Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Early Indicators of Autism Spectrum Disorders in the Second Year of Life

Three groups of 18 children were selected for this study, one group with autism spectrum disorders (ASD), one group with developmental delays in which ASD was ruled out (DD), and one group with typical development (TD), from a pool of 3026 children who were screened with the Communication and Symbolic Behavior Scales Developmental Profile (CSBS DP, Wetherby & Prizant, 2002) Infant-Toddler Checklist under 24 months of age. The CSBS DP Behavior Sample was videotaped on selected children as a second-level evaluation during the second year of life. The Infant-Toddler Checklist had a sensitivity and specificity of 88.9% for this sample of children. Significant group differences were found on the Infant-Toddler Checklist and the Behavior Sample, however, these differences did not distinguish children with ASD and DD with high accuracy. The videotapes of the Behavior Sample were reanalyzed to identify red flags of ASD. Nine red flags differentiated children in the ASD group from both the DD and TD groups and four red flags differentiated children in the ASD Group from the TD group but not the DD group. These 13 red flags were found to discriminate the three groups with a correct classification rate of 94.4%.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44624/1/10803_2004_Article_492544.pd

AD51B in Familial Breast Cancer

Common variation on 14q24.1, close to RAD51B, has been associated with breast cancer: rs999737 and rs2588809 with the risk of female breast cancer and rs1314913 with the risk of male breast cancer. The aim of this study was to investigate the role of RAD51B variants in breast cancer predisposition, particularly in the context of familial breast cancer in Finland. We sequenced the coding region of RAD51B in 168 Finnish breast cancer patients from the Helsinki region for identification of possible recurrent founder mutations. In addition, we studied the known rs999737, rs2588809, and rs1314913 SNPs and RAD51B haplotypes in 44,791 breast cancer cases and 43,583 controls from 40 studies participating in the Breast Cancer Association Consortium (BCAC) that were genotyped on a custom chip (iCOGS). We identified one putatively pathogenic missense mutation c.541C>T among the Finnish cancer patients and subsequently genotyped the mutation in additional breast cancer cases (n = 5259) and population controls (n = 3586) from Finland and Belarus. No significant association with breast cancer risk was seen in the meta-analysis of the Finnish datasets or in the large BCAC dataset. The association with previously identified risk variants rs999737, rs2588809, and rs1314913 was replicated among all breast cancer cases and also among familial cases in the BCAC dataset. The most significant association was observed for the haplotype carrying the risk-alleles of all the three SNPs both among all cases (odds ratio (OR): 1.15, 95% confidence interval (CI): 1.11–1.19, P = 8.88 x 10−16) and among familial cases (OR: 1.24, 95% CI: 1.16–1.32, P = 6.19 x 10−11), compared to the haplotype with the respective protective alleles. Our results suggest that loss-of-function mutations in RAD51B are rare, but common variation at the RAD51B region is significantly associated with familial breast cancer risk

Measurements of differential production cross sections for a Z boson in association with jets in pp collisions at root s=8 TeV

Peer reviewe

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

Peer reviewe

Search for black holes and other new phenomena in high-multiplicity final states in proton-proton collisions at root s=13 TeV

Peer reviewe

Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search

Peer reviewe

Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos, and b quarks

Peer reviewe

Search for neutral resonances decaying into a Z boson and a pair of b jets or τ leptons

A search is performed for a new resonance decaying into a lighter resonance and a Z boson. Two channels are studied, targeting the decay of the lighter resonance into either a pair of oppositely charged τ leptons or a bb‾ pair. The Z boson is identified via its decays to electrons or muons. The search exploits data collected by the CMS experiment at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.8 fb −1 . No significant deviations are observed from the standard model expectation and limits are set on production cross sections and parameters of two-Higgs-doublet models

Search for a low-mass pseudoscalar Higgs boson produced in association with a bb⁻ pair in pp collisions at √s=8 TeV

A search is reported for a light pseudoscalar Higgs boson decaying to a pair of tau leptons, produced in association with a b (b) over bar pair, in the context of two-Higgs-doublet models. The results are based on pp collision data at a centre-of-mass energy of 8 TeV collected by the CMS experiment at the LHC and corresponding to an integrated luminosity of 19.7 fb(-1). Pseudoscalar boson masses between 25 and 80 GeV are probed. No evidence for a pseudoscalar boson is found and upper limits are set on the product of cross section and branching fraction to tau pairs between 7 and 39 pb at the 95% confidence level. This excludes pseudoscalar A bosons with masses between 25 and 80 GeV, with SM-like Higgs boson negative couplings to down-type fermions, produced in association with bb pairs, in Type II, two-Higgs-doublet models. (C) 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommonnorg/licensesiby/4.01)