A generalization of the Center Theorem of the Thurston-Wolpert-Goldman Lie algebra

The Goldman Lie algebra of an oriented surface was defined by Goldman. By the natural involution that opposes the orientation of curves, the Goldman Lie algebra becomes a $\mathbb{Z}_{2}$-graded Lie algebra. Its even part is isomorphic to the Thurston-Wolpert-Goldman Lie algebra or, briefly, the TWG Lie algebra. Chas and Kabiraj proved the center of the TWG Lie algebra is generated by the class of the unoriented trivial loop and the classes of unoriented loops parallel to boundary components or punctures. The center of the even part can be rephrased as the set of elements of the even part annihilated by all the elements of the even part. We also prove some similar statements for the remaining 3 cases involving the odd part. Moreover, we compute the elements of the symmetric algebra and the universal enveloping algebra of the Goldman Lie algebra annihilated by all the even elements of the Goldman Lie algebra, and those annilated by all the odd elements.Comment: 13 pages, 2 figure

Perinatal Asphyxia Reduces Dentate Granule Cells and Exacerbates Methamphetamine-Induced Hyperlocomotion in Adulthood

浜松医科大学博士（医学）浜松医科大学学位論文 医博第548号(平成21年3月18日）doctoral医学系研究科Background: Obstetric complications have been regarded as a risk factor for schizophrenia later in life. One of the mechanisms underlying the association is postulated to be a hypoxic process in the brain in the offspring around the time of birth. Hippocampus is one of the brain regions implicated in the late-onset dopaminergic dysfunction associated with hypoxic obstetric complications. Methodology/Principal Findings: We used an animal model of perinatal asphyxia, in which rat pups were exposed to 15 min of intrauterine anoxia during Cesarean section birth. At 6 and 12 weeks after birth, the behavior of the pups was assessed using a methamphetamine-induced locomotion test. In addition, the histopathology of the hippocampus was examined by means of stereology. At 6 weeks, there was no change in the methamphetamine-induced locomotion. However, at 12 weeks of age, we found an elevation in methamphetamine-induced locomotor activity, which was associated with an increase of dopamine release in the nucleus accumbens. At the same age, we also found a reduction of the dentate granule cells of the hippocampus. Conclusions/Significance: These results suggest that the dopaminergic dysregulation after perinatal asphyxia is associated with a reduction in hippocampal dentate granule cells, and this may partly contribute to the pathogenesis of schizophrenia.doctoral thesi

Optimising the design of textured surfaces for reducing lubricated friction coefficient

Under operating conditions which are unfavourable for lubrication, such as high load and low velocity, the use of textured surfaces significantly promotes the formation of a thick lubricant film and an improvement of the friction coefficient. This paper relates to the manufacture of textures using a photolithography and chemical etching process. Different surface geometries, texturing densities and depths were designed to analyse the influence of these parameters. The friction coefficient was measured in a ball-on-disc tribometer under different lubrication regimes, and the results have been used to develop an artificial neural network with texturing optimisation potential

‘Opening doors’ for long-term institutionalised patients with schizophrenia in Japan

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Analysis of Unavailability in Middleboxes With Multiple Backup Servers Under Shared Protection

Middlebox functions, implemented as software on general-purpose servers via network function virtualization, require reliable protection mechanisms to ensure service continuity. Assessing the unavailability of these functions is critical, as failures can lead to significant service disruptions. However, existing analytical models primarily assume that a function is protected by at most one or two backup servers, limiting their applicability in scenarios requiring higher resilience. To address this limitation, this paper proposes an analytical model for evaluating the unavailability of middlebox functions under a multiple-backup shared protection strategy, where multiple backup servers protect one or more functions. Our model allows each function to be protected by multiple backup servers, ensuring availability while ensuring that each backup server can simultaneously recover at most one function. Utilizing a Markov chain, we analyze state transitions and establish equilibrium-state equations, providing an analytical foundation for evaluating the performance of the multiple-backup shared protection strategy. Numerical results demonstrate that this strategy significantly enhances availability, reducing unavailability by up to 72.3% compared to the single-backup shared protection strategy in the scenarios examined. Our study provides a detailed analysis of backup allocation strategies, focusing on their impact on function availability and offering more profound insights into their effectiveness through theoretical properties and performance comparisons with existing strategies. Our evaluation reveals that the multiple-backup shared protection strategy reduces unavailability by up to 64.8% compared to the single-backup shared protection strategy in the examined allocation cases