Related papers: Infinite Size-Biased Orders
Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in the…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
It is often desirable to summarise a probability measure on a space $X$ in terms of a mode, or MAP estimator, i.e.\ a point of maximum probability. Such points can be rigorously defined using masses of metric balls in the small-radius…
We argue that the quantum probability law follows, in the large N limit, from the compatibility of quantum mechanics with classical-like properties of macroscopic objects. For a finite sample, we find that likely and unlikely measurement…
We introduce the concept of {\it self-referential order} which provides a way to quantify structural organization in non crystalline materials. The key idea consists in the observation that, in a disordered system, where there is no ideal,…
For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of…
We use some of the largest order statistics of the random projections of a reference signal to construct a binary embedding that is adapted to signals correlated with such signal. The embedding is characterized from the analytical…
For partially ordered sets $X$ we consider the square matrices $M^{X}$ with rows and columns indexed by linear extensions of the partial order on $X$. Each entry $\left( M^{X}\right)_{PQ}$ is a formal variable defined by a pedestal of the…
Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide…
Consider the following dynamic factor model: $\mathbf{R}_t=\sum_{i=0}^q \mathbf{\Lambda}_i \mathbf{f}_{t-i}+\mathbf{e}_t,t=1,...,T$, where $\mathbf{\Lambda}_i$ is an $n\times k$ loading matrix of full rank, $\{\mathbf{f}_t\}$ are i.i.d.…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
We give a complete list of indecomposable characters of the infinite symmetric semigroup. In comparison with the analogous list for the infinite symmetric group, one should introduce only one new parameter, which has a clear combinatorial…
We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense…
The ordered structures of natural, integer, rational and real numbers are studied here. It is known that the theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language…
We analyse q-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive…
Causal Bayesian Networks provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…