Breaking Instance-Independent Symmetries In Exact Graph Coloring

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI, such as planning, time-tabling and scheduling. Provably optimal solutions may be desirable for commercial and defense applications. Additionally, for applications such as register allocation and code optimization, naturally-occurring instances of graph coloring are often small and can be solved optimally. A recent wave of improvements in algorithms for Boolean satisfiability (SAT) and 0-1 Integer Linear Programming (ILP) suggests generic problem-reduction methods, rather than problem-specific heuristics, because (1) heuristics may be upset by new constraints, (2) heuristics tend to ignore structure, and (3) many relevant problems are provably inapproximable. Problem reductions often lead to highly symmetric SAT instances, and symmetries are known to slow down SAT solvers. In this work, we compare several avenues for symmetry breaking, in particular when certain kinds of symmetry are present in all generated instances. Our focus on reducing CSPs to SAT allows us to leverage recent dramatic improvement in SAT solvers and automatically benefit from future progress. We can use a variety of black-box SAT solvers without modifying their source code because our symmetry-breaking techniques are static, i.e., we detect symmetries and add symmetry breaking predicates (SBPs) during pre-processing. An important result of our work is that among the types of instance-independent SBPs we studied and their combinations, the simplest and least complete constructions are the most effective. Our experiments also clearly indicate that instance-independent symmetries should mostly be processed together with instance-specific symmetries rather than at the specification level, contrary to what has been suggested in the literature

Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity

It is shown that in non-linear electrodynamics (in particular, Born-Infeld one) in the framework of general relativity there exist "weakly singular" configurations such that (i) the proper mass M is finite in spite of divergences of the energy density, (ii) the electric charge q and Schwarzschild mass m ~ q can be made as small as one likes, (iv) all field and energy distributions are concentrated in the core region. This region has an almost zero surface area but a finite longitudinal size L=2M. Such configurations can be viewed as a new version of a classical analogue of an elementary particle.Comment: 11 pages. 1 reference added. To appear in Grav. Cosm

An Open Inflationary Model for Dimensional Reduction and its Effects on the Observable Parameters of the Universe

Assuming that higher dimensions existed in the early stages of the universe where the evolution was inflationary, we construct an open, singularity-free, spatially homogeneous and isotropic cosmological model to study the effects of dimensional reduction that may have taken place during the early stages of the universe. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. By imposing suitable boundary conditions we trace their effects on the present day parameters of the universe.Comment: 5 pages, accepted for publication in Int. J. of Mod. Phys.

Parity violating cylindrical shell in the framework of QED

We present calculations of Casimir energy (CE) in a system of quantized electromagnetic (EM) field interacting with an infinite circular cylindrical shell (which we call `the defect'). Interaction is described in the only QFT-consistent way by Chern-Simon action concentrated on the defect, with a single coupling constant $a$. For regularization of UV divergencies of the theory we use % physically motivated Pauli-Villars regularization of the free EM action. The divergencies are extracted as a polynomial in regularization mass $M$, and they renormalize classical part of the surface action. We reveal the dependence of CE on the coupling constant $a$. Corresponding Casimir force is attractive for all values of $a$. For $a\to\infty$ we reproduce the known results for CE for perfectly conducting cylindrical shell first obtained by DeRaad and Milton.Comment: Typos corrected. Some references adde

Влияние релаксационных процессов при деформировании на электрическое сопротивление полипропиленовых композитов с техническим углеродом

Objectives. To study the relationship between bending deformation and the change in the electrical resistance of carbon black polypropylene composites.Methods. Conductive polypropylene composites filled with carbon black UM-76 were investigated. The samples were deformed and kept under constant bending at temperatures of 20–155 °C.Results. The deformation of the samples led to a reversible increase in their electrical resistance, while subsequent holding of the samples in the deformed state was accompanied by an exponential drop in their electrical resistance. The average times and activation energies of the electrical relaxation of the deformed polypropylene composites were calculated (30–32 kJ/mol) and compared with similar characteristics of polyethylene composites (15–16 kJ/mol).Conclusions. The electrical resistance relaxation of deformed carbon black polypropylene composites at elevated temperatures is similar to their stress relaxation. The average times and activation energies of the electrical relaxation of deformed polypropylene composites are comparable with similar data on their mechanical relaxation. It was found that these electrical and mechanical phenomena are based on the same underlying physical processes.Цели. Работа посвящена изучению влияния деформации изгиба при повышенных температурах на изменение электрического сопротивления электропроводящих полипропиленовых композитов, наполненных техническим углеродом.Методы. Исследовались полипропиленовые композиты с техническим углеродом УМ-76. Образцы изгибались и выдерживались при заданном прогибе в интервале 20–155 °C.Результаты. При деформировании образцов наблюдался обратимый рост электрического сопротивления. Последующая выдержка образцов в деформированном состоянии сопровождалась экспоненциальным падением их электрического сопротивления. Были рассчитаны средние времена и энергия активации электрической релаксации деформированных полипропиленовых композитов (30–32 кДж/моль), а также проведено их сравнение с аналогичными характеристиками полиэтиленовых композитов (около 14–16 кДж/моль).Выводы. При механическом деформировании электропроводящих полипропиленовых композитов с техническим углеродом, в том числе при повышенных температурах, характер релаксации электрического сопротивления аналогичен характеру релаксации механического напряжения. Средние времена и энергия активации электрической релаксации деформированных полипропиленовых композитов сопоставимы с аналогичными показателями для механической релаксации. Это указывает на общий механизм этих процессов

Effective slip over superhydrophobic surfaces in thin channels

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.Comment: 4+ page

Geometry of a Centrosymmetric Electric Charge

The gravitational description given for an electric on the basis of exact solution of the Einstein-Maxwell equations eliminates Coulomb divergence. The internal pulsating semiconfined world formed by neutral dust is smoothly joined with parallel Reissner-Nordstrem vacuum worlds via two static bottlenecks. The charge, rest mass, and electric field are expressed in terms of the space curvatures. The internal and external parameters of the maximon, electron, and the universe form a power series.Comment: 12 pages, 2 figures, 1 tabl

The Universe out of an Elementary Particle?

We consider a model of an elementary particle as a 2 + 1 dimensional brane evolving in a 3 + 1 dimensional space. Introducing gauge fields that live in the brane as well as normal surface tension can lead to a stable "elementary particle" configuration. Considering the possibility of non vanishing vacuum energy inside the bubble leads, when gravitational effects are considered, to the possibility of a quantum decay of such "elementary particle" into an infinite universe. Some remarkable features of the quantum mechanics of this process are discussed, in particular the relation between possible boundary conditions and the question of instability towards Universe formation is analyzed

The Boltzmann equation for colourless plasmons in hot QCD plasma. Semiclassical approximation

Within the framework of the semiclassical approximation, we derive the Boltzmann equation describing the dynamics of colorless plasmons in a hot QCD plasma. The probability of the plasmon-plasmon scattering at the leading order in the coupling constant is obtained. This probability is gauge-independent at least in the class of the covariant and temporal gauges. It is noted that the structure of the scattering kernel possesses important qualitative difference from the corresponding one in the Abelian plasma, in spite of the fact that we focused our study on the colorless soft excitations. It is shown that four-plasmon decay is suppressed by the power of $g$ relative to the process of nonlinear scattering of plasmons by thermal particles at the soft momentum scale. It is stated that the former process becomes important in going to the ultrasoft region of the momentum scale.Comment: 41, LaTeX, minor changes, identical to published versio