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. Given a map of raw EEG data to coloured ovals in which different colours stand for different amplitudes, the theorem suggests that the sum of the electric amplitudes measured inside every oval equals the amplitudes measured just on the oval's edge. This means that the collection of the vector fields detected from the scalp can be described by a novel, single parameter summarizing the counterclockwise electric flow detected in the outer electrodes. To evaluate the predictive power of this parameter, in a pilot study we investigated EEG traces from ten young females performing Raven's intelligence tests of various complexity, from easy tasks (n = 5) to increasingly complex tasks (n = 5). Despite the seemingly unpredictable behavior of EEG electric amplitudes, the novel parameter proved to be a valuable tool to to discriminate between the two groups and detect hidden, statistically significant differences. We conclude that the application of this promising parameter could be expanded to assess also data sets extracted from neurotechniques other than EEG.

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. This means that lone individuals experience the nearby fluid medium (i.e., the air in case of birds/insects and the water in case of fishes) differently from flock members. In particular, our framework suggests that a bird belonging to a group and acting collectively with its neighbors perceives the nearby atmosphere as denser, compared with an isolated bird.

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. Supporting a protein-first scenario alternative to the RNA world hypothesis, we propose the primeval occurrence of short two-dimensional peptides termed "selective amino acid- and nucleotide-matching oligopeptides" (henceforward SANMAOs) that noncovalently bind at the same time the polymerized amino acids and the single nucleotides dispersed in the prebiotic milieu. In this theoretical paper, we describe the chemical features of this hypothetical oligopeptide, its biological plausibility and its virtues from an evolutionary perspective. We provide a theoretical example of SANMAO's selective pairing between amino acids and nucleosides, simulating a poly-Glycine peptide that acts as a template to build a purinic chain corresponding to the glycine's extant triplet codon GGG. Further, we discuss how SANMAO might have endorsed the formation of low-fidelity RNA's polymerized strains, well before the appearance of the accurate genetic material's transmission ensured by the current translation apparatus.

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.e., necessities/utilities, must be taxed more. We hypothesize that the Ramsey's economical approach might provide a general mechanism to investigate far-flung biological issues, such as preys/predators dynamics, food restriction in ecological niches, local changes in blood flow in rival or complementary organs of multicellular organisms. In particular, RR suggests a quantifiable relationship between the physiological decrease in cortical spike frequency occurring during sleep and energy consumption. Since small decreases in spike frequency during sleep are correlated with large decreases in the amount of consumed ATP, the brain could be considered an inelastic commodity which can be "taxed" more than other organs, allowing the whole organism to spare energy. Shedding light on the energy budget of the central nervous system, RR improves our knowledge of cerebral perfusion during sensory-evoked responses and tissue hypoxia caused by decreased blood flow, suggesting that energy from outside can be provided to counteract brain ischemia. In sum, the economical approach provided by Ramsey stands for a useful methodological tool that could be used in biological contexts to investigate the dynamical correlations among different organs in multicellular organisms.

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. The objective of this study is the description of gene flows in branching species/populations in terms of converging trees instead of bifurcating trees. To provide an operational example, the paleoanthropological issue of the date of Neanderthal genome's introgression in non-African humans is examined. Neanderthals and ancient humans are not anymore two species that exchange chunks of DNA, rather become a single, novel cluster of extant hominins that must be considered by itself. The novel converging, non-ultrametric phylogenetic trees permit the calibration of molecular clocks with a twofold benefit. When the date of the branching of two population/species from a common ancestor is known, the novel approach allows to calculate the time of subsequent introgressions. On the contrary, when the date of the introgression between two population/species is known, the novel approach allows to detect the time of their previous branching from a common ancestor.

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. The Monge's theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo-fetal tissues.

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"). We discuss the state-of-the-art in bipolar logics and recall two medieval forerunners, i.e., William of Ockham and Nicholas of Autrecourt, who embodied a bipolar mode of thought that is eminently modern. Starting from the trivial observation that "once a wheat sheaf is sealed and tied up, the packed down straws display the same orientation", we work up a new theory of the bipolar nature of networks, suggesting that orthodromic (i.e., feedforward, bottom-up) projections might be functionally coupled with antidromic (i.e., feedback, top-down) projections via the mathematical apparatus of presheaves/globular sets. When an entrained oscillation such as a neuronal spike propagates from A to B, changes in B might lead to changes in A, providing unexpected antidromic effects. Our account points towards the methodological feasibility of novel neural networks in which message feedback is guaranteed by backpropagation mechanisms endowed in the same feedforward circuits. Bottom-up/top-down transmission at various coarse-grained network levels provides fresh insights in far-flung scientific fields such as object persistence, memory reinforcement, visual recognition, Bayesian inferential circuits and multidimensional activity of the brain. Implying that axonal stimulation by external sources might backpropagate and modify neuronal electric oscillations, our theory also suggests testable previsions concerning the optimal location of transcranial magnetic stimulation's coils in patients affected by drug-resistant epilepsy.

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.e., the evaluation of the multicellular living organisms' energetic requirements and constraints. Our problem is to find at each time the optimum distribution and the right balance of the cellular energy budget between consumption and storage: how much must a living organism spare to increase its chances of survival over long periods? To give an operational example, we discuss the ATP requirements in the central nervous system during the spontaneous and the evoked activity of the brain, showing that the experimentally detected values of energetic expenditure during neural computations match well with the estimations provided by RTS. Suggesting how to find the optimum allocation of the available energy between expenditure and saving at each time, RTS approaches to biological energy budgets may have a wide range of experimental applications, such as: a) optimization of the long-term survival chances of either immortalized cell cultures, or beneficial bacterial colonies and exogenous probiotic mixtures; b) eradication of detrimental biofilms, such as, e.g., heart valves' Streptococcus colonies; c) novel anti-stress and anti-ageing strategies.

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. Humans need to pursue unifying frameworks, classificatory criteria and theories of everything. Still, the fact that our cognitive abilities tend towards simplification and groupings does not necessarily entail that this is the way the world works. Here we ask: what if singularity does not pave the way to multiplicity? How will we be sure if the Ockham's razor holds in real life? We will show in the sequel that the propensity to reduce to simplicity the relationships among the events leads to misleading interpretations of scientific issues. We are not going to take a full sceptic turn: we will engage in active outreach, suggesting examples from biology and physics to demonstrate how a novel methodological antiunitary approach might help to improve our scientific attitude towards world affairs. We will provide examples from aggregation of SARS-Cov-2 particles, unclassified extinct creatures, pathological brain stiffness. Further, we will describe how antiunitary strategies, plagiarising medieval concepts from William od Ockham and Gregory of Rimini, help to explain novel relational approaches to quantum mechanics and the epistemological role of our mind in building the real world.

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). As a starting point we consider the recently-raised observation that, when electromagnetic oscillations propagate with a spherical wave front, there must be at least one point of the tangential components of the vector fields where the electromagnetic field vanishes. We show how this description holds also for the electric waves produced by the brain and detectable by EEG. Once located these zero-points in EEG traces, we confirm that they are able to modify the electric wave fronts detectable in the brain. This sheds new light on the functional features of a nonlinear, metastable nervous system at the edge of chaos, based on the neuroscientific model of Operational Architectonics of brain-mind functioning. As an example of practical application of this theorem, we provide testable previsions, suggesting the proper location of transcranial magnetic stimulation's coils to improve the clinical outcomes of drug-resistant epilepsy.

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). We compared this global score with the ranking of European countries in terms of death number per million persons. RESULTS: The ranking of the AAT*air pollution global risk score matched the ranking of the countries in terms of the observed COVID-19 deaths per 1M inhabitants, namely in the case of the first European countries: Belgium, UK, Spain, Italy, Sweden, France. We observed parallelism between the number of COVID deaths and the AAT*air pollution global risk in Europe. AAT anti-protease, immune-modulating and coagulation-modulating activities may explain this finding, although very speculatively. CONCLUSIONS: Even if further studies taking into account genetic background, population density, temporal dynamics of individual epidemics, access to healthcare, social disparities and immunological response to SARS-CoV2 are needed, our preliminary observation urges to open a discussion on gene-environment interactions in COVID-19.

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. Synthesis of surface shape components, viewed topologically as shape descriptions in the form of feature vectors that vary over time, leads to a 4D view of cerebral activity. This novel, relatively straightforward architecture permits to increase the amount of available qbits in a fixed volume.

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. The fact that GERD diagnosis was made by morphological studies was believed to be an incorrect deduction. We revisit the pathophysiologic data concerning the gastroesophageal junction and gastric function and review the data in the literature of the past 30 years.

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. This method, that allows the detection of topological holes development and disappearance, makes it possible to solve the problem of uncertainty in the assessment of countless dynamical phenomena, such as cognitive processes, protein homeostasis deterioration, fire propagation, wireless sensor networks, migration flows, and cosmic bodies analysis.

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., vortex structures that cover brain activated regions. Measure of persistence of vortex shapes in BOLD signal propagation is carried out in terms of Betti numbers that rise and fall over time during spontaneous activity of the brain. Importantly, a topology of data given in terms of geometric shapes of BOLD signal propagation offers a practical approach in coping with and sidestepping massive noise in neurodata, such as unwanted dark (low intensity) regions in the neighborhood of non-zero BOLD signals. Our findings have been codified and visualized in plots able to track the non-trivial BOLD signals that appear intermittently in a sequence of rs-fMRI videoframes. The end result of this tracking of changing lag structures is a so-called persistent barcode, which is a pictograph that offers a convenient visual means of exhibiting, comparing, and classifying brain activation patterns.

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. We illustrate how simple topological claims, seemingly far away from scientific inquiry (e.g., "given at least some wind on Earth, there must at all times be a cyclone or anticyclone somewhere"; "if one stirs to dissolve a lump of sugar in a cup of coffee, it appears there is always a point without motion"; "at any moment, there is always a pair of antipodal points on the Earth's surface with equal temperatures and barometric pressures") reflect the action of non-causal topological rules. To do so, we introduce some fundamental topological tools and illustrate how phenomena such as double slit experiments, cellular mechanisms and some aspects of brain function can be explained in terms of geometric projections and mappings, rather than local physical effects. We conclude that unavoidable, passive, spontaneous topological modifications may lead to novel functional biophysical features, independent of exerted physical forces, thermodynamic constraints, temporal correlations and probabilistic a priori knowledge of previous cases.

Points and lines inside human brains.

Starting from the tenets of human imagination, i.e., 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. We elucidate the psychological and neuroscientific features hardwired in our brain that lead us humans to think to points and lines as truly occurring in our environment. Therefore, our current scientific descriptions of objects' shapes, graphs and biological trajectories in phase spaces need to be revisited, leading to a proper portrayal of the real world's events: miniscule bounded physical surface regions stand for the basic objects in a traversal of spacetime, instead of the usual Euclidean points. Our account makes it possible to erase of a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events: the unwanted occurrence of infinite values in equations. We propose a novel approach, based on point-free geometrical standpoints, that banishes infinitesimals, leads to a tenable physical/biological geometry compatible with human reasoning and provides a region-based topological account of the power laws endowed in nervous activities. We conclude that points, lines, volumes and infinity do not describe the world, rather they are fictions introduced by ancient surveyors of land surfaces.

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. In this review, I show how further dimensions may not just represent a convenient methodological tool that allows a better mathematical treatment of otherwise elusive cortical activities, but may also reflect genuine functional or anatomical relationships among real nervous functions. I then describe how to extract hidden multidimensional information from real or artificial neurodata series, and make clear how our mind dilutes, rather than concentrates as currently believed, inputs coming from the environment. Finally, I argue that the principle "the higher the dimension, the greater the information" may explain the occurrence of mental activities and elucidate the mechanisms of human diseases associated with dimensionality reduction.

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., they are "dual". "Duality" refers to the case where two seemingly different physical systems turn out to be equivalent. We describe a method, based on novel topological findings, that makes different manifolds (standing for different brain activities) able to scatter, collide and combine, in order that they merge, condense and stitch together in a quantifiable way. We develop a computational tool which explains how, despite their local cortical functional differences, all mental processes, from perception to emotions, from cognition to mind wandering, may be reduced to a single, general brain activity that takes place in dimensions higher than the classical three-dimensional plus time. This framework permits a topological duality among different brain activities and neuro-techniques, because it holds for all the types of spatio-temporal nervous functions, independent of their cortical location, inter- and intra-level relationships, strength, magnitude and boundaries.