461 research outputs found
Packing ellipsoids with overlap
The problem of packing ellipsoids of different sizes and shapes into an
ellipsoidal container so as to minimize a measure of overlap between ellipsoids
is considered. A bilevel optimization formulation is given, together with an
algorithm for the general case and a simpler algorithm for the special case in
which all ellipsoids are in fact spheres. Convergence results are proved and
computational experience is described and illustrated. The motivating
application - chromosome organization in the human cell nucleus - is discussed
briefly, and some illustrative results are presented
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A Behavioral Approach Toward Strengthening Self-concept in Mental Retardates
The objective of this study was to systematize a method of strengthening self-concept in mental retardates through the use of operant conditioning techniques. This objective was pursued by investigating the effect of rewarding positive responses about self
Differentially Private Model Selection with Penalized and Constrained Likelihood
In statistical disclosure control, the goal of data analysis is twofold: The
released information must provide accurate and useful statistics about the
underlying population of interest, while minimizing the potential for an
individual record to be identified. In recent years, the notion of differential
privacy has received much attention in theoretical computer science, machine
learning, and statistics. It provides a rigorous and strong notion of
protection for individuals' sensitive information. A fundamental question is
how to incorporate differential privacy into traditional statistical inference
procedures. In this paper we study model selection in multivariate linear
regression under the constraint of differential privacy. We show that model
selection procedures based on penalized least squares or likelihood can be made
differentially private by a combination of regularization and randomization,
and propose two algorithms to do so. We show that our private procedures are
consistent under essentially the same conditions as the corresponding
non-private procedures. We also find that under differential privacy, the
procedure becomes more sensitive to the tuning parameters. We illustrate and
evaluate our method using simulation studies and two real data examples
Causality in digital medicine
Ben Glocker (an expert in machine learning for medical imaging, Imperial College London), Mirco Musolesi (a data science and digital health expert, University College London), Jonathan Richens (an expert in diagnostic machine learning models, Babylon Health) and Caroline Uhler (a computational biology expert, MIT) talked to Nature Communications about their research interests in causality inference and how this can provide a robust framework for digital medicine studies and their implementation, across different fields of application
Pionic Deuterium
The strong interaction shift and broadening in pionic deuterium have been
remeasured with high statistics by means of the (3p-1s) X-ray transition using
the cyclotron trap and a high-resolution crystal spectrometer. Preliminary
results are (-2325+/-31) meV (repulsive) for the shift and (1171+23/-49} meV
for the width, which yields precise values for the pion-deuteron scattering
length and the threshold parameter for pion production.Comment: Conf. Proc. Few Body 19 (FB19), August 31 - September 5, 2009, Bonn,
Germany 9 pages, 13 figure
Likelihood Geometry
We study the critical points of monomial functions over an algebraic subset
of the probability simplex. The number of critical points on the Zariski
closure is a topological invariant of that embedded projective variety, known
as its maximum likelihood degree. We present an introduction to this theory and
its statistical motivations. Many favorite objects from combinatorial algebraic
geometry are featured: toric varieties, A-discriminants, hyperplane
arrangements, Grassmannians, and determinantal varieties. Several new results
are included, especially on the likelihood correspondence and its bidegree.
These notes were written for the second author's lectures at the CIME-CIRM
summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition
Defect-induced perturbations of atomic monolayers on solid surfaces
We study long-range morphological changes in atomic monolayers on solid
substrates induced by different types of defects; e.g., by monoatomic steps in
the surface, or by the tip of an atomic force microscope (AFM), placed at some
distance above the substrate. Representing the monolayer in terms of a suitably
extended Frenkel-Kontorova-type model, we calculate the defect-induced density
profiles for several possible geometries. In case of an AFM tip, we also
determine the extra force exerted on the tip due to the tip-induced
de-homogenization of the monolayer.Comment: 4 pages, 2 figure
Identifiability of Gaussian structural equation models with equal error variances
We consider structural equation models in which variables can be written as a
function of their parents and noise terms, which are assumed to be jointly
independent. Corresponding to each structural equation model, there is a
directed acyclic graph describing the relationships between the variables. In
Gaussian structural equation models with linear functions, the graph can be
identified from the joint distribution only up to Markov equivalence classes,
assuming faithfulness. In this work, we prove full identifiability if all noise
variables have the same variances: the directed acyclic graph can be recovered
from the joint Gaussian distribution. Our result has direct implications for
causal inference: if the data follow a Gaussian structural equation model with
equal error variances and assuming that all variables are observed, the causal
structure can be inferred from observational data only. We propose a
statistical method and an algorithm that exploit our theoretical findings
On the driven Frenkel-Kontorova model: I. Uniform sliding states and dynamical domains of different particle densities
The dynamical behavior of a harmonic chain in a spatially periodic potential
(Frenkel-Kontorova model, discrete sine-Gordon equation) under the influence of
an external force and a velocity proportional damping is investigated. We do
this at zero temperature for long chains in a regime where inertia and damping
as well as the nearest-neighbor interaction and the potential are of the same
order. There are two types of regular sliding states: Uniform sliding states,
which are periodic solutions where all particles perform the same motion
shifted in time, and nonuniform sliding states, which are quasi-periodic
solutions where the system forms patterns of domains of different uniform
sliding states. We discuss the properties of this kind of pattern formation and
derive equations of motion for the slowly varying average particle density and
velocity. To observe these dynamical domains we suggest experiments with a
discrete ring of at least fifty Josephson junctions.Comment: Written in RevTeX, 9 figures in PostScrip
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