We introduce Reflective Hamiltonian Monte Carlo (ReHMC), an HMC-based algorithm, to sample from a log-concave distribution restricted convex body. prove that, starting warm start, the walk mixes target $\pi(x) \propto e^{-f(x)}$, where $f$ is $L$-smooth and $m$-strongly-convex, within accuracy $\varepsilon$ after $\widetilde O(\kappa d^2 \ell^2 \log (1 / \varepsilon))$ steps for well-rounded bo...

We study multivariate entire functions and polynomials with non-negative coefficients. A class of Strongly Log-Concave entire functions, generalizingMinkowski volume polynomials, is introduced: an entire function f in m variables is called Strongly Log-Concave if the function (∂x1) c1 ...(∂xm) mf is either zero or log((∂x1) c1 ...(∂xm) mf) is concave on R + . We start with yet another point of ...

To ensure the operational reliability of power systems, it is important for wind speed signal forecasting systems turbines to be efficient, accurate and stable. This paper proposes a two-phase deep learning structure with network augmentation pruning. By introducing cross-correlation quasi-convex optimization, fractional quadratic programming problem related convex optimization models are const...

Kirkpatrick and Seidel [I 3,14] recently proposed an algorithm for computing the convex hull of n points in the plane that runs in O(n log h) worst case time, where h denotes the number of points on the convex hull of the set. Here a modification of their algorithm is proposed that is believed to run in O(n) expected time for many reasonable distributions of points. The above O(n log h) algorit...

Let G be a weighted, complete, directed acyclic graph whose edge weights obey the concave Monge condition. We give an efficient algorithm for finding the minimum weight k-link path between a given pair of vertices for any given k. The log k log log n ' O Ž . Ž . algorithm runs in n2 time, for k s V log n . Our algorithm can be applied to get efficient solutions for the following problems, impro...

*Correspondence: [email protected] 3Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea Full list of author information is available at the end of the article Abstract In the present paper we consider ageing properties in a deterioration model in which the stochastic process measuring deterioration is a process with independent increments. Preservation of increasing and decre...

This paper considers the generalized Stirling numbers of the first and second kinds. First, we show that the sequences of the above generalized Stirling numbers are both log-concave under some mild conditions. Then, we show that some polynomials related to the above generalized Stirling numbers are q-log-concave or q-log-convex under suitable conditions. We further discuss the log-convexity of ...

We investigate the problem of constructing a shortest path of a point{like robot between two conngurations in the euclidean plane cluttered with (intersecting) convex polygonal obstacles. One common approach is to construct the visibility graph and search within this graph in a total time of O(n 2). We show that in general it is not necessary to construct the entire visibility graph. In contras...

In this paper we present randomized algorithms for sorting and convex hull that achieves optimal performance (for speed-up and cache misses) on the multicore model with private cache model. Our algorithms are cache oblivious and generalize the randomized divide and conquer strategy given by Reischuk [14] and Reif and Sen [17]. Although the approach yielded optimal speed-up in the PRAM model, we...

Given a set S of n points in the Euclidean plane, two-center problem is to find two congruent disks smallest radius whose union covers all S. Previously, Eppstein (SODA’97) gave randomized algorithm $$O(n\log ^2\!n)$$ expected time and Chan (CGTA’99) presented deterministic ^2\!n\log ^2\log n)$$ time. In this paper, we propose an algorithm, which improves Chan’s matches bound Eppstein. If conve...