Superspecial Abelian Varieties and the Eichler Basis Problem for Hilbert Modular Forms

Let $p$ be an unramified prime in a totally real field $L$ such that $h^+(L)=1$. Our main result shows that Hilbert modular newforms of parallel weight two for $\Gamma_0(p)$ can be constructed naturally, via classical theta series, from modules of isogenies of superspecial abelian varieties with real multiplication on a Hilbert moduli space. This can be viewed as a geometric reinterpretation of the Eichler Basis Problem for Hilbert modular forms.Comment: to appear in J.N.

Stratifications of Newton polygon strata and Traverso's conjectures for p-divisible groups

The isomorphism number (resp. isogeny cutoff) of a p-divisible group D over an algebraically closed field is the least positive integer m such that D[p^m] determines D up to isomorphism (resp. up to isogeny). We show that these invariants are lower semicontinuous in families of p-divisible groups of constant Newton polygon. Thus they allow refinements of Newton polygon strata. In each isogeny class of p-divisible groups, we determine the maximal value of isogeny cutoffs and give an upper bound for isomorphism numbers, which is shown to be optimal in the isoclinic case. In particular, the latter disproves a conjecture of Traverso. As an application, we answer a question of Zink on the liftability of an endomorphism of D[p^m] to D.Comment: 50 pages, to appear in Annals of Mathematic

Excitation of planetary electromagnetic waves in the inhomogeneous ionosphere

In this paper we develop a new method for the analysis of excitation and propagation of planetary electromagnetic waves (PEMW) in the ionosphere of the Earth. The nonlinear system of equations for PEMW, valid for any height, from D to F regions, including intermediate altitudes between D and E and between E and F regions, is derived. In particular, we have found the system of nonlinear one-fluid MHD equations in the β-plane approximation valid for the ionospheric F region (Aburjania et al., 2003a, 2005). The series expansion in a "small" (relative to the local geomagnetic field) non-stationary magnetic field has been applied only at the last step of the derivation of the equations. The small mechanical vertical displacement of the media is taken into account. We have shown that obtained equations can be reduced to the well-known system with Larichev–Reznik vortex solution in the equatorial region (see e.g. Aburjania et al., 2002). The excitation of planetary electromagnetic waves by different initial perturbations has been investigated numerically. Some means for the PEMW detection and data processing are discussed

A “Push and Slide” Mechanism Allows Sequence-Insensitive Translocation of Secretory Proteins by the SecA ATPase

SummaryIn bacteria, most secretory proteins are translocated across the plasma membrane by the interplay of the SecA ATPase and the SecY channel. How SecA moves a broad range of polypeptide substrates is only poorly understood. Here we show that SecA moves polypeptides through the SecY channel by a “push and slide” mechanism. In its ATP-bound state, SecA interacts through a two-helix finger with a subset of amino acids in a substrate, pushing them into the channel. A polypeptide can also passively slide back and forth when SecA is in the predominant ADP-bound state or when SecA encounters a poorly interacting amino acid in its ATP-bound state. SecA performs multiple rounds of ATP hydrolysis before dissociating from SecY. The proposed push and slide mechanism is supported by a mathematical model and explains how SecA allows translocation of a wide range of polypeptides. This mechanism may also apply to hexameric polypeptide-translocating ATPases

Enhanced inverse bremsstrahlung heating rates in a strong laser field

Test particle studies of electron scattering on ions, in an oscillatory electromagnetic field have shown that standard theoretical assumptions of small angle collisions and phase independent orbits are incorrect for electron trajectories with drift velocities smaller than quiver velocity amplitude. This leads to significant enhancement of the electron energy gain and the inverse bremsstrahlung heating rate in strong laser fields. Nonlinear processes such as Coulomb focusing and correlated collisions of electrons being brought back to the same ion by the oscillatory field are responsible for large angle, head-on scattering processes. The statistical importance of these trajectories has been examined for mono-energetic beam-like, Maxwellian and highly anisotropic electron distribution functions. A new scaling of the inverse bremsstrahlung heating rate with drift velocity and laser intensity is discussed.Comment: 12 pages, 12 figure

Simple Random Sampling-Based Probe Station Selection for Fault Detection in Wireless Sensor Networks

Fault detection for wireless sensor networks (WSNs) has been studied intensively in recent years. Most existing works statically choose the manager nodes as probe stations and probe the network at a fixed frequency. This straightforward solution leads however to several deficiencies. Firstly, by only assigning the fault detection task to the manager node the whole network is out of balance, and this quickly overloads the already heavily burdened manager node, which in turn ultimately shortens the lifetime of the whole network. Secondly, probing with a fixed frequency often generates too much useless network traffic, which results in a waste of the limited network energy. Thirdly, the traditional algorithm for choosing a probing node is too complicated to be used in energy-critical wireless sensor networks. In this paper, we study the distribution characters of the fault nodes in wireless sensor networks, validate the Pareto principle that a small number of clusters contain most of the faults. We then present a Simple Random Sampling-based algorithm to dynamic choose sensor nodes as probe stations. A dynamic adjusting rule for probing frequency is also proposed to reduce the number of useless probing packets. The simulation experiments demonstrate that the algorithm and adjusting rule we present can effectively prolong the lifetime of a wireless sensor network without decreasing the fault detected rate

Analysis of cross-correlations in electroencephalogram signals as an approach to proactive diagnosis of schizophrenia

We apply flicker-noise spectroscopy (FNS), a time series analysis method operating on structure functions and power spectrum estimates, to study the clinical electroencephalogram (EEG) signals recorded in children/adolescents (11 to 14 years of age) with diagnosed schizophrenia-spectrum symptoms at the National Center for Psychiatric Health (NCPH) of the Russian Academy of Medical Sciences. The EEG signals for these subjects were compared with the signals for a control sample of chronically depressed children/adolescents. The purpose of the study is to look for diagnostic signs of subjects' susceptibility to schizophrenia in the FNS parameters for specific electrodes and cross-correlations between the signals simultaneously measured at different points on the scalp. Our analysis of EEG signals from scalp-mounted electrodes at locations F3 and F4, which are symmetrically positioned in the left and right frontal areas of cerebral cortex, respectively, demonstrates an essential role of frequency-phase synchronization, a phenomenon representing specific correlations between the characteristic frequencies and phases of excitations in the brain. We introduce quantitative measures of frequency-phase synchronization and systematize the values of FNS parameters for the EEG data. The comparison of our results with the medical diagnoses for 84 subjects performed at NCPH makes it possible to group the EEG signals into 4 categories corresponding to different risk levels of subjects' susceptibility to schizophrenia. We suggest that the introduced quantitative characteristics and classification of cross-correlations may be used for the diagnosis of schizophrenia at the early stages of its development.Comment: 36 pages, 6 figures, 2 tables; to be published in "Physica A

Friction and wear properties of nano-Si<inf>3</inf>N<inf>4</inf>/nano-SiC composite under nanolubricated conditions

Friction and wear properties of nano-Si3N4/nano-SiC composite were studied under nanolubricated conditions. Mineral oil mixed with nanoparticles of diamond was used as lubricant. A friction coefficient of 0.043 and a wear coefficient of 4.2×10-7 were obtained for nano-Si3N4/nano-SiC composite under normal load of 600 N with mineral oil + 0.5 wt% nanodiamond, whereas a friction coefficient of 0.077 and a wear coefficient of 10.3×10-7 were obtained for nano-Si3N4/nano-SiC composite under normal load of 600 N with mineral oil. 3D surface profilometer was used to study the surface morphology of wear scars. Scanning electron microscopy (SEM) and X-ray diffraction (XRD) studies were conducted to illustrate reduction in friction and wear

Revisiting Date and Party Hubs: Novel Approaches to Role Assignment in Protein Interaction Networks

The idea of 'date' and 'party' hubs has been influential in the study of protein-protein interaction networks. Date hubs display low co-expression with their partners, whilst party hubs have high co-expression. It was proposed that party hubs are local coordinators whereas date hubs are global connectors. Here we show that the reported importance of date hubs to network connectivity can in fact be attributed to a tiny subset of them. Crucially, these few, extremely central, hubs do not display particularly low expression correlation, undermining the idea of a link between this quantity and hub function. The date/party distinction was originally motivated by an approximately bimodal distribution of hub co-expression; we show that this feature is not always robust to methodological changes. Additionally, topological properties of hubs do not in general correlate with co-expression. Thus, we suggest that a date/party dichotomy is not meaningful and it might be more useful to conceive of roles for protein-protein interactions rather than individual proteins. We find significant correlations between interaction centrality and the functional similarity of the interacting proteins.Comment: 27 pages, 5 main figures, 4 supplementary figure