Primates have an unparalleled ability to produce a wide range of dexterous movements, each sensitive to context and robust to perturbation. Recent progress in understanding the neural basis of movement generation comes from two largely independent ideas, “Optimal Feedback Control” and “Neural Dynamical Systems”. The optimal control framework was largely inspired by research programs from the ‘80s showing that the brain doesn’t seem to plan a simple desired movement trajectory, but instead produces movements by transforming sensory information into motor output that satisfies an optimality criterion. The more recent idea that the motor cortex acts as a dynamical system came about only as it became possible to analyze large numbers of simultaneously recorded single neurons. These two framings of the motor system have been largely incommensurate, neither able to contribute much to the understanding of the other. In this review, we reconcile these two views into a single model we call “Dynamical Feedback Control”. We propose that the dynamics in the motor cortex emerge from a sensorimotor transformation that couples the motor cortex to sensory input from the periphery, and to contextual inputs from other cortical and subcortical areas. Dynamics in motor cortex can be thought to approximate gains of a feedback controller, and by moving the neural state to different regions of state space, the motor system can rapidly alternate between different controllers. The DFC framework presents a new lens to interpret neural dynamics, and to understand how ensembles of neurons generate flexible and responsive patterns of muscle activity.

Consider a uniquely ergodic $C^*$-dynamical system ba\-sed on a unital $*$-endomorphism $\Phi$ of a $C^*$-algebra. We prove the uniform convergence of Cesaro averages $\frac1{n}\sum_{k=0}^{n-1}\lambda^{-n}\Phi(a)$ for all values $\lambda$ in the unit circle which are not eigenvalues corresponding to "measurable non continuous" eigenfunctions. This result generalises the analogous one in commutative ergodic theory presented in [19], which turns out to be a combination of the Wiener-Wintner Theorem (cf. [22]) and the uniformly convergent ergodic theorem of Krylov and Bogolioubov (cf. [15]).

Predicting how a genetic change affects a given character is a major challenge in biology, and being able to tackle this problem relies on our ability to develop realistic models of gene networks. However, such models are rarely tractable mathematically. In this paper, we propose a mathematical analysis of the sigmoid variant of the Wagner gene-network model. By considering the simplest case, that is, one unique self-regulating gene, we show that numerical simulations are not the only tool available to study such models: theoretical studies can be done too, by mathematical analysis of discrete dynamical systems. It is first shown that the particular sigmoid function can be theoretically investigated. Secondly, we provide an illustration on how to apply such investigations in the case of the dynamical system representing the one self-regulating gene.

First, we propose a scale-invariant modified gravity interacting with a neutral scalar inflaton and a Higgs-like SU(2) × U(1) iso-doublet scalar field based on the formalism of non-Riemannian (metric-independent) spacetime volume-elements. This model describes in the physical Einstein frame a quintessential inflationary scenario driven by the “inflaton” together with gravity-inflaton assisted dynamical spontaneous SU(2) × U(1) symmetry breaking in the post-inflationary universe, whereas SU(2) × U(1) symmetry remains intact in the inflationary epoch. Next, we find the explicit representation of the latter quintessential inflationary model with a dynamical Higgs effect as an Eddington-type purely affine gravity.

In this paper, we study the dynamics of following system of nonlinear difference equations x_n+1 = x_n-1y_n - 1, y_n+1 = y_n-1z_n - 1, z_n+1 = z_n-1x_n - 1. Especially we investigate the periodicity, boundedness and stability of related system of difference equations.

Previous work has shown that perturbation analysis in algorithmic information dynamics can uncover generative causal processes of finite objects and quantify each of its element's information contribution to computably constructing the objects. One of the challenges for defining emergence is that the dependency on the observer's previous knowledge may cause a phenomenon to present itself as emergent for one observer at the same time that reducible for another observer. Thus, in order to quantify emergence of algorithmic information in computable generative processes, perturbation analyses may inherit such a problem of the dependency on the observer's previous formal knowledge. In this sense, by formalizing the act of observing as mutual perturbations, the emergence of algorithmic information becomes invariant, minimal, and robust to information costs and distortions, while it indeed depends on the observer. Then, we demonstrate that the unbounded increase of emergent algorithmic information implies asymptotically observer-independent emergence, which eventually overcomes any formal theory that any observer might devise. In addition, we discuss weak and strong emergence and analyze the concepts of observer-dependent emergence and asymptotically observer-independent emergence found in previous definitions and models in the literature of deterministic dynamical and computable systems.

Motivated by the way animals react in nature, we introduce a fully-connected neural-network model, which incorporates the external pattern presented to the system as a fundamental tool of the recognition process. In this new scenario, in the absence of this external field, memories are not attractors inside basins of attraction, as in usual attractor neural networks, although basins may be created according to the external pattern, thus allowing storing a much larger number of memories. The key point consists in calibrating the influence of the external pattern such as to cancel the noise generated by those memories not correlated with the external pattern.We illustrate how this proposal works by including this new contribution in the standard Hopfield model, showing a significant increase in its recognition capacity (typically by a factor $10^{2}$). As an additional feature of this model, we show its ability to react promptly to changes in the external environment, a crucial attribute of living beings. This procedure can be applied to a wide variety of neural-network models to increase considerably their recognition and reaction capabilities.

Background: Underreporting of Visceral Leishmaniasis (VL) in India remains a problem to public health controls. Effective and reliable surveillance systems are critical for monitoring disease outbreaks and public health control programs. However, in India, government surveillance systems are affected by levels of scarcity in resources and therefore, uncertainty surrounds the true incidence of asymptomatic and clinical cases, affecting morbidity and mortality rates. The State of Bihar alone contributes up to the 40\% of the worldwide VL cases. The inefficiency of surveillance systems occurs because of multiple reasons including delay in seeking health care, accessing non-authentic health care clinics, and existence of significant asymptomatic self healing infectious cases. This results in a failure of the system to adequately report true transmission rates and number of symptomatic cases that have sought medical advice (thus, high underreporting of cases). Objectives and Methods: There are several methods to estimate the extent of underreporting in the surveillance system. In this research, we use a mathematical dynamic model and two different types of data sets, namely, monthly incidence for 2003-2005 and yearly incidence from 2006-2012 from the Bihar's 21 most VL affected districts out of its 38 districts. The goals of the study are to estimate critical metrics to measure level of transmission and to evaluate the estimation process between the two data sets and 21 districts. In particularly, our focus is on (i) estimating infection transmission potential, underreporting level in incidence and proportion of self-healing cases, (ii) quantifying reproduction number of the$R_0$, and (iii) comparing underreporting incidence levels and proportion of self-healing cases between the two periods 2003-2005 and 2006-2012 and between 21 districts. Results: Our research suggests that the number of asymptomatic individuals in the population who eventually self-heal may have a significant effect on the dynamics of VL spread. The estimated mean self-healing proportion (out of all infected) is found to be $\sim 0.6$ with only 7 out of 21 affected districts having self-healing proportion less than $0.5$ for both data sets. The estimated mean underreporting level is at least $64$\% for the state of Bihar. The estimates of the basic reproduction numbers obtained are similar in magnitude for most of the districts, being in the range of (0.88, 2.79) and (0.98, 1.01) for 2003-2005 and 2006-2012, respectively. Conclusions: The estimates for the two types (monthly and yearly) of temporal data suggest that monthly data are better for estimation if less number of data points are available, however, in general, using such data set results in larger variances in parameters as compared to estimates obtained through aggregated yearly data. Estimated values of transmission related metrics are lower than those obtained from earlier analyses in the literature, and the implications of this for VL control are discussed. The spatial heterogeneity in these control metrics increases the risk of epidemics and makes the control strategies more complex.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

In the present study we introduce a deterministic mathematical model in order to study the interaction between the human immune system and a virus, like COVID 19. The mathematical analysis is based on the tools of dynamical systems theory, by modeling the interactions between the immune system and the virus, using a predator-prey method and following the ideas of G. Moza, from \cite{TGV}. It will be obtained some conclusions with medical relevance and the main three of them are the followings: 1) A deficiency of a single type of immunity in the early stages of virus proliferation, may lead to a large virus multiplication and the human body can loses the fight against this virus; 2) If the level of all components of the immunity system are at the normal threshold from the first moment of the infection and the immune system kill the virus at higher rate than the rate of virus reproduction, then the human body has the ability to stop the multiplication of the virus and liquidate it, that means the virus will be destroyed; 3) If the level of at least one type of immunity can be increased beyond the normal threshold, by medical interventions (like vaccination) in the early stages of virus infection, then the immune system has a better chance to win the fight with the virus.

The semi-logarithmic plot of the cumulative number of cases of epidemics resembles the response of a first-order systems for a step load. This similarity was utilized to develop a first order model that can be used for extracting information about the dynamics of infectious disease epidemics. The developed model was validated using COVID-19 data of China. It was also heuristically fitted to other 13 countries. Obtained results indicated that the model can reliably forecasts the number of infected person, epidemic growth speed towards steady-state condition (process time constant, T), and time to reach steady-state condition (4T). The developed model will help public health authorities in developing more effective control strategies of epidemics.

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

In this paper, we study the existence of the random -pullback attractor of a non-autonomous local modified stochastic Swift-Hohenberg equation with multiplicative noise in stratonovich sense. It is shown that a random -pullback attractor exists in when its external force has exponential growth. Due to the stochastic term, the estimate are delicate, we overcome this difficulty by using the Ornstein-Uhlenbeck(O-U) transformation and its properties.

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. As discrete dynamics, return map analysis was applied to the time series of movements during kendo matches, and six coordination patterns were classified. Furthermore, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

The reinforcing ability of the fillers results in significant improvements in properties of polymer matrix at extremely low filler loadings compared to conventional fillers. In view of this, present review article describes the different methods used in preparation of different rubber nanocomposites reinforced with nanodimensional individual carbonaceous fillers, such as graphene, expanded graphite, single walled carbon nanotubes, multiwalled carbon nanotubes and graphite oxide, graphene oxide and hybrid fillers consisting combination of individual fillers. This is followed by review of mechanical properties (tensile strength, elongation at break, Young modulus, and fracture toughness) and dynamic mechanical properties (glass transition temperature, crystallization temperature, melting point) of these rubber nanocomposites. Finally, Payne and Mullin Effects have also been reviewed in rubber filled with different carbon based nanofillers.

In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ($\tau$-space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter $\tau$. Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one.

A fully analytical treatment of the base-pair and codon dynamics in double-stranded DNA molecules is introduced, by means of a realistic treatment which considers different mass values for G, A, T, and C nucleotides and takes into account the intrinsic three-dimensional, helicoidal geometry of DNA in terms of a Hamitonian in cylindrical coordinates. Within the framework of the Peyrard-Dauxois-Bishop model we consider the coupling between stretching and stacking radial oscillations as well as the twisting motion of each base pair around the helix axis. By comparing the linearized dynamical equations for the angular and radial variables when going from the bp local scale to the longer triplet codon scale, we report an underlying hierarchical symmetry. The existence of synchronized collective oscillations of the base-pairs and their related codon triplet units are disclosed from the study of their coupled dynamical equations. The possible biological role of these correlated, long-range oscillation effects in double standed DNA molecules containing mirror-symmetric codons of the form XXX, XX’X, X’XX’, YXY, and XYX is discussed in terms of the dynamical equations solutions and their related dispersion relations.

Under the big unified framework of quantum gravitational field and quantum repulsive field, the earlier in this series of work has comprehensively expanded the general relativity and loop quantum ring gravitation theory, set up the quantum repulsive field equation corresponding to the quantum gravitational field equation, and then established the quantum hedge-unified field equation describing the interaction of quantum gravitational field and quantum repulsive field; On this basis, the quantum repulsive universe equation corresponding to the quantum gravitational universe equation has be established, thus a set of new equations describing the expansive universe model under the condition of fully considering the hedge effect of quantum gravitational field and quantum repulsion field, which can be called the expansive universe equation of quantum hedge-unified field theory, has be established. Now, let's go deep into the arche-unified physics behind the creation of the universe. Although all kinds of inflationary universe models can solve cosmological problems to a certain extent, there is no natural and reasonable analysis and explanation for all cosmological and physical consequences. For example, it is impossible to predict a large tensor-scale ratio and a relatively large spectral index run at the same time. At present, string theory, membrane theory, loop quantum gravity theory, super-gravitational holography principle and M theory, which are the theoretical basis of cosmology, are basically established by simplification in the case of breaking away from the extreme background conditions of the universe. While cosmology, which is deficient in nature, cannot provide strong support for particle physics to further advance to a wider field and a deeper level. Due to the lack of new ideas, the construction of existing theoretical models is difficult. Therefore, the existing research can only be further promoted by new astronomical observation. Unlike existing studies, we concentrate on the emergence of the big rip-rebound clusters of quantum chaotic-reticulate distribution between the outwards-push of the universe as a whole (related to pseudo-vacuum energy, Higgs field, dark energy, etc.) and the inwards-pull of the universe in local scale (related to dark matter, quantum gravity and initial gravity separated from high-dimensional supergravity, and the initial strong force separated from the grand unified force subsequently). On the one hand, we find a great impetus to make the inflation of the universe into firstly-imposed suppression, then-imposed acceleration and finally-imposed deceleration, which really explains why the universe expands at a critical rate and has the same temperature in different regions, on the other hand, we find a fundamental unit of matter and its emerging clusters evolving in the big bang, inflation and expansion of the universe accompanied by the great rip-rebound clusters of quantum chaos-reticulate distribution, which can be reduced to an arche-pulsator of neither punctiform particle nor linear string. From these two aspects, it can been seen that the evolution of the early universe is much more complicated than people originally thought. The complexity of the super inflation of the universe is mainly reflected in the big rip-rebound cluster emerging behind the gravitational disturbance (the pressure and tensor disturbance related to dark matter), the repulsive disturbance (the pressure and scalar disturbance related to dark energy), the cosmological disturbance (related to the interaction between high-dimensional supergravity and high-dimensional superrepulsion). This is a system of nonlinear stochastic differential dynamics, or a quantum statistical physical process of nonlinear nonequilibrium state. In the new research paradigms established in this series, the arche-conjugation between the high-dimensional supergravity and the high-dimensional superrepulsion, as well as between the quantum gravity and the quantum repulsion, is higher than the supersymmetry, and then becomes the core concept of the new theory. In this series, cluster-inflating configuration, spin network space and cosmic paradigm vectors are proposed, so the model of the super-inflated universe with quantum chaos-reticulate distribution emerged under the great impetus. The new model reveals that the unified inflation of the universe as a whole and the local inflation of the universe emerge together in the great impetus of the big rip-rebound cluster of quantum chaos-reticulate distribution. As a spin network model variable, the spatiotemporal mode variable is a vector composed of a series of variables, which variables include: dimension, curvature, range, expansion speed, dynamics, quantization, chaotic-reticulate distribution (inhomogeneity, concentration, fluctuation), synergy, and so on. Between particle physics and cosmology, this series of papers proposes the cosmic quantum evolution mode, the physical-sphere distributing configuration and the interaction situation variables, organizes the concepts, variables and models of these three levels, and establishes a systematic super-synergy paradigm. In this paradigm, the general Langevan equation and the general Fokker-Planck equation are established. For the quantum cosmic-sphere, a series of trend parameters are introduced to establish the dynamics of quantum gravitational mode and its master equation, and then to establish the operator distribution function and its motion equation of the action mode. For the Tachyon of upheaval in the rip-rebound-inflating of the universe, the hypothesis on the bifurcate-chaos wave of quantum is given, the quantum theory of the early photons in upheaval is set up, and the analysis on the particles of the ultrahigh energy cosmic ray from the γ ray burst is made. Finally, using Wigner-Ville distribution as a nonlinear time-frequency distribution, we establish the ultra-synergistic field equation of quantum-classic unifying action-sphere.

Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretically the development of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter and we present results for the lifetime of these states and their occupation in the non-equilibrium. The direct physical impact of the mathematical precision of the Floquet-Keldysh theory is evident when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium for a case of ZnO. The physical consequences of the topological non-equilibrium effects in our results for correlated systems are explained with their impact on optoelectronic applications.

Climate change effect on human-living in verities of way such as health and food security. This study presents predicting crop yields, and production risk in the near future (2020-2029) in northern Thailand using coupling 1 km resolution of regional climate model which is downscaled using a conservative remapping method and the Decision Support System for the Transfer of Agrotechnology (DSSAT) modeling system. The accuracy of the climate and agricultural model was appropriate compared to the observations with Index of Agreement (IOA) in ranges of 0.65 - 0.89. The DSSAT modeling system predicts that rice, and maize production will decrease by 5% and 4% in northern Thailand. In addition, a short-term risk analysis of rice and maize production has shown that, in the context of climate change, maize production appears to be at a high risk of low production in the near future, while rice cultivation might be a low risk.

We theoretically study the dynamical Casimir effect (DCE), i.e., parametric amplification of a quantum vacuum, in an optomechanical cavity interacting with a photonic crystal, which is considered to be an ideal system to study the microscopic dissipation effect on the DCE. Starting from a total Hamiltonian including the photonic band system as well as the optomechanical cavity, we have derived an effective Floquet-Liouvillian by applying the Floquet method and Brillouin-Wigner-Feshbach projection method. The microscopic dissipation effect is rigorously taken into account in terms of the energy-dependent self-energy. The obtained effective Floquet-Liouvillian exhibits the two competing instabilities, i.e., parametric and resonance instabilities, which determine the stationary mode as a result of the balance between them in the dissipative DCE. Solving the complex eigenvalue problem of the Floquet-Liouvillian, we have determined the stationary mode with vanishing values of the imaginary parts of the eigenvalues. We find a new non-local multimode DCE represented by a multimode Bogoliubov transformation of the cavity mode and the photon band. We show the practical advantage for the observation of DCE in that we can largely reduce the pump frequency when the cavity system is embedded in a narrow band photonic crystal with a bandgap.

Electron Channeling Contrast Imaging (ECCI) is becoming a powerful tool in Materials Science for characterizing deformation defects. Dislocations observed by ECCI in Scanning Electron Microscope, exhibit several features depending on the crystal orientation relative to the incident beam (white/black line on a dark/bright background). In order to bring new insights concerning these contrasts, we report an original theoretical approach based on the dynamical diffraction theory. Our calculations led, for the first time, to an explicit formulation of the backscattered intensity as a function of various physical and practical parameters governing the experiment. Intensity profiles are modeled for dislocations parallel to the sample surface for different channeling conditions. All theoretical predictions are consistent with experimental results.

In this paper, we propose the expansion of the Planck distribution functions which is derived from the Boltzmann principle. Furthermore, we examine to expand Planck's law using new distribution functions. Moreover, using the ideas applied to the expansion of the Planck distribution function, we show that the derivation of Von Koch's inequality without using the Riemann Hypothesis and the negative consequence of the abc conjecture. Besides, we describe some issues for the future. Namely, we discuss that the Entropy is associated with the dynamical system, and the classical gravity theory of Newton's law and the electromagnetism of Coulomb's law by the law of inverse squares.

This paper considers the general ocean circulation within the thermodynamical closure of our climate theory, which aims to deduce the generic climate state from first principles. The preceding papers of the theory have reduced planetary fluids to warm/cold masses and determined their bulk thermal properties, which provide prior constraints for the derivation of the upper-bound circulation when the potential vorticity is homogenized in moving masses. In a companion paper on the atmosphere, this upper bound is seen to reproduce the prevailing wind, forsaking therefore previous discordant explanations of the easterly trade and the polar jet stream. In this paper on the ocean, we again show that this upper bound may replicate broad features of the observed circulation, including a western-intensified subtropical gyre and a counter-rotating tropical gyre feeding the equatorial undercurrent. Together, we posit that PV homogenization may provide a unifying dynamical principle of the large-scale planetary circulation, which may be interpreted as the maximum macroscopic motion extractable by microscopic stirring --- within the confine of the thermal differentiation.

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solutions of the coupled system of equations that characterizes the associated dynamics. In addition, we supply the modes of oscillation and demonstrate the weak coupling condition is inappropriate in practice, while for collective modes of motion (and strong coupling) only a peak of the mass can be detected. Phase portraits and power spectra are employed to illustrate how the trajectory executes quasiperiodic motion on the surface of torus, namely a Kolmogorov-Arnold-Moser (KAM) torus. In an attempt to better describe dynamical stability of the system, we introduce a model that characterizes dynamical stability and the critical points based on the Hessian matrix approach. The model is then applied to investigate quantum dynamics for many-body systems consisting of identical ions, levitated in 2D and 3D ion traps. Finally, the same model is applied to the case of a combined 3D Quadrupole Ion Trap (QIT) with axial symmetry, for which we obtain the associated Hamilton function. The ion distribution can be described by means of numerical modeling, based on the Hamilton function we assign to the system. The approach we introduce is effective to infer the parameters of distinct types of traps by applying a unitary and coherent method, and especially for identifying equilibrium configurations, of large interest for ion crystals or quantum logic.

Metal nanoparticles are used to modify/enhance the properties of a polymer matrix for a broad range of applications in bio-nanotechnology. Here, we study the properties of polymer/gold nanoparticle (NP) nanocomposites through atomistic molecular dynamics, MD, simulations. We probe the structural, conformational and dynamical properties of polymer chains at the vicinity of a gold (Au) NP and a functionalized (core/shell) Au NP, and compare them against the behavior of bulk PE. The bare Au NPs were constructed via a systematic methodology starting from ab-initio calculations and an atomistic Wulff construction algorithm resulting in the crystal shape with the minimum surface energy. For the functionalized NPs the interactions between gold atoms and chemically adsorbed functional groups change their shape. As a model polymer matrix we consider polyethylene of different molecular lengths, from the oligomer to unentangled Rouse like systems. By computing the different properties the concept of the interface, and the interphase as well, in polymer nanocomposites with metal NPs are critically examined. Results concerning polymer density profiles, bond order parameter, segmental and terminal dynamics show clearly that the size of the interface / interphase, depends on the actual property under study. In addition, the anchored polymeric chains change the behavior/properties, and especially the chain density profile and the dynamics, of the polymer chain at the vicinity of the Au NP.

Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

A coupled stratospheric chemistry-meteorology model was developed by combining the Canadian operational weather prediction model Global Environmental Multiscale (GEM) with a comprehensive stratospheric photochemistry model from the Belgian Assimilation System for Chemical ObsErvations (BASCOE). The coupled model was called GEM-BACH for GEM-Belgian Atmospheric CHemistry. The coupling was made across a chemical interface that preserves time splitting while being modular, allowing GEM to run with or without chemistry. An evaluation of the coupling was performed by comparing the coupled model, refreshed by meteorological analyses every 6 hours, against the standard offline chemical transport model (CTM) approach. Results show that the dynamical meteorological consistency between meteorological analysis times far outweighs the error created by the jump resulting from the meteorological analysis increments at regular time intervals, irrespective whether a 3D-Var or 4D-Var meteorological analysis is used. GEM-BACH forecast refreshed by meteorological analyses every 6 hours were compared against independent measurements of temperature, long-lived species, ozone and water vapor. The comparison showed a relatively good agreement throughout the stratosphere except for an upper-level warm temperature bias and an ozone deficit of nearly 15%. Arguments in favor of using the same horizontal resolution for chemistry, meteorology, and meteorological analysis increments are also presented. In particular, the coupled model simulation during an ozone hole event gives better ozone concentrations than a 4D-Var chemical assimilation at a lower resolution.

We introduce poly-symplectic extension of Souriau Lie groups Thermodynamics based on higher-order model of statistical physics introduced by R.S. Ingarden. This extended model could be used for small data analytics and Machine Learning on Lie groups. Souriau Geometric Theory of Heat is well adapted to describe density of probability (Maximum Entropy Gibbs density) of data living on groups or on homogeneous manifolds. For Small Data Analytics (Rarified Gases , sparse statistical survey,…), density of maximum entropy should consider Higher Order Moments constraints (Gibbs density is not only defined by first moment but fluctuations request 2nd order and higher moments) as introduced by R.S. Ingarden. We use Poly-sympletic model introduced by Christian Günther, replacing the symplectic form by a vector-valued form. The poly-symplectic approach generalizes the Noether theorem, the existence of momentum mappings, the Lie algebra structure of the space of currents, the (non-)equivariant cohomology and the classification of G-homogeneous systems. The formalism is covariant, i.e. no special coordinates or coordinate systems on the parameter space are used to construct the Hamiltonian equations. We underline the contextures of these models, and the process to build these generic structures.

The Autopoiesis and Cognition Theory (ACT), by Maturana and Varela, based on the notions of Biological Closure and Structural Coupling, is a well-known theory on how to understand biological organization [1, 2, 3]. Although, for example, the Free Energy Principle framework evokes some entailments of autopoiesis in a more formal setting [4, 5]; and ACT has been used in many fields, its impact has been restricted because it lacks quantitative analysis. Here we present a theoretical framework grounded in accepted and well-developed ideas from Mathematics and Physics which advance the understanding of the Principles of Biological Organization under the guidance of Biological Closure and Structural Coupling. The disciplines of Differential Geometry/Topology, Mechanics and Complex Dynamical Systems provide a powerful, elegant, and well-established body of knowledge to support our Biological Organization Principles (BOP) framework. In particular, Stochastic Mechanics and KAM theory (from Kolmogorov, Arnold and Moser theorem) allow us to develop, using the notions of Biological Closure and Structural Coupling, a central core of BOP termed Dynamical Closure Mechanism. Under the proposed framework, a wide variety of bio- logical phenomena can be understood, shedding new light on biological explanations. However, an understanding of biological organization may require the re-evaluation of dogmas on how we think on biology as it seems inescapable that what is needed is an integration of analysis and notions derived from mathematics, physics, and biology to generate a new landscape of ideas.

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

Reservoir computers (RCs) are a biology inspired computational framework for signal processing typically implemented using recurrent neural networks. Recent work has shown that Boolean networks (BN) can also be used as reservoirs. We analyze the performance of BN RCs, measuring their flexibility and identifying factors that determine effective approximation of Boolean functions that are applied in a sliding-window fashion over a binary signal, either non-recursively or recursively. We train and test BN RCs of different sizes, signal connectivity, and in-degree to approximate 3-bit, 5-bit and 3-bit recursive binary functions. We analyze how BN RC parameters and function average sensitivity, a measure of function smoothness, affect approximation accuracy as well as the spread of accuracies for a single reservoir. We found that approximation accuracy and reservoir flexibility are highly dependent on RC parameters. Overall, our results indicate that not all reservoirs are equally flexible and RC instantiation and training can be more efficient if this is taken into account. The optimum range of RC parameters opens up an angle of exploration for understanding how biological systems might be tuned to balance system restraints with processing capacity.

Discrete, logic-based models are increasingly used to describe biological mechanisms. Initially introduced to study gene regulation, these models evolved to cover various molecular mechanisms, such as signalling, transcription factor cooperativity, and even metabolic processes. The abstract nature and amenability of discrete models to robust mathematical analyses make them appropriate for addressing a wide range of complex biological problems. Recent technological breakthroughs have generated a wealth of high throughput data. Novel, literature-based representations of biological processes and emerging algorithms offer new opportunities for model construction. Here, we review up-to-date efforts to address challenging biological questions by incorporating omic data into logic-based models, and discuss critical difficulties in constructing and analysing integrative, large-scale, logic-based models of biological mechanisms.

Climate change impacts and adaptations is subject to ongoing issues that attract the attention of many researchers. Insight into the wind power potential in an area and its probable variation due to climate change impacts can provide useful information for energy policymakers and strategists for sustainable development and management of the energy. In this study, spatial variation of wind power density at the turbine hub-height and its variability under future climatic scenarios are taken under consideration. An ANFIS based post-processing technique was employed to match the power outputs of the regional climate model with those obtained from the reference data. The near-surface wind data obtained from a regional climate model are employed to investigate climate change impacts on the wind power resources in the Caspian Sea. Subsequent to converting near-surface wind speed to turbine hub-height speed and computation of wind power density, the results have been investigated to reveal mean annual power, seasonal, and monthly variability for a 20-year period in the present (1981-2000) and in the future (2081-2100). The results of this study revealed that climate change does not affect the wind climate over the study area, remarkably. However, a small decrease was projected for future simulation revealing a slightly decrease in mean annual wind power in the future compared to historical simulations. Moreover, the results demonstrated strong variation in wind power in terms of temporal and spatial distribution when winter and summer have the highest values of power. The findings of this study indicated that the middle and northern parts of the Caspian Sea are placed with the highest values of wind power. However, the results of the post-processing technique using adaptive neuro-fuzzy inference system (ANFIS) model showed that the real potential of the wind power in the area is lower than those of projected from the regional climate model.

In crystal structure prediction, Newton's second law can always be applied to particles (atoms or ions) in a cell to determine their positions. However the values of the period vectors (crystal cell edge vectors) should be determined as well. Here we applied the dynamical equations of period vectors derived recently based on Newton's laws (doi:/10.1139/cjp-2014-0518) for that purpose, where the period vectors are driven by the imbalance between the internal and external pressures/stresses. For equilibrium states, they became equations of state, which essentially turn out the equilibrium conditions of crystals from mechanical point of view. For external pressure, by ignoring some effects, they reduced to the Mie-Gruneisen equation. Since the internal stress has both a full kinetic energy term and a full interaction term, the influences of both external temperature and stress/pressure on crystal structures can be calculated, then thermodynamical properties and processes were presented. Contrary to usual ideas, the equations show that pure harmonic vibrating phonons can result in thermal expansion in crystals when the external temperature is changed. Finally, crystal system collapse due to temperature and/or stress/pressure change was discussed.

Since crystals are made of periodic structures in space, predicting their three period vectors starting from any values based on the inside interactions is a basic theoretical physics problem. For the general situation where crystals are under constant external stress, we derived dynamical equations of the period vectors in the framework of Newtonian dynamics, for pair potentials recently (doi:/10.1139/cjp-2014-0518). The derived dynamical equations show that the period vectors are driven by the imbalance between the internal and external stresses. This presents a physical process where when the external stress changes, the crystal structure changes accordingly, since the original internal stress can not balance the external stress. The internal stress has both a full kinetic energy term and a full interaction term. It is extended to many-body interactions in this paper. As a result, all conclusions in the pair-potential case also apply for many-body potentials.

A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved.

At INFN-LNS, and in collaboration with the ATOMKI laboratories, an innovative multi-diagnostic system with advanced analytical methods has been designed and implemented. This is based on several detectors and techniques (Optical Emission Spectroscopy, RF systems, Interfero-polarimetry, X-ray detectors) and here we focus on high resolution spatially-resolved X-ray spectroscopy, performed by means of a X-ray pin-hole camera setup operating in the 0.5−20 keV energy domain. The diagnostic system was installed at a 14 GHz Electron Cyclotron Resonance (ECR) ion source (ATOMKI, Debrecen), enabling high precision X-ray spectrally-resolved imaging of ECR plasmas heated by hundreds of Watts. The achieved spatial and energy resolution were 0.5 mm and 300 eV at 8 keV, respectively. We here present the innovative analysis algorithm that we properly developed for obtaining Single Photon-Counted (SPhC) images providing the local plasma emitted spectrum in a High-Dynamic-Range (HDR) mode, by distinguishing fluorescence lines of the materials of the plasma chamber (Ti, Ta) from plasma (Ar). This method allows a quantitative characterization of warm electrons population in the plasma (and its 2D distribution) which are the most important for ionization, and also to estimate local plasma density and spectral temperatures. The developed post-processing analysis is also able to remove the readout noise, that is often observable at very low exposure times (msec). The setup is now under update including fast shutters and trigger systems in order to allow simultaneously space and time-resolved plasma spectroscopy during transients, stable and turbulent regimes.