Results 21 to 30 of about 21,954 (219)
Poly-Bernoulli Numbers and Eulerian Numbers
J. Integer Seq., 2018 In this note we prove combinatorially some new formulas connecting poly-Bernoulli numbers with negative indices to Eulerian numbers.
Beáta Bényi, Péter Hajnal
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Advanced Science, EarlyView.This work provides a practical guide for neuroengineers to design advanced neural interfaces, embracing and tailoring the concept of functional disorder. By bridging 2D and 3D in vitro models, this work highlights how non‐periodic, spatially heterogeneous, multiscale nanotopography can enable more physiologically relevant platforms for studying neural ...
F. Maita +4 more
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Advanced Science, EarlyView.SpaMode introduces a versatile framework for spatial multi‐omics integration across vertical, horizontal, and mosaic scenarios. By disentangling modality‐invariant and variant features through a mixture‐of‐experts mechanism, it adaptively reconfigures spatially heterogeneous signals.
Xubin Zheng +6 more
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A Data‐Driven Inverse Design Methodology for Magnetic Soft Millirobots Navigating in Confined Spaces
Advanced Science, EarlyView.A data‐efficient inverse design framework automates the optimization of magnetic soft millirobots for confined‐space navigation. Integrating a physics‐based Cosserat rod model with Bayesian optimization efficiently identifies high‐performance geometries.
Ziyu Ren +5 more
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stMixer for Scalable Mosaic Integration and Label Transfer in Spatial Histology and Multi‐Omics
Advanced Science, EarlyView.stMixer is an unsupervised framework for scalable integration and label transfer across spatial histology and multi‐slide multi‐omics data with incomplete modality overlap. It combines self‐looped cross‐attention, multimodal metric learning, and graph‐guided cluster voting to align heterogeneous sections, correct batch effects, and propagate ...
Qixing Yang +3 more
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A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials [PDF]
Transactions of the American Mathematical Society, 1996 Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta functions for totally real numbers. The coefficients of such polynomials are finite combinations of products of Bernoulli numbers which are difficult to get hold of.
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Uncertainty‐Aware Deep Ensembles for Robust and Reliable Chemical Sensor Arrays
Advanced Science, EarlyView.A reliability‐aware electronic nose is developed using photothermally anchored metal‐catalyst decorated metal oxide nanofiber sensor arrays combined with deep ensemble learning. Diverse catalytic nanofiber channels generate gas‐specific response patterns, enabling selective identification and quantification of sulfur‐containing gases.
Sungwoo Eo +5 more
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q-Bernoulli numbers and polynomials
Duke Mathematical Journal, 1948 Verf. definiert die \(q\)-Bernoullischen Zahlen \(\beta_m\) durch \(\beta_0=1\), \(\beta_1=-1/(q+1)\) und die symboli\-sche Rekursionsformel \(q(q\beta+1)^m=0\) \((m>1)\), wobei \(\beta^i\) nach Entwicklung durch \(\beta_i\) zu ersetzen ist. Die Zahlen \(\beta_m\) stimmen für \(q=1\) mit den gewöhnlichen Bernoullischen Zahlen überein.
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A Steerable and Expandable Magnetic Aspiration Catheter for Enhanced Aspiration Thrombectomy
Advanced Intelligent Systems, EarlyView.This article presents a novel magnetic aspiration catheter (MAC) that can be both actively steered and undergo distal‐end expansion via externally applied magnetic fields. The MAC facilitates precise branch selection and enhances clot engagement by improving endovascular navigation and aspiration efficiency. Phantom experiments validate its feasibility
Hakjoon Lee +7 more
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BERNOULLI'S LAW OF LARGE NUMBERS [PDF]
ASTIN Bulletin, 2013 AbstractThis year we celebrate the 300th anniversary of Jakob Bernoulli's path-breaking work Ars conjectandi, which appeared in 1713, eight years after his death. In Part IV of his masterpiece, Bernoulli proves the law of large numbers which is one of the fundamental theorems in probability theory, statistics and actuarial science.
Bolthausen, Erwin, Wüthrich, Mario V
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