Further implications of the Bessis-Moussa-Villani conjecture

We find further implications of the BMV conjecture, which states that for hermitian matrices A and B, the function Tr exp(A - t B) is the Laplace transform of a positive measure.Comment: LaTeX, 8 page

Issues related to direct seeding of rice in rainfed cropping systems in northwest Bangladesh

Economic factors and developments in rice production technologies are the major drivers that have led to the adoption of direct seeding of rice in place of transplanting in Asia. The primary economic motives for a shift to direct seeding are the savings in labor cost and the possibility of crop intensification. A key development challenge in the drought-prone rainfed agriculture of the Barind Tract of northwest Bangladesh is to simultaneously improve the reliability and yield of monsoon rice while improving total system productivity by increasing the area planted to drought-tolerant postrice crops. Research trials and field-scale evaluation by farmers have demonstrated that dry direct seeding or wet seeding of pregerminated rice seed reduces labor for crop establishment, results in rice yields similar to or higher than those from conventional transplanting, and advances harvest by 7-10 days. Earlier harvest has the potential to reduce the risk of terminal drought in rice when the monsoon ends abruptly and increases the opportunity for establishing a postrice crop of chickpea on residual moisture. Herbicide use is essential with direct seeding and this further reduces rice production costs. This modified rice/legume system using direct seeding is knowledge-intensive. Widespread sustained adoption will depend on farmers undertaking timely tillage, adequate land leveling, and timely application of herbicides. Extension/farmer training supported by clear decision support frameworks will be needed to provide farmers with access to the knowledge needed to implement direct seeding effectively

Sums of totally positive matrices

AbstractIt is shown that an arbitrary m×n positive matrix can be written as a sum of at most min{m,n} totally positive matrices, and that this is in general the best possible value for the number of summands. Sufficient conditions are given under which fewer than min{m,n} totally positive summands are needed

Converse to the Parter–Wiener theorem: The case of non-trees

AbstractThrough a succession of results, it is known that if the graph of an Hermitian matrix A is a tree and if for some index j, λ∈σ(A)∩σ(A(j)), then there is an index i such that the multiplicity of λ in σ(A(i)) is one more than that in A. We exhibit a converse to this result by showing that it is generally true only for trees. In particular, it is shown that the minimum rank of a positive semidefinite matrix with a given graph G is ⩽n-2 when G is not a tree. This raises the question of how the minimum rank of a positive semidefinite matrix depends upon the graph in general

Path Integral Solubility of a General Two-Dimensional Model

The solubility of a general two dimensional model, which reduces to various models in different limits, is studied within the path integral formalism. Various subtleties and interesting features are pointed out.Comment: 7 pages, UR1386, ER40685-83

On a Generalized Matching Problem Arising in Estimating the Eigenvalue Variation of Two Matrices

It is shown that if G is a graph having vertices P1, P2, ..., Pn, Q1, Q2, ..., Qn and satisfying some conditions, then there is a permutation σ of {1, 2, ..., n} such that there is a path, for i = 1, 2, ..., n connecting Pi with Qσ(i) having a length at most {n/2}. This is used to prove a theorem having applications in eigenvalue variation estimation

A Probabilistic Analysis of Kademlia Networks

Kademlia is currently the most widely used searching algorithm in P2P (peer-to-peer) networks. This work studies an essential question about Kademlia from a mathematical perspective: how long does it take to locate a node in the network? To answer it, we introduce a random graph K and study how many steps are needed to locate a given vertex in K using Kademlia's algorithm, which we call the routing time. Two slightly different versions of K are studied. In the first one, vertices of K are labelled with fixed IDs. In the second one, vertices are assumed to have randomly selected IDs. In both cases, we show that the routing time is about c*log(n), where n is the number of nodes in the network and c is an explicitly described constant.Comment: ISAAC 201

Fully biodegradable and biocompatible emulsion template polymer scaffolds by thiol-acrylate polymerisation of polycaprolactone macropolymers

The emulsion templating process offers a route to highly porous polymers with well-defined morphologies. This study describes the preparation of such porous polymers (polyHIPEs) via the photopolymerization of a multi-functional thiol and polycaprolactone macromonomer. The resulting materials have nominal porosities of 90% and 95%, and are seen to have an interconnected pore morphology, with an average pore diameter of approximately 60 μm. Initial biocompatibility assessments with fibroblast cells (L929) have shown that the polymers are capable of supporting cell growth over 7 days and degradation products are non-toxic to cells up to a concentration of 0.1 mg ml−1

Canine mesenchymal stem cells are neurotrophic and angiogenic:an in vitro assessment of their paracrine activity

Mesenchymal stem cells (MSCs) have been used in cell replacement therapies for connective tissue damage, but also can stimulate wound healing through paracrine activity. In order to further understand the potential use of MSCs to treat dogs with neurological disorders, this study examined the paracrine action of adipose-derived canine MSCs on neuronal and endothelial cell models. The culture-expanded MSCs exhibited a MSC phenotype according to plastic adherence, cell morphology, CD profiling and differentiation potential along mesenchymal lineages. Treating the SH-SY5Y neuronal cell line with serum-free MSC culture-conditioned medium (MSC CM) significantly increased SH-SY5Y cell proliferation (P < 0.01), neurite outgrowth (P = 0.0055) and immunopositivity for the neuronal marker βIII-tubulin (P = 0.0002). Treatment of the EA.hy926 endothelial cell line with MSC CM significantly increased the rate of wound closure in endothelial cell scratch wound assays (P = 0.0409), which was associated with significantly increased endothelial cell proliferation (P < 0.05) and migration (P = 0.0001). Furthermore, canine MSC CM induced endothelial tubule formation in EA.hy926 cells in a soluble basement membrane matrix. Hence, this study has demonstrated that adipose-derived canine MSC CM stimulated neuronal and endothelial cells probably through the paracrine activity of MSC-secreted factors. This supports the use of canine MSC transplants or their secreted products in the clinical treatment of dogs with neurological disorders and provides some insight into possible mechanisms of action

Dynamical compactification from de Sitter space

We show that D-dimensional de Sitter space is unstable to the nucleation of non-singular geometries containing spacetime regions with different numbers of macroscopic dimensions, leading to a dynamical mechanism of compactification. These and other solutions to Einstein gravity with flux and a cosmological constant are constructed by performing a dimensional reduction under the assumption of q-dimensional spherical symmetry in the full D-dimensional geometry. In addition to the familiar black holes, black branes, and compactification solutions we identify a number of new geometries, some of which are completely non-singular. The dynamical compactification mechanism populates lower-dimensional vacua very differently from false vacuum eternal inflation, which occurs entirely within the context of four-dimensions. We outline the phenomenology of the nucleation rates, finding that the dimensionality of the vacuum plays a key role and that among vacua of the same dimensionality, the rate is highest for smaller values of the cosmological constant. We consider the cosmological constant problem and propose a novel model of slow-roll inflation that is triggered by the compactification process.Comment: Revtex. 41 pages with 24 embedded figures. Minor corrections and added reference