Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and fu…

Set partitions closed under certain operations form a tensor category. They give rise to certain subgroups of the free orthogonal quantum group $O_n^…

The bound of Theorem 1 is sharp and is reached by all surfaces of the following family, as long as λ≠0:

We prove that a K3 quartic surface defined over a field of characteristic 2 can contain at most 68 lines. If it contains 68 lines, then it is project…

In this section, we assume that g is of type A2 and prove Theorem 1 (iii). We begin by showing that we can restrict our attention to certain elements λ and μ of P+(λ,2).

Let g be a complex finite-dimensional simple Lie algebra. Given a positive integer k and a dominant weight \lambda, we define a preorder on the set $…

We assume without loss of generality that a0=0. First we introduce a parameter r>0 in order to normalize the period to 2π and in order to obtain (HS0) as a limit of a corresponding family of systems (HSr). More precisely, we consider the Hamiltonian

We are concerned with the dynamics of $N$ point vortices $z_1,\dots,z_N\in\Omega\subset\mathbb{R}^2$ in a planar domain. This is described by a Hamil…

In Section 3.7 of [19] Spieß constructs extensions of the Steinberg representation associated to characters of the multiplicative group of a p-adic field. Such extensions were already constructed by Breuil in [5] in case the character under consider…

Let E be a quadratic extension of a totally real number field. We construct Stickelberger elements for Hilbert modular forms of parallel weight 2 in …

In this section we apply a recent striking result of M. Weiss [Wei16] to exhibit examples where the conditions of Theorem 3 are satisfied. As a byproduct we will obtain a proof of Theorem 1.

We prove that the Teichm\"{u}ller space $\mathcal{T}^{<0}(M)$ of negatively curved metrics on a hyperbolic manifold $M$ has nontrivial $i$-th rationa…

By their very definition, the family of coadjoint orbits O2n(ε) possess two natural real polarizations, singular over the set {I=0}, and invariant under a family of groups of symplectomorphisms isomorphic to a deformation of the Euclidean group. The…

A classification of the linear deformations of phase space $(\mathbb{R}^{n}\oplus\mathbb{R}^{n},\omega = \sum_{i = 1}^{n} dx_{i}\wedge dp_{i})$ prese…

Throughout this paper we work in the ∞-categories of spaces and spectra. We take [Lurie:bh] and [Lurie:ha] as standard references for ∞-categories.

Let $F$ be a local field with residue field $k$. The classifying space of $GL_n(F)$ comes canonically equipped with a map to the delooping of the $K$…

In this section we will explicitly study the noncommutative Dirac operators discussed in Section 3 on two noncommutative (curved) spacetimes. For their attractive features, e.g. as solutions to noncommutative Einstein equations, we will focus on sem…

We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate c…

In this section we derive a relation between the topology of the union C of closed Reeb orbits on a compact K-cosymplectic manifold M and the (basic) cohomology of M, similar to the K-contact case treated in [19]. As in [19], the proof follows from …

In this paper we study K-cosymplectic manifolds, i.e., smooth cosymplectic manifolds for which the Reeb field is Killing with respect to some Riemann…

This Section is devoted to proving Theorem 3. For any given dimension there are only finitely many possible values for the first Betti number, so we prove instead:

Let $A$ be the product of an abelian variety and a torus defined over a number field $K$. Fix some prime number $\ell$. If $\alpha \in A(K)$ is a poi…

For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (2008 Inverse Problems 24 065009) have shown that a piecewise polynomial conductivity on a fixed partit…

For the linearized reconstruction problem in Electrical Impedance Tomography (EIT) with the Complete Electrode Model (CEM), Lechleiter and Rieder (20…

If Γ⊆Γ′ are finite subsets of B0d, then the following commutative diagram gives a natural surjective morphism MF(Γ′)↠MF(Γ):

A Mustafin degeneration is a degeneration of a flag variety induced by a vertex configuration in the Bruhat-Tits building of the projective linear gr…

From now on, we assume r>λ−11+ε0 since then |μ|<r−(1+ε) implies |μ|<λ0, hence Theorem 8.3 is applicable to sequences in E(r):=span(r,r−(1+ε)) respectively Es(r):=RsE(r). This last theorem completes the proof of Theorem A.

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition …

Following [1] denote by Km,n=Km,n[X,Y] a complete bipartite graph such that |X|=m and |Y|=n. In the case when m=1 or n=1 such graphs are called stars.

A metric space $X$ is rigid if the isometry group of $X$ is trivial. The finite ultrametric spaces $X$ with $|X| \geq 2$ are not rigid since for ever…

Let Γ be the space of all locally finite subsets of Rd, see (1.1). We endow Γ with the smallest topology such that, for any continuous function f:Rd⟶R having compact support, Γ∋γ⟼∑x∈γf(x) is continuous. In particular, Γ is a Polish space [KK06]. The…

This work is devoted to the study of a certain class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquen…

The authors would like to thank Willem Fouché, Yonatan Gutman, Alexander Kechris, André Nies, Arno Pauly, Jan Reimann, and Carol Wood for helpful conversations.

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability…

A parabolic Higgs field Φ on a parabolic bundle E∗ is a meromorphic End(E)-valued differential on CP1, holomorphic on CP1∖{z1,…,zn}, and with simple poles at each zi whose residues belong to the Lie algebras

We present an explicit construction of the moduli spaces of rank 2 stable parabolic bundles of parabolic degree 0 over the Riemann sphere, correspond…

The proof of Theorem 3.1 builds on the proof of convergence in [20] - with an addition which accounts for the approximation of the derivative. We estimate

We propose a derivative-free Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativi…

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