Related papers: Morley sequences in dependent theories
The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal…
Automatic sequences have many properties that other sequences (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of different methods that can be used to prove that a given sequence…
The results in this paper provide new information on asymptotic properties of classical models: the neutral Kingman coalescent under a general finite-alleles, parent-dependent mutation mechanism, and its generalisation, the ancestral…
We establish Cram\'er-type moderate deviation theorems for sums of locally dependent random variables and combinatorial central limit theorems. Under some mild exponential moment conditions, optimal error bounds and convergence ranges are…
We present necessary conditions for monotonicity, in one form or another, of fixed point iterations of mappings that violate the usual nonexpansive property. We show that most reasonable notions of linear-type monotonicity of fixed point…
We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…
This note explains an approach to producing examples of 'generalized Kuga-Satake theory' based on establishing special cases of Simpson's conjecture that rigid local systems are motivic. This strategy is then carried out, using work of…
We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to…
We introduce and examine some special classes of invariant types$\unicode{x2014}$bi-invariant, strongly bi-invariant, extendibly invariant, and reliably invariant types$\unicode{x2014}$and show that they are related to certain…
Jaligot's Lemma states that the Fitting subgroups of distinct Borel subgroups do not intersect in a tame minimal simple groups of finite Morley. Such a strong result appears hopeless without tameness. Here we use the 0-unipotence theory to…
Since physical theories employ mathematical models to describe and predict physical phenomena, our knowledge depends on the models available to that end. To increase their scope we present a particular type of simplified models, serial…
We improve lower bounds on the $k$th-order nonlinear complexity of pseudorandom sequences over finite fields and we establish a probabilistic result on the behavior of the $k$th-order nonlinear complexity of random sequences over finite…
We derive large-sample and other limiting distributions of the ``frequency of frequencies'' vector, ${\bf M_n}$, together with the number of species, $K_n$, in a Poisson-Dirichlet or generalised Poisson-Dirichlet gene or species sampling…
We present a general non-parametric statistical inference theory for integrals of quantiles without assuming any specific sampling design or dependence structure. Technical considerations are accompanied by examples and discussions,…
Finsler's lemma is a classic mathematical result with applications in control and optimization. When the lemma is applied to parameter-dependent LMIs, as such those that arise from problems of robust stability, the extra variables…
The purpose of this work is to develop a version of Forman's discrete Morse theory for simplicial complexes, based on internal strong collapses. Classical discrete Morse theory can be viewed as a generalization of Whitehead's collapses,…
This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of…
We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…
We present a new coherence theorem for comprehension categories, providing strict models of dependent type theory with all standard constructors, including dependent products, dependent sums, identity types, and other inductive types.…
We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be…