Related papers: Natural Density and The Quantifier 'Most'
Let $h$ be a positive integer and $A, B_1, B_2,\dots, B_h$ be finite sets in a commutative group. We bound $|A+B_1+...+B_h|$ from above in terms of $|A|, |A+B_1|,\dots,|A+B_h|$ and $h$. Extremal examples, which demonstrate that the bound is…
Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…
We classify the propositional modal validities arising from the category of sets under its natural classes of morphisms. The resulting validities depend on the morphism class, the size of the world, and the permitted substitution instances.…
The large size and complex decision mechanisms of state-of-the-art text classifiers make it difficult for humans to understand their predictions, leading to a potential lack of trust by the users. These issues have led to the adoption of…
We obtain algebraic characterizations of relative notions of size in a discrete semigroup that generalize the usual combinatorial notions of syndetic, thick, and piecewise syndetic sets. "Filtered" syndetic and piecewise syndetic sets were…
\textit{Let $E$ be an infinite set on which a property $(\bf P)$ is defined. Suppose that $E=\cup_{i\in I} E_i$ is a partition, where each $E_i$ is infinite. Suppose also that, in each $E_i$, the number of elements satisfying $(\bf P)$ is…
Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought…
In physics, density matrices are used to represent mixed states, i.e. probabilistic mixtures of pure states. This concept has previously been used to model lexical ambiguity. In this paper, we consider metaphor as a type of lexical…
With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
The quantified constraint satisfaction problem (QCSP) is the problem of deciding, given a structure and a first-order prenex sentence whose quantifier-free part is the conjunction of atoms, whether or not the sentence holds on the…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
We show that for any set $A \subset \mathbb{N}$ with positive upper density and any $\ell,m \in \mathbb{N}$, there exist an infinite set $B\subset \mathbb{N}$ and some $t\in \mathbb{N}$ so that $\{mb_1 + \ell b_2 \colon b_1,b_2\in B\…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
Theoretical linguists have suggested that some languages (e.g., Chinese and Japanese) are "cooler" than other languages based on the observation that the intended meaning of phrases in these languages depends more on their contexts. As a…
This paper defines a new pseudometric for binary relations between finite sets that measures consensus among subsets. The main results are (1) a concise restatement of this pseudometric with an intuitively appealing interpretation via a…
In this paper, we introduce a new measure called Term_Class relevance to compute the relevancy of a term in classifying a document into a particular class. The proposed measure estimates the degree of relevance of a given term, in placing…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
A classical Kamae-Weiss theorem states that an increasing sequence $(n_i)_{i\in\mathbb N}$ of positive lower density is \emph{normality preserving}, i.e. has the property that for any normal binary sequence $(b_n)_{n\in\mathbb N}$, the…
The amount of contextuality is quantified in terms of the probability of the necessary violations of noncontextual assignments to counterfactual elements of physical reality.