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The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of applied to . This paper focuses on the situation...
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant§ refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure....
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients.
The main example, we consider outside vector spaces, concerns Boolean algebras,...
In this article, we formalize integral linear spaces, that is a linear space with integer coefficients. Integral linear spaces are necessary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm that outputs short lattice base and cryptographic systems with lattice [8].
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