Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations

We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of two-dimensional hard-disk and three-dimensional hard-sphere systems as well as liquid-gas phase separation in a patchy colloid model. As we demonstrate, PCA autonomously discovers order-parameter-like quantities that report on phase transitions, mitigating the need for a priori construction or identification of a suitable order parameter--thus streamlining the routine analysis of phase behavior. In a companion paper, we further develop the method established here to explore the detection of phase transitions in various model systems controlled by compositional demixing, liquid crystalline ordering, and non-equilibrium active forces

Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to study 1) the nonequilibrium random organization (RandOrg) model that exhibits a phase transition from quiescent to steady-state behavior as a function of density, 2) orientationally and positionally driven equilibrium phase transitions for hard ellipses, and 3) compositionally driven demixing transitions in the non-additive binary Widom-Rowlinson mixture

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Dihydropyrimidine-thiones and clioquinol synergize to target beta-amyloid cellular pathologies through a metal-dependent mechanism

The lack of therapies for neurodegenerative diseases arises from our incomplete understanding of their underlying cellular toxicities and the limited number of predictive model systems. It is critical that we develop approaches to identify novel targets and lead compounds. Here, a phenotypic screen of yeast proteinopathy models identified dihydropyrimidine-thiones (DHPM-thiones) that selectively rescued the toxicity caused by β-amyloid (Aβ), the peptide implicated in Alzheimer’s disease. Rescue of Aβ toxicity by DHPM-thiones occurred through a metal-dependent mechanism of action. The bioactivity was distinct, however, from that of the 8-hydroxyquinoline clioquinol (CQ). These structurally dissimilar compounds strongly synergized at concentrations otherwise not competent to reduce toxicity. Cotreatment ameliorated Aβ toxicity by reducing Aβ levels and restoring functional vesicle trafficking. Notably, these low doses significantly reduced deleterious off-target effects caused by CQ on mitochondria at higher concentrations. Both single and combinatorial treatments also reduced death of neurons expressing Aβ in a nematode, indicating that DHPM-thiones target a conserved protective mechanism. Furthermore, this conserved activity suggests that expression of the Aβ peptide causes similar cellular pathologies from yeast to neurons. Our identification of a new cytoprotective scaffold that requires metal-binding underscores the critical role of metal phenomenology in mediating Aβ toxicity. Additionally, our findings demonstrate the valuable potential of synergistic compounds to enhance on-target activities, while mitigating deleterious off-target effects. The identification and prosecution of synergistic compounds could prove useful for developing AD therapeutics where combination therapies may be required to antagonize diverse pathologies.D.F.T was funded by NRSA Fellowship NIH 5F32NS061419. D.F.T. and S.L. were supported by WIBR funds in support of research on Regenerative Disease, the Picower/JPB Foundation, and the Edward N. and Della L. Thome Foundation. G.A.C. and S.L. were funded by a Howard Hughes Medical Institute (HHMI) Collaborative Innovation Award. L.E.B., R.T., and S.E.S. were funded by NIH GM086180, NIH GM067041, and NIH GM111625. (5F32NS061419 - NRSA Fellowship NIH; WIBR funds in support of research on Regenerative Disease; Picower/JPB Foundation; Edward N. and Della L. Thome Foundation; Howard Hughes Medical Institute (HHMI) Collaborative Innovation Award; GM086180 - NIH; NIH GM067041 - NIH; NIH GM111625 - NIH)https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5705239/Accepted manuscrip

Head--on Collision of Two Unequal Mass Black Holes

We present results from the first fully nonlinear numerical calculations of the head--on collision of two unequal mass black holes. Selected waveforms of the most dominant l=2, 3 and 4 quasinormal modes are shown, as are the total radiated energies and recoil velocities for a range of mass ratios and initial separations. Our results validate the close and distant separation limit perturbation studies, and suggest that the head--on collision scenario is not likely to produce an astrophysically significant recoil effect.Comment: 5 pages, 3 figure

Conservative formulations of general relativistic kinetic theory

Experience with core-collapse supernova simulations shows that accurate accounting of total particle number and 4-momentum can be a challenge for computational radiative transfer. This accurate accounting would be facilitated by the use of particle number and 4-momentum transport equations that allow transparent conversion between volume and surface integrals in both configuration and momentum space. Such conservative formulations of general relativistic kinetic theory in multiple spatial dimensions are presented in this paper, and their relevance to core-collapse supernova simulations is described.Comment: 48 page

Crayfish feeding preferences for fresh water macrophytes: The influence of plant structure and chemistry

The omnivorous crayfish Procambarus clarkii fed selectively on several species of macrophytes, preferring delicate fresh plants that had filamentous or finely-branched architectures. When the macrophytes were dried, powdered, and reconstituted into an alginate gel (thus eliminating among-species differences in physical characteristics). crayfish preferences were altered; previously tough plants that were high in nitrogen and protein were preferred over previously delicate plants that were low in nitrogen and protein. Even though plant structure influences feeding decision of crayfish, the structurally identical macrophyte gels were fed upon differently, demonstrating that nonstructural traits are important feeding determinants. However, plant tissue constituents such as nitrogen, protein, phenolics, lignin, cellulose, or ash were not significantly con-elated with feeding preferences. Two high-nitrogen plants that were avoided by crayfish as fresh and as reconstituted tissue (Nuphar luteum macrophyllum and Alternanthera philoxeroides) possessed extracts that reduced crayfish feeding in laboratory assays, demonstrating that macrophyte metabolites can deter some herbivores. As is often observed with large generalist herbivores and omnivores in terrestrial and marine systems, the freshwater crayfish made feeding decisions based upon multiple plant cues (structure, nutrition, chemical defenses)

Bulk gravitons from a cosmological brane

We investigate the emission of gravitons by a cosmological brane into an Anti de Sitter five-dimensional bulk spacetime. We focus on the distribution of gravitons in the bulk and the associated production of `dark radiation' in this process. In order to evaluate precisely the amount of dark radiation in the late low-energy regime, corresponding to standard cosmology, we study numerically the emission, propagation and bouncing off the brane of bulk gravitons.Comment: 27 pages, 5 figures, minor corrections. Final versio

Binary black holes in circular orbits. II. Numerical methods and first results

We present the first results from a new method for computing spacetimes representing corotating binary black holes in circular orbits. The method is based on the assumption of exact equilibrium. It uses the standard 3+1 decomposition of Einstein equations and conformal flatness approximation for the 3-metric. Contrary to previous numerical approaches to this problem, we do not solve only the constraint equations but rather a set of five equations for the lapse function, the conformal factor and the shift vector. The orbital velocity is unambiguously determined by imposing that, at infinity, the metric behaves like the Schwarzschild one, a requirement which is equivalent to the virial theorem. The numerical scheme has been implemented using multi-domain spectral methods and passed numerous tests. A sequence of corotating black holes of equal mass is calculated. Defining the sequence by requiring that the ADM mass decrease is equal to the angular momentum decrease multiplied by the orbital angular velocity, it is found that the area of the apparent horizons is constant along the sequence. We also find a turning point in the ADM mass and angular momentum curves, which may be interpreted as an innermost stable circular orbit (ISCO). The values of the global quantities at the ISCO, especially the orbital velocity, are in much better agreement with those from third post-Newtonian calculations than with those resulting from previous numerical approaches.Comment: 27 pages, 20 PostScript figures, improved presentation of the regularization procedure for the shift vector, new section devoted to the check of the momentum constraint, references added + minor corrections, accepted for publication in Phys. Rev.