We appreciate the comments from the associate editor and all reviewers in this paper. We have made necessary experiments and modifications to cope with all the comments. The basic notations for different fonts are: Bold face fonts are from reviewers' original comments. Italic face fonts are the modified/added texts in the paper. Plain fonts are our answers to reviewers' comments. Q1: There is a...

State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Qlearning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value. We show that such smoothed Q-values still satisfy a Bellman equation, making them learnable from experience sampled from an environment. ...

A cylindrical acoustic resonator was externally driven at the first resonance frequency by a compression driver. The acoustic energy stored in the resonator and the power dissipated per unit time were evaluated through the simultaneous measurements of acoustic pressure and velocity, in order to determine the Q value of the resonator. The resulting Q value, being employed as a measure of the dam...

In this article, we calculate the scalar form factors fππ(Q 2) and fKK(Q 2) within the framework of the light-cone QCD sum rules approach. The numerical value of fππ(Q 2) changes quickly with variation of Q2 near zero momentum transfer, while the fKK(Q 2) has rather good behavior at small momentum transfer. The value fKK(0) = 2.21 +0.35 −0.19GeV is compatible with the values from the leading or...

Its value depends on the shape of φπ(x). In particular, using the asymptotic form[2, 1] φ as π (x) = 6fπx(1 − x) one obtains I0 = 3fπ which gives the F as γγ∗π0(Q ) = 4πfπ/Q 2 prediction for the large-Q behavior[1]. Brodsky and Lepage[1] proposed the interpolation formula F γγ∗π0(Q ) = 1/[πfπ(1 + Q2/s0)] which reproduces, for s0 = 4π f π , both the Q 2 = 0 value and the high-Q behavior. The sam...

then σ is a singular value of A and u and v are corresponding left and right singular vectors, respectively. (For generality it is assumed that the matrices here are complex, although given these results, the analogs for real matrices are obvious.) If, for a given positive singular value, there are exactly t linearly independent corresponding right singular vectors and t linearly independent co...

State-action value functions (i.e., Q-values) are ubiquitous in reinforcement learning (RL), giving rise to popular algorithms such as SARSA and Q-learning. We propose a new notion of action value defined by a Gaussian smoothed version of the expected Q-value. We show that such smoothed Q-values still satisfy a Bellman equation, making them learnable from experience sampled from an environment....

The von Neumann and Newman poker models are simplified two-person poker models in which hands are modeled by real values drawn uniformly at random from the unit interval. We analyze a simple extension of both models that introduces an element of uncertainty about the final strength of each player’s own hand, as is present in real poker games. Whenever a showdown occurs, an unfair coin with fixe...

In this article, we calculate the scalar form factors fππ(Q 2) and fKK(Q 2) within the framework of the light-cone QCD sum rules approach. The numerical value of fππ(Q 2) changes quickly with the variation of Q2 at about Q2 < 0.1GeV 2, while fKK(Q 2) has rather good behavior at small momentum transfer, the value fKK(0) = 2.21 +0.35 −0.19GeV is compatible with the values from the leading order c...

This paper presents a novel approach, called validation-driven algorithm (VDA) for improving support vector clustering (SVC). The SVC algorithm is a well-known kernel-based clustering approach, but its clustering results keenly rely on the proper choice of parameters of kernel functions. Particularly, we have found that performance of SVC is very sensitive to the initial value of the kernel par...