相关论文: Scale Invariant $O(g^4)$ Lipatov Kernels at Non-Ze…

We study the scale-invariant $O(g^4)$ kernel which appears as an infra-red contribution in the BFKL evolution equation and is constructed via multiparticle $t$-channel unitarity. We detail the variety of Ward identity constraints and…

The scale-invariant $O(g^4)$ Lipatov kernel has been determined by t-channel unitarity. The forward kernel responsible for parton evolution is evaluated and its eigenvalue spectrum determined. In addition to a logarithmic modification of…

The Lipatov equation can regarded as a reggeon Bethe-Salpeter equation in which higher-order reggeon interactions give higher-order kernels. Infra-red singular contributions in a general kernel are produced by t-channel nonsense states and…

We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…

We show that a scale invariant approximation to the next-to-leading order BFKL kernel, constructed via transverse momentum diagrams, has a simple conformally invariant representation in impact parameter space i.e. K(r1,r2,r1',r2') = g^4 N^2…

Using reggeon diagrams as a partial implementation of $t$-channel unitarity, $O(g^4)$ corrections to the BFKL evolution equation have been obtained. We describe the spectrum and holomorphic factorization properties of the resulting…

The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…

We consider the problem of learning a linear operator $\theta$ between two Hilbert spaces from empirical observations, which we interpret as least squares regression in infinite dimensions. We show that this goal can be reformulated as an…

We discuss, within the context of first order perturbation theory, the correction to the NLO BFKL wavefuncyion for scattering processes with non-zero momentum transfer, arising from the fact that in NLO the kernel is not covariant under…

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…

We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent is not defined. This map has a Lorenz-like singularity and…

We consider weakly positive semidefinite kernels valued in ordered $*$-spaces with or without certain topological properties, and investigate their linearisations (Kolmogorov decompositions) as well as their reproducing kernel spaces. The…

The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…

Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum…

A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\cal U}_{\epsilon}(sl(2))$ transformations in nilpotent irreps for $\epsilon^3=1$. Some…

A new nonparametric approach for system identification has been recently proposed where the impulse response is seen as the realization of a zero--mean Gaussian process whose covariance, the so--called stable spline kernel, guarantees that…

Suppose that the compact and connected Lie group G acts holomorphically on the irreducible complex projective manifold M, and that the action linearizes to the Hermitian ample line bundle L on M. Assume that 0 is a regular value of the…

Momentum space Ward identities are derived for the amputated n-point Green's functions in 3+1 dimensional non-relativistic conformal field theory. For n=4 and 6 the implications for scattering amplitudes (i.e. on-shell amputated Green's…

Graphons are symmetric measurable functions that arise from a sequence of graphs. A graphon variety is the a set of all graphons defined by a condition of the form $t(g, W) = 0$ for a fixed quantum graph $g$, where $t(.,.)$ is the…

We study positive kernels on $X\times X$, where $X$ is a set equipped with an action of a group, and taking values in the set of $\mathcal A$-sesquilinear forms on a (not necessarily Hilbert) module over a $C^*$-algebra $\mathcal A$. These…