Related papers: A note on uniform ultrafilters in a choiceless con…
When modeling directional data, that is, unit-norm multivariate vectors, a first natural question is to ask whether the directions are uniformly distributed or, on the contrary, whether there exist modes of variation significantly different…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
This note reveals an explicit relationship between two representative finite impulse response (FIR) filters, i.e. the newly derived and popularized Kalman-Like unbiased FIR filter (UFIR) and the receding horizon Kalman FIR filter (RHKF). It…
An ultrafilter $p$ on $\omega$ is said to be discrete if, given any function $f\colon \omega \to X$ to any completely regular Hausdorff space, there is an $A \in p$ such that $f(A)$ is discrete. Basic properties of discrete ultrafilters are…
The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers. We show that similar methods can be used to characterize the…
This is a reply to the comment of Dr Sakov on the work "Ensemble Kalman filter with the unscented transform" of Luo and Moroz (2009).
We give a new proof of a polynomial recurrence result due to Bergelson, Furstenberg, and McCutcheon, using idempotent ultrafilters instead of IP-limits.
Kirchberg asked in 2004 whether the commutant of L(H)$ in its (norm) ultrapower is trivial. Assuming the Continnuum Hypothesis, we prove that the answer depends on the choice of the ultrafilter.
The problem of dephasing channel discrimination is addressed for finite-dimensional systems. In particular, the optimization with respect to input states without energy constraint is solved analytically for qubit, qutrit and ququart.…
We present three models concerning Tukey types of ultrafilters on $\omega$. The first model is built via a countable support iteration, and we show there is no basically generated ultrafilter in such model. The second and third models are…
We develop techniques to investigate relativized hierarchical unambiguous computation. We apply our techniques to generalize known constructs involving relativized unambiguity based complexity classes (UP and \mathcal{UP}) to new constructs…
In this paper, we show that Higher-Order Coloured Unification - a form of unification developed for automated theorem proving - provides a general theory for modeling the interface between the interpretation process and other sources of…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
We study the question which Boolean algebras have the property that for every generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For cardinality aleph-one the…
We point out one of the differences between rapid ultrafilters and Q-points: Rapid ultrafilters may have empty intersection with van der Waerden ideal, whereas every Q-point has a non-empty intersection with van der Waerden ideal. Assuming…
Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…
In ultrasound imaging the appearance of homogeneous regions of tissue is subject to speckle, which for certain applications can make the detection of tissue irregularities difficult. To cope with this, it is common practice to apply speckle…
We address the question of the consistency strength of certain filters and ultrafilters which fail to satisfy the Galvin property. We answer questions \cite[Questions 7.8,7.9]{TomMotiII}, \cite[Question 5]{NegGalSing} and improve theorem…
We introduce the decomposability spectrum $K_D=\{\lambda \geq \omega| D \text{is} \lambda\text{-decomposable}\}$ of an ultrafilter $D$, and show that Shelah's $\pcf$ theory influences the possible values $K_D$ can take. For example, we show…
First, we show that universality and other properties of general jumping finite automata are undecidable, which answers a question asked by Meduna and Zemek in 2012. Second, we close the study raised by \v{C}erno and Mr\'{a}z in 2010 by…