Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots

We study a recent result of Bourgain, Clozel and Kahane, a version of which states that a sufficiently nice function $f:\mathbb{R} \rightarrow \mathbb{R}$ that coincides with its Fourier transform and vanishes at the origin has a root in the interval $(c, \infty)$, where the optimal $c$ satisfies $0.41 \leq c \leq 0.64$. A similar result holds in higher dimensions. We improve the one-dimensional result to $0.45 \leq c \leq 0.594$, and the lower bound in higher dimensions. We also prove that extremizers exist, and have infinitely many double roots. With this purpose in mind, we establish a new structure statement about Hermite polynomials which relates their pointwise evaluation to linear flows on the torus, and applies to other families of orthogonal polynomials as well.Comment: 26 pages, 4 figure

Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory

Nonlinear functions of multivariate financial time series can exhibit longmemory and fractional cointegration. However, tools for analysingthese phenomena have principally been justified under assumptionsthat are invalid in this setting. Determination of asymptotic theoryunder more plausible assumptions can be complicated and lengthy.We discuss these issues and present a Monte Carlo study, showingthat asymptotic theory should not necessarily be expected to provide agood approximation to finite-sample behaviour.Fractional cointegration, memory estimation,stochastic volatility.

Fractional Cointegration In StochasticVolatility Models

Asset returns are frequently assumed to be determined by one or more commonfactors. We consider a bivariate factor model, where the unobservable commonfactor and idiosyncratic errors are stationary and serially uncorrelated, but havestrong dependence in higher moments. Stochastic volatility models for the latentvariables are employed, in view of their direct application to asset pricing models.Assuming the underlying persistence is higher in the factor than in the errors, afractional cointegrating relationship can be recovered by suitable transformation ofthe data. We propose a narrow band semiparametric estimate of the factorloadings, which is shown to be consistent with a rate of convergence, and its finitesample properties are investigated in a Monte Carlo experiment.Fractional cointegration, stochastic volatility, narrow band leastsquares, semiparametric analysis.

Strategic Interaction in Local Fiscal Policy: Evidence from Portuguese Municipalities

This paper aims at testing the degree of interaction between Portuguese municipalities’ expenditure levels by estimating a dynamic panel model, based on jurisdictional reaction functions. The analysis is performed for all 278 Portuguese mainland municipalities from 1986 to 2006, using alternative ways to measure neighbourhood. Results indicate that local governments’ spending decisions are significantly influenced by the actions of neighbouring municipalities. For total expenditures, there is evidence that a 10% increase in nearby municipalities’ expenditures boosts expenditures in a given municipality by around 3.8%.spending interactions, local government, spatial econometrics, dynamic panel data

NGS Panels applied to Hereditary Cancer Syndromes

Cancer is among the leading causes of morbidity and mortality worldwide (Okur et al, 2017). Germline pathogenic variants for monogenic, highly penetrant cancer susceptibility genes are observed in 5%–10% of all cancers (Lu et al, 2014). Hereditary cancers due to monogenic causes are characterized by earlier age of onset, other associated cancers, and often a family history of specific cancers. From the clinical perspective, it is important to recognize the affected individuals to provide them the best clinical management (Hennessy et al, 2010; Ledermann et al, 2014; Pennington et al, 2014) and to identify at-risk family members who will benefit from predictive genetic testing and enhanced surveillance, including early detection and/or risk reduction measures (Kurian et al, 2010; Okur et al, 2017). Germline variants identified in major cancer susceptibility genes associated with hereditary breast or ovarian cancer (HBOC) or hereditary colorectal cancer (HCRC), also account for 5-10% of the patients with these cancers. In the last years, new susceptibility genes, with different penetrance degrees, have been identified. Variants in any of those genes are rare and classical methodologies (e.g. Sanger sequencing - SS) are time consuming and expensive. Next-generation sequencing (NGS) has several advantages compared to SS, including the simultaneous analysis of many samples and sequencing of a large set of genes, higher sensitivity (down to 1% vs 15-20% in SS), lower cost and faster turnaround time, reasons that make NGS the best approach for molecular diagnosis. It is possible nowadays to choose between whole-genome sequencing (WGS), whole-exome sequencing (WES) and NGS limited to a set of genes (NGS-Panel). In cases where a suspected genetic disease or condition has been identified, targeted sequencing of specific genes or genomic regions is preferred (Grada et al, 2013). For that reason, we use NGS-Panel approach using TruSight Cancer (Illumina) to sequence DNA extracted from blood samples of patients with personal and/or familiar history of cancer. This hereditary cancer gene panel sequences 94 genes associated with both common (e.g., breast, colorectal) and rare hereditary cancers and allows the creation of virtual gene panels according to each phenotype or disease under study. NGS workflow analysis (Figure 1) includes five steps: quality assessment of raw data, read alignment to a reference genome, variant identification/calling, variant annotation and data visualization (Pabinger et al, 2013). The establishment of the most appropriate bioinformatics pipeline is crucial in order to achieve the best results. NGS data allows the identification of several types of variants like single nucleotide variants (SNVs), small insertions/deletions, inversions and also copy number variants (CNVs).FCT - UID/BIM/0009/2016info:eu-repo/semantics/publishedVersio