Results 51 to 60 of about 3,126 (152)

A study on Type-2 isomorphic circulant graphs. Part 3: 384 pairs of Type-2 isomorphic circulant graphs $C_{32}(R)$

This study is the $3^{rd}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 2. Here, we obtain all the 384 pairs of Type-2 isomorphic circulant graphs of order 32.
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Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part III -- Gradient Descent, Neural Plasticity, and the Emergence of Deep Intelligence

CoRR
In Parts I and II of this series, we established isomorphisms between ant colony decision-making and two major families of ensemble learning: random forests (parallel, variance reduction) and boosting (sequential, bias reduction). Here we complete the trilogy by demonstrating that the fundamental learning algorithm underlying deep neural networks ...
Ernest Fokoué, Gregory Babbitt, Yuval Levental   +2 more
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A study on Type-2 isomorphic circulant graphs. Part 4: 960 triples of Type-2 isomorphic circulant graphs $C_{54}(R)$

This study is the $4^{th}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10} and is a continuation of Part 3. Here, we study Type-2 isomorphic circulant graphs of order 54 and show that there are 960 triples of Type-2 isomorphic circulant graphs of order 54 and each triple of isomorphic circulant ...
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A study on Type-2 isomorphic circulant graphs. Part 1: Type-2 isomorphic circulant graphs $C_n(R)$ w.r.t. $m$ = 2

This study is the first part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Circulant graphs $C_n(R)$ and $C_n(S)$ are said to be \emph{Adam's isomorphic} if there exist some $a\in \mathbb{Z}_n^*$ such that $S = a R$ under arithmetic reflexive modulo $n$ \cite{ad67}.
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Isomorphic Functionalities between Ant Colony and Ensemble Learning: Part II-On the Strength of Weak Learnability and the Boosting Paradigm

In Part I of this series, we established a rigorous mathematical isomorphism between ant colony decision-making and random forest learning, demonstrating that variance reduction through decorrelation is a universal principle shared by biological and computational ensembles.
Fokoué, Ernest, Babbitt, Gregory, Levental, Yuval   +2 more
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Gluing diagrams part 1: A constructive solution for the Higman-Thompson group isomorphism problem

This paper introduces gluing diagrams a combinatorial tool to construct homomorphisms between the shift pseudogroups of directed graphs and thus also their full groups of shifts. We will establish which of these diagrams produce isomorphisms. As an application, using the interpretation of Higman-Thompson groups as full groups of shifts of specific ...
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Extension of partial atom-to-atom maps: uniqueness and algorithms. [PDF]

Algorithms Mol Biol
Laffitte MEG, Phan TL, Stadler PF.
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Detection Ontology, Part 16: The Biological Phase Transition, GRN Spectral Gaps, and the DNA-Prime Isomorphism

Standard evolutionary biology treats life as an accidental emergent property of complex chemistry. In Detection Ontology, life is a mathematically mandatory phase transition that sequesters excess Informational Load Jn J_n Jn generated by the Unfolding Equation, preventing premature cosmic Refolding.
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Non-isomorphic abelian varieties with the same arithmetic. [PDF]

R Soc Open Sci
Bell J.
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The Holographic Circlette: Part 19 — The F2 Pati-Salam Isomorphism and the Cosmological Cooling of the Error-Correcting Vacuum

The four parity-check constraints R1-R4 are identified as the exact F2 binary generators of the Pati-Salam GUT (SU(4)_C x SU(2)_L x SU(2)_R). Parity checks activate sequentially as the universe cools past Landauer thresholds. The R2 constraint scale (~10^15 GeV) converges with the GUT scale.
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