Some Statistical Problems with High Dimensional Financial data

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important problem of estimating high dimensional covariance matrix. Then we explore some of the important statistical techniques such as high dimensional regression, principal component analysis, multiple testing problems and classification. We describe some of the fast algorithms that can be readily applied in practice.Comment: 22 pages, 5 figure

Train unit scheduling guided by historic capacity provisions and passenger count surveys

Train unit scheduling concerns the assignment of train unit vehicles to cover all the journeys in a fixed timetable. Coupling and decoupling activities are allowed in order to achieve optimal utilization while satisfying passenger demands. While the scheduling methods usually assume unique and well-defined train capacity requirements, in practice most UK train operators consider different levels of capacity provisions. Those capacity provisions are normally influenced by information such as passenger count surveys, historic provisions and absolute minimums required by the authorities. In this paper, we study the problem of train unit scheduling with bi-level capacity requirements and propose a new integer multicommodity flow model based on previous research. Computational experiments on real-world data show the effectiveness of our proposed methodology

Genome-Wide Association Study of Human Immunodeficiency Virus (HIV)-1 Coreceptor Usage in Treatment-Naive Patients from An AIDS Clinical Trials Group Study

OBJECTIVES: We conducted a genome-wide association study to explore whether common host genetic variants (>5% frequency) were associated with presence of virus able to use CXCR4 for entry. METHODS: Phenotypic determination of human immunodeficiency virus (HIV)-1 coreceptor usage was performed on pretreatment plasma HIV-1 samples from treatment-naive participants in AIDS Clinical Trials Group A5095, a study of initial antiretroviral regimens. Associations between genome-wide single-nucleotide polymorphisms (SNPs), CCR5 Δ32 genotype, and human leukocyte antigen (HLA) class I alleles and viral coreceptor usage were explored. RESULTS: Viral phenotypes were obtained from 593 patients with available genome-wide SNP data. Forty-four percent of subjects had virus capable of using CXCR4 for entry as determined by phenotyping. Overall, no associations, including those between polymorphisms in genes encoding viral coreceptors and their promoter regions or in HLA genes previously associated with HIV-1 disease progression, passed the statistical threshold for genome-wide significance (P < 5.0 × 10(-8)) in any comparison. However, the presence of viruses able to use CXCR4 for entry was marginally associated with the CCR5 Δ32 genotype in the nongenome-wide analysis. CONCLUSIONS: No human genetic variants were significantly associated with virus able to use CXCR4 for entry at the genome-wide level. Although the sample size had limited power to definitively exclude genetic associations, these results suggest that host genetic factors, including those that influence coreceptor expression or the immune pressures leading to viral envelope diversity, are either rare or have only modest effects in determining HIV-1 coreceptor usage

Propagation of an Earth-directed coronal mass ejection in three dimensions

Solar coronal mass ejections (CMEs) are the most significant drivers of adverse space weather at Earth, but the physics governing their propagation through the heliosphere is not well understood. While stereoscopic imaging of CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided some insight into their three-dimensional (3D) propagation, the mechanisms governing their evolution remain unclear due to difficulties in reconstructing their true 3D structure. Here we use a new elliptical tie-pointing technique to reconstruct a full CME front in 3D, enabling us to quantify its deflected trajectory from high latitudes along the ecliptic, and measure its increasing angular width and propagation from 2-46 solar radii (approximately 0.2 AU). Beyond 7 solar radii, we show that its motion is determined by an aerodynamic drag in the solar wind and, using our reconstruction as input for a 3D magnetohydrodynamic simulation, we determine an accurate arrival time at the Lagrangian L1 point near Earth.Comment: 5 figures, 2 supplementary movie

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

An extracellular steric seeding mechanism for Eph-ephrin signaling platform assembly

Erythropoetin-producing hepatoma (Eph) receptors are cell-surface protein tyrosine kinases mediating cell-cell communication. Upon activation, they form signaling clusters. We report crystal structures of the full ectodomain of human EphA2 (eEphA2) both alone and in complex with the receptor-binding domain of the ligand ephrinA5 (ephrinA5 RBD). Unliganded eEphA2 forms linear arrays of staggered parallel receptors involving two patches of residues conserved across A-class Ephs. eEphA2-ephrinA5 RBD forms a more elaborate assembly, whose interfaces include the same conserved regions on eEphA2, but rearranged to accommodate ephrinA5 RBD. Cell-surface expression of mutant EphA2s showed that these interfaces are critical for localization at cell-cell contacts and activation-dependent degradation. Our results suggest a 'nucleation' mechanism whereby a limited number of ligand-receptor interactions 'seed' an arrangement of receptors which can propagate into extended signaling arrays

Inverse Modeling for MEG/EEG data

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur

Adaptive Evolutionary Clustering

In many practical applications of clustering, the objects to be clustered evolve over time, and a clustering result is desired at each time step. In such applications, evolutionary clustering typically outperforms traditional static clustering by producing clustering results that reflect long-term trends while being robust to short-term variations. Several evolutionary clustering algorithms have recently been proposed, often by adding a temporal smoothness penalty to the cost function of a static clustering method. In this paper, we introduce a different approach to evolutionary clustering by accurately tracking the time-varying proximities between objects followed by static clustering. We present an evolutionary clustering framework that adaptively estimates the optimal smoothing parameter using shrinkage estimation, a statistical approach that improves a naive estimate using additional information. The proposed framework can be used to extend a variety of static clustering algorithms, including hierarchical, k-means, and spectral clustering, into evolutionary clustering algorithms. Experiments on synthetic and real data sets indicate that the proposed framework outperforms static clustering and existing evolutionary clustering algorithms in many scenarios.Comment: To appear in Data Mining and Knowledge Discovery, MATLAB toolbox available at http://tbayes.eecs.umich.edu/xukevin/affec