In this paper we analyze metastability and nucleation in the context of the Kawasaki dynamics for the two-dimensional Ising lattice gas at very low temperature. Let
Λ
⊂
Z
2
be a finite box. Particles ...perform simple exclusion on
Λ
, but when they occupy neighboring sites they feel a binding energy
-
U
1
<
0
in the horizontal direction and
-
U
2
<
0
in the vertical one. Thus the Kawasaki dynamics is conservative inside the volume
Λ
. Along each bond touching the boundary of
Λ
from the outside to the inside, particles are created with rate
ρ
=
e
-
Δ
β
, while along each bond from the inside to the outside, particles are annihilated with rate 1, where
β
>
0
is the inverse temperature and
Δ
>
0
is an activity parameter. Thus, the boundary of
Λ
plays the role of an infinite gas reservoir with density
ρ
. We consider the parameter regime
U
1
>
2
U
2
also known as the strongly anisotropic regime. We take
Δ
∈
(
U
1
,
U
1
+
U
2
)
, so that the empty (respectively full) configuration is a metastable (respectively stable) configuration. We consider the asymptotic regime corresponding to finite volume in the limit as
β
→
∞
. We investigate how the transition from empty to full takes place with particular attention to the critical configurations that asymptotically have to be crossed with probability 1. The derivation of some geometrical properties of the saddles allows us to identify the full geometry of the minimal gates and their boundaries for the nucleation in the strongly anisotropic case. We observe very different behaviors for this case with respect to the isotropic (
U
1
=
U
2
) and weakly anisotropic (
U
1
<
2
U
2
) ones. Moreover, we derive mixing time, spectral gap and sharp estimates for the asymptotic transition time for the strongly anisotropic case.
We consider the ferromagnetic
q
-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature ...asymptotic limit. Our analysis concerns the multi-spin system that has
q
stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical paths and prove that the probability to deviate from it during the transition is exponentially small.
This review outlines novel, emerging legal risks for in-vitro fertilization (IVF) providers and patients.
This article reviews recent antiabortion legal developments that create novel legal risks to ...IVF. This article examines new potential liability for the handling or managing of embryos, and threats to safe, efficient, standard-of-care practice of IVF. It reviews established US and international judicial and regulatory frameworks based on scientifically grounded recognition of IVF embryos as deserving of 'special respect', and finds this approach to be an alternative for law and policy makers.
Defining life as 'beginning at fertilization' (or 'conception') or otherwise embracing 'embryonic personhood' creates emerging legal vulnerabilities and concerns for IVF patients and professionals who handle embryos and threatens standard-of-care IVF. Internationally and domestically established, scientifically grounded understandings of IVF embryos, rather than religious beliefs, should be the basis for legal frameworks that accord appropriate - but not unlimited - protections to IVF embryos. This article presents this framework as an alternative to the current path being embraced by some US policymakers and courts, as a means of protecting the rights of patients, providers and the families they create.
We consider the problem of metastability for stochastic dynamics with exponentially small transition probabilities in the low temperature limit. We generalize previous model-independent results in ...several directions. First, we give an estimate of the mixing time of the dynamics in terms of the maximal stability level. Second, assuming the dynamics is reversible, we give an estimate of the associated spectral gap. Third, we give precise asymptotics for the expected transition time from any metastable state to the stable state using potential-theoretic techniques. We do this in a general reversible setting where two or more metastable states are allowed and some of them may even be degenerate. This generalizes previous results that hold for a series of only two metastable states. We then focus on a specific Probabilistic Cellular Automata (PCA) with configuration space Formula omitted where Formula omitted is a finite box with periodic boundary conditions. We apply our model-independent results to find sharp estimates for the expected transition time from any metastable state in Formula omitted to the stable state Formula omitted. Here Formula omitted denote the odd and the even chessboard respectively. To do this, we identify rigorously the metastable states by giving explicit upper bounds on the stability level of every other configuration. We rely on these estimates to prove a recurrence property of the dynamics, which is a cornerstone of the pathwise approach to metastability.
We consider random‐access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its ...queue length, provided none of its neighbors is active. We consider arbitrary bipartite graphs in the limit as the initial queue lengths become large and identify the transition time between the two states where one half of the network is active and the other half is inactive. The transition path is decomposed into a succession of transitions on complete bipartite subgraphs. We formulate a randomized greedy algorithm that takes the graph as input and gives as output the set of transition paths the network is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rates, we identify three regimes of behavior.
Sum of exit times in a series of two metastable states Cirillo, Emilio N. M.; Nardi, Francesca R.; Spitoni, Cristian
The European physical journal. ST, Special topics,
07/2017, Letnik:
226, Številka:
10
Journal Article
Recenzirano
Odprti dostop
The problem of not degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains is considered. Metastability has been widely studied both in ...the mathematical and physical literature. Metastable states arises close to a first order phase transition, when the system can be trapped for a long time (exponentially long with respect to the inverse of the temperature) before switching to the thermodynamically stable phase. In this paper, under rather general conditions, we give a sharp estimate of the exit time from a metastable state in a presence of a second metastable state that must be necessarily visited by the system before eventually reaching the stable phase. In this framework we give a sharp estimate of the exit time from the metastable state at higher energy and, on the proper exponential time scale, we prove an addition rule. As an application of the theory, we study the Blume-Capel model in the zero chemical potential case.
COVID-19 exposed major gaps in global, regional, state, and local responses to public health emergencies. In preparation for the WHA Special Session to consider the benefits of developing an ...international instrument on pandemic preparedness, the O'Neill Institute in partnership with Foundation for the National Institutes of Health convened 30 of the world's leading authorities on global health law, financing, biomedical science, implementation, and emergency response along with leaders from prominent international organizations. This meeting was followed by regional consultations convened in Latin America-Caribbean, Africa, and Southeast Asia. These high-level expert consultations generated in-depth discussions on weaknesses and persisting gaps in global pandemic preparedness and what a new international agreement might include to address them. Regional intergovernmental organizations like PAHO can work closely with related multilateral development banks to develop financial instruments that can smooth systemic economic disruption; and regional centers of research and manufacturing excellence can offer a strong front line for producing medicines and vaccines rapidly during a pandemic. With our research focused on the regional response to COVID-19 we are able to look at country responses individually and collectively to see how Latin America - Caribbean countries can capitalize and leverage their regional connections to strengthen their pandemic preparedness and response. By identifying existing gaps and examining the responses and approaches taken by PAHO, we can better understand the role of international and regional organizations and their collaborating centers in preparing and responding to pandemics.
Interleukin-12 (IL-12), produced by dendritic cells in response to activation, is central to pathogen eradication and tumor rejection. The trafficking pathways controlling spatial distribution and ...intracellular transport of IL-12 vesicles to the cell surface are still unknown. Here, we show that intracellular IL-12 localizes in late endocytic vesicles marked by the SNARE VAMP7. Dendritic cells (DCs) from VAMP7-deficient mice are partially impaired in the multidirectional release of IL-12. Upon encounter with antigen-specific T cells, IL-12-containing vesicles rapidly redistribute at the immune synapse and release IL-12 in a process entirely dependent on VAMP7 expression. Consistently, acquisition of effector functions is reduced in T cells stimulated by VAMP7-null DCs. These results provide insights into IL-12 intracellular trafficking pathways and show that VAMP7-mediated release of IL-12 at the immune synapse is a mechanism to transmit innate signals to T cells.
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•Intracellular trafficking of IL-12 in dendritic cells is mediated by the SNARE VAMP7•VAMP7 is required for optimal secretion of IL-12 in the extracellular space•IL-12/VAMP7+ vesicles gather at the immune synapse•VAMP7 controls synaptic release of IL-12 and IFN-γ production in T cells
Efficient priming of T cells requires antigenic and soluble cytokine signals. Chiaruttini et al. analyze the intracellular trafficking pathway of IL-12 in dendritic cells and identify the SNARE VAMP7 as a key regulator of cytokine release and T cell activation.
The study of systems with multiple (not necessarily degenerate) metastable states presents subtle difficulties from the mathematical point of view related to the variational problem that has to be ...solved in these cases. We prove sufficient conditions to identify multiple metastable states. Since this analysis typically involves non-trivial technical issues, we give different conditions that can be chosen appropriately depending on the specific model under study. We show how these results can be used to attack the problem of multiple metastable states via the use of the modern approaches to metastability. We finally apply these general results to the Blume–Capel model for a particular choice of the parameters for which the model happens to have two multiple not degenerate in energy metastable states. We estimate in probability the time for the transition from the metastable states to the stable state. Moreover we identify the set of critical configurations that represent the minimal gate for the transition.
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