2,377 research outputs found
Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility
We study the hitting times of Markov processes to target set , starting
from a reference configuration or its basin of attraction. The
configuration can correspond to the bottom of a (meta)stable well, while
the target could be either a set of saddle (exit) points of the well, or a
set of further (meta)stable configurations. Three types of results are
reported: (1) A general theory is developed, based on the path-wise approach to
metastability, which has three important attributes. First, it is general in
that it does not assume reversibility of the process, does not focus only on
hitting times to rare events and does not assume a particular starting measure.
Second, it relies only on the natural hypothesis that the mean hitting time to
is asymptotically longer than the mean recurrence time to or .
Third, despite its mathematical simplicity, the approach yields precise and
explicit bounds on the corrections to exponentiality. (2) We compare and relate
different metastability conditions proposed in the literature so to eliminate
potential sources of confusion. This is specially relevant for evolutions of
infinite-volume systems, whose treatment depends on whether and how relevant
parameters (temperature, fields) are adjusted. (3) We introduce the notion of
early asymptotic exponential behavior to control time scales asymptotically
smaller than the mean-time scale. This control is particularly relevant for
systems with unbounded state space where nucleations leading to exit from
metastability can happen anywhere in the volume. We provide natural sufficient
conditions on recurrence times for this early exponentiality to hold and show
that it leads to estimations of probability density functions
Asymptotically exponential hitting times and metastability:A pathwise approach without reversibility
We study the hitting times of Markov processes to target set G, starting from a reference configuration x0 or its basin of attraction and we discuss its relation to metastability. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. We consider only the natural hypothesis that the mean hitting time to G is asymptotically longer than the mean recurrence time to the refernce configuration x0 or G. Despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature. This is specially relevant for evolutions of infinite-volume systems. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions.</p
Z', new fermions and flavor changing processes, constraints on E models from --> eee
We study a new class of flavor changing interactions, which can arise in
models based on extended gauge groups (rank 4) when new charged fermions are
present together with a new neutral gauge boson. We discuss the cases in which
the flavor changing couplings in the new neutral current coupled to the
are theoretically expected to be large, implying that the observed
suppression of neutral flavor changing transitions must be provided by heavy
masses together with small - mixing angles.
Concentrating on E models, we show how the tight experimental limit on implies serious constraints on the mass and mixing
angle. We conclude that if the value of the flavor changing parameters is
assumed to lie in a theoretically natural range, in most cases the presence of
a much lighter than 1 TeV is unlikely.Comment: plain tex, 22 pages + 2 pages figures in PostScript (appended after
`\bye'), UM-TH 92-1
Sharp asymptotics for Kawasaki dynamics on a finite box with open boundary
In this paper we study the metastable behavior of the lattice gas in two and three dimensions subject to Kawasaki dynamics in the limit of low temperature and low density. We consider the local version of the model, where particles live on a finite box and are created, respectively, annihilated at the boundary of the box in a way that reflects an infinite gas reservoir. We are interested in how the system nucleates, i.e., how it reaches a full box when it starts from an empty box. Our approach combines geometric and potential theoretic arguments. In two dimensions, we identify the full geometry of the set of critical droplets for the nucleation, compute the average nucleation time up to a multiplicative factor that tends to one in the limit of low temperature and low density, express the proportionality constant in terms of certain capacities associated with simple random walk, and compute the asymptotic behavior of this constant as the system size tends to infinity. In three dimensions, we obtain similar results but with less control over the geometry and the constant. A special feature of Kawasaki dynamics is that in the metastable regime particles move along the border of a droplet more rapidly than they arrive from the boundary of the box. The geometry of the critical droplet and the sharp asymptotics for the average nucleation time are highly sensitive to this motion
Early mandibular canine-lateral incisor transposition: case report
Purpose. The main aim of the present study is to present a case of mandibular transposition between lateral incisor and
canine in a paediatric patient.
Materials and methods. A fixed multibracket orthodontic treatment was performed by means of a modified welded arch
as to correct the transposition and obtaining a class I functional and symmetrical occlusion, also thanks to the early diagnosis
of the eruption anomaly.
Results. Our case report shows that a satisfactory treatment of mandibular transpositions is obtained when detected at
an early stage of the tooth development.
Conclusions. The main treatment options to be taken into consideration in case of a mandibular transposition are two:
correcting the transposition or aligning it leaving the dental elements in their transposed order; in both cases, the followups
show a stable condition, maintained without relapses. Several factors, such as age of the patient, occlusion, aesthetics,
patient’s collaboration, periodontal support and duration of treatment have to be considered as to prevent potential damage
to dental elements and support appliances. The choice between the two treatment approaches for mandibular lateral
incisor/canine transpositions mainly depends on the time the anomaly is detected
Correlation between parodontal indexes and orthodontic retainers: prospective study in a group of 16 patients
Purpose. Fixed retainers are used to stabilize dental elements after orthodontic treatment. Being it a permanent treatment, it is necessary to instruct patients about a constant and continuous monitoring of their periodontal conditions and a correct oral hygiene. The aim of this study was to highlight the possible adverse effects of bonded retainers on parameters
correlated to the health conditions of periodontal tissues.
Materials and methods. We selected 16 patients, under treatment in the Orthodontics Department of University of Bari Dental School, who had undergone a lingual retainer insertion at the end of the orthodontic treatment. The patients were then divided into two groups (Control Group and Study Group) and monitored for 3 and 36 months, respectively. The following indexes were taken into consideration: gingival index (GI), plaque index (PI) and the presence of calculus (Calculus Index, CI), the probing depth and the presence of gingival recession on the six inferior frontal dental elements.
Results. After the observation was carried out, any of the patients showed periodontal sockets and gingival recession. In the Study Group, only 1 patient had a PI score=3, the 7 left had scores between 0.66 and 2.83. In the Control Group, one patient had score=0, the other ones showed values between 0.5 and 1.66. The mean GI in the Study Group peaked at a score of 2.83, the minimum was 0.66; whereas in the Control Group the maximum value was 2 and the minimum 0.66.
The CI in the Group Study was between 1 and 2. In the Control Group it was absent in only 1 patient, whereas in the remaining 7, it had a value between 0.3 and 1. The clinical data were studied by means of the Wilcoxon test. We found a statistically significant difference for what concerns the Plaque Indexes (PI) (P>0.05) and Calculus Indexes (CI) (P>0.1) in both groups, with higher scores in the Study Group, having retainers for 36 months. Any statistically significant difference was calculated for the GI.
Conclusions. We can therefore conclude that patients with lingual retainers need periodontal hygiene and treatment as
to prevent, in the course of time, periodontal damages non-detectable in short-term
Kawasaki dynamics with two types of particles: stable/metastable configurations and communication heights
This is the second in a series of three papers in which we study a
two-dimensional lattice gas consisting of two types of particles subject to
Kawasaki dynamics at low temperature in a large finite box with an open
boundary. Each pair of particles occupying neighboring sites has a negative
binding energy provided their types are different, while each particle has a
positive activation energy that depends on its type. There is no binding energy
between particles of the same type. At the boundary of the box particles are
created and annihilated in a way that represents the presence of an infinite
gas reservoir. We start the dynamics from the empty box and are interested in
the transition time to the full box. This transition is triggered by a critical
droplet appearing somewhere in the box. In the first paper we identified the
parameter range for which the system is metastable, showed that the first
entrance distribution on the set of critical droplets is uniform, computed the
expected transition time up to and including a multiplicative factor of order
one, and proved that the nucleation time divided by its expectation is
exponentially distributed, all in the limit of low temperature. These results
were proved under three hypotheses, and involve three model-dependent
quantities: the energy, the shape and the number of critical droplets. In this
second paper we prove the first and the second hypothesis and identify the
energy of critical droplets. The paper deals with understanding the geometric
properties of subcritical, critical and supercritical droplets, which are
crucial in determining the metastable behavior of the system. The geometry
turns out to be considerably more complex than for Kawasaki dynamics with one
type of particle, for which an extensive literature exists. The main motivation
behind our work is to understand metastability of multi- type particle systems.Comment: 31 pages, 22 figure
Transition time asymptotics of queue-based activation protocols in random-access networks
We consider networks where each node represents a server with a queue. An active node deactivates at unit rate. An inactive node activates at a rate that depends on its queue length, provided none of its neighbors is active. For complete bipartite networks, in the limit as the queues become large, we compute the average transition time between the two states where one half of the network is active and the other half is inactive. We show that the law of the transition time divided by its mean exhibits a trichotomy, depending on the activation rate functions
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