Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904 (2006

Stability of stochastic pricing models under volatility fluctuations

The standard theory of the stochastic models used to value financial derivatives contracts involves models whose input parameters are deterministic functions and often constants. Because of the random nature of the changes in the market prices of the financial instruments, the coefficients of these models are inevitably susceptible to random perturbation from their initial estimates. In this paper we will investigate the behavior of some of the most widely used models when small changes are applied to their volatility component. Starting with the Black-Scholes model for the price of a European call option, we will continue our analysis of the traditional models for pricing American options, Asian options, Barrier options, as well as some of the models for the short term rate of interest. In addition to obtaining convergence results for all of the models, we will examine a method of controlling the deviations in the volatility parameter of the Black-Scholes model and the resulting estimate can be used for further extensions on the topic. Moreover, we will present an example of how to calculate probabilities of unlikely events, using a technique called importance sampling. We will concentrate only on the case of discrete random variables but the same algorithm can be applied to estimate the probabilities of the deviations of the pricing functions of the models under question. The latter is left for future research

Resolution of degree ≤ 6 algebraic equations by genus two theta constants

We adjoin complete first kind Abelian integrals of genus two to solve the general degree six algebraic equation a 0 z 6 + a 1 z 5 + ... + a 6 = 0 by genus two theta constants. Using the same formulas, later we resolve degree five, four and three algebraic equations. We study the monodromy group, which permutes the roots of degree six polynomials

Towards Large Volume Big Divisor D3-D7 "mu-Split Supersymmetry" and Ricci-Flat Swiss-Cheese Metrics, and Dimension-Six Neutrino Mass Operators

We show that it is possible to realize a "mu-split SUSY" scenario [1] in the context of large volume limit of type IIB compactifications on Swiss-Cheese Calabi-Yau's in the presence of a mobile space-time filling D3-brane and a (stack of) D7-brane(s) wrapping the "big" divisor Sigma_B. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy Higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of mu-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the 3-body decays of the gluino into a quark, a squark and a neutralino or Goldstino, as well as 2-body decays of the gluino into either a neutralino or a Goldstino and a gluon. Guided by the geometric Kaehler potential for Sigma_B obtained in [2] based on GLSM techniques, and the Donaldson's algorithm [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in [4] pertaining to our proposed metric for the full Swiss-Cheese Calabi-Yau, but for simplicity of calculation, close to Sigma_B, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the Higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kaehler potential, is suppressed relative to the Weinberg-type dimension-five operators.Comment: v3: an error in the Higgsino content of the neutralino and the consequent estimates of tree-level 3-body and 1-loop 2-body gluino decay (involving the neutralino) widths and lifetimes, corrected; conclusions, qualitatively, unchanged. arXiv admin note: text overlap with arXiv:1105.0365 by other autho

Ultimate Execution Speed of FPGA based Edge Detection: Parallel Addition

Addition is a fundamental integer arithmetic operation in digital image processing. Ultimate execution speed of FPGA based edge detection which uses Gaussian filtering has two parameters: maximum operating frequency and minimum number of clock cycles required to obtain mathematically accurate result. The computational specifics of weighed average function define adding a number of addends in parallel as critical to the concept of achieving ultimate execution speed of FPGA based edge detection. This paper is focused on exploring the capabilities of parallel addition to contribute to the goal of securing a Gaussian filtered pixel every single clock cycle at the maximum operating frequency. Ten Intel (Altera) FPGA families are used in the explorations

Mass-spin relation of black holes obtained by twin high-frequency quasi-periodic oscillations

The paper studies the uniqueness and the monotonicity of the mass-spin relation of black holes the X-ray power density spectra of which contain twin high-frequency quasi-periodic oscillations in 3:2 ratio. It is found that for geodesic models the properties of the mass-spin relation are independent of the observed frequencies, i.e. they are independent of the particular object. Some results are valid for all geodesic models. For concreteness two of the most commonly used models are studied here: the 3 : 1 nonlinear epicyclic resonance model and its Keplerian version