Integrating cluster formation and cluster evaluation in interactive visual analysis

Cluster analysis is a popular method for data investigation where data items are structured into groups called clusters. This analysis involves two sequential steps, namely cluster formation and cluster evaluation. In this paper, we propose the tight integration of cluster formation and cluster evaluation in interactive visual analysis in order to overcome the challenges that relate to the black-box nature of clustering algorithms. We present our conceptual framework in the form of an interactive visual environment. In this realization of our framework, we build upon general concepts such as cluster comparison, clustering tendency, cluster stability and cluster coherence. Additionally, we showcase our framework on the cluster analysis of mixed lipid bilayers

Agrammatic but numerate

A central question in cognitive neuroscience concerns the extent to which language enables other higher cognitive functions. In the case of mathematics, the resources of the language faculty, both lexical and syntactic, have been claimed to be important for exact calculation, and some functional brain imaging studies have shown that calculation is associated with activation of a network of left-hemisphere language regions, such as the angular gyrus and the banks of the intraparietal sulcus. We investigate the integrity of mathematical calculations in three men with large left-hemisphere perisylvian lesions. Despite severe grammatical impairment and some difficulty in processing phonological and orthographic number words, all basic computational procedures were intact across patients. All three patients solved mathematical problems involving recursiveness and structure-dependent operations (for example, in generating solutions to bracket equations). To our knowledge, these results demonstrate for the first time the remarkable independence of mathematical calculations from language grammar in the mature cognitive system

Physical Education 2

Exam paper for first semester 201

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Multigene interactions and the prediction of depression in the Wisconsin Longitudinal Study

Objectives: Single genetic loci offer little predictive power for the identification of depression. This study examined whether an analysis of gene-gene (G x G) interactions of 78 single nucleotide polymorphisms (SNPs) in genes associated with depression and agerelated diseases would identify significant interactions with increased predictive power for depression. Design: A retrospective cohort study. Setting: A survey of participants in the Wisconsin Longitudinal Study. Participants: A total of 4811 persons (2464 women and 2347 men) who provided saliva for genotyping; the group comes from a randomly selected sample of Wisconsin high school graduates from the class of 1957 as well as a randomly selected sibling, almost all of whom are non-Hispanic white. Primary outcome measure: Depression as determine by the Composite International Diagnostic Interview-Short-Form. Results: Using a classification tree approach (recursive partitioning (RP)), the authors identified a number of candidate G 3 G interactions associated with depression. The primary SNP splits revealed by RP (ANKK1 rs1800497 (also known as DRD2 Taq1A) in men and DRD2 rs224592 in women) were found to be significant as single factors by logistic regression (LR) after controlling for multiple testing (p=0.001 for both). Without considering interaction effects, only one of the five subsequent RP splits reached nominal significance in LR (FTO rs1421085 in women, p=0.008). However, after controlling for G x G interactions by running LR on RP-specific subsets, every split became significant and grew larger in magnitude (OR (before) → (after): men: GNRH1 novel SNP: (1.43 → 1.57); women: APOC3 rs2854116: (1.28 → 1.55), ACVR2B rs3749386: (1.11 → 2.17), FTO rs1421085: (1.32 → 1.65), IL6 rs1800795: (1.12 → 1.85)). Conclusions: The results suggest that examining G x G interactions improves the identification of genetic associations predictive of depression. 4 of the SNPs identified in these interactions were located in two pathways well known to impact depression: neurotransmitter (ANKK1 and DRD2) and neuroendocrine (GNRH1 and ACVR2B) signalling. This study demonstrates the utility of RP analysis as an efficient and powerful exploratory analysis technique for uncovering genetic and molecular pathway interactions associated with disease aetiology

Realization of the mean-field universality class in spin-crossover materials

In spin-crossover materials, the volume of a molecule changes depending on whether it is in the high-spin (HS) or low-spin (LS) state. This change causes distortion of the lattice. Elastic interactions among these distortions play an important role for the cooperative properties of spin-transition phenomena. We find that the critical behavior caused by this elastic interaction belongs to the mean-field universality class, in which the critical exponents for the spontaneous magnetization and the susceptibility are $\beta = 1/2$ and $\gamma = 1$, respectively. Furthermore, the spin-spin correlation function is a constant at long distances, and it does not show an exponential decay in contrast to short-range models. The value of the correlation function at long distances shows different size-dependences: $O(1/N)$, $O(1/\sqrt{N})$, and constant for temperatures above, at, and below the critical temperature, respectively. The model does not exhibit clusters, even near the critical point. We also found that cluster growth is suppressed in the present model and that there is no critical opalescence in the coexistence region. During the relaxation process from a metastable state at the end of a hysteresis loop, nucleation phenomena are not observed, and spatially uniform configurations are maintained during the change of the fraction of HS and LS. These characteristics of the mean-field model are expected to be found not only in spin-crossover materials, but also generally in systems where elastic distortion mediates the interaction among local states.Comment: 13 pages, 16 figure

Infrared receivers for low background astronomy: Incoherent detectors and coherent devices from one micrometer to one millimeter

The status of incoherent detectors and coherent receivers over the infrared wavelength range from one micrometer to one millimeter is described. General principles of infrared receivers are included, and photon detectors, bolometers, coherent receivers, and important supporting technologies are discussed, with emphasis on their suitability for low background astronomical applications. Broad recommendations are presented and specific opportunities are identified for development of improved devices

How can exact and approximate solutions of Einstein's field equations be compared?

The problem of comparison of the stationary axisymmetric vacuum solutions obtained within the framework of exact and approximate approaches for the description of the same general relativistic systems is considered. We suggest two ways of carrying out such comparison: (i) through the calculation of the Ernst complex potential associated with the approximate solution whose form on the symmetry axis is subsequently used for the identification of the exact solution possessing the same multipole structure, and (ii) the generation of approximate solutions from exact ones by expanding the latter in series of powers of a small parameter. The central result of our paper is the derivation of the correct approximate analogues of the double-Kerr solution possessing the physically meaningful equilibrium configurations. We also show that the interpretation of an approximate solution originally attributed to it on the basis of some general physical suppositions may not coincide with its true nature established with the aid of a more accurate technique.Comment: 32 pages, 5 figure