In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot without changing certain part of its homology, and consequently, we show that there exists stable homology of torus knots conjectured by Dunfield, Gukov and Ras...

New matrix multiplication algorithms are proposed for massively parallel supercomputers with 2D/3D, all-port torus interconnection networks. The proposed algorithms are based on the traditional row-by-column multiplication matrix product model and employ a special routing pattern for better scalability. They compare favorably to the variants of Cannon’s and DNS algorithms since they allow matri...

The presence of obscuring material (or a dusty ‘torus’) in active galactic nuclei (AGN) is central to the unification model for AGN. Two models, the multi-population model for radio sources and the receding torus model, are capable of describing observational properties of powerful radio galaxies and radio quasars. Here, I study the changes of the opening angle of the obscuring torus with radio...

Computation of rate in auditory signals is essential to call recognition in anurans. This task is ascribed to a group of central nervous system nuclei in the dorsal midbrain or torus semicircularis, homologous to the inferior colliculus of mammals. We have mapped the connections of the subnuclei of the torus semicircularis in Xenopus laevis to determine which receive auditory and which receive ...

We propose a criterion for the destruction of a two-dimensional torus through the formation of an infinite set of cusp points on the closed invariant curves defining the resonance torus. This mechanism is specific to noninvertible maps. The cusp points arise when the tangent to the torus at the point of intersection with the critical curve L(0) coincides with the eigendirection corresponding to...

When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2] + 1 (N is the population size). A global phase shift invariance allows to reduce the model to N − 1 dimensions using the phase differences, and doing so the invariant torus becomes [N/2]-dimensional. By means of perturbative calculations based on the renormalization ...

Routing in mesh networks is studied in great detail in the literature. Interest in torus networks however is steadily increasing due to its symmetry in traac distribution. In this paper, we present a new concept of virtual mesh network to map the torus inter-connection networks on to the mesh networks. Using this concept, we show how the routing algorithms for meshes can be applied to the torus...

This paper analyzes a product network generated from torus and hypercube networks known as Torus embedded hypercube scalable interconnection network suitable for parallel architecture. It is shown here that how good a Torus embedded Hypercube interconnection network can be compared to the existing Mesh embedded hypercube interconnection network with minor modifications in its architecture. A co...

Abstmct. Wagner’s theorem (any two maximal plane graphs having p vertices are equivalent under diagonal transformations) is extended to maximal torus graphs, graphs embedded in the torus with a maximal set of edges present. Thus any maximal torus graph havingp vertices may be diagonally transformed into any other maximal torus p;aph having p vertices. As with Wag mr’s theorem, a normal form rep...

Observation that DNA molecules in bacteriophage capsids preferentially form torus type of knots provided a sensitive gauge to evaluate various models of DNA arrangement in phage heads. Only models resulting in a preponderance of torus knots could be considered as close to reality. Recent studies revealed that experimentally observed enrichment of torus knots can be qualitatively reproduced in n...