Estimation of means in graphical Gaussian models with symmetries

We study the problem of estimability of means in undirected graphical Gaussian models with symmetry restrictions represented by a colored graph. Following on from previous studies, we partition the variables into sets of vertices whose corresponding means are restricted to being identical. We find a necessary and sufficient condition on the partition to ensure equality between the maximum likelihood and least-squares estimators of the mean.Comment: Published in at http://dx.doi.org/10.1214/12-AOS991 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Lattices of Graphical Gaussian Models with Symmetries

In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously been introduced in the literature. The models can be represented by vertex and edge coloured graphs. The need for model selection methods makes it imperative to understand the structure of model classes. We identify four model classes that form complete lattices of models with respect to model inclusion, which qualifies them for an Edwards-Havr\'anek model selection procedure. Two classes turn out most suitable for a corresponding model search. We obtain an explicit search algorithm for one of them and provide a model search example for the other.Comment: 29 pages, 18 figures. Restructured Section 5, results unchanged; added references in Section 6; amended example in Section 6.

Graphical Gaussian models with symmetries

This thesis is concerned with graphical Gaussian models with equality constraints on the concentration or partial correlation matrix introduced by Højsgaard and Lauritzen (2008) as RCON and RCOR models. The models can be represented by vertex and edge coloured graphs G = (V,ε), where parameters associated with equally coloured vertices or edges are restricted to being identical. In the first part of this thesis we study the problem of estimability of a non-zero model mean μ if the covariance structure Σ is restricted to satisfy the constraints of an RCON or RCOR model but is otherwise unknown. Exploiting results in Kruskal (1968), we obtain a characterisation of suitable linear spaces Ω such that if Σ is restricted as above, the maximum likelihood estimator μ(with circumflex) and the least squares estimator μ* of μ coincide for μ ∈ Ω, thus allowing μ and Σ to be estimated independently. For the special case of Ω being specified by equality relations among the entries of μ according to a partition M of the model variables V, our characterisation translates into a necessary and sufficient regularity condition on M and (V,ε). In the second part we address model selection of RCON and RCOR models. Due to the large number of models, we study the structure of four model classes lying strictly within the sets of RCON and RCOR models, each of which is defined by desirable statistical properties corresponding to colouring regularity conditions. Two of these appear in Højsgaard and Lauritzen (2008), while the other two arise from the regularity condition ensuring equality of estimators μ(with circumflex) = μ* we find in the first part. We show each of the colouring classes to form complete lattices, which qualifies the corresponding model spaces for an Edwards-Havránek model selection procedure (Edwards and Havránek, 1987). We develop a coresponding algorithm for one of the model classes and give an algorithm for a systematic search in accordance with the Edwards-Havránek principles for a second class. Both are applied to data sets previously analysed in the literature, with very encouraging performances.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Development of NMDAR antagonists with reduced neurotoxic side effects: a study on GK11

The NMDAR glutamate receptor subtype mediates various vital physiological neuronal functions. However, its excessive activation contributes to neuronal damage in a large variety of acute and chronic neurological disorders. NMDAR antagonists thus represent promising therapeutic tools that can counteract NMDARs’ overactivation. Channel blockers are of special interest since they are use-dependent, thus being more potent at continuously activated NMDARs, as may be the case in pathological conditions. Nevertheless, it has been established that NMDAR antagonists, such as MK801, also have unacceptable neurotoxic effects. Presently only Memantine is considered a safe NMDAR antagonist and is used clinically. It has recently been speculated that antagonists that preferentially target extrasynaptic NMDARs would be less toxic. We previously demonstrated that the phencyclidine derivative GK11 preferentially inhibits extrasynaptic NMDARs. We thus anticipated that this compound would be safer than other known NMDAR antagonists. In this study we used whole-genome profiling of the rat cingulate cortex, a brain area that is particularly sensitive to NMDAR antagonists, to compare the potential adverse effects of GK11 and MK801. Our results showed that in contrast to GK11, the transcriptional profile of MK801 is characterized by a significant upregulation of inflammatory and stress-response genes, consistent with its high neurotoxicity. In addition, behavioural and immunohistochemical analyses confirmed marked inflammatory reactions (including astrogliosis and microglial activation) in MK801-treated, but not GK11-treated rats. Interestingly, we also showed that GK11 elicited less inflammation and neuronal damage, even when compared to Memantine, which like GK11, preferentially inhibits extrasynaptic NMDAR. As a whole, our study suggests that GK11 may be a more attractive therapeutic alternative in the treatment of CNS disorders characterized by the overactivation of glutamate receptors

Physics Briefing Book: Input for the European Strategy for Particle Physics Update 2020

The European Particle Physics Strategy Update (EPPSU) process takes a bottom-up approach, whereby the community is first invited to submit proposals (also called inputs) for projects that it would like to see realised in the near-term, mid-term and longer-term future. National inputs as well as inputs from National Laboratories are also an important element of the process. All these inputs are then reviewed by the Physics Preparatory Group (PPG), whose role is to organize a Symposium around the submitted ideas and to prepare a community discussion on the importance and merits of the various proposals. The results of these discussions are then concisely summarised in this Briefing Book, prepared by the Conveners, assisted by Scientific Secretaries, and with further contributions provided by the Contributors listed on the title page. This constitutes the basis for the considerations of the European Strategy Group (ESG), consisting of scientific delegates from CERN Member States, Associate Member States, directors of major European laboratories, representatives of various European organizations as well as invitees from outside the European Community. The ESG has the mission to formulate the European Strategy Update for the consideration and approval of the CERN Council

Physics Briefing Book: Input for the European Strategy for Particle Physics Update 2020

The European Particle Physics Strategy Update (EPPSU) process takes a bottom-up approach, whereby the community is first invited to submit proposals (also called inputs) for projects that it would like to see realised in the near-term, mid-term and longer-term future. National inputs as well as inputs from National Laboratories are also an important element of the process. All these inputs are then reviewed by the Physics Preparatory Group (PPG), whose role is to organize a Symposium around the submitted ideas and to prepare a community discussion on the importance and merits of the various proposals. The results of these discussions are then concisely summarised in this Briefing Book, prepared by the Conveners, assisted by Scientific Secretaries, and with further contributions provided by the Contributors listed on the title page. This constitutes the basis for the considerations of the European Strategy Group (ESG), consisting of scientific delegates from CERN Member States, Associate Member States, directors of major European laboratories, representatives of various European organizations as well as invitees from outside the European Community. The ESG has the mission to formulate the European Strategy Update for the consideration and approval of the CERN Council