Demystifying neuroblastoma malignancy through fractal dimension, entropy, and lacunarity.

Purpose: Neuroblastoma is a pediatric solid tumor with a prognosis associated with histology and age of the patient, which are the parameters of the well-established current classification (Shimada classification). Despite the development of new treatment options, the prognosis of high-risk neuroblastoma patients is still poor. Therefore, there is a continuous need to stratify the children suffering from this tumor.

Publisher Correction: Collective behavior of oscillating electric dipoles.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Collective behavior of oscillating electric dipoles.

We investigate the dynamics of a population of identical biomolecules mimicked as electric dipoles with random orientations and positions in space and oscillating with their intrinsic frequencies. The biomolecules, beyond being coupled among themselves via the dipolar interaction, are also driven by a common external energy supply. A collective mode emerges by decreasing the average distance among the molecules as testified by the emergence of a clear peak in the power spectrum of the total dipole moment.

Persistent homology analysis of phase transitions.

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called mean-field XY model and by the ϕ^{4} lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.

Random walk of passive tracers among randomly moving obstacles.

Background: This study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target.

Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles.

Results: The relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance.

Topological Strata of Weighted Complex Networks.

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and -more recently- correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks.