The tensor product of polynomials.
The theorem of Fine and Wilf for relational periods
We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.
The theorem of Fine and Wilf for relational periods
We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.
The theory of function structure models.
The theory of invertible algorithms
The topological structure of adherences of regular languages
The topologies of sofic subshifts have computable Pierce invariants
The topology of continuous partially-additive monoids
The traveling salesman problem for cubic graphs.
The tree of shapes of an image
In [30], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation...
The tree of shapes of an image
In [CITE], Kronrod proves that the connected components of isolevel sets of a continuous function can be endowed with a tree structure. Obviously, the connected components of upper level sets are an inclusion tree, and the same is true for connected components of lower level sets. We prove that in the case of semicontinuous functions, those trees can be merged into a single one, which, following its use in image processing, we call “tree of shapes”. This permits us to solve a classical representation problem...
The Tribonacci substitution.
The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions.
The UD RLS algorithm for training feedforward neural networks
A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.
The uncertainty measure of hierarchical quotient space structure.
The Uniform Minimum-Ones 2SAT Problem and its Application to Haplotype Classification
Analyzing genomic data for finding those gene variations which are responsible for hereditary diseases is one of the great challenges in modern bioinformatics. In many living beings (including the human), every gene is present in two copies, inherited from the two parents, the so-called haplotypes. In this paper, we propose a simple combinatorial model for classifying the set of haplotypes in a population according to their responsibility for a certain genetic disease. This model is based...
The Union of Balls and Its Dual Shape.
The unsolvability of the emptiness problem of the two deterministic finite transducer mappings
The Upper Envelope of Piecewise Linear Functions: Algorithms and Applications.
The Upper Envelope of Piecewise Linear Functions: Tight Bounds on the Number of Faces.