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Patterns that appear rarely or unusually in the data can be defined as outlier patterns. The basic idea behind detecting outlier patterns is comparison of their relative frequencies with frequent patterns. Their frequencies of appearance…
We extend effective field theory to the case of spontaneous symmetry breaking in genuinely finite quantum systems such as small superfluid systems, molecules or atomic nuclei, and focus on deformed nuclei. In finite superfluids, symmetry…
This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
Outlier detection has received special attention in various fields, mainly for those dealing with machine learning and artificial intelligence. As strong outliers, anomalies are divided into the point, contextual and collective outliers.…
Many organisations manage service quality and monitor a large set devices and servers where each entity is associated with telemetry or physical sensor data series. Recently, various methods have been proposed to detect behavioural…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
Recently, it was realized that anomalies can be completely classified by topological orders, symmetry protected topological (SPT) orders, and symmetry enriched topological orders in one higher dimension. The anomalies that people used to…
Adversarial actions and a rapid climate change are disrupting operations of infrastructure networks (e.g., energy, water, and transportation systems). Unaddressed disruptions lead to system-wide shutdowns, emphasizing the need for quick and…
Compactified string theories give rise to discrete symmetries which are essential if they are to provide a realistic low energy theory. We find that in a class of four dimensional string theories these symmetries are constrained by similar…
We calculated numerically the localization length of one-dimensional Anderson model with diagonal disorder. For weak disorder, we showed that the localization length changes continuously as the energy changes from the band center to the…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
Motivated by the search for possible CP violating terms in the trace of the energy-momentum tensor in theories coupled to gravity we revisit the problem of trace anomalies in chiral theories. We recalculate the latter and ascertain that in…
For massless $\phi^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the…
Configuration interaction in many-electron atoms may cause anomalies in the fine structure which make the intervals small and very sensitive to variation of the fine structure constant. Repeated precision measurements of these intervals…
Anomaly detection is concerned with identifying data patterns that deviate remarkably from the expected behaviour. This is an important research problem, due to its broad set of application domains, from data analysis to e-health,…
A number theoretic algorithm is given for writing gauge theory amplitudes in a compact manner. It is possible to write down all details of the complete $L$ loop amplitude with two integers, or a complex integer. However, a more symmetric…
It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents…