971 research outputs found
A spacetime not characterised by its invariants is of aligned type II
By using invariant theory we show that a (higher-dimensional) Lorentzian
metric that is not characterised by its invariants must be of aligned type II;
i.e., there exists a frame such that all the curvature tensors are
simultaneously of type II. This implies, using the boost-weight decomposition,
that for such a metric there exists a frame such that all positive boost-weight
components are zero. Indeed, we show a more general result, namely that any set
of tensors which is not characterised by its invariants, must be of aligned
type II. This result enables us to prove a number of related results, among
them the algebraic VSI conjecture.Comment: 14pages, CQG to appea
Metrics With Vanishing Quantum Corrections
We investigate solutions of the classical Einstein or supergravity equations
that solve any set of quantum corrected Einstein equations in which the
Einstein tensor plus a multiple of the metric is equated to a symmetric
conserved tensor constructed from sums of terms the involving
contractions of the metric and powers of arbitrary covariant derivatives of the
curvature tensor. A classical solution, such as an Einstein metric, is called
{\it universal} if, when evaluated on that Einstein metric, is a
multiple of the metric. A Ricci flat classical solution is called {\it strongly
universal} if, when evaluated on that Ricci flat metric,
vanishes. It is well known that pp-waves in four spacetime dimensions are
strongly universal. We focus attention on a natural generalisation; Einstein
metrics with holonomy in which all scalar invariants are zero
or constant. In four dimensions we demonstrate that the generalised
Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is
strongly universal; indeed, we show that universality extends to all
4-dimensional Einstein metrics. We also discuss generalizations
to higher dimensions.Comment: 23 page
Late-time behaviour of the tilted Bianchi type VI models
We study tilted perfect fluid cosmological models with a constant equation of
state parameter in spatially homogeneous models of Bianchi type VI
using dynamical systems methods and numerical simulations. We study models with
and without vorticity, with an emphasis on their future asymptotic evolution.
We show that for models with vorticity there exists, in a small region of
parameter space, a closed curve acting as the attractor.Comment: 13 pages, 1 figure, v2: typos fixed, minor changes, matches published
versio
Properties of kinematic singularities
The locally rotationally symmetric tilted perfect fluid Bianchi type V
cosmological model provides examples of future geodesically complete spacetimes
that admit a `kinematic singularity' at which the fluid congruence is
inextendible but all frame components of the Weyl and Ricci tensors remain
bounded. We show that for any positive integer n there are examples of Bianchi
type V spacetimes admitting a kinematic singularity such that the covariant
derivatives of the Weyl and Ricci tensors up to the n-th order also stay
bounded. We briefly discuss singularities in classical spacetimes.Comment: 13 pages. Published version. One sentence from version 2 correcte
An algorithmic framework for synthetic cost-aware decision making in molecular design
Small molecules exhibiting desirable property profiles are often discovered
through an iterative process of designing, synthesizing, and testing sets of
molecules. The selection of molecules to synthesize from all possible
candidates is a complex decision-making process that typically relies on expert
chemist intuition. We propose a quantitative decision-making framework,
SPARROW, that prioritizes molecules for evaluation by balancing expected
information gain and synthetic cost. SPARROW integrates molecular design,
property prediction, and retrosynthetic planning to balance the utility of
testing a molecule with the cost of batch synthesis. We demonstrate through
three case studies that the developed algorithm captures the non-additive costs
inherent to batch synthesis, leverages common reaction steps and intermediates,
and scales to hundreds of molecules. SPARROW is open source and can be found at
http://github.com/coleygroup/sparrow
Computer-Aided Multi-Objective Optimization in Small Molecule Discovery
Molecular discovery is a multi-objective optimization problem that requires
identifying a molecule or set of molecules that balance multiple, often
competing, properties. Multi-objective molecular design is commonly addressed
by combining properties of interest into a single objective function using
scalarization, which imposes assumptions about relative importance and uncovers
little about the trade-offs between objectives. In contrast to scalarization,
Pareto optimization does not require knowledge of relative importance and
reveals the trade-offs between objectives. However, it introduces additional
considerations in algorithm design. In this review, we describe pool-based and
de novo generative approaches to multi-objective molecular discovery with a
focus on Pareto optimization algorithms. We show how pool-based molecular
discovery is a relatively direct extension of multi-objective Bayesian
optimization and how the plethora of different generative models extend from
single-objective to multi-objective optimization in similar ways using
non-dominated sorting in the reward function (reinforcement learning) or to
select molecules for retraining (distribution learning) or propagation (genetic
algorithms). Finally, we discuss some remaining challenges and opportunities in
the field, emphasizing the opportunity to adopt Bayesian optimization
techniques into multi-objective de novo design
On Scaling Solutions with a Dissipative Fluid
We study the asymptotic behaviour of scaling solutions with a dissipative
fluid and we show that, contrary to recent claims, the existence of stable
accelerating attractor solution which solves the `energy' coincidence problem
depends crucially on the chosen equations of state for the thermodynamical
variables. We discuss two types of equations of state, one which contradicts
this claim, and one which supports it.Comment: 8 pages and 5 figures; to appear in Class. Quantum Gra
Qualitative Analysis of Causal Anisotropic Viscous Fluid Cosmological Models
The truncated Israel-Stewart theory of irreversible thermodynamics is used to
describe the bulk viscous pressure and the anisotropic stress in a class of
spatially homogeneous viscous fluid cosmological models. The governing system
of differential equations is written in terms of dimensionless variables and a
set of dimensionless equations of state is utilized to complete the system. The
resulting dynamical system is then analyzed using standard geometric
techniques. It is found that the presence of anisotropic stress plays a
dominant role in the evolution of the anisotropic models. In particular, in the
case of the Bianchi type I models it is found that anisotropic stress leads to
models that violate the weak energy condition and to the creation of a periodic
orbit in some instances. The stability of the isotropic singular points is
analyzed in the case with zero heat conduction; it is found that there are
ranges of parameter values such that there exists an attracting isotropic
Friedmann-Robertson-Walker model. In the case of zero anisotropic stress but
with non-zero heat conduction the stability of the singular points is found to
be the same as in the corresponding case with zero heat conduction; hence the
presence of heat conduction does not apparently affect the global dynamics of
the model.Comment: 35 pages, REVTeX, 3 Encapsulated PostScript Figure
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