Continued fractions are linked to Stern’s diatomic sequence 0, 1, 1, 2, 1, 3, 2, 3, 1, 4, . . . (given by the recursion relations α2n = αn and α2n+1 = αn + αn+1, where α0 = 0 and α1 = 1), which has long been known. Using a particular multidimensional continued fraction algorithm (the Farey algorithm), we generalize the diatomic sequence to a sequence of numbers that quite naturally can be terme...

Graph contrastive learning (GCL) has been subject to more attention and widely applied numerous graph tasks such as node classification link prediction. Although it achieved great success even performed better than supervised methods in some tasks, most of them depend on node-level comparison, while ignoring the rich semantic information contained topology, especially for social networks. Howev...

It is known that if Ln, respectively Rn9 are n x n matrices with the (/, j ) * entry the binomial coefficient (y~l)? respectively (^l)), then Ln = In (mod 2), respectively R„=In (mod 2), where In is the identity matrix of dimension n>\ (see, e.g., Problem PI 073 5 in the May 1999 issue of Arner. Math Monthly). The entries of Ln form a left-justified Pascal triangle and the entries of Rn result ...

The transient potassium A-current is present in almost all neurons and plays an essential role in determining the timing and frequency of action potential generation. We use a three-variable mathematical model to examine the role of the A-current in a rhythmic inhibitory network, as is common in central pattern generation. We focus on a feed-forward architecture consisting of an oscillator neur...

Introduction: Recent studies have acknowledged the potential of convolutional neural networks (CNNs) in distinguishing healthy and morbid samples by using heart sound analyses. Unfortunately the performance of CNNs is highly dependent on the filtering procedure which is applied to signal in their convolutional layer. The present study aimed to address this problem by a...

PURPOSE To examine the effects of panretinal photocoagulation (PRP) using a pattern scanning laser (PASCAL) system on the retinal nerve fiber layer (RNFL) thickness in patients with diabetic retinopathy. METHODS This retrospective study included 105 eyes with diabetic retinopathy, which consisted of three groups: the PASCAL group that underwent PRP with the PASCAL method (33 eyes), the conven...

In a recent work by the author an extrapolation method, the W-transformation, was developed, by which a large class of oscillatory infinite integrals can be computed very efficiently. The results of this work are extended to a class of divergent oscillatory infinite integrals in the present paper. It is shown in particular that these divergent integrals exist in the sense of Abel summability an...