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.

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 bowel, providing extensive data that may serve as reference for future studies. We assess the intestinal gases in healthy humans, including their volume, composition, source and local distribution in proximal as well as distal gut. We analyse each one of the most abundant intestinal gases including nitrogen, oxygen, nitric oxide, carbon dioxide, methane, hydrogen, hydrogen sulfide, sulfur dioxide and cyanide. For every gas, we describe diffusive patterns, active trans-barrier transport dynamics, chemical properties, intra-/extra-intestinal metabolic effects mediated by intracellular, extracellular, paracrine and distant actions. Further, we highlight the local and systemic roles of gasotransmitters, i.e., signalling gaseous molecules that can freely diffuse through the intestinal cellular membranes. Yet, we provide testable hypotheses concerning the still unknown effects of some intestinal gases on the myenteric and submucosal neurons.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

Multidimensional brain activity dictated by winner-take-all mechanisms

A novel demon-based architecture is introduced to elucidate brain functions such as pattern recognition during human perception and mental interpretation of visual scenes. Starting from the topological concepts of invariance and persistence, we introduce a Selfridge pandemonium variant of brain activity that takes into account a novel feature, namely, demons that recognize short straight-line segments, curved lines and scene shapes, such as shape interior, density and texture. Low-level representations of objects can be mapped to higher-level views (our mental interpretations): a series of transformations can be gradually applied to a pattern in a visual scene, without affecting its invariant properties. This makes it possible to construct a symbolic multi-dimensional representation of the environment. These representations can be projected continuously to an object that we have seen and continue to see, thanks to the mapping from shapes in our memory to shapes in Euclidean space. Although perceived shapes are 3-dimensional (plus time), the evaluation of shape features (volume, color, contour, closeness, texture, and so on) leads to n-dimensional brain landscapes. Here we discuss the advantages of our parallel, hierarchical model in pattern recognition, computer vision and biological nervous system's evolution.

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. Indeed, brain activity exhibits a scale-free distribution that leads to the variations in the power law exponent typical of different functional neurophysiological states. Here we show that modifications in scaling slope are associated with variations in Rényi entropy, a generalization of Shannon informational entropy. From a three-dimensional object's perspective, by changing its orientation (standing for the cortical scale-free exponent), we detect different two-dimensional shadows from different perception angles (standing for Rényi entropy in different brain areas). We show how, starting from known values of Rényi entropy (easily detectable in brain fMRIs or EEG traces), it is feasible to calculate the scaling slope in a given moment and in a given brain area. Because changes in scale-free cortical dynamics modify brain activity, this issue points towards novel approaches to mind reading and description of the forces required for transcranial stimulation.

Towards plasma-like collisionless trajectories in the brain

Plasma studies depict collisionless, collective movements of charged particles. In touch with these concepts, originally developed by the far-flung branch of high energy physics, here we evaluate the role of collective behaviors and long-range functional couplingsof charged particlesin brain dynamics. We build a novel, empirically testable, brain model which takes into account collisionless movements of charged particles in a system, the brain, equipped with oscillations. The model is cast in a mathematical fashion with the potential of being operationalized, because it can be assessed in terms of McKean-Vlasov equations, derived from the classical Vlasov equations for plasma. A plasma-like brain also elucidates cortical phase transitions in the context of a brain at the edge of chaos, describing the required order parameters. In sum, showing how the brain might exhibit plasma-like features,we go through the concept of holistic behavior of nervous functions.

A timeless biology

Contrary to claims that physics is timeless while biology is time-dependent, we take the opposite standpoint: physical systems' dynamics are constrained by the arrow of time, while living assemblies are time-independent. Indeed, the concepts of "constraints" and "displacements" shed new light on the role of continuous time flow in life evolution, allowing us to sketch a physical gauge theory for biological systems in long timescales. In the very short timescales of biological systems' individual lives, time looks like "frozen" and "fixed", so that the second law of thermodynamics is momentarily wrecked. The global symmetries (standing for biological constrained trajectories, i.e. the energetic gradient flows dictated by the second law of thermodynamics in long timescales) are broken by local "displacements" where time is held constant, i.e., modifications occurring in living systems. Such displacements stand for brief local forces, able to temporarily "break" the cosmic increase in entropy. The force able to restore the symmetries (called "gauge field") stands for the very long timescales of biological evolution. Therefore, at the very low speeds of life evolution, time is no longer one of the four phase space coordinates of a spacetime Universe: it becomes just a gauge field superimposed to three-dimensional biological systems. We discuss the implications in biology: when assessing living beings, the underrated role of isolated "spatial" modifications needs to be emphasized, living apart the evolutionary role of time.

Relationships between short and fast brain timescales

Brain electric activity exhibits two important features: oscillations with different timescales, characterized by diverse functional and psychological outcomes, and a temporal power law distribution. In order to further investigate the relationships between low- and high- frequency spikes in the brain, we used a variant of the Borsuk-Ulam theorem which states that, when we assess the nervous activity as embedded in a sphere equipped with a fractal dimension, we achieve two antipodal points with similar features (the slow and fast, scale-free oscillations). We demonstrate that slow and fast nervous oscillations mirror each other over time via a sinusoid relationship and provide, through the Bloch theorem from solid-state physics, the possible equation which links the two timescale activities. We show that, based on topological findings, nervous activities occurring in micro-levels are projected to single activities at meso- and macro-levels. This means that brain functions assessed at the higher scale of the whole brain necessarily display a counterpart in the lower ones, and vice versa. Our topological approach makes it possible to assess brain functions both based on entropy, and in the general terms of particle trajectories taking place on donut-like manifolds. Condensed brain activities might give rise to ideas and concepts by combination of different functional and anatomical levels. Furthermore, cognitive phenomena, as well as social activity can be described by the laws of quantum mechanics; memories and decisions exhibit holographic organization. In physics, the term duality refers to a case where two seemingly different systems turn out to be equivalent. This topological duality holds for all the types of spatio-temporal brain activities, independent of their inter- and intra-level relationships, strength, magnitude and boundaries, allowing us to connect the physiological manifestations of consciousness to the electric activities of the brain.

Cellular Gauge Symmetry and the Li Organization Principle: A Mathematical Addendum. Quantifying energetic dynamics in physical and biological systems through a simple geometric tool and geodetic curves

The present Addendum complements the accompanying paper "Cellular Gauge Symmetry and the Li Organization Principle"; it illustrates a recently-developed geometrical physical model able to assess electronic movements and energetic paths in atomic shells. The model describes a multi-level system of circular, wavy and zigzag paths which can be projected onto a horizontal tape. This model ushers in a visual interpretation of the distribution of atomic electrons' energy levels and the corresponding quantum numbers through rather simple tools, such as compasses, rulers and straightforward calculations. Here we show how this geometrical model, with the due corrections, among them the use of geodetic curves, might be able to describe and quantify the structure and the temporal development of countless physical and biological systems, from Langevin equations for random paths, to symmetry breaks occurring ubiquitously in physical and biological phenomena, to the relationships among different frequencies of EEG electric spikes. Therefore, in our work we explore the possible association of binomial distribution and geodetic curves configuring a uniform approach for the research of natural phenomena, in biology, medicine or the neurosciences.

Can Stereotactic Body Radiation Therapy Be a Viable and Efficient Therapeutic Option for Unresectable Locally Advanced Pancreatic Adenocarcinoma? Results of a Phase 2 Study

PURPOSE

To assess the efficacy of stereotactic body radiotherapy in patients with unresectable locally advanced pancreatic cancer.

MATERIALS AND METHODS

All patients received a prescription dose of 45 Gy in 6 fractions. Primary end point was freedom from local progression. Secondary end points were overall survival, progression-free survival, and toxicity. Actuarial survival analysis and univariate or multivariate analysis were investigated.

RESULTS

Forty-five patients were enrolled in a phase 2 trial. Median follow-up was 13.5 months. Freedom from local progression was 90% at 2 years. On univariate ( P < .03) and multivariate analyses ( P < .001), lesion size was statistically significant for freedom from local progression. Median progression-free survival and overall survival were 8 and 13 months, respectively. On multivariate analysis, tumor size ( P < .001) and freedom from local progression ( P < .002) were significantly correlated with overall survival. Thirty-two (71%) patients with locally advanced pancreatic cancer received chemotherapy before stereotactic body radiotherapy. Median overall survival from diagnosis was 19 months. Multivariate analysis showed that freedom from local progression ( P < .035), tumor diameter ( P < .002), and computed tomography before stereotactic body radiotherapy ( P < .001) were significantly correlated with overall survival from diagnosis.

CONCLUSION

Stereotactic body radiotherapy is a safe and effective treatment for patients with locally advanced pancreatic cancer with no G3 toxicity or greater and could be a promising therapeutic option in multimodality treatment regimen.

From abstract topology to real thermodynamic brain activity

Recent approaches to brain phase spaces reinforce the foremost role of symmetries and energy requirements in the assessment of nervous activity. Changes in thermodynamic parameters and dimensions occur in the brain during symmetry breakings and transitions from one functional state to another. Based on topological results and string-like trajectories into nervous energy landscapes, we provide a novel method for the evaluation of energetic features and constraints in different brain functional activities. We show how abstract approaches, namely the Borsuk-Ulam theorem and its variants, may display real, energetic physical counterparts. When topology meets the physics of the brain, we arrive at a general model of neuronal activity, in terms of multidimensional manifolds and computational geometry, that has the potential to be operationalized.