Helly numbers of Algebraic Subsets of Rd\mathbb R^d

We study $S$-convex sets, which are the geometric objects obtained as the intersection of the usual convex sets in $\mathbb R^d$ with a proper subset $S\subset \mathbb R^d$. We contribute new results about their $S$-Helly numbers. We extend prior work for $S=\mathbb R^d$, $\mathbb Z^d$, and $\mathbb Z^{d-k}\times\mathbb R^k$; we give sharp bounds on the $S$-Helly numbers in several new cases. We considered the situation for low-dimensional $S$ and for sets $S$ that have some algebraic structure, in particular when $S$ is an arbitrary subgroup of $\mathbb R^d$ or when $S$ 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 SS-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 $N$ convex constraints which is a relaxation of the original. Calafiore and Campi provided an explicit estimate on the size $N$ 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 $N$. 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 $S$ of $\mathbb R^d$. The key elements are generalizations of Helly's theorem where the convex sets are required to intersect $S \subset \mathbb R^d$. The size of samples in both algorithms will be directly determined by the $S$-Helly numbers. Motivated by the first half of the paper, for any subset $S \subset \mathbb R^d$, we introduce the notion of an $S$-optimization problem, where the variables take on values over $S$. It generalizes continuous, integer, and mixed-integer optimization. We illustrate with examples the expressive power of $S$-optimization to capture sophisticated combinatorial optimization problems with difficult modular constraints. We reinforce the evidence that $S$-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 $S$.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

Age problem in holographic dark energy

We study the age problem of the universe with the holographic DE model introduced in [21], and test the model with some known old high redshift objects (OHRO). The parameters of the model have been constrained using the SNIa, CMB and BAO data set. We found that the age of the old quasar APM 08 279+5255 at z = 3.91 can be described by the model.Comment: 13 page

An unbiased genetic screen reveals the polygenic nature of the influenza virus anti-interferon response.

Influenza A viruses counteract the cellular innate immune response at several steps, including blocking RIG I-dependent activation of interferon (IFN) transcription, interferon (IFN)-dependent upregulation of IFN-stimulated genes (ISGs), and the activity of various ISG products; the multifunctional NS1 protein is responsible for most of these activities. To determine the importance of other viral genes in the interplay between the virus and the host IFN response, we characterized populations and selected mutants of wild-type viruses selected by passage through non-IFN-responsive cells. We reasoned that, by allowing replication to occur in the absence of the selection pressure exerted by IFN, the virus could mutate at positions that would normally be restricted and could thus find new optimal sequence solutions. Deep sequencing of selected virus populations and individual virus mutants indicated that nonsynonymous mutations occurred at many phylogenetically conserved positions in nearly all virus genes. Most individual mutants selected for further characterization induced IFN and ISGs and were unable to counteract the effects of exogenous IFN, yet only one contained a mutation in NS1. The relevance of these mutations for the virus phenotype was verified by reverse genetics. Of note, several virus mutants expressing intact NS1 proteins exhibited alterations in the M1/M2 proteins and accumulated large amounts of deleted genomic RNAs but nonetheless replicated to high titers. This suggests that the overproduction of IFN inducers by these viruses can override NS1-mediated IFN modulation. Altogether, the results suggest that influenza viruses replicating in IFN-competent cells have tuned their complete genomes to evade the cellular innate immune system and that serial replication in non-IFN-responsive cells allows the virus to relax from these constraints and find a new genome consensus within its sequence space. IMPORTANCE In natural virus infections, the production of interferons leads to an antiviral state in cells that effectively limits virus replication. The interferon response places considerable selection pressure on viruses, and they have evolved a variety of ways to evade it. Although the influenza virus NS1 protein is a powerful interferon antagonist, the contributions of other viral genes to interferon evasion have not been well characterized. Here, we examined the effects of alleviating the selection pressure exerted by interferon by serially passaging influenza viruses in cells unable to respond to interferon. Viruses that grew to high titers had mutations at many normally conserved positions in nearly all genes and were not restricted to the NS1 gene. Our results demonstrate that influenza viruses have fine-tuned their entire genomes to evade the interferon response, and by removing interferon-mediated constraints, viruses can mutate at genome positions normally restricted by the interferon response

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