In this paper, we propose a novel algorithm for a decomposition of 3D binary shapes to rectangular blocks. The aim is to minimize the number of blocks. Theoretically optimal brute-force algorithm is known to be NP-hard and practically infeasible. We introduce its sub-optimal polynomial heuristic approximation, which transforms the decomposition problem onto a graph-theoretical problem. We compare its performance with the state of the art Octree and Delta methods. We show by extensive experiments that the proposed method outperforms the existing ones in terms of the number of blocks on statistically significant level. We also discuss potential applications of the method in image processing.
Let $A$ be a uniformly closed and locally m-convex $\Phi $-algebra. We obtain internal conditions on $A$ stated in terms of its closed ideals for $A$ to be isomorphic and homeomorphic to $C_k(X)$, the $\Phi $-algebra of all the real continuous functions on a normal topological space $X$ endowed with the compact convergence topology.
We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.
We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.
Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.
This experiment tested the effect of clozapine on the sympathetic and thermogenic effects induced by orexin A. The firing rates of the sympathetic nerves to interscapular brown adipose tissue (IBAT), along with IBAT and colonic temperatures were monitored in urethane-anesthetized male Sprague-Dawley rats before and for 5 h after an injection of orexin A (1.5 nmol) into the lateral cerebral ventricle. The same procedure was carried out in rats treated with orexin A plus an intraperitoneal administration of clozapine (8 mg/kg bw), an atypical antipsychotic that is largely used in the therapy of schizophrenia. The same variables were monitored in rats with clozapine alone. A group of rats with saline injection served as control. The results show that orexin A increases the sympathetic firing rate, IBAT and colonic temperatures. Clozapine blocks completely the reactions due to orexin A. These findings suggest that clozapine influences strongly the thermogenic role of orexin A. Furthermore, the remarkable hyperthermic role played by orexin A is confirmed.
The cluster analysis and the formal concept analysis are both used to
identify significant groups of sirnilar objects. The Rice & Siff’s algorithm joins these two methods for a two-valued object-attribute (0-A) model and often significantly reduces the amount of concepts and the complexity. We consider an 0-A model with graded degrees of attributes. We define a new type of one-sided fuzzification of a conceptual lattice. We generalize the Rice & Siff’s algorithm for this case wrt a fixed rnetric. We prove the basic properties of this new lattice, metric and algorithm and discuss it on a real example.