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Acute and minor skin wounds are common in daily life. However, in clinical practice, after initial management in the acute phase, the wounds are managed mainly through observation, and the patients are usually lost to follow-up. Considering a multicomponent hydrolipidic dressing (MAS063DP) long-known for its safe application in eczema and recently in laser-induced wounds, we aimed to evaluate its ability in functional recovery of impaired skin integrity during wound healing. Sixteen patients (N = 16) were enrolled and completed (n = 8 vs n = 8) this prospective, open-label, vehicle-controlled clinical trial with 12-week follow-up. Transepidermal water, skin viscoelasticity and bioimpedance analysis were measured initially, at the 1st, 4th, 8th, and 12th weeks. Improvements in these parameters were greater in the MAS063DP group (from 31.4 ± 9.0 to 16.4 ± 4.3 g/m2 h, P < .001; from 77 ± 16% to 88 ± 9%, P < .05; from 4182 ± 3823 to 2644 ± 1772 Ω) than in the white petrolatum group. No significant adverse events occurred, and all participants were more satisfied with the intervention. In this study, MAS063DP can restore skin integrity and reinstitute physiologic function as a feasible and safe intervention more markedly than management through observation during the healing process by providing protective hydrolipidic layer on the skin with simultaneous anti-inflammatory and antioxidant activities from its key ingredients such as glycyrrhetinic acid, Vitis vinifera, telmesteine, and vitamins C and E.

Multiple penetration depths of high-intensity focused ultrasound (HIFU) treatment for facial rejuvenation have not been quantified.We enrolled 12 participants (n=24) to undergo one session of HIFU rejuvenation between January 1, 2019, and January 10, 2020. We used a 2-, 4.5-, and 6-mm focal depth transducer on the upper and middle face. We evaluated efficacy on days 60 and 90 by using our specific assessment system.The average eyebrow peak and pupil-eyebrow peak angles significantly increased by 2° (p0.0005) and decreased by 1° (p0.0001), respectively, at day 90. The shortened eyebrow-iris length indicated that the forehead tissues had lifted and moved medially to the central face. Supraorbital tissues were also vertically elevated, marked by the eyebrow-orbital (p = 0.0016) and vertical palpebral fissure lengths (p = 0.0052), which both exhibited a 0.8-cm elevation. For the midface, the increased canthus-oral-nasal angle (p = 0.5881) and decreased tragus-oral length (p = 0.5881) indicated that laxity had been corrected through lifted oral commissure, though the data were not statistically significant. No serious side effects were observed.HIFU treatment with multiple depths quantitatively improved both upper-facial rejuvenation and midface rejuvenation after a single session.

BACKGROUND The aging face is characterized by skin laxity and volume loss. Attenuation of facial retaining ligaments significantly contributes to skin sagginess and soft tissue volume loss. AIMS We designed a prospective cohort study to quantitatively assess the efficacy of hyaluronic acid (HA) with adjunct poly-L-lactic acid (PLLA) injections in strengthening the retaining ligaments. PATIENTS/METHODS A total of 12 Asian women were treated with HA injections to the orbital, zygomatic, buccal-maxillary, and mandibular retaining ligaments with adjunct supraperiosteal and subdermal PLLA injections to the temporal region, midface, and lower face. Cephalometric measurements were done before treatment and 2, 4, 12, and 24 weeks post-procedurally. RESULTS Eyebrow peak and tail angles increased 20.0° ± 3.8° to 21.0° ± 3.8° (p

In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter $\sqrt{\varepsilon}$ in front of the noise and let $\varepsilon \to 0$. We prove that the one-point large deviation rate function has a $\frac{3}{2}$ power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the KPZ equation as $\varepsilon \to 0$. This confirms the physics prediction in Kolokolov and Korshunov (2007), Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Kamenev, Meerson, and Sasorov (2016), and Le Doussal, Majumdar, Rosso, and Schehr (2016)., Comment: 23 pages, 1 figure. An error in Lemma 3.1 in the first version of the paper is corrected

This systematic review and meta-analysis investigated differences in accuracy, operation time, and radiation exposure time between robot-assisted and freehand techniques for pedicle screw insertion. Two investigators independently searched for articles on randomized controlled trials (RCTs) published from 2012 to 2019. The final meta-analysis included seven RCTs. We compared the accuracy of pedicle screw placement, operation time, and radiation exposure time between robot-assisted and conventional freehand groups. Seven RCTs included 540 patients and placement of 2,476 pedicle screws, of which 1,220 were inserted using the robot-assisted technique and 1,256 were inserted using the conventional freehand technique. The pedicle screw positions were classified using the Gertzbein and Robbins classification (grade A-E). The combined results of Grade A [odds ratio (OR) =1.68; 95% confidence intervals (CI): 0.82-3.44; P=0.16), Grade A+B (OR =1.70; 95% CI: 0.47-6.13; P=0.42), and Grade C+D+E (OR =0.59; 95% CI: 0.16-2.12; P=0.42) for the accuracy rate revealed no significant difference between the two groups. Subgroup analysis results revealed that the TiRobot-assisted technique presented a significantly improved pedicle screw insertion accuracy rate compared with that of the conventional freehand technique, based on Grade A, Grade A+B, and Grade C+D+E classifications. The SpineAssist-assisted technique presented an inferior pedicle screw insertion accuracy rate compared with that of the conventional freehand technique, based on Grade A, Grade A+B, and Grade C+D+E classifications. No difference between the Renaissance-assisted and conventional freehand techniques was noted for pedicle screw insertion accuracy rates, based on both Grade A (OR =1.58; 95% CI: 0.85-2.96; P=0.15), Grade A+B (OR =2.20; 95% CI: 0.39-12.43; P=0.37), and Grade C+D+E (OR =0.45; 95% CI: 0.08-2.56; P=0.37) classifications. Regarding operation time, robot-assisted surgery had significantly longer operation time than conventional freehand surgery. The robot-assisted group had significantly shorter radiation exposure time. Regarding the pedicle screw insertion accuracy rate, the TiRobot-assisted technique was superior, the SpineAssist-assisted technique was inferior, and Renaissance was similar to the conventional freehand technique.

We establish the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter $ \sqrt{\varepsilon} $ to the noise, and establish an LDP for the trajectory of the solution. Such a Freidlin--Wentzell LDP gives the short-time, one-point LDP for the KPZ equation in terms of a variational problem. Analyzing this variational problem under the narrow wedge initial data, we prove a quadratic law for the near-center tail and a $ \frac52 $ law for the deep lower tail. These power laws confirm existing physics predictions Kolokolov and Korshunov (2007), Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Le Doussal, Majumdar, Rosso, and Schehr (2016), and Kamenev, Meerson, and Sasorov (2016)., Comment: 24 pages, 3 figures

Consider the solution $\mathcal{Z}(t,x)$ of the one-dimensional stochastic heat equation, with a multiplicative spacetime white noise, and with the delta initial data $\mathcal{Z}(0,x) = \delta(x)$. For any real $p>0$, we obtained detailed estimates of the $p$-th moment of $e^{t/12}\mathcal{Z}(2t,0)$, as $t\to\infty$, and from these estimates establish the one-point upper-tail large deviation principle of the Kardar-Parisi-Zhang equation. The deviations have speed $t$ and rate function $\Phi_+(y)=\frac{4}{3}y^{3/2}$. Our result confirms the existing physics predictions [Le Doussal, Majumdar, Schehr 16] and also [Kamenev, Meerson, Sasorov 16]., Comment: 20 pages

For the heat equation driven by a smooth, Gaussian random potential: \begin{equation*}\partial_{t}u_{\varepsilon}=\frac{1}{2}\Delta u_{\varepsilon}+u_{\varepsilon}(\xi_{\varepsilon}-c_{\varepsilon}),\quad t>0,x\in\mathbb{R},\end{equation*} where $\xi_{\varepsilon}$ converges to a spacetime white noise, and $c_{\varepsilon}$ is a diverging constant chosen properly, we prove that $u_{\varepsilon}$ converges in $L^{n}$ to the solution of the stochastic heat equation for any $n\geq1$. Our proof is probabilistic, hence provides another perspective of the general result of Hairer and Pardoux (J. Math. Soc. Japan 67 (2015) 1551–1604), for the special case of the stochastic heat equation. We also discuss the transition from homogenization to stochasticity.

We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the mollification radius $ \varepsilon\to 0 $, we tune the coupling constant near the critical point, and show that the single time correlation functions converge to a limit written in terms of an explicit non-trivial semigroup. Our approach consists of two steps. First we show the convergence of the resolvent of the (tuned) two-dimensional delta Bose gas, by adapting the framework of Dimock and Rajeev (2004) to our setup of spatial mollification. Then we match this to the Laplace transform of our semigroup., 30 pages, 3 figures. Updated to match the version to be published

Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice $ \mathbb{Z} $. We study the functional Large Deviations of the integrated current $ \mathsf{h}(t,x) $ under the hyperbolic scaling of space and time by $ N $, i.e., $ \mathsf{h}_N(t,\xi) := \frac{1}{N}\mathsf{h}(Nt,N\xi) $. As hinted by the asymmetry in the upper- and lower-tail large deviations of the exponential Last Passage Percolation, the TASEP exhibits two types of deviations. One type of deviations occur with probability $ \exp(-O(N)) $, referred to as speed-$ N $; while the other with probability $ \exp(-O(N^{2})) $, referred to as speed-$ N^2 $. In this work we study the speed-$ N^2 $ functional LDP of the TASEP, and establishes (non-matching) large deviation upper and lower bounds., Comment: 13 figures, 59 pages; updated to match the version to be published

In this article we study the stochastic six vertex model under the scaling proposed by Borodin and Gorin (2018), where the weights of corner-shape vertices are tuned to zero, and prove Conjecture 6.1 therein: that the height fluctuation converges in finite dimensional distributions to the solution of stochastic telegraph equation., 14 pages, 2 figures

Nous montrons qu’une generalisation du processus d’exclusion asymetrique appelee $\operatorname{ASEP}(q,j)$, introduite dans (Probab. Theory Related Fields 166 (2016) 887–933), converge sous faible asymetrie vers la solution de l’equation KPZ au sens de Cole–Hopf.

We establish a large deviation principle for the Kardar-Parisi-Zhang (KPZ) equation, providing precise control over the left tail of the height distribution for narrow wedge initial condition. Our analysis exploits an exact connection between the KPZ one-point distribution and the Airy point process-an infinite particle Coulomb gas that arises at the spectral edge in random matrix theory. We develop the large deviation principle for the Airy point process and use it to compute, in a straightforward and assumption-free manner, the KPZ large deviation rate function in terms of an electrostatic problem (whose solution we evaluate). This method also applies to the half-space KPZ equation, showing that its rate function is half of the full-space rate function. In addition to these long-time estimates, we provide rigorous proof of finite-time tail bounds on the KPZ distribution, which demonstrate a crossover between exponential decay with exponent 3 (in the shallow left tail) to exponent 5/2 (in the deep left tail). The full-space KPZ rate function agrees with the one computed in Sasorov et al. [J. Stat. Mech. (2017) 063203JSMTC61742-546810.1088/1742-5468/aa73f8] via a WKB approximation analysis of a nonlocal, nonlinear integrodifferential equation generalizing Painleve II which Amir et al. [Commun. Pure Appl. Math. 64, 466 (2011)CPMAMV0010-364010.1002/cpa.20347] related to the KPZ one-point distribution.

We analyze a class of non-simple exclusion processes and the corresponding growth models by generalizing Gaertners Cole-Hopf transformation. We identify the main non-linearity and eliminate it by imposing a gradient type condition. For hopping range at most 3, using the generalized transformation, we prove the convergence of the exclusion process toward the Kardar-Parisi-Zhang (KPZ) equation. This is the first universality result concerning interacting particle systems in the context of KPZ universality class. While this class of exclusion processes are not explicitly solvable, we obtain the exact one-point limiting distribution for the step initial condition by using the previous result of Amir et al. (2011) and our convergence result., 32 pages, 1 figure. Comm. Math. Phys. in press. Reverted to v3 (i.e. v5 == v3) because v4 was a different paper that was mistakenly uploaded and should be ignored. v1 has errors; major changes made in v2

In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional Stochastic Differential Equation (SDE) corresponding to the bulk limit of Dyson's Brownian Motion (DBM), for all $\beta\geq 1$. Our construction applies to an explicit and general class of initial conditions, including the lattice configuration $\{x_i\}=\mathbb{Z}$ and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (2010) for the solution of this SDE at $\beta=2$., Comment: 40 pages; no figure. PTRF in press; updated to match published version. Mayor improvement (Theorem 1.4 and 1.5) introduced in v2

We study the stochastic six vertex model and prove that under weak asymmetry scaling (i.e., when the parameter $\Delta\to 1^+$ so as to zoom into the ferroelectric/disordered phase critical point) its height function fluctuations converge to the solution to the KPZ equation. We also prove that the one-dimensional family of stochastic Gibbs states for the symmetric six vertex model converge under the same scaling to the stationary solution to the stochastic Burgers equation. Our proofs rely upon the Markov (self) duality of our model. The starting point is an exact microscopic Hopf-Cole transform for the stochastic six vertex model which follows from the model's known one-particle Markov self-duality. Given this transform, the crucial step is to establish self-averaging for specific quadratic function of the transformed height function. We use the model's two-particle self-duality to produce explicit expressions (as Bethe ansatz contour integrals) for conditional expectations from which we extract time-decorrelation and hence self-averaging in time. The crux of our Markov duality method is that the entire convergence result reduces to precise estimates on the one-particle and two-particle transition probabilities. Previous to our work, Markov dualities had only been used to prove convergence of particle systems to linear Gaussian SPDEs (e.g. the stochastic heat equation with additive noise)., Comment: 74 pages, 21 figures

We study ASEP in a spatially inhomogeneous environment on a torus $ \mathbb{T}^{(N)} = \mathbb{Z}/N\mathbb{Z} $ of $ N $ sites. A given inhomogeneity $ \widetilde{a}(x) \in (0,\infty) $, $x \in \mathbb{T} $, perturbs the overall asymmetric jumping rates $ r < \ell \in (0,1) $ at bonds, so that particles jump from site $ x $ to $ x+1 $ with rate $ r\widetilde{a}(x) $ and from $x+1$ to $x$ with rate $ \ell\widetilde{a}(x) $ (subject to the exclusion rule in both cases). Under the limit $ N\to\infty $, we suitably tune the asymmetry $ (\ell-r) $ to zero like $N^{-\frac{1}{2}}$ and the inhomogeneity $ \widetilde{a}(x) $ to unity, so that the two compete on equal footing. At the level of the G\"{a}rtner (or microscopic Hopf--Cole) transform, we show convergence to a new SPDE -- the Stochastic Heat Equation with a mix of spatial and spacetime multiplicative noise. Equivalently, at the level of the height function we show convergence to the Kardar--Parisi--Zhang equation with a mix of spatial and spacetime additive noise. Our method applies to a general class of $ \widetilde{a}(x) $, which, in particular, includes i.i.d., long-range correlated, and periodic inhomogeneities. The key technical component of our analysis consists of a host of estimates on the \emph{kernel} of the semigroup $ \mathcal{Q}(t):=e^{t\mathcal{H}} $ for a Hill-type operator $ \mathcal{H}:= \frac12\partial_{xx} + \mathcal{A}'(x) $, and its discrete analog, where $ \mathcal{A} $ (and its discrete analog) is a generic H\"{o}lder continuous function., Comment: 45 pages, 2 figures

We study the fluctuation of the Atlas model, where a unit drift is assigned to the lowest ranked particle among a semi-infinite ($ \mathbb{Z}_+ $-indexed) system of otherwise independent Brownian particles, initiated according to a Poisson point process on $ \mathbb{R}_+ $. In this context, we show that the joint law of ranked particles, after being centered and scaled by $t^{-1/4}$, converges as $t \to \infty$ to the Gaussian field corresponding to the solution of the additive stochastic heat equation on $\mathbb{R}_+$ with Neumann boundary condition at zero. This allows us to express the asymptotic fluctuation of the lowest ranked particle in terms of a $ \frac{1}{4} $-fractional Brownian motion. In particular, we prove a conjecture of Pal and Pitman (2008) about the asymptotic Gaussian fluctuation of the ranked particles., Comment: 28 pages

Consider an advancing `front' $ R(t) \in \mathbb{Z}_{\geq 0} $ and particles performing independent continuous time random walks on $ (R(t),\infty)\cap\mathbb{Z} $. Starting at $R(0)=0$, whenever a particle attempts to jump into $R(t)$ the latter instantaneously moves $k \ge 1$ steps to the right, absorbing all particles along its path. We take $ k $ to be the minimal random integer such that exactly $ k $ particles are absorbed by the move of $ R $, and view the particle system as a discrete version of the Stefan problem \begin{align*} &\partial_t u_*(t,��) = \tfrac12 \partial^2_�� u_*(t,��), \quad ��>r(t), &u_*(t,r(t))=0, &\tfrac{d~}{dt}r(t) = \tfrac12 \partial_��u_*(t,r(t)), &t\mapsto r(t) \text{ non-decreasing }, \quad r(0):=0. \end{align*} For a constant initial particles density $u_*(0,��)=��{\bf 1}_{\{��>0\}}$, at $��, 43 pages, 6 figures. Updated to match the version to be published

We investigate the time-asymptotic behavior for rarefied gases in the spherical domain with variable boundary temperature in \({\mathbb{R}^d,}\)d=1,2,3, under the diffuse reflection boundary condition. First, we obtain an optimal convergence rate of (1 + t)−d to the steady state for free molecular flow. Next, we use this to construct the steady state solution of the Boltzmann equation for sufficiently large Knudsen number and small boundary temperature variation. We also obtain an exponential convergence to the steady state for the Boltzmann equation for small perturbation.

In this article we study the Atlas model, which constitutes of Brownian particles on $ \mathbb{R} $, independent except that the Atlas (i.e., lowest ranked) particle $ X_{(1)}(t) $ receive drift $ \gamma dt $, $ \gamma\in\mathbb{R} $. For any fixed shape parameter $ a>2\gamma_- $, we show that, up to a shift $ \frac{a}{2}t $, the entire particle system has an invariant distribution $ \nu_a $, written in terms an explicit Radon-Nikodym derivative with respect to the Poisson point process of density $ a e^{a\xi} d\xi $. We further show that $ \nu_a $ indeed has the product-of-exponential gap distribution $ \pi_a $ derived in Sarantsev and Tsai (2016). As a simple application, we establish a bound on the fluctuation of the Atlas particle $ X_{(1)}(t) $ uniformly in $ t $, with the gaps initiated from $ \pi_a $ and $ X_{(1)}(0)=0 $., Comment: 10 pages; 0 figure; Updated to match the published version

Consider the infinite Atlas model: a semi-infinite collection of particles driven by independent standard Brownian motions with zero drifts, except for the bottom-ranked particle which receives unit drift. We derive a continuum one-parameter family of product-of-exponentials stationary gap distributions, with exponentially growing density at infinity. This result shows that there are infinitely many stationary gap distributions for the Atlas model, and hence resolves a conjecture of Pal and Pitman (2008) in the negative. This result is further generalized for infinite systems of competing Brownian particles with generic rank-based drifts., Comment: 18 pages. Keywords: competing Brownian particles, infinite Atlas model, stationary distribution, gap process

We study the dissipative effect of the boundary condition in the kinetic theory. We focus our study on the simplest situation of the free molecular flow with diffuse reflection boundary condition and constant boundary temperature, T*. The geometry is also chosen to be the simplest ones, a bounded symmetric domain in \({\mathbb{R}^d}\) : an interval for d = 1, a disk for d = 2, and a ball for d = 3. It is shown that the solution converges to the global Maxwellian with the given boundary temperature T*. We obtain the optimal convergence rates of (t + 1)−d. The stochastic formulation of Shih-Hsien Yu is refined and generalized for our analysis.

We prove that under a particular weak scaling, the 4-parameter interacting particle system introduced by Corwin and Petrov converges to the KPZ equation. This expands the relatively small number of systems for which weak universality of the KPZ equation has been demonstrated., 24 pages

We study the 'Up the River' problem formulated by Aldous (2002), where a unit drift is distributed among a finite collection of Brownian particles on $ \mathbb{R}_+ $, which are annihilated once they reach the origin. Starting $ K $ particles at $ x=1 $, we prove a conjecture of Aldous (2002) that the 'push-the-laggard' strategy of distributing the drift asymptotically (as $ K\to\infty $) maximizes the total number of surviving particles, with approximately $ \frac{4}{\sqrt{\pi}} K^{1/2} $ surviving particles. We further establish the hydrodynamic limit of the particle density, in terms of a two-phase PDE with a moving boundary, by utilizing certain integral identities and coupling techniques., Comment: 39 pages; no figure. Updated to match the version to be published