Differentially private inference via noisy optimization

We propose a general optimization-based framework for computing differentially private M-estimators and a new method for constructing differentially private confidence regions. Firstly, we show that robust statistics can be used in conjunction with noisy gradient descent or noisy Newton methods in order to obtain optimal private estimators with global linear or quadratic convergence, respectively. We establish local and global convergence guarantees, under both local strong convexity and self-concordance, showing that our private estimators converge with high probability to a nearly optimal neighborhood of the non-private M-estimators. Secondly, we tackle the problem of parametric inference by constructing differentially private estimators of the asymptotic variance of our private M-estimators. This naturally leads to approximate pivotal statistics for constructing confidence regions and conducting hypothesis testing. We demonstrate the effectiveness of a bias correction that leads to enhanced small-sample empirical performance in simulations. We illustrate the benefits of our methods in several numerical examples

A Dynamical Systems Hypothesis of Schizophrenia

We propose a top-down approach to the symptoms of schizophrenia based on a statistical dynamical framework. We show that a reduced depth in the basins of attraction of cortical attractor states destabilizes the activity at the network level due to the constant statistical fluctuations caused by the stochastic spiking of neurons. In integrate-and-fire network simulations, a decrease in the NMDA receptor conductances, which reduces the depth of the attractor basins, decreases the stability of short-term memory states and increases distractibility. The cognitive symptoms of schizophrenia such as distractibility, working memory deficits, or poor attention could be caused by this instability of attractor states in prefrontal cortical networks. Lower firing rates are also produced, and in the orbitofrontal and anterior cingulate cortex could account for the negative symptoms, including a reduction of emotions. Decreasing the GABA as well as the NMDA conductances produces not only switches between the attractor states, but also jumps from spontaneous activity into one of the attractors. We relate this to the positive symptoms of schizophrenia, including delusions, paranoia, and hallucinations, which may arise because the basins of attraction are shallow and there is instability in temporal lobe semantic memory networks, leading thoughts to move too freely round the attractor energy landscape

Bethe-Ansatz density-functional theory of ultracold repulsive fermions in one-dimensional optical lattices

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions.Comment: 14 pages, 11 figures, 1 table, submitte

Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near $3\times 10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

The protein–DNA contacts in RutR·carAB operator complexes

Pyrimidine-specific regulation of the upstream carP1 promoter of the carbamoylphosphate synthase operon of Escherichia coli requires numerous trans-acting factors: the allosteric transcription regulator RutR, the nucleoid-associated protein integration host factor, and the trigger enzymes aminopeptidase A and PyrH (UMP-kinase). RutR, a TetR family member, binds far upstream of carP1. Here, we establish a high-resolution contact map of RutR•carP1 complexes for backbone and base-specific contacts, analyze DNA bending, determine the DNA sequence specificity of RutR binding by saturation mutagenesis, demonstrate that uracil but not thymine is the physiologically relevant ligand that inhibits the DNA binding capacity of RutR and build a model of the RutR·operator DNA complex based on the crystal structures of RutR and of the DNA-bound family member QacR. Finally, we test the validity of this model with site-directed mutagenesis of the helix–turn–helix DNA binding motif and in vitro binding studies with the cognate purified mutant RutR proteins

Integrative genomic analyses in adipocytes implicate DNA methylation in human obesity and diabetes

DNA methylation variations are prevalent in human obesity but evidence of a causative role in disease pathogenesis is limited. Here, we combine epigenome-wide association and integrative genomics to investigate the impact of adipocyte DNA methylation variations in human obesity. We discover extensive DNA methylation changes that are robustly associated with obesity (N = 190 samples, 691 loci in subcutaneous and 173 loci in visceral adipocytes, P 500 target genes, and identify putative methylation-transcription factor interactions. Through Mendelian Randomisation, we infer causal effects of methylation on obesity and obesity-induced metabolic disturbances at 59 independent loci. Targeted methylation sequencing, CRISPR-activation and gene silencing in adipocytes, further identifies regional methylation variations, underlying regulatory elements and novel cellular metabolic effects. Our results indicate DNA methylation is an important determinant of human obesity and its metabolic complications, and reveal mechanisms through which altered methylation may impact adipocyte functions