Time series prediction via aggregation : an oracle bound including numerical cost

We address the problem of forecasting a time series meeting the Causal Bernoulli Shift model, using a parametric set of predictors. The aggregation technique provides a predictor with well established and quite satisfying theoretical properties expressed by an oracle inequality for the prediction risk. The numerical computation of the aggregated predictor usually relies on a Markov chain Monte Carlo method whose convergence should be evaluated. In particular, it is crucial to bound the number of simulations needed to achieve a numerical precision of the same order as the prediction risk. In this direction we present a fairly general result which can be seen as an oracle inequality including the numerical cost of the predictor computation. The numerical cost appears by letting the oracle inequality depend on the number of simulations required in the Monte Carlo approximation. Some numerical experiments are then carried out to support our findings

PAC-Bayesian Bounds for Randomized Empirical Risk Minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control the risk of the latter. These results allow to bound the risk of very general estimation procedures, as well as to perform model selection

Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

Ca2+/Calmodulin-Dependent Protein Kinase Kinase Is Not Involved in Hypothalamic AMP-Activated Protein Kinase Activation by Neuroglucopenia

Hypoglycemia and neuroglucopenia stimulate AMP-activated protein kinase (AMPK) activity in the hypothalamus and this plays an important role in the counterregulatory responses, i.e. increased food intake and secretion of glucagon, corticosterone and catecholamines. Several upstream kinases that activate AMPK have been identified including Ca2+/Calmodulin-dependent protein kinase kinase (CaMKK), which is highly expressed in neurons. However, the involvement of CaMKK in neuroglucopenia-induced activation of AMPK in the hypothalamus has not been tested. To determine whether neuroglucopenia-induced AMPK activation is mediated by CaMKK, we tested whether STO-609 (STO), a CaMKK inhibitor, would block the effects of 2-deoxy-D-glucose (2DG)-induced neuroglucopenia both ex vivo on brain sections and in vivo. Preincubation of rat brain sections with STO blocked KCl-induced α1 and α2-AMPK activation but did not affect AMPK activation by 2DG in the medio-basal hypothalamus. To confirm these findings in vivo, STO was pre-administrated intracerebroventricularly (ICV) in rats 30 min before 2DG ICV injection (40 µmol) to induce neuroglucopenia. 2DG-induced neuroglucopenia lead to a significant increase in glycemia and food intake compared to saline-injected control rats. ICV pre-administration of STO (5, 20 or 50 nmol) did not affect 2DG-induced hyperglycemia and food intake. Importantly, activation of hypothalamic α1 and α2-AMPK by 2DG was not affected by ICV pre-administration of STO. In conclusion, activation of hypothalamic AMPK by 2DG-induced neuroglucopenia is not mediated by CaMKK

Neuroanatomical characterisation of the expression of the lipodystrophy and motor-neuropathy gene Bscl2 in adult mouse brain

Peer reviewedPublisher PD

Rank-based model selection for multiple ions quantum tomography

The statistical analysis of measurement data has become a key component of many quantum engineering experiments. As standard full state tomography becomes unfeasible for large dimensional quantum systems, one needs to exploit prior information and the "sparsity" properties of the experimental state in order to reduce the dimensionality of the estimation problem. In this paper we propose model selection as a general principle for finding the simplest, or most parsimonious explanation of the data, by fitting different models and choosing the estimator with the best trade-off between likelihood fit and model complexity. We apply two well established model selection methods -- the Akaike information criterion (AIC) and the Bayesian information criterion (BIC) -- to models consising of states of fixed rank and datasets such as are currently produced in multiple ions experiments. We test the performance of AIC and BIC on randomly chosen low rank states of 4 ions, and study the dependence of the selected rank with the number of measurement repetitions for one ion states. We then apply the methods to real data from a 4 ions experiment aimed at creating a Smolin state of rank 4. The two methods indicate that the optimal model for describing the data lies between ranks 6 and 9, and the Pearson $\chi^{2}$ test is applied to validate this conclusion. Additionally we find that the mean square error of the maximum likelihood estimator for pure states is close to that of the optimal over all possible measurements.Comment: 24 pages, 6 figures, 3 table

Chronic exposure to KATP channel openers results in attenuated glucose sensing in hypothalamic GT1-7 neurons

Individuals with Type 1 diabetes (T1D) are often exposed to recurrent episodes of hypoglycaemia. This reduces hormonal and behavioural responses that normally counteract low glucose in order to maintain glucose homeostasis, with altered responsiveness of glucose sensing hypothalamic neurons implicated. Although the molecular mechanisms are unknown, pharmacological studies implicate hypothalamic ATP-sensitive potassium channel (KATP) activity, with KATP openers (KCOs) amplifying, through cell hyperpolarization, the response to hypoglycaemia. Although initial findings, using acute hypothalamic KCO delivery, in rats were promising, chronic exposure to the KCO NN414 worsened the responses to subsequent hypoglycaemic challenge. To investigate this further we used GT1-7 cells to explore how NN414 affected glucose-sensing behaviour, the metabolic response of cells to hypoglycaemia and KATP activity. GT1-7 cells exposed to 3 or 24 h NN414 exhibited an attenuated hyperpolarization to subsequent hypoglycaemic challenge or NN414, which correlated with diminished KATP activity. The reduced sensitivity to hypoglycaemia was apparent 24 h after NN414 removal, even though intrinsic KATP activity recovered. The NN414-modified glucose responsiveness was not associated with adaptations in glucose uptake, metabolism or oxidation. KATP inactivation by NN414 was prevented by the concurrent presence of tolbutamide, which maintains KATP closure. Single channel recordings indicate that NN414 alters KATP intrinsic gating inducing a stable closed or inactivated state. These data indicate that exposure of hypothalamic glucose sensing cells to chronic NN414 drives a sustained conformational change to KATP, probably by binding to SUR1, that results in loss of channel sensitivity to intrinsic metabolic factors such as MgADP and small molecule agonists.We thank Novo Nordisk for providing NN414. This study was funded by grants from Diabetes UK (to MLJA, RJM) and the Juvenile Diabetes Research Foundation (postdoctoral fellowship 3-576-2010 to CB and 1-2008-728 to RJM)

Pre- and early-postnatal nutrition modify gene and protein expressions of muscle energy metabolism markers and phospholipid fatty acid composition in a muscle type specific manner in sheep.

We previously reported that undernutrition in late fetal life reduced whole-body insulin sensitivity in adult sheep, irrespective of dietary exposure in early postnatal life. Skeletal muscle may play an important role in control of insulin action. We therefore studied a range of putative key muscle determinants of insulin signalling in two types of skeletal muscles (longissimus dorsi (LD) and biceps femoris (BF)) and in the cardiac muscle (ventriculus sinister cordis (VSC)) of sheep from the same experiment. Twin-bearing ewes were fed either 100% (NORM) or 50% (LOW) of their energy and protein requirements during the last trimester of gestation. From day-3 postpartum to 6-months of age (around puberty), twin offspring received a high-carbohydrate-high-fat (HCHF) or a moderate-conventional (CONV) diet, whereafter all males were slaughtered. Females were subsequently raised on a moderate diet and slaughtered at 2-years of age (young adults). The only long-term consequences of fetal undernutrition observed in adult offspring were lower expressions of the insulin responsive glucose transporter 4 (GLUT4) protein and peroxisome proliferator-activated receptor gamma, coactivator 1α (PGC1α) mRNA in BF, but increased PGC1α expression in VSC. Interestingly, the HCHF diet in early postnatal life was associated with somewhat paradoxically increased expressions in LD of a range of genes (but not proteins) related to glucose uptake, insulin signalling and fatty acid oxidation. Except for fatty acid oxidation genes, these changes persisted into adulthood. No persistent expression changes were observed in BF and VSC. The HCHF diet increased phospholipid ratios of n-6/n-3 polyunsaturated fatty acids in all muscles, even in adults fed identical diets for 1½ years. In conclusion, early postnatal, but not late gestation, nutrition had long-term consequences for a number of determinants of insulin action and metabolism in LD. Tissues other than muscle may account for reduced whole body insulin sensitivity in adult LOW sheep

Metformin Prevents Nigrostriatal Dopamine Degeneration Independent of AMPK Activation in Dopamine Neurons

Metformin is a widely prescribed drug used to treat type-2 diabetes, although recent studies show it has wide ranging effects to treat other diseases. Animal and retrospective human studies indicate that Metformin treatment is neuroprotective in Parkinson’s Disease (PD), although the neuroprotective mechanism is unknown, numerous studies suggest the beneficial effects on glucose homeostasis may be through AMPK activation. In this study we tested whether or not AMPK activation in dopamine neurons was required for the neuroprotective effects of Metformin in PD. We generated transgenic mice in which AMPK activity in dopamine neurons was ablated by removing AMPK beta 1 and beta 2 subunits from dopamine transporter expressing neurons. These AMPK WT and KO mice were then chronically exposed to Metformin in the drinking water then exposed to MPTP, the mouse model of PD. Chronic Metformin treatment significantly attenuated the MPTP-induced loss of Tyrosine Hydroxylase (TH) neuronal number and volume and TH protein concentration in the nigrostriatal pathway. Additionally, Metformin treatment prevented the MPTP-induced elevation of the DOPAC:DA ratio regardless of genotype. Metformin also prevented MPTP induced gliosis in the Substantia Nigra. These neuroprotective actions were independent of genotype and occurred in both AMPK WT and AMPK KO mice. Overall, our studies suggest that Metformin’s neuroprotective effects are not due to AMPK activation in dopaminergic neurons and that more research is required to determine how metformin acts to restrict the development of PD