Related papers: Introduction to Set Shaping Theory
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
Given a string of characters, the Burrows-Wheeler Transform rearranges the characters in it so as to produce another string of the same length which is more amenable to compression techniques such as move to front, run-length encoding, and…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
We reexamine democratic open string field theories, namely, theories in which string fields are not constrained to a single picture number and picture changing is obtained as a gauge transformation. We describe several possibilities for…
Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression…
Target class classification is a mixed classification and transition model whose integrated goal is to assign objects to a certain, so called target or normal class. The classification process is iterative, and in each step an object in a…
The work lays the foundations of the theory of changeable sets. In author opinion, this theory, in the process of it's development and improvement, can become one of the tools of solving the sixth Hilbert problem least for physics of…
The biological process of gene assembly has been modeled based on three types of string rewriting rules, called string pointer rules, defined on so-called legal strings. It has been shown that reduction graphs, graphs that are based on the…
The analysis of data sometimes requires fitting many free parameters in a theory to a large number of data points. Questions naturally arise about the compatibility of specific subsets of the data, such as those from a particular experiment…
Representation learning is a fundamental but challenging problem, especially when the distribution of data is unknown. We propose a new representation learning method, termed Structure Transfer Machine (STM), which enables feature learning…
We present functions that quantify the contribution of a set of arguments in quantitative bipolar argumentation graphs to (the final strength of) an argument of interest, a so-called topic. Our set contribution functions are generalizations…
Machine learning problems involving sparse datasets may benefit from the use of convolutional neural networks if the numbers of samples and features are very large. Such datasets are increasingly more frequently encountered in a variety of…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them.…
When users can benefit from certain predictive outcomes, they may be prone to act to achieve those outcome, e.g., by strategically modifying their features. The goal in strategic classification is therefore to train predictive models that…
A key problem in text summarization is finding a salience function which determines what information in the source should be included in the summary. This paper describes the use of machine learning on a training corpus of documents and…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
The variant of calculation of functions of set and their application is offered. In particular: the new measure of system of sets generalizing classical concept of a measure is entered; the variation of set that has allowed to construct a…