Results 81 to 90 of about 51,880 (308)
Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices
Abstract and Applied Analysis, 2014 We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identities D2k(n)=(1/4)σ2k+1,0(n;2)-2·42kσ2k+1(n/4) -(1/2)[∑d|n,d ...
Daeyeoul Kim +2 more
doaj +1 more source
On a new congruence in the Catalan triangle [PDF]
Notes on Number Theory and Discrete MathematicsFor 0≤k≤n, the number C(n,k) represents the number of all lattice paths in the plane from the point (0,0) to the point (n,k), using steps (1,0) and (0,1), that never rise above the main diagonal y = x.
Jovan Mikić
doaj +1 more source
Deep Convolutional Sum-Product Networks
Proceedings of the AAAI Conference on Artificial Intelligence, 2019 We give conditions under which convolutional neural networks (CNNs) define valid sum-product networks (SPNs). One subclass, called convolutional SPNs (CSPNs), can be implemented using tensors, but also can suffer from being too shallow. Fortunately, tensors can be augmented while maintaining valid SPNs.
Jhonatan de S. Oliveira +3 more
openaire +3 more sources
Molecular Oncology, EarlyView.Screening 166 FDA‐approved anticancer drugs identifies the aromatase inhibitor Exemestane as a synergistic partner of PARP inhibitor Olaparib in BRCA‐proficient triple‐negative breast cancer. Exemestane induces ROS‐mediated replication stress, enhancing DNA damage and apoptosis alongside Olaparib.
Nur Aininie Yusoh +5 more
wiley +1 more source
The $D^6 R^4$ interaction as a Poincaré series, and a related shifted convolution sum [PDF]
, 2022 Kim Klinger-Logan +2 more
openalex +1 more source
The Binomial Combinatorial Convolution Sums
British Journal of Mathematics & Computer Science, 2014 In [1] we can find some formulas of binomial combinatorial convolution sums. Starting from these formulas, we obtain various binomial combinatorial convolution sums.
openaire +2 more sources
Decrypting cancer's spatial code: from single cells to tissue niches
Molecular Oncology, EarlyView.Spatial transcriptomics maps gene activity across tissues, offering powerful insights into how cancer cells are organised, switch states and interact with their surroundings. This review outlines emerging computational, artificial intelligence (AI) and geospatial approaches to define cell states, uncover tumour niches and integrate spatial data with ...
Cenk Celik +4 more
wiley +1 more source
Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions
Journal of Applied Mathematics, 2012 Based on the theories of Ramanujan's elliptic functions and the (p, k)-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006) we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of
Ernest X. W. Xia, Olivia X. M. Yao
doaj +1 more source
Molecular Oncology, EarlyView.This study explores salivary RNA for breast cancer (BC) diagnosis, prognosis, and follow‐up. High‐throughput RNA sequencing identified distinct salivary RNA signatures, including novel transcripts, that differentiate BC from healthy controls, characterize histological and molecular subtypes, and indicate lymph node involvement.
Nicholas Rajan +9 more
wiley +1 more source