On computation of the first Baues--Wirsching cohomology of a freely-generated small category

The Baues--Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues--Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues--Wirsching cohomology whose kernel is the vector space of inner derivations.Comment: 11 page

Blow-up solutions for linear perturbations of the Yamabe equation

For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we are interested in the critical equation $$\Delta_g u+(N-2/4(N-1) S_g+\epsilon h)u=u^{N+2/N-2} in M, u>0 in M,$$ where \Delta_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,\alpha}(M)$, and $\epsilon$ is a small parameter

The Cross-Quantilogram: Measuring Quantile Dependence and Testing Directional Predictability between Time Series

This paper proposes the cross-quantilogram to measure the quantile dependence between two time series. We apply it to test the hypothesis that one time series has no directional predictability to another time series. We establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic. The limiting distributions depend on nuisance parameters. To construct consistent confidence intervals we employ the stationary bootstrap procedure; we show the consistency of this bootstrap. Also, we consider the self-normalized approach, which is shown to be asymptotically pivotal under the null hypothesis of no predictability. We provide simulation studies and two empirical applications. First, we use the cross-quantilogram to detect predictability from stock variance to excess stock return. Compared to existing tools used in the literature of stock return predictability, our method provides a more complete relationship between a predictor and stock return. Second, we investigate the systemic risk of individual financial institutions, such as JP Morgan Chase, Goldman Sachs and AIG. This article has supplementary materials online

The Size-Ramsey Number of 3-uniform Tight Paths

Given a hypergraph H, the size-Ramsey number ˆr2(H) is the smallest integer m such that there exists a hypergraph G with m edges with the property that in any colouring of the edges of G with two colours there is a monochromatic copy of H. We prove that the size-Ramsey number of the 3-uniform tight path on n vertices Pn(3) is linear in n, i.e., ˆr2(Pn(3)) = O(n). This answers a question by Dudek, La Fleur, Mubayi, and Rödl for 3-uniform hypergraphs [On the size-Ramsey number of hypergraphs, J. Graph Theory 86 (2016), 417–434], who proved ˆr2(Pn(3)) = O(n3/2 log3/2 n)

Computational Study of Tunneling Transistor Based on Graphene Nanoribbon

Tunneling field-effect transistors (FETs) have been intensely explored recently due to its potential to address power concerns in nanoelectronics. The recently discovered graphene nanoribbon (GNR) is ideal for tunneling FETs due to its symmetric bandstructure, light effective mass, and monolayer-thin body. In this work, we examine the device physics of p-i-n GNR tunneling FETs using atomistic quantum transport simulations. The important role of the edge bond relaxation in the device characteristics is identified. The device, however, has ambipolar I-V characteristics, which are not preferred for digital electronics applications. We suggest that using either an asymmetric source-drain doping or a properly designed gate underlap can effectively suppress the ambipolar I-V. A subthreshold slope of 14mV/dec and a significantly improved on-off ratio can be obtained by the p-i-n GNR tunneling FETs

Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles

The EPRB experiment with massive partcles can be formulated if one defines spin in a relativistic way. Two versions are discussed: The one using the spin operator defined via the relativistic center-of-mass operator, and the one using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction for the EPRB experiment: The degree of violation of the Bell inequality DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The phenomenon can be physically understood as a combined effect of the Lorentz contraction and the Moller shift of the relativistic center of mass. The effect is therefore stronger than standard relativistic phenomena such as the Lorentz contraction or time dilatation. The fact that the Bell inequality is in general less violated than in the nonrelativistic case will have to be taken into account in tests for eavesdropping if massive particles will be used for a key transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important in the formula for eigenvector in Sec. IV); link to the unpublished 1984 paper containing the results (without typos!) of Sec. IV is adde

Coulomb suppression of NMR coherence peak in fullerene superconductors

The suppressed NMR coherence peak in the fullerene superconductors is explained in terms of the dampings in the superconducting state induced by the Coulomb interaction between conduction electrons. The Coulomb interaction, modelled in terms of the onsite Hubbard repulsion, is incorporated into the Eliashberg theory of superconductivity with its frequency dependence considered self-consistently at all temperatures. The vertex correction is also included via the method of Nambu. The frequency dependent Coulomb interaction induces the substantial dampings in the superconducting state and, consequently, suppresses the anticipated NMR coherence peak of fullerene superconductors as found experimentally.Comment: 4 pages, Revtex, and 2 figures. Revised and final version to appear in Phys. Rev. Lett. (1998

Randomized controlled trial of traditional Chinese medicine (acupuncture and Tuina) in cerebral palsy: Part 1 - Any increase in seizure in integrated acupuncture and rehabilitation group versus rehabilitation group?

Objective: The objective of this study was to observe for any change in baseline seizure frequency with acupuncture in children with cerebral palsy. Methods: A randomized controlled study was conducted: Group I consisted of integrated acupuncture, tuina, and rehabilitation (physiotherapy, occupational therapy, and hydrotherapy) for 12 weeks; and Group II consisted of rehabilitation (physiotherapy, occupational therapy, and hydrotherapy) for 12 weeks. After a washout period of 4 weeks, Group II then received acupuncture and tuina for 12 weeks. Each subject received 5 daily acupuncture sessions per week for 12 weeks (total = 60 sessions). All children were assessed for any change in seizure frequency during treatment. Results: One hundred and sixteen (116) children were recruited and randomized into Group I (N = 58) and Group II (N = 58). Thirty-three (33) children withdrew (9 from Group I and 24 from Group II). Of the remaining 83 children, Group I consisted of 49 and Group II of 34 children. For baseline, 5 children (6%; 5/83) had seizures. During phase 1 (12 weeks) of integrative treatment and subsequent 4-week follow-up, 3 children in Group I had seizures. Among those 3 children with seizures, 1 child with prior history of recurrent febrile seizure had 3 more recurrent febrile seizures during acupuncture treatment and 2 children without any prior history of seizures had new-onset seizures (1 with 3 recurrent febrile seizures and 1 with afebrile seizure). For Group I, 2 children with epilepsy had no increase in seizure frequency during acupuncture treatment. For Group II during the phase 2 acupuncture period, none had increase in seizure frequency. In both groups, 4 of 5 children (80%; 2 in Group I and 2 in Group II) with seizures had no increase in seizure frequency during acupuncture treatment and follow-up. Conclusions: The risk of increasing seizure is not increased with acupuncture treatment for cerebral palsy. © 2008 Mary Ann Liebert, Inc.published_or_final_versio

Learning with Biased Complementary Labels

In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do \textbf{not} belong to. Let $Y$ and $\bar{Y}$ be the true and complementary labels, respectively. We first model the annotation of complementary labels via transition probabilities $P(\bar{Y}=i|Y=j), i\neq j\in\{1,\cdots,c\}$, where $c$ is the number of classes. Previous methods implicitly assume that $P(\bar{Y}=i|Y=j), \forall i\neq j$, are identical, which is not true in practice because humans are biased toward their own experience. For example, as shown in Figure 1, if an annotator is more familiar with monkeys than prairie dogs when providing complementary labels for meerkats, she is more likely to employ "monkey" as a complementary label. We therefore reason that the transition probabilities will be different. In this paper, we propose a framework that contributes three main innovations to learning with \textbf{biased} complementary labels: (1) It estimates transition probabilities with no bias. (2) It provides a general method to modify traditional loss functions and extends standard deep neural network classifiers to learn with biased complementary labels. (3) It theoretically ensures that the classifier learned with complementary labels converges to the optimal one learned with true labels. Comprehensive experiments on several benchmark datasets validate the superiority of our method to current state-of-the-art methods.Comment: ECCV 2018 Ora