To study the depinning transition in the limit of strong disorder, Derrida and Retaux (J Stat Phys 156(2):26–290,
2014
) introduced a discrete-time max-type recursive model. It is believed that for a ...large class of recursive models, including Derrida and Retaux’ model, there is a highly non-trivial phase transition. In this article, we present a continuous-time version of Derrida and Retaux model, built on a Yule tree, which yields an exactly solvable model belonging to this universality class. The integrability of this model allows us to study in details the phase transition near criticality and can be used to confirm the infinite order phase transition predicted by physicists. We also study the scaling limit of this model at criticality, which we believe to be universal.
We are interested in the recursive model
(
Y
n
,
n
≥
0
)
studied by Collet et al. (Commun Math Phys 94:353–370, 1984) and by Derrida and Retaux (J Stat Phys 156:268–290, 2014). We prove that at ...criticality, the probability
P
(
Y
n
>
0
)
behaves like
n
-
2
+
o
(
1
)
as
n
goes to infinity; this gives a weaker confirmation of predictions made in Collet et al. (1984), Derrida and Retaux (2014) and Chen et al. (in: Sidoravicius (ed) Sojourns in probability theory and statistical physics-III, Springer, Singapore, 2019). Our method relies on studying the number of pivotal vertices and open paths, combined with a delicate coupling argument.
A rod-shaped liquid plasticine was produced here, which was then shown to serve as a versatile gas detector based on a coloration mechanism. It not only indicated gas existence but also visually ...revealed the gas frontier positions, which allowed the calculation of diffusion speeds and gas concentrations. This study demonstrated the feasibility of multifunctional applications in a liquid plasticine using its shape and optical advantages.
We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers ...a question of Biggins and Kyprianou Electron. J. Probab. 10 (2005) 609-631. Our method applies, furthermore, to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of convergence in probability), already described by Derrida and Spohn J. Statist. Phys. 51 (1988) 817-840. Surprisingly, this phase transition phenomenon disappears in the sense of upper almost sure limits.
Ovarian cancer is one of the most common gyneacologic malignancies, with high morbidity and high mortality. Hsa‐miR‐122‐5p (miR‐122) has been reported with tumor‐suppressing roles in various cancers. ...In this study, miR‐122 was overexpressed in ovarian cancer cells, and phenotypic experiments demonstrated that miR‐122 inhibited migration and invasion in SKOV3 and OVCAR3 cells. MiR‐122 also suppressed epithelial mesenchymal transition (EMT), evidenced by expression changes of E‐cadherin, vimentin, matrix metalloproteinase (MMP)2, and MMP14. Prolyl‐4‐hydroxylase subunit alpha‐1 (P4HA1) was identified as a target of miR‐122, and downregulated by miR‐122. MiR‐122‐induced the elevation of migration, invasion, and EMT were recovered by P4HA1. Additionally, miR‐122 restrained the tumor metastasis of SKOV3 cells in peritoneal cavity of nude mice. In summary, we demonstrated that miR‐122 inhibited migration, invasion, EMT, and metastasis in peritoneal cavity of ovarian cancer cells by targeting P4HA1 for the first time, which shed lights on the discovery of miR‐122 and P4HA1 as possible potential diagnostic markers and therapeutic targets for ovarian cancer.
The classical Ray-Knight theorems for the Brownian motion determine the law of its local time process either at the first hitting time of a given value
a
by the local time at the origin, or at the ...first hitting time of a given position
b
by the Brownian motion. We extend these results by describing the local time process jointly for all
a
and
b
, by means of the stochastic integral with respect to an appropriate white noise. Our result applies to
μ
-processes, and has an immediate application: a
μ
-process is the height process of a Feller continuous-state branching process (CSBP) with immigration (Lambert (2002)), whereas a Feller CSBP with immigration satisfies a stochastic differential equation (SDE) driven by a white noise (Dawson and Li (2012)); our result gives an explicit relation between these two descriptions and shows that the SDE in question is a reformulation of Tanaka’s formula.
Consider a branching random walk
in
with the genealogy tree
formed by a sequence of i.i.d. critical Galton–Watson trees. Let
be the set of points in
visited by
when the index
explores the first
...subtrees in
. Our main result states that for
, the capacity of
is almost surely equal to
as
.
We consider a random walk on $\Z$ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_n$. Then we determine all possible ...limiting law for the sequence $M_n -\alpha n$ where $\alpha$ is a deterministic constant.
We are interested in the biased random walk on a supercritical Galton–Watson tree in the sense of Lyons (Ann. Probab. 18:931–958,
1990
) and Lyons, Pemantle and Peres (Probab. Theory Relat. Fields ...106:249–264,
1996
), and study a phenomenon of slow movement. In order to observe such a slow movement, the bias needs to be random; the resulting random walk is then a tree-valued random walk in random environment. We investigate the recurrent case, and prove, under suitable general integrability assumptions, that upon the system’s non-extinction, the maximal displacement of the walk in the first
n
steps, divided by (log
n
)
3
, converges almost surely to a known positive constant.
This paper studies the influence of different piloti rates (0%, 20%, 40%, 60%, 80%, 100%) on outdoor wind comfort for three building groups, i.e., determinant type, point type, and enclosure type. ...LES (Large Eddy Simulation) is used to simulate the wind environment of three clusters at six different piloti rates. This paper mainly studies the effect of piloti rate on wind speed at pedestrian level (1.5 m). The outdoor wind environment was analyzed using the average wind speed ratio, and outdoor wind comfort was evaluated using the comfortable wind ratio. The following results were obtained: (1) The piloti setting has little influence on the overall wind speed in the target area, and even an inappropriate piloti rate setting may reduce the overall average wind speed in the target area. (2) A comprehensive comparison of the three building layouts shows that the comfortable wind ratio of the determinant layout is the highest when the piloti ratio is 80%. The results of this study can provide architects and urban planners with reference for piloti and urban layout settings.
PDF
