Related papers: From eventually different functions to pandemic nu…
How many odd numbers are there? How many even numbers? From Galileo to Cantor, the suggestion was that there are the same number of odd, even and natural numbers, because all three sets can be mapped in one-one fashion to each other. This…
Quantifying uncertainty in predictions or, more generally, estimating the posterior conditional distribution, is a core challenge in machine learning and statistics. We introduce Convex Nonparanormal Regression (CNR), a conditional…
Recurrent neural networks have gained widespread use in modeling sequential data. Learning long-term dependencies using these models remains difficult though, due to exploding or vanishing gradients. In this paper, we draw connections…
We prove that a function definable with parameters in an o-minimal structure is bounded away from infinity as its argument goes to infinity by a function definable without parameters, and that this new function can be chosen independently…
The concept of a variance on a category is introduced as a two-sided strict factorization system. By employing variances, we define functors of variance in a more general setting than is usually considered, thereby eliminating the need for…
Resampling is an operation costly in calculation time and accuracy. It regularizes irregular sampling, replacing N data by N periodic estimations. This stage can be suppressed, using formulas built with incoming data and completed by…
This paper illustrates the richness of the concept of regular sets of time bounds and demonstrates its application to problems of computational complexity. There is a universe of bounds whose regular subsets allow to represent several time…
Using specializations of unfold and fold on a generic tree data type we derive unranking and ranking functions providing natural number encodings for various Hereditarily Finite datatypes. In this context, we interpret unranking operations…
In this paper, we propose a realistic mathematical model taking into account the mutual interference among the interacting populations. This model attempts to describe the control (vaccination) function as a function of the number of…
We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…
The function f:X -> Y is called k-monotonically increasing if there is a partition X = X_1 U ... U X_k such that f|X_i : X_i -> Y is monotonically increasing for i=1,...,k. It is proved that a one-to-one function f:N -> N is k-monotonically…
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…
We introduce countably Markov interval functions and show that two inverse limits with countably Markov interval bonding functions are homeomorphic if the functions follow the same pattern. This result presents a generalization of…
There is a substantial literature on testing for the equality of the cumulative incidence functions associated with one specific cause in a competing risks setting across several populations against specific or all alternatives. In this…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…
Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chains…
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…
Recurrent Neural Networks (RNNs) are very successful at solving challenging problems with sequential data. However, this observed efficiency is not yet entirely explained by theory. It is known that a certain class of multiplicative RNNs…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
Consider a difference equation which takes the k-th largest output of m functions of the previous m terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves this is analogous to a…