Learning to discover: expressive Gaussian mixture models for multi-dimensional simulation and parameter inference in the physical sciences

We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable spectra are deformed by hypothesis variations, and is made more expressive by projecting data onto a configurable latent space. It may be used as a statistical model for scientific discovery in interpreting experimental observations, for example when constraining the parameters of a physical model or tuning simulation parameters according to calibration data. The model may also be sampled for use within a Monte Carlo simulation chain, or used to estimate likelihood ratios for event classification. The method is demonstrated on simulated high-energy particle physics data considering the anomalous electroweak production of a $Z$ boson in association with a dijet system at the Large Hadron Collider, and the accuracy of inference is tested using a realistic toy example. The developed methods are domain agnostic; they may be used within any field to perform simulation or inference where a dataset consisting of many real-valued observables has conditional dependence on external parameters.

Genetic Co-Occurrence Network across Sequenced Microbes

The phenotype of any organism on earth is, in large part, the consequence of interplay between numerous gene products encoded in the genome, and such interplay between gene products affects the evolutionary fate of the genome itself through the resulting phenotype. In this regard, contemporary genomes can be used as molecular records that reveal associations of various genes working in their natural lifestyles. By analyzing thousands of orthologs across ~600 bacterial species, we constructed a map of gene-gene co-occurrence across much of the sequenced biome. If genes preferentially co-occur in the same organisms, they were called herein correlogs; in the opposite case, called anti-correlogs. To quantify correlogy and anti-correlogy, we alleviated the contribution of indirect correlations between genes by adapting ideas developed for reverse engineering of transcriptional regulatory networks. Resultant correlogous associations are highly enriched for physically interacting proteins and for co-expressed transcripts, clearly differentiating a subgroup of functionally-obligatory protein interactions from conditional or transient interactions. Other biochemical and phylogenetic properties were also found to be reflected in correlogous and anti-correlogous relationships. Additionally, our study elucidates the global organization of the gene association map, in which various modules of correlogous genes are strikingly interconnected by anti-correlogous crosstalk between the modules. We then demonstrate the effectiveness of such associations along different domains of life and environmental microbial communities. These phylogenetic profiling approaches infer functional coupling of genes regardless of mechanistic details, and may be useful to guide exogenous gene import in synthetic biology.

Macroscopic Kinetic Effect of Cell-to-Cell Variation in Biochemical Reactions

Genetically identical cells under the same environmental conditions can show strong variations in protein copy numbers due to inherently stochastic events in individual cells. We here develop a theoretical framework to address how variations in enzyme abundance affect the collective kinetics of metabolic reactions observed within a population of cells. Kinetic parameters measured at the cell population level are shown to be systematically deviated from those of single cells, even within populations of homogeneous parameters. Because of these considerations, Michaelis-Menten kinetics can even be inappropriate to apply at the population level. Our findings elucidate a novel origin of discrepancy between in vivo and in vitro kinetics, and offer potential utility for analysis of single-cell metabolomic data.

The elastic constants of MgSiO3 perovskite at pressures and temperatures of the Earths mantle

The temperature anomalies in the Earths mantle associated with thermal convection1 can be inferred from seismic tomography, provided that the elastic properties of mantle minerals are known as a function of temperature at mantle pressures. At present, however, such information is difficult to obtain directly through laboratory experiments. We have therefore taken advantage of recent advances in computer technology, and have performed finite-temperature ab initio molecular dynamics simulations of the elastic properties of MgSiO3 perovskite, the major mineral of the lower mantle, at relevant thermodynamic conditions. When combined with the results from tomographic images of the mantle, our results indicate that the lower mantle is either significantly anelastic or compositionally heterogeneous on large scales. We found the temperature contrast between the coldest and hottest regions of the mantle, at a given depth, to be about 800K at 1000 km, 1500K at 2000 km, and possibly over 2000K at the core-mantle boundary.

Proposal for generating and detecting multi-qubit GHZ states in circuit QED

We propose methods for the preparation and entanglement detection of multi-qubit GHZ states in circuit quantum electrodynamics. Using quantum trajectory simulations appropriate for the situation of a weak continuous measurement, we show that the joint dispersive readout of several qubits can be utilized for the probabilistic production of high-fidelity GHZ states. When employing a nonlinear filter on the recorded homodyne signal, the selected states are found to exhibit values of the Bell-Mermin operator exceeding 2 under realistic conditions. We discuss the potential of the dispersive readout to demonstrate a violation of the Mermin bound, and present a measurement scheme avoiding the necessity for full detector tomography.

Phase Lags in the Optical-Infrared Light Curves of AGB Stars

To search for phase lags in the optical-infrared light curves of asymptotic giant branch stars, we have compared infrared data from the COBE DIRBE satellite with optical light curves from the AAVSO and other sources. We found 17 examples of phase lags in the time of maximum in the infrared vs. that in the optical, and 4 stars with no observed lags. There is a clear difference between the Mira variables and the semi-regulars in the sample, with the maximum in the optical preceding that in the near-infrared in the Miras, while in most of the semi-regulars no lags are observed. Comparison to published theoretical models indicates that the phase lags in the Miras are due to strong titanium oxide absorption in the visual at stellar maximum, and suggests that Miras pulsate in the fundamental mode, while at least some semi-regulars are first overtone pulsators. There is a clear optical-near-infrared phase lag in the carbon-rich Mira V CrB; this is likely due to C2 and CN absorption variations in the optical.

Classification of 2.4-45.2 Micron Spectra from the ISO Short Wavelength Spectrometer

The Infrared Space Observatory observed over 900 objects with the Short Wavelength Spectrometer in full-grating-scan mode (2.4-45.2 micron). We have developed a comprehensive system of spectral classification using these data. Sources are assigned to groups based on the overall shape of the spectral energy distribution (SED). The groups include naked stars, dusty stars, warm dust shells, cool dust shells, very red sources, and sources with emission lines but no detected continuum. These groups are further divided into subgroups based on spectral features that shape the SED such as silicate or carbon-rich dust emission, silicate absorption, ice absorption, and fine-structure or recombination lines. Caveats regarding the data and data reduction, and biases intrinsic to the database, are discussed. We also examine how the subgroups relate to the evolution of sources to and from the main sequence and how this classification scheme relates to previous systems.

Artifacts at 4.5 and 8.0 um in Short Wavelength Spectra from the Infrared Space Observatory

Spectra from the Short Wavelength Spectrometer (SWS) on ISO exhibit artifacts at 4.5 and 8 um. These artifacts appear in spectra from a recent data release, OLP 10.0, as spurious broad emission features in the spectra of stars earlier than ~F0, such as alpha CMa. Comparison of absolutely calibrated spectra of standard stars to corresponding spectra from the SWS reveals that these artifacts result from an underestimation of the strength of the CO and SiO molecular bands in the spectra of sources used as calibrators by the SWS. Although OLP 10.0 was intended to be the final data release, these findings have led to an additional release addressing this issue, OLP 10.1, which corrects the artifacts.

Complementary approaches to the ab initio calculation of melting properties

Several research groups have recently reported {em ab initio} calculations of the melting properties of metals based on density functional theory, but there have been unexpectedly large disagreements between results obtained by different approaches. We analyze the relations between the two main approaches, based on calculation of the free energies of solid and liquid and on direct simulation of the two coexisting phases. Although both approaches rely on the use of classical reference systems consisting of parameterized empirical interaction models, we point out that in the free energy approach the final results are independent of the reference system, whereas in the current form of the coexistence approach they depend on it. We present a scheme for correcting the predictions of the coexistence approach for differences between the reference and {em ab initio} systems. To illustrate the practical operation of the scheme, we present calculations of the high-pressure melting properties of iron using the corrected coexistence approach, which agree closely with earlier results from the free energy approach. A quantitative assessment is also given of finite-size errors, which we show can be reduced to a negligible size.

Ab-initio chemical potentials of solid and liquid solutions and the chemistry of the Earths core

A general set of methods is presented for calculating chemical potentials in solid and liquid mixtures using {em ab initio} techniques based on density functional theory (DFT). The methods are designed to give an {em ab initio} approach to treating chemical equilibrium between coexisting solid and liquid solutions, and particularly the partitioning ratio of solutes between such solutions. For the liquid phase, the methods are based on the general technique of thermodynamic integration, applied to calculate the change of free energy associated with the continuous interconversion of solvent and solute atoms, the required thermal averages being computed by DFT molecular dynamics simulation. For the solid phase, free energies and hence chemical potentials are obtained using DFT calculation of vibrational frequencies of systems containing substitutional solute atoms, with anharmonic contributions calculated, where needed, by thermodynamic integration. The practical use of the methods is illustrated by applying them to study chemical equilibrium between the outer liquid and inner solid parts of the Earths core, modelled as solutions of S, Si and O in Fe. The calculations place strong constraints on the chemical composition of the core, and allow an estimate of the temperature at the inner-core/outer-core boundary.