Localization for a matrix-valued Anderson model

We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on L^2(\R)\otimes \C^N, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the F\"urstenberg group of these operators, valid on an interval $I\subset \R$, they exhibit localization properties on $I$, both in the spectral and dynamical sense. After looking at the regularity properties of the Lyapunov exponents and of the integrated density of states, we prove a Wegner estimate and apply a multiscale analysis scheme to prove localization for these operators. We also study an example in this class of operators, for which we can prove the required assumptions on the F\"urstenberg group. This group being the one generated by the transfer matrices, we can use, to prove these assumptions, an algebraic result on generating dense Lie subgroups in semisimple real connected Lie groups, due to Breuillard and Gelander. The algebraic methods used here allow us to handle with singular distributions of the random parameters

Expansion in perfect groups

Let Ga be a subgroup of GL_d(Q) generated by a finite symmetric set S. For an integer q, denote by Ga_q the subgroup of Ga consisting of the elements that project to the unit element mod q. We prove that the Cayley graphs of Ga/Ga_q with respect to the generating set S form a family of expanders when q ranges over square-free integers with large prime divisors if and only if the connected component of the Zariski-closure of Ga is perfect.Comment: 62 pages, no figures, revision based on referee's comments: new ideas are explained in more details in the introduction, typos corrected, results and proofs unchange

Expansion in SL_d(Z/qZ), q arbitrary

Let S be a fixed finite symmetric subset of SL_d(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of pi_q(G) with respect to the generating set pi_q(S) form a family of expanders, where pi_q is the projection map Z->Z/qZ

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Bounds on the diameter of Cayley graphs of the symmetric group

In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.Comment: 17 pages, 6 table

Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

Discrete ELF/VLF (Extremely Low Frequency/Very Low Frequency) chorus emissions are one of the most intense electromagnetic plasma waves observed in radiation belts and in the outer terrestrial magnetosphere. These waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. The objective of our study is to reconstruct the realistic distribution of chorus wave-normals in radiation belts for all magnetic latitudes. To achieve this aim, the data from the electric and magnetic field measurements onboard Cluster satellite are used to determine the wave-vector distribution of the chorus signal around the equator region. Then the propagation of such a wave packet is modeled using three-dimensional ray tracing technique, which employs K. Rönnmark's WHAMP to solve hot plasma dispersion relation along the wave packet trajectory. The observed chorus wave distributions close to waves source are first fitted to form the initial conditions which then propagate numerically through the inner magnetosphere in the frame of the WKB approximation. Ray tracing technique allows one to reconstruct wave packet properties (electric and magnetic fields, width of the wave packet in k-space, etc.) along the propagation path. The calculations show the spatial spreading of the signal energy due to propagation in the inhomogeneous and anisotropic magnetized plasma. Comparison of wave-normal distribution obtained from ray tracing technique with Cluster observations up to 40&deg; latitude demonstrates the reliability of our approach and applied numerical schemes

European Sea Bass (Dicentrarchus labrax) immune status and disease resistance are impaired by arginine dietary supplementation

Infectious diseases and fish feeds management are probably the major expenses in the aquaculture business. Hence, it is a priority to define sustainable strategies which simultaneously avoid therapeutic procedures and reinforce fish immunity. Currently, one preferred approach is the use of immunostimulants which can be supplemented to the fish diets. Arginine is a versatile amino acid with important mechanisms closely related to the immune response. Aiming at finding out how arginine affects the innate immune status or improve disease resistance of European seabass (Dicentrarchus labrax) against vibriosis, fish were fed two arginine-supplemented diets (1% and 2% arginine supplementation). A third diet meeting arginine requirement level for seabass served as control diet. Following 15 or 29 days of feeding, fish were sampled for blood, spleen and gut to assess cell-mediated immune parameters and immune-related gene expression. At the same time, fish from each dietary group were challenged against Vibrio anguillarum and survival was monitored. Cell-mediated immune parameters such as the extracellular superoxide and nitric oxide decreased in fish fed arginine-supplemented diets. Interleukins and immune-cell marker transcripts were down-regulated by the highest supplementation level. Disease resistance data were in accordance with a generally depressed immune status, with increased susceptibility to vibriosis in fish fed arginine supplemented diets. Altogether, these results suggest a general inhibitory effect of arginine on the immune defences and disease resistance of European seabass. Still, further research will certainly clarify arginine immunomodulation pathways thereby allowing the validation of its potential as a prophylactic strategy.European Union's Seventh Framework Programme AQUAEXCEL (Aquaculture Infrastructures for Excellence in European Fish Research) [262336]; AQUAIMPROV [NORTE-07-0124-FEDER-000038]; North Portugal Regional Operational Programme (ON. 2 - O Novo Norte) , under the National Strategic Reference Framework, through the European Regional Development Fund; North Portugal Regional Operational Programme (ON. 2 - O Novo Norte), under the National Strategic Reference Framework through the COMPETE - Operational Competitiveness Programme; Fundacao para a Ciencia e Tecnologia; Fundacao para a Ciencia e Tecnologia [SFRH/BD/89457/2012, SFRH/BPD/77210/2011]; Generalitat Valenciana through the project REVIDPAQUA [ISIC/2012/003]; [PEst-C/MAR/LA0015/2013]; [UID/Multi/04423/2013]info:eu-repo/semantics/publishedVersio

C*-simplicity and the unique trace property for discrete groups

In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to settle the longstanding open problem of characterizing groups with the unique trace property