On the existence of 0/1 polytopes with high semidefinite extension complexity

In Rothvo\ss{} it was shown that there exists a 0/1 polytope (a polytope whose vertices are in \{0,1\}^{n}) such that any higher-dimensional polytope projecting to it must have 2^{\Omega(n)} facets, i.e., its linear extension complexity is exponential. The question whether there exists a 0/1 polytope with high PSD extension complexity was left open. We answer this question in the affirmative by showing that there is a 0/1 polytope such that any spectrahedron projecting to it must be the intersection of a semidefinite cone of dimension~2^{\Omega(n)} and an affine space. Our proof relies on a new technique to rescale semidefinite factorizations

Stochastic resonance in a suspension of magnetic dipoles under shear flow

We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e. the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss limitations and role of the linear response theory in its applications to the theory of stochastic resonance.Comment: 17 pages, 5 figures, approved for publication in PR

A Simple Reactive Obstacle Avoidance Algorithm and Its Application in Singapore Harbor

Autonomous surface craft (ASC) are increasingly attractive as a means for performing harbor operations including monitoring and inspection. However, due to the presence of many fixed and moving structures such as pilings, moorings, and vessels, harbor environments are extremely dynamic and cluttered. In order to move autonomously in such conditions ASC’s must be capable of detecting stationary and moving objects and plan their paths accordingly. We propose a simple and scalable online navigation scheme, wherein the relative motion of surrounding obstacles is estimated by the ASC, and the motion plan is modified accordingly at each time step. Since the approach is model-free and its decisions are made at a high frequency, the system is able to deal with highly dynamic scenarios. We deployed ASC’s in the Selat Pauh region of Singapore Harbor to test the technique using a short-range 2-D laser sensor; detection in the rough waters we encountered was quite poor. Nonetheless, the ASC’s were able to avoid both stationary as well as mobile obstacles, the motions of which were unknown a priori. The successful demonstration of obstacle avoidance in the field validates our fast online approach.Massachusetts Institute of Technology. Singapore-MIT Alliance in Research and Technology (SMART

Global Analysis of Neutrino Data

In this talk I review the present status of neutrino masses and mixing and some of their implications for particle physics phenomenology. I first discuss the minimum extension of the Standard Model of particle physics required to accommodate neutrino masses and introduce the new parameters present in the model and in particular the possibility of leptonic mixing. I then describe the phenomenology of neutrino masses and mixing leading to flavour oscillations and present the existing evidence from solar, reactor, atmospheric and long-baseline neutrinos as well as the results from laboratory searches at short distances. I derive the allowed ranges for the mass and mixing parameters when the bulk of data is consistently analyzed in the framework of mixing between the three active neutrinos and obtain as a result the most up-to-date determination of the leptonic mixing matrix. Then I briefly summarize the status of some proposed phenomenological explanations to accommodate the LSND results: the role of sterile neutrinos and the violation of CPT. Finally I comment how within the present experimental precision it is possible to use the observation of oscillation patterns to impose severe constraints on the possible violation of fundamental symmetries in particle physics such as Lorentz invariance or the weak equivalence principle.Comment: Talk given at the Nobel Symposium on Neutrino Physics, Haga Slott, Enkoping, Swede

Continuous k-to-1 functions between complete graphs of even order

A function between graphs is k-to-1 if each point in the co-domain has precisely k pre-images in the domain. Given two graphs, G and H, and an integer k ≥ 1, and considering G and H as subsets of R 3, there may or may not be a k-to-1 continuous function (i.e. a k-to-1 map in the usual topological sense) from G onto H. In this paper we review and complete the determination of whether there are finitely discontinuous, or just infinitely discontinuous k-to-1 functions between two intervals, each of which is one of the following: ]0, 1[, [0, 1[and [0, 1]. We also show that for k even and 1 ≤ r < 2s, (r, s) 6= (1, 1) and (r, s) 6= (3, 2), there is a k-to-1 map from K2r onto K2s if and only if k ≥ 2s.peer-reviewe

Incorporating topological and age uncertainty into event-based biogeography of sand spiders supports paleo-islands in galapagos and ancient connections among neotropical dry forests

Event-based biogeographic methods, such as dispersal-extinction-cladogenesis, have become increasingly popular for attempting to reconstruct the biogeographic history of organisms. Such methods employ distributional data of sampled species and a dated phylogenetic tree to estimate ancestral distribution ranges. Because the input tree is often a single consensus tree, uncertainty in topology and age estimates are rarely accounted for, even when they may affect the outcome of biogeographic estimates. Even when such uncertainties are taken into account for estimates of ancestral ranges, they are usually ignored when researchers compare competing biogeographic hypotheses. We explore the effect of incorporating this uncertainty in a biogeographic analysis of the 21 species of sand spiders (Sicariidae: Sicarius) from Neotropical xeric biomes, based on a total-evidence phylogeny including a complete sampling of the genus. Using a custom R script, we account for uncertainty in ages and topology by estimating ancestral ranges over a sample of trees from the posterior distribution of a Bayesian analysis, and for uncertainty in biogeographic estimates by using stochastic maps. This approach allows for counting biogeographic events such as dispersal among areas, counting lineages through time per area, and testing biogeographic hypotheses, while not overestimating the confidence in a single topology. Including uncertainty in ages indicates that Sicarius dispersed to the Galapagos Islands when the archipelago was formed by paleo-islands that are now submerged; model comparison strongly favors a scenario where dispersal took place before the current islands emerged. We also investigated past connections among currently disjunct Neotropical dry forests; failing to account for topological uncertainty underestimates possible connections among the Caatinga and Andean dry forests in favor of connections among Caatinga and Caribbean + Mesoamerican dry forests. Additionally, we find that biogeographic models including a founder-event speciation parameter (“+J”) are more prone to suffer from the overconfidence effects of estimating ancestral ranges using a single topology. This effect is alleviated by incorporating topological and age uncertainty while estimating stochastic maps, increasing the similarity in the inference of biogeographic events between models with or without a founder-event speciation parameter. We argue that incorporating phylogenetic uncertainty in biogeographic hypothesis-testing is valuable and should be a commonplace approach in the presence of rogue taxa or wide confidence intervals in age estimates, and especially when using models including founder-event speciation.Fil: Fiorini de Magalhaes, Ivan Luiz. Universidade Federal de Minas Gerais; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Santos, Adalberto J.. Universidade Federal de Minas Gerais; BrasilFil: Ramirez, Martin Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin

Realizability of Polytopes as a Low Rank Matrix Completion Problem

This article gives necessary and sufficient conditions for a relation to be the containment relation between the facets and vertices of a polytope. Also given here, are a set of matrices parameterizing the linear moduli space and another set parameterizing the projective moduli space of a combinatorial polytope