We apply the Message from Monte Carlo (MMC) algorithm to inference of univariate polynomials. MMC is an algorithm for point estimation from a Bayesian posterior sample. It partitions the posterior sample into sets of regions that contain similar models. Each region has an associated message length (given by Dowe’s MMLD approximation) and a point estimate that is representative of models in the ...

We consider one-dimensional discrete-time random walks (RWs) in the presence of finite size traps length $\ell$ over which RWs can jump. study survival probability such when are periodically distributed and separated by a distance $L$. obtain exact results for mean first-passage time special case double-sided exponential jump distribution. While typically survive longer than if they could not l...

There is a substantial evidence that plyometric training significantly increases muscular strength and vertical jump. Due to the vigorous nature of this type of training, however, there is a risk of incurring musculoskeletal injuries. Therefore, conducting plyometric exercise programs in an aquatic environment might lead to significant improvements in vertical jump with possibly a lower risk of...

The rate at which a given site in a gene sequence alignment evolves over time may vary. This phenomenon--known as heterotachy--can bias or distort phylogenetic trees inferred from models of sequence evolution that assume rates of evolution are constant. Here, we describe a phylogenetic mixture model designed to accommodate heterotachy. The method sums the likelihood of the data at each site ove...

We establish uniqueness for a class of first-order Hamilton–Jacobi equations with Hamiltonians that arise from the large deviations empirical measure and flux pair weakly interacting Markov jump processes. As corollary, we obtain such deviation principle in context processes time-periodic rates which period-length converges to 0.

We study inversions of the jump operator on Π1 classes, combined with certain basis theorems. These jump inversions have implications for the study of the jump operator on the random degrees—for various notions of randomness. For example, we characterize the jumps of the weakly 2-random sets which are not 2-random, and the jumps of the weakly 1-random relative to 0′ sets which are not 2-random....

We study a new search problem on the plane involving a robot and an immobile treasure, initially placed at distance 1 from each other. The length β of an arc (a fence) within the perimeter of the corresponding circle, as well as the promise that the treasure is outside the fence, is given as part of the input. The goal is to device movement trajectories so that the robot locates the treasure in...

Foss and Zachary (2003) Foss, Palmowski (2005) studied the probability of achieving a receding boundary on time interval random length by walk with heavy-tailed jump distribution. They have proposed developed new approach that allows one to generalise results Asmussen (1998) case arbitrary stopping times wide class nonlinear boundaries, obtain uniform over all times. In this paper, we consider ...

We prove that a set is K-trivial if and only if it is not weakly ML-cuppable. Further, we show that a set below zero jump is K-trivial if and only if it is not ML-cuppable. These results settle a question of Kučera, who introduced both cuppability notions.