相关论文: Some features of natural sequence totals in variou…
Every set of natural numbers determines a generating function convergent for $q \in (-1,1)$ whose behavior as $q \rightarrow 1^-$ determines a germ. These germs admit a natural partial ordering that can be used to compare sets of natural…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
Through extensive studies of dynamical system modeling cellular growth and reproduction, we find evidence that complexity arises in multicellular organisms naturally through evolution. Without any elaborate control mechanism, these systems…
Recently uncovered second derivative discontinuous solutions of the simplest linear ordinary differential equation define not only an nonstandard extension of the framework of the ordinary calculus, but also provide a dynamical…
The problem of the universal form of the size spectrum is analyzed. The half-widths of two wings of spectrum is introduced and it is shown that their ratio is very close to the golden fraction. In appendix it is shown that behind the golden…
This survey paper is not a complete reference guide to number-theoretical applications of ergodic theory. Instead, it considers an approach to a class of problems involving Diophantine properties of $n$-tuples of real numbers, namely,…
We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…
Every set of natural numbers determines a generating function convergent for $q \in (-1,1)$ whose behavior as $q \rightarrow 1^-$ determines a germ. These germs admit a natural partial ordering that can be used to compare sizes of sets of…
One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…
The number of distinct symbols appearing in digit expansions generated by full-branch affine countable iterated function systems is studied whose branch weights are regularly varying. The Hausdorff dimensions of the exceptional sets in…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…
In homotopy type theory, a natural number type is freely generated by an element and an endomorphism. Similarly, an integer type is freely generated by an element and an automorphism. Using only dependent sums, identity types, extensional…
An interesting feature of growth in animals is that different parts of the body grow at approximately the same rate. This property is called proportionate growth. In this paper, we review our recent work on patterns formed by adding $N$…
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
A first-principles theory is developed for the general evolution of a key structural characteristic of planar granular systems - the cell order distribution. The dynamic equations are constructed and solved in closed form for a number of…
Several systems can be represented by hypergraphs, an extension of graphs with associations between any number of vertices. These natural hypergraphs doe not appear at once. They are generated by some dynamical process of hypergraph…
Among three natural numbers there is always one which is larger than or equal to the Nim sum of the remaining two numbers. This amazing fact has many applications.
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
We develop a network in which the natural numbers are the vertices. We use the decomposition of natural numbers by prime numbers to establish the connections. We perform data collapse and show that the degree distribution of these networks…
Living organisms are not just random collections of organic molecules. There is continuous information processing going on in the apparent bouncing around of molecules of life. Optimisation criteria in this information processing can be…