相关论文: Some conjectures looking for a NCG theory

We consider discretizations of the Einstein action of general relativity such that the resulting discrete equations of motion form a consistent constrained system. Upon ``spin foam'' quantization of the system, consistency allows a natural…

Second gradient theories have to be used to capture how local micro heterogeneities macroscopically affect the behavior of a continuum. In this paper a configurational space for a solid matrix filled by an unknown amount of fluid is…

In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…

In the theories of generalized modified gravity, the acceleration equation is generally fourth order. So it is hard to analyze the evolution of the Universe. In this paper, we present a class of generalized modified gravity theories which…

A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.

This paper studies the problem of modeling complex domains of actions and change within high-level action description languages. We investigate two main issues of concern: (a) can we represent complex domains that capture together different…

This paper discusses experiments with single-particle systems, some of whose states appear to be entangled. It shows that the interpretation of the experiments in terms of entanglement is ill-defined. Three forms of ambiguity are discussed.…

Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can…

We give a partly new proof of the fluctuation bounds for the second class particle and current in the stationary asymmetric simple exclusion process. One novelty is a coupling that preserves the ordering of second class particles in two…

Explainable AI has brought transparency into complex ML blackboxes, enabling, in particular, to identify which features these models use for their predictions. So far, the question of explaining predictive uncertainty, i.e. why a model…

It is proposed that a non-Abelian adjoint two-form in BF type theories transform inhomogeneously under the gauge group. The resulting restrictions on invariant actions are discussed. The auxiliary one-form which is required for maintaining…

A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…

In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…

A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include…

Accurate calculation of the motion of a compact object in a background spacetime induced by a supermassive black hole is required for the future detection of such binary systems by the gravitational-wave detector LISA. Reaching the desired…

I consider selected (most important according to my own choice) unsolved problems in particle theory, both those related to extensions of the Standard Model (neutrino oscillations, which probably do not fit the usual three-generation…

Deep neural networks are often seen as different from other model classes by defying conventional notions of generalization. Popular examples of anomalous generalization behaviour include benign overfitting, double descent, and the success…

General Relativity resembles a very elegant crystal glass: If we touch its principles, that is, its Lagrangian, there is a risk of breaking everything. Or, if we will, it is like a short blanket: Curing some problems creates new problems.…

In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…