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This paper introduces a new concept of Caputo type interval-valued fractional conformable calculus. Based on this, some theorems and properties related to fractional conformable calculus are presented. As an application, this paper attempts to investigate an initial value problem of functional integro-differential equations with Caputo type interval-valued fractional conformable derivatives. We not only prove the existence of at least one solution, the extremal solutions and the unique solution of the above problem, but also establish some monotone iterative sequences converging to the extremal solutions. More meaningful and important, some comparison principles and generalized Gronwall inequality related to the proposed problem are also proved. Two examples are presented to illustrate the main results. We firmly believe that the concept of interval-valued fractional conformable calculus, new comparison principles and generalized Gronwall inequality introduced here can be conveniently applied to qualitative analysis of a variety of new interval-valued fractional conformable biological models, economic models, etc., which will better describe and explain various complex phenomena derived from the real world. [ABSTRACT FROM AUTHOR]

First-order compartment models are common tools for modelling many biological processes, including pharmacokinetics. Given the compartments and the transfer rates, solutions for the time-dependent quantity (or concentration) curves can normally be described by a sum of exponentials. This paper investigates cases that go beyond simple sums of exponentials. With specific relations between the transfer rate constants, two exponential rate constants can be equal, in which case the normal solution cannot be used. The conditions for this to occur are discussed, and advice is provided on how to circumvent these cases. An example of an analytic solution is given for the rare case where an exact equality is the expected result. Furthermore, for models with at least three compartments, cases exist where the solution to a real-valued model involves complex-valued exponential rate constants. This leads to solutions with an oscillatory element in the solution for the tracer concentration, i.e., there are cases where the solution is not a simple sum of (real-valued) exponentials but also includes sine and cosine functions. Detailed solutions for three-compartment cases are given. As a tentative conclusion of the analysis, oscillatory solutions appear to be tied to cases with a cyclic element in the model itself. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a reaction-diffusion model incorporating delay and nonlocal effects. The normal form of double Hopf bifurcation is derived. The diffusive model of pollen tube tip growth is discussed and numerical simulations show that spatially homogeneous and inhomogeneous periodic solutions can be both stable or connected by a heteroclinic orbit under certain conditions. In addition, the diffusive Lotka-Volterra model with delay and nonlocality is considered and spatially inhomogeneous quasi-periodic solution is obtained. • Derive the algorithm of normal form of double Hopf bifurcation for reaction-diffusion system with delay and spatial average. • Investigate the dynamics near the double Hopf bifurcation point for two biological models. • Find bistability of homogeneous and inhomogeneous periodic solutions and pattern transitions for pollen tube tip growth model. • Find stable inhomogeneous quasi-periodic solutions and pattern transitions of periodic and quasi-periodic solutions for Lotka-Volterra model. [ABSTRACT FROM AUTHOR]

Rutin is a flavonoid present in numerous fruits and vegetables and therefore widely consumed by humans. It is also a popular dietary supplement of 250–500 mg/day. There is considerable consumer interest in rutin due to numerous reports in the biomedical literature of its multi-system chemo-preventive properties. The present paper provides the first assessment of rutin-induced hormetic concentration/dose responses, their quantitative features and mechanistic basis, along with their biological, biomedical, clinical, and public health implications. The findings indicate that rutin-induced hormetic dose responses are widespread, being reported in numerous biological models and cell types for a wide range of endpoints. Of critical importance is that the optimal hormetic findings shown in in vitro systems are currently not achievable for human populations due to low gastrointestinal tract bioavailability. These findings have the potential to strengthen future experimental studies with rutin, particularly concerning study design parameters. [Display omitted] • Rutin is a flavonoid present in fruits and vegetables consumed by humans. • Rutin displays multi-system chemo-preventive properties. • First assessment of rutin-induced hormetic dose responses and its implications. • Several biological models and cells show rutin-induced hormetic dose responses. • Findings have the potential to strengthen future experimental studies with rutin. [ABSTRACT FROM AUTHOR]

The learning of QSAR/QSPR models is crucial for predicting the physicochemical properties/biological activities of compounds. For compounds with the same/similar structure, there is a high probability that the molecular descriptors describing the molecular structure undergo degeneracy such that it is impossible to distinguish between these compounds, which in turn leads to modeling failure. In this paper, we construct a two-layer graph structure to design new feature descriptors with high discriminability, and propose a graph signal processing (GSP)-based method for nonlinear QSAR/QSPR model learning for compounds. Considering the molecular descriptors computed based on the molecular graph as a high-dimensional signal, we construct on top of the molecular graph a higher-level graph structure – a compound graph – to describe the similarity between different compounds. We use local complex network metrics to quantify the local topological information on each vertex (compound) in the compound graph, which can naturally be used as new discriminative feature descriptors, based on which we learn two types of nonlinear QSAR/QSPR models. Three datasets with the same/similar molecular graphs are used to learn to model their biological activity, entropy and octanol–water partition coefficient, respectively, and the experimental results well validate the effectiveness of the proposed method. • A GSP-based method for nonlinear QSAR/QSPR model learning of compounds. • Two-layer graph structure to design new feature descriptors with high discriminability. • Three different polynomial/SVR models for three datasets with compounds having the same/similar structure. [ABSTRACT FROM AUTHOR]

This paper represents the first integrative assessment and documentation of taurine-induced hormetic effects in the biological and biomedical areas, their dose response features, mechanistic frameworks, and possible public health, therapeutic and commercial applications. Taurine-induced hormetic effects are documented in a wide range of experimental models, cell types and for numerous biological endpoints, with most of these experimental findings being reported within the past five years. It is suggested that the concept of hormesis may have a transformative effect on taurine research and its public health and therapeutic applications. • Hormesis is a biphasic dose response relationship. • Taurine commonly induces hormetic dose responses. • Numerous tissues show taurine-induced hormesis. • Taurine acts via activation of Nrf2 to induce hormetic effects. [ABSTRACT FROM AUTHOR]

Quercetin is a polyphenol present in numerous fruits and vegetables and therefore widely consumed by humans with average daily dietary intakes of 10–20 mg/day. It is also a popular dietary supplement of 250-1000 mg/day. However, despite the widespread consumer interest in quercetin, due to its possible chemopreventive properties, the extensively studied quercetin presents a highly diverse and complex array of biological effects. Consequently, the present paper provides the first assessment of quercetin-induced hormetic concentration/dose responses, their quantitative features and mechanistic foundations, and their biological, biomedical, clinical, and public health implications. The findings indicate that quercetin-induced hormetic dose responses are widespread, being independent of biological model, cell type, and endpoint. These findings have the potential to enlighten future experimental studies with quercetin especially with respect to study design parameters and may also affect the appraisal of possible public health benefits and risks associated with highly diverse consumer consumption practices. • Quercetin commonly induces hormetic responses. • Hormetic responses induced by quercetin occur in numerous cell types. • Hormetic mechanisms have been reported in numerous studies. • Public health applications are provided. [ABSTRACT FROM AUTHOR]

• An unsymmetric 8-node hexahedral element without additional DOF is developed for modeling biological tissues. • The analytical general solutions for anisotropic elasticity are firstly employed in trial functions. • The element performance is validated by commonly used benchmarks and cardiac examples. • The present formulation possesses high accuracy, fast convergence rates and is quite insensitive to mesh distortion. • The present formulation is free of various locking in modeling nearly-incompressible problems. In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this paper, the recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with different test and analytical trial functions (ATFs) is modified for the analysis of the anisotropic nearly-incompressible hyperelastic soft tissues. Unlike the original formulation, the linear analytical general solutions for anisotropic elasticity and the consistent tangent modulus are firstly employed for formulating the trial functions, and are used to construct the incremental displacement fields that result in the incremental deformation gradient. The total deformation gradient is obtained by multiplying the incremental deformation gradient by the deformation gradient, after which the Cauchy stresses can be directly calculated from a total-form constitutive equation relating to the deformation gradient. Numerical tests, including commonly used benchmarks and cardiac examples, demonstrate attractive properties of the proposed finite element formulation in modeling nearly-incompressible anisotropic hyperelastic materials. It is free of various locking and quite insensitive to mesh distortions, and provides high accuracy with faster convergence rates when compared with other existing models. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper, we study an existence theory as well as stability results to the new fractional Nabla difference biological model of glucose–insulin regulatory system (GIRS) on diabetes mellitus involving the Atangana Baleanu–Caputo (ABC) derivative. We consider the proposed model under ABC derivative, and it has the nonsingular Mittag-Leffler function as its kernel. We utilize the fixed point technique for the existence and uniqueness analysis. The stability of the concerned solution in Hyers–Ulam sense is also investigated. Further to derive the approximate solution in the form of series to the considered model, we use iterative technique method. Numerical simulations are given to support the theoretical results. The results show that order of the fractional derivative has a significant effect on the dynamic process. Many informations on the dynamics of GIRS in diabetes mellitus were obtained using this model. It is recognized as a deterministic fractional Nabla difference model for diabetes mellitus that provides a better control approach at fractional values for the development of an artificial pancreas. [ABSTRACT FROM AUTHOR]

• Synthesis of Schiff's base from furfural and sulfanilamide. • Detailed structure, FTIR, PED, Vibrational assignment, 1HNMR, 13CNMR and UV reported. • Interaction between solvent water and compound analyzed using RDG and EDA. • Antimicrobial study and docking indicate moderate activity. • Wave function studies also reported in this paper. A new Schiff base (Z)-4-((furan-2-ylmethylene)amino)benzenesulfonamide (FURNI) was synthesized by the reaction reaction between furfural and sulfanilamide followed by characterization using IR, UV–Visible, 1HNMR, and 13CNMR spectral techniques. This was followed by electronic structure studies using DFT and TD-DFT. We simulated the IR spectrum using B3LYP/aug-ccPVDZ level of theory, followed by a comparison with experimental spectra and detailed potential energy distribution and vibrational assignment analysis. The comparison of experimental UV and simulated UV spectrum using TD-DFT CAM-B3LYP/ aug-ccPVDZ in DMSO solvent atmosphere gave good agreement. The compound is found to interact with the solvent water molecule. Energy decomposition analysis showed that there exists a strong hydrogen bond between the compound and the solvent water. As Schiff bases are biologically active, we checked for the potential activity of the synthesized compound with the help of ADMET prediction and found it to be active. Wavefunctions related properties like ELF, ALIE, LOL, and ELF are also reported. Prediction of biological activity spectrum study indicated possible antimicrobial activity against bacteria and fungus, which is supported by molecular docking against human mitochondrial (2WYA) protein with a docking score of −7.2 kcal/mol. Experimental antibacterial and antifungal studies using the compound and standard drugs confirmed this prediction. [ABSTRACT FROM AUTHOR]

The paper investigates peculiarities of infection evolution and spreading models in non-uniform biological systems of individuals (humans, animals, plants) using the approach of mathematical modeling. The effects of different characteristic features are revealed. A robust tool for prediction of infection evolution (growth and spreading) under different external conditions is developed accounting for spatial non-uniformity of governing parameters. • Peculiarities of infection evolution and spreading models in non-uniform systems studied. • Evolution of systems of individuals (humans, animals, plants) is subject for mathematical modeling. • The effects of different characteristic features are revealed. • A robust tool for prediction of infection evolution is developed accounting for spatial non-uniformity. [ABSTRACT FROM AUTHOR]

We study a simplified version of a class of constitutive relations used to describe large deformations of soft tissues, where the elastic energy density involves an exponential term. The class was originally introduced by Y.C. Fung as a model of many biological soft tissues in a series of papers during the Seventies. We prove existence and uniqueness of the equilibrium solution for a general measure-valued external load, under quite general boundary conditions, and study the validity of the associated Euler–Lagrange equation in the sense of distributions. • A class of hyperelastic materials involving an exponential term is studied. • We prove existence and uniqueness of the equilibrium solution for a general measure-valued external load. • The validity of the associated Euler–Lagrange equation in the sense of distributions is proved. [ABSTRACT FROM AUTHOR]

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains difficult to deal with high-dimensional applications and extrapolative generalization. This paper introduces deep learning techniques under the data-driven framework to address these fundamental issues in nonlinear materials modeling. To this end, an autoencoder neural network architecture is introduced to learn the underlying low-dimensional representation (embedding) of the given material database. The offline trained autoencoder and the discovered embedding space are then incorporated in the online data-driven computation such that the search of optimal material state from database can be performed on a low-dimensional space, aiming to enhance the robustness and predictability with projected material data. To ensure numerical stability and representative constitutive manifold, a convexity-preserving interpolation scheme tailored to the proposed autoencoder-based data-driven solver is proposed for constructing the material state. In this study, the applicability of the proposed approach is demonstrated by modeling nonlinear biological tissues. A parametric study on data noise, data size and sparsity, training initialization, and model architectures, is also conducted to examine the robustness and convergence property of the proposed approach. • Autoencoder based data-driven modeling approach is proposed for nonlinear materials. • Autoencoders enable noise filtering and dimensionality reduction of material data. • Convexity-preserving interpolation is employed for enhanced stability in data search. • Improved generalization capability is demonstrated by modeling biological tissues. [ABSTRACT FROM AUTHOR]

• Biologically inspired heuristics for target search lack modularity and modifiability. • The proposed hyper-heuristic is based on modular and adaptive swarm behavior. • Combining stigmergy, flocking and evolution outperforms bio-inspired heuristics. Target search aims to discover elements of various complexity in a physical environment, by minimizing the overall discovery time. Different swarm intelligence algorithms have been proposed in the literature, inspired by biological species. Despite the success of bio-inspired techniques (bio-heuristics), there are relevant algorithm selection and parameterization costs associated with every new type of mission and with new instances of known missions. In this paper, evolutionary optimization is proposed for achieving significant improvements of the mission performance. Although adaptive, the logic of bio-heuristics is nevertheless constrained by models of biological species. To generate more adaptable logics, a novel design approach based on hyper-heuristics is proposed, in which the differential evolution optimizes the aggregation and tuning of modular heuristics for a given application domain. A modeling and optimization testbed has been developed and publicly released. Experimental results on real-world scenarios show that the hyper-heuristics based on stigmergy and flocking significantly outperform the adaptive bio-heuristics. [Display omitted] [ABSTRACT FROM AUTHOR]

Biomimetics is an opportunity for the development of energy efficient building systems. Several biomimetic building skins (Bio-BS) have been built over the past decade, however few addressed multi-regulation although the biological systems they are inspired by have multi-functional properties. Recent studies have suggested that despite numerous tools and methods described in the literature for the development of biomimetic systems, their use for designing Bio-BS is scarce. To assess the main challenges of biomimetic design processes and their influence on the final design, this paper presents a comparative analysis of several existing Bio-BS. The analyses were carried out with univariable and multivariate descriptive tools in order to highlight the main trends, similarities and differences between the projects. The authors evaluated the design process of thirty existing Bio-BS, including a focus on the steps related to the understanding of the biological models. Data was collected throughout interviews. The univariate analysis revealed that very little Bio-BS followed a biomimetic design framework (5%). None of the Bio-BS was as multi-functional as their biological model(s) of inspiration. A further conclusion drawn that Bio-BS are mostly inspired by single biological organisms (82%), which mostly belong to the kingdom of animals (53%) and plants (37%). The multivariate analysis outlined that the Bio-BS were distributed into two main groups: (1) academic projects which present a strong correlation with the inputs in biology in their design processes and resulted in radical innovation; (2) public building projects which used conventional design and construction methods for incremental innovation by improving existing building systems. These projects did not involve biologists neither a thorough understanding of biological models during their design process. Since some biomimetic tools are available and Bio-BS have shown limitations in terms of multifunctionality, there is a need to promote the use of multidisciplinary tools in the design process of Bio-BS, and address the needs of the designers to enhance the application of multi-regulation capabilities for improved performances. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a reaction–diffusion–advection two-species competition biological model by employing the methods of Lyapunov–Schmidt reduction, perturbation theory and the implicit function theorem and so on. For any given diffusion rates we obtain the existence of positive steady states by using the advection rate η and the competitive coefficients c and b as the bifurcation parameters. [ABSTRACT FROM AUTHOR]