Related papers: Contour calculus for many-particle functions
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
It's pointed out that the values of the generators derived by the modern gyrokinetic theory are inappropriately amplified by the pullback transform with the existence of electromagnetic perturbation, and the trajectory equations of the…
Motivated by variational models in continuum mechanics, we introduce a novel algorithm to perform nonsmooth and nonconvex minimizations with linear constraints in Euclidean spaces. We show how this algorithm is actually a natural…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
We present equations of motion for charged particles using balanced equations, and without introducing explicitly divergent quantities. This derivation contains as particular cases some well known equations of motion, as the Lorentz-Dirac…
Systems of equations are invariant under "polydimensional transformations" which reshuffle the geometry such that what is a line or a plane is dependent upon the frame of reference. This leads us to propose an extension of Clifford calculus…
We investigate quadrature rules for measures supported on real algebraic and rational curves, focusing on the {odd-degree} case \(2s-1\). Adopting an optimization viewpoint, we minimize suitable penalty functions over the space of…
We develop the theory of discrete-time gradient flows for convex functions on Alexandrov spaces with arbitrary upper or lower curvature bounds. We employ different resolvent maps in the upper and lower curvature bound cases to construct…
A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet…
Large-scale knowledge graphs provide structured representations of human knowledge. However, as it is impossible to collect all knowledge, knowledge graphs are usually incomplete. Reasoning based on existing facts paves a way to discover…
We develop a Lagrange multiplier theory for nonconvex set-valued optimization problems under Lipschitz-type regularity conditions. Instead of classical continuous linear functionals, we introduce closed convex processes -- set-valued…
High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They…
We explore the extension of chiral perturbation theory out of thermal equilibrium. The pion decay constant becomes then a time-dependent function and we work within the Schwinger-Keldysh contour technique. A useful connection with curved…
We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour…
We present a practical numerical method for evaluating the Lagrange multipliers necessary for maintaining a constrained linear geometry of particles in dynamical simulations. The method involves no iterations, and is limited in accuracy…