Measuring the phylogenetic diversity of communities has become a key issue for biogeography and conservation. However, most diversity indices that rely on interspecies phylogenetic distances may increase with species loss and thus violate the principle of weak monotonicity. Moreover, most published phylogenetic diversity indices ignore the abundance distribution along phylogenetic trees, even t...

New one-leg multistep time discretizations of nonlinear evolution equations are investigated. The main features of the scheme are the preservation of the nonnegativity and the entropy-dissipation structure of the diffusive equations. The key ideas are to combine Dahlquist’s G-stability theory with entropy-dissipation methods and to introduce a nonlinear transformation of variables which provide...

For a compact Kähler manifold X and a strongly primitive automorphism g of positive entropy, it is shown that X has at most ρ(X) of g-periodic prime divisors. When X is a projective threefold, every prime divisor containing infinitely many g-periodic curves, is shown to be g-periodic (a result in the spirit of the Dynamic Manin-Mumford conjecture as in [17]).

We solve the question of the existence of a Poisson-Pinsker factor for conservative ergodic infinite measure preserving action of a countable amenable group by proving the following dichotomy: either it has totally positive Poisson entropy (and is of zero type), or it possesses a Poisson-Pinsker factor. If G is abelian and the entropy positive, the spectrum is absolutely continuous (Lebesgue co...

Self-consistent approximations allowing the calculation of the entropy and the baryon density of a quark-gluon plasma are presented. These approximations incorporate the essential physics of the hard thermal loops, involve only ultraviolet-finite quantities , and are free from overcounting ambiguities. While being nonperturbative in the strong coupling constant g, agreement with ordinary pertur...

Let X = S where G is a countable group and S is a finite set. A cellular automaton (CA) is an endomorphism T : X → X (continuous, commuting with the action of G). Shereshevsky [14] proved that for G = Z with d > 1 no CA can be forward expansive, raising the following conjecture: For G = Z, d > 1 the topological entropy of any CA is either zero or infinite. Morris and Ward [11], proved this for ...

We consider the nonlinear degenerate elliptic-parabolic-hyperbolic equation ∂tg(u)−∆b(u)− div Φ(u) = f(g(u)) in (0, T )× Ω, where g and b are nondecreasing continuous functions, Φ is vectorial and continuous, and f is Lipschitz continuous. We prove the existence, comparison and uniqueness of entropy solutions for the associated initial-boundary-value problem where Ω is a bounded domain in RN . ...

Let X = S where G is a countable group and S is a finite set. A cellular automaton (CA) is an endomorphism T : X → X (continuous, commuting with the action of G). Shereshevsky [13] proved that for G = Z with d > 1 no CA can be forward expansive, raising the following conjecture: For G = Z, d > 1 the topological entropy of any CA is either zero or infinite. Morris and Ward [10], proved this for ...

The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity of the MEPP and to test the scope of its applicability, it is necessary to conduct experiments in which the entropy prod...

We present a unified algorithmic framework to obtain nearly optimal space bounds for text compression and compressed text indexing, apart from lower-order terms. For a text T of n symbols drawn from an alphabet Σ, our bounds are stated in terms of the hth-order empirical entropy of the text, Hh. In particular, we provide a tight analysis of the Burrows-Wheeler transform (bwt) establishing a bou...