Related papers: The Search for the Primitive
The purpose of this article is to introduce the concept of invariance and its properties. These properties can be used to check the primality of a number. Combining these properties with the Euler theorem, it is possible to generalize this…
The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…
I give a brief review of some of the implications of Fermi data for theories of the identity of dark matter, and their combination with data from other complementary probes. I also preview some of the prospects for probing such models with…
Predicting the outcomes of species invasions is a central goal of ecology, a task made especially challenging due to ecological feedbacks. To address this, we develop a general theory of ecological invasions applicable to a wide variety of…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…
It is the purpose of the present article to collect arguments for, that there should exist in fact -- although not necessarily yet found -- some law, which imply an adjustment to special features to occur in the future. In our own "complex…
Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…
This paper outlines the implications of neural-level accounts of insight, and models of the conceptual interactions that underlie creativity, for a theory of cultural evolution. Since elements of human culture exhibit cumulative, adaptive,…
Rejoinder to "The Future of Indirect Evidence" [arXiv:1012.1161]
Deep generative models are powerful tools that have produced impressive results in recent years. These advances have been for the most part empirically driven, making it essential that we use high quality evaluation metrics. In this paper,…
This is an essay about a certain family of elements in the general linear group GL(d,q) called primitive prime divisor elements, or ppd-elements. A classification of the subgroups of GL(d,q) which contain such elements is discussed, and the…
Let $p$ be a prime. If an integer $g$ generates a subgroup of index $t$ in $(\mathbb Z/p\mathbb Z)^*,$ then we say that $g$ is a $t$-near primitive root modulo $p$. We point out the easy result that each primitive residue class contains a…
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do…
This is an overview and a preview of the theory of "mixed motives of level 1" explaining some results, projects, ideas and indicating a bunch of problems.
The induction principle for natural numbers expresses that when a property holds for some natural number a and is hereditary, then it holds for all numbers greater than or equal to a. We present a similar principle for real numbers.
In this article we establish certain variants of the Inverse Cluster Size problem. We introduce the notion of primitive extensions and establish the Primitive variant of the problem. Precisely, we prove the existence of primitive extensions…
A nonnegative matrix A is said to be primitive if there exists a positive integer m such that entries in A^m are positive and smallest such m is called the exponent of A: Primitive matrices are useful in the study of finite Markov chains…
Leading towards the classification of primitive commutative association schemes as the ultimate goal, Bannai and some of his school have been trying to * identify the major sources of (primitive) commutative association schemes, * collect…
The idea that the search efficiency can be increased with the help of a number of autonomous agents is often relevant in many situations, which is known among biologists and roboticists as a stigmergy. This is due to the fact that, in any…