Related papers: Measuring club-sequences with a large continuum
We consider a hard core (HC) model with a countable set $\mathbb{Z}$ of spin values on the Cayley tree. This model is defined by a countable set of parameters $\lambda_{i}>0, i \in \mathbb{Z}\setminus\{0\}$. For all possible values of…
In recent years, many different approaches have been proposed to quantify the performances of soccer players. Since player performances are challenging to quantify directly due to the low-scoring nature of soccer, most approaches estimate…
We consider the case with boundary of the classical Kazdan-Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular…
When two spatially separated parties make measurements on an unknown entangled quantum state, what correlations can they achieve? How difficult is it to determine whether a given correlation is a quantum correlation? These questions are…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
The Axiom of Full Reflection at a measurable cardinal has been conjectured to be equiconsitent with the existence of a coherent sequence of measures with a repeat point. However we prove that the Axiom of Full Reflection at a measurable…
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…
We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular…
To the families of geometric measures of convex bodies (the area measures of Aleksandrov-Fenchel-Jessen, the curvature measures of Federer, and the recently discovered dual curvature measures) a new family is added. The new family of…
We study two models of the Majority problem. We are given n balls and an unknown coloring of them with two colors. We can ask sets of balls of size k as queries, and in the so-called General Model the answer to a query shows if all the…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Correlations between planetary and stellar properties, particularly age, can provide insight on planetary formation and evolution processes. However, the underlying source of such trends can be unclear, and measurement uncertainties and…
In the presence of model risk, it is well-established to replace classical expected values by worst-case expectations over all models within a fixed radius from a given reference model. This is the "robustness" approach. We show that…
Problems with uniform probabilities on an infinite support show up in contemporary cosmology. This paper focuses on the context of inflation theory, where it complicates the assignment of a probability measure over pocket universes. The…
This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate…
We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a (non necessarily normal) ideal $J$ extending the nonstationary ideal…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
Cardinal characteristics of the continuum represent the boundaries in size between the countable and the continuum with respect to certain properties of sets. They are often defined as the minimum sizes of families of reals that meet some…
The concept of ``countable set'' is attributed to Georg Cantor, who set the boundary between countable and uncountable sets in 1874. The concept of ``computable set'' arose in the study of computing models in the 1930s by the founders of…
We show if we use countable support iteration of forcing notions not adding reals that satisfy additional conditions, then the limit forcing does not add reals. As a result we prove that we can amalgamate two earlier methods and prove the…