Abstract:
Breast cancer mortality rates across the entire population in the USA have remained almost unchanged since 1970 [1]. In terms of numbers, it is estimated that 43 300 women died of breast cancer in the USA in 1999 [2]. Those who succumbed to this disease did so as a consequence of metastatic dissemination or the treatment of metastasis. A large percentage of these women were treated with cytotoxic chemotherapy, with drugs that are demonstrated to be effective against breast carcinoma cells both in vitro and in vivo. Nevertheless, despite being treated with the optimal doses at the optimal schedule, a significant percentage of women will relapse and die. For example, recurrence-free and survival rates at 10 years for women receiving polychemotherapy, for all ages, as estimated in the Oxford Overview, were 44 and 51.3%, respectively [3].This leads us to ask several questions. First, why are these treatments unable to cure a large percentage of women? Is it the result of cells that are resistant, either kinetically or by means of clonal evolution, to the drugs? Is it a problem of inefficient delivery to the tumor cells or a problem that pertains to the tumor microenvironment? A second question, undoubtedly related to the first set of questions, is why does breast cancer continue to recur up to 20 years after treatment of the primary tumor [4,5,6,7,8,9,10].One discipline that can be helpful in answering the questions posed above is mathematical modeling. It has been observed that trial and error manipulation of cancer treatment can be an inefficient method of understanding and developing treatment strategies [11,12**]. The use of mathematical models can aid researchers by explaining why some strategies fail; by suggesting refinements to current clinical approaches; and, finally, by suggesting alternative treatment strategies based on mathematical models that are derived from both known and hypothesized physiologic phenomena. Furthermore, many variations in the alternativ

Abstract:
For each r, 0 <= r <= m, it is presented the class of quaternary linear codes LRM(r,m) whose images under the Gray map are binary codes with parameters of Reed-Muller RM(r,m) code of order r.

Scientific data concerning the impact of emotional stress to human genomic instability very seldom describes in literature. For many scientists this connection is not supposed to be obvious, although oncologists and psychologists know that a prolonged state of heightened emotional tension is fraught with serious problems for the nervous-immune-endocrine system of the or-ganism. Moreover, oncologists know that cancer is often the result of resentment and loneliness. At the same time, the role of genome instability in processes of tumor induction and progression is proved very correctly. In the report will be paying attention to 3 aspects of human life in context of emotional stress expression and its connection with genomic instability: envi-ronmental pollution, genomic predisposes, ethic and social-economic problems. The report will contain data from literature and results of own research directed to the analyzing the impact of the degree of emotional stress expression on the children’s and adults’ genomic instability. Special attention will be paid to the investigation how emotional state of parents and teachers im-pact on young children’s genomic instability. Methods. For evaluation of stress expression levels we used the complex of standard psychological tests: questionnaires— for adults and 8-coloured M. Luscher’s test—for children. Estimation of genomic instability was carried out in blood cultures by test on chromosome aberration and micronuclei test with Cytochalasin B. Alteration of biochemical indices were detected by standard methods.

Abstract:
The utility of the extensible systematic force field (ESFF) was tested for copper(II) binding to a 34-amino-acid Cu(II) peptide, which includes five histidine residues and is the putative copper-binding site of lysyl oxidase. To improve computational efficiency, distance geometry calculations were used to constrain all combinations of three histidine ligands to be within bonding distance of the copper and the best results were utilized as starting structures for the ESFF computations. All likely copper geometries were modeled, but the results showed only a small dependence on the geometrical model in that all resulted in a distorted square pyramidal geometry about the copper, some of the imidazole rings were poorly oriented for ligation to the Cu(II), and the copper-nitrogen bond distances were too long. The results suggest that ESFF should be used with caution for Cu(II) complexes where the copper-ligand bonds have significant covalency and when the ligands are not geometrically constrained to be planar. 1. Introduction Molecular modeling of peptides and proteins interacting with transition-metal ions has the promise of elucidating a wide variety of biophysical phenomena. Such simulations can help establish both the native structure and reaction paths of metalloproteins and explain the roles of metal ions in protein folding and stability [1]. However, the effectiveness of such simulations depends critically on the availability of accurate and computationally reliable force fields for metal ions interacting with proteins. The classical force fields in common use for structure determination using NMR or other internuclear distance data are designed and parameterized for proteins, nucleic acids, and carbohydrates and thus are not optimal for systems with associated metal ions. The extensible systematic force field (ESFF) [2] attempts to provide the widest possible coverage of the periodic table including transition metals with reasonable accuracy and has been successfully used to model several proteins containing metals such as sodium, zinc, iron, and cobalt [2–5]. However only a few studies have been reported for Cu(II) compounds, most of which had severely constrained ligand geometries [3, 4, 6], and ESFF has been used for very few copper-containing proteins or peptides [6–8]. We recently modeled the copper-binding site of lysyl oxidase using a 34-residue peptide homologous to the putative copper-binding region of the enzyme [9] and we now present the results of ESFF computations to model the structure of the copper peptide both to help clarify the

Abstract:
We introduce sum-frequency generation (SFG) as an effective physical two-photon detector for high power two-mode squeezed coherent states with arbitrary frequency separation, as produced by parametric oscillators well above the threshold. Using a formalism of "collective modes", we describe both two-mode squeezing and degenerate squeezing on equal footing and derive simple relations between the input degree of squeezing and the measured SFG quadrature noise. We compare the proposed SFG detection to standard homodyne measurement, and show advantages in robustness to detection inefficiency (loss of SFG photons) and acceptance bandwidth.

Abstract:
A trivial upper bound on the size k of an arc in an r-net is $k leq r + 1$. It has been known for about 20 years that if the r-net is Desarguesian and has odd order, then the case $k = r + 1$ cannot occur, and $k geq r - 1$ implies that the arc is contained in a conic. In this paper, we show that actually the same must hold provided that the difference $r - k$ does not exceed $sqrt{k/18}$. Moreover, it is proved that the same assumption ensures that the arc can be extended to an oval of the net.

Abstract:
There are many ways of calculating photon statistics in quantum optics in general and single molecule spectroscopy in particular such as the generating function method, the quantum jump approach or time ordering methods. In this paper starting with the optical Bloch equation, within the paths interpretation of Zoller, Marte and Walls we obtain the photon statistics from a sequence of laser pulses expressed by means of quantum trajectories. We find general expressions for Pn(t) - the probability of emitting n photons up to time t, discuss several consequences and show that the interpretation of the quantum trajectories (i) emphasizes contribution to the photon statistics of the coherence paths accumulated in the delay interval between the pulses and (ii) allows simple classification of the terms negligible under certain physical constraints . Applying this method to the concrete example of two square laser pulses we find the probabilities of emitting 0,1 and 2 photons, examine several limiting cases and investigate the upper and lower bounds of P0(t), P1(t) and P2(t) for a sequence of two strong pulses in the limit of long measurement times. Implication to single molecule non-linear spectroscopy and theory of pairs of photons on demand are discussed briefly.

Abstract:
In our modeling of the long-term carbon cycle we find potential multiple steady-states in Phanerozoic climates. We include the effects of biotic enhancement of weathering on land, organic carbon burial, oxidation of reduced organic carbon in terrestrial sediments and the variation of biotic productivity with temperature, finding a second stable steady-state appearing between 20 and 50 oC. The very warm early Triassic climate as well as an oceanic anoxic event in the late Cretaceous may be the potential candidates for an upper temperature steady-state. Given our results, the anthropogenic driven rise of atmospheric carbon dioxide could potentially push the climate into tipping points to a modestly higher temperature steady-state, instead of relaxing back to pre-anthropogenic conditions.

Abstract:
We consider the two-level system approximation of a single emitter driven by a continuous laser pump and simultaneously coupled to the electromagnetic vacuum and to a thermal reservoir beyond the Markovian approximation. We discuss the connection between a rigorous microscopic theory and the phenomenological spectral diffusion approach, used to model the interaction of the emitter with the thermal bath, and obtained analytic expressions relating the thermal correlation function to the single emitter photon statistics.