1,010 research outputs found
Systematics of the Cumacea (Crustacea)
Cumaceans are small benthic crustaceans. They have a marine cosmopolitan distribution with diversity increasing with depth. There are approximately 1,400 described species of cumaceans. Despite the fact that they offer a good model for the study of morphological evolution and biogeography, the studies on the Order Cumacea are almost restricted to work at the alpha taxonomy level. This thesis contributes to the systematics of Cumacea. The phylogenetic relationships within the Cumacea were studied using newly obtained partial amino acid sequences from the mitochondria1 gene Cytochrome Oxidase I. Among other findings, phylogenetic analyses revealed that the families Bodotriidae, Leuconidae, and Nannastacidae, characterized by the presence of a pleotelson (telson fused to last abdominal segment), form a monophyletic and derived clade. The gene tree topology suggests that some characters traditionally used in cumacean diagnoses represent homoplasies. The cumacean family Bodotriidae is divided into three subfamilies and 34 genera with over 350 species, all of which were morphologically analyzed for 114 variable characters. Two main accomplishments were a result of this study. First, the phylogenetic relationships of the subfamilies and genera within the family were studied. The subfamily Mancocumatinae failed to resolve as a monophyletic group, the subfamily Vaunthompsoniinae are basal bodotriids, and the subfamily Bodotriinae is the most derived clade. A Tethyan origin for the bodotriid fauna is suggested, with radiation along the Atlantic Ocean during the Cretaceous. Phylogenetic and character evolution analyses support several changes to the classification of Bodotriidae. For example, the subfamily Mancocumatinae should be incorporated into the subfamily Vaunthornpsoniinae, the genus Coricuma should be incorporated into the Bodotriinae, and the species of the genera Heternma, Mossambicuma, Pseudocydaspis, should be incorporated into the genera Cumopsis, Eocuma and Cydaspis, respectively. Second, a comprehensive morphological work on the Family Bodotriidae was completed incorporating the suggested changes in the taxonomy . The generic review includes a dichotomous key and rediagnosis of each of the genera of the Family. A new species of Austrocuma from the eastern coast of lndii is described. Among other characters, the uniqueness of this species relies on the presence of onty four pleopods on the males
Maximal Localisation in the Presence of Minimal Uncertainties in Positions and Momenta
Small corrections to the uncertainty relations, with effects in the
ultraviolet and/or infrared, have been discussed in the context of string
theory and quantum gravity. Such corrections lead to small but finite minimal
uncertainties in position and/or momentum measurements. It has been shown that
these effects could indeed provide natural cutoffs in quantum field theory. The
corresponding underlying quantum theoretical framework includes small
`noncommutative geometric' corrections to the canonical commutation relations.
In order to study the full implications on the concept of locality it is
crucial to find the physical states of then maximal localisation. These states
and their properties have been calculated for the case with minimal
uncertainties in positions only. Here we extend this treatment, though still in
one dimension, to the general situation with minimal uncertainties both in
positions and in momenta.Comment: Latex, 21 pages, 2 postscript figure
Quantitative Tverberg theorems over lattices and other discrete sets
This paper presents a new variation of Tverberg's theorem. Given a discrete
set of , we study the number of points of needed to guarantee the
existence of an -partition of the points such that the intersection of the
convex hulls of the parts contains at least points of . The proofs
of the main results require new quantitative versions of Helly's and
Carath\'eodory's theorems.Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:1503.0611
Quantitative combinatorial geometry for continuous parameters
We prove variations of Carath\'eodory's, Helly's and Tverberg's theorems
where the sets involved are measured according to continuous functions such as
the volume or diameter. Among our results, we present continuous quantitative
versions of Lov\'asz's colorful Helly theorem, B\'ar\'any's colorful
Carath\'eodory's theorem, and the colorful Tverberg theorem.Comment: 22 pages. arXiv admin note: substantial text overlap with
arXiv:1503.0611
Quantitative Tverberg, Helly, & Carath\'eodory theorems
This paper presents sixteen quantitative versions of the classic Tverberg,
Helly, & Caratheodory theorems in combinatorial convexity. Our results include
measurable or enumerable information in the hypothesis and the conclusion.
Typical measurements include the volume, the diameter, or the number of points
in a lattice.Comment: 33 page
Space Representation of Stochastic Processes with Delay
We show that a time series evolving by a non-local update rule with two different delays can be mapped onto a local
process in two dimensions with special time-delayed boundary conditions
provided that and are coprime. For certain stochastic update rules
exhibiting a non-equilibrium phase transition this mapping implies that the
critical behavior does not depend on the short delay . In these cases, the
autocorrelation function of the time series is related to the critical
properties of directed percolation.Comment: 6 pages, 8 figure
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
Optical frequency comb generation from a monolithic microresonator
Optical frequency combs provide equidistant frequency markers in the
infrared, visible and ultra-violet and can link an unknown optical frequency to
a radio or microwave frequency reference. Since their inception frequency combs
have triggered major advances in optical frequency metrology and precision
measurements and in applications such as broadband laser-based gas sensing8 and
molecular fingerprinting. Early work generated frequency combs by intra-cavity
phase modulation while to date frequency combs are generated utilizing the
comb-like mode structure of mode-locked lasers, whose repetition rate and
carrier envelope phase can be stabilized. Here, we report an entirely novel
approach in which equally spaced frequency markers are generated from a
continuous wave (CW) pump laser of a known frequency interacting with the modes
of a monolithic high-Q microresonator13 via the Kerr nonlinearity. The
intrinsically broadband nature of parametric gain enables the generation of
discrete comb modes over a 500 nm wide span (ca. 70 THz) around 1550 nm without
relying on any external spectral broadening. Optical-heterodyne-based
measurements reveal that cascaded parametric interactions give rise to an
optical frequency comb, overcoming passive cavity dispersion. The uniformity of
the mode spacing has been verified to within a relative experimental precision
of 7.3*10(-18).Comment: Manuscript and Supplementary Informatio
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