Flexible Modeling of Diversity with Strongly Log-Concave Distributions

Strongly log-concave (SLC) distributions are a rich class of discrete probability distributions over subsets of some ground set. They are strictly more general than strongly Rayleigh (SR) distributions such as the well-known determinantal point process. While SR distributions offer elegant models of diversity, they lack an easy control over how they express diversity. We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance. We develop two fundamental tools needed to apply SLC distributions to learning and inference: sampling and mode finding. For sampling we develop an MCMC sampler and give theoretical mixing time bounds. For mode finding, we establish a weak log-submodularity property for SLC functions and derive optimization guarantees for a distorted greedy algorithm

Does chemical cross-linking with NHS esters reflect the chemical equilibrium of protein-protein noncovalent interactions in solution?

Chemical cross-linking in combination with mass spectrometry has emerged as a powerful tool to study noncovalent protein complexes. Nevertheless, there are still many questions to answer. Does the amount of detected cross-linked complex correlate with the amount of protein complex in solution? In which concentration and affinity range is specific cross-linking possible? To answer these questions, we performed systematic cross-linking studies with two complexes, using the N-hydroxysuccinimidyl ester disuccinimidyl suberate (DSS): (1) NCoA-1 and mutants of the interacting peptide STAT6Y, covering a KD range of 30 nM to >25 μM, and (2) α-thrombin and basic pancreatic trypsin inhibitor (BPTI), a system that shows a buffer-dependent KD value between 100 and 320 μM. Samples were analyzed by matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). For NCoA-1· STAT6Y, a good correlation between the amount of cross-linked species and the calculated fraction of complex present in solution was observed. Thus, chemical cross-linking in combination with MALDI-MS can be used to rank binding affinities. For the mid-affinity range up to about KD ≈ 25 μM, experiments with a nonbinding peptide and studies of the concentration dependence showed that only specific complexes undergo cross-linking with DSS. To study in which affinity range specific cross-linking can be applied, the weak α-thrombin · BPTI complex was investigated. We found that the detected complex is a nonspecifically cross-linked species. Consequently, based on the experimental approach used in this study, chemical cross-linking is not suitable for studying low-affinity complexes with KD ≫ 25 μ

Expressive Sign Equivariant Networks for Spectral Geometric Learning

Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector. However, we show that sign invariance is theoretically limited for tasks such as building orthogonally equivariant models and learning node positional encodings for link prediction in graphs. In this work, we demonstrate the benefits of sign equivariance for these tasks. To obtain these benefits, we develop novel sign equivariant neural network architectures. Our models are based on a new analytic characterization of sign equivariant polynomials and thus inherit provable expressiveness properties. Controlled synthetic experiments show that our networks can achieve the theoretically predicted benefits of sign equivariant models. Code is available at https://github.com/cptq/Sign-Equivariant-Nets.Comment: NeurIPS 2023 Spotligh

20 Minute Neighbourhoods in a Scottish Context

The Programme for Government 2020 commits the Scottish Government to working with local government and other partners to take forward ambitions for 20 minute neighbourhoods: Places that are designed so residents have the ability to meet the vast majority of their day-to-day needs within a 20 minute walk (approximately 800 metres) of their home; through access to safe walking and cycling routes, or by public transport. This projects supports this by: 1) Considering the ambition for 20 minute neighbourhoods in Scotland, taking account of the differing settlement patterns across the country, and to highlight interventions that would support delivery of the concept, supported by findings from the baseline analysis. 2) Analysing international evidence of the success of interventions to achieve these ambitions, including identifying specific success factors, place-making impacts, barriers to success, regulatory frameworks, funding mechanisms and stakeholder engagement and buy-in. It uses five dimensions to capture the features and infrastructure, and quality of services and experience that make up a 20 minute neighbourhood: Stewardship, Civic, Movement, Resources and Spaces. The baseline assessment has shown that communities across Scotland have the required services and infrastructure that would allow them to be 20 minute neighbourhoods. This is the case across both urban and rural settlement areas

Sign and Basis Invariant Networks for Spectral Graph Representation Learning

Many machine learning tasks involve processing eigenvectors derived from data. Especially valuable are Laplacian eigenvectors, which capture useful structural information about graphs and other geometric objects. However, ambiguities arise when computing eigenvectors: for each eigenvector $v$, the sign flipped $-v$ is also an eigenvector. More generally, higher dimensional eigenspaces contain infinitely many choices of basis eigenvectors. These ambiguities make it a challenge to process eigenvectors and eigenspaces in a consistent way. In this work we introduce SignNet and BasisNet -- new neural architectures that are invariant to all requisite symmetries and hence process collections of eigenspaces in a principled manner. Our networks are universal, i.e., they can approximate any continuous function of eigenvectors with the proper invariances. They are also theoretically strong for graph representation learning -- they can approximate any spectral graph convolution, can compute spectral invariants that go beyond message passing neural networks, and can provably simulate previously proposed graph positional encodings. Experiments show the strength of our networks for molecular graph regression, learning expressive graph representations, and learning implicit neural representations on triangle meshes. Our code is available at https://github.com/cptq/SignNet-BasisNet .Comment: 35 page

Modeling Multi-Wavelength Stellar Astrometry. I. SIM Lite Observations of Interacting Binaries

Interacting binaries consist of a secondary star which fills or is very close to filling its Roche lobe, resulting in accretion onto the primary star, which is often, but not always, a compact object. In many cases, the primary star, secondary star, and the accretion disk can all be significant sources of luminosity. SIM Lite will only measure the photocenter of an astrometric target, and thus determining the true astrometric orbits of such systems will be difficult. We have modified the Eclipsing Light Curve code (Orosz & Hauschildt 2000) to allow us to model the flux-weighted reflex motions of interacting binaries, in a code we call REFLUX. This code gives us sufficient flexibility to investigate nearly every configuration of interacting binary. We find that SIM Lite will be able to determine astrometric orbits for all sufficiently bright interacting binaries where the primary or secondary star dominates the luminosity. For systems where there are multiple components that comprise the spectrum in the optical bandpass accessible to SIM Lite, we find it is possible to obtain absolute masses for both components, although multi-wavelength photometry will be required to disentangle the multiple components. In all cases, SIM Lite will at least yield accurate inclinations, and provide valuable information that will allow us to begin to understand the complex evolution of mass-transferring binaries. It is critical that SIM Lite maintains a multi-wavelength capability to allow for the proper deconvolution of the astrometric orbits in multi-component systems.Comment: 12 pages, 6 figures, 6 tables. Accepted for publication in the Astrophysical Journa

Optical and UV Light Curves of the Accretion Disk Corona Source 4U 1822-371

The eclipsing low-mass X-ray binary 4U is the prototypical accretion disk corona (ADC) system. We have obtained new time-resolved UV spectrograms of 4U with the Hubble Space Telescope and new V- and J-band light curves with the 1.3-m SMARTS telescope at CTIO. We present an updated ephemeris for the times of the optical/UV eclipses. Model light curves do not give acceptable fits to the UV eclipses unless the models include an optically-thick ADC.Comment: 3 pages, 2 figures, from A Population Explosion: The Nature and Evolution of X-ray Binaries in Diverse Environment

Project finance as a driver of economic growth in low-income countries

This study investigates the role of project finance as a driver of economic growth. We hypothesize that project finance is beneficial to the least developed economies as it is able to compensate for a lack of domestic financial development. The contractual structure unique to project finance leads to better investment management and governance. Investigating 90 countries from 1991 to 2005, we find support for our hypothesis. Results show that project finance fosters economic growth and that its effect is strongest in low-income countries, where financial development and governance is weakest