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Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss the systematic expansion in large intermediate spin…
We compute the large size limit of the moment formula derived in \cite{DHS} for the Hermitian Jacobi process at fixed time. Our computations rely on the polynomial division algorithm which allows to obtain cancellations similar to those…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…
Several physics-based algorithms for factorizing large number were recently published. A notable recent one by Schleich et al. uses Gauss sums for distinguishing between factors and non-factors. We demonstrate two NMR techniques that…
The resummation for the event-shape variable jet broadening is extended to next-to-next-to-leading logarithmic accuracy by computing the relevant jet and soft functions at one-loop order and the collinear anomaly to two-loop accuracy. The…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
The deep inelastic scattering data on the nucleon F_2 structure function, accumulated by BCDMS, SLAC and NMC collaborations in fixed-target experiments, are analyzed in the non-singlet approximation within the frameworks of both…
We extend the class of factorization theorems for non-global observables from fixed angular constraints to cross sections defined in terms of sequential jet clustering. The associated hard and soft functions depend not only on the…
We summarize recent progress in the resummation of perturbative evolution at small x. We show that the problem of incorporating BFKL small x logs in GLAP evolution is now completely solved, and that the main effect of small x resummation is…
We present a method for the analytic solution of small $x$ structure functions. The essential small $x$ logarithms are summed to all orders in the anomalous dimensions and coefficient functions. Although we work at leading logarithmic…
Infinite lattice summation scheme based on the idea of renormalization is generalized to enable evaluation of infinite lattice sums with Bloch phase factors which can occur when treating long-range interactions in infinite periodic systems.…
We discuss resummation strategies for free energy in quantum field theories at nonzero temperatures T. We point out that resummations should be performed for the short- and long-distance parts separately in order to avoid spurious…
This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…
This talk reviews some recent results on the NLL resummed small-x gluon splitting function, as determined including renormalisation-group improvements. It also discusses the observation that the LO, NLO, NNLO, etc. hierarchy for the gluon…
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions of certain types of parametrized partial differential…
We offer multiplication method for factoring big natural numbers which extends the group of the Fermat's and Lehman's factorization algorithms and has run-time complexity $O(n^{1/3})$. This paper is argued the finiteness of proposed…
Perturbative calculations for processes involving heavy flavours can be carried out using two approaches: the massive and the massless schemes. These schemes can also be combined to leverage their respective strengths. Additionally, both…