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Time‐Delayed Spiking Reservoir Computing Enables Efficient Time Series Prediction
Advanced Intelligent Systems, EarlyView.This study proposes time‐delayed spiking reservoir computing (TDSRC) for efficient time series prediction. By concatenating time‐lagged states, TDSRC constructs an expanded readout feature vector without altering internal reservoir dynamics. This approach enables highly accurate forecasting with significantly fewer neurons, providing a resource ...
Pin Jin +3 more
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Advanced Intelligent Systems, EarlyView.Single‐cell Spatial Transcriptomics Analysis and Denoising Engine is introduced as a unified deep learning framework that jointly performs denoising, clustering, and gene prioritization in spatial transcriptomics. By integrating linear and nonlinear representations within a dual‐channel architecture, it improves robustness and accuracy, uncovers ...
Yaxuan Cui +11 more
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On Separable Polynomials and Skew Polynomial Rings (Skew Polynomial Rings, Group Rings and Related Topics)openaire
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On Radicals of Polynomial Rings
Acta Mathematica Hungarica, 2014Let \(A[X_n]\) be the ring of \(n\geq 0\) commutative independent variables over an associative ring \(A\), where \(A[X_0]=A\) and \(A[X_1]=A[x]\). Let \(R\) be a radical in the sense of Kurosh and Amitsur. If \(R(A)=A\), then we write \(A\in R\). The semisimple class of the radical class \(R\) will be denoted by \(SR\). The aim in the present paper is
L. Márki, S. Tumurbat
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Essential graded algebra over polynomial rings with real exponents
Advances in Mathematics, 2020The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of Nakayama's lemma;
Ezra Miller
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ON THE CONNECTION BETWEEN DIFFERENTIAL POLYNOMIAL RINGS AND POLYNOMIAL RINGS OVER NIL RINGS
Bulletin of the Australian Mathematical Society, 2019In this paper, we study some connections between the polynomial ring $R[y]$ and the differential polynomial ring $R[x;D]$. In particular, we answer a question posed by Smoktunowicz, which asks whether $R[y]$ is nil when $R[x;D]$ is nil, provided that $R$ is an algebra over a field of positive characteristic and $D$ is a locally nilpotent derivation.
LOUISA CATALANO, MEGAN CHANG-LEE
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On the Endomorphisms of a Polynomial Ring
Canadian Journal of Mathematics, 1976This paper arises in the attempt to solve the following problem related to the Zariski Problem. Let A be a polynomial ring in three variables over a field, . Suppose there is a subring B of A such that k ⊆ B and there is variable t over B such that B[t] = A. Then is it true that B is a polynomial ring over k?
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How far can we go with Amitsur’s theorem in differential polynomial rings?
, 2015A well-known theorem by S. A. Amitsur shows that the Jacobson radical of the polynomial ring R[x] equals I[x] for some nil ideal I of R. In this paper, however, we show that this is not the case for differential polynomial rings, by proving that there is
A. Smoktunowicz
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