Related papers: Problems with models of a fundamental length
HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…
Large language models (LLMs) are widely used for long-form text generation. However, factual errors in the responses would undermine their reliability. Despite growing attention to LLM factuality, the effect of response length on factuality…
This thesis is a study of large sets of unit vectors in $\cx^n$ such that the absolute value of their standard inner products takes on only a small number of values. We begin with bounds: what is the maximal size of a set of lines with only…
The effective field theory containing higher dimensional operators violates the unitarity of the $2 \rightarrow 2$ scattering processes in the Standard Model. This unitarity violation depends on the values of the Wilson coefficients…
We consider neutrino oscillations in the minimal Standard-Model Extension describing general Lorentz and CPT violation. Among the models without neutrino mass differences is one with two degrees of freedom that reproduces most major…
We generalize the notion of length to an ordinal-valued invariant defined on the class of finitely generated modules over a Noetherian ring. A key property of this invariant is its semi-additivity on short exact sequences. We show how to…
A brief summary is given of recent developments concerning a Lorentz-violating extension of the standard model and its implications for experiments testing Lorentz and CPT symmetry.
We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…
Transformers have become the foundational architecture for a broad spectrum of sequence modeling applications, underpinning state-of-the-art systems in natural language processing, vision, and beyond. However, their theoretical limitations…
A new scalar particle with generic couplings to the standard-model particles is a possible source for the lepton anomalous magnetic moment and the violation of the weak equivalence principle. Here, one-loop contributions to the lepton…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
Nonlinear longitudinal proportional effect models have been proposed to improve power and provide direct estimates of the proportional treatment effect in randomized clinical trials. These models assume a fixed proportional treatment effect…
We interpret anomalies, deviations, from the standard model as being in fact due to effects not given by perturbation, because the top Yukawa coupling is after all so large that not by perturbation effects become important. Most of the…
The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical…
The successes and shortcomings of the Standard Model are reviewed, with emphasis on the reasons motivating the need to extend it. The basic elements of grand unification and supersymmetry are described, exploring their phenomenological…
We explore the implications of the finiteness of homological dimensions for Ext modules, focusing on projective dimension, injective dimension, and their Gorenstein counterpart. In this direction, we establish several finiteness criteria…
It had been conjectured that Diffusion Limited Aggregates and Laplacian Growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a 1-parameter family of fractal growth…
A proper elementary extension of a model is called small if it realizes no new types over any finite set in the base model. We answer a question of Marker, and show that it is possible to have an o-minimal structure with a maximal small…
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring…
We consider the possibility that there may be causality violation detectable at higher energies. We take a scalar nonlocal theory containing a mass scale $\Lambda$ as a model example and make a preliminary study of how the causality…