Finding multiple solutions to general integer linear programs

Integer linear programming (ILP) problems occur frequently in many applications. In practice, alternative optima are useful since they allow the decision maker to choose from multiple solutions without experiencing any deterioration in the objective function. This study proposes a general integer cut to exclude the previous solution and presents an algorithm to identify all alternative optimal solutions of an ILP problem. Numerical examples in real applications are presented to demonstrate the usefulness of the proposed method.     

A variational approach to a quasi-one-dimensional blume-emery-griffiths model

Summary The system considered consists of spin-1 objects arranged on a three-dimensional lattice. It is characterized by an anisotropic Blume-Emery-Griffiths Hamiltonian in which the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain coupling constants so that the system can be considered quasi-one-dimensional. The method of analysis utilizes first the exact solution of the one-dimensional case and then the Bogolubov variational principle. The critical properties are examined and the phase diagram derived.

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Riassunto Il sistema considerato consiste di oggetti a spin-1 disposti su un reticolo tridimensionale ed è caratterizzato da una Hamiltoniana anisotropa in cui le costanti dipolari e quadrupolari di accoppiamento all’interno delle catene sono molto maggiori delle corrispondenti costanti di accoppiamento fra catene, cosicché il sistema può essere considerato quasi unidimensionale. Il metodo di analisi impiegato utilizza anzitutto la soluzione esatta del caso unidimensionale e successivamente il principio variazionale di Bogolubov. Si esaminano le proprietà critiche e si ricava il diagramma di fase.

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Резюме Рассматривается система, которая состоит из объектов со спином 1, образующих трехмерную решетку. Эта система характеризуется Гамильтонианом Ълуме-Эмери-Гриффитса, в котором дипольные и квадрапольные внутрицепочечные постоянные связи являются более сильными, чем соответствующие постоянные связи между цепочками, так что система может быть рассмотрена, как квази-одномерная. Метод анализа использует сначала точное решение для одномерного случая, а затем вариационный принцип Ъоголюбова. Исслеледуются критические свойства и выводится фазовая диаграмма.

     

Behavior of human serum albumin on strong cation exchange resins: II. Model analysis

Experiments with human serum albumin on a strong cation exchange resin exhibit a peculiar elution pattern: the protein elutes with two peaks in a modifier gradient. This behavior is modeled with a general rate model, where the two elution peaks are modeled with two binding conformations, one of which is at equilibrium conditions, while for the other, the adsorption process is rate limited. Isocratic experiments under nonadsorbing conditions were used to characterize the mass transfer process. The isotherm of both adsorption conformations as well as the kinetic of adsorption and desorption for the second conformation are functions of the modifier concentration. They are evaluated with linear modifier gradient experiments and step experiments with various adsorption times. All experimental features are well reproduced by the proposed modified general rate model.     

Singular densities,test particles and generalized Hamiltonian systems in general relativity

We derive the motion equations and the structure equations of neutral and charged test particles, starting from the gravitational field equations. The method consists in the application of conservation laws to singular tensor densities, which represent regions of strong matter concentration. Moreover, a Hamiltonian formulation of the particle equations is given, in the form of implicit differential equations generated by Hamiltonian Morse families.     

Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Constrained independent component analysis (CICA) eliminates the order ambiguity of standard ICA by incorporating prior information into the learning process to sort the components intrinsically. However, the original CICA (OCICA) and its variants depend on a learning rate, which is not easy to be tuned for various applications. To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept. A complete stability analysis was provided for the proposed methods, which also made a correction to the stability analysis given to OCICA. Variations for adding constraints either to the components or to the associated time courses were derived too. Using synthetic data, the proposed methods yielded a better stability and a better source separation quality in terms of higher signal-to-noise-ratio and smaller performance index than OCICA. For the artificially generated brain activations, the new CICAs demonstrated a better sensitivity/specificity performance than standard univariate general linear model (GLM) and standard ICA. Original CICA showed a similar sensitivity/specificity gain but failed to converge for several times. Using functional magnetic resonance imaging (fMRI) data acquired with a well-characterized sensorimotor task, the proposed CICAs yielded better sensitivity than OCICA, standard ICA and GLM in all the target functional regions in terms of either higher t values or larger suprathreshold cluster extensions using the same significance threshold. In addition, they were more stable than OCICA and standard ICA for analyzing the sensorimotor fMRI data.     

Infinite horizon stopping problems with (nearly) total reward criteria

We study an infinite horizon optimal stopping Markov problem which is either undiscounted (total reward) or with a general Markovian discount rate. Using ergodic properties of the underlying Markov process, we establish the feasibility of the stopping problem and prove the existence of optimal and ε$\epsilon$-optimal stopping times. We show the continuity of the value function and its variational characterisation (in the viscosity sense) under different sets of assumptions satisfied by large classes of diffusion and jump–diffusion processes. In the case of a general discounted problem we relax a classical assumption that the discount rate is uniformly separated from zero.     

On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models

Necessary and sufficient conditions are derived for the equalities of the best linear unbiased estimators (BLUEs) of parametric functions under a general linear model and its restricted and stochastically restricted models to hold.