Understanding biological functions through molecular networks

The completion of genome sequences and subsequent high-throughput mapping of molecular networks have allowed us to study biology from the network perspective. Experimental, statistical and mathematical modeling approaches have been employed to study the structure, function and dynamics of molecular networks, and begin to reveal important links of various network properties to the functions of the biological systems. In agreement with these functional links, evolutionary selection of a network is apparently based on the function, rather than directly on the structure of the network. Dynamic modularity is one of the prominent features of molecular networks. Taking advantage of such a feature may simplify network-based biological studies through construction of process-specific modular networks and provide functional and mechanistic insights linking genotypic variations to complex traits or diseases, which is likely to be a key approach in the next wave of understanding complex human diseases. With the development of ready-to-use network analysis and modeling tools the networks approaches will be infused into everyday biological research in the near future.

The Extension of Cauchy Integral Formula to the Boundaries of Fundamental Domains

The Cauchy integral formula expresses the value of a function f(z), which is analytic in a simply connected domain D, at any point z0 interior to a simple closed contour C situated in D in terms of the values of on C. We deal in this paper with the question whether C can be the boundary ∂Ω of a fundamental domain Ω of f(z). At the first look the answer appears to be negative since ∂Ω contains singular points of the function and it can be unbounded. However, the extension of Cauchy integral formula to some of these unbounded curves, respectively arcs ending in singular points of f(z) is possible due to the fact that they can be obtained at the limit as r → ∞ of some bounded curves contained in the pre-image of the circle |z| = r and of some circles |z-a| = 1/r for which the formula is valid.

Dark Current Compensation and Sensitivity Adjustment on Gallium Arsenide Linear Array Detector for X-Ray Imaging

For the last several years, the linear array x-ray detector for x-ray imaging with gallium arsenide direct conversion sensitive elements has been developed and tested at the In-stitute for High Energy Physics. The array consists of 16 sensitive modules. Each module has 128 gallium arsenide (GaAs) sensitive elements with 200 μm pitch. Current article describes two key program procedures of initial dark current compensation of each sensitive element in the linear array, and sensitivity adjustment for alignment of strip pattern in the raw image data. As a part of evaluation process a modular transfer function (MTF) was measured with the slanted sharp-edge object under RQA5 technique as it described in the International Electrotechnical Commission 62220-1 standard (high voltage 70 kVp, additional aluminium filter 21 mm) for images with compensated dark currents and adjusted sensitivity of detector elements. The 10% level of the calculated MTF function has spatial resolution within 2 - 3 pair of lines per mm for both vertical and horizontal orientation.

Functional modular organization unfolded by chimera-like dynamics in a large-scale brain network model

The brain is organized as a complex network architecture, which can be mapped into structural(SC) and functional connectivity(FC) by advanced neuroimaging techniques. Achievements in brain network research have revealed that modularity is a universal trait in brain networks and may be vital for cognitive segregation and integration. Large-scale brain network modeling is a promising computational approach to combine neuroimaging data with generative rules for brain dynamics. Recently, it has been proposed that chimera states, a type of dynamics referring to the coexistence of coherent and incoherent participants, have traits in common with cognitive functions like segregated and integrated brain processing. Previous studies have reported the existence of chimera-like dynamics in large-scale brain network models, whereas they did not account for the relationship between chimeralike dynamics and corresponding functional modular organizations of the brain network. By specifying qualitatively different network dynamics in an anatomically-constrained brain network model, we compare the different modular organizations of FC unfolded by network dynamics. Our simulations reveal that chimera-like dynamics support a meaningful pattern of functional modular organization, which promotes a diversity of node roles with a distributed pattern of functional cartography. The distinct node roles in modular FC are also found to occur with a spatial preference in speciflc brain regions, and, to some extent, reflect the underlying structure constraints. Our results support the view that chimera-like dynamics is a functionally meaningful scenario that may play a fundamental role in the segregation and integration of brain functioning.

p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.

Theta Function and Hilbert Modular Forms of Half Integral Weight

In this paper a kind of theta function is constructed by means of spherical function. And we also obtain some Hilbert modular forms of half integral weight.

Ramanujan's cubic transformation and generalized modular equation

We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.