If a model structure is not identifiable, then it is not possible to uniquely identify its parameters from measured data. This contribution describes how solvers for differential-algebraic equations (DAE) can be used to examine if a model structure is locally identifiable. The procedure can be applied to both linear and nonlinear systems. If a model structure is not identifiable, it is also pos...

Each Bers slice is a holomorphically embedded copy of Teichmüller space within XC(S). While it follows that BY can be locally described as the common zero locus of finitely many analytic functions on XC(S), it is known that the Bers slice is not a locally algebraic set [DK]—this is used to show that W. Thurston’s skinning map is not a constant function [DK]. We prove a stronger result about the...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

The motivation for this work comes from two problems– test algebraic independence of arithmetic circuits over a field of small characteristic, and generalize the structural property of algebraic dependence used by (Kumar, Saraf CCC’16) to arbitrary fields. It is known that in the case of zero, or large characteristic, using a classical criterion based on the Jacobian, we get a randomized poly-t...

For a fairly general reductive group G/Qp , we explicitly compute the space of locally algebraic vectors in the Breuil-Herzig construction Π(ρ)ord, for a potentially semistable Borel-valued representation ρ of Gal(Q̄p/Qp). The point being we deal with the whole representation, not just its socle – and we go beyond GLn(Qp). In the case of GL2(Qp), this relation is one of the key properties of the...

Let L/Qp be a finite extension, and let G be a locally L-analytic group such as the L-points of an algebraic group over L. The categories of smooth and of finite-dimensional algebraic representations of G may be viewed as subcategories of the category of continuous representations of G in locally convex L-vector spaces. This larger category contains many interesting new objects, such as the act...

We discuss the approximability of locally compact groups by finite semigroups and finite quasigroups (latin squares). We show that if a locally compact group G is approximable by finite semigroups, then it is approximable by finite groups, and thus many important groups are not approximable by finite semigroups. This result implies, in particular, the impossibility to simulate the field of real...

Let L/Qp be a finite extension, and let G be a locally L-analytic group such as the L-points of an algebraic group over L. The categories of smooth and of finite-dimensional algebraic representations of G may be viewed as subcategories of the category of continuous representations of G in locally convex L-vector spaces. This larger category contains many interesting new objects, such as the act...

Let X ⊂ PK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H0(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H0(X ,F)′. The graded pieces of this filtration are locally analytic i...

Let X ⊂ PdK be Drinfeld’s upper half space over a finite extension K of Qp. We construct for every GLd+1-equivariant vector bundle F on PdK , a GLd+1(K)equivariant filtration by closed subspaces on the K-Fréchet H(X ,F). This gives rise by duality to a filtration by locally analytic GLd+1(K)-representations on the strong dual H(X ,F). The graded pieces of this filtration are locally analytic in...