4,578 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
Pattern formation in a predator-prey system characterized by a spatial scale of interaction
We describe pattern formation in ecological systems using a version of the
classical Lotka-Volterra model characterized by a spatial scale which controls
the predator-prey interaction range. Analytical and simulational results show
that patterns can emerge in some regions of the parameters space where the
instability is driven by the range of the interaction. The individual-based
implementation captures realistic ecological features. In fact, spatial
structures emerge in an erratic oscillatory regime which can contemplate
predators' extinction.Comment: 5 pages, 4 figure
Magneto--Acoustic Energetics Study of the Seismically Active Flare of 15 February 2011
Multi--wavelength studies of energetic solar flares with seismic emissions
have revealed interesting common features between them. We studied the first
GOES X--class flare of the 24th solar cycle, as detected by the Solar Dynamics
Observatory (SDO). For context, seismic activity from this flare
(SOL2011-02-15T01:55-X2.2, in NOAA AR 11158) has been reported in the
literature (Kosovichev, 2011; Zharkov et al., 2011). Based on Dopplergram data
from the Helioseismic and Magnetic Imager (HMI), we applied standard methods of
local helioseismology in order to identify the seismic sources in this event.
RHESSI hard X-ray data are used to check the correlation between the location
of the seismic sources and the particle precipitation sites in during the
flare. Using HMI magnetogram data, the temporal profile of fluctuations in the
photospheric line-of-sight magnetic field is used to estimate the magnetic
field change in the region where the seismic signal was observed. This leads to
an estimate of the work done by the Lorentz-force transient on the photosphere
of the source region. In this instance this is found to be a significant
fraction of the acoustic energy in the attendant seismic emission, suggesting
that Lorentz forces can contribute significantly to the generation of
sunquakes. However, there are regions in which the signature of the
Lorentz-force is much stronger, but from which no significant acoustic emission
emanates.Comment: Submitted to Solar Physic
The Impact of Single vs. Poly Victimization by Maltreatment Type on Pre-Treatment PTSD Scores
Studies show that an estimated 21-50% of children who have experienced maltreatment will develop post-traumatic stress disorder (PTSD) within their lifetime (Schuck & Widom 2019). Research suggests that the type and number of exposures to trauma may influence symptom severity. Further, trauma symptom scores of children who experienced child sexual abuse (CSA) were higher among the children who endorsed poly-victimization, meaning when CSA was combined with another form of maltreatment (Racine et al 2022). This study seeks to examine the impact of poly-victimization and combined types of maltreatment on childrenâs PTSD scores in an archival dataset from a child advocacy center (CAC) serving children exposed to various forms of trauma. Participants from the overall child sample (N = 721) who have pre-treatment PTSD scores (n = 290) will be analyzed. The analyzed sample includes 83 minors exposed to poly-victimization, 175 exposed to single victimization, and 32 where the trauma type was missing from the dataset. Specifically, the following hypotheses will be tested: (1) victims of poly-victimization will have higher PTSD scores than victims of single victimization; (2) among participants with poly-victimization, those with a combination of sexual abuse and physical abuse will have the highest PTSD scores compared to other combinations. Results will be discussed in the context of current referral pathways for child advocacy centers
Childhood Trauma and PTSD symptoms: Disentangling the Roles of Emotion Regulation and Distress Tolerance
Background: Research documents that individuals with a history of childhood trauma experience greater emotion regulation difficulties (ED), as well as lower distress tolerance (DT), two constructs that independent lines of research implicate as transdiagnostic factors in post-traumatic stress disorder (PTSD). To help elucidate how such mechanisms may influence the etiology, maintenance, and treatment of PTSD, the current study investigates the distinct mediating roles of ED and DT and explores which accounts for more unique variance.
Methods: Participants (N = 385, aged 18-48) with a childhood trauma history provided self-ratings of cumulative trauma exposure, and endorsed current ED, DT, and PTSD symptoms. Single and dual mediation analyses were conducted to assess the roles of ED and DT in the relation between childhood trauma exposure and current PTSD symptoms.
Results: ED and DT were inversely related. Higher childhood trauma exposure predicted higher PTSD symptoms in adulthood. ED and DT each mediated/explained the association between childhood trauma exposure and current PTSD symptoms; ED accounted for a larger effect size.
Limitations: Cross-sectional design precludes determining causality. Retrospective self-report in measurement is subject to bias and findings may not generalize to behavioral measures.
Conclusions: The current study results provide preliminary evidence of ED and DT as distinct mechanisms. Of clinical relevance, current findings support post-trauma processing theories that contend individualsâ recovery requires accepting and learning to modulate trauma-related emotional states. Implications for potential pathways from childhood trauma to PTSD, as well as methods of treatment and prevention are discussed
- âŠ