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	<title>Math</title>
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		<title>Sums-of-squares Polyconvexity</title>
		<link>https://dcn.nat.fau.eu/sums-of-squares-polyconvexity/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Thu, 11 Jun 2026 11:13:50 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Ajay Murali]]></category>
		<category><![CDATA[Math Giovanni Fantuzzi]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=33013</guid>

					<description><![CDATA[Sums-of-squares Polyconvexity Find this post at FAU DCN-AvH Math &#038; Research posts. &#160; 1 Introduction Polyconvex functions are functions of a matrix variable characterized by a convex dependence on the minors of the matrix. This generalization of convexity is fundamental in the Calculus of Variations, where it provides a sufficient condition for the well-posedness of [&#8230;]]]></description>
		
		
		
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		<title>Activation Saturation and Jacobian Attenuation in Neural Ordinary Differential Equations</title>
		<link>https://dcn.nat.fau.eu/activation-saturation-and-jacobian-attenuation-in-neural-ordinary-differential-equations/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Sun, 31 May 2026 18:42:03 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Nikos Matzakos]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32951</guid>

					<description><![CDATA[Neural Ordinary Differential Equations (Neural ODEs) offer a principled way to model continuous dynamical systems with neural networks [1]. The hidden state evolves according to where is a multilayer perceptron with trained weights . Once training is finished, is fixed and will not change. The network no longer adapts&#8212;it defines a static vector field on [&#8230;]]]></description>
		
		
		
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		<title>Optimal control for renormalized solutions of nonlinear evolution equations</title>
		<link>https://dcn.nat.fau.eu/optimal-control-for-renormalized-solutions-of-nonlinear-evolution-equations/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Wed, 01 Apr 2026 01:00:10 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Pedro Blöss]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32695</guid>

					<description><![CDATA[&#160; 1 Introduction We aim to develop a comprehensive theory of optimal control for nonlinear parabolic equations of Leray-Lions type, whose solutions may fail to exist in the classical weak sense for low regularity data. In this case, the appropriate notion of solution is the renormalized solution, introduced by Lions and Di Perna [8] for [&#8230;]]]></description>
		
		
		
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		<title>Network design and control: Shape and topology optimization for the turnpike property for the wave equation</title>
		<link>https://dcn.nat.fau.eu/network-design-and-control-shape-and-topology-optimization-for-the-turnpike-property-for-the-wave-equation/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Tue, 17 Mar 2026 17:13:40 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Jan Sokolowski]]></category>
		<category><![CDATA[Math Martin Gugat]]></category>
		<category><![CDATA[Math Meizhi Qian]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32521</guid>

					<description><![CDATA[Network design and control: Shape and topology optimization for the turnpike property for the wave equation &#160; 1 Introduction We consider two optimal control problems. The first problem, denoted by , is an optimal control problem governed by an evolution equation. The second problem, denoted by , is the optimal control problem for the associated [&#8230;]]]></description>
		
		
		
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		<title>Reinforcement Learning and LQR with special control structure: switched and multilevel systems</title>
		<link>https://dcn.nat.fau.eu/reinforcement-learning-and-lqr-with-special-control-structure-switched-and-multilevel-systems/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Mon, 16 Mar 2026 21:31:41 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Nicolas Schlosser]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32509</guid>

					<description><![CDATA[Reinforcement Learning and LQR with special control structure: switched and multilevel systems &#160; 1 Introduction In this post we study the well-known linear-quadratic regulator problem in continuous time where , , , , and is the initial state. The goal is to choose a control in such a way that at time , we have [&#8230;]]]></description>
		
		
		
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		<title>Exact Controllability of Stochastic First-Order Multi-Dimensional Hyperbolic Systems</title>
		<link>https://dcn.nat.fau.eu/exact-controllability-of-stochastic-first-order-multi-dimensional-hyperbolic-systems/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Wed, 11 Mar 2026 04:01:31 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Yu Wang]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32466</guid>

					<description><![CDATA[Exact Controllability of Stochastic First-Order Multi-Dimensional Hyperbolic Systems In the real world, the evolution of many physical quantities can be described by first-order hyperbolic systems. Notable examples include the Saint-Venant equations for open channels, the Aw-Rascle model for road traffic, gas dynamics, and shallow water equations. Over the past few decades, the boundary control theory [&#8230;]]]></description>
		
		
		
			</item>
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		<title>Optimal Output Regulation for General Linear Systems via Adaptive Dynamic Programming</title>
		<link>https://dcn.nat.fau.eu/optimal-output-regulation-for-general-linear-systems-via-adaptive-dynamic-programming/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Fri, 27 Feb 2026 15:13:32 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Yanzhi Wu]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32426</guid>

					<description><![CDATA[&#160; 1 Introduction In this study, we consider an adaptive optimal output regulation problem for general linear systems. The purpose is to obtain both optimal feedback control gain and optimal feedforward control gain, which appear in the optimal controller and can help realize asymptotic and disturbance rejection. First, adaptive dynamic programming technique is used to [&#8230;]]]></description>
		
		
		
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		<title>Aggregation of Finite-Valued Networks Based on Bisimulation</title>
		<link>https://dcn.nat.fau.eu/aggregation-of-finite-valued-networks-based-on-bisimulation/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Thu, 26 Feb 2026 19:18:57 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Zhenping Ji]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32434</guid>

					<description><![CDATA[&#160; 1 Backgrounds The finite-valued networks are important models in complex system engineering. These systems are characterized as multi-agent dynamics with nodes taking values in finite sets endowed with operators. The study of finite-valued functions and systems can be traced back to finite automata [6], encryption-decryption in cryptography [1], and Boolean networks in theoretical biology [&#8230;]]]></description>
		
		
		
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		<title>In search of the origins of matrix multiplication</title>
		<link>https://dcn.nat.fau.eu/in-search-of-the-origins-of-matrix-multiplication/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Thu, 05 Feb 2026 04:27:19 +0000</pubDate>
				<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Jerzy Respondek]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32337</guid>

					<description><![CDATA[In search of the origins of matrix multiplication &#160; 1 Origins of matrices and determinants In this note we present the history of the development of matrices and determinants. To the best of our knowledge, we found the first general definition of matrix multiplication. This is particularly important given the wealth of algorithms currently available [&#8230;]]]></description>
		
		
		
			</item>
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		<title>Sentiment Analysis with Transformers</title>
		<link>https://dcn.nat.fau.eu/ndw25-sentiment-analysis-with-transformers/</link>
		
		<dc:creator><![CDATA[darlis.dcn]]></dc:creator>
		<pubDate>Fri, 14 Nov 2025 12:00:05 +0000</pubDate>
				<category><![CDATA[Hub]]></category>
		<category><![CDATA[Hub Albert Alcalde]]></category>
		<category><![CDATA[Hub Giovanni Fantuzzi]]></category>
		<category><![CDATA[Math]]></category>
		<category><![CDATA[Math Albert Alcalde]]></category>
		<category><![CDATA[Math Giovanni Fantuzzi]]></category>
		<guid isPermaLink="false">https://dcn.nat.fau.eu/?p=32036</guid>

					<description><![CDATA[Sentiment Analysis with Transformers This post includes an app SentimentAnalysisTransformersApp created for a public outreach activity organized by the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship (FAU DCN-AvH) during the Lange Nacht der Wissenschaften 2025 (Long Night Sciences 2025). Live demo https://albertalcalde.github.io/SentimentAnalysisTransformersApp/ Overview This interactive app lets you type [&#8230;]]]></description>
		
		
		
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