There exist gravitational memory effects in Brans-Dicke theory. They are closely related to the Bondi-Metzner-Sachs symmetries living on the null infinity in an isolated system. By studying the asymptotically flat spacetime in Brans-Dicke theory and...
The Sine Gordon theory is generalized to include several cosine terms. This is similar to the world sheet description of a string propagating in a tachyon background. This model is studied as a (boundary) 2d euclidean field theory and also using an $...
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgm...
To supplement our recent brief report on the theory of holon-pair boson approach to the t-J Hamiltonian [S.-S. Lee and Sung-Ho Suck Salk, Phys. Rev. B {\bf 64}, 052501(2001)], in this paper we present a full exposure to the theory, detailed physica...
The mathematical features of a string theory compactification determine the physics of the effective four-dimensional theory. For this reason, understanding the mathematical structure of the possible compactification spaces is of profound importance....
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios. With recent...
Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now...
The quantum theory of Ur-alternatives of Carl Friedrich von Weizsaecker tries to constitute general quantum theory based on the concept of logical alternatives in time. Based on this interpretation of quantum theory the existence of free objects in s...
In this paper we examine the detailed theory of the American football in flight, with spin and air resistance included. We find the theory has much in common with the theory of a gyroscope and also rocket trajectory with a misaligned thruster. Unfo...
For years, the biggest unspeakable in quantum theory has been why quantum theory and what is quantum theory telling us about the world. Recent efforts are unveiling a surprisingly simple answer. Here we show that two characteristic limits of quantum...
Grey system theory is an important mathematical tool for describing uncertain information in the real world. It has been used to solve the uncertainty problems specially caused by lack of information. As a novel theory, the theory can deal with vario...
If we are to build human-like robots that can interact naturally with people, our robots must know not only about the properties of objects but also the properties of animate agents in the world. One of the fundamental social skills for humans is the attributi…
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Meet NotebookLM, the AI research tool and thinking partner that can analyze your sources, turn complexity into clarity and transform your content.
Can AI based methods help us make advances in complexity theory? We provide evidence towards answering this in the affirmative, using AlphaEvolve (an LLM code mutation agent) to obtain new results in three settings: a) We improve a recent result of...
Why are large, complex ecosystems stable? Both theory and simulations of current models predict the onset of instability with growing size and complexity, so for decades it has been conjectured that ecosystems must have some unidentified structural p...
A central problem in the theory of multi-agent reinforcement learning (MARL) is to understand what structural conditions and algorithmic principles lead to sample-efficient learning guarantees, and how these considerations change as we move from few...
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify robust natural distributed algorithms that converge quickly to an equilibrium. This paper...
We prove new results concerning the topology and Hodge theory of singular varieties. A common theme is that concrete conditions on the complexity of the singularities, from a number of different perspectives, are closely related to the symmetries of...
A dictionary is a set of finite words over some finite alphabet X. The omega-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [Omega-powers and descriptive set theory, JSL 200...