Existence Results for Some Damped Second-Order Volterra Integro-Differential Equations

In this paper we make a subtle use of operator theory techniques and the well-known Schauder fixed-point principle to establish the existence of pseudo-almost automorphic solutions to some second-order damped integro-differential equations with pseudo-almost automorphic coefficients. In order to illustrate our main results, we will study the existence of pseudo-almost automorphic solutions to a structurally damped plate-like boundary value problem.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1402.563

Euler-like recurrences for smallest parts functions

We obtain recurrences for smallest parts functions which resemble Euler's recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular forms of weight 2

Conformally equivariant quantization: Existence and uniqueness

We prove the existence and the uniqueness of a conformally equivariant symbol calculus and quantization on any conformally flat pseudo-Riemannian manifold (M,\rg). In other words, we establish a canonical isomorphism between the spaces of polynomials on $T^*M$ and of differential operators on tensor densities over $M$, both viewed as modules over the Lie algebra \so(p+1,q+1) where $p+q=\dim(M)$. This quantization exists for generic values of the weights of the tensor densities and compute the critical values of the weights yielding obstructions to the existence of such an isomorphism. In the particular case of half-densities, we obtain a conformally invariant star-product.Comment: LaTeX document, 32 pages; improved versio

Classical elliptic current algebras

In this paper we discuss classical elliptic current algebras and show that there are two different choices of commutative test function algebras on a complex torus leading to two different elliptic current algebras. Quantization of these classical current algebras give rise to two classes of quantized dynamical quasi-Hopf current algebras studied by Enriquez-Felder-Rubtsov and Arnaudon-Buffenoir-Ragoucy-Roche-Jimbo-Konno-Odake-Shiraishi. Different degenerations of the classical elliptic algebras are considered. They yield different versions of rational and trigonometric current algebras. We also review the averaging method of Faddeev-Reshetikhin, which allows to restore elliptic algebras from the trigonometric ones

Ultrafilter and Constructible topologies on spaces of valuation domains

Let $K$ be a field and let $A$ be a subring of $K$. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar$(K|A)$ of all valuation domains having $K$ as quotient field and containing $A$. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar$(K|A)$. We extend results regarding distinguished spectral topologies on spaces of valuation domains.Comment: Comm. Algebra (accepted for publication

The burden of breast cancer in Italy: mastectomies and quadrantectomies performed between 2001 and 2008 based on nationwide hospital discharge records.

BACKGROUND: Where population coverage is limited, the exclusive use of Cancer Registries might limit ascertainment of incident cancer cases. We explored the potentials of Nationwide hospital discharge records (NHDRs) to capture incident breast cancer cases in Italy. METHODS: We analyzed NHDRs for mastectomies and quadrantectomies performed between 2001 and 2008. The average annual percentage change (AAPC) and related 95% Confidence Interval (CI) in the actual number of mastectomies and quadrantectomies performed during the study period were computed for the full sample and for subgroups defined by age, surgical procedure, macro-area and singular Region. Re-admissions of the same patients were separately presented. RESULTS: The overall number of mastectomies decreased, with an AAPC of -2.1% (-2.3 -1.8). This result was largely driven by the values observed for women in the 45 to 64 and 65 to 74 age subgroups (-3.0%, -3.4 -3.6 and -3.3%, -3.8 -2.8, respectively). We observed no significant reduction in mastectomies for women in the remaining age groups. Quadrantectomies showed an overall +4.7 AAPC (95%CI:4.5-4.9), with no substantial differences by age. Analyses by geographical area showed a remarkable decrease in mastectomies, with inter-regional discrepancies possibly depending upon variability in mammography screening coverage and adherence. Quadrantectomies significantly increased, with Southern Regions presenting the highest average rates. Data on repeat admissions within a year revealed a total number of 46,610 major breast surgeries between 2001 and 2008, with an overall +3.2% AAPC (95%CI:2.8-3.6). CONCLUSIONS: In Italy, NHDRs might represent a valuable supplemental data source to integrate Cancer Registries in cancer surveillance

Associations between social connections and cognition: a global collaborative individual participant data meta-analysis

Background Poor social connections (eg, small networks, infrequent interactions, and loneliness) are modifiable risk factors for cognitive decline. Existing meta-analyses are limited by reporting aggregate responses, a focus on global cognition, and combining social measures into single constructs. We aimed to investigate the association between social connection markers and the rate of annual change in cognition (ie, global and domain-specific), as well as sex differences, using an individual participant data meta-analysis. Methods We harmonised data from 13 longitudinal cohort studies of ageing in North America, South America, Europe, Africa, Asia, and Australia. Studies were eligible for inclusion if they had baseline data for social connection markers and at least two waves of cognitive scores. Follow-up periods ranged from 0 years to 15 years across cohorts. We included participants with cognitive data for at least two waves and social connection data for at least one wave. We then identified and excluded people with dementia at baseline. Primary outcomes were annual rates of change in global cognition and cognitive domain scores over time until final follow-up within each cohort study analysed by use of an individual participant data meta-analysis. Linear mixed models within cohorts used baseline social connection markers as predictors of the primary outcomes. Effects were pooled in two stages using random-effects meta-analyses. We assessed the primary outcomes in the main (partially adjusted) and fully adjusted models. Partially adjusted models controlled for age, sex, and education; fully adjusted models additionally controlled for diabetes, hypertension, smoking, cardiovascular risk, and depression. Findings Of the 40 006 participants in the 13 cohort studies, we excluded 1392 people with dementia at baseline. 38 614 individual participants were included in our analyses. For the main models, being in a relationship or married predicted slower global cognitive decline (b=0·010, 95% CI 0·000–0·019) than did being single or never married; living with others predicted slower global cognitive (b=0·007, 0·002–0·012), memory (b=0·017, 0·006–0·028), and language (b=0·008, 0·000–0·015) decline than did living alone; and weekly interactions with family and friends (b=0·016, 0·006–0·026) and weekly community group engagement (b=0·030, 0·007–0·052) predicted slower memory decline than did no interactions and no engagement. Never feeling lonely predicted slower global cognitive (b=0·047, 95% CI 0·018–0·075) and executive function (b=0·047, 0·017–0·077) decline than did often feeling lonely. Degree of social support, having a confidante, and relationship satisfaction did not predict cognitive decline across global cognition or cognitive domains. Heterogeneity was low (I2=0·00–15·11%) for all but two of the significant findings (association between slower memory decline and living with others [I2=58·33%] and community group engagement, I2=37·54–72·19%), suggesting robust results across studies. Interpretation Good social connections (ie, living with others, weekly community group engagement, interacting weekly with family and friends, and never feeling lonely) are associated with slower cognitive decline. Funding EU Joint Programme–Neurodegenerative Disease Research grant, funded by the National Health and Medical Research Council Australia, and the US National Institute on Aging of the US National Institutes of Health

Social connections and risk of incident mild cognitive impairment, dementia, and mortality in 13 longitudinal cohort studies of ageing.

INTRODUCTION: Previous meta-analyses have linked social connections and mild cognitive impairment, dementia, and mortality. However, these used aggregate data from North America and Europe and examined a limited number of social connection markers. METHODS: We used individual participant data (N = 39271, Mage  = 70.67 (40-102), 58.86% female, Meducation  = 8.43 years, Mfollow-up  = 3.22 years) from 13 longitudinal ageing studies. A two-stage meta-analysis of Cox regression models examined the association between social connection markers with our primary outcomes. RESULTS: We found associations between good social connections structure and quality and lower risk of incident mild cognitive impairment (MCI); between social structure and function and lower risk of incident dementia and mortality. Only in Asian cohorts, being married/in a relationship was associated with reduced risk of dementia, and having a confidante was associated with reduced risk of dementia and mortality. DISCUSSION: Different aspects of social connections - structure, function, and quality - are associated with benefits for healthy aging internationally. HIGHLIGHTS: Social connection structure (being married/in a relationship, weekly community group engagement, weekly family/friend interactions) and quality (never lonely) were associated with lower risk of incident MCI. Social connection structure (monthly/weekly friend/family interactions) and function (having a confidante) were associated with lower risk of incident dementia. Social connection structure (living with others, yearly/monthly/weekly community group engagement) and function (having a confidante) were associated with lower risk of mortality. Evidence from 13 longitudinal cohort studies of ageing indicates that social connections are important targets for reducing risk of incident MCI, incident dementia, and mortality. Only in Asian cohorts, being married/in a relationship was associated with reduced risk of dementia, and having a confidante was associated with reduced risk of dementia and mortality. Highlights Social connection structure (being married/in a relationship, weekly community group engagement, weekly family/friend interactions) and quality (never lonely) were associated with lower risk of incident MCI. Social connection structure (monthly/weekly friend/family interactions) and function (having a confidante) were associated with lower risk of incident dementia. Social connection structure (living with others, yearly/monthly/weekly community group engagement) and function (having a confidante) were associated with lower risk of mortality. Evidence from 13 longitudinal cohort studies of ageing indicates that social connections are important targets for reducing risk of incident MCI, incident dementia, and mortality. Only in Asian cohorts, being married/in a relationship was associated with reduced risk of dementia, and having a confidante was associated with reduced risk of dementia and mortality.fals