Related papers: Computing Real Numbers with Large-Population Proto…
This paper introduces the R package drpop to flexibly estimate total population size from incomplete lists. Total population estimation, also called capture-recapture, is an important problem in many biological and social sciences. A…
Broadcast consensus protocols (BCPs) are a model of computation, in which anonymous, identical, finite-state agents compute by sending/receiving global broadcasts. BCPs are known to compute all number predicates in…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
We consider questions related to the computation of the capacity of codes that avoid forbidden difference patterns. The maximal number of $n$-bit sequences whose pairwise differences do not contain some given forbidden difference patterns…
We study a class of countably-infinite-dimensional linear programs (CILPs) whose feasible sets are bounded subsets of appropriately defined spaces of measures. The optimal value, optimal points, and minimal points of these CILPs can be…
In this paper we study representations of real numbers in a numeral system with the base $a>1$ and alphabet (digits set) $A\equiv\{0,1,...,r\}$, $a-1<r\in N$ given by \[x=\sum\limits_{n=1}^{\infty}\frac{\alpha_n}{a^n}\equiv…
Let $p/q$ ($p, q \in \mathbb{N}^*$) be a positive rational number such that $p > q^2$. We show that for any $\epsilon > 0$, there exists a set $A(\epsilon) \subset [0, 1[$, with finite border and with Lebesgue measure $< \epsilon$, for…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
We define a class of functions termed "Computable in the Limit", based on the Machine Learning paradigm of "Identification in the Limit". A function is Computable in the Limit if it defines a property P_p of a recursively enumerable class A…
The recent woes of the supercomputer industry and changes in federal funding have caused some scientists to re-evaluate the means by which they hope to solve Grand Challenge problems. I evaluate the potential of Massively Parallel…
Data originating from the Web, sensor readings and social media result in increasingly huge datasets. The so called Big Data comes with new scientific and technological challenges while creating new opportunities, hence the increasing…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic…
In this paper, we study matrix scaling and balancing, which are fundamental problems in scientific computing, with a long line of work on them that dates back to the 1960s. We provide algorithms for both these problems that, ignoring…
An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
Population protocols are a model of distributed computation intended for the study of networks of independent computing agents with dynamic communication structure. Each agent has a finite number of states, and communication opportunities…
We exhaustively explore the reprogrammability capabilities and the intrinsic universality of the Cartesian product $P \times C$ of the space $P$ of all possible computer programs of increasing size and the space $C$ of all possible…