Convex analysis in groups and semigroups: a sampler

Mathematical Programming - We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and...     

Functions that have read‐twice constant width branching programs are not necessarily testable

We construct a property on 0/1‐strings that has a representation by a collection of width‐3 read‐twice oblivious branching programs, but for which any two‐sided ?‐testing algorithm must query at least Ω(n^δ) many queries for some fixed ? and δ. This shows that Newman's result [Testing of functions that have small width branching programs, SIAM J Comput 31 (2002), 1557–1570] cannot be generalized to read‐k‐times functions for k > 1. In addition, we exhibit a property that has also a representation by a CNF formula of constant clause size. Hence, the nontestability results extend to properties that in addition have small (constant size) 0‐witnesses. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

A Constructive Inversion Framework for Twisted Convolution

In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be interpreted as another twisted convolution on a finite cyclic group. In analogy with the twisted convolution of finite discrete signals, we derive an anti-homomorphism between the sequence space and a suitable matrix algebra which preserves the algebraic structure. In this way, the problem reduces to the analysis of finite matrices whose entries are sequences supported on corresponding cosets. The invertibility condition then follows from Cramer’s rule and Wiener’s lemma for this special class of matrices. The problem results from a well known approach of studying the invertibility properties of the Gabor frame operator in the rational case. The presented approach gives further insights into Gabor frames. In particular, it can be applied for both the continuous (on \Bbb R^d{\Bbb R}^d ) and the finite discrete setting. In the latter case, we obtain algorithmic schemes for directly computing the inverse of Gabor frame-type matrices equivalent to those known in the literature.     

Spectroscopic Study of the Interaction of Styrylcyanine Dyes Sbo,Sil and Their Derivatives with Bovine Serum Albumin

The spectral-luminescent characteristics of newly synthesized styrylcyanine dyes on the base of dyes Sbo ((E)-2-(4-(dimethylamino)styryl)-3-methylbenzo[d]oxazol-3-ium iodide) and Sil ((E)-2-(4-(dimethylamino)styryl)-1,3,3-trimethyl-3H-indolium perchlorate) in aqueous solutions without and in the presence of bovine serum albumin (BSA) were studied. It was established that the absorption spectra of dyes Tol-6, Dbo-10 and Dil-10 with increasing amount of BSA appear new bands with λ_max = 505 nm, λ_max = 512 nm and λ_max = 566 nm, respectively, whose intensity increases in proportion to the amount of albumin. The intensity of the glow of the main band of fluorescence in the presence of BSA sharply increases. The binding constant (K) and the number of binding sites (N) of studied dyes with BSA were determined. The dependence of binding constants with BSA on the dipole moment of dye molecules was determined, which indicates that besides electrostatic forces of attraction between molecules styrylcyanine dyes with BSA, hydrophobic interactions are essential.     

Laser-based large detection area speed measurement methods and systems

In this paper, the development principles of laser-based large detection area speed measurement systems are considered. The optical schemes of the single light barrier–single photodetector, double light barriers–single photodetector and double light barriers–double photodetectors are developed and investigated. Advantages and disadvantages of these schemes are explained. Important proposals are given for the development of the optical schemes. A double light barriers–double photodetectors system measuring the bullet speed is developed. Equations describing the errors occurring in the system are derived.     

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.     

Prognostic Value of Immunohistochemical Markers for Locally Advanced Rectal Cancer

The aim of this study is to reveal the potential roles of apoptosis markers (Bcl2 and p53), proliferation markers (Ki-67 and CyclD1), and the neuroendocrine marker Chromogranin A as markers for the radioresistance of rectal cancer. Statistically significant differences were found in the expression of p53, Ki-67, and Chromogranin A in groups of patients with and without a favorable prognosis after radiotherapy. The survival analysis revealed that the marker of neuroendocrine differentiation, Chromogranin A, also demonstrated a high prognostic significance, indicating a poor prognosis. Markers of proliferation and apoptosis had no prognostic value for patients who received preoperative radiotherapy. Higher Chromogranin A values were predictors of poor prognosis. The results obtained from studying the Chromogranin A expression suggest that the secretion of biologically active substances by neuroendocrine cells causes an increase in tumor aggressiveness.     

Argon,krypton and xenon adsorption coefficients on various activated carbons under dynamic conditions

Journal of Radioanalytical and Nuclear Chemistry - Currently, a method based on the radioactive isotopes retention of argon, krypton and xenon on an adsorption column with activated carbon is...