Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Clinical impact of double protease inhibitor boosting with Lopinavir/Ritonavir and Amprenavir as part of salvage antiretroviral therapy

Purpose: Double protease inhibitor (PI) boosting is being explored as a new strategy in salvage antiretroviral (ARV) therapy. However, if a negative drug interaction leads to decreased drug levels of either or both PIs, double PI boosting could lead to decreased virologic response. A negative drug interaction has been described between amprenavir (APV) and lopinavir/ritonavir (LPV/r). This observational cohort study assessed the virologic impact of the addition of APV to a salvage ARV regimen, which also contains LPV/r, compared to a regimen containing LPV/r alone. Method: Patients initiated on a salvage ARV regimen that included LPV/r obtained from the expanded access program in Toronto, Canada, were evaluated. APV (600-1,200 mg bid) was added at the discretion of the treating physician. Results: Using multivariate Cox proportional hazards models, we found that the addition of APV to a LPV/r-containing salvage regimen was not significantly associated with time to virologic suppression (< 50 copies/mL; adjusted hazard ratio [HR] = 0.75, p = .12) or with time to virologic rebound (adjusted HR = 1.46, p = .34). Those patients who received higher doses of APV had an increased chance of virologic suppression (p = .03). In a subset of 27 patients, the median LPV Ctrough was significantly lower in patients receiving APV (p = .04), and the median APV Ctrough was reduced compared to reported controls. Conclusion: Our data do not support an additional benefit in virologic reduction of double boosting with APV and LPV/r relative to LPV/r alone in salvage ARV therapy. Our study's limitations include its retrospective nature and the imbalance between the two groups potentially confounding the results. Although these factors were adjusted for in the multivariate analysis, a prospective randomized controlled trial is warranted to confirm our findings

The Top Window for dark matter

We investigate a scenario that the top quark is the only window to the dark matter particle. We use the effective Lagrangian approach to write down the interaction between the top quark and the dark matter particle. Requiring the dark matter satisfying the relic density we obtain the size of the effective interaction. We show that the scenario can be made consistent with the direct and indirect detection experiments by adjusting the size of the effective coupling. Finally, we calculate the production cross section for $t\bar t + \chi \bar \chi$ at the Large Hadron Collider (LHC), which will give rise to an interesting signature of a top-pair plus large missing energy.Comment: 17 pages including 8 figures; added references and a footnot

A computational method for genotype calling in family-based sequencing data

Background: As sequencing technologies can help researchers detect common and rare variants across the human genome in many individuals, it is known that jointly calling genotypes across multiple individuals based on linkage disequilibrium (LD) can facilitate the analysis of low to modest coverage sequence data. However, genotype-calling methods for family-based sequence data, particularly for complex families beyond parent-offspring trios, are still lacking. Results: In this study, first, we proposed an algorithm that considers both linkage disequilibrium (LD) patterns and familial transmission in nuclear and multi-generational families while retaining the computational efficiency. Second, we extended our method to incorporate external reference panels to analyze family-based sequence data with a small sample size. In simulation studies, we show that modeling multiple offspring can dramatically increase genotype calling accuracy and reduce phasing and Mendelian errors, especially at low to modest coverage. In addition, we show that using external panels can greatly facilitate genotype calling of sequencing data with a small number of individuals. We applied our method to a whole genome sequencing study of 1339 individuals at ~10X coverage from the Minnesota Center for Twin and Family Research. Conclusions: The aggregated results show that our methods significantly outperform existing ones that ignore family constraints or LD information. We anticipate that our method will be useful for many ongoing family-based sequencing projects. We have implemented our methods efficiently in a C++ program FamLDCaller, which is available from http://www.pitt.edu/~wec47/famldcaller.html

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Tailoring the atomic structure of graphene nanoribbons by STM lithography

The practical realization of nano-scale electronics faces two major challenges: the precise engineering of the building blocks and their assembly into functional circuits. In spite of the exceptional electronic properties of carbon nanotubes only basic demonstration-devices have been realized by time-consuming processes. This is mainly due to the lack of selective growth and reliable assembly processes for nanotubes. However, graphene offers an attractive alternative. Here we report the patterning of graphene nanoribbons (GNRs) and bent junctions with nanometer precision, well-defined widths and predetermined crystallographic orientations allowing us to fully engineer their electronic structure using scanning tunneling microscope (STM) lithography. The atomic structure and electronic properties of the ribbons have been investigated by STM and tunneling spectroscopy measurements. Opening of confinement gaps up to 0.5 eV, allowing room temperature operation of GNR-based devices, is reported. This method avoids the difficulties of assembling nano-scale components and allows the realization of complete integrated circuits, operating as room temperature ballistic electronic devices.Comment: 8 pages text, 5 figures, Nature Nanotechnology, in pres

A Fuzzy Social Network Analysis Method and a Case Study on Tianya

Social networking service (SNS) has become online service platforms that focus on facilitating the building of social networks among people who share interests, activities, backgrounds, or real-life connections and has had a rapid development in China in the past few years. This paper aims to develop a fuzzy social network service analysis method, which combines graph theory with related fuzzy approach, to analyze the social network structural features and the distribution characteristics of interpersonal nodes in SNS community. A case study on a very famous Chinese tourism BBS-Tianya-is conducted to illustrate and validate the proposed approach. The research findings are as follows: (1) The attraction degrees of various areas in the forum are significantly different; (2) interpersonal nodes in the forum are concentrated relatively; (3) the fuzzy out-degrees and the fuzzy in-degrees of interpersonal nodes in the forum conflict each other; and (4) the distribution of interpersonal nodes is influenced by geographical relations. These findings can directly support social network service management and particularly tourism online service developments. © Springer-Verlag Berlin Heidelberg 2014

Limits on light WIMPs from the CDEX-1 experiment with a p-type point-contact germanium detector at the China Jingping Underground Laboratory

We report results of a search for light Dark Matter WIMPs with CDEX-1 experiment at the China Jinping Underground Laboratory, based on 53.9 kg-days of data from a p-type point-contact germanium detector enclosed by a NaI(Tl) crystal scintillator as anti-Compton detector. The event rate and spectrum above the analysis threshold of 475 eVee are consistent with the understood background model. Part of the allowed regions for WIMP-nucleus coherent elastic scattering at WIMP mass of 6-20 GeV are probed and excluded. Independent of interaction channels, this result contradicts the interpretation that the anomalous excesses of the CoGeNT experiment are induced by Dark Matter, since identical detector techniques are used in both experiments.Comment: 5 pages, 5 figure