Revisiting two strong approximation results of Dudley and Philipp

We demonstrate the strength of a coupling derived from a Gaussian approximation of Zaitsev (1987a) by revisiting two strong approximation results for the empirical process of Dudley and Philipp (1983), and using the coupling to derive extended and refined versions of them.Comment: Published at http://dx.doi.org/10.1214/074921706000000824 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Sum-of-squares lower bounds for planted clique

Finding cliques in random graphs and the closely related "planted" clique variant, where a clique of size k is planted in a random G(n, 1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for k ~ sqrt(n). In this paper we study the complexity of the planted clique problem under algorithms from the Sum-of-squares hierarchy. We prove the first average case lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to logarithmic factors). Thus, for any constant number of rounds planted cliques of size n^{o(1)} cannot be found by this powerful class of algorithms. This is shown via an integrability gap for the natural formulation of maximum clique problem on random graphs for SOS and Lasserre hierarchies, which in turn follow from degree lower bounds for the Positivestellensatz proof system. We follow the usual recipe for such proofs. First, we introduce a natural "dual certificate" (also known as a "vector-solution" or "pseudo-expectation") for the given system of polynomial equations representing the problem for every fixed input graph. Then we show that the matrix associated with this dual certificate is PSD (positive semi-definite) with high probability over the choice of the input graph.This requires the use of certain tools. One is the theory of association schemes, and in particular the eigenspaces and eigenvalues of the Johnson scheme. Another is a combinatorial method we develop to compute (via traces) norm bounds for certain random matrices whose entries are highly dependent; we hope this method will be useful elsewhere

Phonon and crystal field excitations in geometrically frustrated rare earth titanates

The phonon and crystal field excitations in several rare earth titanate pyrochlores are investigated. Magnetic measurements on single crystals of Gd2Ti2O7, Tb2Ti2O7, Dy2Ti2O7 and Ho2Ti2O7 are used for characterization, while Raman spectroscopy and terahertz time domain spectroscopy are employed to probe the excitations of the materials. The lattice excitations are found to be analogous across the compounds over the whole temperature range investigated (295-4 K). The resulting full phononic characterization of the R2Ti2O7 pyrochlore structure is then used to identify crystal field excitations observed in the materials. Several crystal field excitations have been observed in Tb2Ti2O7 in Raman spectroscopy for the first time, among which all of the previously reported excitations. The presence of additional crystal field excitations, however, suggests the presence of two inequivalent Tb3+ sites in the low temperature structure. Furthermore, the crystal field level at approximately 13 cm-1 is found to be both Raman and dipole active, indicating broken inversion symmetry in the system and thus undermining its current symmetry interpretation. In addition, evidence is found for a significant crystal field-phonon coupling in Tb2Ti2O7. These findings call for a careful reassessment of the low temperature structure of Tb2Ti2O7, which may serve to improve its theoretical understanding.Comment: 13 pages, 7 figure

Dynamin-related protein 1 is required for normal mitochondrial bioenergetic and synaptic function in CA1 hippocampal neurons.

Disrupting particular mitochondrial fission and fusion proteins leads to the death of specific neuronal populations; however, the normal functions of mitochondrial fission in neurons are poorly understood, especially in vivo, which limits the understanding of mitochondrial changes in disease. Altered activity of the central mitochondrial fission protein dynamin-related protein 1 (Drp1) may contribute to the pathophysiology of several neurologic diseases. To study Drp1 in a neuronal population affected by Alzheimer's disease (AD), stroke, and seizure disorders, we postnatally deleted Drp1 from CA1 and other forebrain neurons in mice (CamKII-Cre, Drp1lox/lox (Drp1cKO)). Although most CA1 neurons survived for more than 1 year, their synaptic transmission was impaired, and Drp1cKO mice had impaired memory. In Drp1cKO cell bodies, we observed marked mitochondrial swelling but no change in the number of mitochondria in individual synaptic terminals. Using ATP FRET sensors, we found that cultured neurons lacking Drp1 (Drp1KO) could not maintain normal levels of mitochondrial-derived ATP when energy consumption was increased by neural activity. These deficits occurred specifically at the nerve terminal, but not the cell body, and were sufficient to impair synaptic vesicle cycling. Although Drp1KO increased the distance between axonal mitochondria, mitochondrial-derived ATP still decreased similarly in Drp1KO boutons with and without mitochondria. This indicates that mitochondrial-derived ATP is rapidly dispersed in Drp1KO axons, and that the deficits in axonal bioenergetics and function are not caused by regional energy gradients. Instead, loss of Drp1 compromises the intrinsic bioenergetic function of axonal mitochondria, thus revealing a mechanism by which disrupting mitochondrial dynamics can cause dysfunction of axons

Neonatal treatment of CINCA syndrome.

ABSTRACT: Chronic Infantile Neurological Cutaneous Articular (CINCA) syndrome, also called Neonatal Onset Multisystem Inflammatory Disease (NOMID) is a chronic disease with early onset affecting mainly the central nervous system, bones and joints and may lead to permanent damage. We report two preterm infants with severe CINCA syndrome treated by anti-interleukin-1 in the neonatal period, although, so far, no experience with this treatment in infants younger than three months of age has been reported. A review of the literature was performed with focus on treatment and neonatal features of CINCA syndrome. CASE REPORT: Two cases suspected to have CINCA syndrome were put on treatment with anakinra in the early neonatal period due to severe clinical presentation. We observed a rapid and persistent decline of clinical signs and systemic inflammation and good drug tolerance. Diagnosis was confirmed in both cases by mutations in the NLRP3/CIAS1-gene coding for cryopyrin. As particular neonatal clinical signs polyhydramnios and endocardial overgrowth are to be mentioned. CONCLUSION: We strongly suggest that specific treatment targeting interleukin-1 activity should be started early. Being well tolerated, it can be introduced already in neonates presenting clinical signs of severe CINCA syndrome in order to rapidly control inflammation and to prevent life-long disability

Scavenging of aerosol particles by rain in a cloud resolving model

International audienceWe describe a below-cloud scavenging module of aerosol particles by raindrops for use in a three-dimensional mesoscale cloud resolving model. The rate of particle removal is computed by integrating the scavenging efficiency over the aerosol particle and the drop size distributions. Here the numerical integration is performed accurately with a Gauss quadrature algorithm. The efficiency of the scavenging module is partially confirmed with experimental data. More interestingly, it is illustrated by two numerical experiments: the simulation of a forced convective circulation in a tropical cloudy boundary layer and a two-dimensional simulation of an African squall line. The results show a very selective wet removal of the aerosol particles which clearly depends on the mode radius, the width and the vertical profile of concentration. Furthermore, the squall line case shows the importance of resolving internal circulations to redistribute layers of aerosol particles in order to improve estimates of particle removal by below-cloud scavenging

Outbreak of West Nile virus causing severe neurological involvement in children, Nuba Mountains, Sudan, 2002.

An atypical outbreak of West Nile virus (WNV) occurred in Ngorban County, South Kordophan, Sudan, from May to August 2002. We investigated the epidemic and conducted a case-control study in the village of Limon. Blood samples were obtained for cases and controls. Patients with obvious sequelae underwent cerebrospinal fluid (CSF) sampling as well. We used enzyme-linked immunosorbent assay (ELISA) and neutralization tests for laboratory diagnosis and identified 31 cases with encephalitis, four of whom died. Median age was 36 months. Bivariate analysis did not reveal any significant association with the risk factors investigated. Laboratory analysis confirmed presence of IgM antibodies caused by WNV in eight of 13 cases, indicative of recent viral infection. The unique aspects of the WNW outbreak in Sudan, i.e. disease occurrence solely among children and the clinical domination of encephalitis, involving severe neurological sequelae, demonstrate the continuing evolution of WNV virulence. The spread of such a virus to other countries or continents cannot be excluded

Complexation of lanthanides, actinides and transition metal cations with a 6-(1,2,4-triazin-3-yl)-2,2’:6’,2’’-terpyridine ligand: implications for actinide(III) /lanthanide(III) partitioning

The quadridentate N-heterocyclic ligand 6-(5,5,8,8-tetramethyl-5,6,7,8-tetrahydro-1,2,4-benzotriazin-3-yl)-2,2’:6’,2’’-terpyridine (CyMe4-hemi-BTBP) has been synthesized and its interactions with Am(III), U(VI), Ln(III) and some transition metal cations have been evaluated by X-ray crystallographic analysis, Am(III)/Eu(III) solvent extraction experiments, UV absorption spectrophotometry, NMR studies and ESI-MS. Structures of the 1:1 complexes with Eu(III), Ce(III) and the linear uranyl (UO22+) ion were obtained by X-ray crystallographic analysis, and showed similar coordination behavior to related BTBP complexes. In methanol, the stability constants of the Ln(III) complexes are slightly lower than those of the analogous quadridentate bis-triazine BTBP ligands, while the stability constant for the Yb(III) complex is higher. 1H NMR titrations and ESI-MS with lanthanide nitrates showed that the ligand forms only 1:1 complexes with Eu(III), Ce(III) and Yb(III), while both 1:1 and 1:2 complexes were formed with La(III) and Y(III) in acetonitrile. A mixture of isomeric chiral 2:2 helical complexes was formed with Cu(I), with a slight preference (1.4:1) for a single directional isomer. In contrast, a 1:1 complex was observed with the larger Ag(I) ion. The ligand was unable to extract Am(III) or Eu(III) from nitric acid solutions into 1-octanol, except in the presence of a synergist at low acidity. The results show that the presence of two outer 1,2,4-triazine rings is required for the efficient extraction and separation of An(III) from Ln(III) by quadridentate N-donor ligand

18 Nov 2013 In situ detection of electrified aerosols in the upper troposphere and stratosphere

Electrified aerosols have been observed in the lower troposphere and in the mesosphere, but have never been detected in the stratosphere and upper troposphere. We present measurements of aerosols obtained during a balloon flight to an altitude of 24 km. The measurements were per- formed with an improved version of the Stratospheric and Tropospheric Aerosol Counter (STAC) aerosol counter dedi- cated to the search for charged aerosols. It is found that most of the aerosols are charged in the upper troposphere for altitudes below 10 km and in the stratosphere for altitudes above 20 km. Conversely, the aerosols seem to be uncharged between 10 km and 20 km. Model calculations are used to quantify the electrification of the aerosols with a stratospheric aerosol–ion model. The percentages of charged aerosols obtained with model calculations are in excellent agreement with the observations below 10 km and above 20 km. However, the model cannot reproduce the absence of electrification found in the lower stratosphere, as the processes leading to neutralisation in this altitude range are unknown. The presence of sporadic transient layers of electrified aerosol in the upper troposphere and in the stratosphere could have significant implications for sprite formatio

Suppression of growth by multiplicative white noise in a parametric resonant system

The author studied the growth of the amplitude in a Mathieu-like equation with multiplicative white noise. The approximate value of the exponent at the extremum on parametric resonance regions was obtained theoretically by introducing the width of time interval, and the exponents were calculated numerically by solving the stochastic differential equations by a symplectic numerical method. The Mathieu-like equation contains a parameter $\alpha$ that is determined by the intensity of noise and the strength of the coupling between the variable and the noise. The value of $\alpha$ was restricted not to be negative without loss of generality. It was shown that the exponent decreases with $\alpha$, reaches a minimum and increases after that. It was also found that the exponent as a function of $\alpha$ has only one minimum at $\alpha \neq 0$ on parametric resonance regions of $\alpha = 0$. This minimum value is obtained theoretically and numerically. The existence of the minimum at $\alpha \neq 0$ indicates the suppression of the growth by multiplicative white noise.Comment: The title and the description in the manuscript are change