Kinetically constrained spin models

We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physical literature as simple models sharing some of the features of a glass transition. KCSM are interacting particle systems on $\Z^d$ with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli($p$) measure. The essential feature of a KCSM is that the creation/destruction of a particle at a given site can occur only if the current configuration of empty sites around it satisfies certain constraints which completely define each specific model. No other interaction is present in the model. From the mathematical point of view, the basic issues concerning positivity of the spectral gap inside the ergodicity region and its scaling with the particle density $p$ remained open for most KCSM (with the notably exception of the East model in $d=1$ \cite{Aldous-Diaconis}). Here for the first time we: i) identify the ergodicity region by establishing a connection with an associated bootstrap percolation model; ii) develop a novel multi-scale approach which proves positivity of the spectral gap in the whole ergodic region; iii) establish, sometimes optimal, bounds on the behavior of the spectral gap near the boundary of the ergodicity region and iv) establish pure exponential decay for the persistence function. Our techniques are flexible enough to allow a variety of constraints and our findings disprove certain conjectures which appeared in the physical literature on the basis of numerical simulations

Mixing time of a kinetically constrained spin model on trees: power law scaling at criticality

On the rooted k-ary tree we consider a 0-1 kinetically constrained spin model in which the occupancy variable at each node is re-sampled with rate one from the Bernoulli(p) measure iff all its children are empty. For this process the following picture was conjectured to hold. As long as p is below the percolation threshold pc = 1/k the process is ergodic with a finite relaxation time while, for p > pc, the process on the infinite tree is no longer ergodic and the relaxation time on a finite regular sub-tree becomes exponentially large in the depth of the tree. At the critical point p = pc the process on the infinite tree is still ergodic but with an infinite relaxation time. Moreover, on finite sub-trees, the relaxation time grows polynomially in the depth of the tree. The conjecture was recently proved by the second and forth author except at crit- icality. Here we analyse the critical and quasi-critical case and prove for the relevant time scales: (i) power law behaviour in the depth of the tree at p = pc and (ii) power law scaling in (pc − p)−1 when p approaches pc from below. Our results, which are very close to those obtained recently for the Ising model at the spin glass critical point, represent the first rigorous analysis of a kinetically constrained model at criticality

The Subfossil Trunk of Chiarano (TV)

This paper reports the results of the characterization of a subfossil trunk found buried in the mud of the Piavon canal, at Chiarano (TV), when dredging took place in 2008. The trunk, of imposing dimensions, lacking branches and bark, has a black, deeply cracked and strongly deteriorated outer surface with a carbonized appearance, while internally it has the typical blackish colour of the so-called drowned oak. The studies have demonstrated that it is a tree belonging to the genus Quercus, common oak or sessile oak, that may have been felled between the end of the 12 th and early 14 th century A.D.. Determination of the MWC and residual basic density indicate that the deterioration decreases from the outside inwards; the ash content is high externally and diminishes moving toward the centre. Nowadays, the Piavon is an irrigation canal, but in Venetian times it was navigable and was used for the transport of goods and timber. There were extensive woodlands of common oak and sessile oak all along the Piavon, the size and composition of which is documented in the Venetian cadastres, which also report the distances between the woodlands and the nearest water courses, proof of the importance of river transport for the timber. In particular, an 18 hectare oak woodland is recorded in the Surian cadastre (1569-70) for the villa at Chiarano. The oaks were used by the Republic of Venice mainly for the construction and maintenance of the shipping fleet. The Chiarano trunk, given its age and the area where it was found, may therefore be a trunk felled in Venetian times, perhaps destined for naval use, which was lost during its transport by floating.In questo lavoro si riportano i risultati della caratterizzazione di un tronco subfossile rinvenuto in profondità nel fango del canale Piavon, a Chiarano (TV), in occasione dei lavori di scavo del canale nel 2008. Il tronco, di imponenti dimensioni, privo di rami e corteccia, presenta la superficie esterna profondamente fessurata, nera, fortemente degradata, dall’apparenza carbonizzata, mentre internamente ha la tipica colorazione nerastra della cosiddetta quercia annegata. Gli studi hanno dimostrato che si tratta di un albero appartenente al genere Quercus, farnia o rovere. La datazione al radiocarbonio e le analisi dendrocronologiche hanno collocato il periodo di crescita della pianta in epoca medievale, intorno al XIII secolo. La determinazione della MCW e della densità basale residua indicano che il degrado decresce dall’esterno all’interno; il contenuto delle ceneri è elevato esternamente, e diminuisce andando verso l’interno. Il Piavon è attualmente un canale di irrigazione, ma in epoca veneziana era navigabile e veniva utilizzato per il trasporto di merci e legname. Tutta l’area lungo il Piavon presentava boschi di farnia e rovere di notevole estensione, la cui dimensione e composizione è documentata dai catasti veneziani, che riportano anche le distanze tra i boschi e i corsi d’acqua più vicini, a testimonianza dell’importanza del trasporto fluviale del legname. In particolare, nella villa di Chiarano, nel catasto Surian (1569-70) si trova censito un bosco di roveri di 18 ettari. I roveri erano utilizzati dalla Serenissima soprattutto per la costruzione e manutenzione della flotta navale. Il tronco di Chiarano, considerata la collocazione temporale e la zona di ritrovamento, può essere quindi un tronco abbattuto in epoca veneziana, forse destinato all’impresa navale, andato perduto durante il trasporto per fluitazione

Facilitated oriented spin models:some non equilibrium results

We analyze the relaxation to equilibrium for kinetically constrained spin models (KCSM) when the initial distribution $\nu$ is different from the reversible one, $\mu$. This setting has been intensively studied in the physics literature to analyze the slow dynamics which follows a sudden quench from the liquid to the glass phase. We concentrate on two basic oriented KCSM: the East model on \bbZ, for which the constraint requires that the East neighbor of the to-be-update vertex is vacant and the model on the binary tree introduced in \cite{Aldous:2002p1074}, for which the constraint requires the two children to be vacant. While the former model is ergodic at any $p\neq 1$, the latter displays an ergodicity breaking transition at $p_c=1/2$. For the East we prove exponential convergence to equilibrium with rate depending on the spectral gap if $\nu$ is concentrated on any configuration which does not contain a forever blocked site or if $\nu$ is a Bernoulli($p'$) product measure for any $p'\neq 1$. For the model on the binary tree we prove similar results in the regime $p,p'<p_c$ and under the (plausible) assumption that the spectral gap is positive for $p<p_c$. By constructing a proper test function we also prove that if $p'>p_c$ and $p\leq p_c$ convergence to equilibrium cannot occur for all local functions. Finally we present a very simple argument (different from the one in \cite{Aldous:2002p1074}) based on a combination of combinatorial results and ``energy barrier'' considerations, which yields the sharp upper bound for the spectral gap of East when $p\uparrow 1$.Comment: 16 page

Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page

Tannic Acid-Iron Complex-Based Nanoparticles as a Novel Tool against Oxidative Stress

: Accumulation of reactive oxygen species in cells leads to oxidative stress, with consequent damage for cellular components and activation of cell-death mechanisms. Oxidative stress is often associated with age-related conditions, as well as with several neurodegenerative diseases. For this reason, antioxidant molecules have attracted a lot of attention, especially those derived from natural sources─like polyphenols and tannins. The main issue related to the use of antioxidants is their inherent tendency to be oxidized, their quick enzymatic degradation in biological fluids, and their poor bioavailability. Nanomedicine, in this sense, has helped in finding new solutions to deliver and protect antioxidants; however, the concentration of the encapsulated molecule in conventional nanosystems could be very low and, therefore, less effective. We propose to exploit the properties of tannic acid, a known plant-derived antioxidant, to chelate iron ions, forming hydrophobic complexes that can be coated with a biocompatible and biodegradable phospholipid to improve stability in biological media. By combining nanoprecipitation and hot sonication procedures, we obtained three-dimensional networks composed of tannic acid-iron with a hydrodynamic diameter of ≈200 nm. These nanostructures show antioxidant properties and scavenging activity in cells after induction of an acute chemical pro-oxidant insult; moreover, they also demonstrated to counteract damage induced by oxidative stress both in vitro and on an in vivo model organism (planarians)

Analysis of tissue structure and remodeling ion alveolar ridges augmented with human palate or tuberosity mucosa

Previous clinical reports found different clinical outcomes of localized alveolar ridge augmentation with soft tissue harvested either from the palate or from the tuberosity over time, showing that the palatal grafts had a better tissue stability than those from the tuberosity, which tended to a hyperplastic reaction. The mechanisms responsible for a different maturation of the grafted tissue using the two donor sites are still unclear, very likely depending on differences of the structure and extracellular matrix of connective tissue (CT). The current study aimed at comparing the morphology and collagen turnover-related molecular pathways of sites grafted with CT from either the palate (group A = 7 patients) or the tuberosity (group B = 7 patients) one year after surgical procedures for ridge augmentation. Cultured fibroblasts were obtained to analyze by real-time PCR the mRNA levels for collagen type I and III (COL-I, COL-III), matrix metalloproteinases (MMP-1 and 2), long lysyl hydroxylase 2b (LH2b). Collagen protein levels were assessed by slot blot, collagen degradation by SDS-zymography. No significant differences in collagen content were found. COLI and III, MMP-1 and 2 expression was similar in cell culture supernatants from palate and tuberosity fibroblasts, although COL-I and COL-III protein levels resulted up-regulated, respectively, in 57% and 66% of the samples. LH2b/COL-I mRNA ratio 69% was higher in the tuberosity fibroblasts, suggesting that the tuberosity collagen could be cross-linked at a higher extent, and therefore less susceptible to degradation by MMPs, leading to its excessive accumulation. Our data show that in group B the higher LH2b/COL-I mRNA ratio may be responsible for differences in collagen maturation as the major determinants in the hyperplastic response, and that grafting using the maxillary tuberosity could avoid unwanted tissue contraction over time

Association of 3q21q26 syndrome with different RPN1/EVI1 fusion transcripts

Patients with acute myeloblastic leukemia (AML) with features of myelodysplastic syndrome and abnormalities of megakaryocytopoiesis often have cytogenetic aberrations of 3q21 and 3q26 bands involving the paracentric inversion [inv(3) (q21q26)] or a reciprocal translocation [t(3;3) (q21;q26)]. These abnormalities frequently cause inappropriate expression of the EVI1 gene located at 3q26. Other genes that have been implicated at the rearrangement breakpoint are GR6 and RPN1 (both on 3q21). The aim of this study was to investigate the expression of the EVI1 fusion genes in AML patients with 3q21q26 syndrome