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Artificial Intelligence in Bulk RNA-Seq: Challenges and Potential Solutions. [PDF]
Rezapour M +3 more
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Reconstructing noisy gene regulation dynamics using extrinsic-noise-driven neural stochastic differential equations. [PDF]
Zhang J +8 more
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The KPZ Equation of Kinetic Interface Roughening: A Variational Perspective. [PDF]
Wio HS +5 more
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Learning to Diagnose Privately: DP-Powered LLMs for Radiology Report Classification. [PDF]
Bhattacharjee P +7 more
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Stochastic approximation with discontinuous dynamics, differential inclusions, and applications
This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled
George Yin
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Marek T Malinowski, Mariusz Michta
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On the Solution of Stochastic Differential Inclusion
Let \((\Omega, \Lambda,p)\) be a probability space, \(I = [0,T]\), \(\{\Lambda_t \}_{t \in I}\) an increasing family of \(\sigma\)- subalgebras such that \(\bigcap_{\alpha > 0} \Lambda _{t + \alpha} = \Lambda_t\), and \(\beta_t\) a \(\sigma\)-algebra of all Borel subsets of \([0,t]\) for fixed \(t \in I\). Let us denote by \(\beta \Lambda\) a \(\sigma\)
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Stochastic Invariance for Differential Inclusions
Set-Valued Analysis, 2000The first objective of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a stochastic uncertainty driven by a Wiener process and a contingent uncertainty driven by a set-valued map. The second point consists to extend to stochastic differential inclusions the invariance theorem for nonstochastic ...
Aubin, Jean-Pierre +2 more
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Stochastic differential inclusions with Hilfer fractional derivative
Annals of the University of Craiova, Mathematics and Computer Science Series, 2022In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Meryem Chaouche, Toufik Guendouzi
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