Degree of locally condensing perturbations of Fredholm maps with positive index and applications

2018 ◽  
Vol 275 (10) ◽  
pp. 2573-2613
Author(s):  
Victor Zvyagin ◽  
Nadezhda Ratiner
Keyword(s):  
Fredholm Maps ◽  
Positive Index

Linear Operators in Banach Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Fredholm Maps

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to derive important results later in the book.

scholarly journals Tuberculosis contact investigation results among paediatric contacts in low-incidence settings in Finland

2021 ◽  
Author(s):  
Antti Kontturi ◽  
Satu Kekomäki ◽  
Eeva Ruotsalainen ◽  
Eeva Salo
Keyword(s):  
Early Diagnosis ◽  
Young Children ◽  
Large Scale ◽  
Index Case ◽  
Contact Tracing ◽  
Sputum Smear ◽  
Endemic Country ◽  
Household Contacts ◽  
Contact Investigation ◽  
Positive Index

AbstractTuberculosis (TB) risk is highest immediately after primary infection, and young children are vulnerable to rapid and severe TB disease. Contact tracing should identify infected children rapidly and simultaneously target resources effectively. We conducted a retrospective review of the paediatric TB contact tracing results in the Hospital District of Helsinki and Uusimaa from 2012 to 2016 and identified risk factors for TB disease or infection. Altogether, 121 index cases had 526 paediatric contacts of whom 34 were diagnosed with TB disease or infection. The maximum delay until first contact investigation visit among the household contacts under 5 years of age with either TB disease or infection was 7 days. The yield for TB disease or infection was 4.6% and 12.8% for household contacts, 0.5% and 0% for contacts exposed in a congregate setting and 1.4% and 5.0% for other contacts, respectively. Contacts born in a TB endemic country (aOR 3.07, 95% CI 1.10–8.57), with household exposure (aOR 2.96, 95% CI 1.33–6.58) or a sputum smear positive index case (aOR 3.96, 95% CI 1.20–13.03) were more likely to have TB disease or infection.Conclusions: Prompt TB investigations and early diagnosis can be achieved with a well-organised contact tracing structure. The risk for TB infection or disease was higher among contacts with household exposure, a sputum smear positive index case or born in a TB endemic country. Large-scale investigations among children exposed in congregate settings can result in a very low yield and should be cautiously targeted. What is Known:• Vulnerable young children are a high priority in contact tracing and should be evaluated as soon as possible after TB exposure What is New:• Prompt investigations for paediatric TB contacts and early diagnosis of infected children can be achieved with a well-organised contact tracing structure• Large-scale investigations among children exposed in congregate settings can result in a very low yield and should be cautiously targeted

scholarly journals Interaction Between Negative and Positive Index Medium Waveguides

2008 ◽  
Vol 26 (21) ◽  
pp. 3560-3566 ◽  
Author(s):  
Wei Yan ◽  
Linfang Shen ◽  
Yu Yuan ◽  
Tzong Jer Yang
Keyword(s):  
Positive Index

scholarly journals Duration of Exposure Among Close Contacts of Patients With Infectious Tuberculosis and Risk of Latent Tuberculosis Infection

2020 ◽  
Vol 71 (7) ◽  
pp. 1627-1634
Author(s):  
Mary R Reichler ◽  
Awal Khan ◽  
Yan Yuan ◽  
Bin Chen ◽  
James McAuley ◽  
...  
Keyword(s):  
Latent Tuberculosis Infection ◽  
Multivariable Analysis ◽  
Latent Tuberculosis ◽  
Index Patient ◽  
The United States ◽  
Tuberculosis Infection ◽  
Ltbi Prevalence ◽  
Male Sex ◽  
Positive Index ◽  
Close Contacts

Abstract Background Predictors of latent tuberculosis infection (LTBI) among close contacts of persons with infectious tuberculosis (TB) are incompletely understood, particularly the number of exposure hours. Methods We prospectively enrolled adult patients with culture-confirmed pulmonary TB and their close contacts at 9 health departments in the United States and Canada. Patients with TB were interviewed and close contacts were interviewed and screened for TB and LTBI during contact investigations. Results LTBI was diagnosed in 1390 (46%) of 3040 contacts, including 624 (31%) of 2027 US/Canadian-born and 766 (76%) of 1013 non-US/Canadian-born contacts. In multivariable analysis, age ≥5 years, male sex, non-US/Canadian birth, smear-positive index patient, and shared bedroom with an index patient (P < .001 for each), as well as exposure to >1 index patient (P < .05), were associated with LTBI diagnosis. LTBI prevalence increased with increasing exposure duration, with an incremental prevalence increase of 8.2% per 250 exposure hours (P < .0001). For contacts with <250 exposure hours, no difference in prevalence was observed per 50 exposure hours (P = .63). Conclusions Hours of exposure to a patient with infectious TB is an important LTBI predictor, with a possible risk threshold of 250 hours. More exposures, closer exposure proximity, and more extensive index patient disease were additional LTBI predictors.

scholarly journals Logarithmic Asymptotics for Multidimensional Extremes Under Nonlinear Scalings

2015 ◽  
Vol 52 (1) ◽  
pp. 68-81 ◽  
Author(s):  
K. M. Kosiński ◽  
M. Mandjes
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Random Vectors ◽  
Deviation Principle ◽  
Logarithmic Asymptotics ◽  
Rate Functions ◽  
Regularly Varying ◽  
Positive Index

Let W = {Wn: n ∈ N} be a sequence of random vectors in Rd, d ≥ 1. In this paper we consider the logarithmic asymptotics of the extremes of W, that is, for any vector q > 0 in Rd, we find that logP(there exists n ∈ N: Wnuq) as u → ∞. We follow the approach of the restricted large deviation principle introduced in Duffy (2003). That is, we assume that, for every q ≥ 0, and some scalings {an}, {vn}, (1 / vn)logP(Wn / an ≥ uq) has a, continuous in q, limit JW(q). We allow the scalings {an} and {vn} to be regularly varying with a positive index. This approach is general enough to incorporate sequences W, such that the probability law of Wn / an satisfies the large deviation principle with continuous, not necessarily convex, rate functions. The equations for these asymptotics are in agreement with the literature.

scholarly journals Indices of Change, Expectations, and Popularity of Biological Treatments for Major Depressive Disorder between 1988 and 2017: A Scientometric Analysis

2019 ◽  
Vol 16 (13) ◽  
pp. 2255 ◽  
Author(s):  
Bach X. Tran ◽  
Giang H. Ha ◽  
Giang T. Vu ◽  
Long H. Nguyen ◽  
Carl A. Latkin ◽  
...  
Keyword(s):  
Major Depressive Disorder ◽  
Depressive Disorder ◽  
Repetitive Transcranial Magnetic Stimulation ◽  
Grey Literature ◽  
Scientometric Analysis ◽  
Major Depressive ◽  
Wide Range ◽  
Biological Treatments ◽  
Meta Analyses ◽  
Positive Index

Background. Major Depressive Disorder (MDD) is the most common psychiatric disorder with high prevalence and disease burden. Biological treatments of MDD over the last several decades include a wide range of antidepressants and neurostimulation therapies. While recent meta-analyses have explored the efficacy and tolerability of antidepressants, the changing trends of biological treatments have not been evaluated. Our study measured the indices of change, expectations, and popularity of biological treatments of MDD between 1988 and 2017. Methods. We performed a scientometric analysis to identify all relevant publications related to biological treatments of MDD from 1988 to 2017. We searched the Web of Science websites for publications from 1 January 1988 to 31 December 2017. We included publications of fluoxetine, paroxetine, citalopram, sertraline, amitriptyline, fluvoxamine, escitalopram, venlafaxine, duloxetine, milnacipran, desvenlafaxine, levomilnacipran, clomipramine, nortriptyline, bupropion, trazodone, nefazodone, mirtazapine, agomelatine, vortioxetine, vilazodone, electroconvulsive therapy (ECT), repetitive transcranial magnetic stimulation (rTMS), vagus nerve stimulation (VNS), deep brain stimulation (DBS), and transcranial direct current stimulation (tDCS). We excluded grey literature, conference proceedings, books/book chapters, and publications with low quality as well as publications not related to medicine or human health. The primary outcomes assessed were indices of change, expectations, and popularity. Results. Of 489,496 publications identified, we included 355,116 publications in this scientometric analysis. For the index of change, fluoxetine, sertraline and ECT demonstrated a positive index of change in 6 consecutive periods. Other neurostimulation therapies including rTMS, VNS, DBS and tDCS had shown a positive index of change since 1998. We calculated the index of change of popularity index (PI), which indicates that from 2013 to 2017, the number of publications on tricyclic antidepressants (TCAs) and monoamine oxidase inhibitors (MAOIs) were reduced by 85.0% and 81.3% respectively, as compared with the period 2008–2012. For the index of expectation, fluoxetine and ECT showed the highest index of expectations in six consecutive periods and remained the highest in 2013–2017. For popularity, the three antidepressants with highest PI were fluoxetine (4.01), paroxetine (2.09), and sertraline (1.66); the three antidepressants with lowest PI were desvenlafaxine (0.08), vilazodone (0.04) and levomilnacipran (0.03). Among neurostimulation therapies, ECT has the highest PI (2.55), and tDCS the lowest PI (0.14). The PI of SSRI remained the highest among all biological treatments of MDD in 2013–2017. In contrast, the PI of ECT was reduced by approximately 50% during the period 2008 to2012 than that in the period 2013 to 2017. Conclusions. This scientometric analysis represents comprehensive evidence on the popularity and change in prospects of biological treatments for MDD from 1988 to 2017. The popularity of SSRI peaked between 1998 and 2002, when their efficacy, tolerability and safety profile allowed them to replace the TCAs and MAOIs. While the newer neurostimulation therapies are gaining momentum, the popularity of ECT has sustained.

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