When modeling complex biological systems, exploring parameter space is critical, because parameter values are typically poorly known a priori. This exploration can be challenging, because parameter space often has high dimension and complex structure. Recent work, however, has revealed universal structure in parameter space of models for nonlinear systems. In particular, models are often sloppy...

In this article I wish to convey to beginners how analytic, algebro-geometric, and arithmetic techniques come together in the study of abelian varieties and their variation in families. For many modern arithmetic applications it is crucial that the entire theory admits an algebraic foundation (requiring the full force of the theory of schemes and beyond), but much of our geometric intuition and...

The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group acting on it. As a consequence, we are able to study the singularities of W and prove that the biologically meaningfu...

Gravity data inversion is one of the important steps in the interpretation of practical gravity data. The inversion result can be obtained by minimization of the Tikhonov objective function. The determination of an optimal regularization parameter is highly important in the gravity data inversion. In this work, an attempt was made to use the active constrain balancing (ACB) method to select the...

A consistent combination of quantum geometry effects rules out a large class of models of loop quantum cosmology and their critical densities as they have been used in the recent literature. In particular, the critical density at which an isotropic universe filled with a free, massless scalar field would bounce must be well below the Planck density. In the presence of anisotropy, no model of th...

Let B be an A∞-category with finitely many objects (X1, . . . ,Xm). We impose some technical restrictions (finite-dimensional hom spaces, strict unitality). Consider the directed subcategory A ⊂ B, which retains only morphisms from Xi to Xj for i < j, together with the identity endomorphisms. Following [10], we associate to the pair (A,B) a further object D, which is a filtered A∞-category with...

In this report we compare the predictions of the collinear parton model and the kT -factorization approach in J/Ψ and D ⋆ meson photoproduction at HERA energies. It is shown that obtained D⋆ meson spectra over pT and η are very similar in the parton model and kT -factorization approach and they underestimate the experimental data. Opposite, the predictions of the both approaches for pT and z-sp...