the kinematical and dynamical properties of flat infinite membrane solutions in the conjectured M theory proposed by Banks, Fischler, Shenker and Susskind. In particular, we compute the long range potential between membranes and anti-membranes, ... More

Improved Bounds for 3SUM, K-SUM, and Linear DegeneracyDec 16 2015Given a set of $n$ real numbers, the 3SUM problem is to decide whether there are three of them that sum to zero. Until a recent breakthrough by Gr{\o}nlund and Pettie [FOCS'14], a simple $\Theta(n^2)$-time deterministic algorithm for this problem was ... More

Preheating and Thermalization after InflationJan 28 2003After a short review of inlationary preheating, we discuss the development of equilibrium in the frameworks of massless $\lambda \Phi^4$ model. It is shown that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards ... More

Dynamic Time Warping and Geometric Edit Distance: Breaking the Quadratic BarrierJul 20 2016Nov 05 2016Dynamic Time Warping (DTW) and Geometric Edit Distance (GED) are basic similarity measures between curves or general temporal sequences (e.g., time series) that are represented as sequences of points in some metric space $(X, \mathsf{dist})$. The DTW ... More

Dominance Product and High-Dimensional Closest Pair under $L_\infty$May 26 2016Jun 24 2017Given a set $S$ of $n$ points in $\mathbb{R}^d$, the Closest Pair problem is to find a pair of distinct points in $S$ at minimum distance. When $d$ is constant, there are efficient algorithms that solve this problem, and fast approximate solutions for ... More

Distinct distances from three pointsAug 04 2013Let $p_1,p_2,p_3$ be three non-collinear points in the plane, and let $P$ be a set of $n$ other points in the plane. We show that the number of distinct distances between $p_1,p_2,p_3$ and the points of $P$ is $\Omega(n^{6/11})$, improving the lower bound ... More

Distinct distances between a collinear set and an arbitrary set of pointsDec 15 2016We consider the number of distinct distances between two finite sets of points in ${\bf R}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary points, such ... More

TzK: Flow-Based Conditional Generative ModelFeb 05 2019Apr 22 2019We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge ... More

Dominance Products and Faster Algorithms for High-Dimensional Closest Pair under $L_\infty$May 26 2016We give improved algorithmic time bounds for two fundamental problems, and establish a new complexity connection between them. The first is computing dominance product: given a set of $n$ points $p_1,\ldots, p_n$ in $\mathbb{R}^d$, compute a matrix $D$, ... More

Matrix Theory, AdS/CFT and Higgs-Coulomb EquivalenceJul 13 1999Oct 25 1999We discuss the relation between the Matrix theory definitions of a class of decoupled theories and their AdS/CFT description in terms of the corresponding near-horizon geometry. The near horizon geometry, naively part of the Coulomb branch, is embedded ... More

New IR Dualities in Supersymmetric Gauge Theory in Three DimensionsOct 30 1998Nov 30 1998We present nontrivial examples of d=3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the gauge theories ... More

TzK: Flow-Based Conditional Generative ModelFeb 05 2019We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require {\em a priori} ... More

TzK: Flow-Based Conditional Generative ModelFeb 05 2019Mar 14 2019We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge ... More

String Dualities from Matrix TheoryMay 22 1997We suggest that the (2,0) six dimensional field theory compactified on $S^1\times K3$ is the Matrix model description of both M-theory on $K3$ and the Heterotic string on $T^3$. This proposal is different from existing proposals for the Heterotic theory. ... More

A Generalized Version of the Residue TheoremAug 02 2018We define a generalization of the winding number of a piecewise $C^1$ cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal value, but is ... More

TzK: Flow-Based Conditional Generative ModelFeb 05 2019Feb 19 2019We formulate a new class of conditional generative models based on probability flows. Trained with maximum likelihood, it provides efficient inference and sampling from class-conditionals or the joint distribution, and does not require a priori knowledge ... More

Incidences between points and lines in three dimensionsJan 12 2015We give a fairly elementary and simple proof that shows that the number of incidences between $m$ points and $n$ lines in ${\mathbb R}^3$, so that no plane contains more than $s$ lines, is $$ O\left(m^{1/2}n^{3/4}+ m^{2/3}n^{1/3}s^{1/3} + m + n\right) ... More

Incidences between points and lines in R^4Nov 04 2014Mar 25 2015We show that the number of incidences between $m$ distinct points and $n$ distinct lines in ${\mathbb R}^4$ is $O\left(2^{c\sqrt{\log m}} (m^{2/5}n^{4/5}+m) + m^{1/2}n^{1/2}q^{1/4} + m^{2/3}n^{1/3}s^{1/3} + n\right)$, for a suitable absolute constant ... More

Counting Plane Graphs: Cross-Graph Charging SchemesSep 02 2012We study cross-graph charging schemes for graphs drawn in the plane. These are charging schemes where charge is moved across vertices of different graphs. Such methods have been recently applied to obtain various properties of triangulations that are ... More

Finding the Maximal Empty Rectangle Containing a Query PointJun 18 2011Let $P$ be a set of $n$ points in an axis-parallel rectangle $B$ in the plane. We present an $O(n\alpha(n)\log^4 n)$-time algorithm to preprocess $P$ into a data structure of size $O(n\alpha(n)\log^3 n)$, such that, given a query point $q$, we can find, ... More

Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequencesOct 16 2017We study the persistence probability for some two-sided discrete-time Gaussian sequences that are discrete-time analogs of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in ... More

Non-integer valued winding numbers and a generalized Residue TheoremAug 02 2018Mar 13 2019We define a generalization of the winding number of a piecewise $C^1$ cycle in the complex plane which has a geometric meaning also for points which lie on the cycle. The computation of this winding number relies on the Cauchy principal value, but is ... More

Strong General PositionSep 09 2014We say that a finite set S of points in R^d is in "strong general position" if for any collection {F_1,..., F_r} of r pairwise disjoint subsets of S (1 <= r <= |S|) we have: d-dim (the intersection of aff F_1,aff F_2,...,aff F_r) = min{d+1, (d-dim aff ... More

Instanton Corrections for m and OmegaDec 19 2016In this paper, we study instanton corrections in the N=2* gauge theory by using its description in string theory as a freely-acting orbifold. The latter is used to compute, using the worldsheet, the deformation of the Yang-Mills action. In addition, we ... More

Five-branes in M(atrix) TheoryOct 30 1996We propose a construction of five-branes which fill both light-cone dimensions in Banks, Fischler, Shenker and Susskind's matrix model of M theory. We argue that they have the correct long-range fields and spectrum of excitations. We prove Dirac charge ... More

Blockers for simple Hamiltonian paths in convex geometric graphs of odd orderJun 06 2018Let G be a complete convex geometric graph, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that has an edge in common with every element of F. In [C. Keller and M. A. Perles, Blockers for simple ... More

Characterization of co-blockers for simple perfect matchings in a convex geometric graphNov 25 2010Consider the complete convex geometric graph on $2m$ vertices, $CGG(2m)$, i.e., the set of all boundary edges and diagonals of a planar convex $2m$-gon $P$. In [C. Keller and M. Perles, On the Smallest Sets Blocking Simple Perfect Matchings in a Convex ... More

Reconstruction of the geometric structure of a set of points in the plane from its geometric tree graphDec 29 2014Let P be a finite set of points in general position in the plane. The structure of the complete graph K(P) as a geometric graph includes, for any pair [a,b],[c,d] of vertex-disjoint edges, the information whether they cross or not. The simple (i.e., non-crossing) ... More

On Convex Geometric Graphs with no $k+1$ Pairwise Disjoint EdgesMay 15 2014May 01 2015A well-known result of Kupitz from 1982 asserts that the maximal number of edges in a convex geometric graph (CGG) on $n$ vertices that does not contain $k+1$ pairwise disjoint edges is $kn$ (provided $n>2k$). For $k=1$ and $k=n/2-1$, the extremal examples ... More

A generalization of Tverberg's TheoremOct 25 2007Sep 09 2014The well know theorem of Tverberg states that if n > (d+1)(r-1) then one can partition any set of n points in R^d to r disjoint subsets whose convex hulls have a common point. The numbers T(d,r) = (d + 1)(r - 1) + 1 are known as Tverberg numbers. Reay ... More

Turbulent ThermalizationMar 09 2004We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our ... More

Relativistic Turbulence: A Long Way from Preheating to EquilibriumOct 14 2002We study, both numerically and analytically, the development of equilibrium after preheating. We show that the process is characterised by the appearance of Kolmogorov spectra and the evolution towards thermal equilibrium follows self-similar dynamics. ... More

TzK Flow - Conditional Generative ModelNov 05 2018Nov 30 2018We introduce TzK (pronounced "task"), a conditional probability flow-based model that exploits attributes (e.g., style, class membership, or other side information) in order to learn tight conditional prior around manifolds of the target observations. ... More

TzK Flow - Conditional Generative ModelNov 05 2018Feb 19 2019We introduce TzK (pronounced "task"), a conditional probability flow-based model that exploits attributes (e.g., style, class membership, or other side information) in order to learn tight conditional prior around manifolds of the target observations. ... More

Blockers for simple Hamiltonian paths in convex geometric graphs of even orderJul 04 2016Let G be a complete convex geometric graph on 2m vertices, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that meets every element of F. In [C. Keller and M. A. Perles, On the smallest sets blocking ... More

On the smallest sets blocking simple perfect matchings in a convex geometric graphNov 17 2009In this paper we present a complete characterization of the smallest sets which block all the simple perfect matchings in a complete convex geometric graph on $2m$ vertices. In particular, we show that all these sets are caterpillar graphs with a special ... More

The number of unit-area triangles in the plane: Theme and variationsJan 02 2015Apr 11 2015We show that the number of unit-area triangles determined by a set $S$ of $n$ points in the plane is $O(n^{20/9})$, improving the earlier bound $O(n^{9/4})$ of Apfelbaum and Sharir [Discrete Comput. Geom., 2010]. We also consider two special cases of ... More

Depth contours in arrangements of halfplanesSep 25 2016Sep 28 2016Let $H$ be a set of $n$ halfplanes in $\mathbb{R}^2$ in general position, and let $k<n$ be a given parameter. We show that the number of vertices of the arrangement of $H$ that lie at depth exactly $k$ (i.e., that are contained in the interiors of exactly ... More

Relative $(p,ε)$-Approximations in GeometrySep 03 2009Jan 25 2010We re-examine the notion of relative $(p,\eps)$-approximations, recently introduced in [CKMS06], and establish upper bounds on their size, in general range spaces of finite VC-dimension, using the sampling theory developed in [LLS01] and in several earlier ... More

Bosonic Preheating in Left-Right-Symmetric SUSY GUTsAug 03 1999We investigate the possibility of a bosonic preheating in the simplest model of supersymmetric Hybridinflation (F-term inflation), which was considered first by Dvali et al. Here the inflationary superpotential is of the O'Raifertaigh-Witten type. The ... More

Open String Moduli in KKLT CompactificationsAug 11 2005In the Kachru-Kallosh-Linde-Trivedi (KKLT) de-Sitter construction one introduces an anti-D3-brane that breaks the supersymmetry and leads to a positive cosmological constant. In this paper we investigate the open string moduli associated with this anti-D3-brane, ... More

4d N=2 superconformal linear quivers with type IIA dualsJun 26 2012Jul 17 2012We discuss the gravity duals of 4d N=2 superconformal field theories (SCFTs) arising from the low-energy limit of brane configurations of D4-branes stretched between and intersecting NS5-branes and D6-branes. This gives rise to a product of SU(N_i) groups, ... More

Interstellar C2 Molecule as Seen in HST/STIS DataJul 10 2006Carbon chains are sometimes considered as possible carriers of some diffuse interstellar bands. Spectroscopic observations in UV band carried by spectrometer STIS fed with HST, give us the possibility to detect many interstellar molecules. We focused ... More

Polynomials vanishing on grids: The Elekes-Rónyai problem revisitedJan 29 2014Mar 19 2014In this paper we characterize real bivariate polynomials which have a small range over large Cartesian products. We show that for every constant-degree bivariate real polynomial $f$, either $|f(A,B)|=\Omega(n^{4/3})$, for every pair of finite sets $A,B\subset{\mathbb ... More

"Double-trace" Deformations, Boundary Conditions and Spacetime SingularitiesDec 31 2001Mar 20 2002Double-trace deformations of the AdS/CFT duality result in a new perturbation expansion for string theory, based on a non-local worldsheet. We discuss some aspects of the deformation in the low energy gravity approximation, where it appears as a change ... More

On the Conformal Field Theory Duals of type IIA AdS_4 Flux CompactificationsJan 22 2008Feb 05 2008We study the conformal field theory dual of the type IIA flux compactification model of DeWolfe, Giryavets, Kachru and Taylor, with all moduli stabilized. We find its central charge and properties of its operator spectrum. We concentrate on the moduli ... More

A faster algorithm for the discrete Fréchet distance under translationJan 15 2015The discrete Fr\'echet distance is a useful similarity measure for comparing two sequences of points $P=(p_1,\ldots, p_m)$ and $Q=(q_1,\ldots,q_n)$. In many applications, the quality of the matching can be improved if we let $Q$ undergo some transformation ... More

Distinct distances on two linesFeb 13 2013Jun 02 2013Let P_1 and P_2 be two sets of points in the plane, so that P_1 is contained in a line L_1, P_2 is contained in a line L_2, and L_1 and L_2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs of P_1xP_2 is ... More

Improved bounds for incidences between points and circlesJul 31 2012Jun 16 2014We establish an improved upper bound for the number of incidences between m points and n circles in three dimensions. The previous best known bound, originally established for the planar case and later extended to any dimension $\ge 2$, is $O*(m^{2/3}n^{2/3} ... More

Improved Bounds for Geometric PermutationsJul 19 2010We show that the number of geometric permutations of an arbitrary collection of $n$ pairwise disjoint convex sets in $\mathbb{R}^d$, for $d\geq 3$, is $O(n^{2d-3}\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.

A Fermi Surface Model for Large Supersymmetric AdS_5 Black HolesApr 04 2006Aug 31 2006We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their ... More

Eliminating Depth Cycles among Triangles in Three DimensionsJul 20 2016Mar 07 2019Given $n$ pairwise openly disjoint triangles in 3-space, their vertical depth relation may contain cycles. We show that, for any $\varepsilon>0$, the triangles can be cut into $O(n^{3/2+\varepsilon})$ connected semi-algebraic pieces, whose description ... More

Chord diagrams, exact correlators in spin glasses and black hole bulk reconstructionJun 12 2018The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. ... More

Convex Integration and Legendrian Approximation of CurvesJul 28 2015Jul 21 2016Using convex integration we give a constructive proof of the well-known fact that every continuous curve in a contact $3$-manifold can be approximated by a Legendrian curve.

Non-local string theories on AdS_3 times S^3 and stable non-supersymmetric backgroundsDec 19 2001Dec 19 2001We exhibit a simple class of exactly marginal "double-trace" deformations of two dimensional CFTs which have AdS_3 duals, in which the deformation is given by a product of left and right-moving U(1) currents. In this special case the deformation on AdS_3 ... More

Multiple-Trace Operators and Non-Local String TheoriesMay 30 2001Jul 13 2001We propose that a novel deformation of string perturbation theory, involving non-local interactions between strings, is required to describe the gravity duals of field theories deformed by multiple-trace operators. The new perturbative expansion involves ... More

Are adaptive allocation designs beneficial for improving power in binary response trials?Feb 24 2011Mar 20 2011We consider the classical problem of selecting the best of two treatments in clinical trials with binary response. The target is to find the design that maximizes the power of the relevant test. Many papers use a normal approximation to the power function ... More

Eliminating Depth Cycles among Triangles in Three DimensionsJul 20 2016Given $n$ non-vertical pairwise disjoint triangles in 3-space, their vertical depth (above/below) relation may contain cycles. We show that, for any $\varepsilon>0$, the triangles can be cut into $O(n^{3/2+\varepsilon})$ pieces, where each piece is a ... More