1,206 research outputs found
Censored Glauber Dynamics for the mean field Ising Model
We study Glauber dynamics for the Ising model on the complete graph on
vertices, known as the Curie-Weiss Model. It is well known that at high
temperature () the mixing time is , whereas at low
temperature () it is . Recently, Levin, Luczak and
Peres considered a censored version of this dynamics, which is restricted to
non-negative magnetization. They proved that for fixed , the
mixing-time of this model is , analogous to the
high-temperature regime of the original dynamics. Furthermore, they showed
\emph{cutoff} for the original dynamics for fixed . The question
whether the censored dynamics also exhibits cutoff remained unsettled.
In a companion paper, we extended the results of Levin et al. into a complete
characterization of the mixing-time for the Currie-Weiss model. Namely, we
found a scaling window of order around the critical temperature
, beyond which there is cutoff at high temperature. However,
determining the behavior of the censored dynamics outside this critical window
seemed significantly more challenging.
In this work we answer the above question in the affirmative, and establish
the cutoff point and its window for the censored dynamics beyond the critical
window, thus completing its analogy to the original dynamics at high
temperature. Namely, if for some with
, then the mixing-time has order . The cutoff constant is , where is the unique positive root of
, and the cutoff window has order .Comment: 55 pages, 4 figure
Superconducting Order Parameter in Bi-Layer Cuprates: Occurrence of Phase Shifts in Corner Junctions
We study the order parameter symmetry in bi-layer cuprates such as YBaCuO,
where interesting phase shifts have been observed in Josephson junctions.
Taking models which represent the measured spin fluctuation spectra of this
cuprate, as well as more general models of Coulomb correlation effects, we
classify the allowed symmetries and determine their associated physical
properties. phase shifts are shown to be a general consequence of
repulsive interactions, independent of whether a magnetic mechanism is
operative. While it is known to occur in d-states, this behavior can also be
associated with (orthorhombic) s-symmetry when the two sub-band gaps have
opposite phase. Implications for the magnitude of are discussed.Comment: 5 pages, RevTeX 3.0, 9 figures (available upon request
Entropy-driven cutoff phenomena
In this paper we present, in the context of Diaconis' paradigm, a general
method to detect the cutoff phenomenon. We use this method to prove cutoff in a
variety of models, some already known and others not yet appeared in
literature, including a chain which is non-reversible w.r.t. its stationary
measure. All the given examples clearly indicate that a drift towards the
opportune quantiles of the stationary measure could be held responsible for
this phenomenon. In the case of birth- and-death chains this mechanism is
fairly well understood; our work is an effort to generalize this picture to
more general systems, such as systems having stationary measure spread over the
whole state space or systems in which the study of the cutoff may not be
reduced to a one-dimensional problem. In those situations the drift may be
looked for by means of a suitable partitioning of the state space into classes;
using a statistical mechanics language it is then possible to set up a kind of
energy-entropy competition between the weight and the size of the classes.
Under the lens of this partitioning one can focus the mentioned drift and prove
cutoff with relative ease.Comment: 40 pages, 1 figur
Study of the bufadienolides of the skin secretion of green toads (Bufo viridis Laur, 1758)
The composition of the skin secretion of Bufo viridis toads, which inhabit the Kharkov region, has been studied in this work
Smoothed Complexity Theory
Smoothed analysis is a new way of analyzing algorithms introduced by Spielman
and Teng (J. ACM, 2004). Classical methods like worst-case or average-case
analysis have accompanying complexity classes, like P and AvgP, respectively.
While worst-case or average-case analysis give us a means to talk about the
running time of a particular algorithm, complexity classes allows us to talk
about the inherent difficulty of problems.
Smoothed analysis is a hybrid of worst-case and average-case analysis and
compensates some of their drawbacks. Despite its success for the analysis of
single algorithms and problems, there is no embedding of smoothed analysis into
computational complexity theory, which is necessary to classify problems
according to their intrinsic difficulty.
We propose a framework for smoothed complexity theory, define the relevant
classes, and prove some first hardness results (of bounded halting and tiling)
and tractability results (binary optimization problems, graph coloring,
satisfiability). Furthermore, we discuss extensions and shortcomings of our
model and relate it to semi-random models.Comment: to be presented at MFCS 201
Glauber dynamics for the quantum Ising model in a transverse field on a regular tree
Motivated by a recent use of Glauber dynamics for Monte-Carlo simulations of
path integral representation of quantum spin models [Krzakala, Rosso,
Semerjian, and Zamponi, Phys. Rev. B (2008)], we analyse a natural Glauber
dynamics for the quantum Ising model with a transverse field on a finite graph
. We establish strict monotonicity properties of the equilibrium
distribution and we extend (and improve) the censoring inequality of Peres and
Winkler to the quantum setting. Then we consider the case when is a regular
-ary tree and prove the same fast mixing results established in [Martinelli,
Sinclair, and Weitz, Comm. Math. Phys. (2004)] for the classical Ising model.
Our main tool is an inductive relation between conditional marginals (known as
the "cavity equation") together with sharp bounds on the operator norm of the
derivative at the stable fixed point. It is here that the main difference
between the quantum and the classical case appear, as the cavity equation is
formulated here in an infinite dimensional vector space, whereas in the
classical case marginals belong to a one-dimensional space
Adiabatic times for Markov chains and applications
We state and prove a generalized adiabatic theorem for Markov chains and
provide examples and applications related to Glauber dynamics of Ising model
over Z^d/nZ^d. The theorems derived in this paper describe a type of adiabatic
dynamics for l^1(R_+^n) norm preserving, time inhomogeneous Markov
transformations, while quantum adiabatic theorems deal with l^2(C^n) norm
preserving ones, i.e. gradually changing unitary dynamics in C^n
The magnetic field influence on magnetostructural phase transition in Ni2.19Mn0.81Ga
Magnetic properties of a polycrystalline alloy NiMnGa,
which undergoes a first-order magnetostructural phase transition from cubic
paramagnetic to tetragonal ferromagnetic phase, are studied. Hysteretic
behavior of isothermal magnetization has been observed in a temperature
interval of the magnetostructural transition in magnetic fields from 20 to 100
kOe. Temperature dependencies of magnetization , measured in magnetic fields
and 60 kOe, indicate that the temperature of the magnetostructural
transition increases with increasing magnetic field.Comment: Presented at the Second Moscow International Symposium on Magnetism
(Moscow-2002
Criticality in confined ionic fluids
A theory of a confined two dimensional electrolyte is presented. The positive
and negative ions, interacting by a potential, are constrained to move on
an interface separating two solvents with dielectric constants and
. It is shown that the Debye-H\"uckel type of theory predicts that
the this 2d Coulomb fluid should undergo a phase separation into a coexisting
liquid (high density) and gas (low density) phases. We argue, however, that the
formation of polymer-like chains of alternating positive and negative ions can
prevent this phase transition from taking place.Comment: RevTex, no figures, in press Phys. Rev.
Program Components and Results From an Organized Colorectal Cancer Screening Program Using Annual Fecal Immunochemical Testing.
Programmatic colorectal cancer (CRC) screening increases uptake, but the design and resources utilized for such models are not well known. We characterized program components and participation at each step in a large program that used mailed fecal immunochemical testing (FIT) with opportunistic colonoscopy.
Mixed-methods with site visits and retrospective cohort analysis of 51-75-year-old adults during 2017 in the Kaiser Permanente Northern California integrated health system.
Among 1,023,415 screening-eligible individuals, 405,963 (40%) were up to date with screening at baseline, and 507,401 of the 617,452 not up-to-date were mailed a FIT kit. Of the entire cohort (n = 1,023,415), 206,481 (20%) completed FIT within 28 days of mailing, another 61,644 (6%) after a robocall at week 4, and 40,438 others (4%) after a mailed reminder letter at week 6. There were over 800,000 medical record screening alerts generated and about 295,000 FIT kits distributed during patient office visits. About 100,000 FIT kits were ordered during direct-to-patient calls by medical assistants and 111,377 people (11%) completed FIT outside of the automated outreach period. Another 13,560 (1.3%) completed a colonoscopy, sigmoidoscopy, or fecal occult blood test unrelated to FIT. Cumulatively, 839,463 (82%) of those eligible were up to date with screening at the end of the year and 12,091 of 14,450 patients (83.7%) with positive FIT had diagnostic colonoscopy.
The >82% screening participation achieved in this program resulted from a combination of prior endoscopy (40%), large initial response to mailed FIT kits (20%), followed by smaller responses to automated reminders (10%) and personal contact (12%)
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