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A constructive approach for investigating the stability of incommensurate fractional differential systems
Get PDFThis paper is devoted to studying the asymptotic behaviour of solutions to generalized incommensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary and sufficient to ensure the stability of such systems. Next, from the fractional order pseudospectrum definition proposed by Šanca et al., we formulate the concept of a rational approximation for the fractional spectrum of incommensurate fractional systems with general, not necessarily rational, orders. Our first important new contribution is to show the equivalence between the fractional spectrum of a incommensurate linear system and its rational approximation. With this result in hand, we use ideas developed in our earlier work to demonstrate the stability of an equilibrium point to nonlinear systems in arbitrary finite-dimensional spaces. A second novel aspect of our work is the fact that the approach is constructive. It is effective and widely applicable in studying the asymptotic behaviour of solutions to linear incommensurate fractional differential systems with constant coefficient matrices and linearized stability theory for nonlinear incommensurate fractional differential systems. Finally, we give numerical simulations to illustrate the merit of the proposed theoretical results
Generalization potential of large language models
Get PDFThe rise of deep learning techniques and especially the advent of large language models (LLMs) intensified the discussions around possibilities that artificial intelligence with higher generalization capability entails. The range of opinions on the capabilities of LLMs is extremely broad: from equating language models with stochastic parrots to stating that they are already conscious. This paper represents an attempt to review LLM landscape in the context of their generalization capacity as an information theoretic property of those complex systems. We discuss the suggested theoretical explanations for generalization in LLMs and highlight possible mechanisms responsible for these generalization properties. Through an examination of existing literature and theoretical frameworks, we endeavor to provide insights into the mechanisms driving the generalization capacity of LLMs, thus contributing to a deeper understanding of their capabilities and limitations in natural language processing tasks
Spiritual Capital, Leadership, and Performance Across Cultural Contexts
No full text“Spiritual Capital, Leadership, and Performance Across Cultural Contexts”, together with Jörg Meyer, Rainer Wehner, Sindhu Shantha Nair, Emmanuel Nwosu, Bello Muhammad Abdullahi. in: Rainer Wehner & Emin Akçaoğlu (ed.), “Global Business Dynamics, Value Chains, and Cultural Linkages”, Würzburg International Business Press, p. 142-181
