An optimization algorithm for a penalized knapsack problem

We study a variation of the knapsack problem in which each item has a profit, a weight and a penalty; the sum of profits of the selected items minus the largest penalty associated with the selected items must be maximized. We present an ILP formulation and an exact optimization algorithm.     

On the spectrum of certain noncommutative harmonic oscillators

Abstract Some spectral properties of certain 2×2 globally elliptic systems of ordinary differential operators, a class of vector-valued deformations of the classical harmonic oscillator here called noncommutative harmonic oscillators, will be described, with special emphasis on the Poisson relation and clustering properties of the eigenvalues. Keywords: Clustering theorems, Periodic trajectories, Poisson relations, Noncommutative harmonic oscillators     

Online weighted flow time and deadline scheduling

In this paper we study some aspects of weighted flow time. We first show that the online algorithm Highest Density First is an O(1)-speed O(1)-approximation algorithm for P|r_i,pmtn|∑w_iF_i. We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any c-competitive online algorithm for weighted flow time must also be c-competitive for deadline scheduling. We then give an O(1)-competitive algorithm for deadline scheduling.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

An Improved Anharmonic Force Field of Difluoromethanimine, F2C NH

The anharmonic force field of difluoromethanimine, F₂C NH, has been reinvestigated theoretically using a coupled-cluster singles and doubles approach, augmented for structural optimization and harmonic force field by a contribution of connected triple excitations, CCSD(T). The cubic and quartic force constants have been obtained by numerical derivatives computed from analytical quadratic force constants calculated by second-order Møller-Plesset perturbation theory, MP2. The quadratic force constants and the equilibrium structure of F₂C NH have then been scaled by a global least-squares fitting procedure to the spectroscopic data and parameters experimentally determined for this molecule. This force field, obtained in the internal coordinates space and therefore valid for all isotopomers of difluoromethanimine, yields a complete set of spectroscopic molecular constants providing a critical assessment of the experimental rotational and centrifugal distortion constants, fundamentals, overtones, and combination bands determined so far for F₂C NH. In addition, the final force field can be used to make predictions of all important vibrational and rotational parameters which should be accurate and useful for new spectroscopic investigations.     

Inverse Pattern Matching

Let a textstringTofnsymbols from some alphabet Σ and an integerm < nbe given. A patternPof lengthmover Σ is sought such thatPminimizes (alternatively, maximizes) the total number of pairwise character mismatches generated whenPis compared with allm-character substrings ofT. Two additional variants of the problem are obtained by adding the constraint thatPbe (respectively, not be) a substring ofT. Efficient sequential algorithms are proposed in this paper for the problem and its variants.     

Abelian BF Theories and Knot Invariants

In the context of the Batalin–Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander–Conway polynomial. The three-dimensional case is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula for the second coefficient of the Alexander–Conway polynomial is obtained. An account on the higher-dimensional generalizations is also given. Received: 2 October 1996 / Accepted: 21 March 1997