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8th International conference MBE

AIM: Stomach contractions show two types of specific patterns in many species, that is migrating motor contraction (MMC) and postprandial contractions (PPCs), in the fasting and fed states respectively. We found gastric PPCs terminated with migrating strong contractions in humans, dogs and suncus. In this study, we reveal the detailed characteristics and physiological implications of these strong contractions of PPC. METHODS: Human, suncus and canine gastric contractions were recorded with a motility-monitoring ingestible capsule and a strain-gauge force transducer. The response of motilin and ghrelin and its receptor antagonist on the contractions were studied by using free-moving suncus. RESULTS: Strong gastric contractions were observed at the end of a PPC in human, dog and suncus models, and we tentatively designated this contraction to be a postprandial giant contraction (PPGC). In the suncus, the PPGC showed the same property as those of a phase III contraction of MMC (PIII-MMC) in the duration, motility index and response to motilin or ghrelin antagonist administration. Ghrelin antagonist administration in the latter half of the PPC (LH-PPC) attenuated gastric contraction prolonged the duration of occurrence of PPGC, as found in PII-MMC. CONCLUSION: It is thought that the first half of the PPC changed to PII-MMC and then terminated with PIII-MMC, suggesting that PPC consists of a digestive phase (the first half of the PPC) and a discharge phase (LH-PPC) and that LH-PPC is coincident with MMC. In this study, we propose a new approach for the understanding of postprandial contractions.

Increases in typhoon intensity and sea level rise could pose significant challenges to coastal defences around Tokyo Bay. In order to analyse the extent of future problems the authors determined the increase storm surge that could result from an increase in typhoon intensity and sea level rise to this area around the turn of the 21st century. Results show how the various settlements around Tokyo Bay are at considerable risk of storm surges and sea level rise in the future. If defences are breached the potential direct economic consequences could be significant, potentially in excess of 100 trillion yen, with the indirect costs likely to be even greater. As a result it is likely that sea defences will have to be strengthened around Tokyo Bay in the future, which could cost in the order of 370bn yen to defend against a 1 in 100 year storm by the year 2100. Alternatively, a storm surge barrier could be built, which would be more expensive (possibly in the range of 700-800bn yen), though it could increase the protection level and would be able to cope with 1 in 200 or 500 year events, amongst other benefits., Hydraulic Engineering, Civil Engineering and Geosciences

Increases in typhoon intensity and sea level rise could pose significant challenges to coastal defences around Tokyo Bay. In order to analyse the extent of future problems the authors determined the increase storm surge that could result from an increase in typhoon intensity and sea level rise to this area around the turn of the 21st century. Results show how the various settlements around Tokyo Bay are at considerable risk of storm surges and sea level rise in the future. If defences are breached the potential direct economic consequences could be significant, potentially in excess of 100 trillion yen, with the indirect costs likely to be even greater. As a result it is likely that sea defences will have to be strengthened around Tokyo Bay in the future, which could cost in the order of 370bn yen to defend against a 1 in 100 year storm by the year 2100. Alternatively, a storm surge barrier could be built, which would be more expensive (possibly in the range of 700-800bn yen), though it could increase the protection level and would be able to cope with 1 in 200 or 500 year events, amongst other benefits., Hydraulic Engineering, Civil Engineering and Geosciences

Since 2004, there is a growing awareness of the risks that tsunamis pose to coastal communities globally. Despite the fact that these events were already an intrinsic part of the culture of some countries such as Chile and Japan, many other places had virtually not heard about such phenomenon before 2004. Nevertheless, the frequent reoccurrence of major tsunamis in recent years has led to the emergence of a “tsunami culture” in many areas of the world, which has resulted in increased awareness, disaster preparedness and willingness of local populations to evacuate when the threat of these events arises. However, evacuation during a tsunami is still not successfully carried out by the different elements of society, pointing to lack of awareness, an over-reliance in defence mechanisms or lacking in the transmitting of knowledge from previous events. This paper will explore these cultural issues using as a basis questionnaires carried out by the authors during their own field visits to the last three major events (Chile in 2009, Indonesia in 2010 and Japan in 2011), and interpret these through the willingness of coastal communities to build protection measures along the shore and the impact that these can have on sustainable development. The existence of a “traditional tsunami culture” will be explored through an analysis of the existence of multi-layer safety system constructed by previous generations, and whether this is being preserved nowadays or past lessons are being forgotten., Hydraulic Engineering, Civil Engineering and Geosciences

Since 2004, there is a growing awareness of the risks that tsunamis pose to coastal communities globally. Despite the fact that these events were already an intrinsic part of the culture of some countries such as Chile and Japan, many other places had virtually not heard about such phenomenon before 2004. Nevertheless, the frequent reoccurrence of major tsunamis in recent years has led to the emergence of a “tsunami culture” in many areas of the world, which has resulted in increased awareness, disaster preparedness and willingness of local populations to evacuate when the threat of these events arises. However, evacuation during a tsunami is still not successfully carried out by the different elements of society, pointing to lack of awareness, an over-reliance in defence mechanisms or lacking in the transmitting of knowledge from previous events. This paper will explore these cultural issues using as a basis questionnaires carried out by the authors during their own field visits to the last three major events (Chile in 2009, Indonesia in 2010 and Japan in 2011), and interpret these through the willingness of coastal communities to build protection measures along the shore and the impact that these can have on sustainable development. The existence of a “traditional tsunami culture” will be explored through an analysis of the existence of multi-layer safety system constructed by previous generations, and whether this is being preserved nowadays or past lessons are being forgotten., Hydraulic Engineering, Civil Engineering and Geosciences

Since 2004 there is a growing global awareness of the risks that tsunamis pose to coastal communities. Despite the fact that these events were already an intrinsic part of the culture of some countries (such as Chile and Japan), in many other places they had been virtually unheard of before 2004. Nevertheless, the frequent reoccurrence of these events in recent years has led to the emergence of a “tsunami culture” in many areas of the world, which has resulted in increased awareness, disaster preparedness and willingness of local populations to evacuate when the threat of these events arises. This paper will explore these cultural issues using as a basis questionnaires carried out by the authors during their own field visits to the last three major events (in Japan, Chile and Indonesia), and interpret these through the willingness of coastal communities to build protection measures along the shore and the impact that these can have on sustainable development., Hydraulic Engineering, Civil Engineering and Geosciences

Historically, sugar beets were selected from fodder beets. We used mitochondrial minisatellite loci to analyze cytoplasmic genetic diversity in fodder beet and sugar beet. Among the 8 sugar beet accessions examined we identified 3 multi-locus haplotypes. These 3 haplotypes were a subset of 5 haplotypes identified among the 29 fodder beet accessions examined. All but one haplotype in fodder beet comprised, in turn, a subset of 12 haplotypes identified previously in leaf beets. Such apparent decreases in cytoplasmic genetic diversity must result from genetic bottlenecks associated with domestication and the ensuing breeding processes. We also detected the haplotype associated with the male-sterile Owen cytoplasm of sugar beet in the fodder beet gene pool. Furthermore, the presence of a 39 kDa protein associated with the Owen cytoplasm was confirmed in two fodder beet plants by Western blot analysis. These results lead us to speculate that the Owen cytoplasm may have originated in fodder beet, from which sugar beet was derived

Historically, sugar beets were selected from fodder beets. We used mitochondrial minisatellite loci to analyze cytoplasmic genetic diversity in fodder beet and sugar beet. Among the 8 sugar beet accessions examined we identified 3 multi-locus haplotypes. These 3 haplotypes were a subset of 5 haplotypes identified among the 29 fodder beet accessions examined. All but one haplotype in fodder beet comprised, in turn, a subset of 12 haplotypes identified previously in leaf beets. Such apparent decreases in cytoplasmic genetic diversity must result from genetic bottlenecks associated with domestication and the ensuing breeding processes. We also detected the haplotype associated with the male-sterile Owen cytoplasm of sugar beet in the fodder beet gene pool. Furthermore, the presence of a 39 kDa protein associated with the Owen cytoplasm was confirmed in two fodder beet plants by Western blot analysis. These results lead us to speculate that the Owen cytoplasm may have originated in fodder beet, from which sugar beet was derived

Historically, sugar beets were selected from fodder beets. We used mitochondrial minisatellite loci to analyze cytoplasmic genetic diversity in fodder beet and sugar beet. Among the 8 sugar beet accessions examined we identified 3 multi-locus haplotypes. These 3 haplotypes were a subset of 5 haplotypes identified among the 29 fodder beet accessions examined. All but one haplotype in fodder beet comprised, in turn, a subset of 12 haplotypes identified previously in leaf beets. Such apparent decreases in cytoplasmic genetic diversity must result from genetic bottlenecks associated with domestication and the ensuing breeding processes. We also detected the haplotype associated with the male-sterile Owen cytoplasm of sugar beet in the fodder beet gene pool. Furthermore, the presence of a 39 kDa protein associated with the Owen cytoplasm was confirmed in two fodder beet plants by Western blot analysis. These results lead us to speculate that the Owen cytoplasm may have originated in fodder beet, from which sugar beet was derived

Since 2004 there is a growing global awareness of the risks that tsunamis pose to coastal communities. Despite the fact that these events were already an intrinsic part of the culture of some countries (such as Chile and Japan), in many other places they had been virtually unheard of before 2004. Nevertheless, the frequent reoccurrence of these events in recent years has led to the emergence of a “tsunami culture” in many areas of the world, which has resulted in increased awareness, disaster preparedness and willingness of local populations to evacuate when the threat of these events arises. This paper will explore these cultural issues using as a basis questionnaires carried out by the authors during their own field visits to the last three major events (in Japan, Chile and Indonesia), and interpret these through the willingness of coastal communities to build protection measures along the shore and the impact that these can have on sustainable development., Hydraulic Engineering, Civil Engineering and Geosciences

Contains fulltext : 70079.pdf (publisher's version ) (Closed access), Heparan sulphate proteoglycans (HSPGs) have multiple functions relevant to the control of the CNS injury response, particularly in modulating the effects of growth factors and localizing molecules that affect axon growth. We examined the pattern of expression and glycanation of HSPGs in the normal and damaged CNS, and in astrocytes and oligodendrocyte precursors because of their participation in the injury reaction. The composition of HS glycosaminoglycan (GAG) chains was analysed by biochemical analysis and by the binding of antibodies that recognize sulphated epitopes. We also measured levels of HS sulphotransferases and syndecans. Compared with oligodendrocytes, oligodendrocyte precursors have more 2-O-sulphation in their HS GAG. This is accompanied by higher expression of the enzyme responsible for 2-O-sulphation, HS 2-O-sulphotransferase (HS2ST) and a fall in syndecan-1. Astrocytes treated with tumour growth factor (TGF)alpha or TGFbeta to mimic the injury response showed upregulation of syndecan-1 and HS2ST correlating with an increase in 2-O-sulphate residues in their HS GAGs. This also correlated with increased staining with AO4B08 anti-GAG antibody that recognizes high sulphation, and reduced staining with RB4EA12 recognizing low sulphation. After injury to the adult rat brain there was an overall increase in the quantity of HSPG around the injury site, mRNA for HS2ST was increased, and the changes in staining with sulphation-specific antibodies were consistent with an increase in 2-O-sulphated HS. Syndecan-1 was upregulated in astrocytes. The major injury-related change, seen in injured brain and cultured glia, was an increase in 2-O-sulphated HS and increased syndecan-1, suggesting novel approaches to modulating scar formation.

Contains fulltext : 70079.pdf (publisher's version ) (Closed access), Heparan sulphate proteoglycans (HSPGs) have multiple functions relevant to the control of the CNS injury response, particularly in modulating the effects of growth factors and localizing molecules that affect axon growth. We examined the pattern of expression and glycanation of HSPGs in the normal and damaged CNS, and in astrocytes and oligodendrocyte precursors because of their participation in the injury reaction. The composition of HS glycosaminoglycan (GAG) chains was analysed by biochemical analysis and by the binding of antibodies that recognize sulphated epitopes. We also measured levels of HS sulphotransferases and syndecans. Compared with oligodendrocytes, oligodendrocyte precursors have more 2-O-sulphation in their HS GAG. This is accompanied by higher expression of the enzyme responsible for 2-O-sulphation, HS 2-O-sulphotransferase (HS2ST) and a fall in syndecan-1. Astrocytes treated with tumour growth factor (TGF)alpha or TGFbeta to mimic the injury response showed upregulation of syndecan-1 and HS2ST correlating with an increase in 2-O-sulphate residues in their HS GAGs. This also correlated with increased staining with AO4B08 anti-GAG antibody that recognizes high sulphation, and reduced staining with RB4EA12 recognizing low sulphation. After injury to the adult rat brain there was an overall increase in the quantity of HSPG around the injury site, mRNA for HS2ST was increased, and the changes in staining with sulphation-specific antibodies were consistent with an increase in 2-O-sulphated HS. Syndecan-1 was upregulated in astrocytes. The major injury-related change, seen in injured brain and cultured glia, was an increase in 2-O-sulphated HS and increased syndecan-1, suggesting novel approaches to modulating scar formation.

Contains fulltext : 70079.pdf (publisher's version ) (Closed access), Heparan sulphate proteoglycans (HSPGs) have multiple functions relevant to the control of the CNS injury response, particularly in modulating the effects of growth factors and localizing molecules that affect axon growth. We examined the pattern of expression and glycanation of HSPGs in the normal and damaged CNS, and in astrocytes and oligodendrocyte precursors because of their participation in the injury reaction. The composition of HS glycosaminoglycan (GAG) chains was analysed by biochemical analysis and by the binding of antibodies that recognize sulphated epitopes. We also measured levels of HS sulphotransferases and syndecans. Compared with oligodendrocytes, oligodendrocyte precursors have more 2-O-sulphation in their HS GAG. This is accompanied by higher expression of the enzyme responsible for 2-O-sulphation, HS 2-O-sulphotransferase (HS2ST) and a fall in syndecan-1. Astrocytes treated with tumour growth factor (TGF)alpha or TGFbeta to mimic the injury response showed upregulation of syndecan-1 and HS2ST correlating with an increase in 2-O-sulphate residues in their HS GAGs. This also correlated with increased staining with AO4B08 anti-GAG antibody that recognizes high sulphation, and reduced staining with RB4EA12 recognizing low sulphation. After injury to the adult rat brain there was an overall increase in the quantity of HSPG around the injury site, mRNA for HS2ST was increased, and the changes in staining with sulphation-specific antibodies were consistent with an increase in 2-O-sulphated HS. Syndecan-1 was upregulated in astrocytes. The major injury-related change, seen in injured brain and cultured glia, was an increase in 2-O-sulphated HS and increased syndecan-1, suggesting novel approaches to modulating scar formation.

Contains fulltext : 53423.pdf (Publisher’s version ) (Open Access), Chondroitin sulfate (CS) and dermatan sulfate (DS) have been implicated in the processes of neural development in the brain. In this study, we characterized developmentally regulated brain CS/DS chains using a single chain antibody, GD3G7, produced by the phage display technique. Evaluation of the specificity of GD3G7 toward various glycosaminoglycan preparations showed that this antibody specifically reacted with squid CS-E (rich in the GlcUAbeta1-3GalNAc(4,6-O-sulfate) disaccharide unit E), hagfish CS-H (rich in the IdoUAalpha1-3GalNAc(4,6-O-sulfate) unit iE), and shark skin DS (rich in both E and iE units). In situ hybridization for the expression of N-acetylgalac-tosamine-4-sulfate 6-O-sulfotransferase in the postnatal mouse brain, which is involved in the biosynthesis of CS/DS-E, showed a widespread expression of the transcript in the developing brain except at postnatal day 7, where strong expression was observed in the external granule cell layer in the cerebellum. The expression switched from the external to internal granule cell layer with development. Immunohistochemical localization of GD3G7 in the mouse brain showed that the epitope was relatively abundant in the cerebellum, hippocampus, and olfactory bulb. GD3G7 suppressed the growth of neurites in embryonic hippocampal neurons mediated by CS-E, suggesting that the epitope is embedded in the neurite outgrowth-promoting motif of CS-E. In addition, a CS-E decasaccharide fraction was found to be the critical minimal structure needed for recognition by GD3G7. Four discrete decasaccharide epitopic sequences were identified. The antibody GD3G7 has broad applications in investigations of CS/DS chains during the central nervous system's development and under various pathological conditions.

In this study, we have analyzed the temporal oscillations of precipitation in meso-scale zones of Sri Lanka to examine potential existence of periodic oscillatory behavior in rainfall. Only a few statistically significant cycles were identified: a 3.5-year cycle in most of central Sri Lanka during the January-March rainfall regime and a cycle of the same length in southwestern Sri Lanka during the October regime. A 2.1-year cycle marks the northeastern parts of Sri Lanka during the December/April contrast rainfall regime. This cycle is shown to be strongly related to Quasi-Biennial Oscillation. October and November rainfall are found to be coupled with ENSO fluctuations, and on average, more than 900mm more rainfall is observed per month over all stations during El Nifio than during La Nina years. Analysis of relationships between the observed meso-scale rainfall regions and the Sea Surface Temperatures (SSTs) in the Indian Ocean north of the Equator showed that the northern Indian Ocean can be divided into three particular regions based on similarity in the SST fluctuations: (a) a region with cool upwelling water, (b) non upwelling water, and (c) the Indian Ocean Warm Pool. We found that there are no statistically significant relationships between the observed SST regions in the Indian Ocean and the meso-scale precipitation patterns in Sri Lanka., authorCount :6

Contains fulltext : 53423.pdf (Publisher’s version ) (Open Access), Chondroitin sulfate (CS) and dermatan sulfate (DS) have been implicated in the processes of neural development in the brain. In this study, we characterized developmentally regulated brain CS/DS chains using a single chain antibody, GD3G7, produced by the phage display technique. Evaluation of the specificity of GD3G7 toward various glycosaminoglycan preparations showed that this antibody specifically reacted with squid CS-E (rich in the GlcUAbeta1-3GalNAc(4,6-O-sulfate) disaccharide unit E), hagfish CS-H (rich in the IdoUAalpha1-3GalNAc(4,6-O-sulfate) unit iE), and shark skin DS (rich in both E and iE units). In situ hybridization for the expression of N-acetylgalac-tosamine-4-sulfate 6-O-sulfotransferase in the postnatal mouse brain, which is involved in the biosynthesis of CS/DS-E, showed a widespread expression of the transcript in the developing brain except at postnatal day 7, where strong expression was observed in the external granule cell layer in the cerebellum. The expression switched from the external to internal granule cell layer with development. Immunohistochemical localization of GD3G7 in the mouse brain showed that the epitope was relatively abundant in the cerebellum, hippocampus, and olfactory bulb. GD3G7 suppressed the growth of neurites in embryonic hippocampal neurons mediated by CS-E, suggesting that the epitope is embedded in the neurite outgrowth-promoting motif of CS-E. In addition, a CS-E decasaccharide fraction was found to be the critical minimal structure needed for recognition by GD3G7. Four discrete decasaccharide epitopic sequences were identified. The antibody GD3G7 has broad applications in investigations of CS/DS chains during the central nervous system's development and under various pathological conditions.

Contains fulltext : 53423.pdf (Publisher’s version ) (Open Access), Chondroitin sulfate (CS) and dermatan sulfate (DS) have been implicated in the processes of neural development in the brain. In this study, we characterized developmentally regulated brain CS/DS chains using a single chain antibody, GD3G7, produced by the phage display technique. Evaluation of the specificity of GD3G7 toward various glycosaminoglycan preparations showed that this antibody specifically reacted with squid CS-E (rich in the GlcUAbeta1-3GalNAc(4,6-O-sulfate) disaccharide unit E), hagfish CS-H (rich in the IdoUAalpha1-3GalNAc(4,6-O-sulfate) unit iE), and shark skin DS (rich in both E and iE units). In situ hybridization for the expression of N-acetylgalac-tosamine-4-sulfate 6-O-sulfotransferase in the postnatal mouse brain, which is involved in the biosynthesis of CS/DS-E, showed a widespread expression of the transcript in the developing brain except at postnatal day 7, where strong expression was observed in the external granule cell layer in the cerebellum. The expression switched from the external to internal granule cell layer with development. Immunohistochemical localization of GD3G7 in the mouse brain showed that the epitope was relatively abundant in the cerebellum, hippocampus, and olfactory bulb. GD3G7 suppressed the growth of neurites in embryonic hippocampal neurons mediated by CS-E, suggesting that the epitope is embedded in the neurite outgrowth-promoting motif of CS-E. In addition, a CS-E decasaccharide fraction was found to be the critical minimal structure needed for recognition by GD3G7. Four discrete decasaccharide epitopic sequences were identified. The antibody GD3G7 has broad applications in investigations of CS/DS chains during the central nervous system's development and under various pathological conditions.

Contains fulltext : 47495.pdf (publisher's version ) (Closed access), Chondroitin sulphate proteoglycans (CSPGs) are up-regulated in the CNS after injury and inhibit axon regeneration mainly through their glycosaminoglycan (CS-GAG) chains. We have analysed the mRNA levels of the CS-GAG synthesizing enzymes and measured the CS-GAG disaccharide composition by chromatography and immunocytochemistry. Chondroitin 6-sulfotransferase 1 (C6ST1) is up-regulated in most glial types around cortical injuries, and its sulphated product CS-C is also selectively up-regulated. Treatment with TGFalpha and TGFbeta, which are released after brain injury, promotes the expression of C6ST1 and the synthesis of 6-sulphated CS-GAGs in primary astrocytes. Oligodendrocytes, oligodendrocyte precursors and meningeal cells are all inhibitory to axon regeneration, and all express high levels of CS-GAG, including high levels of 6-sulphated GAG. In axon growth-inhibitory Neu7 astrocytes C6ST1 and 6-sulphated GAGs are expressed at high levels, whereas in permissive A7 astrocytes they are not detectable. These results suggest that the up-regulation of CSPG after CNS injury is associated with a specific sulphation pattern on CS-GAGs, mediating the inhibitory properties of proteoglycans on axonal regeneration.

Contains fulltext : 47495.pdf (publisher's version ) (Closed access), Chondroitin sulphate proteoglycans (CSPGs) are up-regulated in the CNS after injury and inhibit axon regeneration mainly through their glycosaminoglycan (CS-GAG) chains. We have analysed the mRNA levels of the CS-GAG synthesizing enzymes and measured the CS-GAG disaccharide composition by chromatography and immunocytochemistry. Chondroitin 6-sulfotransferase 1 (C6ST1) is up-regulated in most glial types around cortical injuries, and its sulphated product CS-C is also selectively up-regulated. Treatment with TGFalpha and TGFbeta, which are released after brain injury, promotes the expression of C6ST1 and the synthesis of 6-sulphated CS-GAGs in primary astrocytes. Oligodendrocytes, oligodendrocyte precursors and meningeal cells are all inhibitory to axon regeneration, and all express high levels of CS-GAG, including high levels of 6-sulphated GAG. In axon growth-inhibitory Neu7 astrocytes C6ST1 and 6-sulphated GAGs are expressed at high levels, whereas in permissive A7 astrocytes they are not detectable. These results suggest that the up-regulation of CSPG after CNS injury is associated with a specific sulphation pattern on CS-GAGs, mediating the inhibitory properties of proteoglycans on axonal regeneration.

Contains fulltext : 47495.pdf (publisher's version ) (Closed access), Chondroitin sulphate proteoglycans (CSPGs) are up-regulated in the CNS after injury and inhibit axon regeneration mainly through their glycosaminoglycan (CS-GAG) chains. We have analysed the mRNA levels of the CS-GAG synthesizing enzymes and measured the CS-GAG disaccharide composition by chromatography and immunocytochemistry. Chondroitin 6-sulfotransferase 1 (C6ST1) is up-regulated in most glial types around cortical injuries, and its sulphated product CS-C is also selectively up-regulated. Treatment with TGFalpha and TGFbeta, which are released after brain injury, promotes the expression of C6ST1 and the synthesis of 6-sulphated CS-GAGs in primary astrocytes. Oligodendrocytes, oligodendrocyte precursors and meningeal cells are all inhibitory to axon regeneration, and all express high levels of CS-GAG, including high levels of 6-sulphated GAG. In axon growth-inhibitory Neu7 astrocytes C6ST1 and 6-sulphated GAGs are expressed at high levels, whereas in permissive A7 astrocytes they are not detectable. These results suggest that the up-regulation of CSPG after CNS injury is associated with a specific sulphation pattern on CS-GAGs, mediating the inhibitory properties of proteoglycans on axonal regeneration.

We study the asymptotic behavior, in the zero noise limit, of solu­tions to Schrodinger's functional equations and that of h-pass pro­cesses, and give a new proof of the existence of the minimizer of Monge's problem with a quadratic cost.

We construct a random crystalline ( or polyhedral) approximation of a convexified Gauss curvature flow of bounded open sets in an anisotropic external field. We also show that a weak solution to the PDE which describes the motion of a bounded open set is unique and is a viscosity solution of it.

We propose and study a random crystalline algorithm (a discrete approximation) of the Gauss curvature flow of smooth simple closed convex curves in R2 as a stepping stone to the full understanding of such phenomena as the wearing process of stones on a beach.

We introduce covariance kernels for Borel probability measures on Rd, and study the relation between the central limit theorem in the total variation distance and the convergence of covariance kernels.

We shmv the existence of ,veak solutions to the PDE which de­scribes the motion by R-curvaturc in Rd , by the continuum limit of a class of infinite particle systems. We also show that weak solutions of the PDE arc viscosity solutions and give the uniqueness result on both weak and viscosity solutions.

We study the optimal control problem for Rd-valued absolutely continuous stochastic processes with given marginal distributions at every time. This can be considered as a generalization of Monge-Kantorovich problem in which they fix marginal distributions only at an initial and a terminal times. When d = 1, we show that there exists a minimizer which is a function of a time and an initial point, that is, an optimal mass transportation. When d > 1, we only show that minimizers satisfy the same ordinary differential equation.

In this paper we propose a two dimensional random crystalline algorithm for Gauss cur­vature flow.

R. Jordan, D. Kinderlehrer and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional and the Gibbs-Boltzmann entropy func­tional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker-Planck equation and characterize the limit as a solution to a class of variational problems. We also give a simple approach in a one-dimensional case.

In this paper we discuss a class of Markov marginal problems (MMP). By MMP, we mean the problem to construct a Markov process with given (marginal) constraints on the path space. As an application we consider Markov optimal control problems.