New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Effects of anesthesia on functional activation of cerebral blood flow and metabolism

Functional brain mapping based on changes in local cerebral blood flow (lCBF) or glucose utilization (lCMRglc) induced by functional activation is generally carried out in animals under anesthesia, usually α-chloralose because of its lesser effects on cardiovascular, respiratory, and reflex functions. Results of studies on the role of nitric oxide (NO) in the mechanism of functional activation of lCBF have differed in unanesthetized and anesthetized animals. NO synthase inhibition markedly attenuates or eliminates the lCBF responses in anesthetized animals but not in unanesthetized animals. The present study examines in conscious rats and rats anesthetized with α-chloralose the effects of vibrissal stimulation on lCMRglc and lCBF in the whisker-to-barrel cortex pathway and on the effects of NO synthase inhibition with NG-nitro-l-arginine methyl ester (l-NAME) on the magnitude of the responses. Anesthesia markedly reduced the lCBF and lCMRglc responses in the ventral posteromedial thalamic nucleus and barrel cortex but not in the spinal and principal trigeminal nuclei. l-NAME did not alter the lCBF responses in any of the structures of the pathway in the unanesthetized rats and also not in the trigeminal nuclei of the anesthetized rats. In the thalamus and sensory cortex of the anesthetized rats, where the lCBF responses to stimulation had already been drastically diminished by the anesthesia, l-NAME treatment resulted in loss of statistically significant activation of lCBF by vibrissal stimulation. These results indicate that NO does not mediate functional activation of lCBF under physiological conditions.

Age-related losses of cognitive function and motor skills in mice are associated with oxidative protein damage in the brain.

The hypothesis that age-associated impairment of cognitive and motor functions is due to oxidative molecular damage was tested in the mouse. In a blind study, senescent mice (aged 22 months) were subjected to a battery of behavioral tests for motor and cognitive functions and subsequently assayed for oxidative molecular damage as assessed by protein carbonyl concentration in different regions of the brain. The degree of age-related impairment in each mouse was determined by comparison to a reference group of young mice (aged 4 months) tested concurrently on the behavioral battery. The age-related loss of ability to perform a spatial swim maze task was found to be positively correlated with oxidative molecular damage in the cerebral cortex, whereas age-related loss of motor coordination was correlated with oxidative molecular damage within the cerebellum. These results support the view that oxidative stress is a causal factor in brain senescence. Furthermore, the findings suggest that age-related declines of cognitive and motor performance progress independently, and involve oxidative molecular damage within different regions of the brain.

Efeitos dos agrotóxicos Kraft®36EC e Score®250EC (e seus princípios ativos) em ecossistemas aquáticos: análises comparativas e ecossistêmicas

Com o advento da agricultura ampliou-se a produção alimentar e os bens de consumo, no entanto, os riscos ambientais também foram maximizados em função da adoção de técnicas produtivas baseadas no uso intensivo de insumos agrícolas. Esta problemática é mundial, embora mais evidenciada nos países em desenvolvimento e que tem, na produção agrícola, a base de sua economia. O Brasil enquadra-se nesta situação e desde 2009 é considerado o maior consumidor de agrotóxicos do mundo, criando um cenário de risco ambiental e de saúde humana. Os efeitos ambientais, base deste estudo, estão relacionados não somente à perda de espécies não-alvo, uma vez que os agrotóxicos não são seletivos, mas também as alterações em nível ecossistêmico, a qual se relaciona com as perdas das funções e dos serviços gerados pelos sistemas naturais. Adiciona-se a esta complexidade, a forma de ação de cada agrotóxico, a distribuição dos mesmos nos diferentes compartimentos (ar, solo e água), o período de permanência de cada um, as relações sinérgicas decorrentes das interações entre diferentes produtos, a formação de subprodutos no processo de degradação, entre outros fatores, como as diferenças existentes entre o ingrediente ativo e a formulação comercial, na qual existem os chamados ingredientes inertes em sua composição, os quais podem ser muito mais tóxicos para espécies e ecossistemas. Considerando esta abordagem, a presente pesquisa foi desenvolvida com base na realidade de um local de referência, o município de Bom Repouso (MG/BR), no qual a intensificação da produção de morango e batata tem trazido uma série de riscos sociais e ambientais. Semelhante a outras regiões produtivas do país, o uso de agrotóxicos é recorrente, amplo e irrestrito, com destaque para as formulações comerciais Kraft®36EC e Score®250EC, as quais, juntamente com seus respectivos ingredientes ativos (abamectina e difenoconazol), foram avaliadas por meio de testes de toxicidade com espécies de diferentes níveis tróficos representativas de um ecossistema aquático, gerando informações que foram avaliadas em nível de espécie e de ecossistema, simulando o cenário de aplicação dos produtos no local de referência. Os resultados obtidos permitiram concluir sobre as diferenças de sensibilidade das espécies e quais seriam as mais indicadas para se avaliar os efeitos tóxicos de ambos os agrotóxicos; os efeitos diferenciados entre a formulação comercial e os ingredientes ativos; bem como as respostas em termos de espécies e de ecossistemas, demonstrando a necessidade de que ambas as análises sejam consideradas na avaliação de risco ecológico.

Loss of Outer Retinal Neurons and Circuitry Alterations in the DBA/2J Mouse

Purpose. The DBA/2J mouse line develops essential iris atrophy, pigment dispersion, and glaucomatous age-related changes, including an increase of IOP, optic nerve atrophy, and retinal ganglion cell (RGC) death. The aim of this study was to evaluate possible morphological changes in the outer retina of the DBA/2J mouse concomitant with disease progression and aging, based on the reduction of both the a- and b-waves and photopic flicker ERGs in this mouse line. Methods. Vertically sectioned DBA/2J mice retinas were evaluated at 3, 8, and 16 months of age using photoreceptor, horizontal, and bipolar cell markers. Sixteen-month-old C57BL/6 mice retinas were used as controls. Results. The DBA/2J mice had outer retinal degeneration at all ages, with the most severe degeneration in the oldest retinas. At 3 months of age, the number of photoreceptor cells and the thickness of the OPL were reduced. In addition, there was a loss of horizontal and ON-bipolar cell processes. At 8 months of age, RGC degeneration occurred in patches, and in the outer retina overlying these patches, cone morphology was impaired with a reduction in size as well as loss of outer segments and growth of horizontal and bipolar cell processes into the outer nuclear layer. At 16 months of age, connectivity between photoreceptors and horizontal and bipolar cell processes overlying these patches was lost. Conclusions. Retinal degeneration in DBA/2J mice includes photoreceptor death, loss of bipolar and horizontal cell processes, and loss of synaptic contacts in an aging-dependent manner.

Behaviours, Processes and Probabilistic Environmental Functions in H-Open Systems

The Patten’s Theory of the Environment, supposes an impotent contribution to the Theoretical Ecology. The hypothesis of the duality of environments, the creaon and genon functions and the three developed propositions are so much of great importance in the field of the Applied Mathematical as Ecology. The authors have undertaken an amplification and revision of this theory, developing the following steps: 1) A theory of processes. 2) A definition of structural and behavioural functions. 3) A probabilistic definition of the environmental functions. In this paper the authors develop the theory of behavioural functions, begin the theory of environmental functions and give a complementary focus to the theory of processes that has been developed in precedent papers.

Social Support Networks and Self-Efficacy of Peruvian Women Diagnosed with Cancer: A Biocultural Analysis of Health Behavior Constructs

Thesis (Ph.D.)--University of Washington, 2016-06

Gene-environment interactions between adult lead exposure and Apolipoprotein E4 on adult hippocampal neurogenesis and cognitive behavior in mice

Thesis (Ph.D.)--University of Washington, 2016-06

HIV Status and Risk Factors for Hypertension in South African Adults

Thesis (Master's)--University of Washington, 2016-06

Antidepressant Use and Risk of Dementia and Cognitive Decline

Thesis (Ph.D.)--University of Washington, 2016-06

Double-strand break repair gene polymorphisms and risk of breast or ovarian cancer

Deficiencies in DNA repair have been hypothesized to increase cancer risk and excess cancer incidence is a feature of inherited diseases caused by defects in DNA damage recognition and repair. We investigated, using a case-control design, whether the double-strand break repair gene polymorphisms RAD51 5' untranslated region -135 G > C, XRCC2 R188H G > A, and XRCC3 T241M C > T were associated with risk of breast or ovarian cancer in Australian women. Sample sets included 1,456 breast cancer cases and 793 age-matched controls ages under 60 years of age, 549 incident ovarian cancer cases, and 335 controls of similar age distribution. For the total sample and the subsample of Caucasian women, there were no significant differences in genotype distribution between breast cancer cases and controls or between ovarian cancer cases and combined control groups. The crude odds ratios (OR) and 95% confidence intervals (95% CI) associated with the RAD51 GC/CC genotype frequency was OR, 1.10; 95% CI, 0.80-1.41 for breast cancer and OR, 1.22; 95% CI, 0.92-1.62 for ovarian cancer. Similarly, there were no increased risks associated with the XRCC2 GA/AA genotype (OR, 0.98; 95% CI, 0.76-1.26 for breast cancer and OR, 0.93; 95% CI, 0.69-1.25 for ovarian cancer) or the XRCC3 CT/TT genotype (OR, 0.92; 95% Cl, 0.77-1.10 for breast cancer and OR, 0.87; 95% CI, 0.71-1.08 for ovarian cancer). Results were little changed after adjustment for age and other measured risk factors. Although there was little statistical power to detect modest increases in risk for the homozygote variant genotypes, particularly for the rare RAD51 and XRCC2 variants, the data suggest that none of these variants play a major role in the etiology of breast or ovarian cancer.

Polymorphisms in glutathione S-transferases and non-melanoma skin cancer risk in Australian renal transplant recipients

Caucasian renal transplant recipients from Queensland, Australia have the highest non-melanoma skin cancer (NMSC) risk worldwide. Although ultraviolet light (UVR) exposure is critical, genetic factors also appear important. We and others have shown that polymorphism in the glutathione S-transferases (GST) is associated with NMSC in UK recipients. However, the effect of high UVR exposure and differences in immunosuppressive regimen on these associations is unknown. In this study, we examined allelism in GSTM1, GSTM3, GSTT1 and GSTP1 in 361 Queensland renal transplant recipients. Data on squamous (SCC) and basal cell carcinoma (BCC), UVR/tobacco exposure and genotype were obtained. Associations with both NMSC risk and numbers were examined using logistic and negative binomial regression, respectively. In the total group, GSTM1 AB [P = 0.049, rate ratio (RR) = 0.23] and GSTM3 AA (P = 0.015, RR = 0.50) were associated with fewer SCC. Recipients were then stratified by prednisolone dose (less than or equal to7 versus >7 mg/day). In the low-dose group, GSTT1 null (P = 0.006, RR = 0.20) and GSTP1 Val/Val (P = 0.021, RR = 0.20) were associated with SCC numbers. In contrast, in the high-dose group, GSTM1 AB (P = 0.009, RR = 0.05), GSTM3 AB (P = 0.042, RR = 2.29) and BB (P = 0.014, RR = 5.31) and GSTP1 Val/Val (P = 0.036, RR = 2.98) were associated with SCC numbers. GSTM1 AB (P = 0.016) and GSTP1 Val/Val (P = 0.046) were also associated with fewer BCC in this group. GSTP1 associations were strongest in recipients with lower UVR/tobacco exposure. The data confirm our UK findings, suggesting that protection against UVR-induced oxidative stress is important in NMSC development in recipients, but that this effect depends on the immunosuppressant regimen.