Search

The ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes ("restratification," "stable," "deepening," and "strong deepening") are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration. Plain Language Summary: Vertical mixing of water near the ocean surface occurs when cold air temperatures create dense cold water at the surface that tends to sink in the ocean or when a strong wind induces turbulence at the ocean surface. These processes mix heat and salt and create a layer at the top of the ocean that has a uniform temperature and salinity and that is called the "mixed layer." This mixed layer plays a fundamental role in the Earth climate system, and the representation of its evolution in ocean models hence needs to be assessed. For this purpose, we propose to map the mixed layer evolution in a three‐dimensional space where the first axis is related to the wind and the surface heat flux, the second axis to the stability of the water column, and the third axis to the Earth's rotation. We show that this tool performs statistically well and we present how to use it in the context of realistic ocean models. Key Points: A parameter space is proposed to assess the evolution of the mixed layer depth for realistic forcings and preconditioning conditionsAn evaluation of a collection of 1D simulations shows a statistically good performance of the parameter spaceTwo applications demonstrate the utility of the parameter space for assessing and comparing realistic 3D simulations [ABSTRACT FROM AUTHOR]

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey's fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters. [ABSTRACT FROM AUTHOR]

Abstract The ocean surface mixed layer plays a crucial role as an entry or exit point for heat, salt, momentum, and nutrients from the surface to the deep ocean. In this study, we introduce a framework to assess the evolution of the mixed layer depth (MLD) for realistic forcings and preconditioning conditions. Our approach involves a physically‐based parameter space defined by three dimensionless numbers: λs representing the relative contribution of the buoyancy flux and the wind stress at the air‐sea interface, Rh the Richardson number which characterizes the stability of the water column relative to the wind shear, and f/Nh which characterizes the importance of the Earth's rotation (ratio of the Coriolis frequency f and the pycnocline stratification Nh). Four MLD evolution regimes (“restratification,” “stable,” “deepening,” and “strong deepening”) are defined based on the values of the normalized temporal evolution of the MLD. We evaluate the 3D parameter space in the context of 1D simulations and we find that considering only the two dimensions (λs, Rh) is the best choice of 2D projection of this 3D parameter space. We then demonstrate the utility of this two‐dimensional λs − Rh parameter space to compare 3D realistic ocean simulations: we discuss the impact of the horizontal resolution (1°, 1/12°, or 1/60°) and the Gent‐McWilliams parameterization on MLD evolution regimes. Finally, a proof of concept of using observational data as a truth indicates how the parameter space could be used for model calibration.

A number of iterative schemes with high convergence order to solve nonlinear equations are presented in the literature. In this paper, a sixth-order multiple-zero finder has been developed and the dynamics of selected iterative schemes with uniparametric polynomial weight function are investigated using Möbius conjugacy map applied to the form ((z-A)(z-B))m. The complex dynamics on the Riemann sphere by analyzing the parameter spaces associated with the free critical points are studied, and the numerical experiments are carried out. [ABSTRACT FROM AUTHOR]

For a parameter-controlled Newton-secant method, we investigate the complex dynamics with the stability surfaces and parameter spaces using Möbious conjugacy map applied to the form ((z-A)(z-B))m. The basins of attraction of test functions is illustrated according to the color palette. The nonlinear equation related to blood rheology model has been employed to show the basins of attraction. [ABSTRACT FROM AUTHOR]

This study aims to analyze how the parameter flow rate and amplitude of walling waves affect the peristaltic flow of Jeffrey’s fluid through an irregular channel. The movement of the fluid is described by a set of non-linear partial differential equations that consider the influential parameters. These equations are transformed into non-dimensional forms with appropriate boundary conditions. The study also utilizes dynamic systems theory to analyze the effects of the parameters on the streamline and to investigate the position of critical points and their local and global bifurcation of flow. The research presents numerical and analytical methods to illustrate the impact of flow rate and amplitude changes on fluid transport. It identifies three types of streamline patterns that occur: backwards, trapping, and augmented flow resulting from changes in the value of flow rate parameters.

In order to implement the application of machine learning in the field of cardiopulmonary resuscitation (CPR) into real clinical work, an assisted diagnosis and treatment algorithm based on machine learning and fused with CPR diagnosis and treatment standards was proposed. Random forest, gradient boosting tree and extreme gradient boosting were used as the base model. The voting method was used for model fusion, and the shapley additive explanation algorithm (SHAP) was introduced to filter out the features with lower shapley values for retraining, and the resulting model creates a parameter space under the cardiopulmonary resuscitation diagnostic and treatment standard for optimization, and finally obtains the optimal diagnostic and treatment plan. The resulting model was optimized by creating a parameter space under the CPR diagnosis and treatment criteria, and the optimal treatment plan was finally obtained. The results show that the algorithm after integrating the CPR diagnosis and treatment standards is more in line with the clinical reality, which can provide assistance for clinical diagnosis and treatment and improve the success rate of CPR. [ABSTRACT FROM AUTHOR]

Bistable shallow arches are ubiquitous in many engineering systems ranging from compliant mechanisms and biomedical stents to energy harvesters and passive fluidic controllers. In all these scenarios, the bistable states of the arch and the sudden transitions between them via snap-through instability are harnessed. However, bistable arches have been traditionally studied and characterized by triggering snap-through instability using quasi-static forces. Here, we analytically examine the effect of oscillatory loads on bistable arches and investigate the dynamic behaviors ranging from intrawell motion to periodic and chaotic interwell motion. The linear and nonlinear dynamic responses of both elastically and plastically deformed shallow arches are presented. Introducing an energy potential criterion, we classify the structure's behavior within the parameter space. This energy-based approach allows us to explore the parameter space for high-dimensional models of the arch by varying the force amplitude and excitation frequency. Bifurcation diagrams, Lyapunov exponents, and maximum critical energy plots are presented to characterize the dynamic response of the system. Our results reveal that unstable solutions admitted through higher modes govern the critical energy required for interwell motion. This study investigates the rich nonlinear dynamic behavior of the arch element and it introduces an energy potential criterion that can scale easily to classify motion of arrays of bistable arches for future developments of multistable mechanical metamaterials. [ABSTRACT FROM AUTHOR]

BACKGROUND: Yin-Yang and the golden mean are the core concepts of Chinese culture, but there is a lack of a bridge connecting with modern science. The power-law model has good robustness or anti-interference ability in complex system science, suggesting that it is closely related to Yin-Yang and the golden mean. OBJECTIVE: To analyze the Yin-Yang dialectical characteristics of long-term aerobic exercise against Alzheimer’s disease based on the power-law model and to discuss the potential role of Yin-Yang theory of power-law model in the complex systems of the human body. METHODS: Referring to the theory of Yin-Yang, the relationship rationality and the golden mean, this paper uses power law to characterize each pair of parameters, and the factors that cause the power law coefficient and index changes are referred to as Yin-Yang causes. Then, a parametric pair model of human Yin-Yang is proposed and applied to experimental animal studies of Alzheimer’s disease. The parameters of the human body constitute the parameter space, and the geometric mean of the parameter space is defined as the golden center of the parameter space. RESULT AND CONCLUSION: Yin and Yang are subjective feelings of power-law relationship of objective parameters. Yin-Yang attribute of two subspaces exists in relation to the joint space of two subspaces. Yin-Yang secret or Yin-Yang imbalance in two subspaces correspond to the same-level power law or upgraded power law in two subspaces respectively. Animal experimental data shows that Alzheimer’s disease modeling can cause Yin-Yang imbalance, and habitual swimming before modeling can resist the changes in Yin-Yang parameters caused by Alzheimer’s disease modeling. The above results indicate that the reasonable explanation of Yin-Yang theory of power-law model by human complex system parameters can be used for Yin-Yang dialectic in data space and the power-law relationship in objective parameters can represent the Yin-Yang characteristics of subjective feelings. [ABSTRACT FROM AUTHOR]

The approach described in this paper handles the parameters and characteristics (analog and discrete ones) of a Buck DC-DC converter (in its power and control parts) in a common manner. The usage of probably complicated differential equations for discrete dynamical systems is avoided by means of index matrix equations, which can be easily understood. Compared to classical matrix models, the proposed index matrix models are more descriptive and also smaller in size. Such functionality is widely applied by the authors, and a new operation is defined and used as well. The relevance of the proposed techniques in power electronics, because of switching topologies and a limited numbers of components, is argued. Respective examples of functioning modes of the considered converter, in which power circuits and controllers are modeled jointly, are given. Estimations of analog values are based on partly linear dependencies, which are shown to be adequate in first-order analyses. Specific expressions for a Buck DC-DC converter are presented. A model-solving technique and an exhaustive search on a parameter space are considered in detail and automated via well-formalized algorithms. Nested parameter intervals and verifications with normal probability distributions are used in an optimization procedure. The full agreement of implementation via MATLAB source code with results obtained via Simulink is demonstrated. The short simulation times of this software (compared to Simulink and a.NET desktop application developed by the authors) justify the search for optimal variants in a wide multi-dimensional space. A max–min procedure with 10,000 simulations in each verification step is presented. [ABSTRACT FROM AUTHOR]

We study the complex dynamics by analyzing the dynamical planes associated with the family of third order multiple root finders and the parameter spaces related to the free critical points. The conjugacy maps with the theoretical results of dynamical analysis for the iterative schemes are investigated. In addition, the various experiments are implemented to draw the dynamics of the cubic-order schemes as well as existing methods. [ABSTRACT FROM AUTHOR]

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be arbitrarily small in any considered population and hence practically ignorable. In addition, the set of parameter values where this discrepancy is negligible is shown to possess the same dimensionality as that of the underlying model parameter space. The article contributes to the measurement and related literature by pointing out that (a) approximate or strict loading identity is not a necessary condition for the utility of alpha as a trustworthy index of scale reliability, and (b) coefficient alpha can be a dependable reliability measure with any extent of inequality in the component loadings. [ABSTRACT FROM AUTHOR]

Migration is a natural behavior and an integral part of many species' life cycles. Although most commonly found in many species of mammals and birds, it also occurs in several other species such as fish, insects, etc. Animals migrate in response to the spatial and temporal variability of environmental factors, such as food availability, habitat safety, climate, and mating opportunities. The present study investigates the role of middle predator's migration (immigration and emigration) in the dynamics of a well-known tri-trophic food chain model. We perform extensive numerical simulations of this model system with simultaneous variation of migration and another system parameter related to the half-saturation constant of the middle predator, and present a collection of high-resolution isospike and Lyapunov exponent diagrams drawn in the biparametric space illustrating the intricate nature of the system dynamics. We mainly find that a moderate amount of migration (both immigration and emigration) promotes regularity in the dynamics of the system. High migration rates, however, lead to the extinction of one or more species from the system. The isospike diagrams uncover several periodic windows of different periodicity inside the chaotic region, some of them crossing one another. We demonstrate with the aid of phase portraits and basins of attraction that these overlappings induce bistability between coexisting attractors. We notice that these basins have a self-similar nature. Additionally, the system exhibits shrimp-shaped periodic structures, period-bubbling route to chaos, and multiple-times stability switching. We also include several animations related to stability switching and the basin of attraction for better visualization of the dynamics of the system. [ABSTRACT FROM AUTHOR]

The complex dynamical analysis of the cubic-order iterative family is proposed to draw the fractal images via M¨obius conjugacy map applied to a quadratic polynomial (z −A) m(z −B) m. The resulting dynamics is clearly visualized through various stability surfaces and parameter spaces using Mathematica. [ABSTRACT FROM AUTHOR]

In this paper, we study the approximation orders of a real number x ∈ (0 , 1) by the partial sums of its β -expansions as β varies in the parameter space { β ∈ ℝ : β > 1 }. More precisely, letting S n (x , β) be the partial sum of the first n items of the β -expansion of x , we prove that for any real number x ∈ (0 , 1) , the approximation order of x by S n (x , β) is β − n for Lebesgue almost all β > 1. Moreover, we obtain the size of the set of β > 1 for which x can be approximated with a more general order β − φ (n) , where φ : ℕ → ℝ + is a positive function. We also determine the Hausdorff dimension of the set C φ (α) = β > 1 : lim sup n → ∞ l n (x , β) φ (n) = α , 0 ≤ α ≤ ∞ , where l n (x , β) is the number of the longest consecutive zeros just after the n th digit in the β -expansion of x. [ABSTRACT FROM AUTHOR]

In order to study the influence of dynamic parameters on the gait of biped robots, a passive walking robot with flat feet is taken as the research object, the dynamic equation using Lagrange method and conservation of angular momentum is established and the numerical simulation is carried out. The gait of the flat-foot robot's periodic motion is explained with the help of a stable limit cycle. Based on the bifurcation theory, the effects of the sole, heel, center of mass position, mass ration, and inclined plane inclination on the stable gait of the flat-foot robot are analyzed. The point mapping is used to quickly track the dynamic behavior of the system in the two-dimensional parameter space. The results show that the energy loss of the flat-foot robot mainly occurs when the swinging leg collides with the inclined plane. With the change of the heel, center of mass position, and mass ratio, the gait of the flat-foot robot presents inverse doubling periodic bifurcation. It is found that the flat-foot robot is very sensitive to changes in the position of the heel and the center of mass. At the same time, through the combination of dynamic parameters of the flat-foot robot in maintaining a stable gait in the two-dimensional parameter space and the influence of different foot shapes on the global stability of the system, the importance of the foot shape on the stable walking of the biped robot is proved. The research results provide an important basis for the structural design and energy-saving control of the biped robot.

Confidence contours in parameter space are a helpful tool to compare and classify determined estimators. For more intricate parameter estimations of nonlinear nature or complex error structures, the procedure of determining confidence contours is a statistically complex task. For polymer chemists, such particular cases are encountered in determination of reactivity ratios in copolymerization. Hereby, determination of reactivity ratios in copolymerization requires nonlinear parameter estimation. Additionally, data may possess (possibly correlated) errors in both dependent and independent variables. A common approach for such nonlinear estimations is the error‐in‐variables model yielding statistically unbiased estimators. Regarding reactivity ratios, to date published procedures neglect the non‐Gaussian structure of the error estimates that is a consequence of the nonlinearity of the model. In this publication, this issue is addressed by employing a Bayesian hierarchical model, which correctly propagates the errors of all variables. The statistical procedure is discussed in chemist friendly language to encourage confident usage of the tool. The approach is based on a Python program requiring minimal installation effort. A detailed manual of the code is included in the appendix of this work, in an effort to make this procedure available to all interested polymer chemists. [ABSTRACT FROM AUTHOR]

Many different macroevolutionary models can produce the same observations. Despite efforts in building more complex and realistic models, it may still be difficult to distinguish the processes that have generated the biodiversity we observe. In this opinion we argue that we can make new progress by reaching out across disciplines, relying on independent data and theory to constrain macroevolutionary inference. Using mainly paleontological insights and data, we illustrate how we can eliminate less plausible or implausible models, and/or parts of parameter space, while applying comparative phylogenetic approaches. We emphasize that such cross-disciplinary insights and data can be drawn between many other disciplines relevant to macroevolution. We urge cross-disciplinary training, and collaboration using common-use databases as a platform for increasing our understanding. The rapid accumulation of information from diverse sources – such as cheap sequencing and growing community databases, together with improvements in computational speed – has fueled a growth in increasingly complex models in many fields, including macroevolutionary biology. Despite the rate of increase in data accumulation, temporal, taxonomic, and other data gaps will always exist. It has become apparent that macroevolutionary models are often impossible to distinguish, even with huge volumes of data. A way out of this quandary is to use independent information across disciplines to limit plausible models and to constrain parameters. [ABSTRACT FROM AUTHOR]

In this work we report numerical results involving a certain Hopfield-type three-neurons network, with the hyperbolic tangent as the activation function. Specifically, we investigate a place of a two-dimensional parameter-space of this system where typical periodic structures, the so-called shrimps, are embedded in a chaotic region. We show that these structures are organized themselves as a spiral that coil up toward a focal point, while undergo period-adding bifurcations. We also indicate the locations along this spiral in the parameter-space, where such bifurcations happen.

Biological neurons show significant cell-to-cell variability but have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. Using a population of multi-compartment models consisting of soma, neurites, and axon for the lateral pyloric neuron in the crab stomatogastric ganglion, we explore how rebound bursting is preserved when the 14 channel conductances in each model are all randomly varied. The coupling between the axon and other compartments is critical for the ability of the axon to spike during bursts and consequently determines the set of successful solutions. When the coupling deviates from a biologically realistic range, the neuronal tolerance of conductance variations is lessened. Thus, the gross morphological features of these neurons enhance their robustness to perturbations of channel densities and expand the space of individual variability that can maintain a desired output pattern. [ABSTRACT FROM AUTHOR]

The beta generator technique entails constructing a univariate distribution function as a composite function of two distribution functions. The success of this technique in the univariate setting has prompted research into the possibility of generalization to the bivariate case. Such a generalization, using copulas, has already been proposed in the literature. In this paper, we construct bivariate distribution functions by passing a bivariate distribution function as an argument to the univariate beta distribution function. The class of distributions obtained is identical to an existing class of distributions; however, the elementary elements of the two classes differ (i.e., some distributions are simple to construct using one of the techniques considered and difficult to construct using the other). This paper provides a rigorous derivation of the parameter space of the beta-generated distributions, as well as a result relating to the dependence structure of the marginals. Finally, a practical example is included demonstrating the use of a beta-generated distribution in the modeling of observed losses in the energy market. [ABSTRACT FROM AUTHOR]

In this paper, by applying Petković's iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter r and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes. [ABSTRACT FROM AUTHOR]

The subject of research in the article is dynamic control systems with optimal slow motions. The goal of the work is to obtain an asymptotic approximation of the control in the form of feedback, which, not being uniform in the domain of the system definition, forms slow motions of the system uniformly close to optimal ones. The objectives of the study are to conduct an asymptotic analysis of the controller for small values of the parameters. Applied methods: methods of minimization of quadratic functions and methods of matrix algebra. The obtained results: the problem of the optimal equation with two small singularly exciting parameters is considered. Requirements for the characteristics and controllability of the selected system have been introduced. The problem under consideration, in contrast to well-known studies, is connected with a fundamental problem: as the system parameters tend to zero, certain components of the matrix that satisfies the Ricatti equation, due to the limiting condition for it, acquire singularities in certain time intervals. The practical significance of the work lies in the fact that with the use of minimization methods, general methods are obtained for constructing a uniform region of asymptotics for optimal control systems with two small singular-exciting parameters with respect to another small parameter.

The approach described in this paper handles the parameters and characteristics (analog and discrete ones) of a Buck DC-DC converter (in its power and control parts) in a common manner. The usage of probably complicated differential equations for discrete dynamical systems is avoided by means of index matrix equations, which can be easily understood. Compared to classical matrix models, the proposed index matrix models are more descriptive and also smaller in size. Such functionality is widely applied by the authors, and a new operation is defined and used as well. The relevance of the proposed techniques in power electronics, because of switching topologies and a limited numbers of components, is argued. Respective examples of functioning modes of the considered converter, in which power circuits and controllers are modeled jointly, are given. Estimations of analog values are based on partly linear dependencies, which are shown to be adequate in first-order analyses. Specific expressions for a Buck DC-DC converter are presented. A model-solving technique and an exhaustive search on a parameter space are considered in detail and automated via well-formalized algorithms. Nested parameter intervals and verifications with normal probability distributions are used in an optimization procedure. The full agreement of implementation via MATLAB source code with results obtained via Simulink is demonstrated. The short simulation times of this software (compared to Simulink and a .NET desktop application developed by the authors) justify the search for optimal variants in a wide multi-dimensional space. A max–min procedure with 10,000 simulations in each verification step is presented.

For the family of quadratic rational functions having a 2-cycle of bounded type Siegel disks, we prove that each of the boundaries of these Siegel disks contains at most one critical point. In the parameter plane, we prove that the locus for which the boundaries of the 2-cycle of Siegel disks contain two critical points is a Jordan curve. [ABSTRACT FROM AUTHOR]

In this article, a new isogeometrical level set topology optimization is introduced. In previous studies, the level set function is approximated by b‐splines basis functions and the control net is updated during the optimization process. Since control points are not basically on the level set surface, a discrepancy between zero level of function that represents boundaries of the structure, and zero level of its control netis appeared. In this article, the idea is solving level set equation (LSE) over the parameter space of b‐splines basis functions defined in the IGA model. Afterwards, the updated level set function is mapped into the physical space. The level set function is approximated over a grid defined in parameter space which is constantly a unit square. By doing so, control net of the IGA model and the grid for solving LSE are separated. Two well‐known radial basis functions (RBF) and reaction–diffusion (RD) based methods are employed to solve the LSE. The proposed method is applied to minimize the mean compliance when certain amount of material is used and also for weight minimization subject to local stress constraints. Several numerical examples are presented to demonstrate performance and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

In this paper, a family of Ostrowski-type iterative schemes with a biparameter was analyzed. We present the dynamic view of the proposed method and study various conjugation properties. The stability of the strange fixed points for special parameter values is studied. The parameter spaces related to the critical points and dynamic planes are used to visualize their dynamic properties. Eventually, we find the most stable member of the biparametric family of six-order Ostrowski-type methods. Some test equations are examined for supporting the theoretical results. [ABSTRACT FROM AUTHOR]

Does the parameter space of the success probability p in the binomial distribution include 0 and 1? From existing literature, including well known undergraduate books, it is not clear whether 0 < p < 1 or 0 ≤ p ≤ 1. In this article, we discuss the issues related to the existing way of defining the binomial probability mass function. Finally, we suggest a simple and intuitive correction in the existing probability mass function of the binomial distribution that addresses the issues. [ABSTRACT FROM AUTHOR]

Abstract Background The human microbiota are complex systems with important roles in our physiological activities and diseases. Sequencing the microbial genomes in the microbiota can help in our interpretation of their activities. The vast majority of the microbes in the microbiota cannot be isolated for individual sequencing. Current metagenomics practices use short-read sequencing to simultaneously sequence a mixture of microbial genomes. However, these results are in ambiguity during genome assembly, leading to unsatisfactory microbial genome completeness and contig continuity. Linked-read sequencing is able to remove some of these ambiguities by attaching the same barcode to the reads from a long DNA fragment (10–100 kb), thus improving metagenome assembly. However, it is not clear how the choices for several parameters in the use of linked-read sequencing affect the assembly quality. Results We first examined the effects of read depth (C) on metagenome assembly from linked-reads in simulated data and a mock community. The results showed that C positively correlated with the length of assembled sequences but had little effect on their qualities. The latter observation was corroborated by tests using real data from the human gut microbiome, where C demonstrated minor impact on the sequence quality as well as on the proportion of bins annotated as draft genomes. On the other hand, metagenome assembly quality was susceptible to read depth per fragment (C R ) and DNA fragment physical depth (C F ). For the same C, deeper C R resulted in more draft genomes while deeper C F improved the quality of the draft genomes. We also found that average fragment length (μ FL ) had marginal effect on assemblies, while fragments per partition (N F/P ) impacted the off-target reads involved in local assembly, namely, lower N F/P values would lead to better assemblies by reducing the ambiguities of the off-target reads. In general, the use of linked-reads improved the assembly for contig N50 when compared to Illumina short-reads, but not when compared to PacBio CCS (circular consensus sequencing) long-reads. Conclusions We investigated the influence of linked-read sequencing parameters on metagenome assembly comprehensively. While the quality of genome assembly from linked-reads cannot rival that from PacBio CCS long-reads, the case for using linked-read sequencing remains persuasive due to its low cost and high base-quality. Our study revealed that the probable best practice in using linked-reads for metagenome assembly was to merge the linked-reads from multiple libraries, where each had sufficient C R but a smaller amount of input DNA. Video Abstract

In this paper, by applying Petković’s iterative method to the Möbius conjugate mapping of a quadratic polynomial function, we attain an optimal eighth-order rational operator with a single parameter r and research the stability of this method by using complex dynamics tools on the basis of fractal theory. Through analyzing the stability of the fixed point and drawing the parameter space related to the critical point, the parameter family which can make the behavior of the corresponding iterative method stable or unstable is obtained. Lastly, the consequence is verified by showing their corresponding dynamical planes.

Polynomial approximation based on collocation method is an emerging technique to establish the relationship between changeable parameters and interested transient trajectory in a given parameter space. If transient stability region boundary (TSRB) exists in the parameter space, the approximation may have low accuracy due to the high sensitivity of the real trajectory with respect to parameters on TSRB. Utilizing the approximated trajectory and the high sensitivity characteristic, this letter proposes a complementary method to obtain TSRB by calculating the local maxima of a sensitivity-based index. The effectiveness of the method is verified in IEEE 39-bus test system. [ABSTRACT FROM AUTHOR]

Formation and study of periodic orbits in phase space in the case of nonlinear oscillators have been a topic of much interest in the recent past. In the current work, a method to go deep inside the limit cycle zone on one side of the bifurcation curve of a 2D non-Lienard biochemical oscillator has been introduced. It is discussed how such an introduction facilitates predicting the boundaries of limit cycles at various points of parameter space, nearly accurately, by the use of perturbative Renormalization Group. Sel'kov model of Glycolytic oscillator has been chosen as the base model to introduce the method. [ABSTRACT FROM AUTHOR]

In this article, we suggest the local analysis of a uni-parametric third and fourth order class of iterative algorithms for addressing nonlinear equations in Banach spaces. The proposed local convergence is established using an w-continuity condition on the first Fréchet derivative. In this way, the utility of the discussed schemes is extended and the application of Taylor expansion in convergence analysis is removed. Furthermore, this study provides radii of convergence balls and the uniqueness of the solution along with the calculable error distances. The dynamical analysis of the discussed family is also presented. Finally, we provide numerical explanations that show the suggested analysis performs well in the situation where the earlier approach cannot be implemented. [ABSTRACT FROM AUTHOR]

• A novel, optimization-based method for design space calculation. • Yields a multivariate design space compliant with ICH Q8 guidelines. • Design space as linear combination of process parameter ranges. • Conservative design space by evaluating tolerance intervals within parameter space. • Improved accuracy and computing time compared to grid-based approaches. According to ICH Q8 guidelines, a biopharmaceutical manufacturer may submit a design space (DS) definition as part of the regulatory approval application, in which case process parameter (PP) deviations within this space are not considered changes and do not trigger a regulatory post approval procedure. A DS can be described by non-linear PP ranges, i.e., the range of one PP conditioned on specific values of another. However, independent PP ranges (linear combinations) are often preferred in biopharmaceutical manufacturing due to their operational simplicity, as mentioned in the guideline. While statistical software such as Modde supports the calculation of a DS comprised of linear combinations, their algorithms are generally based on discretizing the parameter space - an approach that suffers from the curse of dimensionality as the number of PPs increases. Here, we introduce a novel method for finding linear PP combinations using a numeric optimizer to calculate the largest design space within the parameter space that results in critical quality attribute boundaries within acceptance criteria, predicted by a regression model. A precomputed approximation of tolerance intervals is used in inequality constraints to facilitate fast evaluations of this boundary using a single matrix multiplication. The correctness of the method was validated by comparing results to that of a grid-based approach and, in a simple case, to an analytically defined ground truth. In the examples investigated, the volume of the resulting DS was significantly larger than that of the grid method, with the improvement being proportional to the granularity of the grid and the number of parameters involved. Furthermore, computational time for the optimization-based approach is several orders of magnitude faster in higher dimensions. In addition, a proposed weighting scheme can be used to favor certain PPs over others and therefore enabling a more dynamic approach to DS definition and exploration. The increased PP ranges of the larger DS provide greater operational flexibility for biopharmaceutical manufacturers. [ABSTRACT FROM AUTHOR]

Robust chaos in the discrete system is suggested to have practical as well as theoretical importance since it can obtain reliable operation in the chaotic mode. However, it receives only moderate attention and only focuses on a finite chaotic parameter space and small Lyapunov exponents. This paper introduces a two-dimensional smooth map and studies its robustness of chaos in the infinite parameter space. Then, a compound operation-based optimization control method is introduced to increase the map complexity in the measure of Lyapunov exponent. The introduced method is simple and provides a new pathway for exploring the robustness and complexity of discrete chaotic system. Finally, we design a chaos-based pseudo-random number generator (CPNG) based on the optimized robust chaotic map, and the careful analysis shows that the proposed CPNG has high quality of randomness and has passed the rigorous National Institute of Standards and Technology (NIST) test.

Existing approaches that describe the quality of inequality constrained estimates are not sufficient to meet the demands of inequality constrained least-square problems. We reconstruct the existing Monte Carlo method by converting the sampling space from observation space to parameter space, and propose a workflow to improve the computational efficiency. The proposed method is verified by a straight-line fitting example with independent and dependent inequality constraints, and the constraints have different intensities. The results show that the proposed workflow has higher computational efficiency than the existing workflow and that the saved time is almost linearly related to the intensity of the inequality constraints. [ABSTRACT FROM AUTHOR]