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Timely and accurate detection of anomalies in power electronics is becoming increasingly critical for maintaining complex production systems. Robust and explainable strategies help decrease system downtime and preempt or mitigate…
These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory. We begin with several derivations of the abelian anomaly: anomalous transformation of the…
We analyze the structure of the stress-energy tensor correlation functions in Lifshitz field theories and construct the corresponding anomalous Ward identities. We develop a framework for calculating the anomaly coefficients that employs a…
Detecting anomalies in energy consumption data is crucial for identifying energy waste, equipment malfunction, and overall, for ensuring efficient energy management. Machine learning, and specifically deep learning approaches, have been…
Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…
We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the…
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
The formulation of the non-linear sigma model in terms of flat connection allows the construction of a perturbative solution of a local functional equation encoding the underlying gauge symmetry. In this paper we discuss some properties of…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Some recent experimental and theoretical work on 1) charge symmetry-breaking, 2) parity non-conservation, and 3) searches for breaking of time reversal invariance are reviewed. The examples illustrate the uses of symmetry to learn about…
We consider single-particle spectra of a symmetric narrow-band Anderson impurity model, where the host bandwidth $D$ is small compared to the hybridization strength $\Delta_{0}$. Simple 2nd order perturbation theory (2PT) in $U$ is found to…
Linear systems under the influence of nonlinear and random linear perturbations, and with random initial and boundary conditions, are discussed. The notion of states of a system is substituted by the notion of the generating vectors for…
Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy…
Scattering of electromagnetic waves lies at the heart of most experimental techniques over nearly the entire electromagnetic spectrum, ranging from radio waves to optics and X-rays. Hence, deep insight into the basics of scattering theory…
The study of string models including both unoriented closed strings and open strings presents a number of new features when compared to the standard case of models of oriented closed strings only. We review some basic features of the…
An anomaly detection method based on deep autoencoders is proposed to address anomalies that often occur in enterprise-level ETL data streams. The study first analyzes multiple types of anomalies in ETL processes, including delays, missing…
We discuss a local, diff-invariant quantum effective action for gravity that captures the trace anomaly via a counter-term. We discuss why this counter-term is the most significant among infinitely many possible ones, and show how the…