dd-abelian quotients of (d+2)(d+2)-angulated categories

Let ${\mathscr T}$ be a triangulated category. If $T$ is a cluster tilting object and $I = [ \operatorname{add} T ]$ is the ideal of morphisms factoring through an object of $\operatorname{add} T$, then the quotient category ${\mathscr T} / I$ is abelian. This is an important result of cluster theory, due to Keller-Reiten and K\"{o}nig-Zhu. More general conditions which imply that ${\mathscr T} / I$ is abelian were determined by Grimeland and the first author. Now let ${\mathscr T}$ be a suitable $( d+2 )$-angulated category for an integer $d \geqslant 1$. If $T$ is a cluster tilting object in the sense of Oppermann-Thomas and $I = [ \operatorname{add} T ]$ is the ideal of morphisms factoring through an object of $\operatorname{add} T$, then we show that ${\mathscr T} / I$ is $d$-abelian. The notions of $( d+2 )$-angulated and $d$-abelian categories are due to Geiss-Keller-Oppermann and Jasso. They are higher homological generalisations of triangulated and abelian categories, which are recovered in the special case $d = 1$. We actually show that if $\Gamma = \operatorname{End}_{ \mathscr T }T$ is the endomorphism algebra of $T$, then ${\mathscr T} / I$ is equivalent to a $d$-cluster tilting subcategory of $\operatorname{mod} \Gamma$ in the sense of Iyama; this implies that ${\mathscr T} / I$ is $d$-abelian. Moreover, we show that $\Gamma$ is a $d$-Gorenstein algebra. More general conditions which imply that ${\mathscr T} / I$ is $d$-abelian will also be determined, generalising the triangulated results of Grimeland and the first author.Comment: 19 pages. This is the final accepted version, which has been accepted for publication in the Journal of Algebr

Subsidising consumer services: effects on employment, welfare and the informal economy

It is widely agreed that the opportunities for expansion of aggregate employment in the OECD area must be sought mainly in the private service sector. Thus,because of budgetary problems and voter resistance to higher tax rates, the scope for further expansion of public sector employment seems limited in most OECD countries. Furthermore, the primary sector will undoubtedly continue to release labour resources and, with normal growth rates, there is little prospect of a secular rise in manufacturing employment, since the increase in demand for manufactures is likely to be met through increases in labour productivity. In particular, the ongoing shifts in the international division of labour and the associated transition to the ‘knowledge-based economy’ within the OECD are likely to destroy a large number of manufacturing jobs for unskilled and lowskilled workers in the OECD area.

Labour Tax Reform, The Good Jobs and the Bad Jobs.

We analyse recent proposals to shift the tax burden away from low-paid labour, assuming a dual labour market where the 'good' high-paying jobs are rationed. A shift in the tax burden from low-paid to high-paid workers has an ambiguous effect on the level of aggregate employment while the allocation of aggregate employment is likely to be further distorted. Even if the tax reform raises total employment, economic efficiency may be reduced because labour is reallocated from high-productive to low-productive jobs. Opportunities for on--the--job search have important implications for the policy effects. When these opportunities are small, the tax reform is more likely to raise employment and welfare.

Rich Ground State Chemical Ordering in Nanoparticles: Exact Solution of a Model for Ag-Au Clusters

We show that nanoparticles can have very rich ground state chemical order. This is illustrated by determining the chemical ordering of Ag-Au 309-atom Mackay icosahedral nanoparticles. The energy of the nanoparticles is described using a cluster expansion model, and a Mixed Integer Programming (MIP) approach is used to find the exact ground state configurations for all stoichiometries. The chemical ordering varies widely between the different stoichiometries, and display a rich zoo of structures with non-trivial ordering.Comment: Revised version. New figure added, discussion expanded, some material moved into supplementary fil

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

Optimal Taxation with Household Production.

This paper suggests that the optimal tax system should favour market-produced services which are close substitutes for home-produced services. First, we modify the classical Corlett-Hague rule for optimal commodity taxation by showing that it may be optimal to impose a relatively low tax rate on consumer services even if such services are complements to leisure. Second, we find that when services and other goods are equally substitutable for leisure, so that uniform commodity taxation would be optimal in the absence of home production, the optimal tax structure will certainly involve a relatively low tax rate on consumer services.