Towards Effective Exact Algorithms for the Maximum Balanced Biclique Problem

The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP. Firstly, we introduce an Upper Bound Propagation procedure to pre-compute an upper bound involving each vertex. Then we extend an existing branch-and-bound algorithm by integrating the pre-computed upper bounds. We also present a set of new valid inequalities induced from the upper bounds to tighten an existing mathematical formulation for MBBP. Lastly, we investigate another exact algorithm scheme which enumerates a subset of balanced bicliques based on our upper bounds. Experiments show that compared to existing approaches, the proposed algorithms and formulations are more efficient in solving a set of random graphs and large real-life instances

Robust Model Predictive Control for Signal Temporal Logic Synthesis

Most automated systems operate in uncertain or adversarial conditions, and have to be capable of reliably reacting to changes in the environment. The focus of this paper is on automatically synthesizing reactive controllers for cyber-physical systems subject to signal temporal logic (STL) specifications. We build on recent work that encodes STL specifications as mixed integer linear constraints on the variables of a discrete-time model of the system and environment dynamics. To obtain a reactive controller, we present solutions to the worst-case model predictive control (MPC) problem using a suite of mixed integer linear programming techniques. We demonstrate the comparative effectiveness of several existing worst-case MPC techniques, when applied to the problem of control subject to temporal logic specifications; our empirical results emphasize the need to develop specialized solutions for this domain

Boundary conditions and the entropy bound

The entropy-to-energy bound is examined for a quantum scalar field confined to a cavity and satisfying Robin condition on the boundary of the cavity. It is found that near certain points in the space of the parameter defining the boundary condition the lowest eigenfrequency (while non-zero) becomes arbitrarily small. Estimating, according to Bekenstein and Schiffer, the ratio $S/E$ by the $\zeta$-function, $(24\zeta (4))^{1/4}$, we compute $\zeta (4)$ explicitly and find that it is not bounded near those points that signals violation of the bound. We interpret our results as imposing certain constraints on the value of the boundary interaction and estimate the forbidden region in the parameter space of the boundary conditions.Comment: 16 pages, latex, v2: typos corrected, to appear in Phys.Rev.

Specialising finite domain programs with polyhedra

A procedure is described for tightening domain constraints of finite domain logic programs by applying a static analysis based on convex polyhedra. Individual finite domain constraints are over-approximated by polyhedra to describe the solution space over ninteger variables as an n dimensional polyhedron. This polyhedron is then approximated, using projection, as an n dimensional bounding box that can be used to specialise and improve the domain constraints. The analysis can be implemented straightforwardly and an empirical evaluation of the specialisation technique is given

Constraints on transmission, dispersion, and density of states in dielectric multilayers and stepwise potential barriers with arbitrary layer arrangement

Normal-incidence transmission and dispersion properties of optical multilayers and one-dimensional stepwise potential barriers in the non-tunneling regime are analytically investigated. The optical paths of every constituent layer in a multilayer structure, as well as the parameters of every step of the stepwise potential barrier, are constrained by a generalized quarter-wave condition. No other restrictions on the structure geometry is imposed, i.e., the layers are arranged arbitrarily. We show that the density of states (DOS) spectra of the multilayer or barrier in question are subject to integral conservation rules similar to the Barnett-Loudon sum rule but ocurring within a finite frequency or energy interval. In the optical case, these frequency intervals are regular. For the potential barriers, only non-periodic energy intervals can be present in the spectrum of any given structure, and only if the parameters of constituent potential steps are properly chosen. Abstract The integral conservation relations derived analytically have also been verified numerically. The relations can be used in dispersion-engineered multilayer-based devices, e.g., ultrashort pulse compressors or ultracompact optical delay lines, as well as to design multiple-quantum-well electronic heterostructures with engineered DOS.Comment: 10 pages, 5 figures, to be submitted to PR

Neutrino Propagation in a Strongly Magnetized Medium

We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained for neutral and charged media in the strong-field limit ($M_{W}\gg \sqrt{B}\gg m_{e},T,\mu ,| \mathbf{p}|$) using the lowest Landau level approximation. The results found within the lowest Landau level approximation are numerically validated, summing in all Landau levels, for strong $B\gg T^{2}$ and weakly-strong $B \gtrsim T^{2}$ fields. The neutrino energy in leading order of the Fermi coupling constant is expressed as the sum of three terms: a kinetic-energy term, a term of interaction between the magnetic field and an induced neutrino magnetic moment, and a rest-energy term. The leading radiative correction to the kinetic-energy term depends linearly on the magnetic field strength and is independent of the chemical potential. The other two terms are only present in a charged medium. For strong and weakly-strong fields, it is found that the field-dependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered.Comment: 23 pages, 4 figures. Corrected misprints in reference