Towards a single parameter for the assessment of EEG oscillations.

The single macroscopic flow on the boundary of a closed curve equals the sum of the countless microscopic flows in the enclosed area. According to the dictates of the Green's theorem, the counterclockwise movements on the border of a two-dimensional shape must equal all the counterclockwise movements taking place inside the shape. This mathematical approach might be useful to analyse neuroscientific data sets for its potential capability to describe the whole cortical activity in terms of electric flows occurring in peripheral brain areas.

Flock members experience gas pressures higher than lone individuals.

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embedded. Using the K-Nearest Neighbors algorithm to simulate collective animal behavior, we showed that the occurrence of collective dynamics can modify the physical parameters of the phase space in which the interacting individuals' trajectories take place.

Dynamics and metabolic effects of intestinal gases in healthy humans.

Many living beings use exogenous and/or endogenous gases to attain evolutionary benefits. We make a comprehensive assessment of one of the major gaseous reservoirs in the human body, i.e.

The First Nucleic Acid Strands May Have Grown on Peptides via Primeval Reverse Translation.

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids polymers. Arguing in favour of a sort of archaic "reverse translation" from proteins to RNA, our basic premise is a Hadean Earth where key biomolecules such as amino acids, polypeptides, purines, pyrimidines, nucleosides and nucleotides were available under different prebiotically plausible conditions, including meteorites delivery, shallow ponds and hydrothermal vents scenarios.

Laws of taxation for multicellular organisms: The economics of sleep.

In macro-public finance, the Ramsey rule (RR) concerns variable taxation to maximize social welfare and economic efficiency in a purely competitive monopolistic system. To extract tax revenue with the least loss of utility to the representative individual, RR dictates that optimal, proportionate taxes should be such as to diminish in the same proportion the production of each commodity taxed. The sources of supply that are inelastic, i.

Non-ultrametric phylogenetic trees shed new light on Neanderthal introgression.

Ultrametric spaces are widely used to depict evolutionary times in phylogenetic trees since they assume that every population/species is located at the tips of bifurcating branches of the same length. The discrete branching of ultrametric trees permits the measurement of distances between pairs of individuals that are proportional to their divergence time. Here the traditional ultrametric concept of bifurcating and divergent phylogenetic tree is overturned and a new type of non-ultrametric diagram is introduced.

Unusual Mathematical Approaches Untangle Nervous Dynamics.

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses.

Bipolar reasoning in feedback pathways.

Instead of the conventional 0 and 1 values, bipolar reasoning uses -1, 0, +1 to describe double-sided judgements in which neutral elements are halfway between positive and negative evaluations (e.g., "uncertain" lies between "impossible" and "totally sure").

An economic approach to energy budgets: HOW many resources should living organisms spare?

Ramsey's economic theory of saving (RTS) estimates how much of its commodities a nation should save to safeguard the well-being of future generations. Since RTS retains many attractive qualities such as simplicity, strength, breadth and generality, here we ask if it would be useful to investigate biophysical issues. Specifically, we focus on a biological topic that lends itself as a backdrop for the study of the imbalance between intake and expenditure, i.

Topology of eeg wave fronts.

Whenever one attempts to comb a hairy ball flat, there will always be at least one tuft of hair at one point on the ball. This seemingly worthless sentence is an informal description of the hairy ball theorem, an invaluable mathematical weapon that has been proven useful to describe a variety of physical/biological processes/phenomena in terms of topology, rather than classical cause/effect relationships. In this paper we will focus on the electrical brain field-electroencephalogram (EEG).

Do gene-environment interactions play a role in COVID-19 distribution? The case of Alpha-1 Antitrypsin, air pollution and COVID-19.

Background: Gene-environment interactions are relevant for several respiratory diseases. This communication raises the hypothesis that the severity of COVID-19, a complex disease where the individual response to the infection may play a significant role, could partly result from a gene-environment interaction between air-pollution and Alpha-1 Antitrypsin (AAT) genes.

Methods: To evaluate the impact of the AAT and air pollution interaction on COVID-19, we introduced an AAT*air pollution global risk score summing together, in each country, an air pollution score (ozone, nitrogen dioxide and fine particulate matter) and an AAT score (which sums the ranked frequency of MZ, SZ, MS).

Why Should Natural Principles Be Simple?

One of the criteria to a strong principle in natural sciences is simplicity. The conventional view holds that the world is provided with natural laws that must be simple. This common-sense approach is a modern rewording of the medieval philosophical/theological concept of the Multiple arising from (and generated by) the One.

Neural computing in four spatial dimensions.

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information.

Removing uncertainty in neural networks.

Neuroscientists draw lines of separation among structures and functions that they judge different, arbitrarily excluding or including issues in our description, to achieve positive demarcations that permits a pragmatic treatment of the nervous activity based on regularity and uniformity. However, uncertainty due to disconnectedness, lack of information and absence of objects' sharp boundaries is a troubling issue that prevents these scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial neural networks. Starting from the detection of metamorphoses of shapes inside a Euclidean manifold, we propose a technique to detect the topological changes that occur during their reciprocal interactions and shape morphing.

Topological View of Flows Inside the BOLD Spontaneous Activity of the Human Brain.

Spatio-temporal brain activities with variable delay detectable in resting-state functional magnetic resonance imaging (rs-fMRI) give rise to highly reproducible structures, termed cortical lag threads, that propagate from one brain region to another. Using a computational topology of data approach, we found that persistent, recurring blood oxygen level dependent (BOLD) signals in triangulated rs-fMRI videoframes display previously undetected topological findings, i.e.

Gastroesophageal and gastric ultrasound in children: the state of the art.

In previous years, the role of gastroesophageal (GE) ultrasound as a diagnostic tool in gastroesophageal reflux disease (GERD) has been disputed. Most authors believe that it is difficult to diagnose GERD without correlation studies between esophageal pathology and ultrasonographic signs. Indeed, there are many anatomic descriptions of the normal GE junction.

Projective mechanisms subtending real world phenomena wipe away cause effect relationships.

Causal relationships lie at the very core of scientific description of biophysical phenomena. Nevertheless, observable facts involving changes in system shape, dimension and symmetry may elude simple cause and effect inductive explanations. Here we argue that numerous physical and biological phenomena such as chaotic dynamics, symmetry breaking, long-range collisionless neural interactions, zero-valued energy singularities, and particle/wave duality can be accounted for in terms of purely topological mechanisms devoid of causality.

Points and lines inside human brains.

Starting from the tenets of human imagination, ., the concepts of lines, points and infinity, we provide a biological demonstration that the skeptical claim "human beings cannot attain knowledge of the world" holds true. We show that the Euclidean account of the point as "that of which there is no part" is just a conceptual device produced by our brain, untenable in our physical/biological realm: currently used terms like "lines, surfaces and volumes" label non-existent, arbitrary properties.

Towards dewetting monoclonal antibodies for therapeutical purposes.

Dewetting transition - a concept borrowed from fluid mechanics - is a physiological process that takes place inside the hydrophobic pores of ion channels. This transient phenomenon causes a metastable state that forbids water molecules to cross microscopic receptor cavities. This leads to a decreased conductance, a closure of the pore and, subsequently, severe impairment of cellular performance.

Entropy Balance in the Expanding Universe: A Novel Perspective.

We describe cosmic expansion as correlated with the standpoints of local observers' co-moving horizons. In keeping with relational quantum mechanics, which claims that quantum systems are only meaningful in the context of measurements, we suggest that information gets ergodically "diluted" in our isotropic and homogeneous expanding Universe, so that an observer detects just a limited amount of the total cosmic bits. The reduced bit perception is due the decreased density of information inside the expanding cosmic volume in which the observer resides.

The multidimensional brain.

Brain activity takes place in three spatial-plus time dimensions. This rather obvious claim has been recently questioned by papers that, taking into account the big data outburst and novel available computational tools, are starting to unveil a more intricate state of affairs. Indeed, various brain activities and their correlated mental functions can be assessed in terms of trajectories embedded in phase spaces of dimensions higher than the canonical ones.

The common features of different brain activities.

The term "brain activity" refers to a wide range of mental faculties that can be assessed either on anatomical/functional micro-, meso- and macro- spatiotemporal scales of observation, or on intertwined cortical levels with mutual interactions. Our aim is to show that every brain activity encompassed in a given anatomical or functional level necessarily displays a counterpart in others, i.e.

The informational entropy endowed in cortical oscillations.

A two-dimensional shadow may encompass more information than its corresponding three-dimensional object. Indeed, if we rotate the object, we achieve a pool of observed shadows from different angulations, gradients, shapes and variable length contours that make it possible for us to increase our available information. Starting from this simple observation, we show how informational entropies might turn out to be useful in the evaluation of scale-free dynamics in the brain.

EEG dynamics on hyperbolic manifolds.

Biological activities, including cellular metabolic pathways, protein folding and brain function, can be described in terms of curved trajectories in hyperbolic spaces which are constrained by energetic requirements. Here, starting from theorems recently-developed by a deceased Field Medal young mathematician, we show how it is feasible to find and quantify the shortest, energy-sparing functional trajectories taking place in nervous systems' concave phase spaces extracted from real EEG traces. This allows neuroscientists to focus their studies on the few, most prominent functional EEG's paths and loops able to explain, elucidate and experimentally assess the rather elusive mental activity.