Pointwise adaptive estimation for robust and quantile regression

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is extended to image denoising and applied to CT scans in cancer research

Pointwise adaptive estimation for quantile regression

A nonparametric procedure for quantile regression, or more generally nonparametric M-estimation, is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each point M-estimators over different local neighbourhoods and by a local model selection procedure based on sequential testing. Non-asymptotic risk bounds are obtained, which yield rate-optimality for large sample asymptotics under weak conditions. Simulations for different univariate median regression models show good finite sample properties, also in comparison to traditional methods. The approach is the basis for denoising CT scans in cancer research.M-estimation, median regression, robust estimation, local model selection, unsupervised learning, local bandwidth selection, median filter, Lepski procedure, minimax rate, image denoising

Laplace deconvolution and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete observations. The study is motivated by Dynamic Contrast Enhanced imaging using a bolus of contrast agent, a procedure which allows considerable improvement in {evaluating} the quality of a vascular network and its permeability and is widely used in medical assessment of brain flows or cancerous tumors. Although the study is motivated by medical imaging application, we obtain a solution of a general problem of Laplace deconvolution based on noisy data which appears in many different contexts. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. The number $m$ of the terms in the expansion of the estimator is controlled via complexity penalty. The advantage of this methodology is that it leads to very fast computations, does not require exact knowledge of the kernel and produces no boundary effects due to extension at zero and cut-off at $T$. The technique leads to an estimator with the risk within a logarithmic factor of $m$ of the oracle risk under no assumptions on the model and within a constant factor of the oracle risk under mild assumptions. The methodology is illustrated by a finite sample simulation study which includes an example of the kernel obtained in the real life DCE experiments. Simulations confirm that the proposed technique is fast, efficient, accurate, usable from a practical point of view and competitive

Laplace deconvolution on the basis of time domain data and its application to Dynamic Contrast Enhanced imaging

In the present paper we consider the problem of Laplace deconvolution with noisy discrete non-equally spaced observations on a finite time interval. We propose a new method for Laplace deconvolution which is based on expansions of the convolution kernel, the unknown function and the observed signal over Laguerre functions basis (which acts as a surrogate eigenfunction basis of the Laplace convolution operator) using regression setting. The expansion results in a small system of linear equations with the matrix of the system being triangular and Toeplitz. Due to this triangular structure, there is a common number $m$ of terms in the function expansions to control, which is realized via complexity penalty. The advantage of this methodology is that it leads to very fast computations, produces no boundary effects due to extension at zero and cut-off at $T$ and provides an estimator with the risk within a logarithmic factor of the oracle risk. We emphasize that, in the present paper, we consider the true observational model with possibly nonequispaced observations which are available on a finite interval of length $T$ which appears in many different contexts, and account for the bias associated with this model (which is not present when $T\rightarrow\infty$). The study is motivated by perfusion imaging using a short injection of contrast agent, a procedure which is applied for medical assessment of micro-circulation within tissues such as cancerous tumors. Presence of a tuning parameter $a$ allows to choose the most advantageous time units, so that both the kernel and the unknown right hand side of the equation are well represented for the deconvolution. The methodology is illustrated by an extensive simulation study and a real data example which confirms that the proposed technique is fast, efficient, accurate, usable from a practical point of view and very competitive.Comment: 36 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1207.223

Targeting Oxidative Stress and Aberrant Critical Period Plasticity in the Developmental Trajectory to Schizophrenia

Schizophrenia is a neurodevelopmental disorder reflecting a convergence of genetic risk and early life stress. The slow progression to first psychotic episode represents both a window of vulnerability as well as opportunity for therapeutic intervention. Here, we consider recent neurobiological insight into the cellular and molecular components of developmental critical periods and their vulnerability to redox dysregulation. In particular, the consistent loss of parvalbumin-positive interneuron (PVI) function and their surrounding perineuronal nets (PNNs) as well as myelination in patient brains is consistent with a delayed or extended period of circuit instability. This linkage to critical period triggers (PVI) and brakes (PNN, myelin) implicates mistimed trajectories of brain development in mental illness. Strategically introduced antioxidant treatment or later reinforcement of molecular brakes may then offer a novel prophylactic psychiatr

Set shifting ability of rats perinatally exposed to bisphenol A and a high fat diet

Bisphenol-A (BPA) is an endocrine disruptor found ubiquitously in the environment. It has been shown to have a wide variety of effects on behavior and cognition as well as causing inflammation in the brain. Additionally, the traditional American diet is high fat, which also contributes to both physiological, behavioral and inflammation problems. Together, these two factors could exacerbate one another in the brain, which could lead to some cognitive impairment. In order to test this hypothesis, pregnant female rats consumed 0, 40, or 400 μg/kg of BPA daily and either a control (CON; 18.5% kcal) or a high-fat diet (HF, 45% kcal) during gestation. The corresponding dose of BPA was pipetted into male and female pups' mouths from postnatal days (PND) 1-10 while the dams remained on their respective diets. After PND 10, dams were placed on separate chow diet which was maintained for the remainder of the offspring's life. As adults (>PND 90), the perinatally exposed rats were tested on an extra-dimensional set-shifting task. A rotating plus maze with black/white and rough/smooth arms was used. Final analysis indicates that there were no significant treatment differences for the number of trials needed to reach criterion during the initial discrimination. Additionally, there were no significant effects of treatment for accuracy or perseveration during the extra-dimensional shift. There were significant 3-way interactions, one between dose and diet, and the other between dose and diet and block. However, post hoc analyses revealed no significant differences from control doses, only between doses of BPA. Finally, there was a significant sex difference between males and females in number of random errors made with females having more errors than males

Decreased Brain Levels of Vitamin B12 in Aging, Autism and Schizophrenia.

Many studies indicate a crucial role for the vitamin B12 and folate-dependent enzyme methionine synthase (MS) in brain development and function, but vitamin B12 status in the brain across the lifespan has not been previously investigated. Vitamin B12 (cobalamin, Cbl) exists in multiple forms, including methylcobalamin (MeCbl) and adenosylcobalamin (AdoCbl), serving as cofactors for MS and methylmalonylCoA mutase, respectively. We measured levels of five Cbl species in postmortem human frontal cortex of 43 control subjects, from 19 weeks of fetal development through 80 years of age, and 12 autistic and 9 schizophrenic subjects. Total Cbl was significantly lower in older control subjects (> 60 yrs of age), primarily reflecting a >10-fold age-dependent decline in the level of MeCbl. Levels of inactive cyanocobalamin (CNCbl) were remarkably higher in fetal brain samples. In both autistic and schizophrenic subjects MeCbl and AdoCbl levels were more than 3-fold lower than age-matched controls. In autistic subjects lower MeCbl was associated with decreased MS activity and elevated levels of its substrate homocysteine (HCY). Low levels of the antioxidant glutathione (GSH) have been linked to both autism and schizophrenia, and both total Cbl and MeCbl levels were decreased in glutamate-cysteine ligase modulatory subunit knockout (GCLM-KO) mice, which exhibit low GSH levels. Thus our findings reveal a previously unrecognized decrease in brain vitamin B12 status across the lifespan that may reflect an adaptation to increasing antioxidant demand, while accelerated deficits due to GSH deficiency may contribute to neurodevelopmental and neuropsychiatric disorders

Glutathione Deficit Affects the Integrity and Function of the Fimbria/Fornix and Anterior Commissure in Mice: Relevance for Schizophrenia.

Structural anomalies of white matter are found in various brain regions of patients with schizophrenia and bipolar and other psychiatric disorders, but the causes at the cellular and molecular levels remain unclear. Oxidative stress and redox dysregulation have been proposed to play a role in the pathophysiology of several psychiatric conditions, but their anatomical and functional consequences are poorly understood. The aim of this study was to investigate white matter throughout the brain in a preclinical model of redox dysregulation. In a mouse model with impaired glutathione synthesis (Gclm KO), a state-of-the-art multimodal magnetic resonance protocol at high field (14.1 T) was used to assess longitudinally the white matter structure, prefrontal neurochemical profile, and ventricular volume. Electrophysiological recordings in the abnormal white matter tracts identified by diffusion tensor imaging were performed to characterize the functional consequences of fractional anisotropy alterations. Structural alterations observed at peri-pubertal age and adulthood in Gclm KO mice were restricted to the anterior commissure and fornix-fimbria. Reduced fractional anisotropy in the anterior commissure (-7.5% ± 1.9, P<.01) and fornix-fimbria (-4.5% ± 1.3, P<.05) were accompanied by reduced conduction velocity in fast-conducting fibers of the posterior limb of the anterior commissure (-14.3% ± 5.1, P<.05) and slow-conducting fibers of the fornix-fimbria (-8.6% ± 2.6, P<.05). Ventricular enlargement was found at peri-puberty (+25% ± 8 P<.05) but not in adult Gclm KO mice. Glutathione deficit in Gclm KO mice affects ventricular size and the integrity of the fornix-fimbria and anterior commissure. This suggests that redox dysregulation could contribute during neurodevelopment to the impaired white matter and ventricle enlargement observed in schizophrenia and other psychiatric disorders

Impaired fornix-hippocampus integrity is linked to peripheral glutathione peroxidase in early psychosis.

Several lines of evidence implicate the fornix-hippocampus circuit in schizophrenia. In early-phase psychosis, this circuit has not been extensively investigated and the underlying mechanisms affecting the circuit are unknown. The hippocampus and fornix are vulnerable to oxidative stress at peripuberty in a glutathione (GSH)-deficient animal model. The purposes of the current study were to assess the integrity of the fornix-hippocampus circuit in early-psychosis patients (EP), and to study its relationship with peripheral redox markers. Diffusion spectrum imaging and T1-weighted magnetic resonance imaging (MRI) were used to assess the fornix and hippocampus in 42 EP patients compared with 42 gender- and age-matched healthy controls. Generalized fractional anisotropy (gFA) and volumetric properties were used to measure fornix and hippocampal integrity, respectively. Correlation analysis was used to quantify the relationship of gFA in the fornix and hippocampal volume, with blood GSH levels and glutathione peroxidase (GPx) activity. Patients compared with controls exhibited lower gFA in the fornix as well as smaller volume in the hippocampus. In EP, but not in controls, smaller hippocampal volume was associated with high GPx activity. Disruption of the fornix-hippocampus circuit is already present in the early stages of psychosis. Higher blood GPx activity is associated with smaller hippocampal volume, which may support a role of oxidative stress in disease mechanisms