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In this paper, we analyze the human walk movementvia a combined deterministic-stochastic model built on top ofa random walk framework. We discuss how stochastic anddeterministic forces combine to determine the act of moving,adopting a Laban Movement Analysis background to categorizedifferent movement classes. In particular, we recall the four qualitative subcategories of the Laban Effort (space, weight, flow, andtime), and we present their main features through some commonexamples of movement. Major elements of our study are theanalysis of random times when there is a walk movement change,the construction of a distribution (waiting time distribution),and the implementation of a dichotomic stochastic force. Lateron, we report the observed walk trajectories obtained via anexperimental analysis performed in collaboration with a group ofvolunteers to show, to some degree, the relationship between theirwalks and the four subcategories of the Laban Effort. Finally, wepresent our model results via simulated trajectories of a virtualcharacter.

La comprensione delle difese immunitarie non può prescindere da una visione ampia dell'insieme degli esseri viventi e dei loro reciproci rapporti nell'ambiente ecologico di vita. In questo saggio si illustrano le relazioni esistenti tra gli esseri viventi nell'ecosistema, con particolare riguardo ai rapporti tra virus ed animali, per conoscere meglio i criteri biologici che sono alla base degli ampi fenomeni del parassitismo e delle malattie infettive. Il miglioramento delle conoscenze in questo campo è indispensabile non solo per svolgere consapevolmente le professioni sanitarie, ma anche per comprendere e promuovere le pratiche vaccinali oggi fondamentali per difendersi da gravi malattie come la nuova pandemia da SARS-Cov-2. Ciò soprattutto nel contesto di una visione approfondita del paradigma Pnei, che implica integrazione delle diverse discipline in una visione unitaria dell'individuo ed un necessario e continuo aggiornamento delle conoscenze acquisite.

In this paper we revisit the memristor concept within circuit theory. We start from the definition of the basic circuit elements, then we introduce the original formulation of the memristor concept and summarize some of the controversies on its nature. We also point out the ambiguities resulting from a non rigorous usage of the flux linkage concept. After concluding that the memristor is not a fourth basic circuit element, prompted by recent claims in the memristor literature, we look into the application of the memristor concept to electrophysiology, realizing that an approach suitable to explain the observed inductive behavior of the giant squid axon had already been developed in the 1960s, with the introduction of "time-variant resistors." We also discuss a recent memristor implementation in which the magnetic flux plays a direct role, concluding that it cannot strictly qualify as a memristor, because its $v-i$ curve cannot exactly pinch at the origin. Finally, we present numerical simulations of a few memristors and memristive systems, focusing on the behavior in the $\varphi-q$ plane. We show that, contrary to what happens for the most basic memristor concept, for general memristive systems the $\varphi-q$ curve is not single-valued or not even closed., Comment: 13 pages, 19 figures

Purpose Human tau is a highly dynamic, multifunctional protein expressed in different isoforms and conformers, known to modulate microtubule turnover. Tau oligomers are considered pathologic forms of the protein able to initiate specific protein accumulation diseases, called tauopathies. In our study, we investigated the potential association between autophagy and tau oligomers accumulation and its role in the response of prostate cancer cells to docetaxel. Methods We evaluated in vitro the expression of tau oligomers in prostate cancer cell lines, PC3 and DU145, in presence of autophagy inhibitors and investigated the role of tau oligomers accumulation in resistance to docetaxel treatment. Results Tau protein was basally expressed in prostate cancer lines as several monomeric and oligomeric forms. The pharmacologic inhibition of autophagy induced in cancer cells the accumulation of tau protein, with a prevalent expression of oligomeric forms. Immunofluorescence analysis of untreated cells revealed that tau was visible mainly in dividing cells where it was localized on the mitotic spindle. Inhibition of autophagy determined an evident upregulation of tau signal in dividing cells and the presence of aberrant monoastral mitotic spindles. The accumulation of tau oligomers was associated with DNA DSB and increased cytotoxic effect by docetaxel. Conclusions Our data indicate that autophagy could exert a promoting role in cancer growth and during chemotherapy facilitating degradation of tau protein and thus blocking the antimitotic effect of accumulated tau oligomers. Thus, therapeutic strategies aimed at stimulating tau oligomers formation, such as autophagy inhibition, could be an effective adjuvant in cancer therapy.

This article analytically approaches the problem of a propagating wave in a waveguide with a border characterized by an arbitrary angular dependence. We find a relationship between the Fourier coefficients of the function describing the border of the waveguide and the propagation constant $\beta $ of the propagating wave. The proposed solution to the problem provides an analytical tool to obtain information about the shape of a waveguide. The analysis of the propagating wave reveals that, from a theoretical point of view, it is possible to partially, or even completely, reconstruct the border of the waveguide.

In this paper, we analyze the electrostatic charge distribution on arbitrarily shaped conductor surfaces. Following a perturbative approach, we derive an approximate analytical formulation of the problem. We start from the known case of a conducting ellipsoid, we adopt a deformed ellipsoidal coordinate system, and we search for the zero-order approximated solution of the problem. We also focus on arbitrary-shaped thin foils, showing that the charge density is divergent on their borders. We then define the applicability range of the proposed approach expressing the contour equation as the Fourier series. Finally, we present a detailed error analysis for several polygonal contours, comparing the analytical results with those obtained via a numerical analysis based on the Finite Element Methods (FEM).

La recente scomparsa di Noel Rose, noto a livello internazionale come il "padre dell'autoimmunità", ci induce a ricordare brevemente la sua figura di ricercatore e di uomo di scienza per il progresso dell'immunologia e della immunopatologia.

The numerous ongoing research programs aimed at finding and producing rapidly an effective anti-coronavirus vaccine require some explanations about the vaccine immunobiology principles. In this article, the fundamental concepts of modern vaccine preparation are summarized and some of the main research initiatives in vaccine production are illustrated. The author hopes that positive results may emerge soon, allowing the solution of the current coronavirus pandemics emerged at the end of 2019 and still ongoing worldwide.

In this paper we afford a quantitative analysis of the sustainability of current world population growth in relation to the parallel deforestation process adopting a statistical point of view. We consider a simplified model based on a stochastic growth process driven by a continuous time random walk, which depicts the technological evolution of human kind, in conjunction with a deterministic generalised logistic model for humans-forest interaction and we evaluate the probability of avoiding the self-destruction of our civilisation. Based on the current resource consumption rates and best estimate of technological rate growth our study shows that we have very low probability, less than 10% in most optimistic estimate, to survive without facing a catastrophic collapse., 11 pages, 7 figures

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field {where the sojourn time in one of the two states are distributed according to a given waiting time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field}, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous Time Random Walk models., Comment: 16 pages, 11 figures

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

We consider the effect of non-constant parameters on the human-forest interaction logistic model coupled with human technological growth introduced in "Deforestation and world population sustainability: a quantitative analysis"[1]. In recent years in fact, a decrease in human population growth rate has emerged which can be measured to about 1.7% drop per year since 1960 value which coincides with latest UN projections for next decades up to year 2100 [2]. We therefore consider here the effect of decreasing human population growth-rate on the aforementioned model and we evaluate its effect on the probability of survival of human civilisation without going through a catastrophic collapse in population. We find that for realistic values of the human population carrying capacity of the earth (measured by parameter beta) this decrease would not affect previous results leading to a low probability of avoiding a catastrophic collapse. For larger more optimistic values of beta instead, a decrease in growth-rate would tilt the probability in favour of a positive outcome, i.e. from 10-20% up to even 95% likelihood of avoiding collapse., Comment: 2 pages, 1 figure

This chapter presents an introduction to infective diseases and potential biological agents that could potentially be used for bioterrorism. Technical brief description of the possible treatments and preventions of these biothreats is presented with emphasis placed on the principles of immunological defenses, vaccination, and preparation of vaccines. In principle, various types of vaccines that are commercially used as “antibacterial or anticancer vaccines” can be produced using various types of antigenic carbohydrate haptens containing relevant epitopes. This review highlights the strategies used for the characterization of such synthetic neoglycoconjugate vaccines used as a means of protection against biothreats. A complete mass spectrometry-based strategy for validating the preparations of the neoglycoconjugate vaccine is presented.

This brief presents an analysis of the nonlinear dynamics of a memristive inductive–capacitive circuit, driven by a sinusoidal voltage source. The analysis is carried out using multiple-scale technique. The memristance ${M(q)}$ is modeled by a power law series of the electrical charge ${q}$ , considering both passive and active ${M(q)}$ . The steady-state solution behavior, close to the resonant circuit condition, is investigated. Numerical simulations are reported for comparison with analytical results.

This paper studies the exponential of the sum of two non-commuting operators as an infinite product of exponential operators involving repeated commutators of increasing order. It will be shown how to determine two coefficients in front of the nested commutators in the Zassenhaus formula. The knowledge of one coefficient is enough to generate a closed formula that has several applications in solving problems ranging from linear differential equations, quantum mechanics to non-linear differential equations., 18 pages, 4 figures

In this paper, we present a new model of dendrite growth in battery cells through theoretical and numerical analysis. We use a statistical model based on the competition between a deterministic electric field and a stochastic force, which both drive the movement of the particles inside the battery cell. The simulation of the dendrite growth is modeled via Diffusion Limited Aggregation. As a major aspect, we point out the key role played by the intense electric field close to the edges of the electrodes, which statistically drives the particles along the electric field lines.

More than fifty years ago, in a couple of seminal works (Kubo 1962 J. Phys. Soc. Japan 17 1100–20; Kubo 1963 J. Math. Phys. 4 174–83) Kubo introduced the important idea of generalized cumulants, extending to stochastic operators this concept implicitly introduced by Laplace in 1810. Kubo’s idea has been applied in several branches of physics, where the result of the average process is a Lioville operator or an effective time evolution operator for the density matrix of spin systems or the reduced density matrix for boson-fermions etc. Despite this success, the theoretical developments in these Kubo works pose problems that were highlighted many years ago by Fox and van Kampen and never solved. These weaknesses and errors, in particular concerning the factorization property of exponentials of cumulants and the explicit expressions that give generalized cumulants in terms of generalized moments and vice-versa, caused some perplexity (and confusion) about the possible application of this procedure, limiting its use, in practice. In the present paper, we give a sound ground to the approach to cumulant operators, working in a general framework that shows the potentiality of the old Kubo idea, today not yet fully exploited. It results that, for the same moment operators, different definitions of generalized cumulants can be adopted. A general Kubo–Meeron closed-form formula giving cumulant operators in terms of moment operators cannot be obtained, but the reverse one, cumulants in terms of operators, is given and, noticeably, formally it does not depend on the specific nature of the moments, but just on the definition of the generalized cumulants.

Leptin, a cytokine produced by the adipose tissue in response to food intake, is a key player in the regulation of energy balance and body weight control. Physiological action of leptin in modulating the metabolic adaptation of different peripheral tissues supports the hypothesis that it could also exert a direct effect on cancer cells. In vitro, treatment with leptin up-regulated HIF-1α and stimulated adhesion and invasion of prostate cancer cells cultured in hypoxia. Leptin action was effective in both low and high glycolytic cancer cell lines, and determined the up-regulation of lactate exporter MCT4 and its associated protein CD147. HIF-1α stabilization was oligomycin-independent and was associated with an important modulation of mitochondrial homeostasis. In fact, leptin treatment produced mitochondrial biogenesis, stabilization of mitochondrial membrane potential and increased uncoupled respiration through the up-regulation of UCP2. Furthermore, leptin counteracted the downmodulation of SIRT1 induced by hypoxia, and persistent high levels of SIRT1 were directly involved in HIF-1α stabilization. Leptin can sustain cancer progression in hypoxic environment and when mitochondrial respiration is impaired. Leptin signaling axis, including the new proposed intermediate SIRT1, could represent a new diagnostic and therapeutic target in prostate cancer.

In this work we study a non-linear mathematical model based on three different interacting species. We apply our model to Lake Edward ecosystem consisting in hippos, tilapia fishes and human inhabitants. In this case, we estimate the values of the key parameters using actual data and show the reliability of the proposed model as a predictive tool. We also show, via numerical calculations and parameter values that the ecosystem associated to the lake is very far from reaching a stable equilibrium. Through our analysis we provide the conditions for a possible coexistence among the three species.

We study a memristive circuit with included parasitic elements, such as capacitance and inductance. In the multiple-scale scheme, we analytically show how the parasitic elements affect the voltage and the current. Finally, we provide an analytical expression for the intersection point coordinates, through which we discuss the functional behavior of the pinched hysteresis loop versus the operating frequency and the parasitic elements.

In this paper, we will find in terms of Fourier integrals an exact expression for the magnetic and electric fields generated by an infinite solenoid where an arbitrary current density J(t) flows. Considering the central region of an infinite solenoid, we will obtain an exact expression relating the flowing current and the magnetic and electric fields as functions of the time. Being an exact expression, it will allow us to go beyond the quasistatic approximation. The result can apply in theoretical problems and experimental setups where the flowing current may change abruptly in time, such as pulsed or stochastic currents.

The mean field for a complex network consisting of a large but finite number of random two-state elements, \(M\), has been shown to satisfy a nonlinear Langevin equation. The noise intensity is inversely proportional to \(\sqrt{M} \). In the limiting case \(M = \infty \), the solution to the Langevin equation exhibits a transition from exponential to inverse power law relaxation as criticality is approached from above or below the critical point. When \(M < \infty \), the inverse power law is truncated by an exponential decay with rate \(\varGamma \), the evaluation of which is the main purpose of this article. An analytic/numeric approach is used to obtain the lowest-order eigenvalues in the spectral decomposition of the solution to the corresponding Fokker–Planck equation and its equivalent Schrodinger equation representation.

We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out of equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same non-exponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin re-crossings and establishing the corresponding waiting time probability density function (PDF), $\psi(t)$. In the former case, with no crucial events, $\psi(t)$ is exponential and in the latter case, with crucial events, $\psi(t)$ is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes., Comment: 13 pages, 7 figures

In this paper, we study the dynamical properties of a linear system driven by a superposition of a Gaussian white noise and a symmetric Markovian dichotomic noise operating simultaneously on the system. We find exact analytical solutions for the moment generating function and for the probability distribution function. We show analytically that the system presents characteristics belonging to the nonlinear cases, such as a nonequilibrium bimodal distribution. We infer that the white Gaussian noise smooths the two characteristics Diracs delta peaks, generated by a purely dichotomic diffusion, transforming them in two smooth maxima.

The main mechanims and concepts regulating the functioning of the human immune system are illustrated, with the general aims of improving disease prevention and ecosystem dynamics knowledge. These concepts must be known for the best management of infectious diseases and in the paramount view of ecology and parasitism, which are at the basis of stage-sharing of the environment by different species of life, each defending its own uniqueness and biological existence. Man is only one of the many living species sharing the stage of the planet. These considerations are fundamental in the fields of infectious diseases and of bioterrorism which have to be efficiently contrasted.

Following the basic description of the immunological science, we may now go in more detail into the practical applications involving immunological prevention against infectious diseases (vaccine use, requiring availability of suitable antigenic preparations, safe and effective immunization schedules and time to allow for immunity to develop) and immunotherapy of dangerous infective conditions (serotherapy, involving availability of immune sera and their use for injection in subjects needing protection against infectious agents).

In this paper we analytically estimate the magnetic field scale of planets with physical core conditions similar to that of Earth from a statistical physics point of view. We evaluate the magnetic field on the basis of the physical parameters of the center of the planet, such as density, temperature, and core size. We look at the contribution of the Seebeck effect on the magnetic field, showing that a thermally induced electrical current can exist in a rotating fluid sphere. We apply our calculations to Earth, where the currents would be driven by the temperature difference at the outer-inner core boundary, Jupiter and the Jupiter’s satellite Ganymede. In each case we show that the thermal generation of currents leads to a magnetic field scale comparable to the observed fields of the considered celestial bodies.

In this paper, we propose a mathematical model for the Trojan war that, supposedly, took place around 1180 BC. Supported by archaeological findings and by Homer’s Iliad, we estimate the numbers of warriors, the struggle rate parameters, the number of individuals per hectare, and other related quantities. We show that the long siege of the city, described in the Iliad, is compatible with a power-law behaviour for the time evolution of the number of individuals. We are able to evaluate the parameters of our model during the phase of the siege and the fall. The proposed model is general, and it can be applied to other historical conflicts.

We investigate the possibility to exploit the residual magnetism of bearings to characterize their rotation. Several bearings with different characteristics and diameter have been studied. A magnetic field sensor and a search loop register the magnetic field variation due to the rotation. Data are processed by means of a Dynamic Signal Analyzer and frequency components characteristic of the bearing geometry appear to be easily identifiable, which makes this technique promising for applications in the transportation and, in particular, railway industry.

Hypovitaminosis D is increasingly recognized as a cofactor in several diseases. In addition to bone homeostasis, vitamin D status influences immune system, muscle activity and cell differentiation in different tissues. Vitamin D is produced in the skin upon exposure to UVB rays, and sufficient levels of serum 25(OH)D are dependent mostly on adequate sun exposure, and then on specific physiologic variables, including skin type, age and Body Mass Index (BMI). In contrast with common belief, epidemiologic data are demonstrating that hypovitaminosis D must be a clinical concern not only in northern Countries. In our study, we investigated vitamin D status in a male population enrolled in a urology clinic of central Italy. In addition, we evaluated the correlation between vitamin D status and UVB irradiance measured in our region. The two principal pathologies in the 95 enrolled patients (mean age 66years) were benign prostate hypertrophy and prostate carcinoma. >50% of patients had serum 25(OH)D values in the deficient range (