Related papers: The L\"uroth problem
The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
A new pseudospectral calculation of collapsing Euler vortices \cite{HouLi06} has called into question the long-term conclusions of singular behavior described earlier in \cite{Kerr93,Kerr05}. This review is designed to: improve the…
The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence,…
While Vision-Language Models (VLMs) have achieved competitive performance in various tasks, their comprehension of the underlying structure and semantics of a scene remains understudied. To investigate the understanding of VLMs, we study…
Large Language Models (LLMs) are increasingly described as possessing strong reasoning capabilities, supported by high performance on mathematical, logical, and planning benchmarks. However, most existing evaluations rely on aggregate…
A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…
Despite the many applications of rate-independent systems, their regularity theory is still largely unexplored. Usually, only weak solution with potentially very low regularity are considered, which requires non-smooth techniques. In this…
The focus of the present work is on the Cauchy problem for the quadratic gravity models introduced in \cite{stelle}-\cite{stelle2}. These are renormalizable higher order derivative models of gravity, but at cost of ghostly states…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
Many physical problems can be formulated as operator equations of the form Au = f. If these operator equations are ill-posed, we then resort to finding the approximate solutions numerically. Ill-posed problems can be found in the fields of…
Humans continuously make new discoveries, and understanding temporal sequence of events leading to these breakthroughs is essential for advancing science and society. This ability to reason over time allows us to identify future steps and…
Summary of the experimental results presented at the 51st edition of the Moriond Electroweak and Unified Theories conference held in March 2016 at La Thuile, Italy.
We give a short non-technical introduction to the Ising model, and review some successes as well as challenges which have emerged from its study in probability and mathematical physics. This includes the infinite-volume theory of phase…
Handedness, or chirality, has been a continuing source of inspiration across a wide range of scientific problems. After a quick review of some important, instructive historical examples, I present three contemporary case studies involving…
The rapid advancement of Large Language Models (LLMs) and Large Vision-Language Models (LVLMs) has enhanced our ability to process and generate human language and visual information. However, these models often struggle with complex,…
Chain of Thought (CoT) reasoning enhances logical performance by decomposing complex tasks, yet its multimodal extension faces a trade-off. The prevailing Thinking with Images paradigm achieves visual refocusing by explicitly cropping image…
According to Biot's paper in 1956, by using the Lagrangian equations in classical mechanics, we consider a problem of the filtration of a liquid in porous elastic-deformation media whose mechanical behavior is described by the Lam'e system…
About an essential suggestion to Einstein by Levi-Civita in 1915. Unicuique suum.
This is the proceedings of the Seventeenth conference on Theoretical Aspects of Rationality and Knowledge, 17-19 July 2019, Institut de Recherche en Informatique de Toulouse (IRIT), Toulouse University Toulouse, France. The mission of the…