A path from a point s to a point t on the surface of a polyhedral terrain is said to be descent if for every pair of points p = (x(p), y(p), z(p)) and q = (x(q), y(q), z(q)) on the path, if dist(s, p) < dist(s, q) then z(p) ≥ z(q), where dist(s, p) denotes the distance of p from s along the aforesaid path. Although an efficient algorithm to decide if there is a descending path between two point...

Efficient exploration in reinforcement learning (RL) can be achieved by incorporating uncertainty into model predictions. Bayesian deep Q-learning provides a principle way for this by modeling Q-values as probability distributions. We propose an efficient algorithm for Bayesian deep Q-learning by posterior sampling actions in the Q-function via continuous-time flows (CTFs), achieving efficient ...

Let R be a real closed field and D ⊂ R an ordered domain. We give an algorithm that takes as input a polynomial Q ⊂ D[X1, . . . , Xk], and computes a description of a roadmap of the set of zeros, Zer(Q,R), of Q in R. The complexity of the algorithm, measured by the number of arithmetic operations in the domain D, is bounded by d √ , where d = deg(Q) ≥ 2. As a consequence, there exist algorithms...

We present the Q-Cut algorithm, a graph theoretic approach for automatic detection of sub-goals in a dynamic environment, which is used for acceleration of the Q-Learning algorithm. The learning agent creates an on-line map of the process history, and uses an efficient MaxFlow/Min-Cut algorithm for identifying bottlenecks. The policies for reaching bottlenecks are separately learned and added t...

We study the quantum summation (QS) algorithm of Brassard, Høyer, Mosca and Tapp, see [1], which approximates the arithmetic mean of a Boolean function defined on N elements. We present sharp error bounds of the QS algorithm in the worst-average setting with the average performance measured in the Lq norm, q ∈ [1,∞]. We prove that the QS algorithm with M quantum queries, M < N , has the worst-a...

The goal of this paper is to improve the performance of the well known Q learning algorithm, the robust technique of Machine learning to facilitate path planning in an environment. Until this time the Q learning algorithms like Classical Q learning(CQL)algorithm and Improved Q learning (IQL) algorithm deal with an environment without obstacles, while in a real environment an agent has to face o...

Let Fq be a finite field with q elements with prime power q and let r > 1 be an integer with q ≡ 1 (mod r). In this paper, we present a refinement of the Cipolla-Lehmer type algorithm given by H. C. Williams, and subsequently improved by K. S. Williams and K. Hardy. For a given r-th power residue c ∈ Fq where r is an odd prime, the algorithm of H. C. Williams determines a solution of X = c in O...

This thesis presents, in full, a simple linear time algorithm for intersecting two convex 3-polyhedra P and Q. This di ers from the rst such algorithm | due to Chazelle | in that it operates entirely in primal space, whereas Chazelle's algorithm relies heavily on duality transforms. We use the hierarchical representations of polyhedra due to Dobkin and Kirkpatrick to induce a cell complexes bet...

In this paper, q-Gaussian Radial Basis Functions are presented as an alternative to Gaussian Radial Basis Function. This model is based on q-Gaussian distribution, which parametrizes the Gaussian distribution by adding a new parameter q. The q-Gaussian Radial Basis Function allows different Radial Basis Functions to be represented by updating the new parameter q. For example, when the q-Gaussia...

We formulate a single-cluster Monte Carlo algorithm for the simulation of the random-cluster model. This algorithm is a generalization of the Wolff single-cluster method for the q-state Potts model to noninteger values q>1. Its results for static quantities are in a satisfactory agreement with those of the existing Swendsen-Wang-Chayes-Machta (SWCM) algorithm, which involves a full-cluster deco...