131 research outputs found
Quadratic Poisson brackets compatible with an algebra structure
Quadratic Poisson brackets on a vector space equipped with a bilinear
multiplication are studied. A notion of a bracket compatible with the
multiplication is introduced and an effective criterion of such compatibility
is given. Among compatible brackets, a subclass of coboundary brackets is
described, and such brackets are enumerated in a number of examples.Comment: 6 page
Quadratic Poisson brackets and Drinfeld theory for associative algebras
The paper is devoted to the Poisson brackets compatible with multiplication
in associative algebras. These brackets are shown to be quadratic and their
relations with the classical Yang--Baxter equation are revealed. The paper also
contains a description of Poisson Lie structures on Lie groups whose Lie
algebras are adjacent to an associative structure.Comment: 16 pages, latex, no figure
Quadratic Poisson brackets and Drinfel'd theory for associative algebras
Quadratic Poisson brackets on associative algebras are studied. Such a
bracket compatible with the multiplication is related to a differentiation in
tensor square of the underlying algebra. Jacobi identity means that this
differentiation satisfies a classical Yang--Baxter equation. Corresponding Lie
groups are canonically equipped with a Poisson Lie structure. A way to quantize
such structures is suggested.Comment: latex, no figures
Towards a framework to evaluate the ‘total’ performance of buildings
Internationally, buildings are a major contributor to carbon emissions. Despite significant advances in the technology and construction of energy-efficient buildings, in many cases a performance gap between designed and actual performance exists. While much research has investigated the drivers of the building energy performance gap – both static and transient– there has been considerably less research into the total performance gap, defined here as performance gaps in building energy use, occupant satisfaction and Indoor Environmental Quality parameters such as thermal comfort and air quality which may impact on occupant health and wellbeing. This paper presents a meta-analysis of building performance data from buildings in the UK and China – selected due to their contrasting development environments – which illustrate the presence of and complexities of evaluating total performance gaps in both countries. The data demonstrate the need for (1) high end-use, spatial granularity and temporal resolution data for both energy and Indoor Environmental Quality, and (2) developing methodologies that allow meaningful comparisons between buildings internationally to facilitate learning from successful building design, construction methodologies and policy environments internationally. Using performance data from a UK building, a potential forward path is illustrated with the objective of developing a framework to evaluate total building performance.
Practical application: While much research has examined building energy performance gaps, Indoor Environmental Quality and occupant satisfaction gaps are rarely included despite their relationship to energy. We use a meta-analysis of energy, indoor environmental quality, and occupant satisfaction data from buildings in the UK and China to illustrating the presence of and complexities of evaluating total performance gaps for buildings in the two countries, and the need for high resolution dynamic buildings data and novel methodologies for comparison between buildings across different contexts. Illustrative case studies are used to demonstrate potential future directions for evaluating ‘total’ building performance
Connected components of spaces of Morse functions with fixed critical points
Let be a smooth closed orientable surface and be the space
of Morse functions on having exactly critical points of local minima,
saddle critical points, and critical points of local maxima,
moreover all the points are fixed. Let be the connected component of a
function in . By means of the winding number introduced by Reinhart
(1960), a surjection is constructed. In
particular, , and the Dehn twist about the boundary of any
disk containing exactly two critical points, exactly one of which is a saddle
point, does not preserve . Let be the group of orientation
preserving diffeomorphisms of leaving fixed the critical points, be the connected component of in , and
the set of diffeomorphisms preserving
. Let be the subgroup of generated by
and all diffeomorphisms which preserve some
functions , and let be its subgroup
generated and the Dehn twists about the components of level
curves of functions . We prove that if , and construct an epimorphism
, by means of
the winding number. A finite polyhedral complex associated to the
space is defined. An epimorphism and finite generating sets for the groups
and in terms of the 2-skeleton of the complex
are constructed.Comment: 12 pages with 2 figures, in Russian, to be published in Vestnik
Moskov. Univ., a typo in theorem 1 is correcte
Elements of mathematics in problems. Through olympiads and circles to profession
This is a collection of teaching materials used in several Russian
universities, schools, and mathematical circles. Most problems are chosen in
such a way that in the course of the solution and discussion a reader learns
important mathematical ideas and theories. The materials can be used by pupils
and students for self-study, and by teachers.
This is an abridged pre-copyedit version of the published book submitted with
the permission of the publisher. Each included individual material is
self-contained and ready-for-use. Solutions to problems are not included
intentionally. This collection consolidates updates of several arXiv
submissions, e.g., arXiv:1305.2598.Comment: Edited by A. Skopenkov, M. Skopenkov, A. Zaslavsky. In Russian.
Optimized for printing on A5 paper. Moscow Center for Continuous Mathematical
Education, 2018, 592pp (in Russian
Topology of the spaces of Morse functions on surfaces
Let be a smooth closed orientable surface, and let be the space of
Morse functions on such that at least critical points of each
function of are labeled by different labels (enumerated). Endow the space
with -topology. We prove the homotopy equivalence where is one of the manifolds , and the point in dependence on the sign of ,
and is the universal moduli space of framed Morse
functions, which is a smooth stratified manifold. Morse inequalities for the
Betti numbers of the space are obtained.Comment: 15 pages, in Russia
Conjunctival Reconstruction with Progenitor Cell-Derived Autologous Epidermal Sheets in Rhesus Monkey
Severe ocular surface diseases are some of the most challenging problems that the clinician faces today. Conventional management is generally unsatisfactory, and the long-term ocular consequences of these conditions are devastating. It is significantly important to find a substitute for conjunctival epithelial cells. This study was to explore the possibility of progenitor cell-derived epidermal sheets on denuded amniotic membrane to reconstruct ocular surface of conjunctiva damaged monkeys. We isolated epidermal progenitor cells of rhesus monkeys by type IV collagen adhesion, and then expanded progenitor cell-derived epidermal sheets on denuded amniotic membrane ex vivo. At 3 weeks after the conjunctiva injury, the damaged ocular surface of four monkeys was surgically reconstructed by transplanting the autologous cultivated epidermal progenitor cells. At 2 weeks after surgery, transplants were removed and examined with Hematoxylin-eosin staining, Periodic acid Schiff staining, immunofluorescent staining, scanning and transmission electron microscopy. Histological examination of transplanted sheets revealed that the cell sheets were healthy alive, adhered well to the denuded amniotic membrane, and had several layers of epithelial cells. Electron microscopy showed that the epithelial cells were very similar in appearance to those of normal conjunctival epithelium, even without goblet cell detected. Epithelial cells of transplants had numerous desmosomal junctions and were attached to the amniotic membrane with hemidesmosomes. Immunohistochemistry confirmed the presence of the conjunctival specific markers, mucin 4 and keratin 4, in the transplanted epidermal progenitor cells. In conclusion, our present study successfully reconstructed conjunctiva with autologous transplantation of progenitor cell-derived epidermal sheets on denuded AM in conjunctival damaged monkeys, which is the first step toward assessing the use of autologous transplantation of progenitor cells of nonocular surface origin. Epidermal progenitor cells could be provided as a new substitute for conjunctival epithelial cells to overcome the problems of autologous conjunctiva shortage
Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study
Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised
Cancer Biomarker Discovery: The Entropic Hallmark
Background: It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods. Methodology/Principal Findings: Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer. Conclusions/Significance: We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-throughput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases
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