This paper introduces a higher-order neural network called the Binary Pi-sigma Network (BPSN), which is a feedforward network with a single \hidden" layer and product units in the output layer. As training proceeds, the BPSN forms an internal representation of the conjunctive normal form expression corresponding to the Boolean function to be learned. This enables the network to have a regular s...

Let (T,M) be a complete local domain containing the integers. Let p1 ⊆ p2 ⊆ · · · ⊆ pn be a chain of nonmaximal prime ideals of T such that Tpn is a regular local ring. We construct a chain of excellent local domains An ⊆ An−1 ⊆ · · · ⊆ A1 such that for each 1 ≤ i ≤ n, the completion of Ai is T , the generic formal fiber of Ai is local with maximal ideal pi, and if I is a nonzero ideal of Ai th...

Problem 1.1 is solved explicitly by Burkard [3] for the case n = 2 and for arbitrary n, but with at most two distinct values mi. Burkard attributes the problem to Guldan [S], who, in turn, attributes it to Cerny [4]. In [4,5] the problem is stated as follows: How should regular pi-gons, i= 1,2, . . . , n, be inscribed in a circle so as to maximize the distance between the closest vertices on th...

We compare the shell-model results for realistic interactions with those obtained for various ensembles of random matrix elements. We show that, although the quantum numbers of the ground states in the even-even nuclei have a high probability ( approximately 60%) to be J(pi)T = 0(+)0, the overlap of those states with the realistic wave functions is very small in average. The transition probabil...

In this work, we provide estimates of the branching ratios, direct $CP$ asymmetries and triple product in $B_{(s)} \to (\pi\pi)(K\pi)$ decays perturbative QCD approach, where $\pi\pi$ $K\pi$ invariant mass spectra are dominated by vector resonances $\rho(770)$ $K^*(892)$, respectively. Some scalar backgrounds, such as $f_0(500,980) \pi\pi$ $K^*_0(1430) K\pi$ also accounted for. The $\rho(700)$ ...

BACKGROUND The patient-centered medical home (PCMH) is a team-based, comprehensive model of primary care. When effectively implemented, PCMH is associated with higher patient satisfaction, lower staff burnout, and lower hospitalization for ambulatory care-sensitive conditions. However, less is known about what factors contribute to (or hinder) PCMH implementation. We explored the associations o...

Phosphorus (P), in the form of phosphate ion (Pi), is a vital element contributing in biomolecule structures, metabolic reactions, signaling pathways and energy transfer within the living cells. The objective of the present study was to assess the influence of fungal infection on Pi metabolism in compare to the effects of phosphate stress in Arabidopsis. Quantification of total P contents showe...