Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Regularization of statistical inverse problems and the Bakushinskii veto

In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization.Comment: 20 page

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples

Anomalous zipping dynamics and forced polymer translocation

We investigate by Monte Carlo simulations the zipping and unzipping dynamics of two polymers connected by one end and subject to an attractive interaction between complementary monomers. In zipping, the polymers are quenched from a high temperature equilibrium configuration to a low temperature state, so that the two strands zip up by closing up a "Y"-fork. In unzipping, the polymers are brought from a low temperature double stranded configuration to high temperatures, so that the two strands separate. Simulations show that the unzipping time, $\tau_u$, scales as a function of the polymer length as $\tau_u \sim L$, while the zipping is characterized by anomalous dynamics $\tau_z \sim L^\alpha$ with $\alpha = 1.37(2)$. This exponent is in good agreement with simulation results and theoretical predictions for the scaling of the translocation time of a forced polymer passing through a narrow pore. We find that the exponent $\alpha$ is robust against variations of parameters and temperature, whereas the scaling of $\tau_z$ as a function of the driving force shows the existence of two different regimes: the weak forcing ($\tau_z \sim 1/F$) and strong forcing ($\tau_z$ independent of $F$) regimes. The crossover region is possibly characterized by a non-trivial scaling in $F$, matching the prediction of recent theories of polymer translocation. Although the geometrical setup is different, zipping and translocation share thus the same type of anomalous dynamics. Systems where this dynamics could be experimentally investigated are DNA (or RNA) hairpins: our results imply an anomalous dynamics for the hairpins closing times, but not for the opening times.Comment: 15 pages, 9 figure

Pre-existing autoimmunity is associated with increased severity of COVID-19: A retrospective cohort study using data from the National COVID Cohort Collaborative (N3C)

Identifying individuals with a higher risk of developing severe COVID-19 outcomes will inform targeted or more intensive clinical monitoring and management. To date, there is mixed evidence regarding the impact of pre-existing autoimmune disease (AID) diagnosis and/or immunosuppressant (IS) exposure on developing severe COVID-19 outcomes.A retrospective cohort of adults diagnosed with COVID-19 was created in the National COVID Cohort Collaborative enclave. Two outcomes, life-threatening disease, and hospitalization were evaluated by using logistic regression models with and without adjustment for demographics and comorbidities.Of the 2,453,799 adults diagnosed with COVID-19, 191,520 (7.81%) had a pre-existing AID diagnosis and 278,095 (11.33%) had a pre-existing IS exposure. Logistic regression models adjusted for demographics and comorbidities demonstrated that individuals with a pre-existing AID (OR = 1.13, 95% CI 1.09 - 1.17; P< 0.001), IS (OR= 1.27, 95% CI 1.24 - 1.30; P< 0.001), or both (OR = 1.35, 95% CI 1.29 - 1.40; P< 0.001) were more likely to have a life-threatening COVID-19 disease. These results were consistent when evaluating hospitalization. A sensitivity analysis evaluating specific IS revealed that TNF inhibitors were protective against life-threatening disease (OR = 0.80, 95% CI 0.66- 0.96; P=0.017) and hospitalization (OR = 0.80, 95% CI 0.73 - 0.89; P< 0.001).Patients with pre-existing AID, exposure to IS, or both are more likely to have a life-threatening disease or hospitalization. These patients may thus require tailored monitoring and preventative measures to minimize negative consequences of COVID-19

Neuropeptide S alters anxiety, but not depression-like behaviour in Flinders Sensitive Line rats: a genetic animal model of depression

Neuropeptide S (NPS) and its receptor (NPSR) have been implicated in the mediation of anxiolytic-like behaviour in rodents. However, little knowledge is available regarding the NPS system in depression-related behaviours, and whether NPS also exerts anxiolytic effects in an animal model of psychopathology. Therefore, the aim of this work was to characterize the effects of NPS on depression- and anxiety-related parameters, using male and female rats in a well-validated animal model of depression: the Flinders Sensitive Line (FSL), their controls, the Flinders Resistant Line (FRL), and Sprague–Dawley (SD) rats. We found that FSL showed greater immobility in the forced swim test (FST) than FRL, confirming their phenotype. However, NPS did not affect depression-related behaviour in any rat line. No significant differences in baseline anxiety levels between the FSL and FRL strains were observed, but FSL and FRL rats displayed less anxiety-like behaviour compared to SD rats. NPS decreased anxiety-like behaviour on the elevated plus-maze in all strains. The expression of the NPSR in the amygdala, periventricular hypothalamic nucleus, and hippocampus was equal in all male strains, although a trend towards reduced expression within the amygdala was observed in FSL rats compared to SD rats. In conclusion, NPS had a marked anxiolytic effect in FSL, FRL and SD rats, but did not modify the depression-related behaviour in any strain, in spite of the significant differences in innate level between the strains. These findings suggest that NPS specifically modifies anxiety behaviour but cannot overcome/reverse a genetically mediated depression phenotype

Expression Profiling of a Genetic Animal Model of Depression Reveals Novel Molecular Pathways Underlying Depressive-Like Behaviours

The Flinders model is a validated genetic rat model of depression that exhibits a number of behavioural, neurochemical and pharmacological features consistent with those observed in human depression.In this study we have used genome-wide microarray expression profiling of the hippocampus and prefrontal/frontal cortex of Flinders Depression Sensitive (FSL) and control Flinders Depression Resistant (FRL) lines to understand molecular basis for the differences between the two lines. We profiled two independent cohorts of Flinders animals derived from the same colony six months apart, each cohort statistically powered to allow independent as well as combined analysis. Using this approach, we were able to validate using real-time-PCR a core set of gene expression differences that showed statistical significance in each of the temporally distinct cohorts, representing consistently maintained features of the model. Small but statistically significant increases were confirmed for cholinergic (chrm2, chrna7) and serotonergic receptors (Htr1a, Htr2a) in FSL rats consistent with known neurochemical changes in the model. Much larger gene changes were validated in a number of novel genes as exemplified by TMEM176A, which showed 35-fold enrichment in the cortex and 30-fold enrichment in hippocampus of FRL animals relative to FSL.These data provide significant insights into the molecular differences underlying the Flinders model, and have potential relevance to broader depression research

All-In-One: Advanced preparation of Human Parenchymal and Non-Parenchymal Liver Cells

BACKGROUND & AIMS: Liver cells are key players in innate immunity. Thus, studying primary isolated liver cells is necessary for determining their role in liver physiology and pathophysiology. In particular, the quantity and quality of isolated cells are crucial to their function. Our aim was to isolate a large quantity of high-quality human parenchymal and non-parenchymal cells from a single liver specimen. METHODS: Hepatocytes, Kupffer cells, liver sinusoidal endothelial cells, and stellate cells were isolated from liver tissues by collagenase perfusion in combination with low-speed centrifugation, density gradient centrifugation, and magnetic-activated cell sorting. The purity and functionality of cultured cell populations were controlled by determining their morphology, discriminative cell marker expression, and functional activity. RESULTS: Cell preparation yielded the following cell counts per gram of liver tissue: 2.0+/-0.4x107 hepatocytes, 1.8+/-0.5x106 Kupffer cells, 4.3+/-1.9x105 liver sinusoidal endothelial cells, and 3.2+/-0.5x105 stellate cells. Hepatocytes were identified by albumin (95.5+/-1.7%) and exhibited time-dependent activity of cytochrome P450 enzymes. Kupffer cells expressed CD68 (94.5+/-1.2%) and exhibited phagocytic activity, as determined with 1mum latex beads. Endothelial cells were CD146+ (97.8+/-1.1%) and exhibited efficient uptake of acetylated low-density lipoprotein. Hepatic stellate cells were identified by the expression of alpha-smooth muscle actin (97.1+/-1.5%). These cells further exhibited retinol (vitamin A)-mediated autofluorescence. CONCLUSIONS: Our isolation procedure for primary parenchymal and non-parenchymal liver cells resulted in cell populations of high purity and quality, with retained physiological functionality in vitro. Thus, this system may provide a valuable tool for determining liver function and disease