Related papers: On the enumeration of sentences by compactness
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
A typical goal of research in combinatorial optimization is to come up with fast algorithms that find optimal solutions to a computational problem. The process that takes a real-world problem and extracts a clean mathematical abstraction of…
Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…
This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…
Optimization problems in engineering and applied mathematics are typically solved in an iterative fashion, by systematically adjusting the variables of interest until an adequate solution is found. The iterative algorithms that govern these…
The ability to find short representations, i.e. to compress data, is crucial for many intelligent systems. We present a theory of incremental compression showing that arbitrary data strings, that can be described by a set of features, can…
For a sequence $(\lambda_n)$ of positive real numbers we consider the exponential functions $f_{\lambda_n} (z) = \lambda_n e^z$ and the compositions $F_n = f_{\lambda_n} \circ f_{\lambda_{n-1}} \circ ... \circ f_{\lambda_1}$. For such a…
We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…
The standard rational choice model describes individuals as making choices by selecting the best option from a menu. A wealth of evidence instead suggests that individuals often filter menus into smaller sets - consideration sets - from…
Topic models are a useful analysis tool to uncover the underlying themes within document collections. The dominant approach is to use probabilistic topic models that posit a generative story, but in this paper we propose an alternative way…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
We present BSeries.jl, a Julia package for the computation and manipulation of B-series, which are a versatile theoretical tool for understanding and designing discretizations of differential equations. We give a short introduction to the…
Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes, "reliability diagrams" help detect and diagnose…
Technical computing is a challenging application area for programming languages to address. This is evinced by the unusually large number of specialized languages in the area (e.g. MATLAB, R), and the complexity of common software stacks,…
We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to the true value of the capacity. Several…
Program synthesis -- the automatic generation of code given a specification -- is one of the most fundamental tasks in artificial intelligence (AI) and the dream of many programmers. Numerous synthesizers have been developed for program…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Julia has been heralded as a potential successor to Python for scientific machine learning and numerical computing, boasting ergonomic and performance improvements. Since Julia's inception in 2012 and declaration of language goals in 2017,…
We approach string phenomenology from the perspective of computational algebraic geometry, by providing new and efficient techniques for proving stability and calculating particle spectra in heterotic compactifications. This is done in the…
Completeness of a logic program means that the program produces all the answers required by its specification. The cut is an important construct of programming language Prolog. It prunes part of the search space, this may result in a loss…