In this paper we investigate the injectivity of the Parikh matrix mapping. This research is done mainly on the binary alphabet. We identify a family of binary words, refered to as “palindromicly amicable”, such that two such words are palindromicly amicable if and only if they have the same image by the Parikh matrix mapping. Some other related problems are discussed, too.

Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organism carrying the trait. State-of-the-art methods assume that the trait evolves according to a continuous-time Markov chain (CTMC) and works well for small state spaces. The computations slow down considerably for larger state spaces (e.g., space of codons), be...

Reversible integer mapping is essential for lossless source coding by transformation. A general matrix factorization theory for reversible integer mapping of invertible linear transforms is developed in this paper. Concepts of the integer factor and the elementary reversible matrix (ERM) for integer mapping are introduced, and two forms of ERM—triangular ERM (TERM) and single-row ERM (SERM)—are...

Higher peak performance on Field Programmable Gate Arrays (FPGAs) than on microprocessors was shown for sparse matrix vector multiplication (SpMxV) accelerator designs. However due to the frequent memory movement in SpMxV, system performance is heavily affected by memory bandwidth and overheads in real applications. In this paper, we introduce an innovative SpMxV Solver, designed for FPGAs, SSF...

The Jarlskog Invariant Jν−map of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses me and m1 (of ν1) with the smallness of T violation. For small T violating phase χl in the lepton sector, Jν−map is proportional to χl, but me and m1 are proportional to χ2l . This leads to Jν−map ∼= 1 6 √ me mμ +O ( √ memμ m2τ )

The purpose of this notes is to present some useful facts about matrices and determinants and a proof of the inverse mapping theorem that is rather different from the one in Apostol. Notation: Mn(R) denotes the set of all n× n real matrices. Determinants: If A ∈ Mn(R), we can consider the rows of A: r1, . . . , rn. These are elements of R, considered as row vectors. Conversely, given n row vect...

We introduce a couple of families of codifiable languages and investigate properties of these families as well as interrelationships between different families. Also we develop an algorithm based on the Earley algorithm to compute the values of the inverse of the Parikh matrix mapping over a codifiable context-free language. Finally, an attributed grammar that computes the values of the Parikh ...

While we know that the neocortex occupies 85% of our brains and that its circuits allow an enormous flexibility and repertoire of behavior (not to mention unexplained phenomena like consciousness), a century after Cajal we have very little knowledge of the details of the cortical circuits or their mode of function. One simplifying hypothesis that has existed since Cajal is that the neocortex co...

Knowledge graphs are useful resources for numerous AI applications, but they are far from completeness. Previous work such as TransE, TransH and TransR/CTransR regard a relation as translation from head entity to tail entity and the CTransR achieves state-of-the-art performance. In this paper, we propose a more fine-grained model named TransD, which is an improvement of TransR/CTransR. In Trans...

The hierarchical quark masses and small mixing angles are shown to lead to a simple triangular form for the U and D-type quark mass matrices. In the basis where one of the matrices is diagonal, each matrix element of the other is, to a good approximation, the product of a quark mass and a CKM matrix element. The physical content of a general mass matrix can be easily deciphered in its triangula...