Related papers: Frontiers of sphere recognition in practice
We consider ``brane-universes'', where matter is confined to four-dimensional hypersurfaces (three-branes) whereas one extra compact dimension is felt by gravity only. We show that the cosmology of such branes is definitely different from…
Psychophysical studies suggest that face recognition takes place in a narrow band of low spatial frequencies (``critical band''). Here, we examined the recognition performance of an artificial face recognition system as a function of the…
Photon spheres have attracted considerable interest in the studies of black holes and other astrophysical objects. For different categories of spacetimes (or gravitational sources), the existence of photon spheres and their distributions…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
We study the cosmology of models with four space and one time dimension where our universe is a 3-brane and report a few results which extend existing work in several directions. Assuming a stable fifth dimension, we obtain a solution for…
In this paper, we introduce concepts of separable functions in balls and in the whole space, and develop a new method to investigate the qualitative properties of separable functions. We first study the axial symmetry and monotonicity of…
Tackling unsupervised source separation jointly with an additional inverse problem such as deconvolution is central for the analysis of multi-wavelength data. This becomes highly challenging when applied to large data sampled on the sphere…
A kind of fixed-point problem in the area of discrete tomography is proposed and investigated. Our chief concern in this paper is the case of square windows in the plane. Dealing with the arrays which are bounded, of polynomial growth, and…
We discuss a general technique that can be used to form a differentiable bound on the optima of non-differentiable or discrete objective functions. We form a unified description of these methods and consider under which circumstances the…
Many mathematical models utilize limit processes. Continuous functions and the calculus, differential equations and topology, all are based on limits and continuity. However, when we perform measurements and computations, we can achieve…
We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…
Restricted skyline (rskyline) query is widely used in multi-criteria decision making. It generalizes the skyline query by additionally considering a set of personalized scoring functions F. Since uncertainty is inherent in datasets for…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
We establish a precise relationship between spherical harmonics and Fourier basis functions over a hypercube randomly embedded in the sphere. In particular, we give a bound on the expected Boolean noise sensitivity of a randomly rotated…
The possible existence of a complex structure on the 6-sphere has been a famous unsolved problem for over 60 years. In that time many "solutions" have been put forward, in both directions. Mistakes have always been found. In this paper I…
We study the problem of identifying the parameters of a linear system from its response to multiple unknown waveforms. We assume that the system response is a scaled superposition of time-delayed and frequency-shifted versions of the…
Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$, not equal to $K$. We prove the following undecidability results for $R$: If $K$ is recursive, then Hilbert's…
We investigate spherical 4-distance 7-designs by studying their distance distributions. We compute these distance distributions and use their product (an integer) to derive certain divisibility conditions relating the dimension $n$ and the…
Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation…
It is known that every closed curve of length \leq 4 in R^n (n>0) can be surrounded by a sphere of radius 1, and that this is the best bound. Letting S denote the circle of circumference 4, with the arc-length metric, we here express this…