SELECTED ASPECTS OF ETCS-L3 DEPLOYMENT

This paper focuses on selected problem areas in the implementation of ETCS L3, analyz-es their impacts and offers a number of possible solutions as a basis for pilot testing. It compares the suitability of each solution and summarizes their advantages and disadvantages

An Algorithmic Theory of Integer Programming

We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We show that integer programming can be solved in time $g(a,d)\textrm{poly}(n,L)$, where $g$ is some computable function of the parameters $a$ and $d$, and $L$ is the binary encoding length of the input. In particular, integer programming is fixed-parameter tractable parameterized by $a$ and $d$, and is solvable in polynomial time for every fixed $a$ and $d$. Our results also extend to nonlinear separable convex objective functions. Moreover, for linear objectives, we derive a strongly-polynomial algorithm, that is, with running time $g(a,d)\textrm{poly}(n)$, independent of the rest of the input data. We obtain these results by developing an algorithmic framework based on the idea of iterative augmentation: starting from an initial feasible solution, we show how to quickly find augmenting steps which rapidly converge to an optimum. A central notion in this framework is the Graver basis of the matrix $A$, which constitutes a set of fundamental augmenting steps. The iterative augmentation idea is then enhanced via the use of other techniques such as new and improved bounds on the Graver basis, rapid solution of integer programs with bounded variables, proximity theorems and a new proximity-scaling algorithm, the notion of a reduced objective function, and others. As a consequence of our work, we advance the state of the art of solving block-structured integer programs. In particular, we develop near-linear time algorithms for $n$-fold, tree-fold, and $2$-stage stochastic integer programs. We also discuss some of the many applications of these classes.Comment: Revision 2: - strengthened dual treedepth lower bound - simplified proximity-scaling algorith

Calculation of the Positions of the α- and β-bands in the Electronic Spectra of Benzenoid Hydrocarbons Using the Method of Limited Configuration Interaction

The positions of the α- and β-bands in the electronic absorption spectra of twenty aromatic benzenoid hydrocarbons were calculated by the semiempirical method of limited configuration interaction in the π-electron approximation using the Huckel molecular orbitals. The agreement of the experimental and calculated values is good for the β-band whereas a systematic deviation is observed for the α-band. This deviation cannot be removed by extending the configuration interaction of the monoexcited states constructed from the molecular orbitals considered. However, the consideration of electronic repulsion enables us to explain the character of the dependences of the experimental excitation energies on the excitation energies obtained by the simple Huckel method of molecular orbitals. Using a suitable choice of semiempirical parameters different for various electronic transitions (showing no large mutual differences) yields semiempirical interpolation formulas for the; p-, α-, and β-bands which give very good agreement with the corresponding experimental excitation energies for the compounds studied