We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

Real-world complex systems may be mathematically modeled as graphs, revealing properties of the system. Here we study graphs of functional brain organization in healthy adults using resting state functional connectivity MRI. We propose two novel brain-wide graphs, one of 264 putative functional areas, the other a modification of voxelwise networks that eliminates potentially artificial short-di...

Exploring the power of self-representation in form selfies as an affirmation-based practice, artist transforms her frustrations with self-identification through a “trans*glitch performance,” and practices queer self-portraiture use medium to challenge LatinX identity representation.

A face recognition system ought to read out information about the identity, facial expression and invariant properties of faces, such as sex and race. A current debate is whether separate neural units in the brain deal with these face properties individually or whether a single neural unit processes in parallel all aspects of faces. While the focus of studies has been directed toward the proces...

An algebra is inherently non-nitely (Q-)based if it is not a member of any locally nite (quasi-)variety, whose (quasi-)identities are nitely based. We prove that no nite semigroup is inherently non-nitely Q-based. This is in marked contrast to the case of varieties, where there are many inherently non-nitely based nite semigroups which have all been described by the second author.

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identi...

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.

In this paper, using the number of spanning trees in some classes of graphs, we prove the identities: Fn = 2n−1 n √

For knowledge representation based on ontology and its use, it is desirable to understand phenomena in the target world as precisely and deeply as possible. The ontology should reflect the understanding of them and provide a fundamental framework to manage the behavior of instances adequately. The management of instance model requires identity of things. Contrary to the common understanding, th...

We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr+s+t = Fr+1Fs+1Ft+1 + FrFsFt − Fr−1Fs−1Ft−1.