Structured Random Matrices

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact or approximate symmetries, such as matrices with i.i.d. entries, for which precise analytic results and limit theorems are available. Much less well understood are matrices that are endowed with an arbitrary structure, such as sparse Wigner matrices or matrices whose entries possess a given variance pattern. The challenge in investigating such structured random matrices is to understand how the given structure of the matrix is reflected in its spectral properties. This chapter reviews a number of recent results, methods, and open problems in this direction, with a particular emphasis on sharp spectral norm inequalities for Gaussian random matrices.Comment: 46 pages; to appear in IMA Volume "Discrete Structures: Analysis and Applications" (Springer

Inclusion scolaire : dispositif pédagogique pour enfants dyslexiques et dysphasiques au sein d'une école spécialisée

International audienceIn the first part of the article, we describe different types of schooling in France, for children withdisabilities. In the second part, we focus on a particular system of teaching - a local unit for inclusiveeducation - for children aged from 6 to 12 with specific language disorders and learning disabilities,in a specialised school. In the last part, we describe a few exemples of pedagogical accomodationsconceived for the local unit for inclusive education and other accomodations designed to be used inthe inclusion class in history and geography studies.Dans la première partie de l’article, nous décrivons les différents types de scolarisation, en France,pour des élèves en situation de handicap. Dans une deuxième partie, nous présentons un dispositifpédagogique - une Unité locale pour l’inclusion scolaire - mis en place pour l’accompagnementd’élèves âgés de 6 à 12 ans présentant des troubles spécifiques du langage et des apprentissages, cela,au sein d’une école spécialisée. Dans une dernière partie, nous décrivons quelques exemplesd’adaptations pédagogiques menées au sein de ce dispositif ainsi que d’autres adaptations menéesdans la classe de référence des élèves en histoire-géographie

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

p53-dependent control of transactivation of the Pen2 promoter by presenilins

The senile plaques found in the brains of patients with Alzheimer's disease are mainly due to the accumulation of amyloid β-peptides (Aβ) that are liberated by γ-secretase, a high molecular weight complex including presenilins, PEN-2, APH-1 and nicastrin. The depletion of each of these proteins disrupts the complex assembly into a functional protease. Here, we describe another level of regulation of this multimeric protease. The depletion of both presenilins drastically reduces Pen2 mRNA levels and its promoter transactivation. Furthermore, overexpression of presenilin-1 lowers Pen2 promoter transactivation, a phenotype abolished by a double mutation known to prevent presenilin-dependent γ-secretase activity. PEN-2 expression is decreased by depletion of β-amyloid precursor protein (APP) and increased by the APP intracellular domain (AICD). We show that AICD and APP complement for Pen2 mRNA levels in APP/APLP1-2 knockout fibroblasts. Interestingly, overexpression of presenilin-2 greatly increases Pen2 promoter transactivation. The opposite effect triggered by both presenilins was reminiscent of our previous study, which showed that these two proteins elicit antagonistic effects on p53. Therefore, we examined the contribution of p53 on Pen2 transcription. Pen2 promoter transactivation, and Pen2 mRNA and protein levels were drastically reduced in p53–/– fibroblasts. Furthermore, PEN-2 expression could be rescued by p53 complementation in p53- and APP-deficient cells. Interestingly, PEN-2 expression was also reduced in p53-deficient mouse brain. Overall, our study describes a p53-dependent regulation of PEN-2 expression by other members of the γ-secretase complex, namely presenilins

Cellular Prion Protein Expression Is Not Regulated by the Alzheimer's Amyloid Precursor Protein Intracellular Domain

There is increasing evidence of molecular and cellular links between Alzheimer's disease (AD) and prion diseases. The cellular prion protein, PrPC, modulates the post-translational processing of the AD amyloid precursor protein (APP), through its inhibition of the β-secretase BACE1, and oligomers of amyloid-β bind to PrPC which may mediate amyloid-β neurotoxicity. In addition, the APP intracellular domain (AICD), which acts as a transcriptional regulator, has been reported to control the expression of PrPC. Through the use of transgenic mice, cell culture models and manipulation of APP expression and processing, this study aimed to clarify the role of AICD in regulating PrPC. Over-expression of the three major isoforms of human APP (APP695, APP751 and APP770) in cultured neuronal and non-neuronal cells had no effect on the level of endogenous PrPC. Furthermore, analysis of brain tissue from transgenic mice over-expressing either wild type or familial AD associated mutant human APP revealed unaltered PrPC levels. Knockdown of endogenous APP expression in cells by siRNA or inhibition of γ-secretase activity also had no effect on PrPC levels. Overall, we did not detect any significant difference in the expression of PrPC in any of the cell or animal-based paradigms considered, indicating that the control of cellular PrPC levels by AICD is not as straightforward as previously suggested

Αβ Hinders Nuclear Targeting of AICD and Fe65 in Primary Neuronal Cultures

The intracellular domain of the Alzheimer’s amyloid precursor protein (AICD) has been described as an important player in the transactivation of specific genes. It results from proteolytic processing of the Alzheimer’s amyloid precursor protein (APP), as does the neurotoxic Aβ peptide. Although normally produced in cells, Aβ is typically considered to be a neurotoxic peptide, causing devastating effects. By exposing primary neuronal cultures to relatively low Aβ concentrations, this peptide was shown to affect APP processing. Our findings indicate that APP C-terminal fragments are increased with concomitant reduction in the expression levels of APP itself. AICD nuclear immunoreactivity detected under control conditions was dramatically reduced in response to Aβ exposure. Additionally, intracellular protein levels of Fe65 and GSK3 were also decreased in response to Aβ. APP nuclear signaling is altered by Aβ, affecting not only AICD production but also its nuclear translocation and complex formation with Fe65. In effect, Aβ can trigger a physiological negative feedback mechanism that modulates its own production

Temperature and time stability of whole blood lactate: implications for feasibility of pre-hospital measurement.

Background To determine the time and temperature stability of whole blood lactate using experimental conditions applicable to the out-of-hospital environment. Findings We performed a prospective, clinical laboratory-based study at an academic hospital. Whole blood lactate was obtained by venipuncture from five post-prandial, resting subjects. Blood was stored in lithium heparinized vacutainers in three temperature conditions: 1) room temperature (20°C), 2) wrapped in a portable, instant ice pack (0°C), or 3) wet ice (0°C). Lactate concentrations (mmol/L) were measured at 0, 5, 10, 20, and 30 minutes after sampling, and compared using repeated measures analysis of variance. Mean baseline lactate among resting subjects (N = 5) was 1.24 mmol/L (95%CI: 0.49,1.98 mmol/L). After 30 minutes, lactate concentration increased, on average, by 0.08 mmol/L (95%CI: 0.02,0.13 mmol/L), 0.18 mmol/L (95%CI: 0.07,0.28 mmol/L), and 0.36 mmol/L (95%CI: 0.24,0.47 mmol/L) when stored in wet ice, ice pack, and room temperature, respectively. The increase in lactate was similar in samples wrapped in portable ice pack or stored in wet ice at all time points (p > 0.05), and met criteria for equivalence at 30 minutes. However, lactate measurements from whole blood stored at room temperature were significantly greater, on average, than wet ice or portable ice pack within five and ten minutes, respectively (p < 0.05). Conclusions Whole blood lactate measurements using samples stored in a portable ice pack are similar to wet ice for up to 30 minutes. These conditions are applicable to the out-of-hospital environment, and should inform future studies of pre-hospital measurement of lactate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85785/1/Seymour - Temperature and time stability.pd

Alzheimer's Disease-Linked Mutations in Presenilin-1 Result in a Drastic Loss of Activity in Purified γ-Secretase Complexes

BACKGROUND: Mutations linked to early onset, familial forms of Alzheimer's disease (FAD) are found most frequently in PSEN1, the gene encoding presenilin-1 (PS1). Together with nicastrin (NCT), anterior pharynx-defective protein 1 (APH1), and presenilin enhancer 2 (PEN2), the catalytic subunit PS1 constitutes the core of the γ-secretase complex and contributes to the proteolysis of the amyloid precursor protein (APP) into amyloid-beta (Aβ) peptides. Although there is a growing consensus that FAD-linked PS1 mutations affect Aβ production by enhancing the Aβ1-42/Aβ1-40 ratio, it remains unclear whether and how they affect the generation of APP intracellular domain (AICD). Moreover, controversy exists as to how PS1 mutations exert their effects in different experimental systems, by either increasing Aβ1-42 production, decreasing Aβ1-40 production, or both. Because it could be explained by the heterogeneity in the composition of γ-secretase, we purified to homogeneity complexes made of human NCT, APH1aL, PEN2, and the pathogenic PS1 mutants L166P, ΔE9, or P436Q. METHODOLOGY/PRINCIPAL FINDINGS: We took advantage of a mouse embryonic fibroblast cell line lacking PS1 and PS2 to generate different stable cell lines overexpressing human γ-secretase complexes with different FAD-linked PS1 mutations. A multi-step affinity purification procedure was used to isolate semi-purified or highly purified γ-secretase complexes. The functional characterization of these complexes revealed that all PS1 FAD-linked mutations caused a loss of γ-secretase activity phenotype, in terms of Aβ1-40, Aβ1-42 and APP intracellular domain productions in vitro. CONCLUSION/SIGNIFICANCE: Our data support the view that PS1 mutations lead to a strong γ-secretase loss-of-function phenotype and an increased Aβ1-42/Aβ1-40 ratio, two mechanisms that are potentially involved in the pathogenesis of Alzheimer's disease