Cutting plane methods for general integer programming

Integer programming (IP) problems are difficult to solve due to the integer restrictions imposed on them. A technique for solving these problems is the cutting plane method. In this method, linear constraints are added to the associated linear programming (LP) problem until an integer optimal solution is found. These constraints cut off part of the LP solution space but do not eliminate any feasible integer solution. In this report algorithms for solving IP due to Gomory and to Dantzig are presented. Two other cutting plane approaches and two extensions to Gomory's algorithm are also discussed. Although these methods are mathematically elegant they are known to have slow convergence and an explosive storage requirement. As a result cutting planes are generally not computationally successful

Manifold Learning in MR spectroscopy using nonlinear dimensionality reduction and unsupervised clustering

Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion Purpose To investigate whether nonlinear dimensionality reduction improves unsupervised classification of 1H MRS brain tumor data compared with a linear method. Methods In vivo single-voxel 1H magnetic resonance spectroscopy (55 patients) and 1H magnetic resonance spectroscopy imaging (MRSI) (29 patients) data were acquired from histopathologically diagnosed gliomas. Data reduction using Laplacian eigenmaps (LE) or independent component analysis (ICA) was followed by k-means clustering or agglomerative hierarchical clustering (AHC) for unsupervised learning to assess tumor grade and for tissue type segmentation of MRSI data. Results An accuracy of 93% in classification of glioma grade II and grade IV, with 100% accuracy in distinguishing tumor and normal spectra, was obtained by LE with unsupervised clustering, but not with the combination of k-means and ICA. With 1H MRSI data, LE provided a more linear distribution of data for cluster analysis and better cluster stability than ICA. LE combined with k-means or AHC provided 91% accuracy for classifying tumor grade and 100% accuracy for identifying normal tissue voxels. Color-coded visualization of normal brain, tumor core, and infiltration regions was achieved with LE combined with AHC. Conclusion The LE method is promising for unsupervised clustering to separate brain and tumor tissue with automated color-coding for visualization of 1H MRSI data after cluster analysis

Spherical Functions Associated With the Three Dimensional Sphere

In this paper, we determine all irreducible spherical functions \Phi of any K -type associated to the pair (G,K)=(\SO(4),\SO(3)). This is accomplished by associating to \Phi a vector valued function H=H(u) of a real variable u, which is analytic at u=0 and whose components are solutions of two coupled systems of ordinary differential equations. By an appropriate conjugation involving Hahn polynomials we uncouple one of the systems. Then this is taken to an uncoupled system of hypergeometric equations, leading to a vector valued solution P=P(u) whose entries are Gegenbauer's polynomials. Afterward, we identify those simultaneous solutions and use the representation theory of \SO(4) to characterize all irreducible spherical functions. The functions P=P(u) corresponding to the irreducible spherical functions of a fixed K-type \pi_\ell are appropriately packaged into a sequence of matrix valued polynomials (P_w)_{w\ge0} of size (\ell+1)\times(\ell+1). Finally we proved that \widetilde P_w={P_0}^{-1}P_w is a sequence of matrix orthogonal polynomials with respect to a weight matrix W. Moreover we showed that W admits a second order symmetric hypergeometric operator \widetilde D and a first order symmetric differential operator \widetilde E.Comment: 49 pages, 2 figure

Using Self-Adaptive Evolutionary Algorithms to Evolve Dynamism-Oriented Maps for a Real Time Strategy Game

9th International Conference on Large Scale Scientific Computations. The final publication is available at link.springer.comThis work presents a procedural content generation system that uses an evolutionary algorithm in order to generate interesting maps for a real-time strategy game, called Planet Wars. Interestingness is here captured by the dynamism of games (i.e., the extent to which they are action-packed). We consider two different approaches to measure the dynamism of the games resulting from these generated maps, one based on fluctuations in the resources controlled by either player and another one based on their confrontations. Both approaches rely on conducting several games on the map under scrutiny using top artificial intelligence (AI) bots for the game. Statistic gathered during these games are then transferred to a fuzzy system that determines the map's level of dynamism. We use an evolutionary algorithm featuring self-adaptation of mutation parameters and variable-length chromosomes (which means maps of different sizes) to produce increasingly dynamic maps.TIN2011-28627-C04-01, P10-TIC-608

Compressibility effects on the scalar mixing in reacting homogeneous turbulence

The compressibility and heat of reaction influence on the scalar mixing in decaying isotropic turbulence and homogeneous shear flow are examined via data generated by direct numerical simulations (DNS). The reaction is modeled as one-step, exothermic, irreversible and Arrhenius type. For the shear flow simulations, the scalar dissipation rate, as well as the time scale ratio of mechanical to scalar dissipation, are affected by compressibility and reaction. This effect is explained by considering the transport equation for the normalized mixture fraction gradient variance and the relative orientation between the mixture fraction gradient and the eigenvectors of the solenoidal strain rate tensor.Comment: In Turbulent Mixing and Combustion, eds. A. Pollard and S. Candel, Kluwer, 200

Integro-differential diffusion equation for continuous time random walk

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution.Comment: 12 page

Group-wise 3D registration based templates to study the evolution of ant worker neuroanatomy

The evolutionary success of ants and other social insects is considered to be intrinsically linked to division of labor and emergent collective intelligence. The role of the brains of individual ants in generating these processes, however, is poorly understood. One genus of ant of special interest is Pheidole, which includes more than a thousand species, most of which are dimorphic, i.e. their colonies contain two subcastes of workers: minors and majors. Using confocal imaging and manual annotations, it has been demonstrated that minor and major workers of different ages of three species of Pheidole have distinct patterns of brain size and subregion scaling. However, these studies require laborious effort to quantify brain region volumes and are subject to potential bias. To address these issues, we propose a group-wise 3D registration approach to build for the first time bias-free brain atlases of intra- and inter-subcaste individuals and automatize the segmentation of new individuals.Comment: 10 pages, 5 figures, preprint for conference (not reviewed

Semiclassical spin liquid state of easy axis Kagome antiferromagnets

Motivated by recent experiments on Nd-langasite, we consider the effect of strong easy axis single-ion anisotropy $D$ on $S > 3/2$ spins interacting with antiferromagnetic exchange $J$ on the Kagome lattice. When $T \ll DS^2$, the collinear low energy states selected by the anisotropy map on to configurations of the classical Kagome lattice Ising antiferromagnet. However, the low temperature limit is quite different from the cooperative Ising paramagnet that obtains classically for $T \ll JS^2$. We find that sub-leading ${\mathcal O}(J^3S/D^2)$ multi-spin interactions arising from the transverse quantum dynamics result in a crossover from an intermediate temperature classical cooperative Ising paramagnet to a semiclassical spin liquid with distinct short-ranged correlations for $T \ll J^3S/D^2$.Comment: 4 pages, 3 eps figure

Improve the performance of transfer learning without fine-tuning using dissimilarity-based multi-view learning for breast cancer histology images

Breast cancer is one of the most common types of cancer and leading cancer-related death causes for women. In the context of ICIAR 2018 Grand Challenge on Breast Cancer Histology Images, we compare one handcrafted feature extractor and five transfer learning feature extractors based on deep learning. We find out that the deep learning networks pretrained on ImageNet have better performance than the popular handcrafted features used for breast cancer histology images. The best feature extractor achieves an average accuracy of 79.30%. To improve the classification performance, a random forest dissimilarity based integration method is used to combine different feature groups together. When the five deep learning feature groups are combined, the average accuracy is improved to 82.90% (best accuracy 85.00%). When handcrafted features are combined with the five deep learning feature groups, the average accuracy is improved to 87.10% (best accuracy 93.00%)