Differentially Private Nonparametric Hypothesis Testing

Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take as our starting point traditional nonparametric tests, which require no distributional assumption (e.g., normality) about the data distribution. We present private analogues of the Kruskal-Wallis, Mann-Whitney, and Wilcoxon signed-rank tests, as well as the parametric one-sample t-test. These tests use novel test statistics developed specifically for the private setting. We compare our tests to prior work, both on parametric and nonparametric tests. We find that in all cases our new nonparametric tests achieve large improvements in statistical power, even when the assumptions of parametric tests are met

A Low Jitter Analog Circuit for Precisely Correcting Timing Skews in Time Interleaved Analog-to-Digital Converters

Time-interleaved analog-to-digital converters are an attractive architecture for achieving a high speed, high resolution ADC in a power efficient manner. However, due to process and manufacturing variations, timing skews occur between the sampling clocks of the sub ADCs within the TI-ADC. These timing skews compromise the spurious free dynamic range of the converter. In addition, jitter on the sampling clocks, degrades the signal-to-noise ratio of the TI-ADC. Therefore, in order to maintain an acceptable spurious free dynamic range and signal to noise ratio, it is necessary to correct the timing skews while adding minimal jitter. Two analog-based architectures for correcting timing skews were investigated, with one being selected for implementation. The selected architecture and additional test circuitry were designed and fabricated in a 0.18µm CMOS process and tested using a 125 MSPS 16 bit ADC. The circuit achieves a correction precision on the order of 10’s of femtoseconds for timing skews as large as approximately 180 picoseconds, while adding less than 200 femtoseconds of rms jitter

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability properties, response to referees tactfully remove

Photoionization from the ground and excited vibrational states of H+2 and its deuterated isotopologues

Photoionization cross sections and rate coefficients have been calculated for all bound vibrational levels of the 1s$\sigma_{\mathrm{g}}$ state of H$_{2}^{+}$, HD$^{+}$, and D$_{2}^{+}$. The Born-Oppenheimer approximation is employed in our calculation of vibrationally-resolved photoionization cross sections. Vibrationally-resolved and local thermal equilibrium photoionization rate coefficients are presented for photon temperatures less than $50\,000$ K and are found to be several orders of magnitude larger than previous results in the literature. Analytic fits for the vibrationally-resolved and local thermal equilibrium photoionization rate coefficients are provided. Near threshold oscillations in the vibrationall-resolved photoionization are observed. A benchmark set of photoionization cross sections are presented. Fixed-nuclei photoionization cross sections are calculated using two-center true continuum wave functions and are verified by comparison with previous calculations and are found to be in excellent agreement in all cases. Data files for our set of benchmark cross sections, rate coefficients, and fitting parameters for H$_{2}^{+}$, HD$^{+}$, and D$_{2}^{+}$ are available on Zenodo under an open-source Creative Commons Attribution license: https://doi.org/10.5281/zenodo.8304060 .Comment: Accepted in ApJ

Anomalous stress relaxation in random macromolecular networks

Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential long-time decay. The divergence of the static shear viscosity is governed by the critical exponent $k=\phi -\beta$, where $\phi$ is the (first) crossover exponent of random resistor networks, and $\beta$ is the critical exponent for the gel fraction. We also derive new results on the behaviour of normal stress coefficients.Comment: 13 pages, 6 figures; contribution to the proceedings of the Minerva International Workshop on Frontiers In The Physics Of Complex Systems (25-28 March 2001) - to appear in a special issue of Physica

Characterizing and predicting the functional and conformational diversity of seven-transmembrane proteins

The activation of seven-transmembrane receptors (7TMRs) allows cells to sense their environment and convert extracellular signals (like hormone binding) into intracellular signals (through G protein-coupled and/or β arrestin-coupled pathways). A single 7TMR is capable of transducing a wide spectrum of physiological responses inside a cell by coupling to these pathways. This intracellular pleiotropic action is enabled by multiple conformations exhibited by these receptors. Developments in membrane protein structure determination technologies have led to a rapid increase in crystal structures for many 7TMRs. Majority of these receptors have been crystallized in their inactive conformation and, for some, one of the many active conformations has also been crystallized. Given the topological constraints of a lipid bilayer that results in a single fold of seven almost parallel TM helices connected by mostly unstructured loops, these structures exhibit a diversity of conformations not only across the receptors but also across the different functional forms for receptors with structures for one of the functionally active conformations. Here we present a method to characterize this conformational diversity in terms of transmembrane helix topology (TMHTOP) parameters and how to use these helix orientation parameters to predict functionally-distinct multiple conformations for these receptors. The TMHTOP parameters enable a quantification of the structural changes that underlie 7TMR activation and also sheds a unique mechanistic light on the pleiotropic nature of these receptors. It provides a common language to describe the 7TMR activation mechanisms as well as differences across many receptors in terms of visually intuitive structural parameters. Protein structure prediction methods can use these parameters to describe 7TMR conformational ensembles, which coupled to experimental data can be used to develop testable hypotheses for the structural basis of 7TMR functions

The multiple potential biomarkers for predicting immunotherapy response : finding the needle in the haystack

Immune checkpoint inhibitors (ICIs) are being increasingly utilised in a variety of advanced malignancies. Despite promising outcomes in certain patients, the majority will not derive benefit and are at risk of potentially serious immune-related adverse events (irAEs). The development of predictive biomarkers is therefore critical to personalise treatments and improve outcomes. A number of biomarkers have shown promising results, including from tumour (programmed cell death ligand 1 (PD-L1), tumour mutational burden (TMB), stimulator of interferon genes (STING) and apoptosis-associated speck-like protein containing a CARD (ASC)), from blood (peripheral blood mononuclear cells (PBMCs), circulating tumour DNA (ctDNA), exosomes, cytokines and metal chelators) and finally the microbiome