The ham-sandwich theorem states that, given d ≥ 2 measures in R, it is possible to divide all of them in half with a single (d − 1)-dimensional hyperplane. We study an orthogonal version of the ham-sandwich theorem and define an orthogonal cut using at most d hyperplanes orthogonal to coordinate axes. For example, a hyperplane orthogonal to a coordinate axis and the boundary of an orthant are o...

Coordinate systems are a central issue in computational neuroscience: are they explicitly represented at some reductive level of brain function, and if so, are they only trivial products of associated anatomic geometries? This investigation examined these questions in the neural network that holds eye position, the so-called oculomotor integrator. Since neural activity in the integrator is beha...

A coordinate frame in an n-dimensional space is defined by n mutually orthogonal unit vectors. In particular, for a two-dimensional (2D) space, i.e., n = 2, a coordinate frame is defined by an X axis and a Y axis with these two axes being orthogonal to each other. The intersection between the X axis and the Y axis is the origin of the coordinate frame. For a three-dimensional (3D) space, i.e., ...

Clustering has been used as a tool for understanding the content of large text document sets. As the volume of stored data has increased, so has the need for tools to understand output from clustering algorithms. We developed a new visual interface to meet this demand. Our interface helps non-technical users understand documents and clusters in massive databases (e.g., document content, cluster...

Abstract The different three-phase circuit coordinate transformation matrixes were given in relevant literatures, which might cause some difficulties to understand and apply the coordinate transformation. The paper presented a general expression of the coordinate transformation matrixes in three-phase circuit and pointed out that the coordinate transformation matrixes having different specific ...

The free energy profile obtained from the WHAM procedure is a function of the chosen reaction coordinate, with all other degress of freedom integrated out. This implies that these orthogonal degrees of freedom are adequately sampled in each window, which might require much longer timescales than typical window lengths if they feature local minima separated by high free energy barriers. In addit...

In this letter, we provide an asymptotic error rate performance evaluation of space-time block codes from coordinate interleaved orthogonal designs (STBCs-CIODs), especially in shadowed Rayleigh fading channels. By evaluating a simplified probability density function (PDF) of Rayleigh and Rayleigh-lognormal channels affecting the STBC-CIOD system, we derive an accurate closed-form approximation...

This work presents a systematic method to successively minimize the state complexity of the self-dual lattices (in the sense that each section of the trellis has the minimum possible number of states xing its preceding coordinates). This is based on representing the lattice on an orthogonal coordinate system corresponding to the Gram-Schmidt (GS) vectors of a Korkin-Zolotarev (KZ) reduced basis...

We present discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and a generalized higher-order moment equation of the Boltzmann transport equation for general orthogonal coordinate systems like cylindrical and spherical systems. The use of orthogonal coordinate systems allows to reduce the dimension of the problem from three to two. We give an approximation...