FPT-algorithms for some problems related to integer programming

In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The parameter is the maximum absolute value of rank minors of the corresponding matrices. Additionally, we present FPT-algorithms with respect to the same parameter for the problems, when the matrices have no singular rank sub-matrices.Comment: arXiv admin note: text overlap with arXiv:1710.00321 From author: some minor corrections has been don

Kinematic and vertex fitting package for the CMD-3 experiment

In this article, we discuss a new software package of kinematic and vertex fitting for the CMD-3 experiment at the VEPP-2000 electron-positron collider. The authors describe in detail the fitting algorithm, parametrization of four-momenta and trajectories of various particles and present the results of testing the fitting package using events of Monte Carlo simulation of various $e^+e^-$ annihilation processes. The authors also provide several examples of the fitting package validation using Gaussian simulation. Although the package discussed in this article is intended for the CMD-3 experiment, it can also be used in other experiments. The authors consider the described package as their first step towards a more universal and rigrous kinematic and vertex fitting package that can be used in future $e^+e^-$ experiments, such as the Super Charm-Tau factory

A faster algorithm for counting the integer points number in Δ\Delta-modular polyhedra

Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem to count a number of integer points inside $P$, assuming that $P$ is $\Delta$-modular. The polytope $P$ is $\Delta$-modular if all the rank sub-determinants of $A$ are bounded by $\Delta$ in the absolute value. We present a new FPT-algorithm, parameterized by $\Delta$ and by the number of simple cones in the normal fun triangulation of $P$, which is more efficient for $\Delta$-modular problems, than the approach of A.~Barvinok et al. To this end, we do not directly compute the short rational generating function for $P \cap Z^n$, which is commonly used for the considered problem. We compute its particular representation in the form of exponential series that depends on one variable, using the dynamic programming principle. We completely do not use the A.~Barvinok's unimodular sign decomposition technique. Using our new complexity bound, we consider different special cases that may be of independent interest. For example, we give FPT-algorithms for counting the integer points number in $\Delta$-modular simplicies and similar polytopes that have $n + O(1)$ facets. For any fixed $m$, we give an FPT-algorithm to count solutions of the unbounded $m$-dimensional $\Delta$-modular knapsack problem. For the case, when $\Delta$ grows slowly with respect to $n$, we give a counting algorithm, which is more effective, than the state of the art ILP feasibility algorithm

Hamiltonian structures of fermionic two-dimensional Toda lattice hierarchies

By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as particular cases. We develop the generalized graded R-matrix formalism using the generalized graded bracket on the space of graded operators with involution generalizing the graded commutator in superalgebras, which allows one to describe these hierarchies in the framework of the Hamiltonian formalism and construct their first two Hamiltonian structures. The first Hamiltonian structure is obtained for both bosonic and fermionic Lax operators while the second Hamiltonian structure is established for bosonic Lax operators only.Comment: 12 pages, LaTeX, the talks delivered at the International Workshop on Classical and Quantum Integrable Systems (Dubna, January 24 - 28, 2005) and International Conference on Theoretical Physics (Moscow, April 11 - 16, 2005

Hadronic structure aspects of K+→π−+l1++l2+K^+\to \pi^-+ l^{+}_1 + l^{+}_2 decays

As is known from previous studies the lepton number violating decays $K^+\to \pi^- + l^{+}_1 + l^{+}_2$ have good prospects to probe new physics beyond the Standard Model and provide valuable information on neutrino masses and mixing. We analyze these processes with an emphasis on their hadronic structure aspects applying relativistic constituent quark model. We conclude that the previously ignored contribution associated with the t-channel Majorana neutrino exchange is comparable with the s-channel one in a wide range of neutrino masses. We also estimated model independent absolute upper bounds on neutrino contribution to these decays.Comment: 15 pages, 1 figure. Version to appear in PRD, normalization factor in Eq. (25) is correcte

Nonlinear Realizations of the W3(2)W_3^{(2)} Algebra

In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and evolution coordinates. By adding one more space coordinate and introducing two copies of the $W_3^{(2)}$ algebra, the same method yields the $sl(3,R)$ Toda lattice equations.Comment: LaTeX, 10p., Preprint LNF-94/013 (P

AC/DC Susceptibility of the Heavy-Fermion Superconductor CePt3Si under Pressure

We have investigated the pressure dependence of ac and dc susceptibilities of the heavy-fermion superconductor CePt3Si (Tc= 0.75 K) that coexists with antiferromagnetism (TN = 2.2 K). As hydrostatic pressure is increased, Tc first decreases rapidly, then rather slowly near the critical pressure Pc = 0.6 GPa and shows a stronger decrease again at higher pressures, where Pc is the pressure at which TN becomes zero. A transition width and a difference in the two transition temperatures defined in the form of structures in the out-of-phase component of ac susceptibilities also become small near Pc, indicating that a double transition observed in CePt3Si is caused by some inhomogeneous property in the sample that leads to a spatial variation of local pressure. A sudden increase in the Meissner fraction above Pc suggests the influence of antiferromagnetism on superconductivity.Comment: 4 pages with 5 figures. This paper will be published in J. Phys. Soc. Jp