On the equivalence of modes of convergence for log-concave measures

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note

Technology Needs Assessment of an Atmospheric Observation System for Multidisciplinary Air Quality/Meteorology Missions, Part 2

The technology advancements that will be necessary to implement the atmospheric observation systems are considered. Upper and lower atmospheric air quality and meteorological parameters necessary to support the air quality investigations were included. The technology needs were found predominantly in areas related to sensors and measurements of air quality and meteorological measurements

The central limit problem for random vectors with symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein's method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry and we give a brief introduction to the classical method. The spherically symmetric case is treated by a variation of Stein's method which is adapted for continuous symmetries.Comment: AMS-LaTeX, uses xy-pic, 23 pages; v3: added new corollary to Theorem

Remarks on the Central Limit Theorem for Non-Convex Bodies

In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Effects of mesenchymal stromal cells versus serum on tendon healing in a controlled experimental trial in an equine model

Abstract Background Mesenchymal stromal cells (MSC) have shown promising results in the treatment of tendinopathy in equine medicine, making this therapeutic approach seem favorable for translation to human medicine. Having demonstrated that MSC engraft within the tendon lesions after local injection in an equine model, we hypothesized that they would improve tendon healing superior to serum injection alone. Methods Quadrilateral tendon lesions were induced in six horses by mechanical tissue disruption combined with collagenase application 3 weeks before treatment. Adipose-derived MSC suspended in serum or serum alone were then injected intralesionally. Clinical examinations, ultrasound and magnetic resonance imaging were performed over 24 weeks. Tendon biopsies for histological assessment were taken from the hindlimbs 3 weeks after treatment. Horses were sacrificed after 24 weeks and forelimb tendons were subjected to macroscopic and histological examination as well as analysis of musculoskeletal marker expression. Results Tendons injected with MSC showed a transient increase in inflammation and lesion size, as indicated by clinical and imaging parameters between week 3 and 6 (p < 0.05). Thereafter, symptoms decreased in both groups and, except that in MSC-treated tendons, mean lesion signal intensity as seen in T2w magnetic resonance imaging and cellularity as seen in the histology (p < 0.05) were lower, no major differences could be found at week 24. Conclusions These data suggest that MSC have influenced the inflammatory reaction in a way not described in tendinopathy studies before. However, at the endpoint of the current study, 24 weeks after treatment, no distinct improvement was observed in MSC-treated tendons compared to the serum-injected controls. Future studies are necessary to elucidate whether and under which conditions MSC are beneficial for tendon healing before translation into human medicine

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

In situ and ex situ conservation gap analyses of West African priority crop wild relatives

AbstractCrop wild relatives are genetically related wild taxa of crops with unique resources for crop improvement through the transfer of novel and profitable genes. The in situ and ex situ conservation gap analyses for priority crop wild relatives from West Africa were evaluated using species distribution modelling, ecogeographic diversity, and complementary analyses. A total of 20, 125 unique occurrence records were used for the conservation gap analysis, however, 26 taxa had no occurrence data. 64 taxa (62.7%) occurred in protected areas, 56 taxa (55%) were conserved ex situ, while 76.7% (43) of the accessions are underrepresented with less than 50 accessions conserved ex situ. Areas of highest potential diversity were found in the Woroba and Montangnes districts in Cote d’Ivoire, Nzerekore, Faranah, Kindia, and Boke regions of Guinea, South-South, and North-East zones of Nigeria, and Kono and Koinadugu districts in Sierra Leone. Hotspots were found in Atlantique, Littoral, Mono, Kouffo, Atakora, Donga, and Colline provinces of Benin, Accra, and Volta regions of Ghana, North–Central Nigeria, and Lacs district of Cote d’Ivoire and Nzerekore region of Guinea. 29 reserve sites for active in situ conservation were identified, 11 occur in protected areas, while 18 are located outside protected areas. The establishment of the reserve sites will complement existing PAs and ensure long-term active in situ and ex situ conservation and sustainable utilization of priority crop wild relative to underpin food security and mitigate climate change in the region.</jats:p

A transcriptomic analysis of Echinococcus granulosus larval stages:implications for parasite biology and host adaptation

The cestode Echinococcus granulosus--the agent of cystic echinococcosis, a zoonosis affecting humans and domestic animals worldwide--is an excellent model for the study of host-parasite cross-talk that interfaces with two mammalian hosts. To develop the molecular analysis of these interactions, we carried out an EST survey of E. granulosus larval stages. We report the salient features of this study with a focus on genes reflecting physiological adaptations of different parasite stages.We generated ~10,000 ESTs from two sets of full-length enriched libraries (derived from oligo-capped and trans-spliced cDNAs) prepared with three parasite materials: hydatid cyst wall, larval worms (protoscoleces), and pepsin/H(+)-activated protoscoleces. The ESTs were clustered into 2700 distinct gene products. In the context of the biology of E. granulosus, our analyses reveal: (i) a diverse group of abundant long non-protein coding transcripts showing homology to a middle repetitive element (EgBRep) that could either be active molecular species or represent precursors of small RNAs (like piRNAs); (ii) an up-regulation of fermentative pathways in the tissue of the cyst wall; (iii) highly expressed thiol- and selenol-dependent antioxidant enzyme targets of thioredoxin glutathione reductase, the functional hub of redox metabolism in parasitic flatworms; (iv) candidate apomucins for the external layer of the tissue-dwelling hydatid cyst, a mucin-rich structure that is critical for survival in the intermediate host; (v) a set of tetraspanins, a protein family that appears to have expanded in the cestode lineage; and (vi) a set of platyhelminth-specific gene products that may offer targets for novel pan-platyhelminth drug development.This survey has greatly increased the quality and the quantity of the molecular information on E. granulosus and constitutes a valuable resource for gene prediction on the parasite genome and for further genomic and proteomic analyses focused on cestodes and platyhelminths