Linear semigroups with coarsely dense orbits

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit contains a coarsely dense subset of some open cone $C$ in $V$ then the closure of the orbit contains the closure of $C$. In the complex case the orbit is then actually dense in $V$. For the real case we give precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page

Deer as a potential wildlife reservoir for Parachlamydia species.

Wildlife populations represent an important reservoir for emerging pathogens and trans-boundary livestock diseases. However, detailed information relating to the occurrence of endemic pathogens such as those of the order Chlamydiales in such populations is lacking. During the hunting season of 2008, 863 samples (including blood, conjunctival swabs, internal organs and faeces) were collected in the Eastern Swiss Alps from 99 free-living red deer (Cervus elaphus) and 64 free-living roe deer (Capreolus capreolus) and tested using ELISA, PCR and immunohistochemistry for members of the family Chlamydiaceae and the genus Parachlamydia. Parachlamydia spp. were detected in the conjunctival swabs, faeces and internal organs of both species of deer (2.4% positive, with a further 29.5% inconclusive). The very low occurrence of Chlamydiaceae (2.5%) was in line with serological data (0.7% seroprevalence for Chlamydia abortus). Further investigations are required to elucidate the zoonotic potential, pathogenicity, and distribution of Parachlamydia spp. in wild ruminants

Arithmeticity vs. non-linearity for irreducible lattices

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, such as for instance products of topologically simple groups. This applies notably to a (large class of) Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page

A lattice in more than two Kac--Moody groups is arithmetic

Let $\Gamma$ be an irreducible lattice in a product of n infinite irreducible complete Kac-Moody groups of simply laced type over finite fields. We show that if n is at least 3, then each Kac-Moody groups is in fact a simple algebraic group over a local field and $\Gamma$ is an arithmetic lattice. This relies on the following alternative which is satisfied by any irreducible lattice provided n is at least 2: either $\Gamma$ is an S-arithmetic (hence linear) group, or it is not residually finite. In that case, it is even virtually simple when the ground field is large enough. More general CAT(0) groups are also considered throughout.Comment: Subsection 2.B was modified and an example was added ther

Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.Comment: LaTeX, 3 figures, 12 page

Distinction of representations via Bruhat-Tits buildings of p-adic groups

Introductory and pedagogical treatmeant of the article : P. Broussous "Distinction of the Steinberg representation", with an appendix by Fran\c{c}ois Court\`es, IMRN 2014, no 11, 3140-3157. To appear in Proceedings of Chaire Jean Morlet, Dipendra Prasad, Volker Heiermann Ed. 2017. Contains modified and simplified proofs of loc. cit. This article is written in memory of Fran\c{c}ois Court\`es who passed away in september 2016.Comment: 33 pages, 4 figure

Silicon on Nothing Mems Electromechanical Resonator

The very significant growth of the wireless communication industry has spawned tremendous interest in the development of high performances radio frequencies (RF) components. Micro Electro Mechanical Systems (MEMS) are good candidates to allow reconfigurable RF functions such as filters, oscillators or antennas. This paper will focus on the MEMS electromechanical resonators which show interesting performances to replace SAW filters or quartz reference oscillators, allowing smaller integrated functions with lower power consumption. The resonant frequency depends on the material properties, such as Young's modulus and density, and on the movable mechanical structure dimensions (beam length defined by photolithography). Thus, it is possible to obtain multi frequencies resonators on a wafer. The resonator performance (frequency, quality factor) strongly depends on the environment, like moisture or pressure, which imply the need for a vacuum package. This paper will present first resonator mechanisms and mechanical behaviors followed by state of the art descriptions with applications and specifications overview. Then MEMS resonator developments at STMicroelectronics including FEM analysis, technological developments and characterization are detailed.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

Prevalence of Chlamydia abortus in Belgian ruminants

Chlamydia (C.) abortus enzootic abortion still remains the most common cause of reproductive failure in sheep-breeding countries all over the world. Chlamydia abortus in cattle is predominantly associated with genital tract disease and mastitis. In this study, Belgian sheep (n=958), goats (n=48) and cattle (n=1849) were examined, using the ID Screen (TM) Chlamydia abortus indirect multi-species antibody ELISA. In the sheep, the highest prevalence rate was found in Limburg (4.05%). The animals of Antwerp, Brabant and Liege tested negative. The prevalence in the remaining five regions was low (0.24% to 2.74%). Of the nine goat herds, only one herd in Luxembourg was seropositive. In cattle, the highest prevalence rate was found in Walloon Brabant (4.23%). The animals of Limburg and Namur tested negative. The prevalence rate in the remaining seven regions ranged between 0.39% and 4.02%

Univalent Foundations and the UniMath Library

We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander

Zoonotic potential of guinea pigs: Outbreak of cryptosporidiosis combined with chlamydiosis in a breeding guinea pig herd.

In a guinea pig herd with 26 breeding animals, several individuals of all age categories died (16/26) after three animals had been newly introduced from another herd. Furthermore, the population suffered of apathy, anorexia, severe weight loss and conjunctivitis, as well as abortions and stillbirths. At the same time, the owner experienced a SARS-CoV-2 infection with pneumonia, which was confirmed by taking a PCR test. Chlamydia caviae was detected from the conjunctiva and vagina/uterus in one juvenile animal together with an intestinal Cryptosporidium wrairi infection. Oocysts were found histologically in the small intestine, which was confirmed by PCR. C. wairi is a parasite adapted to guinea pigs with zoonotic potential, which causes diarrhoea with frequent deaths in larger guinea pig herds. C. caviae is also a zoonotic pathogen and often the cause of conjunctivitis, pneumonia and abortions in guinea pigs and can lead to upper respiratory tract disease, conjunctivitis but also severe pneumonia in humans. The increased death cases and the clinical signs could be traced back to an infection with Cryptosporidium wrairi, complicated by a co-infection of C. caviae. We suspect that the abortions were caused by C. caviae, but since the population was treated with various antibiotics effective against chlamydial infections, it was no longer possible to verify this by PCR testing. Unfortunately, more animals succumbed and finally only two animals of the originally 26 were left. With this case report, we would like to point out to veterinarians that guinea pigs can be an important source of zoonotic infections for various pathogens, especially since they are popular pets and often come into close contact with children where hygiene might not always be strictly followed