Cell responses to drifting Cartesian (parallel) and non-Cartesian (concentric, radial, and hyperbolic) stimuli were recorded in and beyond the classical receptive field (CRF) in the lateral geniculate nucleus (LGN), V1, and V2 of anesthetized monkeys. Many cells were equally responsive to Cartesian and non-Cartesian, especially concentric, gratings. Around 15% of cells in each area were signifi...

Let R be a commutative noetherian ring. Denote by $${\textsf{mod }}\,R$$ the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in sense Auslander and Bridger, comparing them with n-syzygy modules, satisfying Serre’s condition $$(\mathrm {S}_n)$$ . We mainly investigate closedness properties full subcategories consisting those modules.

A permutation group G?Sym(?) is said to be 2-closed if no H such that G<H?Sym(?) has the same orbits on ?×? as G. simple and efficient inductive criterion for 2-closedness established abelian groups with cyclic transitive constituents.

the broadcast domination number of the cartesian product of two cycles is completely determined.

a modular $k$-coloring, $kge 2,$ of a graph $g$ without isolated vertices is a coloring of the vertices of $g$ with the elements in $mathbb{z}_k$ having the property that for every two adjacent vertices of $g,$ the sums of the colors of the neighbors are different in $mathbb{z}_k.$ the minimum $k$ for which $g$ has a modular $k-$coloring is the modular chromatic number of $g.$ except for some s...

Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity. The resulting theory generalizes the corresponding “crisp” theory in the r...

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are id...

Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for Ea n (t)’s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time...

Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation K+ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “meas...