Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

Basics of Feature Selection and Statistical Learning for High Energy Physics

This document introduces basics in data preparation, feature selection and learning basics for high energy physics tasks. The emphasis is on feature selection by principal component analysis, information gain and significance measures for features. As examples for basic statistical learning algorithms, the maximum a posteriori and maximum likelihood classifiers are shown. Furthermore, a simple rule based classification as a means for automated cut finding is introduced. Finally two toolboxes for the application of statistical learning techniques are introduced.Comment: 12 pages, 8 figures. Part of the proceedings of the Track 'Computational Intelligence for HEP Data Analysis' at iCSC 200

Entropic effects in large-scale Monte Carlo simulations

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic mismatch or divergence between the direct and reverse trial moves. We provide lower and upper bounds for the average acceptance probability in terms of the Renyi divergence of order 1/2. We show that the asymptotic finitude of the entropic divergence is the necessary and sufficient condition for non-vanishing acceptance probabilities in the limit of large dimensions. Furthermore, we demonstrate that the upper bound is reasonably tight by showing that the exponent is asymptotically exact for systems made up of a large number of independent and identically distributed subsystems. For the last statement, we provide an alternative proof that relies on the reformulation of the acceptance probability as a large deviation problem. The reformulation also leads to a class of low-variance estimators for strongly asymmetric distributions. We show that the entropy divergence causes a decay in the average displacements with the number of dimensions n that are simultaneously updated. For systems that have a well-defined thermodynamic limit, the decay is demonstrated to be n^{-1/2} for random-walk Monte Carlo and n^{-1/6} for Smart Monte Carlo (SMC). Numerical simulations of the LJ_38 cluster show that SMC is virtually as efficient as the Markov chain implementation of the Gibbs sampler, which is normally utilized for Lennard-Jones clusters. An application of the entropic inequalities to the parallel tempering method demonstrates that the number of replicas increases as the square root of the heat capacity of the system.Comment: minor corrections; the best compromise for the value of the epsilon parameter in Eq. A9 is now shown to be log(2); 13 pages, 4 figures, to appear in PR

Very High Multiplicity Hadron Processes

The paper contains a description of a first attempt to understand the extremely inelastic high energy hadron collisions, when the multiplicity of produced hadrons considerably exceeds its mean value. Problems with existing model predictions are discussed. The real-time finite-temperature $S$-matrix theory is built to have a possibility to find model-free predictions. This allows to include the statistical effects into consideration and build the phenomenology. The questions to experiment are formulated at the very end of the paper.Comment: 76 pp., 4 fig

Critical Unmixing of Polymer Solutions

We present Monte Carlo simulations of semidilute solutions of long self-attracting chain polymers near their Ising type critical point. The polymers are modeled as monodisperse self-avoiding walks on the simple cubic lattice with attraction between non-bonded nearest neighbors. Chain lengths are up to N=2048, system sizes are up to $2^{21}$ lattice sites and $2.8\times 10^5$ monomers. These simulations used the recently introduced pruned-enriched Rosenbluth method which proved extremely efficient, together with a histogram method for estimating finite size corrections. Our most clear result is that chains at the critical point are Gaussian for large $N$, having end-to-end distances $R\sim\sqrt{N}$. Also the distance $T_\Theta-T_c(N)$ (where $T_\Theta = \lim_{N\to\infty} T_c(N)$) scales with the mean field exponent, $T_\Theta -T_c(N)\sim 1/\sqrt{N}$. The critical density seems to scale with a non-trivial exponent similar to that observed in experiments. But we argue that this is due to large logarithmic corrections. These corrections are similar to the very large corrections to scaling seen in recent analyses of $\Theta$-polymers, and qualitatively predicted by the field theoretic renormalization group. The only serious deviation from this simple global picture concerns the N-dependence of the order parameter amplitudes which disagrees with a minimalistic ansatz of de Gennes. But this might be due to problems with finite size scaling. We find that the finite size dependence of the density of states $P(E,n)$ (where $E$ is the total energy and $n$ is the number of chains) is slightly but significantly different from that proposed recently by several authors.Comment: minor changes; Latex, 22 pages, submitted to J. Chem. Phy

The cavity method for large deviations

A method is introduced for studying large deviations in the context of statistical physics of disordered systems. The approach, based on an extension of the cavity method to atypical realizations of the quenched disorder, allows us to compute exponentially small probabilities (rate functions) over different classes of random graphs. It is illustrated with two combinatorial optimization problems, the vertex-cover and coloring problems, for which the presence of replica symmetry breaking phases is taken into account. Applications include the analysis of models on adaptive graph structures.Comment: 18 pages, 7 figure

Shift-invert diagonalization of large many-body localizing spin chains

We provide a pedagogical review on the calculation of highly excited eigenstates of disordered interacting quantum systems which can undergo a many-body localization (MBL) transition, using shift-invert exact diagonalization. We also provide an example code at https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the simulational parameters of the random field Heisenberg spin chain, we provide a practical guide on how to perform efficient computations. We present data for mid-spectrum eigenstates of spin chains of sizes up to $L=26$. This work is also geared towards readers with interest in efficiency of parallel sparse linear algebra techniques that will find a challenging application in the MBL problem