Jim Q. Smith

FLOWERING LOCUS C mediates natural variation in the high-temperature response of the Arabidopsis circadian clock.

Temperature compensation contributes to the accuracy of biological timing by preventing circadian rhythms from running more quickly at high than at low temperatures. We previously identified quantitative trait loci (QTL) with temperature-specific effects on the circadian rhythm of leaf movement, including a QTL linked to the transcription factor FLOWERING LOCUS C (FLC). We have now analyzed FLC alleles in near-isogenic lines and induced mutants to eliminate other candidate genes. We showed that FLC lengthened the circadian period specifically at 27°C, contributing to temperature compensation of the circadian clock. Known upstream regulators of FLC expression in flowering time pathways similarly controlled its circadian effect. We sought to identify downstream targets of FLC regulation in the molecular mechanism of the circadian clock using genome-wide analysis to identify FLC-responsive genes and 3503 transcripts controlled by the circadian clock. A Bayesian clustering method based on Fourier coefficients allowed us to discriminate putative regulatory genes. Among rhythmic FLC-responsive genes, transcripts of the transcription factor LUX ARRHYTHMO (LUX) correlated in peak abundance with the circadian period in flc mutants. Mathematical modeling indicated that the modest change in peak LUX RNA abundance was sufficient to cause the period change due to FLC, providing a molecular target for the crosstalk between flowering time pathways and circadian regulation.

Orchestrated transcription of biological processes in the marine picoeukaryote Ostreococcus exposed to light/dark cycles.

BackgroundPicoeukaryotes represent an important, yet poorly characterized component of marine phytoplankton. The recent genome availability for two species of Ostreococcus and Micromonas has led to the emergence of picophytoplankton comparative genomics. Sequencing has revealed many unexpected features about genome structure and led to several hypotheses on Ostreococcus biology and physiology. Despite the accumulation of genomic data, little is known about gene expression in eukaryotic picophytoplankton.ResultsWe have conducted a genome-wide analysis of gene expression in Ostreococcus tauri cells exposed to light/dark cycles (L/D). A Bayesian Fourier Clustering method was implemented to cluster rhythmic genes according to their expression waveform. In a single L/D condition nearly all expressed genes displayed rhythmic patterns of expression. Clusters of genes were associated with the main biological processes such as transcription in the nucleus and the organelles, photosynthesis, DNA replication and mitosis.ConclusionsLight/Dark time-dependent transcription of the genes involved in the main steps leading to protein synthesis (transcription basic machinery, ribosome biogenesis, translation and aminoacid synthesis) was observed, to an unprecedented extent in eukaryotes, suggesting a major input of transcriptional regulations in Ostreococcus. We propose that the diurnal co-regulation of genes involved in photoprotection, defence against oxidative stress and DNA repair might be an efficient mechanism, which protects cells against photo-damage thereby, contributing to the ability of O. tauri to grow under a wide range of light intensities.

Conditional independence and chain event graphs

Graphs provide an excellent framework for interrogating symmetric models of measurement random variables and discovering their implied conditional independence structure. However, it is not unusual for a model to be specified from a description of how a process unfolds (i.e. via its event tree), rather than through relationships between a given set of measurements. Here we introduce a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships. This graph is more expressive and flexible than either the Bayesian network-equivalent in the symmetric case-or the probability decision graph. Various separation theorems are proved for the chain event graph. These enable implied conditional independencies to be read from the graphs topology. We also show how the topology can be exploited to tease out the interesting conditional independence structure of functions of random variables associated with the underlying event tree.

Influence diagrams for Bayesian decision analysis

Abstract Influence diagrams for representing Bayesian decision problems are redefined in a formal way using conditional independence. This makes the graphs somewhat more helpful for exploring the consequences of a clients state beliefs. Some important results about the manipulation of influence diagrams are extended and reviewed as is an algorithm for computing an optimal policy. Two new results about the manipulation of influence diagrams are derived. A novel influence diagram representing a practical decision problem is used to illustrate the methodologies presented in this paper.

Implicit inequality constraints in a binary tree model

In this paper we investigate the geometry of a discrete Bayesian network whose graph is a tree all of whose variables are binary and the only observed variables are those labeling its leaves. We provide the full geometric description of these models which is given by a set of polynomial equations together with a set of complementary implied inequalities induced by the positivity of probabilities on hidden variables. The phylogenetic invariants given by the equations can be useful in the construction of simple diagnostic tests. However, in this paper we point out the importance of also incorporating the associated inequalities into any statistical analysis. The full characterization of these inequality constraints derived in this paper helps us determine how and why routine statistical methods can break down for this model class.

Causal analysis with Chain Event Graphs

As the Chain Event Graph (CEG) has a topology which represents sets of conditional independence statements, it becomes especially useful when problems lie naturally in a discrete asymmetric non-product space domain, or when much context-specific information is present. In this paper we show that it can also be a powerful representational tool for a wide variety of causal hypotheses in such domains. Furthermore, we demonstrate that, as with Causal Bayesian Networks (CBNs), the identifiability of the effects of causal manipulations when observations of the system are incomplete can be verified simply by reference to the topology of the CEG. We close the paper with a proof of a Back Door Theorem for CEGs, analogous to Pearls Back Door Theorem for CBNs.

Tree cumulants and the geometry of binary tree models

In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on the theory of partially ordered sets allows us to obtain a convenient parametrization of this model class. The construction of the proposed coordinate system mirrors the combinatorial definition of cumulants. A simple product-like form of the resulting parametrization gives insight into identifiability issues associated with this model class. In particular, we provide necessary and sufficient conditions for such a model to be identified up to the switching of labels of the inner nodes. When these conditions hold, we give explicit formulas for the parameters of the model. Whenever the model fails to be identified, we use the new parametrization to describe the geometry of the unidentified parameter space. We illustrate these results using a simple example.In this paper we investigate undirected discrete graphical tree models when all the variables in the system are binary, where leaves represent the observable variables and where all the inner nodes are unobserved. A novel approach based on the theory of partially ordered sets allows us to obtain a convenient parametrization of this model class. The construction of the proposed coordinate system mirrors the combinatorial definition of cumulants. A simple product-like form of the resulting parametrization gives insight into identifiability issues associated with this model class. In particular, we provide necessary and sufficient conditions for such a model to be identified up to the switching of labels of the inner nodes. When these conditions hold, we give explicit formulas for the parameters of the model. Whenever the model fails to be identified, we use the new parametrization to describe the geometry of the unidentified parameter space. We illustrate these results using a simple example.

Discontinuity in decision-making when objectives conflict: a military command decision case study

In previous work, we considered the representation of human decision-making processes in closed-form simulation models of conflict. An important element of this representation is the rapid planning process that embodies the processing of information for situation assessment to support a course of action decision (eg in a military headquarters). The application of this work is in support of operational analysis models for defence procurement and balance of investment. This paper describes the application of non-linear multi-attribute utility theory in conflict scenarios in order to extend the representation of the rapid planning process to account for a wider set of subjective attributes of the decision-maker. The results show, through examination of experimental data, that decision-making can be modelled through a particular class of utility functions. These utilities embody a geometry which allows us to classify the types of decision being made when there are conflicting objectives and when decision-makers adopt very different and subjective appraisals of constraints and beliefs in outcome. The experimental results help to demonstrate that the subjective nature of the situation assessment, and the personality, training, experience and history of the decision-maker are central to the functional representations. This paper presents a way to capture this deeper representation of human decision-making in a way that is potentially useful for quantitative modelling using the rapid planning process as a basis.

Bayesian MAP model selection of chain event graphs

Chain event graphs are graphical models that while retaining most of the structural advantages of Bayesian networks for model interrogation, propagation and learning, more naturally encode asymmetric state spaces and the order in which events happen than Bayesian networks do. In addition, the class of models that can be represented by chain event graphs for a finite set of discrete variables is a strict superset of the class that can be described by Bayesian networks. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.

Bayesian networks for discrete multivariate data: an algebraic approach to inference

In this paper we demonstrate how Grobner bases and other algebraic techniques can be used to explore the geometry of the probability space of Bayesian networks with hidden variables. These techniques employ a parametrisation of Bayesian network by moments rather than conditional probabilities. We show that whilst Grobner bases help to explain the local geometry of these spaces a complimentary analysis, modelling the positivity of probabilities, enhances and completes the geometrical picture. We report some recent geometrical results in this area and discuss a possible general methodology for the analyses of such problems.