Showing papers on "Bernoulli's principle published in 2012"
29 Oct 2012
TL;DR: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem is answered positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret.
Abstract: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.
521 citations
TL;DR: In this article, it was shown that the Bernoulli convolution with contraction rate ρ ∈ ( 0, 1 ) admits a spectrum if and only if ρ is the reciprocal of an even integer.
172 citations
TL;DR: An efficient direct solver for solving numerically the high-order linear Fredholm integro-differential equations (FIDEs) with piecewise intervals under initial-boundary conditions is developed.
96 citations
TL;DR: Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements, which turns out to require a large number of particles in order to achieve a satisfactory performance.
Abstract: This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient.
79 citations
TL;DR: In this paper, a global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow, and a compact formalism is applied to simplify the isotropy condition and the condition for conformal flatness.
Abstract: A global view is given upon the study of collapsing shear-free perfect fluid spheres with heat flow. We apply a compact formalism, which simplifies the isotropy condition and the condition for conformal flatness. The formulas for the characteristics of the model are straight and tractable. This formalism also presents the simplest possible version of the main junction condition, demonstrated explicitly for conformally flat and geodesic solutions. It gives the right functions to disentangle this condition into well known differential equations like those of Abel, Riccati, Bernoulli and the linear one. It yields an alternative derivation of the general solution with functionally dependent metric components. We bring together the results for static and time-dependent models to describe six generating functions of the general solution to the isotropy equation. Their common features and relations between them are elucidated. A general formula for separable solutions is given, incorporating collapse to a black hole or to a naked singularity.
65 citations
TL;DR: In this paper, the free vibration analysis of a horizontal rectangular plate, either immersed in fluid or floating on its free surface, is studied, and the governing equations for a moderately thick rectangular plate are analytically derived based on the Mindlin plate theory (MPT), whereas the velocity potential function and Bernoulli's equation are employed to obtain the fluid pressure applied on the free surface of the plate.
61 citations
Posted Content•
TL;DR: The question of the optimality of Thompson sampling for solving the stochastic multi-armed bandit problem with Bernoulli rewards has been open since 1933, and the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret was given in this article.
Abstract: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.
52 citations
TL;DR: In this paper, the authors obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-minimizing measures, all of them with non-zero center LyAPunov exponents (at least one with negative exponent and one with a positive exponent).
Abstract: We obtain the following dichotomy for accessible partially hyperbolic diffeomorphisms of three-dimensional manifolds having compact center leaves: either there is a unique entropy-maximizing measure, this measure has the Bernoulli property and its center Lyapunov exponent is 0, or there are a finite number of entropy-maximizing measures, all of them with non-zero center Lyapunov exponents (at least one with a negative exponent and one with a positive exponent), that are finite extensions of a Bernoulli system. In the first case of the dichotomy, we obtain that the system is topologically conjugated to a rotation extension of a hyperbolic system. This implies that the second case of the dichotomy holds for an open and dense set of diffeomorphisms in the hypothesis of our result. As a consequence, we obtain an open set of topologically mixing diffeomorphisms having more than one entropy-maximizing measure.
51 citations
TL;DR: In this paper, a high-speed super-cavitating flow around a two-dimensional symmetric wedge-shaped cavitator was studied using an unsteady Reynolds-averaged Navier-Stokes equations solver based on a cell-centered finite volume method.
51 citations
TL;DR: The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion to solve the autonomous bearings-only tracking problem with observer control.
Abstract: The context is autonomous bearings-only tracking of a single appearing/disappearing target in the presence of detection uncertainty (false and missed detections) with observer control. The optimal tracking method for this problem in the sequential Bayesian estimation framework is the Bernoulli filter. Observer control is based on previously acquired measurements and is formulated as a partially observable Markov decision process (POMDP) where future actions are ranked according to their associated reward. The paper develops a sequential Monte Carlo implementation of the Bernoulli filter and the reward based on an information theoretic criterion.
50 citations
TL;DR: The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, has been clarified and it is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in $C^{1,1}$ and the mass flux is in a suitable regime, there exists a unique globalSubsonic solution in a suited class of general nozzles.
Abstract: We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in $C^{1,1}$ and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, has been clarified.
TL;DR: In this article, the authors investigate the behavior of a relativistic spherically symmetric radiative star with an accelerating, expanding and shearing interior matter distribution in the presence of anisotropic pressures.
Abstract: We investigate the behaviour of a relativistic spherically symmetric radiative star with an accelerating, expanding and shearing interior matter distribution in the presence of anisotropic pressures. The junction condition can be written in standard form in three cases: linear, Bernoulli, and Riccati equations. We can integrate the boundary condition in each case and three classes of new solutions are generated. For particular choices of the metric we investigate the physical properties and consider the limiting behaviour for large values of time. The causal temperature can also be found explicitly.
Posted Content•
TL;DR: In this paper, the authors proposed a method of recycling, which projects Bernoulli components with a low probability of existence onto the Poisson component, as opposed to deleting them.
Abstract: The probability hypothesis density (PHD) and multi-target multi-Bernoulli (MeMBer) filters are two leading algorithms that have emerged from random finite sets (RFS). In this paper we study a method which combines these two approaches. Our work is motivated by a sister paper, which proves that the full Bayes RFS filter naturally incorporates a Poisson component representing targets that have never been detected, and a linear combination of multi-Bernoulli components representing targets under track. Here we demonstrate the benefit (in speed of track initiation) that maintenance of a Poisson component of undetected targets provides. Subsequently, we propose a method of recycling, which projects Bernoulli components with a low probability of existence onto the Poisson component (as opposed to deleting them). We show that this allows us to achieve similar tracking performance using a fraction of the number of Bernoulli components (i.e., tracks).
Proceedings Article•
09 Jul 2012TL;DR: This work proposes a method of recycling, which projects Bernoulli components with a low probability of existence onto the Poisson component (as opposed to deleting them), and shows that this allows us to achieve similar tracking performance using a fraction of the number of Bernouelli components.
Abstract: The probability hypothesis density (PHD) and multitarget multi-Bernoulli (MeMBer) filters are two leading algorithms that have emerged from random finite sets (RFS). In this paper we study a method which combines these two approaches. Our work is motivated by a recent paper, which proves that the full Bayes RFS filter naturally incorporates a Poisson component representing targets that have never been detected, and a linear combination of multi-Bernoulli components representing targets under track. Here we demonstrate the benefit (in speed of track initiation) that maintenance of a Poisson component of never detected targets provides. Subsequently, we propose a method of recycling, which projects Bernoulli components with a low probability of existence onto the Poisson component (as opposed to deleting them). We show that this allows us to achieve similar tracking performance using a fraction of the number of Bernoulli components (i.e., tracks).
TL;DR: An approach for Maximum Likelihood estimation of correspondence and alignment parameters that benefits from the representational skills of graphs that is compared to state-of-the-art non-rigid registration methods and to other graph matching methods which incorporate geometric information.
TL;DR: In this paper, it was shown that in the weakly nonlinear, weakly dispersive regime, the above system of three equations can be reduced to a system of two equations.
Abstract: In Ablowitz, Fokas & Musslimani (J. Fluid Mech., vol. 562, 2006, pp. 313–343) a novel formulation was proposed for water waves in three space dimensions. In the flat-bottom case, this formulation consists of the Bernoulli equation, as well as of a non-local equation. The variable-bottom case, which now involves two non-local equations, was outlined but not explored in the above paper. Here, the variable-bottom formulation is addressed in more detail. First, it is shown that in the weakly nonlinear, weakly dispersive regime, the above system of three equations can be reduced to a system of two equations. Second, by combining the novel non-local formulation of the above authors with conformal mappings, it is shown that in the two-dimensional case, it is possible to obtain a system of two equations without any asymptotic approximations. Furthermore, for the weakly nonlinear, weakly dispersive regime, the nonlinear equations are simpler than the equations obtained without conformal mappings, since they contain lower order derivatives for the terms involving the bottom variable.
TL;DR: In this paper, a mathematical framework for the analysis of the input-output dynamics of externally driven memristors is introduced, and under general assumptions, their dynamics comply with a Bernoulli d...
Abstract: We introduce a mathematical framework for the analysis of the inputoutput dynamics of externally driven memristors. We show that, under general assumptions, their dynamics comply with a Bernoulli d...
TL;DR: In this article, the dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analyzed, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude.
Abstract: The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.
TL;DR: In this article, the vertical structure of neutrino-dominated accretion flows (NDAFs) is revisited in spherical coordinates with a new boundary condition based on the mechanical equilibrium.
Abstract: We revisit the vertical structure of neutrino-dominated accretion flows (NDAFs) in spherical coordinates with a new boundary condition based on the mechanical equilibrium. The solutions show that NDAF is significantly thick. The Bernoulli parameter and neutrino trapping are determined by the mass accretion rate and the viscosity parameter. According to the distribution of the Bernoulli parameter, the possible outflow may appear in the outer region of the disk. The neutrino trapping can essentially affect the neutrino radiation luminosity. The vertical structure of NDAF is like a “sandwich”, and the multilayer accretion may account for the flares in gamma-ray bursts.
Posted Content•
18 May 2012
TL;DR: This paper answers the question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem by providing the first nite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret.
Abstract: The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the rst nite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.
TL;DR: In this paper, the Euler-Bernoulli equation coupled with a wave equation in a bounded domain was considered, and it was shown that in this case the coupled system is not exponentially stable.
Abstract: We consider the
Euler-Bernoulli equation coupled with a wave equation in a bounded
domain. The Euler-Bernoulli has clamped boundary conditions and the
wave equation has Dirichlet boundary conditions. The damping which
is distributed everywhere in the domain under consideration acts
through one of the equations only; its effect is transmitted to the
other equation through the coupling. First we consider the case
where the dissipation acts through the Euler-Bernoulli equation. We
show that in this case the coupled system is not exponentially
stable. Next, using a frequency domain approach combined with the
multiplier techniques, and a recent result of Borichev and Tomilov
on polynomial decay characterization of bounded semigroups, we
provide precise decay estimates showing that the energy of this
coupled system decays polynomially as the time variable goes to
infinity. Second, we discuss the case where the damping acts through
the wave equation. Proceeding as in the first case, we prove that
this new system is not exponentially stable, and we provide precise
polynomial decay estimates for its energy. The results obtained
complement those existing in the literature involving the hinged
Euler-Bernoulli equation.
01 Jan 2012
TL;DR: In this article, a generalized Bernoulli sub-ODE method is proposed to construct exact traveling solutions of nonlinear evolution equations, such as Boussinseq, NNV and Kadomtsev-Petviashvili equations.
Abstract: In this paper, a generalized Bernoulli sub-ODE method is proposed to construct exact traveling solutions of nonlinear evolution equations. We apply the method to establish traveling solutions of the variant Boussinseq equations, (2+1)-dimensional NNV equations and (2+1)-dimensional Boussinesq and Kadomtsev-Petviashvili equations. As a result, some new exact traveling wave solutions are found.
Journal Article•
TL;DR: In this article, the authors focus on the stability and energy budget of collapsible channel flows using a fluid-beam model with the pressure-driven (inlet pressure specified) condition, and highlight its differences to the flow-driven system.
Abstract: Although self-excited oscillations in collapsible channel flows have been extensively studied, our understanding of their origins and mechanisms is still far from complete. In the present paper, we focus on the stability and energy budget of collapsible channel flows using a fluid–beam model with the pressure-driven (inlet pressure specified) condition, and highlight its differences to the flow-driven (i.e. inlet flow specified) system. The numerical finite element scheme used is a spine-based arbitrary Lagrangian–Eulerian method, which is shown to satisfy the geometric conservation law exactly. We find that the stability structure for the pressure-driven system is not a cascade as in the flow-driven case, and the mode-2 instability is no longer the primary onset of the self-excited oscillations. Instead, mode-1 instability becomes the dominating unstable mode. The mode-2 neutral curve is found to be completely enclosed by the mode-1 neutral curve in the pressure drop and wall stiffness space; hence no purely mode-2 unstable solutions exist in the parameter space investigated. By analysing the energy budgets at the neutrally stable points, we can confirm that in the high-wall-tension region (on the upper branch of the mode-1 neutral curve), the stability mechanism is the same as proposed by Jensen and Heil. Namely, self-excited oscillations can grow by extracting kinetic energy from the mean flow, with exactly two-thirds of the net kinetic energy flux dissipated by the oscillations and the remainder balanced by increased dissipation in the mean flow. However, this mechanism cannot explain the energy budget for solutions along the lower branch of the mode-1 neutral curve where greater wall deformation occurs. Nor can it explain the energy budget for the mode-2 neutral oscillations, where the unsteady pressure drop is strongly influenced by the severely collapsed wall, with stronger Bernoulli effects and flow separations. It is clear that more work is required to understand the physical mechanisms operating in different regions of the parameter space, and for different boundary conditions.
TL;DR: In this article, the authors show that the steady-state properties of the Bernoulli cumulative sum (CUSUM) chart and geometric CUSUM chart are the same, because the charts can be designed to be mathematically equivalent.
Abstract: In this article, the authors show that the steady-state properties of the Bernoulli cumulative sum (CUSUM) chart and geometric CUSUM charts are the same because the charts can be designed to be mathematically equivalent.
Posted Content•
TL;DR: In this article, the free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth and two bifurcation mechanisms are described: for waves with fixed Bernoulli's constant and fixed wavelength.
Abstract: The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel shear flow in which counter-currents may be present. Two bifurcation mechanisms are described: for waves with fixed Bernoulli's constant and fixed wavelength. In both cases the corresponding dispersion equations serve for defining wavelengths from which Stokes waves bifurcate. Sufficient conditions guaranteeing the existence of roots of these equations are obtained. Two particular vorticity distributions are considered in order to illustrate general results.
Abstract: The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli and Genocchi polynomials based on the 𝑞-integers. The 𝑞-analogues of well-known formulas are derived. The 𝑞-analogue of the Srivastava-Pintér addition theorem is obtained.
01 Jan 2012
TL;DR: In this article, the Bernoulli product of two Euler polynomials has been investigated and some new and interesting identities and formulae for the product have been investigated.
Abstract: Let ℙn be the space of polynomials of degree less than or equal to n. In this article, using the Bernoulli basis {B0(x ), ..., Bn(x)} for ℙn consisting of Bernoulli polynomials, we investigate some new and interesting identities and formulae for the product of two Bernoulli and Euler polynomials like Carlitz did.
01 Jan 2012
TL;DR: In this paper the solution of a Bernoulli type free boundary problem by means of shape optimization is considered and in case of well-posedness existence and convergence of the approximate shapes is proven.
Abstract: In this paper the solution of a Bernoulli type free boundary problem by means of shape optimization is considered. Four different formulations are compared from an analytical and numerical point of view. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for the discretization of the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second-order shape optimization algorithms are obtained.
TL;DR: In this article, the nonhomogeneous boundary value problem for the steady Navier-Stokes equations is studied in a three-dimensional axially symmetric bounded domain with multiply connected Lipschitz boundary.