Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on capture point. In this paper, we generalize to variable-height (VHIP) and show how it enables 3-D over uneven terrains inputs. Thanks a tailored optimization scheme, can compute these inputs fast enough for real-time predictive control. We implement approach as open-source software demonstrate in dynamic simulations.

We propose an analysis and applications of sample pooling to the epidemiologic monitoring COVID-19. first introduce a model RT-qPCR process used test for presence virus in construct statistical viral load typical infected individual inspired by large-scale clinical datasets. present application group testing prevention epidemic outbreak closed connected communities. then method measure prevalence population taking into account increased number false negatives associated with method.

We consider a generalized Derrida-Retaux model on Galton-Watson tree with geometric offspring distribution. For class of recursive systems, including the either or exponential initial distribution, we characterize critical curve using an involution-type equation and prove that free energy satisfies conjecture.

We consider a branching Brownian motion in Rd with d≥1 which the position Xt(u)∈Rd of particle u at time t can be encoded by its direction θt(u)∈Sd−1 and distance Rt(u) to 0. prove that extremal point process ∑δ (θt(u),Rt(u)−mt(d)) (where sum is over all particles alive mt(d) an explicit centering term) converges distribution randomly shifted, decorated Poisson on Sd−1×R. More precisely, so-called clan-leaders form Cox intensity proportional D∞(θ)e− 2rdrdθ, where D∞(θ) limit derivative...

In this article, we study a branching random walk in an environment which depends on the time. This time-inhomogeneous consists of sequence macroscopic time intervals, each law reproduction remains constant. We prove that asymptotic behaviour maximal displacement process first ballistic order, given by solution optimization problem under constraints, negative logarithmic correction, plus stochastically bounded fluctuations.

Developments for 3D control of the center mass (CoM) biped robots are currently located in two local minima: on one hand, methods that allow CoM height variations but only work 2D sagittal plane; other nonconvex direct transcriptions centroidal dynamics delicate to handle. This paper presents an alternative controls via indirect transcription is both low-dimensional and solvable fast enough real-time control. The key this development notion boundedness condition, which quantifies...

We consider a branching-selection particle system on the real line. In this model total size of population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing independently, making children around their current position according to i.i.d. point processes. Only $\exp\left(a(n+1)^{1/3}\right)$ rightmost survive form $(n+1)^\mathrm{th}$ generation. This process can be seen as generalisation branching random walk with selection $N$...

Le présent article a pour objet l'étude du processus extrémal mouvement Brownien branchant conditionné à avoir une particule anormalement loin droite. Ces mesures ponctuelles limites forment famille un paramètre et apparaissent dans les extrémaux de plusieurs branchement tels que le avec vitesse variable ou certains branchants multitype. Nous donnons nouvelle représentation ces nous montrons qu'elles continue lois. obtenons ainsi expression probabiliste simple la constante qui apparaît...

We call a random point measure infinitely ramified if for every $n\in\mathbb{N}$, it has the same distribution as $n$th generation of some branching walk. On other hand, Lévy processes model evolution population in continuous time, such that individuals move space independently, according to process, and further beget progenies Poissonian dynamics, possibly on an everywhere dense set times. Our main result connects these two classes much way case divisible distributions processes: value at...

Abstract In a reinforced Galton–Watson process with reproduction law and memory parameter , the number of children typical individual either, probability repeats that one its forebears picked uniformly at random, or, complementary is given by an independent sample from . We estimate average size population large generation, in particular, we determine explicitly Malthusian growth rate terms Our approach via analysis transport equations owes much to works Flajolet co‐authors.

For a standard binary branching Brownian motion on the real line, it is known that typical value of maximal position M t among all particles alive at time isFurther, proved independently in Aïdékon et al. ( 2013) and Arguin shifted by m (or ) converges law to some decorated Poisson point process.The goal this work study conditioned .We give complete description limiting extremal process {M ≤ √ 2αt} with α < 1, which reveals phase transition = 1 -√ 2. We also verify conjecture Derrida Shi...

We consider a branching Brownian motion evolving in $\mathbb{R}^d$. prove that the asymptotic behaviour of maximal displacement is given by first ballistic order, plus logarithmic correction increases with dimension $d$. The proof based on simple geometrical evidence. It leads to interesting following side result: high probability, for any $d \geq 2$, individuals frontier process are close parents if and only they geographically close.

The extremal process of a branching random walk is the point measure recording position particles alive at time n, shifted around expected minimal position.Madaule [Mad17] proved that this converges, as n → ∞, toward randomly shifted, decorated Poisson process.In article, we study joint convergence together with its genealogical informations.This result then used to describe law decoration in limiting process, well supercritical Gibbs measures walk.

In this article, we study the maximal displacement in a branching random walk. We prove that its asymptotic behaviour consists first almost sure ballistic term, negative logarithmic correction probability and stochastically bounded fluctuations. This result, proved by Addario-Berry Reed, Hu Shi is given here under close-to-optimal integrability conditions. provide simple proofs for also deducing genealogical structure of individuals are close to displacement.

We work under the A\"{\i}d\'{e}kon-Chen conditions which ensure that derivative martingale in a supercritical branching random walk on line converges almost surely to nondegenerate nonnegative variable we denote by $Z$. It is shown $\mathbb{E} Z\mathbf{1}_{\{Z\le x\}}=\log x+o(\log x)$ as $x\to\infty$. Also, provide necessary and sufficient x+{\rm const}+o(1)$ This more precise asymptotics key tool for proving distributional limit theorems quantify rate of convergence its The methodological...

A branching Lévy process can be seen as the continuous-time version of a random walk. It describes particle system on real line in which particles move and reproduce independently Poissonian manner. Just for processes, law is determined by its characteristic triplet $(\sigma ^2,a,\Lambda )$, where measure $\Lambda $ intensity Poisson point births jumps. We establish Biggins' theorem this framework, that we provide necessary sufficient conditions terms )$ additive martingales to have...

We consider a branching-selection particle system on the real line, introduced by Brunet and Derrida in [7].In this model size of population is fixed to constant N .At each step individuals reproduce independently, making children around their current position.Only rightmost survive at next step.Bérard Gouéré studied speed which cloud drifts [2], assuming tails displacement decays exponential rate; Bérard Maillard [3] took interest case heavy tail displacements.We take an intermediate model,...

Our object of study is the asymptotic growth heaviest paths in a charged (weighted with signed weights) complete directed acyclic graph.Edge charges are i.i.d.random variables common distribution F supported on [-∞, 1] essential supremum equal to 1 (a charge -∞ understood as absence an edge).The rate constant that we denote by C(F ).Even simplest case where = pδ + (1 -p)δ , corresponding longest path Barak-Erdős random graph, there no closed-form expression for this function, but good bounds...