Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

Theoretical models of planetary system formation: mass vs. semi-major axis

Context. Planet formation models have been developed during the past years to try to reproduce what has been observed of both the solar system and the extrasolar planets. Some of these models have partially succeeded, but they focus on massive planets and, for the sake of simplicity, exclude planets belonging to planetary systems. However, more and more planets are now found in planetary systems. This tendency, which is a result of radial velocity, transit, and direct imaging surveys, seems to be even more pronounced for low-mass planets. These new observations require improving planet formation models, including new physics, and considering the formation of systems. Aims: In a recent series of papers, we have presented some improvements in the physics of our models, focussing in particular on the internal structure of forming planets, and on the computation of the excitation state of planetesimals and their resulting accretion rate. In this paper, we focus on the concurrent effect of the formation of more than one planet in the same protoplanetary disc and show the effect, in terms of architecture and composition of this multiplicity. Methods: We used an N-body calculation including collision detection to compute the orbital evolution of a planetary system. Moreover, we describe the effect of competition for accretion of gas and solids, as well as the effect of gravitational interactions between planets. Results: We show that the masses and semi-major axes of planets are modified by both the effect of competition and gravitational interactions. We also present the effect of the assumed number of forming planets in the same system (a free parameter of the model), as well as the effect of the inclination and eccentricity damping. We find that the fraction of ejected planets increases from nearly 0 to 8% as we change the number of embryos we seed the system with from 2 to 20 planetary embryos. Moreover, our calculations show that, when considering planets more massive than ~5 M⊕, simulations with 10 or 20 planetary embryos statistically give the same results in terms of mass function and period distribution.

Planet formation models: the interplay with the planetesimal disc

Context. According to the sequential accretion model (or core-nucleated accretion model), giant planet formation is based first on the formation of a solid core which, when massive enough, can gravitationally bind gas from the nebula to form the envelope. The most critical part of the model is the formation time of the core: to trigger the accretion of gas, the core has to grow up to several Earth masses before the gas component of the protoplanetary disc dissipates. Aims: We calculate planetary formation models including a detailed description of the dynamics of the planetesimal disc, taking into account both gas drag and excitation of forming planets. Methods: We computed the formation of planets, considering the oligarchic regime for the growth of the solid core. Embryos growing in the disc stir their neighbour planetesimals, exciting their relative velocities, which makes accretion more difficult. Here we introduce a more realistic treatment for the evolution of planetesimals' relative velocities, which directly impact on the formation timescale. For this, we computed the excitation state of planetesimals, as a result of stirring by forming planets, and gas-solid interactions. Results: We find that the formation of giant planets is favoured by the accretion of small planetesimals, as their random velocities are more easily damped by the gas drag of the nebula. Moreover, the capture radius of a protoplanet with a (tiny) envelope is also larger for small planetesimals. However, planets migrate as a result of disc-planet angular momentum exchange, with important consequences for their survival: due to the slow growth of a protoplanet in the oligarchic regime, rapid inward type I migration has important implications on intermediate-mass planets that have not yet started their runaway accretion phase of gas. Most of these planets are lost in the central star. Surviving planets have masses either below 10 M⊕ or above several Jupiter masses. Conclusions: To form giant planets before the dissipation of the disc, small planetesimals (~0.1 km) have to be the major contributors of the solid accretion process. However, the combination of oligarchic growth and fast inward migration leads to the absence of intermediate-mass planets. Other processes must therefore be at work to explain the population of extrasolar planets that are presently known.

Tracking the Flow of Information through the Hippocampal Formation in the Rat

The hippocampus receives input from upper levels of the association cortex and is implicated in many mnemonic processes, but the exact mechanisms by which it codes and stores information is an unresolved topic. This work examines the flow of information through the hippocampal formation while attempting to determine the computations that each of the hippocampal subfields performs in learning and memory. The formation, storage, and recall of hippocampal-dependent memories theoretically utilize an autoassociative attractor network that functions by implementing two competitive, yet complementary, processes. Pattern separation, hypothesized to occur in the dentate gyrus (DG), refers to the ability to decrease the similarity among incoming information by producing output patterns that overlap less than the inputs. In contrast, pattern completion, hypothesized to occur in the CA3 region, refers to the ability to reproduce a previously stored output pattern from a partial or degraded input pattern. Prior to addressing the functional role of the DG and CA3 subfields, the spatial firing properties of neurons in the dentate gyrus were examined. The principal cell of the dentate gyrus, the granule cell, has spatially selective place fields; however, the behavioral correlates of another excitatory cell, the mossy cell of the dentate polymorphic layer, are unknown. This report shows that putative mossy cells have spatially selective firing that consists of multiple fields similar to previously reported properties of granule cells. Other cells recorded from the DG had single place fields. Compared to cells with multiple fields, cells with single fields fired at a lower rate during sleep, were less likely to burst, and were more likely to be recorded simultaneously with a large population of neurons that were active during sleep and silent during behavior. These data suggest that single-field and multiple-field cells constitute at least two distinct cell classes in the DG. Based on these characteristics, we propose that putative mossy cells tend to fire in multiple, distinct locations in an environment, whereas putative granule cells tend to fire in single locations, similar to place fields of the CA1 and CA3 regions. Experimental evidence supporting the theories of pattern separation and pattern completion comes from both behavioral and electrophysiological tests. These studies specifically focused on the function of each subregion and made implicit assumptions about how environmental manipulations changed the representations encoded by the hippocampal inputs. However, the cell populations that provided these inputs were in most cases not directly examined. We conducted a series of studies to investigate the neural activity in the entorhinal cortex, dentate gyrus, and CA3 in the same experimental conditions, which allowed a direct comparison between the input and output representations. The results show that the dentate gyrus representation changes between the familiar and cue altered environments more than its input representations, whereas the CA3 representation changes less than its input representations. These findings are consistent with longstanding computational models proposing that (1) CA3 is an associative memory system performing pattern completion in order to recall previous memories from partial inputs, and (2) the dentate gyrus performs pattern separation to help store different memories in ways that reduce interference when the memories are subsequently recalled.

A pure population of lung alveolar epithelial type II cells derived from human embryonic stem cells.

Alveolar epithelial type II (ATII) cells are small, cuboidal cells that constitute approximately 60% of the pulmonary alveolar epithelium. These cells are crucial for repair of the injured alveolus by differentiating into alveolar epithelial type I cells. ATII cells derived from human ES (hES) cells are a promising source of cells that could be used therapeutically to treat distal lung diseases. We have developed a reliable transfection and culture procedure, which facilitates, via genetic selection, the differentiation of hES cells into an essentially pure (>99%) population of ATII cells (hES-ATII). Purity, as well as biological features and morphological characteristics of normal ATII cells, was demonstrated for the hES-ATII cells, including lamellar body formation, expression of surfactant proteins A, B, and C, alpha-1-antitrypsin, and the cystic fibrosis transmembrane conductance receptor, as well as the synthesis and secretion of complement proteins C3 and C5. Collectively, these data document the successful generation of a pure population of ATII cells derived from hES cells, providing a practical source of ATII cells to explore in disease models their potential in the regeneration and repair of the injured alveolus and in the therapeutic treatment of genetic diseases affecting the lung.

deltaNp63 has a role in maintaining epithelial integrity in airway epithelium.

The upper airways are lined with a pseudostratified bronchial epithelium that forms a barrier against unwanted substances in breathing air. The transcription factor p63, which is important for stratification of skin epithelium, has been shown to be expressed in basal cells of the lungs and its ΔN isoform is recognized as a key player in squamous cell lung cancer. However, the role of p63 in formation and maintenance of bronchial epithelia is largely unknown. The objective of the current study was to determine the expression pattern of the ΔN and TA isoforms of p63 and the role of p63 in the development and maintenance of pseudostratified lung epithelium in situ and in culture. We used a human bronchial epithelial cell line with basal cell characteristics (VA10) to model bronchial epithelium in an air-liquid interface culture (ALI) and performed a lentiviral-based silencing of p63 to characterize the functional and phenotypic consequences of p63 loss. We demonstrate that ΔNp63 is the major isoform in the human lung and its expression was exclusively found in the basal cells lining the basement membrane of the bronchial epithelium. Knockdown of p63 affected proliferation and migration of VA10 cells and facilitated cellular senescence. Expression of p63 is critical for epithelial repair as demonstrated by wound healing assays. Importantly, generation of pseudostratified VA10 epithelium in the ALI setup depended on p63 expression and goblet cell differentiation, which can be induced by IL-13 stimulation, was abolished by the p63 knockdown. After knockdown of p63 in primary bronchial epithelial cells they did not proliferate and showed marked senescence. We conclude that these results strongly implicate p63 in the formation and maintenance of differentiated pseudostratified bronchial epithelium.

Active eosinophilic esophagitis is characterized by epithelial barrier defects and eosinophil extracellular trap formation.

BACKGROUND Eosinophilic esophagitis (EoE) exhibits esophageal dysfunction owing to an eosinophil-predominant inflammation. Activated eosinophils generate eosinophil extracellular traps (EETs) able to kill bacteria. There is evidence of an impaired barrier function in EoE that might allow pathogens to invade the esophagus. This study aimed to investigate the presence and distribution of EETs in esophageal tissues from EoE patients and their association with possible epithelial barrier defects. METHODS Anonymized tissue samples from 18 patients with active EoE were analyzed. The presence of DNA nets associated with eosinophil granule proteins forming EETs and the expression of filaggrin, the protease inhibitor lympho-epithelial Kazal-type-related inhibitor (LEKTI), antimicrobial peptides, and cytokines were evaluated by confocal microscopy following immune fluorescence staining techniques. RESULTS Eosinophil extracellular trap formation occurred frequently and was detected in all EoE samples correlating with the numbers of infiltrating eosinophils. While the expression of both filaggrin and LEKTI was reduced, epithelial antimicrobial peptides (human beta-defensin-2, human beta-defensin-3, cathelicidin LL-37, psoriasin) and cytokines (TSLP, IL-25, IL-32, IL-33) were elevated in EoE as compared to normal esophageal tissues. There was a significant correlation between EET formation and TSLP expression (P = 0.02) as well as psoriasin expression (P = 0.016). On the other hand, a significant negative correlation was found between EET formation and LEKTI expression (P = 0.016). CONCLUSION Active EoE exhibits the presence of EETs. Indications of epithelial barrier defects in association with epithelial cytokines are also present which may have contributed to the activation of eosinophils. The formation of EETs could serve as a firewall against the invasion of pathogens.

Theoretical models of planetary system formation II. Post-formation evolution

Aims. We extend the results of planetary formation synthesis by computing the long-term evolution of synthetic systems from the clearing of the gas disk into the dynamical evolution phase. Methods. We use the symplectic integrator SyMBA to numerically integrate the orbits of planets for 100 Myr, using populations from previous studies as initial conditions. Results. We show that within the populations studied, mass and semimajor axis distributions experience only minor changes from post-formation evolution. We also show that, depending upon their initial distribution, planetary eccentricities can statistically increase or decrease as a result of gravitational interactions. We find that planetary masses and orbital spacings provided by planet formation models do not result in eccentricity distributions comparable to observed exoplanet eccentricities, requiring other phenomena, such as stellar fly-bys, to account for observed eccentricities.

Isotone Recursive Methods for Overlapping Generation Models with Stochastic Nonclassical Production

Based on an order-theoretic approach, we derive sufficient conditions for the existence, characterization, and computation of Markovian equilibrium decision processes and stationary Markov equilibrium on minimal state spaces for a large class of stochastic overlapping generations models. In contrast to all previous work, we consider reduced-form stochastic production technologies that allow for a broad set of equilibrium distortions such as public policy distortions, social security, monetary equilibrium, and production nonconvexities. Our order-based methods are constructive, and we provide monotone iterative algorithms for computing extremal stationary Markov equilibrium decision processes and equilibrium invariant distributions, while avoiding many of the problems associated with the existence of indeterminacies that have been well-documented in previous work. We provide important results for existence of Markov equilibria for the case where capital income is not increasing in the aggregate stock. Finally, we conclude with examples common in macroeconomics such as models with fiat money and social security. We also show how some of our results extend to settings with unbounded state spaces.

Stationary Markovian Equilibrium in Overlapping Generation Models with Stochastic Nonclassical Production

This paper provides new sufficient conditions for the existence, computation via successive approximations, and stability of Markovian equilibrium decision processes for a large class of OLG models with stochastic nonclassical production. Our notion of stability is existence of stationary Markovian equilibrium. With a nonclassical production, our economies encompass a large class of OLG models with public policy, valued fiat money, production externalities, and Markov shocks to production. Our approach combines aspects of both topological and order theoretic fixed point theory, and provides the basis of globally stable numerical iteration procedures for computing extremal Markovian equilibrium objects. In addition to new theoretical results on existence and computation, we provide some monotone comparative statics results on the space of economies.

REGULATION OF FOXC2 EXPRESSION AND FUNCTION DURING EPITHELIAL-MESENCHYMAL TRANSITION BY GSK-3β

Metastasis is the ultimate cause for the majority of cancer-related deaths. The forkhead box transcription factor FOXC2 is known to be involved in regulating metastasis as well as a variety of developmental processes, including the formation of lymphatic and cardiovascular systems. Previous studies have shown that FOXC2 protein is localized either in the nucleus and/or in the cytoplasm of human breast tumor cells. This pattern of localization is similar to that of another forkhead family member, FOXO3a. Additionally, localization of FOXO3a is known to be differentially regulated by upstream kinase AKT. Therefore, I investigated whether FOXC2 localization could also be regulated by upstream kinases. Analysis of FOXC2 protein sequence revealed two potential phosphorylation sites for GSK-3β. Furthermore, inhibition of GSK-3βsignificantly reduces FOXC2 protein. In addition, exposure of HMLE Twist cells expressing endogenous FOXC2 to the GSK-3β inhibitor, TWS119, results in accumulation of FOXC2 protein in the cytoplasm with concomitant decrease in the nucleus in a time-dependent manner. Furthermore, continued treatment with TWS119 eventually induces epithelial morphology and decreased stem cell properties including sphere formation in these cells. Further characterization of FOXC2- GSK-3β interaction and the associated signaling cascade are necessary to determine the effect of FOXC2 phosphorylation by GSK-3β on EMT and metastasis.

Oscillatory genetic circuits: new designs and mathematical models

Introduction and motivation: A wide variety of organisms have developed in-ternal biomolecular clocks in order to adapt to cyclic changes of the environment. Clock operation involves genetic networks. These genetic networks have to be mod¬eled in order to understand the underlying mechanism of oscillations and to design new synthetic cellular clocks. This doctoral thesis has resulted in two contributions to the fields of genetic clocks and systems and synthetic biology, generally. The first contribution is a new genetic circuit model that exhibits an oscillatory behav¬ior through catalytic RNA molecules. The second and major contribution is a new genetic circuit model demonstrating that a repressor molecule acting on the positive feedback of a self-activating gene produces reliable oscillations. First contribution: A new model of a synthetic genetic oscillator based on a typical two-gene motif with one positive and one negative feedback loop is pre¬sented. The originality is that the repressor is a catalytic RNA molecule rather than a protein or a non-catalytic RNA molecule. This catalytic RNA is a ribozyme that acts post-transcriptionally by binding to and cleaving target mRNA molecules. This genetic clock involves just two genes, a mRNA and an activator protein, apart from the ribozyme. Parameter values that produce a circadian period in both determin¬istic and stochastic simulations have been chosen as an example of clock operation. The effects of the stochastic fluctuations are quantified by a period histogram and autocorrelation function. The conclusion is that catalytic RNA molecules can act as repressor proteins and simplify the design of genetic oscillators. Second and major contribution: It is demonstrated that a self-activating gene in conjunction with a simple negative interaction can easily produce robust matically validated. This model is comprised of two clearly distinct parts. The first is a positive feedback created by a protein that binds to the promoter of its own gene and activates the transcription. The second is a negative interaction in which a repressor molecule prevents this protein from binding to its promoter. A stochastic study shows that the system is robust to noise. A deterministic study identifies that the oscillator dynamics are mainly driven by two types of biomolecules: the protein, and the complex formed by the repressor and this protein. The main conclusion of this study is that a simple and usual negative interaction, such as degradation, se¬questration or inhibition, acting on the positive transcriptional feedback of a single gene is a sufficient condition to produce reliable oscillations. One gene is enough and the positive transcriptional feedback signal does not need to activate a second repressor gene. At the genetic level, this means that an explicit negative feedback loop is not necessary. Unlike many genetic oscillators, this model needs neither cooperative binding reactions nor the formation of protein multimers. Applications and future research directions: Recently, RNA molecules have been found to play many new catalytic roles. The first oscillatory genetic model proposed in this thesis uses ribozymes as repressor molecules. This could provide new synthetic biology design principles and a better understanding of cel¬lular clocks regulated by RNA molecules. The second genetic model proposed here involves only a repression acting on a self-activating gene and produces robust oscil¬lations. Unlike current two-gene oscillators, this model surprisingly does not require a second repressor gene. This result could help to clarify the design principles of cellular clocks and constitute a new efficient tool for engineering synthetic genetic oscillators. Possible follow-on research directions are: validate models in vivo and in vitro, research the potential of second model as a genetic memory, investigate new genetic oscillators regulated by non-coding RNAs and design a biosensor of positive feedbacks in genetic networks based on the operation of the second model Resumen Introduccion y motivacion: Una amplia variedad de organismos han desarro-llado relojes biomoleculares internos con el fin de adaptarse a los cambios ciclicos del entorno. El funcionamiento de estos relojes involucra redes geneticas. El mo delado de estas redes geneticas es esencial tanto para entender los mecanismos que producen las oscilaciones como para diseiiar nuevos circuitos sinteticos en celulas. Esta tesis doctoral ha dado lugar a dos contribuciones dentro de los campos de los circuitos geneticos en particular, y biologia de sistemas y sintetica en general. La primera contribucion es un nuevo modelo de circuito genetico que muestra un comportamiento oscilatorio usando moleculas de ARN cataliticas. La segunda y principal contribucion es un nuevo modelo de circuito genetico que demuestra que una molecula represora actuando sobre el lazo de un gen auto-activado produce oscilaciones robustas. Primera contribucion: Es un nuevo modelo de oscilador genetico sintetico basado en una tipica red genetica compuesta por dos genes con dos lazos de retroa-limentacion, uno positivo y otro negativo. La novedad de este modelo es que el represor es una molecula de ARN catalftica, en lugar de una protefna o una molecula de ARN no-catalitica. Este ARN catalitico es una ribozima que actua despues de la transcription genetica uniendose y cortando moleculas de ARN mensajero (ARNm). Este reloj genetico involucra solo dos genes, un ARNm y una proteina activadora, aparte de la ribozima. Como ejemplo de funcionamiento, se han escogido valores de los parametros que producen oscilaciones con periodo circadiano (24 horas) tanto en simulaciones deterministas como estocasticas. El efecto de las fluctuaciones es-tocasticas ha sido cuantificado mediante un histograma del periodo y la función de auto-correlacion. La conclusion es que las moleculas de ARN con propiedades cataliticas pueden jugar el misnio papel que las protemas represoras, y por lo tanto, simplificar el diseno de los osciladores geneticos. Segunda y principal contribucion: Es un nuevo modelo de oscilador genetico que demuestra que un gen auto-activado junto con una simple interaction negativa puede producir oscilaciones robustas. Este modelo ha sido estudiado y validado matematicamente. El modelo esta compuesto de dos partes bien diferenciadas. La primera parte es un lazo de retroalimentacion positiva creado por una proteina que se une al promotor de su propio gen activando la transcription. La segunda parte es una interaction negativa en la que una molecula represora evita la union de la proteina con el promotor. Un estudio estocastico muestra que el sistema es robusto al ruido. Un estudio determinista muestra que la dinamica del sistema es debida principalmente a dos tipos de biomoleculas: la proteina, y el complejo formado por el represor y esta proteina. La conclusion principal de este estudio es que una simple y usual interaction negativa, tal como una degradation, un secuestro o una inhibition, actuando sobre el lazo de retroalimentacion positiva de un solo gen es una condition suficiente para producir oscilaciones robustas. Un gen es suficiente y el lazo de retroalimentacion positiva no necesita activar a un segundo gen represor, tal y como ocurre en los relojes actuales con dos genes. Esto significa que a nivel genetico un lazo de retroalimentacion negativa no es necesario de forma explicita. Ademas, este modelo no necesita reacciones cooperativas ni la formation de multimeros proteicos, al contrario que en muchos osciladores geneticos. Aplicaciones y futuras lineas de investigacion: En los liltimos anos, se han descubierto muchas moleculas de ARN con capacidad catalitica. El primer modelo de oscilador genetico propuesto en esta tesis usa ribozimas como moleculas repre¬soras. Esto podria proporcionar nuevos principios de diseno en biologia sintetica y una mejor comprension de los relojes celulares regulados por moleculas de ARN. El segundo modelo de oscilador genetico propuesto aqui involucra solo una represion actuando sobre un gen auto-activado y produce oscilaciones robustas. Sorprendente-mente, un segundo gen represor no es necesario al contrario que en los bien conocidos osciladores con dos genes. Este resultado podria ayudar a clarificar los principios de diseno de los relojes celulares naturales y constituir una nueva y eficiente he-rramienta para crear osciladores geneticos sinteticos. Algunas de las futuras lineas de investigation abiertas tras esta tesis son: (1) la validation in vivo e in vitro de ambos modelos, (2) el estudio del potential del segundo modelo como circuito base para la construction de una memoria genetica, (3) el estudio de nuevos osciladores geneticos regulados por ARN no codificante y, por ultimo, (4) el rediseno del se¬gundo modelo de oscilador genetico para su uso como biosensor capaz de detectar genes auto-activados en redes geneticas.