Related papers: Integration of trace anomaly in 6D
Within a category $\mathtt{C}$, having objects $\mathtt{C}_0$, it may be instructive to know not only that two objects are non-isomorphic, but also how far from being isomorphic they are. We introduce pseudo-metrics $d:\mathtt{C}_0 \times…
For a delta-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching…
The field of time series anomaly detection is constantly advancing, with several methods available, making it a challenge to determine the most appropriate method for a specific domain. The evaluation of these methods is facilitated by the…
We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the 2D nematic and complex scalar field models.…
Trace Dynamics is a classical dynamical theory of noncommuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a…
Anomaly detection is an important problem that has been well-studied within diverse research areas and application domains. The aim of this survey is two-fold, firstly we present a structured and comprehensive overview of research methods…
Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…
Anomaly detection in complex domains poses significant challenges due to the need for extensive labeled data and the inherently imbalanced nature of anomalous versus benign samples. Graph-based machine learning models have emerged as a…
We derive three-dimensional integrable mappings which have two invariants.
An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We…
We define a tracelike transformation to be a natural family of conjugation invariant maps $T_{x,C}: hom_C(x,x) \to hom_C(1,1)$ for all dualisable objects $x$ in any symmetric monoidal infinity-category $C$. This generalises the trace from…
Can the cross product be generalized? Why are the trace and determinant so important in matrix theory? What do all the coefficients of the characteristic polynomial represent? This paper describes a technique for `doodling' equations from…
We calculate the trace anomaly of a Weyl fermion coupled to gravity by using Fujikawa's method supplemented by the choice of a consistent regulator. The latter is constructed out of Pauli-Villars regulating fields. The motivation for…
We provide the full classification, in arbitrary even and odd dimensions, of global conformal invariants, i.e., scalar densities in the spacetime metric and its derivatives that are invariant, possibly up to a total derivative, under local…
In the present talk we briefly demonstrate an elegant and effective technique for calculation of the trace expansion in the derivatives of background fields. One of main advantages of the technique is manifestly (super)symmetrical and gauge…
On the basis of the Navier-Stokes equations we develop the statistical theory of many space-time correlation functions of velocity differences. Their time dependence is {\em not} scale invariant: $n$-order correlations functions exhibit…
Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…