Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Light intensity modulates the regulatory network of the shade avoidance response in Arabidopsis.

Plants such as Arabidopsis thaliana respond to foliar shade and neighbors who may become competitors for light resources by elongation growth to secure access to unfiltered sunlight. Challenges faced during this shade avoidance response (SAR) are different under a light-absorbing canopy and during neighbor detection where light remains abundant. In both situations, elongation growth depends on auxin and transcription factors of the phytochrome interacting factor (PIF) class. Using a computational modeling approach to study the SAR regulatory network, we identify and experimentally validate a previously unidentified role for long hypocotyl in far red 1, a negative regulator of the PIFs. Moreover, we find that during neighbor detection, growth is promoted primarily by the production of auxin. In contrast, in true shade, the system operates with less auxin but with an increased sensitivity to the hormonal signal. Our data suggest that this latter signal is less robust, which may reflect a cost-to-robustness tradeoff, a system trait long recognized by engineers and forming the basis of information theory.

Aeromonas hydrophila lateral flagella gene transcriptional hierarchy

Aeromonas hydrophila AH-3 lateral flagella are not assembled when bacteria grow in liquid media; however, lateral flagellar genes are transcribed. Our results indicate that A. hydrophila lateral flagellar genes are transcribed at three levels (class I to III genes) and share some similarities with, but have many important differences from, genes of Vibrio parahaemolyticus. A. hydrophila lateral flagellum class I gene transcription is σ70 dependent, which is consistent with the fact that lateral flagellum is constitutively transcribed, in contrast to the characteristics of V. parahaemolyticus. The fact that multiple genes are included in class I highlights that lateral flagellar genes are less hierarchically transcribed than polar flagellum genes. The A. hydrophila lafK-fliEJL gene cluster (where the subscript L distinguishes genes for lateral flagella from those for polar flagella) is exclusively from class I and is in V. parahaemolyticus class I and II. Furthermore, the A. hydrophila flgAMNL cluster is not transcribed from the σ54/LafK-dependent promoter and does not contain class II genes. Here, we propose a gene transcriptional hierarchy for the A. hydrophila lateral flagella.

Aeromonas hydrophila lateral flagella gene transcriptional hierarchy

Aeromonas hydrophila AH-3 lateral flagella are not assembled when bacteria grow in liquid media; however, lateral flagellar genes are transcribed. Our results indicate that A. hydrophila lateral flagellar genes are transcribed at three levels (class I to III genes) and share some similarities with, but have many important differences from, genes of Vibrio parahaemolyticus. A. hydrophila lateral flagellum class I gene transcription is σ(70) dependent, which is consistent with the fact that lateral flagellum is constitutively transcribed, in contrast to the characteristics of V. parahaemolyticus. The fact that multiple genes are included in class I highlights that lateral flagellar genes are less hierarchically transcribed than polar flagellum genes. The A. hydrophila lafK-fliEJL gene cluster (where the subscript L distinguishes genes for lateral flagella from those for polar flagella) is exclusively from class I and is in V. parahaemolyticus class I and II. Furthermore, the A. hydrophila flgAMNL cluster is not transcribed from the σ(54)/LafK-dependent promoter and does not contain class II genes. Here, we propose a gene transcriptional hierarchy for the A. hydrophila lateral flagella.

Anticipating linear stochastic differential equations driven by a Lévy process

In this paper we study the existence of a unique solution for linear stochastic differential equations driven by a Lévy process, where the initial condition and the coefficients are random and not necessarily adapted to the underlying filtration. Towards this end, we extend the method based on Girsanov transformations on Wiener space and developped by Buckdahn [7] to the canonical Lévy space, which is introduced in [25].

Boundary identification in the domain of a parabolic partial differential equation

Bakgrunden och inspirationen till föreliggande studie är tidigare forskning i tillämpningar på randidentifiering i metallindustrin. Effektiv randidentifiering möjliggör mindre säkerhetsmarginaler och längre serviceintervall för apparaturen i industriella högtemperaturprocesser, utan ökad risk för materielhaverier. I idealfallet vore en metod för randidentifiering baserad på uppföljning av någon indirekt variabel som kan mätas rutinmässigt eller till en ringa kostnad. En dylik variabel för smältugnar är temperaturen i olika positioner i väggen. Denna kan utnyttjas som insignal till en randidentifieringsmetod för att övervaka ugnens väggtjocklek. Vi ger en bakgrund och motivering till valet av den geometriskt endimensionella dynamiska modellen för randidentifiering, som diskuteras i arbetets senare del, framom en flerdimensionell geometrisk beskrivning. I de aktuella industriella tillämpningarna är dynamiken samt fördelarna med en enkel modellstruktur viktigare än exakt geometrisk beskrivning. Lösningsmetoder för den s.k. sidledes värmeledningsekvationen har många saker gemensamt med randidentifiering. Därför studerar vi egenskaper hos lösningarna till denna ekvation, inverkan av mätfel och något som brukar kallas förorening av mätbrus, regularisering och allmännare följder av icke-välställdheten hos sidledes värmeledningsekvationen. Vi studerar en uppsättning av tre olika metoder för randidentifiering, av vilka de två första är utvecklade från en strikt matematisk och den tredje från en mera tillämpad utgångspunkt. Metoderna har olika egenskaper med specifika fördelar och nackdelar. De rent matematiskt baserade metoderna karakteriseras av god noggrannhet och låg numerisk kostnad, dock till priset av låg flexibilitet i formuleringen av den modellbeskrivande partiella differentialekvationen. Den tredje, mera tillämpade, metoden kännetecknas av en sämre noggrannhet förorsakad av en högre grad av icke-välställdhet hos den mera flexibla modellen. För denna gjordes även en ansats till feluppskattning, som senare kunde observeras överensstämma med praktiska beräkningar med metoden. Studien kan anses vara en god startpunkt och matematisk bas för utveckling av industriella tillämpningar av randidentifiering, speciellt mot hantering av olinjära och diskontinuerliga materialegenskaper och plötsliga förändringar orsakade av “nedfallande” väggmaterial. Med de behandlade metoderna förefaller det möjligt att uppnå en robust, snabb och tillräckligt noggrann metod av begränsad komplexitet för randidentifiering.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Alternative oxidase in the branched mitochondrial respiratory network: an overview on structure, function, regulation, and role

Plants and some other organisms including protists possess a complex branched respiratory network in their mitochondria. Some pathways of this network are not energy-conserving and allow sites of energy conservation to be bypassed, leading to a decrease of the energy yield in the cells. It is a challenge to understand the regulation of the partitioning of electrons between the various energy-dissipating and -conserving pathways. This review is focused on the oxidase side of the respiratory chain that presents a cyanide-resistant energy-dissipating alternative oxidase (AOX) besides the cytochrome pathway. The known structural properties of AOX are described including transmembrane topology, dimerization, and active sites. Regulation of the alternative oxidase activity is presented in detail because of its complexity. The alternative oxidase activity is dependent on substrate availability: total ubiquinone concentration and its redox state in the membrane and O2 concentration in the cell. The alternative oxidase activity can be long-term regulated (gene expression) or short-term (post-translational modification, allosteric activation) regulated. Electron distribution (partitioning) between the alternative and cytochrome pathways during steady-state respiration is a crucial measurement to quantitatively analyze the effects of the various levels of regulation of the alternative oxidase. Three approaches are described with their specific domain of application and limitations: kinetic approach, oxygen isotope differential discrimination, and ADP/O method (thermokinetic approach). Lastly, the role of the alternative oxidase in non-thermogenic tissues is discussed in relation to the energy metabolism balance of the cell (supply in reducing equivalents/demand in energy and carbon) and with harmful reactive oxygen species formation.

Stochastic particle models: mean reversion and burgers dynamics. An application to commodity markets

The aim of this study is to propose a stochastic model for commodity markets linked with the Burgers equation from fluid dynamics. We construct a stochastic particles method for commodity markets, in which particles represent market participants. A discontinuity in the model is included through an interacting kernel equal to the Heaviside function and its link with the Burgers equation is given. The Burgers equation and the connection of this model with stochastic differential equations are also studied. Further, based on the law of large numbers, we prove the convergence, for large N, of a system of stochastic differential equations describing the evolution of the prices of N traders to a deterministic partial differential equation of Burgers type. Numerical experiments highlight the success of the new proposal in modeling some commodity markets, and this is confirmed by the ability of the model to reproduce price spikes when their effects occur in a sufficiently long period of time.

Activité des cellules souches : identification de nouveaux effecteurs dans le système hématopoïétique

Les cellules souches somatiques présentent habituellement un comportement très différent des cellules souches pluripotentes. Les bases moléculaires de l’auto-renouvellement des cellules souches embryonnaires ont été récemment déchiffrées grâce à la facilité avec laquelle nous pouvons maintenant les purifier et les maintenir en culture durant de longues périodes de temps. Par contre, il en va tout autrement pour les cellules souches hématopoïétiques. Dans le but d’en apprendre davantage sur le fonctionnement moléculaire de l’auto-renouvellement des cellules souches hématopoïétiques, j’ai d’abord conçu une nouvelle méthode de criblage gain-de-fonction qui répond aux caprices particuliers de ces cellules. Partant d’une liste de plus de 700 facteurs nucléaires et facteurs de division asymétrique candidats, j’ai identifié 24 nouveaux facteurs qui augmentent l’activité des cellules souches hématopoïétiques lorsqu’ils sont surexprimés. J’ai par la suite démontré que neuf de ces facteurs agissent de manière extrinsèque aux cellules souches hématopoïétiques, c’est-à-dire que l’effet provient des cellules nourricières modifiées en co-culture. J’ai également mis à jour un nouveau réseau de régulation de transcription qui implique cinq des facteurs identifiés, c’est-à-dire PRDM16, SPI1, KLF10, FOS et TFEC. Ce réseau ressemble étrangement à celui soutenant l’ostéoclastogénèse. Ces résultats soulèvent l’hypothèse selon laquelle les ostéoclastes pourraient aussi faire partie de la niche fonctionnelle des cellules souches hématopoïétiques dans la moelle osseuse. De plus, j’ai identifié un second réseau de régulation impliquant SOX4, SMARCC1 et plusieurs facteurs identifiés précédemment dans le laboratoire, c’est-à-dire BMI1, MSI2 et KDM5B. D’autre part, plusieurs indices accumulés tendent à démontrer qu’il existe des différences fondamentales entre le fonctionnement des cellules souches hématopoïétiques murines et humaines.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

Revisiting university students' knowledge that involves basic differential equation questions. 'Conocimiento de los estudiantes universitarios con respecto a preguntas que implican ecuaciones diferenciales : una revisión'.

Resumen basado en el de la publicación