Keskosa interpolatsioonil põhinevad meetodid nõrgalt singulaarsete integraalvõrrandite lahendamiseks

Paljud keemia, polümeeride füüsika, matemaatilise füüsika jt teadusalade probleemid on formuleeritavad integraalvõrrandite kujul ning nende probleemide käsitlus taandub integraalvõrrandite lahendamisele või kvalitatiivsele uurimisele. Integraalvõrrandeid, mida saab täpselt lahendada, on suhteliselt vähe, seega on väga olulised meetodid võrrandite numbriliseks lahendamiseks. Käesolevas doktoritöös pakume välja kaks kõrget järku numbrilist meetodit, mis ei kasuta lineaarse teist liiki singulaarsustega Fredholmi integraalvõrrandi lahendamiseks ebaühtlast võrku. Need meetodid on kollokatsioonimeetod ja korrutise integreerimise meetod. Nimetatud meetodid põhinevad keskosa interpolatsioonil polünoomidega ühtlasel võrgul ja silendaval muutujate vahetusel. Lõigu keskosas on interpolatsioonivea hinnang ligikaudu 2m korda täpsem kui kogu lõigul. Lisaks on interpolatsiooniprotsess ühtlasel võrgul lõigu keskosas m-i kasvades stabiilne. Muutujate vahetuse abil parendame me võrrandi täpse lahendi käitumist. Doktoritöös on kirjeldatud toodud meetodite koondumist ja koondumiskiirustThere are a number of problems from many different fields, for example chemistry, physics of polymers and mathematical physics, which are directly formulated in terms of integral equations; and there are problems that are represented in terms of differential equations with auxiliary conditions, but which can be reduced to integral equations. There are relatively few integral equations which can be solved exactly, hence, numerical schemes are required for dealing with these equations in a proper manner. In this thesis we propose two new classes of high order numerical methods, which do not need graded grids for solving linear Fredholm integral equations of the second kind with singularities. The methods are developed by means of the 'central part' interpolation by polynomials on the uniform grid and smoothing change of variables. In the central parts of the interval, the estimates of interpolation error are approximately 2m times more precise than on the whole interval. In the central parts of the interval, the interpolation process on the uniform grid also has good stability properties as m increases. With the help of a change of variables we improve the boundary behaviour of the exact solution of the problem. The convergence and the convergence order of methods is studied

SNPmasker: automatic masking of SNPs and repeats across eukaryotic genomes

SNPmasker is a comprehensive web interface for masking large eukaryotic genomes. The program is designed to mask SNPs from recent dbSNP database and to mask the repeats with two alternative programs. In addition to the SNP masking, we also offer population-specific substitution of SNP alleles in genomic sequence according to SNP frequencies in HapMap Phase II data. The input to SNPmasker can be defined in chromosomal coordinates or inserted as a sequence. The sequences masked by our web server are most useful as a preliminary step for different primer and probe design tasks. The service is available at and is free for all users

A central part interpolation scheme for log-singular integral equations

A fully discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on “central part” interpolation by polynomials on the uniform grid

Komplekssete probleemide lahendamise oskus ning selle hindamine ja arendamine gümnaasiumis

Siinses uuringus selgitasime, kas komplekssete probleemide lahendamise oskus on kirjeldatav ja arendatav matemaatilise, algoritmilise ja uurimusliku probleemilahendamise strateegiate põhjal. Esmalt kohandasime hindamisvahendid nende oskuste hindamiseks gümnaasiumis ning kirjeldasime 10. klassi õpilaste oskuste taset. Matemaatilisel probleemilahendamisel eristus kaks faktorit: probleemülesande lahendamise kavandamine ja lahendamine ning tulemuste tõlgendamine. Algoritmilisel probleemilahendamisel eristus üks üld- ja kaks spetsiifilist faktorit: algoritmiline mõtlemine ja mustrite äratundmine. Uurimuslikul probleemilahendamisel eristusid suunaseadmine, uurimine ja järeldamine. Kolm probleemide lahendamise strateegiat olid ühendatavad üheks tunnuseks, mida võib vaadelda komplekssete probleemide lahendamise oskusena.  Summar

Adaptation of striated muscles to Wolframin deficiency in mice: Alterations in cellular bioenergetics

Background: Wolfram syndrome (WS), caused by mutations in WFS1 gene, is a multi-targeting disease affecting multiple organ systems. Wolframin is localized in the membrane of the endoplasmic reticulum (ER), influencing Ca2+ metabolism and ER interaction with mitochondria, but the exact role of the protein remains unclear. In this study we aimed to characterize alterations in energy metabolism in the cardiac and in the oxidative and glycolytic skeletal muscles in Wfs1-deficiency. Methods: Alterations in the bioenergetic profiles in the cardiac and skeletal muscles of Wfs1-knock-out (KO) male mice and their wild type male littermates were determined using high resolution respirometry, quantitative RT-PCR, NMR spectroscopy, and immunofluorescence confocal microscopy. Results: Oxygen consumption without ATP synthase activation (leak) was significantly higher in the glycolytic muscles of Wfs1 KO mice compared to wild types. ADP-stimulated respiration with glutamate and malate was reduced in the Wfs1-deficient cardiac as well as oxidative and glycolytic skeletal muscles. Conclusions: Wfs1-deficiency in both cardiac and skeletal muscles results in functional alterations of energy transport from mitochondria to ATP-ases. There was a substrate-dependent decrease in the maximal Complex I –linked respiratory capacity of the electron transport system in muscles of Wfs1 KO mice. Moreover, in cardiac and gastrocnemius white muscles a decrease in the function of one pathway were balanced by the increase in the activity of the parallel pathway. General significance: This work provides new insights to the muscle involvement at early stages of metabolic syndrome like WS as well as developing glucose intoleranc

Preparation of onion-like multilayered particles comprising mainly poly(iso-butyl methacrylate)-block-polystyrene by two-step AGET ATRP

The role of dietary fiber in supporting healthy gut microbiota and overall well-being of the host has been revealed in several studies. Here, we show the effect of a bacterial polyfructan levan on the growth dynamics and metabolism of fecal microbiota in vitro by using isothermal microcalorimetry. Eleven fecal samples from healthy donors were incubated in phosphate-buffered defined medium with or without levan supplementation and varying presence of amino acids. The generation of heat, changes in pH and microbiota composition, concentrations of produced and consumed metabolites during the growth were determined. The composition of fecal microbiota and profile of metabolites changed in response to substrate (levan and amino acids) availability. The main products of levan metabolism were acetic, lactic, butyric, propionic and succinic acids and carbon dioxide. Associated growth of levan-degrading (e.g. Bacteroides) and butyric acid-producing (e.g. Faecalibacterium) taxa was observed in levan-supplemented media. The study shows that the capacity of levan and possibly also other dietary fibers/prebiotics to modulate the composition and function of colon microbiota can be predicted by using isothermal microcalorimetry of fecal samples linked to metabolite and consortia analyses

Altered mitochondrial metabolism in the insulin-resistant heart.

Obesity-induced insulin resistance and type 2 diabetes mellitus can ultimately result in various complications, including diabetic cardiomyopathy. In this case, cardiac dysfunction is characterized by metabolic disturbances such as impaired glucose oxidation and an increased reliance on fatty acid (FA) oxidation. Mitochondrial dysfunction has often been associated with the altered metabolic function in the diabetic heart, and may result from FA-induced lipotoxicity and uncoupling of oxidative phosphorylation. In this review, we address the metabolic changes in the diabetic heart, focusing on the loss of metabolic flexibility and cardiac mitochondrial function. We consider the alterations observed in mitochondrial substrate utilization, bioenergetics and dynamics, and highlight new areas of research which may improve our understanding of the cause and effect of cardiac mitochondrial dysfunction in diabetes. Finally, we explore how lifestyle (nutrition and exercise) and pharmacological interventions can prevent and treat metabolic and mitochondrial dysfunction in diabetes.COST Action MitoEAGL

Colorectal polyps increase the glycolytic activity

In colorectal cancer (CRC) energy metabolism research, the precancerous stage of polyp has remained rather unexplored. By now, it has been shown that CRC has not fully obtained the glycolytic phenotype proposed by O. Warburg and rather depends on mitochondrial respiration. However, the pattern of metabolic adaptations during tumorigenesis is still unknown. Understanding the interplay between genetic and metabolic changes that initiate tumor development could provide biomarkers for diagnosing cancer early and targets for new cancer therapeutics. We used human CRC and polyp tissue material and performed high-resolution respirometry and qRT-PCR to detect changes on molecular and functional level with the goal of generally describing metabolic reprogramming during CRC development. Colon polyps were found to have a more glycolytic bioenergetic phenotype than tumors and normal tissues. This was supported by a greater GLUT1, HK, LDHA, and MCT expression. Despite the increased glycolytic activity, cells in polyps were still able to maintain a highly functional OXPHOS system. The mechanisms of OXPHOS regulation and the preferred substrates are currently unclear and would require further investigation. During polyp formation, intracellular energy transfer pathways become rearranged mainly by increasing the expression of mitochondrial adenylate kinase (AK) and creatine kinase (CK) isoforms. Decreased glycolysis and maintenance of OXPHOS activity, together with the downregulation of the CK system and the most common AK isoforms (AK1 and AK2), seem to play a relevant role in CRC development