Initial algebra for a system of right-linear functors

In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution when ever they enjoy a specific property that we called hierarchicity and that is instrumental to avoid critical mutual recursive definitions. In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided it satisfies a property similar to hierarchicity

ミャンマー語テキストの形式手法による音節分割、正規化と辞書順排列

国立大学法人長岡技術科学大

Initial algebra for a system of right-linear functors

In 2003 we showed that right-linear systems of equations over regular expressions, when interpreted in a category of trees, have a solution whenever they enjoy a specific property that we called hierarchicity and that is instrumental to avoid critical mutual recursive definitions. In this note, we prove that a right-linear system of polynomial endofunctors on a cocartesian monoidal closed category which enjoys parameterized left list arithmeticity, has an initial algebra, provided it satisfies a property similar to hierarchicity

A Python programozási nyelvről statisztikusoknak

A cikk megírásánál az a cél vezérelte a szerzőt, hogy egy olyan bevezető leírást adjon a Python programozási nyelvről, amely könnyen érthető a programfejlesztésben még kezdő, de a statisztikában már jártas szakember számára. A tanulmány lépésről lépésre mutatja be a Python nyelvű programozás szépségeit, felvázol egy utat, amelyen járva könnyen eljutunk egy futtatható kódig, de egyben felhívja a figyelmet a Python nyelvben rejlő buktatókra is. A példaként használt statisztikai módszerek többsége szándékosan alapszintű, egyetlen kivétel a klaszteranalízis. Utolsó lépésként a szerző rámutat az adatvizualizáció fontosságára, és példákon keresztül ismerteti a Python programnyelv lehetőségeit ezen a téren is

A hierarchy of languages, logics, and mathematical theories

We present mathematics from a foundational perspective as a hierarchy in which each tier consists of a language, a logic, and a mathematical theory. Each tier in the hierarchy subsumes all preceding tiers in the sense that its language, logic, and mathematical theory generalize all preceding languages, logics, and mathematical theories. Starting from the root tier, the mathematical theories in this hierarchy are: combinatory logic restricted to the identity I, combinatory logic, ZFC set theory, constructive type theory, and category theory. The languages of the first four tiers correspond to the languages of the Chomsky hierarchy: in combinatory logic Ix = x gives rise to a regular language; the language generated by S, K in combinatory logic is context-free; first-order logic is context-sensitive; and the typed lambda calculus of type theory is recursively enumerable. The logic of each tier can be characterized in terms of the cardinality of the set of its truth values: combinatory logic restricted to I has 0 truth values, while combinatory logic has 1, first-order logic 2, constructive type theory 3, and categeory theory omega_0. We conjecture that the cardinality of objects whose existence can be established in each tier is bounded; for example, combinatory logic is bounded in this sense by omega_0 and ZFC set theory by the least inaccessible cardinal. We also show that classical recursion theory presents a framework for generating the above hierarchy in terms of the initial functions zero, projection, and successor followed by composition and m-recursion, starting with the zero function I in combinatory logic This paper begins with a theory of glossogenesis, i.e. a theory of the origin of language, since this theory shows that natural language has deep connections to category theory and since it was through these connections that the last tier and ultimately the whole hierarchy were discovered. The discussion covers implications of the hierarchy for mathematics, physics, cosmology, theology, linguistics, extraterrestrial communication, and artificial intelligence

Knowledge Transfer, Templates, and the Spillovers

Mathematical models and their modeling frameworks developed to advance knowledge in one discipline are sometimes sourced to answer questions or solve problems in another discipline. Studying this aspect of cross-disciplinary transfer of knowledge objects, philosophers of science have weighed in on the question of whether knowledge about how a mathematical model is previously applied in one discipline is necessary for the success of reapplying said model in a different discipline. However, not much has been said about whether the answer to that epistemological question applies to the reapplication of a modeling framework. More generally, regarding the nature of the production of knowledge in science, a metaphysical question remains to be explored whether historical contingencies associated with a mathematical construct have a genuine impact on the nature—as opposed to sociological practices or individual psychology—of advancing scientific knowledge with said construct. Focusing on this metaphysical question, this paper analyzes the use of mathematical logic in the development of the Chomsky hierarchy and subsequent reapplications of said hierarchy; with these examples, this paper develops the notion of “spillovers” as a way to detect cross-disciplinary justifications for better understanding the relations between reapplications of the same mathematical construct across disciplines

Progress and challenges for the machine learning-based design of fit-for-purpose monoclonal antibodies

Although the therapeutic efficacy and commercial success of monoclonal antibodies (mAbs) are tremendous, the design and discovery of new candidates remain a time and cost-intensive endeavor. In this regard, progress in the generation of data describing antigen binding and developability, computational methodology, and artificial intelligence may pave the way for a new era of in silico on-demand immunotherapeutics design and discovery. Here, we argue that the main necessary machine learning (ML) components for an in silico mAb sequence generator are: understanding of the rules of mAb-antigen binding, capacity to modularly combine mAb design parameters, and algorithms for unconstrained parameter-driven in silico mAb sequence synthesis. We review the current progress toward the realization of these necessary components and discuss the challenges that must be overcome to allow the on-demand ML-based discovery and design of fit-for-purpose mAb therapeutic candidates

Compiler Generator: Considerazioni e Confronti

Dopo aver definito e descritto in modo accurato il linguaggio, la grammatica, gli automi e i riconoscitori deterministici, il presente lavoro si incentra sul descrivere ed esaminare alcuni strumenti atti allo sviluppo di prototipi di traduttori, allo scopo di sottolineare le differenze di gestione e di analisi tra i vari prototipi presi in esame. Vengono messi in evidenza, inoltre, anche l’aspetto sintattico e l’aspetto semantico dei parser esaminati. Quello su cui la nostra tesi si è maggiormente concentrata è il parser generator Yacc per le grammatiche LALR(1), del quale sono stati messi in evidenza le caratteristiche principali e il modo in cui si serve delle grammatiche. Sono state quindi ricercate, negli strumenti successivi come Bison, Essence e Coco/R, le innovazioni rispetto a Yacc, che resta comunque, ancora oggi, uno degli strumenti più diffusi nel settore