Time Series in Linear Programs with Random Right-Hand Sides

Linear programs such that the right-hand sides of their restrictions have the form of multivariate time series may be useful in practical applications. Behavior of the processes formed by the optimal values of the corresponding objective functions is investigated in the following cases: the right-hand side process is (i) a normal white noise; (ii) a normal white noise with a linear trend; (iii) a normal random walk. Some basic probability characteristics of such processes are calculated explicitly

Confidence Regions for Linear Programs with Random Coefficients

If random values in a linear program with random coefficients can be predicted using previous observations on them one can utilize the appropriate prediction region and construct a confidence interval in which the optimal value of the objective function lies with a given probability (or even construct a confidence region for the optimal decision). It is a new statistical approach based on projection of the observed data into the time period of interest. The results are demonstrated by a numerical example

Square root kalman filter with contaminated observations.

The algorithm of square root Kalman filtering for the case of contaminated observations is described in the paper. This algorithm is suitable for the parallel computer implementation allowing to treat dynamic linear systems with large number of state variables in a robust recursive way.Square root Kalman filter; Robust; Parallel algorithm;

Physics of the Riemann Hypothesis

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics. Here we choose a particular number theoretical function, the Riemann zeta function and examine its influence in the realm of physics and also how physics may be suggestive for the resolution of one of mathematics' most famous unconfirmed conjectures, the Riemann Hypothesis. Does physics hold an essential key to the solution for this more than hundred-year-old problem? In this work we examine numerous models from different branches of physics, from classical mechanics to statistical physics, where this function plays an integral role. We also see how this function is related to quantum chaos and how its pole-structure encodes when particles can undergo Bose-Einstein condensation at low temperature. Throughout these examinations we highlight how physics can perhaps shed light on the Riemann Hypothesis. Naturally, our aim could not be to be comprehensive, rather we focus on the major models and aim to give an informed starting point for the interested Reader.Comment: 27 pages, 9 figure

Computer Simulation of Cellular Patterning Within the Drosophila Pupal Eye

We present a computer simulation and associated experimental validation of assembly of glial-like support cells into the interweaving hexagonal lattice that spans the Drosophila pupal eye. This process of cell movements organizes the ommatidial array into a functional pattern. Unlike earlier simulations that focused on the arrangements of cells within individual ommatidia, here we examine the local movements that lead to large-scale organization of the emerging eye field. Simulations based on our experimental observations of cell adhesion, cell death, and cell movement successfully patterned a tracing of an emerging wild-type pupal eye. Surprisingly, altering cell adhesion had only a mild effect on patterning, contradicting our previous hypothesis that the patterning was primarily the result of preferential adhesion between IRM-class surface proteins. Instead, our simulations highlighted the importance of programmed cell death (PCD) as well as a previously unappreciated variable: the expansion of cells' apical surface areas, which promoted rearrangement of neighboring cells. We tested this prediction experimentally by preventing expansion in the apical area of individual cells: patterning was disrupted in a manner predicted by our simulations. Our work demonstrates the value of combining computer simulation with in vivo experiments to uncover novel mechanisms that are perpetuated throughout the eye field. It also demonstrates the utility of the Glazier–Graner–Hogeweg model (GGH) for modeling the links between local cellular interactions and emergent properties of developing epithelia as well as predicting unanticipated results in vivo

Conjectures on exact solution of three - dimensional (3D) simple orthorhombic Ising lattices

We report the conjectures on the three-dimensional (3D) Ising model on simple orthorhombic lattices, together with the details of calculations for a putative exact solution. Two conjectures, an additional rotation in the fourth curled-up dimension and the weight factors on the eigenvectors, are proposed to serve as a boundary condition to deal with the topologic problem of the 3D Ising model. The partition function of the 3D simple orthorhombic Ising model is evaluated by spinor analysis, by employing these conjectures. Based on the validity of the conjectures, the critical temperature of the simple orthorhombic Ising lattices could be determined by the relation of KK* = KK' + KK'' + K'K'' or sinh 2K sinh 2(K' + K'' + K'K''/K) = 1. For a simple cubic Ising lattice, the critical point is putatively determined to locate exactly at the golden ratio xc = exp(-2Kc) = (sq(5) - 1)/2, as derived from K* = 3K or sinh 2K sinh 6K = 1. If the conjectures would be true, the specific heat of the simple orthorhombic Ising system would show a logarithmic singularity at the critical point of the phase transition. The spontaneous magnetization and the spin correlation functions of the simple orthorhombic Ising ferromagnet are derived explicitly. The putative critical exponents derived explicitly for the simple orthorhombic Ising lattices are alpha = 0, beta = 3/8, gamma = 5/4, delta = 13/3, eta = 1/8 and nu = 2/3, showing the universality behavior and satisfying the scaling laws. The cooperative phenomena near the critical point are studied and the results obtained based on the conjectures are compared with those of the approximation methods and the experimental findings. The 3D to 2D crossover phenomenon differs with the 2D to 1D crossover phenomenon and there is a gradual crossover of the exponents from the 3D values to the 2D ones.Comment: 176 pages, 4 figure