Improvements to MCS algorithm for the maximum clique problem

In this paper we present improvements to one of the most recent and fastest branch-and-bound algorithm for the maximum clique problem—MCS algorithm by Tomita et al. (Proceedings of the 4th international conference on Algorithms and Computation, WALCOM’10, pp. 191–203, 2010). The suggested improvements include: incorporating of an efficient heuristic returning a high-quality initial solution, fast detection of clique vertices in a set of candidates, better initial colouring, and avoiding dynamic memory allocation. Our computational study shows some impressive results, mainly we have solved p_hat1000-3 benchmark instance which is intractable for MCS algorithm and got speedups of 7, 3000, and 13000 times for gen400_p0.9_55, gen400_p0.9_65, and gen400_p0.9_75 instances correspondingly.     

Log-efficient search for significant inputs of linear model

This paper is concerned with the search for an unknown s-tuple A of significant inputs in a linear model with t random discrete carriers and finitely supported i.i.d. noise. We study the decision based on s maximal values of Shannon information between various input and the output N-sequences. It was studied in Malyutov and Sadaka (Random Oper. Stochastic Equations 6 (4) (1998) 339) (abbreviated as MS98) as one of two nonparametric decisions introduced there inspired by the related study in Csiszár and Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic Press, New York, NY, 1981. It was shown in MS98 that both decisions have the best asymptotic rates as t→∞ uniformly over arbitrary noise distributions and the set of significant parameters in the corresponding classes of tests. We show here that also provides the best rate of the mean error probability exponential decay (defined in Section 2) among the tests based on separate testing influence of each input to the output sequence for a natural class of random designs. The results of this paper (and MS98 for t→∞) justify the universal optimality of the introduced decisions, when used under random balance designs.     

Statistical inference through AFT model for biotechnical systems

The objective of this paper is to model the phenomenon of degradation-to-failure for assemblies used for lumbar arthrodesis, starting from the analysis of their structure/geometry, the load applied and the kind of failure when several occur. An AFT model is proposed to model the joint effects of the applied load and the structural dimensions of the brand (namely length and diameter of the screw, presence of a connector or not) on the failure time due to a screw failure. The estimations of S–N curves and maximum permissible load (named critical load) values are provided as functions of the structural dimensions of the product. This allows comparisons of devices in terms of key factors determining product behavior and ageing under loading stress.     

Quantity Competition When Most Favored Customers are Strategic

Legal studies usually treat a policy of a manufacturer or retailer as socially harmful if it reduces product output and increases the price. We consider a two‐period model where the first‐period price is fixed and resellers endogenously decide to use meet‐the‐competition clause with a most‐favored‐customer clause (MFC) to counteract strategic customer behavior. As a result of MFC, the second‐period (reduced) price increases and resellers’ inventories decrease. However, customer surplus may increase and aggregate welfare increases in the majority of market situations. MFC can mitigate the losses in welfare and resellers’ profits due to strategic customers. Moreover, under reseller competition, MFC may even lead to higher levels of these values than with myopic customers, that is, to gain from increased strategic behavior. With growing competition, benefits or losses from MFC can be higher than losses from strategic customer behavior.     

Linear latent structure analysis: Mixture distribution models with linear constraints

A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the local independence assumption. LLS analysis explicitly considers a family of mixed distributions as a linear space, and LLS models are obtained by imposing linear constraints on the mixing distribution.LLS models are identifiable under modest conditions and are consistently estimable. A remarkable feature of LLS analysis is the existence of a high-performance numerical algorithm, which reduces parameter estimation to a sequence of linear algebra problems. Simulation experiments with a prototype of the algorithm demonstrated a good quality of restoration of model parameters.     

A concise proof of a theorem on products of power sums

The heart of a direct solution of the problem of moments of moments is a formula for the expected value of a product of sample power sums in terms of a linear function of products of population power sums. Such a result was given by Skellam (1949) and, earlier and more generally, by Dwyer (1938). The approach here leads to a result for the easily handled case which features the product of unit power sums of each multivariate variable from which a general case comes by easy extension without the need of technical material required by the earlier approaches. A corollary provides a new solution for the problem of obtaining the unbiased estimate of any linear function of products of power sums.     

Optimal Taxes on Fossil Fuel in General Equilibrium

We analyze a dynamic stochastic general‐equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO₂ concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well‐known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.