Given a set of taxa S and a complete set of quartet topologies Q over S, the problem of determining a phylogeny that satisfies the maximum number of topologies is called the Maximum Quartet Consistency (MQC) problem. The MQC problem is an NP-problem. MQC has been solved both heuristically and exactly. Exact solutions for MQC include Constraint Programming, Answer Set Programming and Pseudo-Bool...

Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper, we propose a quartet based approach which is agnostic to this number. The key contribution is a novel rank characterization of the tensor associated with th...

The question of compatibility of differential paths plays a central role in second order collision attacks on hash functions. In this context, attacks typically proceed by starting from the middle and constructing the middle-steps quartet in which the two paths are enforced on the respective faces of the quartet structure. Finding paths that can fit in such a quartet structure has been a major ...

Let W be the free monoid over a finite alphabet A. We prove that a congruence of W generated by a finite number of pairs 〈au, u〉, where a ∈ A and u ∈ W , is always decidable.

We describe a method that will reconstruct an unrooted binary phylogenetic level-1 network on [Formula: see text] taxa from the set of all quartets containing a certain fixed taxon, in [Formula: see text] time. We also present a more general method which can handle more diverse quartet data, but which takes [Formula: see text] time. Both methods proceed by solving a certain system of linear equ...

Let Ay = f , A is a linear operator in a Hilbert space H, y ⊥ N (A) := {u : Au = 0}, R(A) := {h : h = Au, u ∈ D(A)} is not closed, f δ − f ≤ δ. Given f δ , one wants to construct u δ such that lim δ→0 u δ − y = 0. A version of the DSM (dynamical systems method) for finding u δ consists of solving the problem ˙ u δ (t) = −u δ (t) + T −1 a(t) A * f δ , u(0) = u 0 , (*) where T := A * A, T a := T ...

The chiral magnetic effect (CME) refers to charge separation along a strong field between left- and right-handed quarks, caused by interactions with topological gluon fields from QCD vacuum fluctuations. We present two approaches handle the dominant elliptic flow (v2) background in three-particle correlator (Δγ112), sensitive CME. In first approach, we Δγ112 Δγ123 measurements U+U Au+Au collisi...