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We present a critical review about the study of linear perturbations of matched spacetimes including gauge problems. We analyse the freedom introduced in the perturbed matching by the presence of background symmetries and revisit the…
We discuss the physics of a restricted Weyl symmetry in a curved space-time where a gauge parameter $\Omega(x)$ of Weyl transformation satisfies a constraint $\Box \Omega = 0$. First, we present a model of QED where we have a restricted…
In Model-Based Design of Cyber-Physical Systems (CPS), it is often desirable to develop several models of varying fidelity. Models of different fidelity levels can enable mathematical analysis of the model, control synthesis, faster…
We demonstrate that the quantum corrections to the classical arrival time for a quantum object in a potential free region of space, as computed by Galapon [Phys. Rev. A {\bf 80}, 030102(R) (2009)], can be eliminated up to a given order of…
Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge -- a feature that was exploited for several applications. Here, we…
We show that the Planck mass scale can be generated from conformal gravity in the Weyl conformal geometry via the Coleman-Weinberg mechanism of dimensional transmutation where quantum corrections stemming from the gravitational field and…
Explainability and fairness have mainly been considered separately, with recent exceptions trying the explain the sources of unfairness. This paper shows that the Shapley value can be used to both define and explain unfairness, under…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
Signal Temporal Logic (STL) has been widely adopted as a specification language for specifying desirable behaviors of hybrid systems. By monitoring a given STL specification, we can detect the executions that violate it, which are often…
Recently a generalization of the Fefferman-Graham gauge for asymptotically locally AdS spacetimes, called the Weyl-Fefferman-Graham (WFG) gauge, has been proposed. It was shown that the WFG gauge induces a Weyl geometry on the conformal…
Physical clocks provide more precision than applications can use. For example, a 64 bit NTP clock allows a precision of 233 picoseconds. In this paper, we focus on whether the least significant bits that are not useful to the applications…
In this talk I review some aspects of the idea that there is an infra-red conformal fixed-point at the TeV scale. In particular, it is shown how gauge coupling unification can be achieved by TeV unification in a semi-simple gauge group.
We show that on any Riemannian manifold with H\"older continuous metric tensor, there exists a $p$-harmonic coordinate system near any point. When $p = n$ this leads to a useful gauge condition for regularity results in conformal geometry.…
We compare the sensitivity of a recent bound on time variation of the fine structure constant from optical clocks with bounds on time varying fundamental constants from atomic clocks sensitive to the electron-to-proton mass ratio, from…
Precision gauge coupling unification is one of the primary quantitative successes of low energy or split supersymmetry. Preserving this success puts severe restrictions on possible matter and gauge sectors that might appear at…
Questioning the presumably most basic assumptions about the structure of space and time has revolutionized our understanding of Nature. State-of-the-art atomic clocks make it possible to precisely test fundamental symmetry properties of…
In this talk I will show that usual spin glasses are a peculiar kind of Abelian gauge theory. I will shortly review the techniques used to study them. At the end I will consider more general models (e.g. spin glasses based on non Abelian…
Modeling and analysis of non-functional properties, such as timing constraints, is crucial in automotive real-time embedded systems. EAST-ADL is a domain specific architectural language dedicated to safetycritical automotive embedded system…
In this brief report, apart from the usual approach, we discriminate among models in the class of \textbf{$SU(4)_{L}\otimes U(1)_{Y}$} electro-weak gauge models by just setting the versors in the method of the exactly solving gauge models…
We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those -highly symmetric -geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of…