Related papers: The Small-Is-Very-Small Principle
The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…
We analyse a proposition which considers quantum theory as a mere tool for calculating probabilities for sequences of outcomes of observations made by an Observer, who him/herself remains outside the scope of the theory. Predictions are…
Most pattern mining methods output a very large number of frequent patterns and isolating a small but relevant subset is a challenging problem of current interest in frequent pattern mining. In this paper we consider discovery of a small…
The size $b$ of the smallest bidirectional macro scheme, which is arguably the most general copy-paste scheme to generate a given sequence, is considered to be the strictest reachable measure of repetitiveness. It is strictly lower-bounded…
Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for a network of infinitely many systems, termed as infinite networks. The proposed small-gain theorem addresses…
To explain the decision of any model, we extend the notion of probabilistic Sufficient Explanations (P-SE). For each instance, this approach selects the minimal subset of features that is sufficient to yield the same prediction with high…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
In this paper we are interested in studying concise representations of concepts and dependencies, i.e., implications and association rules. Such representations are based on equivalence classes and their elements, i.e., minimal generators,…
A serial property is a suitably enumerated sequence $\{F_n\}$ of formulas and is called selector provable in PA if there is a PA-recursive function $s(x)$ such that PA $\vdash \forall x (s(x){:}_{\text{PA}} \ulcorner F_x\urcorner)$ where…
Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…
For a sequence $S$ of terms from an abelian group $G$ of length $|S|$, let $\Sigma_n(S)$ denote the set of all elements that can be represented as the sum of terms in some $n$-term subsequence of $S$. When the subsum set is very small,…
We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…
We identify a structural property of term-rewriting proof systems called operational inexpressibility: no derivation depends on a specified input dimension and also constrains the target question. The canonical instance is direct…
A data processing inequality states that the quantity of shared information between two entities (e.g. signals, strings) cannot be significantly increased when one of the entities is processed by certain kinds of transformations. In this…
Retrieval-based systems approximate access to a corpus by exposing only a truncated subset of available evidence. Even when relevant information exists in the corpus, truncation can prevent compatible evidence from co-occurring, leading to…
We focus on the persistence principle over weak interpretability logic. Our object of study is the logic obtained by adding the persistence principle to weak interpretability logic from several perspectives. Firstly, we prove that this…
We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.
Summarizing event sequences is a key aspect of data mining. Most existing methods neglect conditional dependencies and focus on discovering sequential patterns only. In this paper, we study the problem of discovering both conditional and…
In this paper we prove that no consistent finitely axiomatized theory one-dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose…
We prove that a subtle but substantial bias exists in a common measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The magnitude of this streak selection bias generally decreases as the…