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124
The Landscape of Parallel Computing Research: A View from Berkeley
 TECHNICAL REPORT, UC BERKELEY
, 2006
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Fredholm Determinants, Differential Equations and Matrix Models
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the und ..."
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Cited by 142 (20 self)
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Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the underlying set is the union of intervals J = [J ™ =1 (βiju Λ 2J) The emphasis is on the determinants thought of as functions of the endpoints a k. We show that these Fredholm determinants with kernels of the general form described above are expressible in terms of solutions of systems of PDE's as long as φ and φ satisfy a certain type of differentiation formula. The (φ, φ) pairs for the sine, Airy, and Bessel kernels satisfy such relations, as do the pairs which arise in the finite N Hermite, Laguerre and Jacobi ensembles and in matrix models of 2D quantum gravity. Therefore we shall be able to write down the systems of PDE's for these ensembles as special cases of the general system. An analysis of these equations will lead to explicit representations in terms of Painleve transcendents for the distribution functions of the largest and smallest eigenvalues in the finite N Hermite and Laguerre ensembles, and for the distribution functions of the largest and smallest singular values of rectangular matrices (of arbitrary dimensions) whose entries are independent identically distributed complex Gaussian variables. There is also an exponential variant of the kernel in which the denominator is replaced by e bx — e by, where b is an arbitrary complex number. We shall find an analogous system of differential equations in this setting. If b = i then we can interpret our operator as acting on (a subset of) the unit circle in the complex plane. As an application of this we shall write down a system of PDE's for Dyson's circular ensemble of N x N unitary matrices, and then an ODE if J is an arc of the circle.
The Multiscalar Architecture
, 1993
"... The centerpiece of this thesis is a new processing paradigm for exploiting instruction level parallelism. This paradigm, called the multiscalar paradigm, splits the program into many smaller tasks, and exploits finegrain parallelism by executing multiple, possibly (control and/or data) dependent t ..."
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Cited by 125 (8 self)
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The centerpiece of this thesis is a new processing paradigm for exploiting instruction level parallelism. This paradigm, called the multiscalar paradigm, splits the program into many smaller tasks, and exploits finegrain parallelism by executing multiple, possibly (control and/or data) dependent tasks in parallel using multiple processing elements. Splitting the instruction stream at statically determined boundaries allows the compiler to pass substantial information about the tasks to the hardware. The processing paradigm can be viewed as extensions of the superscalar and multiprocessing paradigms, and shares a number of properties of the sequential processing model and the dataflow processing model. The multiscalar paradigm is easily realizable, and we describe an implementation of the multiscalar paradigm, called the multiscalar processor. The central idea here is to connect multiple sequential processors, in a decoupled and decentralized manner, to achieve overall multiple issue. The multiscalar processor supports speculative execution, allows arbitrary dynamic code motion (facilitated by an efficient hardware memory disambiguation mechanism), exploits communication localities, and does all of these with hardware that is fairly straightforward to build. Other desirable aspects of the
LEARNING BINARY RELATIONS AND TOTAL ORDERS
, 1993
"... The problem of learning a binary relation between two sets of objects or between a set and itself is studied. This paper represents a binary relation between a set of size n and a set of size rn as an n rn matrix of bits whose (i, j) entry is if and only if the relation holds between the correspond ..."
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Cited by 37 (5 self)
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The problem of learning a binary relation between two sets of objects or between a set and itself is studied. This paper represents a binary relation between a set of size n and a set of size rn as an n rn matrix of bits whose (i, j) entry is if and only if the relation holds between the corresponding elements of the two sets. Polynomial prediction algorithms are presented for learning binary relations in an extended online learning model, where the examples are drawn by the learner, by a helpful teacher, by an adversary, or according to a uniform probability distribution on the instance space. The first part of this paper presents results for the case in which the matrix of the relation has at most k row types. It presents upper and lower bounds on the number of prediction mistakes any prediction algorithm makes when learning such a matrix under the extended online learning model. Furthermore, it describes a technique that simplifies the proof of expected mistake bounds against a randomly chosen query sequence. In the second part of this paper the problem of learning a binary relation that is a total order on a set is considered. A general technique using a fully polynomial randomized approximation scheme (fpras) to implement a randomized version of the halving algorithm is described. This technique is applied to the problem of learning a total order, through the use of an fpras for counting the number of extensions of a partial order, to obtain a polynomial prediction algorithm that with high probability makes at most n lg n + (lg e)lg n mistakes when an adversary selects the query sequence. The case in which a teacher or the learner selects the query sequence is also considered
Heavy Traffic Limits for Some Queueing Networks
 Annals of Applied Probability
, 2001
"... Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportio ..."
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Cited by 33 (3 self)
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Using a slight modification of the framework in Bramson [7] and Williams [52], we prove heavy traffic limit theorems for six families of multiclass queueing networks. The first three families are single station systems operating under firstin firstout (FIFO), generalized headoftheline proportional processor sharing (GHLPPS) and static buffer priority (SBP) service disciplines. The next two families are reentrant lines operating under firstbufferfirstserve (FBFS) and lastbufferfirstserve (LBFS) service disciplines; the last family consists of certain 2station, 5class networks operating under an SBP service discipline. Some of these heavy traffic limits have appeared earlier in the literature; our new proofs demonstrate the significant simplifications that can be achieved in the present setting.
Global analysis of threeflavor neutrino masses and mixings
, 2008
"... We present a comprehensive phenomenological analysis of a vast amount of data from neutrino flavor oscillation and nonoscillation searches, performed within the standard scenario with three massive and mixed neutrinos, and with particular attention to subleading effects. The detailed results discus ..."
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Cited by 29 (5 self)
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We present a comprehensive phenomenological analysis of a vast amount of data from neutrino flavor oscillation and nonoscillation searches, performed within the standard scenario with three massive and mixed neutrinos, and with particular attention to subleading effects. The detailed results discussed in this review represent a stateoftheart, accurate and uptodate (as of June 2005) estimate of the threeneutrino massmixing parameters.
Optimal Auctions with Correlated Bidders are Easy
, 2011
"... We consider the problem of designing a revenuemaximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that runs in time polynomial in the size of the support. ..."
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Cited by 26 (3 self)
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We consider the problem of designing a revenuemaximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that runs in time polynomial in the size of the support. We leverage this result to show that in the oracle model introduced by Ronen and Saberi [FOCS’02], there exists a polynomial time truthful in expectation mechanism that provides a (1.5 + ɛ)approximation to the revenue achievable by an optimal truthfulinexpectation mechanism, and a polynomial time deterministic truthful mechanism that guarantees 5 3 approximation to the revenue achievable by an optimal deterministic truthful mechanism. We show that the 5 3approximation mechanism provides the same approximation ratio also with respect to the optimal truthfulinexpectation mechanism. This shows that the performance gap between truthfulinexpectation and deterministic mechanisms is relatively small. En route, we solve an open question of Mehta and Vazirani [EC’04]. Finally, we extend some of our results to the multiitem case, and show how to compute the optimal truthfulinexpectation mechanisms for bidders with more complex valuations. 1
FixedParameter Algorithms for Kemeny Rankings
, 2009
"... The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NPhard. W ..."
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Cited by 24 (9 self)
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The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NPhard. We provide a broad study of the parameterized complexity for computing optimal Kemeny rankings. Beside the three obvious parameters “number of votes”, “number of candidates”, and solution size (called Kemeny score), we consider further structural parameterizations. More specifically, we show that the Kemeny score (and a corresponding Kemeny ranking) of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large. In other words, Kemeny Score is fixedparameter tractable with respect to the parameter “average pairwise KendallTau distance da”. We describe a fixedparameter algorithm with running time 16 ⌈da ⌉ · poly. Moreover, we extend our studies to the parameters “maximum range ” and “average range ” of positions a candidate takes in the input votes. Whereas Kemeny
Immersed Interface Methods For Moving Interface Problems
 Numerical Algorithms
, 1997
"... . A second order difference method is developed for the nonlinear moving interface problem of the form u t + uux = (fiux) x \Gamma f(x; t); x 2 [ 0; ff ) [ ( ff; 1 ]; dff dt = w (t; ff; u; ux ) ; where ff(t) is the moving interface. The coefficients fi(x; t) and the source term f(x; t) can be dis ..."
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Cited by 22 (10 self)
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. A second order difference method is developed for the nonlinear moving interface problem of the form u t + uux = (fiux) x \Gamma f(x; t); x 2 [ 0; ff ) [ ( ff; 1 ]; dff dt = w (t; ff; u; ux ) ; where ff(t) is the moving interface. The coefficients fi(x; t) and the source term f(x; t) can be discontinuous across ff(t) and moreover, f(x; t) may have a delta function singularity there. As a result, although the equation is parabolic, the solution u and its derivatives may be discontinuous across ff(t). Two typical interface conditions are considered. One condition occurs in Stefanlike problems in which the solution is known on the interface. A new stable interpolation strategy is proposed. The other type occurs in a onedimensional model of Peskin's immersed boundary method in which only jump conditions are given across the interface. The CrankNicolson difference scheme with modifications near the interface is used to solve for the solution u(x; t) and the interface ff(t) simultan...
FixedParameter Algorithms for Kemeny Scores
"... Abstract. The Kemeny Score problem is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest ” to the given set of permutations. Computing an optimal consensus permutat ..."
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Cited by 22 (7 self)
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Abstract. The Kemeny Score problem is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest ” to the given set of permutations. Computing an optimal consensus permutation is NPhard. We provide first, encouraging fixedparameter tractability results for computing optimal scores (that is, the overall distance of an optimal consensus permutation). Our fixedparameter algorithms employ the parameters “score of the consensus”, “maximum distance between two input permutations”, and “number of candidates”. We extend our results to votes with ties and incomplete votes, thus, in both cases having no longer permutations as input. 1