15,225 research outputs found
SUBIC: A Supervised Bi-Clustering Approach for Precision Medicine
Traditional medicine typically applies one-size-fits-all treatment for the
entire patient population whereas precision medicine develops tailored
treatment schemes for different patient subgroups. The fact that some factors
may be more significant for a specific patient subgroup motivates clinicians
and medical researchers to develop new approaches to subgroup detection and
analysis, which is an effective strategy to personalize treatment. In this
study, we propose a novel patient subgroup detection method, called Supervised
Biclustring (SUBIC) using convex optimization and apply our approach to detect
patient subgroups and prioritize risk factors for hypertension (HTN) in a
vulnerable demographic subgroup (African-American). Our approach not only finds
patient subgroups with guidance of a clinically relevant target variable but
also identifies and prioritizes risk factors by pursuing sparsity of the input
variables and encouraging similarity among the input variables and between the
input and target variable
Langevin process reflected on a partially elastic boundary I
Consider a Langevin process, that is an integrated Brownian motion,
constrained to stay on the nonnegative half-line by a partially elastic
boundary at 0. If the elasticity coefficient of the boundary is greater than or
equal to a critical value (0.16), bounces will not accumulate in a finite time
when the process starts from the origin with strictly positive velocity. We
will show that there exists then a unique entrance law from the boundary with
zero velocity, despite the immediate accumulation of bounces. This result of
uniqueness is in sharp contrast with the literature on deterministic second
order reflection. Our approach uses certain properties of real-valued random
walks and a notion of spatial stationarity which may be of independent
interest.Comment: 30 pages, 1 figure. In this new version, the introduction and the
preliminaries in particular have been rewritten (for a dramatic change
Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
Three models from statistical physics can be analyzed by employing space-time
determinantal processes: (1) crystal facets, in particular the statistical
properties of the facet edge, and equivalently tilings of the plane, (2)
one-dimensional growth processes in the Kardar-Parisi-Zhang universality class
and directed last passage percolation, (3) random matrices, multi-matrix
models, and Dyson's Brownian motion. We explain the method and survey results
of physical interest.Comment: Lecture Notes: Fundamental Problems in Statistical Mechanics XI,
Leuven, September 4 - 16, 200
Four-dimensional polymer collapse II: Pseudo-First-Order Transition in Interacting Self-avoiding Walks
In earlier work we provided the first evidence that the collapse, or
coil-globule, transition of an isolated polymer in solution can be seen in a
four-dimensional model. Here we investigate, via Monte Carlo simulations, the
canonical lattice model of polymer collapse, namely interacting self-avoiding
walks, to show that it not only has a distinct collapse transition at finite
temperature but that for any finite polymer length this collapse has many
characteristics of a rounded first-order phase transition. However, we also
show that there exists a `-point' where the polymer behaves in a simple
Gaussian manner (which is a critical state), to which these finite-size
transition temperatures approach as the polymer length is increased. The
resolution of these seemingly incompatible conclusions involves the argument
that the first-order-like rounded transition is scaled away in the
thermodynamic limit to leave a mean-field second-order transition. Essentially
this happens because the finite-size \emph{shift} of the transition is
asymptotically much larger than the \emph{width} of the pseudo-transition and
the latent heat decays to zero (algebraically) with polymer length. This
scenario can be inferred from the application of the theory of Lifshitz,
Grosberg and Khokhlov (based upon the framework of Lifshitz) to four
dimensions: the conclusions of which were written down some time ago by
Khokhlov. In fact it is precisely above the upper critical dimension, which is
3 for this problem, that the theory of Lifshitz may be quantitatively
applicable to polymer collapse.Comment: 30 pages, 14 figures included in tex
Magnetic Field Line Random Walk and Solar Energetic Particle Path Lengths: Stochastic Theory and PSP/ISoIS Observation
Context:In 2020 May-June, six solar energetic ion events were observed by the
Parker Solar Probe/ISoIS instrument suite at 0.35 AU from the Sun. From
standard velocity-dispersion analysis, the apparent ion path length is 0.625 AU
at the onset of each event. Aims:We develop a formalism for estimating the path
length of random-walking magnetic field lines, to explain why the apparent ion
pathlength at event onset greatly exceeds the radial distance from the Sun for
these events. Methods:We developed analytical estimates of the average increase
in pathlength of random-walking magnetic field lines, relative to the
unperturbed mean field. Monte Carlo simulations of fieldline and particle
trajectories in a model of solar wind turbulence are used to validate the
formalism and study the path lengths of particle guiding-center and
full-orbital trajectories. The formalism is implemented in a global solar wind
model, and results are compared with ion pathlengths inferred from ISoIS
observations. Results:Both a simple estimate and a rigorous theoretical
formulation are obtained for fieldlines' pathlength increase as a function of
pathlength along the large-scale field. From simulated fieldline and particle
trajectories, we find that particle guiding centers can have pathlengths
somewhat shorter than the average fieldline pathlength, while particle orbits
can have substantially larger pathlengths due to their gyromotion with a
nonzero effective pitch angle. Conclusions:The long apparent path length during
these solar energetic ion events can be explained by 1) a magnetic field line
path length increase due to the field line random walk, and 2) particle
transport about the guiding center with a nonzero effective pitch angle. Our
formalism for computing the magnetic field line path length, accounting for
turbulent fluctuations, may be useful for application to solar particle
transport in general
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