We discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ ...

In this paper we consider the Gaussian thermostat ray transforms on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray ...

We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and ...

We develop a framework for the analysis of large-scale ad auctions where adverts are assigned over a continuum of search types. For this pay-per-click market, we provide an efficient mechanism that maximizes social welfare. ...

We prove Wise’s W-cycles conjecture: Consider a compact graph Γ′ immersing into another graph Γ. For any immersed cycle Λ : S¹ → Γ, we consider the map Λ′ from the circular components S of the pullback to Γ′. Unless Λ′ is ...

We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether ...

Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify ...

We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso (Tibshirani, 1996) can be useful for producing interpretable ...

The hexagonal polygon model arises in a natural way via a transformation of the 1-2 model on the hexagonal lattice, and it is related to the high temperature expansion of the Ising model. There are three types of edge, and ...

In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain ...

We introduce a sheaf of infinite order differential operators D on smooth rigid analytic spaces that is a rigid analytic quantisation of the cotangent bundle. We show that the sections of this sheaf over sufficiently small ...

We prove that the profinite completion of the fundamental group of a compact 3-manifold M satisfies a Tits alternative: if a closed subgroup H does not contain a free pro-p subgroup for any p, then H is virtually soluble, ...

We study random walks on the groups $\Bbb F^d_p \rtimes$ SL$_d$($\Bbb F_p$). We estimate the spectral gap in terms of the spectral gap of the projection to the linear part SL$_d$($\Bbb F_p$). This problem is motivated by ...

We are grateful for the opportunity to discuss this new test, based on marginal screening, of a global null hypothesis in linear models. Marginal screening has become a very popular tool for reducing dimensionality in ...

We compute the abelianisations of the mapping class groups of the manifolds W²ⁿ_g = g(Sⁿ × Sⁿ) for n ≥ 3 and g ≥ 5. The answer is a direct sum of two parts. The first part arises from the action of the mapping class group ...

The Paley graph is a well-known self-complementary pseudo-random graph, defined over a finite field of odd order. We describe an attempt at an analogous construction using fields of even order. Some properties of the graph ...

In this work we let Φ be an irreducible root system, with Coxeter group W. We consider subsets of Φ which are abelian, meaning that no two roots in the set have sum in Φ∪{0}. We classify all maximal abelian sets (i.e., ...

We prove a formality theorem for the Fukaya categories of the symplectic manifolds underlying symplectic Khovanov cohomology over fields of characteristic zero. The key ingredient is the construction of a degree-one ...

© 2017, Mathematical Sciences Publishers. All rights reserved.We study the space of oriented genus-g subsurfaces of a fixed manifold M and, in particular, its homological properties. We construct a “scanning map” which ...