Testing multivariate uniformity based on random geometric graphs

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the null hypothesis as well as under fixed alternatives. The derived tests are consistent and their behaviour for some contiguous alternatives can be controlled. A simulation study suggests that the procedures can compete with or are better than established goodness-of-fit tests. We show with a real data example that the new tests can detect non-uniformity of a small sample data set, where most of the competitors fail.Comment: 36 pages, 2 figure

Characterizations of non-normalized discrete probability distributions and their application in statistics

From the distributional characterizations that lie at the heart of Stein's method we derive explicit formulae for the mass functions of discrete probability laws that identify those distributions. These identities are applied to develop tools for the solution of statistical problems. Our characterizations, and hence the applications built on them, do not require any knowledge about normalization constants of the probability laws. To demonstrate that our statistical methods are sound, we provide comparative simulation studies for the testing of fit to the Poisson distribution and for parameter estimation of the negative binomial family when both parameters are unknown. We also consider the problem of parameter estimation for discrete exponential-polynomial models which generally are non-normalized.Comment: 24 pages, 3 figure

The function of the left angular gyrus in mental arithmetic: Evidence from the associative confusion effect

While the left angular gyrus (lAG) has been repeatedly implicated in mental arithmetic, its precise functional role has not been established. On the one hand, it has been speculated that the lAG is involved in task-specific processes. On the other hand, the observation of relative deactivation during arithmetic has led to the contention that differential lAG activation reflects task-unrelated difficulty effects associated with the default mode network (DMN). Using functional magnetic resonance imaging, we investigated the neural correlates of the associative confusion effect that allowed us to dissociate effects of task difficulty and task-related arithmetic processes on lAG activation. The associative confusion effect is characterized by poorer performance while verifying addition and multiplication equations whose solutions are associated with the other operation (confusion equations: e.g., 9 × 6 = 15 ) compared with solutions unrelated to both operations (non-confusion equations: e.g., 9 × 6 = 52 ). Comparing these two conditions revealed higher activation of the anterior lAG (areas PGa, PFm, and PF) and the left dorsolateral prefrontal cortex for the confusion problems. This effect displayed only slight anatomical overlap with the well-established reverse problem-size effect (small minus large problems) and task-related deactivation in the parietal cortex. The finding of greater lAG activity (less deactivation) in the more difficult task condition is inconsistent with the hypothesis that lAG activation during mental arithmetic reflects task difficulty related modulations of the DMN. Instead, the present findings provide further support for the symbol-referent mapping hypothesis, suggesting that the lAG mediates the automatic mapping of arithmetic problems onto solutions stored in memory. © 2011 Wiley Periodicals, Inc

The Influence of verbalization on the pattern of cortical activation during mental arithmetic

<p>Abstract</p> <p>Background</p> <p>The aim of the present functional magnetic resonance imaging (fMRI) study at 3 T was to investigate the influence of the verbal-visual cognitive style on cerebral activation patterns during mental arithmetic. In the domain of arithmetic, a visual style might for example mean to visualize numbers and (intermediate) results, and a verbal style might mean, that numbers and (intermediate) results are verbally repeated. In this study, we investigated, first, whether verbalizers show activations in areas for language processing, and whether visualizers show activations in areas for visual processing during mental arithmetic. Some researchers have proposed that the left and right intraparietal sulcus (IPS), and the left angular gyrus (AG), two areas involved in number processing, show some domain or modality specificity. That is, verbal for the left AG, and visual for the left and right IPS. We investigated, second, whether the activation in these areas implied in number processing depended on an individual's cognitive style.</p> <p>Methods</p> <p>42 young healthy adults participated in the fMRI study. The study comprised two functional sessions. In the first session, subtraction and multiplication problems were presented in an event-related design, and in the second functional session, multiplications were presented in two formats, as Arabic numerals and as written number words, in an event-related design. The individual's habitual use of visualization and verbalization during mental arithmetic was assessed by a short self-report assessment.</p> <p>Results</p> <p>We observed in both functional sessions that the use of verbalization predicts activation in brain areas associated with language (supramarginal gyrus) and auditory processing (Heschl's gyrus, Rolandic operculum). However, we found no modulation of activation in the left AG as a function of verbalization.</p> <p>Conclusions</p> <p>Our results confirm that strong verbalizers use mental speech as a form of mental imagination more strongly than weak verbalizers. Moreover, our results suggest that the left AG has no specific affinity to the verbal domain and subserves number processing in a modality-general way.</p

Time-optimized high-resolution readout-segmented diffusion tensor imaging

Readout-segmented echo planar imaging with 2D navigator-based reacquisition is an uprising technique enabling the sampling of high-resolution diffusion images with reduced susceptibility artifacts. However, low signal from the small voxels and long scan times hamper the clinical applicability. Therefore, we introduce a regularization algorithm based on total variation that is applied directly on the entire diffusion tensor. The spatially varying regularization parameter is determined automatically dependent on spatial variations in signal-to-noise ratio thus, avoiding over- or under-regularization. Information about the noise distribution in the diffusion tensor is extracted from the diffusion weighted images by means of complex independent component analysis. Moreover, the combination of those features enables processing of the diffusion data absolutely user independent. Tractography from in vivo data and from a software phantom demonstrate the advantage of the spatially varying regularization compared to un-regularized data with respect to parameters relevant for fiber-tracking such as Mean Fiber Length, Track Count, Volume and Voxel Count. Specifically, for in vivo data findings suggest that tractography results from the regularized diffusion tensor based on one measurement (16 min) generates results comparable to the un-regularized data with three averages (48 min). This significant reduction in scan time renders high resolution (1×1×2.5 mm3) diffusion tensor imaging of the entire brain applicable in a clinical context

Three-dimensional imaging of the larynx for pre-operative planning of laryngeal framework surgery

Modern laryngeal framework surgery (LFS) requires an exact understanding of the laryngeal biomechanics and precise pre-operative planning, for which bi-planar imaging is not sufficient. The aim of the study was to test whether MIMICS®, a commercially available software package for three-dimensional (3D) rendering of high-resolution computerised tomography (HRCT), is suitable for 3D imaging of the larynx, analysis of laryngeal biomechanics and pre-operative planning. We examined four cadaver larynx and one patient larynx. In the five larynges, all relevant structures and landmarks could be 3D visualised. Superimposing of two HRCT scans shows that when the arytenoids move from ‘respiration' to ‘phonation', they perform a rotating, translating and tilting motion. Moreover, we could demonstrate that the vocal fold elongates by 7% with cricothyroid approximation. We conclude that MIMCS® is well suited for 3D imaging of the larynx, analysis of laryngeal biomechanics and pre-operative planning of LFS procedure

Magnetization Jump in a Model for Flux Lattice Melting at Low Magnetic Fields

Using a frustrated XY model on a lattice with open boundary conditions, we numerically study the magnetization change near a flux lattice melting transition at low fields. In both two and three dimensions, we find that the melting transition is followed at a higher temperature by the onset of large dissipation associated with the zero-field XY transition. It is characterized by the proliferation of vortex-antivortex pairs (in 2D) or vortex loops (in 3D). At the upper transition, there is a sharp increase in magnetization, in qualitative agreement with recent local Hall probe experiments.Comment: updated figures and texts. new movies available at http://www.physics.ohio-state.edu:80/~ryu/jj.html. Accepted for publication in Physical Review Letter

Conductivity Due to Classical Phase Fluctuations in a Model For High-T_c Superconductors

We consider the real part of the conductivity, \sigma_1(\omega), arising from classical phase fluctuations in a model for high-T_c superconductors. We show that the frequency integral of that conductivity, \int_0^\infty \sigma_1 d\omega, is non-zero below the superconducting transition temperature $T_c$, provided there is some quenched disorder in the system. Furthermore, for a fixed amount of quenched disorder, this integral at low temperatures is proportional to the zero-temperature superfluid density, in agreement with experiment. We calculate \sigma_1(\omega) explicitly for a model of overdamped phase fluctuations.Comment: 4pages, 2figures, submitted to Phys.Rev.

Epidermal Langerhans Cells Rapidly Capture and Present Antigens from C-Type Lectin-Targeting Antibodies Deposited in the Dermis

Antigen-presenting cells can capture antigens that are deposited in the skin, including vaccines given subcutaneously. These include different dendritic cells (DCs) such as epidermal Langerhans cells (LCs), dermal DCs, and dermal langerin+ DCs. To evaluate access of dermal antigens to skin DCs, we used mAb to two C-type lectin endocytic receptors, DEC-205/CD205 and langerin/CD207. When applied to murine and human skin explant cultures, these mAbs were efficiently taken up by epidermal LCs. In addition, anti-DEC-205 targeted langerin+ CD103+ and langerin− CD103− mouse dermal DCs. Unexpectedly, intradermal injection of either mAb, but not isotype control, resulted in strong and rapid labeling of LCs in situ, implying that large molecules can diffuse through the basement membrane into the epidermis. Epidermal LCs targeted in vivo by ovalbumin-coupled anti-DEC-205 potently presented antigen to CD4+ and CD8+ T cells in vitro. However, to our surprise, LCs targeted through langerin were unable to trigger T-cell proliferation. Thus, epidermal LCs have a major function in uptake of lectin-binding antibodies under standard vaccination conditions