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Ligand-receptor interactions are fundamental to many biological processes. For example in antibody-based immunotherapies, the dynamics of an antibody binding with its target antigen directly influence the potency and efficacy of monoclonal antibody (mAb) therapies. In this paper, we present an asymptotic analysis of an ordinary differential equation (ODE) model of bivalent antibody-antigen binding in the context of mAb cancer therapies, highlighting the added complexity associated with bivalency of the antibody. To understand what drives the complex temporal dynamics of bivalent antibody-antigen binding, we construct asymptotic approximations to the model's solutions at different timescales and antibody concentrations that are in good agreement with numerical simulations of the full model. We show how the dynamics differ between two scenarios; a region where unbound antigens are abundant, and one where the number of unbound antigens is small such that the dominant balance within the model equations changes. Of particular importance to the potency and efficacy of mAb treatments are the values of quantities such as antigen occupancy and bound antibody number. We use the results of our asymptotic analysis to approximate the long-time values of these quantities that could be combined with experimental data to facilitate parameter estimation.

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically to the estimation of intrinsic dimension of data sets. The idea is to learn a representation of each data point as a quantum state, encoding both local properties of the point as well as its relation with the entire data. Inspired by ideas from quantum geometry, we then construct from the quantum states a point cloud equipped with a quantum metric. The metric exhibits a spectral gap whose location corresponds to the intrinsic dimension of the data. The proposed estimator is based on the detection of this spectral gap. When tested on synthetic manifold benchmarks, our estimates are shown to be robust with respect to the introduction of point-wise Gaussian noise. This is in contrast to current state-of-the-art estimators, which tend to attribute artificial ``shadow dimensions'' to noise artifacts, leading to overestimates. This is a significant advantage when dealing with real data sets, which are inevitably affected by unknown levels of noise. We show the applicability and robustness of our method on real data, by testing it on the ISOMAP face database, MNIST, and the Wisconsin Breast Cancer Dataset.

Motivated by the Gottesman-Knill theorem, we present a detailed study of the quantum complexity of $p$-shell and $sd$-shell nuclei. Valence-space nuclear shell-model wavefunctions generated by the BIGSTICK code are mapped to qubit registers using the Jordan-Wigner mapping (12 qubits for the $p$-shell and 24 qubits for the $sd$-shell), from which measures of the many-body entanglement ($n$-tangles) and magic (non-stabilizerness) are determined. While exact evaluations of these measures are possible for nuclei with a modest number of active nucleons, Monte Carlo simulations are required for the more complex nuclei. The broadly-applicable Pauli-String $IZ$ exact (PSIZe-) MCMC technique is introduced to accelerate the evaluation of measures of magic in deformed nuclei (with hierarchical wavefunctions), by factors of $\sim 8$ for some nuclei. Significant multi-nucleon entanglement is found in the $sd$-shell, dominated by proton-neutron configurations, along with significant measures of magic. This is evident not only for the deformed states, but also for nuclei on the path to instability via regions of shape coexistence and level inversion. These results indicate that quantum-computing resources will accelerate precision simulations of such nuclei and beyond., Comment: 36 pages, 13 figures

These notes have been adapted from an undergraduate course given by Professor Alan James at the University of Adelaide from around 1965 and onwards. This adaption has put a focus on the definition of projection matrices and the sweep operator. These devices were at the heart of the development of the statistical package Genstat which initially focussed on the analysis of variance using the sweep operator. The notes provide an algebraic background to the sweep operator which has since been used to effect in a number of experimental design settings., Comment: 53 pages, 3 figures

Detection limits (DLs), where a variable is unable to be measured outside of a certain range, are common in research. Most approaches to handle DLs in the response variable implicitly make parametric assumptions on the distribution of data outside DLs. We propose a new approach to deal with DLs based on a widely used ordinal regression model, the cumulative probability model (CPM). The CPM is a type of semiparametric linear transformation model. CPMs are rank-based and can handle mixed distributions of continuous and discrete outcome variables. These features are key for analyzing data with DLs because while observations inside DLs are typically continuous, those outside DLs are censored and generally put into discrete categories. With a single lower DL, the CPM assigns values below the DL as having the lowest rank. When there are multiple DLs, the CPM likelihood can be modified to appropriately distribute probability mass. We demonstrate the use of CPMs with simulations and two HIV data examples. The first example models a biomarker in which 15% of observations are below a DL. The second uses multi-cohort data to model viral load, where approximately 55% of observations are outside DLs which vary across sites and over time.

If ocean-derived materials are present at Europa’s surface, they would represent accessible records of ocean chemistry and habitability, but such materials would be further processed by the moon’s harsh radiation environment. In this study, saturated fatty acids were precipitated onto a Europa-relevant hydrated magnesium sulfate and exposed to gamma radiation doses up to 2 MGy at -196° C. Alkane chains, with carbon numbers one less than those of the starting fatty acids, were the most abundant radiolysis products in solvent and thermal extracts analyzed by gas chromatography mass spectrometry. Detections of monounsaturated fatty acids and combined radiolysis products were attributed to the experiment’s Europa-like parameters. Additionally, elevated concentrations of shorter-chain saturated fatty acids suggest that gamma radiation induced charge remote fragmentation of the alkyl chains of some starting fatty acids under these experimental conditions. Quantitation of fatty acid concentrations in the irradiated samples enabled the calculation of a radiolysis constant that indicated exposure to a 5 MGy dose of gamma radiation would have resulted in a ~90% loss of the initial fatty acid population. The samples were further studied by Raman spectroscopy and laser desorption and ionization mass spectrometry, which characterized the distribution of fatty acids and their radiolysis products on sulfate surfaces. The substantial loss of starting fatty acids typically seen with increasing radiation dose, along with the remarkable diversity of radiolysis products identified, suggest that the detection of fatty acids in irradiated sulfate deposits on Europa will be challenged by rapid destruction of any initial fatty acid populations and scrambling of their residual signals by a myriad of organic radiolysis products. If missions to Europa encounter sulfate deposits, targeting minimally irradiated units may still enable the detection of surviving fatty acid signatures that could inform about Europa’s subsurface chemistry and habitability.

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of strongly correlated molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods -- including heat-bath CI, the density matrix renormalization group approach, and FCIQMC -- to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV., Comment: 16 pages, 5 figures, 3 tables

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that the HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant error. The ability of HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems which require a larger active space than possible with complete active space self-consistent field (CASSCF). Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet-triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.

Ordinal cumulative probability models (CPMs) -- also known as cumulative link models -- such as the proportional odds regression model are typically used for discrete ordered outcomes, but can accommodate both continuous and mixed discrete/continuous outcomes since these are also ordered. Recent papers describe ordinal CPMs in this setting using non-parametric maximum likelihood estimation. We formulate a Bayesian CPM for continuous or mixed outcome data. Bayesian CPMs inherit many of the benefits of frequentist CPMs and have advantages with regard to interpretation, flexibility, and exact inference (within simulation error) for parameters and functions of parameters. We explore characteristics of the Bayesian CPM through simulations and a case study using HIV biomarker data. In addition, we provide the package 'bayesCPM' which implements Bayesian CPM models using the R interface to the Stan probabilistic programing language. The Bayesian CPM for continuous outcomes can be implemented with only minor modifications to the prior specification and, despite some limitations, has generally good statistical performance with moderate or large sample sizes., Comment: 30 pages, 25 figures