The majority of cerebral signals destined for the cerebellum are handed over by the pontine nuclei (PN), which thoroughly reorganize the neocortical topography. The PN maps neocortical signals of wide-spread origins into adjacent compartments delineated by spatially precise distribution of cortical terminals and postsynaptic dendrites. We asked whether and how signals interact on the level of t...

which is valid for any arbitrary volume, so the integrand is zero and we recover a classical continuity equation similar to that derived for mass conservation in hydrodynamics. (1) is the equivalent to a Lagrangian conservation of bird density with dρ/dt = 0, hence, a flock of birds traveling at speed U with an initial density ρn−1 = ρ(xn−1 + ǫ, tn−1) at the interface of patch Pn−1 at time tn−1...

For a path Pn of order n, Chartrand et al. [3] have given an upper bound for radio k-chromatic number when 1 ≤ k ≤ n−1. Liu and Zhu [7] have determined the exact value of radio (n−1)-chromatic number of Pn, namely radio number, rn(Pn), when n ≥ 3. Khennoufa and Togni [5] have given the exact value of radio (n − 2)-chromatic number of Pn, namely antipodal number, ac(Pn), when n ≥ 5. Kola and Pan...

In recent years, Transformer-based models have exhibited significant advancements over previous in natural language processing and vision tasks. This powerful methodology has also been extended to the 3D point cloud domain, where it can mitigate inherent difficulties posed by irregular disorderly nature of clouds. However, attention mechanism within Transformer presents challenges for utilizing...

The bondage number b(G) of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with domination number greater than that of G. Denote Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b(Pn × P2), b(Pn × P3), and b(Pn × P4) for n 2.

The paper presents a new proof-number (PN) search algorithm, called PDS-PN. It is a two-level search (like PN), which performs at the first level a depth-first Proof-number and Disproof-number Search (PDS), and at the second level a bestfirst PN search. Hence, PDS-PN selectively exploits the power of both PN and PDS. Experiments in the domain of Lines of Action are performed. They show that wit...

In the present article we study the asymptotic behavior of the sums n≤x cn+1 pn+1 − cn pn and n≤x pn+1 cn+1 − pn cn , and of the series ∞ n=1 cn+1 pn+1 − cn pn α , where p n denotes the n-th prime number while c n stands for the n-th composed number.

The paper introduces a new proof-number (PN) search algorithm, called PDS-PN. It is a two-level search, which performs at the first level a depth-first Proof-number and Disproof-number Search (PDS), and at the second level a best-first PN search. First, we thoroughly investigate four established algorithms in the domain of LOA endgame positions: PN, PN, PDS and αβ search. It turns out that PN a...