Showing papers on "Constant (mathematics) published in 2011"

Direct Fidelity Estimation from Few Pauli Measurements

Abstract: We describe a simple method for certifying that an experimental device prepares a desired quantum state ρ. Our method is applicable to any pure state ρ, and it provides an estimate of the fidelity between ρ and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels.

On the existence and synthesis of multifinger positive grips

Abstract: We study the criteria under which an object can be gripped by a multifingered dexterous hand, assuming no static friction between the object and the fingers; such grips are calledpositive grips. We study three cases in detail: (i) the body is at equilibrium, (ii) the body is under some constant external force/torque, and (iii) the body is under a varying external force/torque. In each case we obtain tight bounds on the number of fingers needed to obtain grip.

Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation

Abstract: This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow

Pulmonary O2 uptake kinetics as a determinant of high-intensity exercise tolerance in humans

Abstract: Tolerance to high-intensity constant-power (P) exercise is well described by a hyperbola with two parameters: a curvature constant (W′) and power asymptote termed “critical power” (CP). Since the a...

Fast and Accurate k-means For Large Datasets

Abstract: Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies a recently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in o(nk) (where n is the number of data points; note that computing the cost, given a solution, takes Θ(nk) time). We show that our algorithm compares favorably to existing algorithms - both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice.

Multi-structural variational transition state theory. Kinetics of the 1,4-hydrogen shift isomerization of the pentyl radical with torsional anharmonicity

Abstract: We present a new formulation of variational transition state theory (VTST) called multi-structural VTST (MS-VTST) and the use of this to calculate the rate constant for the 1,4-hydrogen shift isomerization reaction of 1-pentyl radical and that for the reverse reaction MS-VTST uses a multi-faceted dividing surface and provides a convenient way to include the contributions of many structures (typically conformers) of the reactant and the transition state in rate constant calculations In this particular application, we also account for the torsional anharmonicity We used the multi-configuration Shepard interpolation method to efficiently generate a semi-global portion of the potential energy surface from a small number of high-level electronic structure calculations using the M06 density functional in order to compute the energies and Hessians of Shepard points along a reaction path The M06-2X density functional was used to calculate the multi-structural anharmonicity effect, including all of the structures of the reactant, product and transition state To predict the thermal rate constant, VTST calculations were performed to obtain the canonical variational rate constant over the temperature range 200–2000 K A transmission coefficient is calculated by the multidimensional small-curvature tunneling (SCT) approximation The final MS-CVT/SCT thermal rate constant was determined by combining a reaction rate calculation in the single-structural harmonic oscillator approximation (including tunneling) with the multi-structural anharmonicity torsional factor The calculated forward rate constant agrees very well with experimentally-based evaluations of the high-pressure limit for the temperature range 300–1300 K, although it is a factor of 25–30 lower than the single-structural harmonic oscillator approximation over this temperature range We anticipate that MS-VTST will be generally useful for calculating the reaction rates of complex molecules with multiple torsions

Constant round non-malleable protocols using one way functions

Abstract: We provide the first constant round constructions of non-malleable commitment and zero-knowledge protocols based only on one-way functions. This improves upon several previous (incomparable) works which required either: (a) super-constant number of rounds, or, (b) non-standard or sub-exponential hardness assumptions, or, (c) non-black-box simulation and collision resistant hash functions. These constructions also allow us to obtain the first constant round multi-party computation protocol relying only on the existence of constant round oblivious transfer protocols. Our primary technique can be seen as a means of implementing the previous "two-slot simulation" idea in the area of non-malleability with only black-box simulation.A simple modification of our commitment scheme gives a construction which makes use of the underlying one-way function in a black-box way. The modified construction satisfies the notion of what we call non-malleability w.r.t. replacement. Non-malleability w.r.t. replacement is a slightly weaker yet natural notion of non-malleability which we believe suffices for many application of non-malleable commitments. We show that a commitment scheme which is non-malleable only w.r.t. replacement is sufficient to obtain a (fully) black-box multi-party computation protocol. This allows us to obtain a constant round multi-party computation protocol making only a black-box use of the standard cryptographic primitives with polynomial-time hardness thus directly improving upon the recent work of Wee (FOCS'10).

Large Time Asymptotics for Partially Dissipative Hyperbolic Systems

Abstract: This work is concerned with (n-component) hyperbolic systems of balance laws in m space dimensions. First, we consider linear systems with constant coefficients and analyze the possible behavior of solutions as t → ∞. Using the Fourier transform, we examine the role that control theoretical tools, such as the classical Kalman rank condition, play. We build Lyapunov functionals allowing us to establish explicit decay rates depending on the frequency variable. In this way we extend the previous analysis by Shizuta and Kawashima under the so-called algebraic condition (SK). In particular, we show the existence of systems exhibiting more complex behavior than the one that the (SK) condition allows. We also discuss links between this analysis and previous literature in the context of damped wave equations, hypoellipticity and hypocoercivity. To conclude, we analyze the existence of global solutions around constant equilibria for nonlinear systems of balance laws. Our analysis of the linear case allows proving existence results in situations that the previously existing theory does not cover.

Strategy iteration is strongly polynomial for 2-player turn-based stochastic games with a constant discount factor.

Abstract: Ye [2011] showed recently that the simplex method with Dantzig’s pivoting rule, as well as Howard’s policy iteration algorithm, solve discounted Markov decision processes (MDPs), with a constant discount factor, in strongly polynomial time. More precisely, Ye showed that both algorithms terminate after at most O(mn1−γ log n1−γ) iterations, where n is the number of states, m is the total number of actions in the MDP, and 0

F(t) models within bianchi type-i universe

Abstract: In this paper, we consider spatially homogeneous and anisotropic Bianchi type I universe in the context of F(T) gravity. We construct some corresponding models using conservation equation and equation of state parameter representing different phases of the universe. In particular, we take matter-dominated era, radiation-dominated era, present dark energy phase and their combinations. It is found that one of the models has a constant solution which may correspond to the cosmological constant. We also derive equation of state parameter by using two well-known F(T) models and discuss cosmic acceleration.

Nonlinear Hybrid Continuous/Discrete-Time Models

Abstract: 1. Introduction.- 2. Linear and quasi-linear systems with piecewise constant argument.- 3. The reduction principle for systems with piecewise constant argument.- 4. The small parameter and differential equations with piecewise constant argument.- 5. Stability.- 6. The state-dependent piecewise constant argument.- 7. Almost periodic solutions.- 8. Stability of neural networks.- 9. The blood pressure distribution.- 10. Integrate-and-fire biological oscillators.

Constant mean curvature surfaces in warped product manifolds

Abstract: We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a generalization of the classical Alexandrov theorem in Euclidean space. In particular, our results apply to the deSitter-Schwarzschild and Reissner-Nordstrom manifolds.

Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations

Abstract: The three-dimensional compressible magnetohydrodynamic equation in the whole space are studied in this paper. The global classical solution is established when the initial data are small perturbations of some given constant state. Moreover, the optimal decay rate of the solution is also obtained.

The best constant in a fractional Hardy inequality

Abstract: We prove an optimal Hardy inequality for the fractional Laplacian on the half-space. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

On relaxed constant rank regularity condition in mathematical programming

Abstract: Regularity conditions or constraint qualifications play an important role in mathematical programming. In this article we present a relaxed version of the constant rank constraint qualification (CRCQ) which is weaker than the original CRCQ for mixed-constrained non-linear programming problems and is still a regularity condition. The main aim of this article is to show that the relaxed CRCQ (and, consequently, CRCQ too) implies the R-regularity (in other terms the error bound property) of a system of inequalities and equalities. In the same way we prove that the constant positive linear dependence (CPLD) condition also implies R-regularity.

Optimization of Linear Cooperative Spectrum Sensing for Cognitive Radio Networks

Abstract: Spectrum sensing is the key to coordinate the secondary users in a cognitive radio network by limiting the probability of interference with the primary users. Linear cooperative spectrum sensing consists of comparing the linear combination of the secondary users' recordings against a given threshold in order to assess the presence of the primary user signal. Simplicity is traded off for a slight suboptimality with respect to the likelihood-ratio test. Tuning the performance of linear cooperative radio sensing is complicated by the fact that optimization of the linear combining vector is required. This is accomplished by solving a nonconvex optimization problem, which is the main focus of this work. The global optimum is found by an explicit algorithm based on the solution of a polynomial equation in one scalar variable. Numerical results are reported for validation purposes and to analyze the effects of the system parameters on the complementary receiver operating characteristic. It is shown that the optimum probability of missed detection for a system with constant local signal-to-noise ratios (SNRs) and constant channel gain correlation coefficients can be expressed in closed form by a simple expression. Simulation results are also included to validate the accuracy of the Gaussian approximation. These results illustrate how large the number of sampling intervals must be in order that the Gaussian approximation holds.

The Dispersion of Lossy Source Coding

Abstract: In this work we investigate the behavior of the minimal rate needed in order to guarantee a given probability that the distortion exceeds a prescribed threshold, at some fixed finite quantization block length. We show that the excess coding rate above the rate-distortion function is inversely proportional (to the first order) to the square root of the block length. We give an explicit expression for the proportion constant, which is given by the inverse Q-function of the allowed excess distortion probability, times the square root of a constant, termed the excess distortion dispersion. This result is the dual of a corresponding channel coding result, where the dispersion above is the dual of the channel dispersion. The work treats discrete memoryless sources, as well as the quadratic-Gaussian case.

A Lagrangian approach for the incompressible Navier-Stokes equations with variable density

Abstract: Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical functional framework. The initial density is required to belong to the multiplier space of $\dot B^{n/p-1}_{p,1}(\R^n)$. In particular, piecewise constant initial densities are admissible data \emph{provided the jump at the interface is small enough}, and generate global unique solutions with piecewise constant densities. Using Lagrangian coordinates is the key to our results as it enables us to solve the system by means of the basic contraction mapping theorem. As a consequence, conditions for uniqueness are the same as for existence.

Apportionment of pay out of casino game with escrow

Abstract: A gaming apparatus which, for each of a plurality of plays of a primary game: randomly generates one of a plurality of different primary game outcomes, displays the generated primary game outcome, and displays any award associated with the displayed primary game outcome. If a bonus triggering event occurs, the gaming apparatus: determines a first part of a constant value, causes the determined first part of the constant value to be provided to a first player, determines a second part of the constant value, wherein the determined first part of the constant value and the determined second part of the constant value form the constant value, and causes the determined second part of the constant value to fund a designated award.

Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case

Abstract: In this article we investigate the boundary value problem where γ is a complex valued L ∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Λγ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from Λγ holds.

Lipschitz bandits without the Lipschitz constant

Abstract: We consider the setting of stochastic bandit problems with a continuum of arms indexed by [0, 1]d. We first point out that the strategies considered so far in the literature only provided theoretical guarantees of the form: given some tuning parameters, the regret is small with respect to a class of environments that depends on these parameters. This is however not the right perspective, as it is the strategy that should adapt to the specific bandit environment at hand, and not the other way round. Put differently, an adaptation issue is raised. We solve it for the special case of environments whose mean-payoff functions are globally Lipschitz. More precisely, we show that the minimax optimal orders of magnitude Ld/(d+2) T(d+1)/(d+2) of the regret bound over T time instances against an environment whose mean-payoff function f is Lipschitz with constant L can be achieved without knowing L or T in advance. This is in contrast to all previously known strategies, which require to some extent the knowledge of L to achieve this performance guarantee.

Stable islands in the stability chart of milling processes due to unequal tooth pitch

Abstract: The use of unequal tooth pitch is a known means to influence and to prevent chatter vibrations in milling. While the process dynamics of equally pitched end mills can be modeled by non-autonomous differential equations with a single constant delay, the dynamics of unequally pitched end mills lead to differential equations with multiple constant delays. In this paper the process stability of an unequally pitched end mill is investigated experimentally and theoretically. The numerical approximation of the stability limit relies on two fundamental methods: Ackermann's method to control systems with delay and the method of the piecewise constant subsystems. On the basis of these two methods two ways for the theoretical stability analysis are derived. The first way neglects the time dependency of the system by replacing the time varying system matrices by their means. The second way accounts for the time dependency of the system by combining Ackermann's method to control systems with delay with the method of the piecewise constant subsystems, which results in the semi-discretization method. Besides the exemplary investigation of a specific end mill the two methods are compared for a simple one degree of freedom system for different number of teeth, different alternating and linear tooth pitch variations and different helix angles. It is shown, that unlike equally pitched end mills also at high radial immersions the time dependency of the system leads to significant differences between the stability limits of the unequally pitched end mills, predicted by the two methods. Depending on the time variance of the system and the unequal tooth pitch stable islands can arise, which are largely located within the stable peaks of the stability diagram of the system where the time varying system matrices are replaced by their means. The correctness of the results are backed up for several operating points by time domain simulations, taking into account the trochoidal movement of the cutting edges, the time varying character of the system and teeth jumping out of contact.

On the complexity of approximating a nash equilibrium

Abstract: We show that computing a relatively (i.e., multiplicatively as opposed to additively) approximate Nash equilibrium in two-player games is PPAD-complete, even for constant values of the approximation. Our result is the first constant inapproximability result for Nash equilibrium, since the original results on the computational complexity of the problem [Daskalakis et al. 2006a; Chen and Deng 2006]. Moreover, it provides an apparent---assuming that PPAD is not contained in TIME(nO(log n))---dichotomy between the complexities of additive and relative approximations, as for constant values of additive approximation a quasi-polynomial-time algorithm is known [Lipton et al. 2003]. Such a dichotomy does not exist for values of the approximation that scale inverse-polynomially with the size of the game, where both relative and additive approximations are PPAD-complete [Chen et al. 2006]. As a byproduct, our proof shows that (unconditionally) the sparse-support lemma [Lipton et al. 2003] cannot be extended to relative notions of constant approximation.

Anisotropic nonlinear Neumann problems

Abstract: We consider nonlinear Neumann problems driven by the p(z)-Laplacian differential operator and with a p-superlinear reaction which does not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. Combining variational methods with Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive, the other negative). In the process, we also prove two results of independent interest. The first is about the L∞-boundedness of the weak solutions. The second relates W1,p(z) and C1 local minimizers.