Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered.Comment: Updated version as publishe

Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered

The Effect of Soluble Uterine Factors on Porcine Embryo Development Within a Three-Dimensional Alginate Matrix System

Between day 10 and 12 of gestation in the pig, the embryo undergoes a dramatic morphological change, known as elongation. During elongation the embryo produces and secretes estrogen, which serves as a key signal for maternal recognition of pregnancy. The uterine environment prepares for embryo elongation and implantation by releasing nutrients, metabolites, and hormones in a time-dependent manner relative to paracrine signals from the conceptus (i.e., estrogen) and endocrine/paracrine signals within the endometrium (i.e., progesterone). Despite advances in identification of specific uterine factors present throughout pregnancy in the pig, little is known about the exact mechanisms by which porcine embryos elongate normally, or how this elongation is altered during embryonic loss. Previously, our laboratory has established an in vitro culture system using alginate hydrogels as a three-dimensional (3-D) matrix to support the development of pre-implantation porcine embryos in base serum media without the addition of hormones. The objective of the current study was to improve our 3-D system and determine if uterine flushes from day 9 or 10 of gestation were capable of supporting in vitro embryonic development of in vivo-developed day 9 porcine embryos using the 3- D alginate culture system. Embryos collected on day 9 of gestation were assigned to be cultured in pooled day 9 flushes, day 10 flushes, or base serum media for five days within 0.7% alginate gels. Our results demonstrate that uterine flushes from day 9 or 10 of gestation supported embryonic development in our 3-D hydrogel system, similar to that from embryos cultured in base serum media. These results illustrate that soluble factors present in uterine flushings at day 9 or 10 of gestation support in vitro embryonic development within our 3-D alginate culture system. Developing better scientific understanding of the factors that regulate embryo elongation and early embryonic mortality can be useful for developing strategies to improve sow productivity and increase the profitability of swine production

Influence of pH on 2,4,6-trinitrotoluene degradation by Yarrowia lipolytica

The microbial reduction of the aromatic ring of 2,4,6-trinitrotoluene (TNT) can lead to its complete destruction. The acid-tolerant yeast Yarrowia lipolytica AN-L15 transformed TNT through hydride ion-mediated reduction of the aromatic ring (as the main pathway), resulting in the accumulation of nitrite and nitrate ions, as well as through nitro group reduction (as minor pathway), resulting in hydroxylamino- and aminoaromatics. TNT transformation depended on the yeasts' ability to acidify the culture medium through the production of organic acids. Aeration and a low medium buffer capacity favored yeast growth and resulted in rapid acidification of the medium, which influenced the rate and extent of TNT transformation. This is the first time that nitrate has been detected as a major product of microbial TNT degradation, and this work demonstrates the importance of pH on TNT biotransformation. The ability of Y. lipolytica AN-L15 to reduce the TNT aromatic ring to form TNT-hydride complexes, followed by their denitration, makes this strain a potential candidate for bioremediation of sites contaminated with explosives. © 2010 Elsevier Ltd. All rights reserved

Effect of ferrihydrite on 2,4,6-trinitrotoluene biotransformation by an aerobic yeast

This study investigated the impact of ferrihydrite on the pathway and rate of 2,4,6-trinitrotoluene (TNT) transformation by Yarrowia lipolytica AN-L15. The presence of ferrihydrite in the culture medium decreased the rate of TNT biotransformation but resulted in the accumulation of the same TNT metabolites as in the absence of ferrihydrite, albeit at slightly different concentrations. Transformation products observed included aromatic ring reduction products, such as hydride-Meisenheimer complexes, and nitro group reduction products, such as hydroxylamino- and amino-dinitrotoluenes. Independently of the presence of ferrihydrite the subsequent degradation of the hydride complex(es) resulted in the release of nitrite followed by its conversion to nitrate and nitric oxide at the low pH values observed during yeast cultivation. Nitric oxide generation was ascertained by electron spin resonance spectroscopy. In addition, increased Fe3+-reduction was observed in the presence of TNT and Y. lipolytica. This study demonstrates that in the presence of yeast cells, TNT-hydride complexes were formed at approximately the same level as in the presence of ferrihydrite, opening up the possibility of aromatic ring cleavage, instead of promoting the production of potentially toxic nitro group reduction products in the presence of iron minerals. © 2012 Springer Science+Business Media Dordrecht

Secreted metabolome of porcine blastocysts encapsulated with in \u3ci\u3ein vitro\u3c/i\u3e 3D alginate hydrogel culture systems under going morphological changes provides insights into specific mechanisms involved in the initiation of porcine conceptus elongation

Context. The exact mechanisms regulating the initiation of porcine conceptus elongation are not known due to the complexity of the uterine environment. Aims. To identify contributing factors for initiation of conceptus elongation in vitro, this study evaluated differential metabolite abundance within media following culture of blastocysts within unmodified alginate (ALG) or Arg-Gly-Asp (RGD)-modified alginate hydrogel culture systems. Methods. Blastocysts were harvested from pregnant gilts, encapsulated within ALG or RGD or as non-encapsulated control blastocysts (CONT), and cultured. At the termination of 96 h culture, media were separated into blastocyst media groups: non-encapsulated control blastocysts (CONT); ALG and RGD blastocysts with no morphological change (ALG− and RGD−); ALG and RGD blastocysts with morphological changes (ALG+ and RGD+) and evaluated for non-targeted metabolomic profiling by liquid chromatography (LC)–mass spectrometry (MS) techniques and gas chromatography– (GC–MS). Key results. Analysis of variance identified 280 (LC–MS) and 1 (GC–MS) compounds that differed (P \u3c 0.05), of which 134 (LC–MS) and 1 (GC–MS) were annotated. Metabolites abundance between ALG+ vs ALG−, RGD+ vs RGD−, and RGD+ vs ALG+ were further investigated to identify potential differences in metabolic processes during the initiation of elongation. Conclusions. This study identified changes in phospholipid, glycosphingolipid, lipid signalling, and amino acid metabolic processes as potential RGD-independent mechanisms of elongation and identified changes in lysophosphatidylcholine and sphingolipid secretions during RGD-mediated elongation. Implications. These results illustrate changes in phospholipid and sphingolipid metabolic processes and secretions may act as mediators of the RGD-integrin adhesion that promotes porcine conceptus elongation

Metabolic compounds within the porcine uterine environment are unique to the type of conceptus present during the early stages of blastocyst elongation

The objective of this study was to identify metabolites within the porcine uterine milieu during the early stages of blastocyst elongation. At Days 9, 10, or 11 of gestation, reproductive tracts of White cross‐bred gilts (n = 38) were collected immediately following harvest and flushed with Roswell Park Memorial Institute‐1640 medium. Conceptus morphologies were assessed from each pregnancy and corresponding uterine flushings were assigned to one of five treatment groups based on these morphologies: (a) uniform spherical (n = 8); (b) heterogeneous spherical and ovoid (n = 8); (c) uniform ovoid (n = 8); (d) heterogeneous ovoid and tubular (n = 8); and (e) uniform tubular (n = 6). Uterine flushings from these pregnancies were submitted for nontargeted profiling by gas chromatography–mass spectrometry (GC–MS) and ultra performance liquid chromatography (UPLC)–MS techniques. Unsupervised multivariate principal component analysis (PCA) was performed using pcaMethods and univariate analysis of variance was performed in R with false discovery rate (FDR) adjustment. PCA analysis of the GC–MS and UPLC–MS data identified 153 and 104 metabolites, respectively. After FDR adjustment of the GC–MS and UPLC–MS data, 38 and 59 metabolites, respectively, differed (p \u3c .05) in uterine flushings from pregnancies across the five conceptus stages. Some metabolites were greater (p \u3c .05) in abundance for uterine flushings containing earlier stage conceptuses (i.e., spherical), such as uric acid, tryptophan, and tyrosine. In contrast, some metabolites were greater (

Typology of seismic motion and seismic engineering design

The paper deals with the influence of the seismic motion typology on the structural response and with engineering design under exceptional actions. Various aspects of seismic motion typology that lead to exceptional actions on the structures are covered. The influence of near fault ground motions, the effect of local site parameters and the magnification of the seismic action on short-period structures are among the parameters identified as dominant for the structural response. The paper presents also a methodology for handling uncertainty in engineering design, based on the mathematical framework of fuzzy analysis. Finally the paper presents various applications of performance based design, which is viewed as a tool as a tool for the analysis of structural behaviour under extreme seismic events. The influence of connection behaviour on the structural response is studied, and applications of the capacity design methodology and of the direct displacement design approach for the evaluation of reinforce concrete structures are presented

Global analysis of differential gene expression within the porcine conceptus transcriptome as it transitions through spherical, ovoid, and tubular morphologies during the initiation of elongation

This study aimed to identify transcriptome differences between distinct or transitional stage spherical, ovoid, and tubular porcine blastocysts throughout the initiation of elongation. We performed a global transcriptome analysis of differential gene expression using RNA‐Seq with high temporal resolution between spherical, ovoid, and tubular stage blastocysts at specific sequential stages of development from litters containing conceptus populations of distinct or transitional blastocysts. After RNA‐Seq analysis, significant differentially expressed genes (DEGs) and pathways were identified between distinct morphologies or sequential development stages. Overall, 1898 significant DEGs were identified between distinct spherical and ovoid morphologies, with 311 total DEGs between developmental stages throughout this first morphological transition, while 15 were identified between distinct ovoid and tubular, with eight total throughout these second morphological transition developmental stages. The high quantity of DEGs and pathways between conceptus stages throughout the spherical to ovoid transition suggests the importance of gene regulation during this first morphological transition for initiating elongation. Further, extensive DEG coverage of known elongation signaling pathways was illustrated from spherical to ovoid, and regulation of lipid signaling and membrane/ECM remodeling across these early conceptus stages were implicated as essential to this process, providing novel insights into potential mechanisms governing this rapid morphological change