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Many copies may be required for entanglement distillationDec 15 2003May 31 2004A mixed quantum state shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of that state into a single ... More

Semidefinite programs for completely bounded normsJan 29 2009Apr 15 2009The completely bounded trace and spectral norms in finite dimensions are shown to be expressible by semidefinite programs. This provides an efficient method by which these norms may be both calculated and verified, and gives alternate proofs of some known ... More

Mixing doubly stochastic quantum channels with the completely depolarizing channelJul 16 2008It is proved that every doubly stochastic quantum channel that is properly averaged with the completely depolarizing channel can be written as a convex combination of unitary channels. As a consequence, we find that the collection of channels expressible ... More

Simpler semidefinite programs for completely bounded normsJul 24 2012Aug 02 2012The completely bounded trace and spectral norms, for finite-dimensional spaces, are known to be efficiently expressible by semidefinite programs (J. Watrous, Theory of Computing 5: 11, 2009). This paper presents two new, and arguably much simpler, semidefinite ... More

Quantum statistical zero-knowledgeFeb 20 2002In this paper we propose a definition for (honest verifier) quantum statistical zero-knowledge interactive proof systems and study the resulting complexity class, which we denote QSZK. We prove several facts regarding this class that establish close connections ... More

PSPACE has 2-round quantum interactive proof systemsJan 27 1999In this paper we consider quantum interactive proof systems, i.e., interactive proof systems in which the prover and verifier may perform quantum computations and exchange quantum messages. It is proved that every language in PSPACE has a quantum interactive ... More

Quantum simulations of classical random walks and undirected graph connectivityDec 11 1998It is not currently known if quantum Turing machines can efficiently simulate probabilistic computations in the space-bounded case. In this paper we show that space-bounded quantum Turing machines can efficiently simulate a limited class of random processes: ... More

Quantum Computational ComplexityApr 21 2008This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive proof systems. Properties of quantum complexity ... More

Zero-knowledge against quantum attacksNov 03 2005This paper proves that several interactive proof systems are zero-knowledge against quantum attacks. This includes a few well-known classical zero-knowledge proof systems as well as quantum interactive proof systems for the complexity class HVQSZK, which ... More

Notes on super-operator norms induced by Schatten normsNov 10 2004This paper considers basic properties of super-operator norms induced by Schatten p-norms. Such super-operator norms arise in various contexts in the study of quantum information. It is proved that for completely positive super-operators, the value of ... More

Quantum algorithms for solvable groupsNov 07 2000Jan 26 2001In this paper we give a polynomial-time quantum algorithm for computing orders of solvable groups. Several other problems, such as testing membership in solvable groups, testing equality of subgroups in a given solvable group, and testing normality of ... More

On quantum and classical space-bounded processes with algebraic transition amplitudesNov 16 1999We define a class of stochastic processes based on evolutions and measurements of quantum systems, and consider the complexity of predicting their long-term behavior. It is shown that a very general class of decision problems regarding these stochastic ... More

Succinct quantum proofs for properties of finite groupsSep 08 2000In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum proofs for properties ... More

Distinguishing quantum operations having few Kraus operatorsOct 03 2007Apr 18 2008Entanglement is sometimes helpful in distinguishing between quantum operations, as differences between quantum operations can become magnified when their inputs are entangled with auxiliary systems. Bounds on the dimension of the auxiliary system needed ... More

Bipartite subspaces having no LOCC-distinguishable basesMar 09 2005Mar 18 2005It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal ... More

Fast parallel circuits for the quantum Fourier transformJun 01 2000We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n + log log (1/epsilon)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2^n with error bounded ... More

On the complementary quantum capacity of the depolarizing channelOct 05 2015The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity ... More

Quantum Arthur-Merlin GamesJun 15 2005This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games in which Arthur and Merlin can perform quantum computations and Merlin can send Arthur quantum information. As in the classical case, messages from Arthur to Merlin are restricted ... More

Two-way finite automata with quantum and classical statesNov 16 1999We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa may include a ... More

Quantum ProofsOct 05 2016Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in which a quantum ... More

Time-reversal of rank-one quantum strategy functionsJan 25 2018Oct 01 2018The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear ... More

Ancilla dimension in quantum channel discriminationApr 27 2016Nov 17 2016Single-shot quantum channel discrimination is a fundamental task in quantum information theory. It is well known that entanglement with an ancillary system can help in this task, and furthermore that an ancilla with the same dimension as the input of ... More

Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurementsJun 02 2014Steering is the entanglement-based quantum effect that embodies the "spooky action at a distance" disliked by Einstein and scrutinized by Einstein, Podolsky, and Rosen. Here we provide a necessary and sufficient characterization of steering, based on ... More

Revisiting the simulation of quantum Turing machines by quantum circuitsAug 06 2018Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a uniformly generated ... More

Toward a general theory of quantum gamesNov 22 2006Apr 02 2007We study properties of quantum strategies, which are complete specifications of a given party's actions in any multiple-round interaction involving the exchange of quantum information with one or more other parties. In particular, we focus on a representation ... More

Quantum Interactive Proofs with Competing ProversDec 22 2004This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language ... More

On the hardness of distinguishing mixed-state quantum computationsJul 22 2004This paper considers the following problem. Two mixed-state quantum circuits Q and R are given, and the goal is to determine which of two possibilities holds: (i) Q and R act nearly identically on all possible quantum state inputs, or (ii) there exists ... More

Oracle Separations for Quantum Statistical Zero-KnowledgeJan 26 2018This paper investigates the power of quantum statistical zero knowledge interactive proof systems in the relativized setting. We prove the existence of an oracle relative to which quantum statistical zero-knowledge does not contain UP intersect coUP, ... More

Ancilla dimension in quantum channel discriminationApr 27 2016Quantum channel discrimination is a fundamental task in quantum information theory. It is well known that entanglement with an ancillary system can help in this task, and furthermore that an ancilla with the same dimension as the input of the channels ... More

Extended Nonlocal Games from Quantum-Classical GamesSep 05 2017Several variants of nonlocal games have been considered in the study of quantum entanglement and nonlocality. This paper concerns two of these variants, called quantum-classical games and extended nonlocal games. We give a construction of an extended ... More

Closed Timelike Curves Make Quantum and Classical Computing EquivalentAug 19 2008While closed timelike curves (CTCs) are not known to exist, studying their consequences has led to nontrivial insights in general relativity, quantum information, and other areas. In this paper we show that if CTCs existed, then quantum computers would ... More

Continuous-time quantum walks on the symmetric groupMay 29 2003In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that for several ... More

Parallel approximation of non-interactive zero-sum quantum gamesAug 20 2008This paper studies a simple class of zero-sum games played by two competing quantum players: each player sends a mixed quantum state to a referee, who performs a joint measurement on the two states to determine the players' payoffs. We prove that an equilibrium ... More

Hedging bets with correlated quantum strategiesApr 06 2011Apr 13 2011This paper studies correlations among independently administered hypothetical tests of a simple interactive type, and demonstrates that correlations arising in quantum information theoretic variants of these tests can exhibit a striking non-classical ... More

On the complementary quantum capacity of the depolarizing channelOct 05 2015Oct 02 2018The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity ... More

Certifying optimality for convex quantum channel optimization problemsOct 31 2018Dec 05 2018We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization ... More

Two-message quantum interactive proofs are in PSPACEMay 08 2009We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE. This relationship is obtained by means of an efficient parallel algorithm, based on the multiplicative weights update method, for ... More

Coherent state exchange in multi-prover quantum interactive proof systemsApr 25 2008Mar 10 2011We show that any number of parties can coherently exchange any one pure quantum state for another, without communication, given prior shared entanglement. Two applications of this fact to the study of multi-prover quantum interactive proof systems are ... More

Quantum interactive proofs with weak error boundsDec 20 2010Sep 06 2011This paper proves that the computational power of quantum interactive proof systems, with a double-exponentially small gap in acceptance probability between the completeness and soundness cases, is precisely characterized by EXP, the class of problems ... More

Quantum interactive proofs with short messagesApr 03 2010Jun 21 2011This paper considers three variants of quantum interactive proof systems in which short (meaning logarithmic-length) messages are exchanged between the prover and verifier. The first variant is one in which the verifier sends a short message to the prover, ... More

Detecting mixed-unitary quantum channels is NP-hardFeb 08 2019A quantum channel is said to be a mixed-unitary channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel, it is NP-hard with respect to polynomial-time Turing reductions ... More

Entanglement in channel discrimination with restricted measurementsApr 06 2010We study the power of measurements implementable with local quantum operations and classical communication (or LOCC measurements for short) in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt ... More

Optimal counterfeiting attacks and generalizations for Wiesner's quantum moneyFeb 17 2012We present an analysis of Wiesner's quantum money scheme, as well as some natural generalizations of it, based on semidefinite programming. For Wiesner's original scheme, it is determined that the optimal probability for a counterfeiter to create two ... More

Sharp Quantum vs. Classical Query Complexity SeparationsNov 15 2000Dec 18 2001We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved exactly in the ... More

Adaptive versus non-adaptive strategies for quantum channel discriminationSep 01 2009We provide a simple example that illustrates the advantage of adaptive over non-adaptive strategies for quantum channel discrimination. In particular, we give a pair of entanglement-breaking channels that can be perfectly discriminated by means of an ... More

Extended nonlocal games and monogamy-of-entanglement gamesOct 06 2015Oct 28 2015We study a generalization of nonlocal games---which we call extended nonlocal games---in which the players, Alice and Bob, initially share a tripartite quantum state with the referee. In such games, the winning conditions for Alice and Bob may depend ... More

Matchgate and space-bounded quantum computations are equivalentAug 11 2009Jan 30 2010Matchgates are an especially multiflorous class of two-qubit nearest neighbour quantum gates, defined by a set of algebraic constraints. They occur for example in the theory of perfect matchings of graphs, non-interacting fermions, and one-dimensional ... More

QIP = PSPACEJul 27 2009Aug 03 2009We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update method to a ... More

Zero-knowledge proof systems for QMAApr 11 2016Prior work has established that all problems in NP admit classical zero-knowledge proof systems, and under reasonable hardness assumptions for quantum computations, these proof systems can be made secure against quantum attacks. We prove a result representing ... More

Consequences and Limits of Nonlocal StrategiesApr 12 2004Jan 11 2010This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible ... More

Quantum fingerprintingFeb 01 2001Classical fingerprinting associates with each string a shorter string (its fingerprint), such that, with high probability, any two distinct strings can be distinguished by comparing their fingerprints alone. The fingerprints can be exponentially smaller ... More

Limitations on separable measurements by convex optimizationAug 29 2014We prove limitations on LOCC and separable measurements in bipartite state discrimination problems using techniques from convex optimization. Specific results that we prove include: an exact formula for the optimal probability of correctly discriminating ... More

One-dimensional quantum walks with absorbing boundariesJul 01 2002Aug 12 2002In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these probabilites both ... More

Operational meaning of quantum measures of recoveryDec 16 2015Aug 04 2016Several information measures have recently been defined which capture the notion of "recoverability." In particular, the fidelity of recovery quantifies how well one can recover a system $A$ of a tripartite quantum state, defined on systems $ABC$, by ... More

All entangled states are useful for channel discriminationJan 15 2009Jul 16 2009We prove that every entangled state is useful as a resource for the problem of minimum-error channel discrimination. More specifically, given a single copy of an arbitrary bipartite entangled state, it holds that there is an instance of a quantum channel ... More

Computing power series expansions of modular formsApr 30 2012Sep 30 2012We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.

Optimal Bacon-Shor codesSep 04 2012We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming independent noise, ... More

Saddlepoint approximations for likelihood ratio like statistics with applications to permutation testsMar 14 2012We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we ... More

Infinitely many knots admitting the same integer surgeryJul 06 2014The construction of knots via annular twisting has been used to create families of knots yielding the same manifold via Dehn surgery. Prior examples have all involved Dehn surgery where the surgery slope is an integral multiple of 2. In this note we prove ... More

Vertex Ramsey problems in the hypercubeNov 01 2012If we 2-color the vertices of a large hypercube what monochromatic substructures are we guaranteed to find? Call a set S of vertices from Q_d, the d-dimensional hypercube, Ramsey if any 2-coloring of the vertices of Q_n, for n sufficiently large, contains ... More

Adaptation of the visibility graph algorithm to find the time lag between hydrogeological time seriesFeb 03 2017Estimating the time lag between two hydrogeologic time series (e.g. precipitation and water levels in an aquifer) is of significance for a hydrogeologist-modeler. In this paper, we present a method to quantify such lags by adapting the visibility graph ... More

Global Stability of the Nontrivial Solutions to the Wave Map Problem from Kerr $|a|\ll M$ to the Hyperbolic Plane under Axisymmetric Perturbations Preserving Angular MomentumOct 13 2016This document proves global boundedness and decay for axisymmetric perturbations of a known solution to the wave map problem from a slowly rotating $|a|\ll M$ Kerr spacetime to the hyperbolic plane. This problem is motivated by the general axisymmetric ... More

Discontinuous Piecewise Polynomial Neural NetworksMay 15 2015Jun 14 2016An artificial neural network is presented based on the idea of connections between units that are only active for a specific range of input values and zero outside that range (and so are not evaluated outside the active range). The connection function ... More

An approach for the automated risk assessment of structural differences between spreadsheets (DiffXL)Aug 20 2009This paper outlines an approach to manage and quantify the risks associated with changes made to spreadsheets. The methodology focuses on structural differences between spreadsheets and suggests a technique by which a risk analysis can be achieved in ... More

Duals for SU(N) SUSY gauge theories with an antisymmetric tensor: five easy flavorsDec 16 1997I consider N=1 supersymmetric SU(N_c) gauge theories with matter fields consisting of one antisymmetric representation, five flavors, and enough anti-fundamental representations to cancel the gauge anomaly. Previous analyses are extended to the case of ... More

Recent Work on Gravitational Waves From a Generic Standard Model-like Effective Higgs PotentialNov 30 2009I present recent work on gravitational waves (GWs) from a generic Standard Model-like effective potential for the electroweak phase transition. We derive a semi-analytic expression for the approximate tunneling temperature, and analytic and approximate ... More

Isomorphism classes of $k$-involutions of algebraic groups of type $E_6$Apr 17 2015Jan 03 2016Automorphisms of order $2$ are studied in order to understand generalized symmetric spaces. The groups of type $E_6$ we consider here can be realized as both the group of linear maps that leave a certain determinant invariant, and also as the identity ... More

New northern common proper motion pairsAug 20 2004Mar 30 2012A list of 705 new Northern Celestial Hemisphere common proper motion pairs as derived from the Second U.S. Naval Observatory CCD Astrograph Catalog is presented, along with details of their separation, motion, brightness and colour. Objects of particular ... More

A Review of Charmed Baryon Experimental DataJun 26 2002A review of the experimental results on charmed baryons, with an accent on those reported most recently. Talk given at FPCP conference, U. Penn, May 2002.

The Topology of $SU(\infty)$ and the Group of Area-Preserving Diffeomorphisms of a Compact 2-manifoldApr 30 2004Given the interest in relating the large $N$ limit of SU(N) to groups of area-preserving diffeomorphisms, we consider the topologies of these groups and show that both in terms of homology and homotopy, they are extremely different. Similar conclusions ... More

3-manifolds as viewed from the curve complexDec 03 1997A Heegaard diagram for a 3-manifold is regarded as a pair of simplexes in the complex of curves on a surface and a Heegaard splitting as a pair of subcomplexes generated by the equivalent diagrams. We relate geometric and combinatorial properties of these ... More

Scheduling Problems and Generalized Graph ColoringNov 29 2016We define a new type of vertex coloring which generalizes vertex coloring in graphs, hypergraphs, and simplicial complexes. This coloring also generalizes oriented coloring, acyclic coloring, and star coloring. There is an associated symmetric function ... More

Short Distance Asymptotics of Ising CorrelationJul 06 2001The short distance asymptotics of the Ising Model scaling functions are computed for the scaling functions that arise as continuum limits of lattice correlations from below the critical temperature.

Absolute Return VolatilityMar 30 2011The use of absolute return volatility has many modelling benefits says John Cotter. An illustration is given for the market risk measure, minimum capital requirements.

Uncovering Long Memory in High Frequency UK FuturesMar 29 2011Accurate volatility modelling is paramount for optimal risk management practices. One stylized feature of financial volatility that impacts the modelling process is long memory explored in this paper for alternative risk measures, observed absolute and ... More

Delocalized $L^2$-InvariantsDec 02 1996We define extensions of the $L^2$-analytic invariants of closed manifolds, called delocalized $L^2$-invariants. These delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group. We show that in many cases, ... More

Deficiencies of Lattice Subgroups of Lie GroupsOct 09 1997Let L be a lattice in a connected Lie group. We show that besides a few exceptional cases, the deficiency of L is nonpositive.

John Clifford Barton: Obituary and BibliographyMay 09 2003John Barton was one of the experimental founders of particle astrophysics, working in deep underground locations all over the world. This note combines the obituary published in The Independent with a complete list of his publications.

A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered FlocksApr 20 2012I reanalyze the hydrodynamic theory of fluid, polar ordered flocks. I find new linear terms in the hydrodynamic equations which slightly modify the anisotropy, but not the scaling, of the damping of sound modes. I also find that the nonlinearities allowed ... More

Minimum Capital Requirement Calculations for UK FuturesMar 28 2011Key to the imposition of appropriate minimum capital requirements on a daily basis requires accurate volatility estimation. Here, measures are presented based on discrete estimation of aggregated high frequency UK futures realisations underpinned by a ... More

Extremal H-colorings of graphs with fixed minimum degreeJul 23 2013For graphs $G$ and $H$, a homomorphism from $G$ to $H$, or $H$-coloring of $G$, is a map from the vertices of $G$ to the vertices of $H$ that preserves adjacency. When $H$ is composed of an edge with one looped endvertex, an $H$-coloring of $G$ corresponds ... More

Non-oblivious Strategy ImprovementMar 15 2010We study strategy improvement algorithms for mean-payoff and parity games. We describe a structural property of these games, and we show that these structures can affect the behaviour of strategy improvement. We show how awareness of these structures ... More

Erratum to "Generalizations of the Poincaré-Birkhoff Theorem"Oct 13 2004May 25 2007This is an erratum to an earlier paper, "Generalizations of the Poincar\'e-Birkhoff theorem." An error in the statement of one of the theorems is corrected.

The rotation set and periodic points for torus homeomorphismsMay 07 1996We consider the rotation set $\rho(F)$ for a lift $F$ of an area preserving homeomorphism $f: \t^2\to \t^2$, which is homotopic to the identity. The relationship between this set and the existence of periodic points for $f$ is least well understood in ... More

Arithmetic of Unicritical Polynomial MapsMar 24 2012This note will study complex polynomial maps of degree $n\ge 2$ with only one critical point.

The O(n) model on the annulusApr 19 2006May 18 2006We use Coulomb gas methods to propose an explicit form for the scaling limit of the partition function of the critical O(n) model on an annulus, with free boundary conditions, as a function of its modulus. This correctly takes into account the magnetic ... More

Conformal Invariance in Percolation, Self-Avoiding Walks and Related ProblemsSep 27 2002Oct 07 2002Over the years, problems like percolation and self-avoiding walks have provided important testing grounds for our understanding of the nature of the critical state. I describe some very recent ideas, as well as some older ones, which cast light both on ... More

Quantum Network Models and Classical Localization ProblemsApr 19 2010A review is given of quantum network models in class C which, on a suitable 2d lattice, describe the spin quantum Hall plateau transition. On a general class of graphs, however, many observables of such models can be mapped to those of a classical walk ... More

SLE for theoretical physicistsMar 13 2005May 02 2005This article provides an introduction to Schramm(stochastic)-Loewner evolution (SLE) and to its connection with conformal field theory, from the point of view of its application to two-dimensional critical behaviour. The emphasis is on the conceptual ... More

Optimization for Mass HierarchyJun 04 2013Jun 21 2013The Delta m^2_13 oscillation frequency for reactor neutrinos differs by 6.4% between normal and inverted mass hierarchy. This frequency difference accumulates to a phase difference over distance and time. The optimal distance is when the maximum phase ... More

Prolegomena to any future Quantum GravitySep 23 2006I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general relativity. ... More

Knots and Quantum Gravity: Progress and ProspectsOct 13 1994Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We review how some ... More

Commissioning strategies and methodsMar 06 2013Accelerator beam commissioning is a challenging and exciting period. It is generally the first integrated operation of the many systems in an accelerator and, most importantly, of the beam. First, general preparation is discussed. Then general methods ... More

Internal Secular Evolution in Disk Galaxies: The Growth of PseudobulgesAug 15 2007Observational and theoretical evidence that internal, slow ("secular") evolution reshapes galaxy disks is reviewed in Kormendy & Kennicutt (2004, ARAA, 42, 603). This update has three aims. First, I emphasize that this evolution is very general -- it ... More

Asymptotic Stochastic Transformations for Nonlinear Quantum Dynamical SystemsDec 29 2012The Ito and Stratonovich approaches are carried over to quantum stochastic systems. Here the white noise representation is shown to be the most appropriate as here the two approaches appear as Wick and Weyl orderings, respectively. This introduces for ... More

Irreducible Modules for the Lie Algebra of Divergence Zero Vector Fields on a TorusNov 15 2014Apr 19 2015This paper investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In "Irreducible Representations of the Lie-Algebra of the Diffeomorphisms of a d-Dimensional Torus," S. Eswara Rao constructs ... More

Duality in Supersymmetric SU($N_c$) Gauge Theory with Two Adjoint Chiral SuperfieldsJun 03 1996We discuss $SU(N_c)$ gauge theory coupled to two adjoint chiral superfields $X$ and $Y$, and a number of fundamental chiral superfields $Q^i$. We add a superpotential that has the form of Arnold's $D$ series $W = \Tr X^{k+1} + \Tr XY^2$. We present a ... More

Exact Solutions of Exceptional Gauge Theories from Toric GeometryMay 11 1997We derive four dimensional gauge theories with exceptional groups $F_4$, $E_8$, $E_7$, and $E_7$ with matter, by starting from the duality between the heterotic string on $K3$ and F-theory on a elliptically fibered Calabi-Yau 3-fold. This configuration ... More

Reviewing METI: A Critical Analysis of the ArgumentsMay 18 2016There is an ongoing debate pertaining to the question of whether Earth should initiate intentional and powerful radio transmissions to putative extra-terrestrial (ET) civilizations in the hope of attracting ET's attention. This practice is known as METI ... More

The Dynamical Evolution of Galaxies in ClustersFeb 23 1999The evolution of galaxies is driven strongly by dynamical processes including internal instabilities, tidal interactions and mergers. The cluster environment is a useful laboratory for studying these effects. I present recent results on simulations of ... More