Related papers: The evaluation of loop amplitudes via differential…
We study the problem of dictionary learning for signals that can be represented as polynomials or polynomial matrices, such as convolutive signals with time delays or acoustic impulse responses. Recently, we developed a method for…
We discuss algebraic/numeric methods to compute one-loop corrections for multiparticle/jet production cross sections. By using efficient reduction algorithms a compact expression for the ggg\gamma\gamma -> 0 amplitude is obtained. Further a…
We point out the need to use probability amplitudes rather than probabilities to model evidence accumulation in decision processes involving real physical sensors. Optical information processing systems are given as typical examples of…
When proving invariance properties of a program, we face two problems. The first problem is related to the necessity of proving tautologies of considered assertion language, whereas the second manifests in the need of finding sufficiently…
The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass.…
We introduce a new technique to generate scattering amplitudes at one loop. Traditional tree algorithms, which handle diagrams with fixed momenta, are promoted to generators of loop-momentum polynomials that we call open loops. Combining…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
We present and develop a general dispersive framework allowing us to construct representations of the amplitudes for the processes $P\pi\to\pi\pi$, $P=K,\eta$, valid at the two-loop level in the low-energy expansion. The construction…
I discuss the physical picture underlying the evolution equations with Pomeron loops recently derived in multicolor QCD at high energy and qualitatively explain the notion of `self-duality'.
We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations.…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
The coupled cluster iteration scheme for determining the cluster amplitudes involves a set of nonlinearly coupled difference equations. In the space spanned by the amplitudes, the set of equations are analysed as a multivariate…
This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…
General scheme for covariant calculation of the amplitudes of processes with the polarized Dirac particles is considered. It is so concretized that the obtained expressions can be used for calculation of the amplitudes of processes with…
Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…
Multi-loop superstring amplitude are calculated in the convenient gauge where Grassmann moduli are carried by the 2D gravitino field. Generally, instead of the modular symmetry, the amplitudes hold the symmetry under modular transformations…
We derive evolution equations for the first and second moments of an initially mismatched, coupled, and displaced arbitrary Gaussian phase-space distribution under the influence of decoherence due to amplitude-dependent tune shift.…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
We study models of quintessence consisting of a number of scalar fields coupled to several dark matter components. In the case of exponential potentials the scaling solutions can be described in terms of a single field. The corresponding…
We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level,…