High Order Upwind Schemes for Multidimensional Magnetohydrodynamics

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint \divb=0 for the magnetic field vector \bb, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the \bb field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate \divb=0 relation for any numerical \bb field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the \bb vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented.Comment: 34 pages, including 14 figure

Earthquake networks based on similar activity patterns

Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross-correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985-1998. We find strong links representing large correlations between patterns in locations separated by more than 1000 km, corroborating prior observations that earthquake interactions have no characteristic length scale. We find network characteristics not attributable to chance alone, including a large number of network links, high node assortativity, and strong stability over time.Comment: 8 pages text, 9 figures. Updated from previous versio

Instabilities in freely expanding sheets of associating viscoelastic fluids

We use the impact of drops on a small solid target as a tool to investigate the behavior of viscoelastic fluids under extreme deformation rates. We study two classes of transient networks: semidilute solutions of supramolecular polymers and suspensions of spherical oil droplets reversibly linked by polymers. The two types of samples display very similar linear viscoelastic properties, which can be described with a Maxwell fluid model, but contrasting nonlinear properties due to different network structure. Upon impact, weakly viscoelastic samples exhibit a behavior qualitatively similar to that of Newtonian fluids: A smooth and regular sheet forms, expands, and then retracts. By contrast, for highly viscoelastic fluids, the thickness of the sheet is found to be very irregular, leading to instabilities and eventually formation of holes. We find that material rheological properties rule the onset of instabilities. We first provide a simple image analysis of the expanding sheets to determine the onset of instabilities. We then demonstrate that a Deborah number related to the shortest relaxation time associated to the sample structure following a high shear is the relevant parameter that controls the heterogeneities in the thickness of the sheet, eventually leading to the formation of holes. When the sheet tears-up, data suggest by contrast that the opening dynamics depends also on the expansion rate of the sheet.Comment: accepted for publication in Soft Matte

On Coloring Resilient Graphs

We introduce a new notion of resilience for constraint satisfaction problems, with the goal of more precisely determining the boundary between NP-hardness and the existence of efficient algorithms for resilient instances. In particular, we study $r$-resiliently $k$-colorable graphs, which are those $k$-colorable graphs that remain $k$-colorable even after the addition of any $r$ new edges. We prove lower bounds on the NP-hardness of coloring resiliently colorable graphs, and provide an algorithm that colors sufficiently resilient graphs. We also analyze the corresponding notion of resilience for $k$-SAT. This notion of resilience suggests an array of open questions for graph coloring and other combinatorial problems.Comment: Appearing in MFCS 201

Improved Approximation Algorithms for Projection Games

The projection games (aka Label-Cover) problem is of great importance to the field of approximation algorithms, since most of the NP-hardness of approximation results we know today are reductions from Label-Cover. In this paper we design several approximation algorithms for projection games: 1. A polynomial-time approximation algorithm that improves on the previous best approximation by Charikar, Hajiaghayi and Karloff [7]. 2. A sub-exponential time algorithm with much tighter approximation for the case of smooth projection games. 3. A PTAS for planar graphs.National Science Foundation (U.S.) (Grant 1218547

Dormancy-associated MADS genes from the EVG locus of peach [Prunus persica (L.) Batsch] have distinct seasonal and photoperiodic expression patterns

Mapping and sequencing of the non-dormant evg mutant in peach [Prunus persica (L.) Batsch] identified six tandem-arrayed DAM (dormancy-associated MADS-box) genes as candidates for regulating growth cessation and terminal bud formation. To narrow the list of candidate genes, an attempt was made to associate bud phenology with the seasonal and environmental patterns of expression of the candidates in wild-type trees. The expression of the six peach DAM genes at the EVG locus of peach was characterized throughout an annual growing cycle in the field, and under controlled conditions in response to a long day–short day photoperiod transition. DAM1, 2, 4, 5, and 6 were responsive to a reduction in photoperiod in controlled conditions and the direction of response correlated with the seasonal timing of expression in field-grown trees. DAM3 did not respond to photoperiod and may be regulated by chilling temperatures. The DAM genes in peach appear to have at least four distinct patterns of expression. DAM1, 2, and 4 are temporally associated with seasonal elongation cessation and bud formation and are the most likely candidates for control of the evg phenotype

Credimus

We believe that economic design and computational complexity---while already important to each other---should become even more important to each other with each passing year. But for that to happen, experts in on the one hand such areas as social choice, economics, and political science and on the other hand computational complexity will have to better understand each other's worldviews. This article, written by two complexity theorists who also work in computational social choice theory, focuses on one direction of that process by presenting a brief overview of how most computational complexity theorists view the world. Although our immediate motivation is to make the lens through which complexity theorists see the world be better understood by those in the social sciences, we also feel that even within computer science it is very important for nontheoreticians to understand how theoreticians think, just as it is equally important within computer science for theoreticians to understand how nontheoreticians think

A Comparison of U. S. and European University-Industry Relations in the Life Sciences

We draw on diverse data sets to compare the institutional organization of upstream life science research across the United States and Europe. Understanding cross-national differences in the organization of innovative labor in the life sciences requires attention to the structure and evolution of biomedical networks involving public research organizations (universities, government laboratories, nonprofit research institutes, and research hospitals), science-based biotechnology firms, and multinational pharmaceutical corporations. We use network visualization methods and correspondence analyses to demonstrate that innovative research in biomedicine has its origins in regional clusters in the United States and in European nations. But the scientific and organizational composition of these regions varies in consequential ways. In the United States, public research organizations and small firms conduct R&D across multiple therapeutic areas and stages of the development process. Ties within and across these regions link small firms and diverse public institutions, contributing to the development of a robust national network. In contrast, the European story is one of regional specialization with a less diverse group of public research organizations working in a smaller number of therapeutic areas. European institutes develop local connections to small firms working on similar scientific problems, while cross-national linkages of European regional clusters typically involve large pharmaceutical corporations. We show that the roles of large and small firms differ in the United States and Europe, arguing that the greater heterogeneity of the U. S. system is based on much closer integration of basic science and clinical development

Interactive Proofs with Approximately Commuting Provers

The class MIP∗ of promise problems that can be decided through an interactive proof system with multiple entangled provers provides a complexity-theoretic framework for the exploration of the nonlocal properties of entanglement. Very little is known in terms of the power of this class. The only proposed approach for establishing upper bounds is based on a hierarchy of semidefinite programs introduced independently by Pironio et al. and Doherty et al. in 2006. This hierarchy converges to a value, the field-theoretic value, that is only known to coincide with the provers’ maximum success probability in a given proof system under a plausible but difficult mathematical conjecture, Connes’ embedding conjecture. No bounds on the rate of convergence are known. We introduce a rounding scheme for the hierarchy, establishing that any solution to its N -th level can be mapped to a strategy for the provers in which measurement operators associated with distinct provers have pairwise commutator bounded by O(ℓ^2/√N) in operator norm, where ℓ is the number of possible answers per prover. Our rounding scheme motivates the introduction of a variant of quantum multiprover interactive proof systems, called MIP∗_δ in which the soundness property is required to hold against provers allowed to operate on the same Hilbert space as long as the commutator of operations performed by distinct provers has norm at most δ. Our rounding scheme implies the upper bound MIP∗_δ ⊆ DTIME(exp(exp(poly)/δ^2)). In terms of lower bounds we establish that MIP∗_(2−poly) contains NEXP with completeness 1 and soundness 1−2^(−poly). We discuss connections with the mathematical literature on approximate commutation and applications to device-independent cryptography