Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Implementing Immersive Worlds for Metaverse-Based Participatory Design through Photogrammetry and Blockchain

This paper explores participatory design methods for the interconnection of digital recording techniques, like digital photogrammetry and Gaussian splatting, with emerging domains such as the metaverse and blockchain technology. The focus lies in community engagement and the economic growth of urban and rural areas through blockchain integration, utilizing low-cost digitalization methods to create Web3 environments mirroring real settlements. Through a case study of an Italian village, the potential of participatory design and community-led development strategies in revitalizing neglected areas are explored, and the use of low-cost drone-based photogrammetry and Gaussian splatting in digitization are compared, highlighting their advantages and drawbacks considering the aim of this work, i.e., the creation of an interactive metaverse space. Ultimately, the study underscores the transformative role of digital technologies in reshaping design processes and fostering community development through a workflow, stressing collaborative decision-making and blockchain-driven economy, manufacturing, and maintenance through self-ownership models and performance-based smart contracts

On the construction of generalized Grassmann representatives of state vectors

Generalized $Z_k$-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors.Comment: 8 page

ОСОБЛИВОСТІ ПІДГОТОВКИ АНГЛОМОВНИХ СТУДЕНТІВ МОЛОДШИХ І СТАРШИХ КУРСІВ НА КАФЕДРАХ ГІГІЄНІЧНОГО ПРОФІЛЮ У ВИЩИХ МЕДИЧНИХ НАВЧАЛЬНИХ ЗАКЛАДАХ

The article describes peculiarities of training English-speaking students of junior and senior years of study in the hygienic profile departments of medical schools. It has been established that for English-language students of junior year of study it is more relevant to hold seminars with discussion of participants’ reports, and for senior students – solution of situational tasks with the analysis of normative documents on the topic of practical classes, assessment of environmental factors with a help of devices, maintenance of protocols on  the topics of practical classes and IWS, interim and final control on tests from “KROK-2”, due to the peculiarities of curriculum on hygiene for foreign students, which study on the 3rd and  6th courses on the specialty “General medicine”.  The questionnaire, conducted among students of junior year of study (40 respondents), according to our own questionnaire, showed that foreign students spend less than 1 hour on training of theoretical subjects: 6 respondents (16.6%);  1–2 hours – 16 (44.4 %);  2–3 hours  – 9 (25 %);  more than 3 hours – 5 (13.8 %).  English-speaking students spend less than 1 hour – 3 (8.3 %) when training for classes in the clinical disciplines;  1–2 hours – 11 (30.5 %);  2–3  hours – 11 (30.5 %);  more than 3 hours – 3 (8.3 %).  In particular, 25 % of respondents (69.4  %) are positively related to the IWS, a quarter of respondents – negatively (14 %).  The majority of students find answers to the control questions from the topics in the Internet (36  %) and in the textbook (33.3 %), and the minority uses textbooks (28 %), which is caused by a decreasing an interest of students in studying.У статті показано особливості підготовки англомовних студентів молодших і старших курсів на кафедрах гігієнічного профілю у вищих медичних навчальних закладах. Встановлено, що для англомовних студентів молодших курсів більш актуальним є проведення семінарів з обговореннями доповідей учасників, а для студентів старших курсів – розв'язання ситуаційних завдань із розбором нормативних документів за темою практичного заняття, оцінка факторів навколишнього середовища за допомогою приладів, ведення протокольних зошитів з тем практичних занять і СРС, проміжний і підсумковий контроль за тестами з бази «Крок 2», що обумовлено особливостями навчальної програми з гігієни для іноземних студентів 3 і 6 курсів за спеціальністю «Лікувальна справа». Анкетування, проведене серед англомовних студентів молодших курсів (40 респондентів) за розробленою нами власною анкетою, показало, що іноземні студенти на підготовку до практичного заняття з теоретичних дисциплін витрачають: менше 1 год – 6 респондентів (16,6 %); 1–2 год – 16 (44,4 %); 2–3 год – 9 (25 %); більше ніж 3 год – 5 (13,8 %). При підготовці до заняття з клінічних дисциплін англомовні студенти витрачають: менше 1 год – 3 (8,3 %); 1–2 год – 11 (30,5 %); більше ніж 3 год – 3 (8,3 %). Зокрема, 25 % респондентів (69,4 %) позитивно ставляться до проведення СРС, чверть опитаних – негативно (14 %). Відповіді на контрольні питання до тем СРС більшість студентів знаходить у матеріалах із мережі «Інтернет» (36 %) і в навчально-методичному посібнику (33,3 %), меншість користується підручниками (28 %), що зумовлено зниженням зацікавленості студентів до навчання

Monomeric alpha-synuclein exerts a physiological role in brain ATP synthase

Misfolded α-synuclein is a key factor in the pathogenesis of Parkinson's disease (PD). However, knowledge about a physiological role for the native, unfolded α-synuclein is limited. Using brains of mice lacking α-, β-, and γ-synuclein, we report that extracellular monomeric α-synuclein enters neurons and localizes to mitochondria, interacts with ATP synthase subunit α, and modulates ATP synthase function. Using a combination of biochemical, live-cell imaging and mitochondrial respiration analysis, we found that brain mitochondria of α-, β-, and γ-synuclein knock-out mice are uncoupled, as characterized by increased mitochondrial respiration and reduced mitochondrial membrane potential. Furthermore, synuclein deficiency results in reduced ATP synthase efficiency and lower ATP levels. Exogenous application of low unfolded α-synuclein concentrations is able to increase the ATP synthase activity that rescues the mitochondrial phenotypes observed in synuclein deficiency. Overall, the data suggest that α-synuclein is a previously unrecognized physiological regulator of mitochondrial bioenergetics through its ability to interact with ATP synthase and increase its efficiency. This may be of particular importance in times of stress or PD mutations leading to energy depletion and neuronal cell toxicity

The cubic chessboard

We present a survey of recent results, scattered in a series of papers that appeared during past five years, whose common denominator is the use of cubic relations in various algebraic structures. Cubic (or ternary) relations can represent different symmetries with respect to the permutation group S_3, or its cyclic subgroup Z_3. Also ordinary or ternary algebras can be divided in different classes with respect to their symmetry properties. We pay special attention to the non-associative ternary algebra of 3-forms (or ``cubic matrices''), and Z_3-graded matrix algebras. We also discuss the Z_3-graded generalization of Grassmann algebras and their realization in generalized exterior differential forms. A new type of gauge theory based on this differential calculus is presented. Finally, a ternary generalization of Clifford algebras is introduced, and an analog of Dirac's equation is discussed, which can be diagonalized only after taking the cube of the Z_3-graded generalization of Dirac's operator. A possibility of using these ideas for the description of quark fields is suggested and discussed in the last Section.Comment: 23 pages, dedicated to A. Trautman on the occasion of his 64th birthda

Loss of PLA2G6 leads to elevated mitochondrial lipid peroxidation and mitochondrial dysfunction

© 2015 The Author.The PLA2G6 gene encodes a group VIA calcium-independent phospholipase A2 beta enzyme that selectively hydrolyses glycerophospholipids to release free fatty acids. Mutations in PLA2G6 have been associated with disorders such as infantile neuroaxonal dystrophy, neurodegeneration with brain iron accumulation type II and Karak syndrome. More recently, PLA2G6 was identified as the causative gene in a subgroup of patients with autosomal recessive early-onset dystonia-Parkinsonism. Neuropathological examination revealed widespread Lewy body pathology and the accumulation of hyperphosphorylated tau, supporting a link between PLA2G6 mutations and Parkinsonian disorders. Here we show that knockout of the Drosophila homologue of the PLA2G6 gene, iPLA2-VIA, results in reduced survival, locomotor deficits and organismal hypersensitivity to oxidative stress. Furthermore, we demonstrate that loss of iPLA2-VIA function leads to a number of mitochondrial abnormalities, including mitochondrial respiratory chain dysfunction, reduced ATP synthesis and abnormal mitochondrial morphology. Moreover, we show that loss of iPLA2-VIA is strongly associated with increased lipid peroxidation levels. We confirmed our findings using cultured fibroblasts taken from two patients with mutations in the PLA2G6 gene. Similar abnormalities were seen including elevated mitochondrial lipid peroxidation and mitochondrial membrane defects, as well as raised levels of cytoplasmic and mitochondrial reactive oxygen species. Finally, we demonstrated that deuterated polyunsaturated fatty acids, which inhibit lipid peroxidation, were able to partially rescue the locomotor abnormalities seen in aged flies lacking iPLA2-VIA gene function, and restore mitochondrial membrane potential in fibroblasts from patients with PLA2G6 mutations. Taken together, our findings demonstrate that loss of normal PLA2G6 gene activity leads to lipid peroxidation, mitochondrial dysfunction and subsequent mitochondrial membrane abnormalities. Furthermore we show that the iPLA2-VIA knockout fly model provides a useful platform for the further study of PLA2G6-associated neurodegeneration

Z3_3-graded differential geometry of quantum plane

In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.Comment: 17 page

Adsorption of cis-dichlorodiammineplatinum by nanostructures based on single-domain magnetite

Magnetosensitive nanocomposites on the basis of monodomain magnetite Fe3O4/meso-2,3-dimercaptosuccinic acid, Fe3O4/c-aminopropyltriethoxysilane, Fe3O4/polyacrylamide, Fe3O4/hydroxyapatite were synthesized. Size distribution of magnetite nanoparticles in ensemble and their magnetic properties were studied. It has been shown that the magnetization curve of the liquid containing monodomain magnetite has a form that is characteristic for superparamagnetics, and its calculations in the framework of Langeven’s paramagnetism theory match satisfactorily to the experimental results. The highest adsorption parameters were observed for magnetosensitive nanocomposites Fe3O4/ polyacrylamide and Fe3O4/c-aminopropyltriethoxysilane. Prospects of the studied nanostructures for medicobiological and technical applications as adsorbents of cis-dichlorodiammineplatinum were shown