Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show num...

UNLABELLED PREMISE OF THE STUDY Lateral root (LR) initiation (LRI) is a central process in root branching. Based on LR and/or LR primordium densities, it has been shown that nitric oxide (NO) promotes LRI. However, because NO inhibits primary root growth, we hypothesized that NO may have an opposite effect if the analysis is performed on a cellular basis. Using a previously proposed paramete...

We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both superBrownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-B...

For 0 < α ≤ 2, a super-α-stable motion X in R with branching of index 1 + β ∈ (1, 2) is considered. If d < α/β, a dichotomy for the density of states Xt at fixed times t > 0 holds: the density function is locally Hölder continuous if d = 1 and α > 1 + β, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal Hölder index.

For 0 < α ≤ 2, a super-α-stable motion X in R with branching of index 1+β ∈ (1, 2) is considered. Fix arbitrary t > 0. If d < α/β, a dichotomy for the density function of the measure Xt holds: the density function is locally Hölder continuous if d = 1 and α > 1 + β, but locally unbounded otherwise. Moreover, in the case of continuity, we determine the optimal local Hölder index.

Duprat and Muller [1] introduced the ingenious “Branching CORDIC” algorithm. It enables a fast implementation of CORDIC algorithm using signed digits and requires a constant normalization factor. The speedup is achieved by performing two basic CORDIC rotations in parallel in two separate modules. In their method, both modules perform identical computation except when the algorithm is in a “bran...

one of the generalizations of the wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. the reliability wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. closed expressions are derived for t...

We propose a novel index of short-term endogeneity (or reflexivity) derived by calibrating the Hawkes self-excited conditional Poisson model on empirical time series of trades. The Hawkes model accounts simultaneously for the co-existence and interplay between the exogenous impact of news and the endogenous mechanism by which past trading activity may influence future trading activity. Technica...

Dendritic complexity of deep layer cat superior colliculus neurons has been studied by means of a stochastic model for dendritic outgrowth with randomly branching and elongating neurites. Branching probabilities are assumed to depend on the position and the number of segments in the growing tree. It is demonstrated that the shape properties of model generated dendrites conform closely to those ...

In this paper we compare implementations of Duprat and Muller’s Branching CORDIC and Phatak’s Double Step Branching (DSB)–CORDIC algorithms for Sine and Cosine evaluation. For reference we also report on classical CORDIC implementations for the same wordlengths. We have also implemented Double Stepping in the classical algorithm and report on the performance of this method. CORDIC evaluation of...