985 research outputs found
Helly numbers of Algebraic Subsets of
We study -convex sets, which are the geometric objects obtained as the
intersection of the usual convex sets in with a proper subset
. We contribute new results about their -Helly
numbers. We extend prior work for , , and ; we give sharp bounds on the -Helly numbers in
several new cases. We considered the situation for low-dimensional and for
sets that have some algebraic structure, in particular when is an
arbitrary subgroup of or when is the difference between a
lattice and some of its sublattices. By abstracting the ingredients of Lov\'asz
method we obtain colorful versions of many monochromatic Helly-type results,
including several colorful versions of our own results.Comment: 13 pages, 3 figures. This paper is a revised version of what was
originally the first half of arXiv:1504.00076v
Beyond Chance-Constrained Convex Mixed-Integer Optimization: A Generalized Calafiore-Campi Algorithm and the notion of -optimization
The scenario approach developed by Calafiore and Campi to attack
chance-constrained convex programs utilizes random sampling on the uncertainty
parameter to substitute the original problem with a representative continuous
convex optimization with convex constraints which is a relaxation of the
original. Calafiore and Campi provided an explicit estimate on the size of
the sampling relaxation to yield high-likelihood feasible solutions of the
chance-constrained problem. They measured the probability of the original
constraints to be violated by the random optimal solution from the relaxation
of size .
This paper has two main contributions. First, we present a generalization of
the Calafiore-Campi results to both integer and mixed-integer variables. In
fact, we demonstrate that their sampling estimates work naturally for variables
restricted to some subset of . The key elements are
generalizations of Helly's theorem where the convex sets are required to
intersect . The size of samples in both algorithms will
be directly determined by the -Helly numbers.
Motivated by the first half of the paper, for any subset , we introduce the notion of an -optimization problem, where the
variables take on values over . It generalizes continuous, integer, and
mixed-integer optimization. We illustrate with examples the expressive power of
-optimization to capture sophisticated combinatorial optimization problems
with difficult modular constraints. We reinforce the evidence that
-optimization is "the right concept" by showing that the well-known
randomized sampling algorithm of K. Clarkson for low-dimensional convex
optimization problems can be extended to work with variables taking values over
.Comment: 16 pages, 0 figures. This paper has been revised and split into two
parts. This version is the second part of the original paper. The first part
of the original paper is arXiv:1508.02380 (the original article contained 24
pages, 3 figures
Rigidity analysis of protein structures and rapid simulations of protein motion
It is a common goal in biophysics to understand protein structural properties
and their relationship to protein function. I investigated protein structural
properties using three coarse graining methods: a rigidity analysis method First, a
geometric simulation method Froda and normal mode analysis as implemented in
Elnemo to identify the protein directions of motion. Furthermore, I also compared
the results between the coarse graining methods with the results from molecular
dynamics and from experiments that I carried out. The results from the rigidity
analysis across a set of protein families presented in chapter 3 highlighted two different
patterns of protein rigidity loss, i.e. "sudden" and "gradual". It was found
that theses characteristic patterns were in line with the rigidity distribution of glassy
networks. The simulations of protein motion by merging flexibility, rigidity and normal
mode analyses presented in chapter 4 were able to identify large conformational
changes of proteins using minimal computational resources. I investigated the use
of RMSD as a measure to characterise protein motion and showed that, despite it
is a good measure to identify structural differences when comparing the same protein,
the use of extensive RMSD better captures the extend of motion of a protein
structure. The in-depth investigation of yeast PDI mobility presented in chapter
5 confirmed former experimental results that predicted a large conformational
change for this enzyme. Furthermore, the results predicted: a characteristic rigidity
distribution for yeast PDI, a minimum and a maximum active site distance and a
relationship between the energy cutoff, i.e. the number of hydrogen bonds part of the
network of bonds, and protein mobility. The results obtained were tested against
molecular dynamics simulations in chapter 6. The MD simulation also showed a
large conformational change for yeast PDI but with a slightly different minimum
and maximum inter-cysteine distance. Furthermore, MD was able to reveal new
data, i.e. the most likely inter-cysteine distance. In order to test the accuracy of the
coarse graining and MD simulations I carried out cross-linking experiments to test
the minimum inter-cysteine distance predictions. The results presented in chapter
7 show that human PDI minimum distance is below 12Å whereas the yeast PDI
minimum distance must be above 12Å as no cross-linking structures where found
with the available (12Å long) cross-linkers
Non-critically squeezed light via spontaneous rotational symmetry breaking
We theoretically address squeezed light generation through the spontaneous
breaking of the rotational invariance occuring in a type I degenerate optical
parametric oscillator (DOPO) pumped above threshold. We show that a DOPO with
spherical mirrors, in which the signal and idler fields correspond to first
order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape
of a Hermite-Gauss mode, within the linearized theory. This occurs at any
pumping level above threshold, hence the phenomenon is non-critical.
Imperfections of the rotational symmetry, due e.g. to cavity anisotropy, are
shown to have a small impact, hence the result is not singular.Comment: 4 pages, 1 figure, replaced with resubmitted versio
Implicaciones genéticas de nuevos datos de Sr y Nd de rocas intrusivas del Arco Laramide en el Norte de Sonora, México
The Laramide Intrusive Arc constitutes a wide intrusive belt broadly parallel to the actual Sonora coastline. It was formed by the subduction of the Farallon Plate beneath the North-American Plate during the Late Cretaceous-Early Tertiary period. New isotopic data on rocks of this arc show initial 87Sr/86Sr and eNd isotopic values of 0.7066 to 0.7070 and -5 to -6, respectively, for two samples from Bacanora area; as well as 0.7074 to 0.7081 and -3 to -5.5 respectively, for five samples from Cananea, Mariquita and La Caridad areas. Isotopic ages were determined by U/Pb in zircons (95 Ma) and Ar/Ar in potassic feldspar (56 to 71 Ma) from a quartz monzonite porphyry, and by Ar/Ar in potassic feldspar (56 Ma) from another plutonic granodiorite, both from Bacanora. Initial 87Sr/86Sr and eNd values for samples reported in this study suggest that the Laramidic magmas had a large influence from the Proterozoic basement in northeastern Sonora. Four different isotopic zones are proposed for Sonora, according with Sr-Nd data of laramidic rocks and the substratum intruded.El Arco Intrusivo Laramide constituye un amplio cinturón de rocas intrusivas orientado burdamente paralelo a la costa actual de Sonora. Este cinturón se originó por la subducción de la Placa Farallón bajo la Placa de Norteamérica durante el período Cretácico Tardío – Terciario Temprano. Nuevos datos isotópicos en rocas de este arco indican valores iniciales de 87Sr/86Sr y de eNd de 0.7066 a 0.7070 y -5 a -6, respectivamente, para dos muestras del área de Bacanora; así como de 0.7074 a 0.7081 y -3 a -5.5, respectivamente, para cinco muestras de las áreas de Cananea, Mariquita y La Caridad. Se determinaron también edades isotópicas por U/Pb en zircones (95 Ma) y Ar/Ar en feldespato potásico (56 a 71 Ma) para un pórfido de monzonita de cuarzo, y por Ar/Ar en feldespato potásico (56 Ma) para otra granodiorita plutónica, ambas de Bacanora. Los valores iniciales de 87Sr/86Sr y eNd para las muestras reportadas en este estudio, sugieren que los magmas laramídicos tuvieron gran influencia del basamento proterozoico en el noreste de Sonora. Cuatro diferentes zonas isotópicas son propuestas para Sonora, de acuerdo con los datos de Sr-Nd de las rocas laramídicas y el sustrato intrusionado
Osteoma osteoide de localización escapular: descripción de un caso
Presentamos el caso de un paciente, con dolor en el hombro de predominio nocturno y que diagnosticamos
como Osteoma Osteoide localizado en la escápula izquierda. El tratamiento con salicilatos no fue efectivo
para mejorar el dolor y se procedió a la resección abierta y cauterización de la lesión. El resultado fue satisfactorio y
actualmente el paciente permanece asintomático.We report a case of a patient with pain worse at night, located at the elbow. Osteoid Osteoma of the
scapula was diagnosed. Pain was not relieved by Salycilates. Open surgical treatment and cauterization were the treatment
elected in our case. Pain regressed inmediatly after surgery and the patient was asimptomatic since the surgery
Spontaneous symmetry breaking as a resource for noncritically squeezed light
In the last years we have proposed the use of the mechanism of spontaneous
symmetry breaking with the purpose of generating perfect quadrature squeezing.
Here we review previous work dealing with spatial (translational and
rotational) symmetries, both on optical parametric oscillators and four-wave
mixing cavities, as well as present new results. We then extend the phenomenon
to the polarization state of the signal field, hence introducing spontaneous
polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in
which the phenomenon can be investigated at the single-photon-pair level in a
non-dissipative case, with the purpose of understanding it from a most
fundamental point of view.Comment: Review for the proceedings of SPIE Photonics Europe. 11 pages, 5
figures
Deformation of anisotropic Fermi surfaces due to electron-electron interactions
We analyze the deformations of the Fermi surface induced by electron-electron
interactions in anisotropic two dimensional systems. We use perturbation theory
to treat, on the same footing, the regular and singular regions of the Fermi
surface. It is shown that, even for weak local coupling, the self-energy
presents a nontrivial behavior showing momentum dependence and interplay with
the Fermi surface shape. Our scheme gives simple analytical expressions based
on local features of the Fermi surface.Comment: 7 pages, 3 figure
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