Given an algebraic geometry code CL(D,αP ), the GuruswamiSudan algorithm produces a list of all codewords in CL(D,αP ) within a specified distance of a received word. The initialization step in the algorithm involves parameter choices that bound the degree of the interpolating polynomial and hence the length of the list of codewords generated. In this paper, we use simple properties of discrimi...

Given an algebraic geometry code CL(D,αP ), the GuruswamiSudan algorithm produces a list of all codewords in CL(D,αP ) within a specified distance of a received word. The initialization step in the algorithm involves parameter choices that bound the degree of the interpolating polynomial and hence the length of the list of codewords generated. In this paper, we use simple properties of discrimi...

Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study expl...

The superfluid phases of helium-3 ((3)He) are predicted to be strongly influenced by mesoscopic confinement. However, mapping out the phase diagram in a confined geometry has been experimentally challenging. We confined a sample of (3)He within a nanofluidic cavity of precisely defined geometry, cooled it, and fingerprinted the order parameter using a sensitive nuclear magnetic resonance spectr...

Statistical geometry furnishes the tool that allows the transfer of results from a lattice with finite lattice parameter to the continuum. Since lattice simulations are simpler than continuum ones, this suggests that larger scale simulations for the continuum might be more effectively carried out on a lattice with finite lattice parameter followed by the indicated transfer. We also show that a ...

The distortion varieties of a given projective variety are parametrized by duplicating coordinates and multiplying them with monomials. We study their degrees and defining equations. Exact formulas are obtained for the case of one-parameter distortions. These are based on Chow polytopes and Gröbner bases. Multi-parameter distortions are studied using tropical geometry. The motivation for distor...

the subject of geometry and proportions has been regarded as an issue which has a close relationship with architecture. since the entire universe, living beings and the human geometry can be seen clearly, that’s why our unconscious essence has accustomed to these proportions whereby reflection of this mentality can be seen in the architect’s hands and thought in the architecture. it can witness...

Parameter walkout of more than 250 power Al0.24Ga0.76As/In0.25Ga0.75As/GaAs double-recessed PHEMTs with different layout geometry and epitaxial structure has been experimentally measured and simulated. The relation between DC, small-signal and large-signal behavior has been recognized. The essential parameters of walkout were defined; their geometry and structural dependence have been derived. ...

A survey of geometry of Bayesian statistics is given. From the viewpoint of differential geometry, a prior distribution in Bayesian statistics is regarded as a volume element on a statistical model. In this paper, properties of Bayesian estimators are studied by applying equiaffine structures of statistical manifolds. In addition, geometry of anomalous statistics is also studied. Deformed expec...