3,550 research outputs found
Compactly generated homotopy categories
Over an associative ring we consider a class of left modules
which is closed under set-indexed coproducts and direct summands. We
investigate when the triangulated homotopy category is
compactly generated, and give a number of examples.Comment: 20 page
Lognormal Approximation of Complex Path-dependent Pension Scheme Payoffs
This paper analyzes an explicit return smoothing mechanism which has recently been introduced as part of a new type of pension savings contract that has been offered by Danish life insurers. We establish the payoff function implied by the return smoothing mechanism and show that its probabilistic properties are accurately approximated by a suitably adapted lognormal distribution. The quality of the lognormal approximation is explored via a range of simulation based numerical experiments, and we point to several other potential practical applications of the paper’s theoretical results.Account-based pension schemes; return smoothing; payoff distributions; density approximation; Monte Carlo simulation; Asian options
The co-stability manifold of a triangulated category
Stability conditions on triangulated categories were introduced by Bridgeland
as a 'continuous' generalisation of t-structures. The set of locally-finite
stability conditions on a triangulated category is a manifold which has been
studied intensively.
However, there are mainstream triangulated categories whose stability
manifold is the empty set. One example is the compact derived category of the
dual numbers over an algebraically closed field.
This is one of the motivations in this paper for introducing co-stability
conditions as a 'continuous' generalisation of co-t-structures. Our main result
is that the set of nice co-stability conditions on a triangulated category is a
manifold. In particular, we show that the co-stability manifold of the compact
derived category of the dual numbers is the complex numbers.Comment: 14 page
Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials
Neural message passing on molecular graphs is one of the most promising
methods for predicting formation energy and other properties of molecules and
materials. In this work we extend the neural message passing model with an edge
update network which allows the information exchanged between atoms to depend
on the hidden state of the receiving atom. We benchmark the proposed model on
three publicly available datasets (QM9, The Materials Project and OQMD) and
show that the proposed model yields superior prediction of formation energies
and other properties on all three datasets in comparison with the best
published results. Furthermore we investigate different methods for
constructing the graph used to represent crystalline structures and we find
that using a graph based on K-nearest neighbors achieves better prediction
accuracy than using maximum distance cutoff or the Voronoi tessellation graph
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