Three-dimensional viscous rotor flow calculations using a viscous-inviscid interaction approach

A three-dimensional viscous-inviscid interaction analysis was developed to predict the performance of rotors in hover and in forward flight at subsonic and transonic tip speeds. The analysis solves the full-potential and boundary-layer equations by finite-difference numerical procedures. Calculations were made for several different model rotor configurations. The results were compared with predictions from a two-dimensional integral method and with experimental data. The comparisons show good agreement between predictions and test data

Convergence of the Poincare Constant

The Poincare constant R(Y) of a random variable Y relates the L2 norm of a function g and its derivative g'. Since R(Y) - Var(Y) is positive, with equality if and only if Y is normal, it can be seen as a distance from the normal distribution. In this paper we establish a best possible rate of convergence of this distance in the Central Limit Theorem. Furthermore, we show that R(Y) is finite for discrete mixtures of normals, allowing us to add rates to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page

Brain Tumor Synthetic Segmentation in 3D Multimodal MRI Scans

The magnetic resonance (MR) analysis of brain tumors is widely used for diagnosis and examination of tumor subregions. The overlapping area among the intensity distribution of healthy, enhancing, non-enhancing, and edema regions makes the automatic segmentation a challenging task. Here, we show that a convolutional neural network trained on high-contrast images can transform the intensity distribution of brain lesions in its internal subregions. Specifically, a generative adversarial network (GAN) is extended to synthesize high-contrast images. A comparison of these synthetic images and real images of brain tumor tissue in MR scans showed significant segmentation improvement and decreased the number of real channels for segmentation. The synthetic images are used as a substitute for real channels and can bypass real modalities in the multimodal brain tumor segmentation framework. Segmentation results on BraTS 2019 dataset demonstrate that our proposed approach can efficiently segment the tumor areas. In the end, we predict patient survival time based on volumetric features of the tumor subregions as well as the age of each case through several regression models

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with computer algebra systems. As an example application, the totally geodesic submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified. The submission also contains an example implementation of the algorithms and formulas of the paper as a package for Maple 10, the technical documentation for this implementation, and a worksheet carrying out the computations for the space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical documentatio

Local Algorithms for Block Models with Side Information

There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding large independent sets in sparse random regular graphs. Montanari (2015) showed that local algorithms are suboptimal for finding a community with high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the symmetric planted partition problem (also named community detection for the block models) on sparse graphs, a simple observation is that local algorithms cannot have non-trivial performance. In this work we consider the effect of side information on local algorithms for community detection under the binary symmetric stochastic block model. In the block model with side information each of the $n$ vertices is labeled $+$ or $-$ independently and uniformly at random; each pair of vertices is connected independently with probability $a/n$ if both of them have the same label or $b/n$ otherwise. The goal is to estimate the underlying vertex labeling given 1) the graph structure and 2) side information in the form of a vertex labeling positively correlated with the true one. Assuming that the ratio between in and out degree $a/b$ is $\Theta(1)$ and the average degree $(a+b) / 2 = n^{o(1)}$, we characterize three different regimes under which a local algorithm, namely, belief propagation run on the local neighborhoods, maximizes the expected fraction of vertices labeled correctly. Thus, in contrast to the case of symmetric block models without side information, we show that local algorithms can achieve optimal performance for the block model with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract here is shorter than that in the PDF fil

Anomalies in Ward Identities for Three-Point Functions Revisited

A general calculational method is applied to investigate symmetry relations among divergent amplitudes in a free fermion model. A very traditional work on this subject is revisited. A systematic study of one, two and three point functions associated to scalar, pseudoscalar, vector and axial-vector densities is performed. The divergent content of the amplitudes are left in terms of five basic objects (external momentum independent). No specific assumptions about a regulator is adopted in the calculations. All ambiguities and symmetry violating terms are shown to be associated with only three combinations of the basic divergent objects. Our final results can be mapped in the corresponding Dimensional Regularization calculations (in cases where this technique could be applied) or in those of Gertsein and Jackiw which we will show in detail. The results emerging from our general approach allow us to extract, in a natural way, a set of reasonable conditions (e.g. crucial for QED consistency) that could lead us to obtain all Ward Identities satisfied. Consequently, we conclude that the traditional approach used to justify the famous triangular anomalies in perturbative calculations could be questionable. An alternative point of view, dismissed of ambiguities, which lead to a correct description of the associated phenomenology, is pointed out.Comment: 26 pages, Revtex, revised version, Refs. adde

Fine Splitting in Charmonium Spectrum with Channel Coupling Effect

We study the fine splitting in charmonium spectrum in quark model with the channel coupling effect, including $DD$, $DD^*$, $D^*D^*$ and $D_sD_s$, $D_sD_s^*$, $D_s^*D_s^*$ channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the one-gluon exchange potentials. By adopting the massive gluon propagator from the lattice calculation in the nonperturbative region, the coupling interaction is further simplified to the four-fermion interaction. The numerical calculation still prefers the assignment $1^{++}$ of X(3872).Comment: Submitted to Chinese Physics

The Bayesian-Laplacian Brain

We discuss here what we feel could be an improvement in future discussions of the brain acting as a Bayesian-Laplacian system, by distinguishing between two classes of priors on which the brain's inferential systems operate. In one category are biological priors (β priors) and in the other artefactual ones (α priors). We argue that β priors are inherited or acquired very rapidly after birth and are much more resistant to varying experiences than α priors which, being continuously acquired at various stages throughout post-natal life, are much more accommodating of, and hospitable to, new experiences. Consequently, the posteriors generated from the two sets of priors are likewise different, being more constrained (i.e., precise) for β than for α priors

Representations of the Self-Concept and Identity-Based Choice

We propose a novel approach to identity-based choice that focuses on peoples’ representations of the cause-effect relationships that exist among features of their self-concepts. More specifically, we propose that people who believe that a specific aspect of identity, such as a social category, is causally central (linked to many other features of the self-concept) are more likely to engage in behaviors consistent with that aspect than those who believe that the same aspect is causally peripheral (linked to fewer other features). Across three studies, we provide evidence for our approach to identity-based choice. We demonstrate that among people who belong to the same social category, those who believe that the associated identity is more causally central are more likely to engage in behaviors consistent with the social category

The role of causal beliefs in political identity and voting

An emerging literature in psychology and political science has identified political identity as an important driver of political decisions. However, less is known about how a person’s political identity is incorporated into their broader self-concept and why it influences some people more than others. We examined the role of political identity in representations of the self-concept as one determinant of people’s political behaviors. We tested the predictions of a recent theoretical account of self-concept representation that, inspired by work on conceptual representation, emphasizes the role of causal beliefs. This account predicts that people who believe that their political identity is causally central (linked to many other features of the self-concept) will be more likely to engage in behaviors consistent with their political identity than those who believe that the same aspect is causally peripheral (linked to fewer other features). Consistent with these predictions, in a study run when political identity was particularly salient—during the 2016 U.S. Presidential election—we found that U.S. voters who believed their political party identity was more causally central (vs those who believe it was causally peripheral) were more likely to vote for their political party’s candidate. Further, in 2 studies, we found that U.K. residents who believed that their English or British national identity was more causally central were more likely to support the U.K. leaving the European Union (Brexit) than those who believed the same identities were more causally peripheral