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This paper introduces the paradigm of "in-context operator learning" and the corresponding model "In-Context Operator Networks" to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update. Existing methods are limited to using a neural network to approximate a specific equation solution or a specific operator, requiring retraining when switching to a new problem with different equations. By training a single neural network as an operator learner, rather than a solution/operator approximator, we can not only get rid of retraining (even fine-tuning) the neural network for new problems but also leverage the commonalities shared across operators so that only a few examples in the prompt are needed when learning a new operator. Our numerical results show the capability of a single neural network as a few-shot operator learner for a diversified type of differential equation problems, including forward and inverse problems of ordinary differential equations, partial differential equations, and mean-field control problems, and also show that it can generalize its learning capability to operators beyond the training distribution. [ABSTRACT FROM AUTHOR]

This paper studies a discontinuous Sturm-Liouville problem in which the spectral parameter appears not only in the differential equation but also in the transmission conditions. By constructing an appropriate Hilbert space and inner product, the eigenvalue and eigenfunction problems of the Sturm-Liouville problem are transformed into an eigenvalue problem of a certain self-adjoint operator. Next, the eigenfunctions of the problem and some properties of the eigenvalues are given via construction of the basic solution. The Green's function for the Sturm-Liouville problem is also given. Finally, the continuity of the eigenvalues and eigenfunctions of the problem is discussed. Especially, the differential expressions of the eigenvalues for some parameters have been obtained, including the parameters in the eigenparameter-dependent transmission conditions. [ABSTRACT FROM AUTHOR]

Artificial Intelligence (AI), the emergence and development of social system model, are gradually affecting the development of system engineering technology and methods. AI mainly focuses on acquiring new knowledge or skills by looking for rules from observation data (samples); social system model mainly focuses on the ability of description and model demonstration from the current situation to the future. The combination of AI and social system model can promote the research of social problems related to system engineering. The synergetic growth of various sectors of the economic system depends on the initial level of output of each sector and its internal relations. This paper focuses on the internal relationship of the two-sector economic model and explores the impact of distribution relations on the synergetic growth of sectors. The study found that the necessary conditions for synergetic growth is a function of the profit rate, the difference between the labor income (or capital income) of the two sectors, and the marginal consumption propensity. This function has a more complex and nonlinear characteristic. By demonstrating the effects of changes in some parameters, we find that an increase in the profit rate requires that the income distribution structure of the two sectors tend to be the same; an increase in the marginal consumption propensity can allow for greater differences in the income distribution structure of the two sectors. [ABSTRACT FROM AUTHOR]

In this paper, we propose a two-grid algorithm for nonlinear time fractional parabolic equations by H 1 -Galerkin mixed finite element discreitzation. First, we use linear finite elements and Raviart-Thomas mixed finite elements for spatial discretization, and L 1 scheme on graded mesh for temporal discretization to construct a fully discrete approximation scheme. Second, we derive the stability and error estimates of the discrete scheme. Third, we present a two-grid method to linearize the nonlinear system and discuss its stability and convergence. Finally, we confirm our theoretical results by some numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid cuckoo search technique is combined with a single-layer neural network (BHCS-ANN) to approximate the solution to a differential equation describing the curvature shape of the cornea of the human eye. The proposed problem is transformed into an optimization problem such that the L 2 – error remains minimal. A single hidden layer is chosen to reduce the sink of the local minimum values. The weights in the neural network are trained with a hybrid cuckoo search algorithm to refine them so that we obtain a better approximate solution for the given problem. To show the efficacy of our method, we considered six different corneal models. For validation, the solution with Adam's method is taken as a reference solution. The results are presented in the form of figures and tables. The obtained results are compared with the fractional order Darwinian particle swarm optimization (FO-DPSO). We determined that results obtained with BHCS-ANN outperformed the ones acquired with other numerical routines. Our findings suggest that BHCS-ANN is a better methodology for solving real-world problems. [ABSTRACT FROM AUTHOR]

Liquidity risk arises from the inability to unwind or hedge trading positions at the prevailing market prices. The risk of liquidity is a wide and complex topic as it depends on several factors and causes. While much has been written on the subject, there exists no clear-cut mathematical description of the phenomena and typical market risk modeling methods fail to identify the effect of illiquidity risk. In this paper, we do not propose a definitive one either, but we attempt to derive novel mathematical algorithms for the dynamic modeling of trading volumes during the closeout period from the perspective of multiple-asset portfolio(s), as well as for financial entities with different subsidiary firms and multiple agents. The robust modeling techniques are based on the application of initial-value-problem differential equations technique for portfolio selection and risk management purposes. This paper provides some crucial parameters for the assessment of the trading volumes of multiple-asset portfolio(s) during the closeout period, where the mathematical proofs for each theorem and corollary are provided. Based on the new developed econophysics theory, this paper presents for the first time a closed-form solution for key parameters for the estimation of trading volumes and liquidity risk, such as the unwinding constant, half-life, and mean lifetime and discusses how these novel parameters can be estimated and incorporated into the proposed techniques. The developed modeling algorithms are appealing in terms of theory and are promising for practical econophysics applications, particularly in developing dynamic and robust portfolio management algorithms in light of the 2007–2009 global financial crunch. In addition, they can be applied to artificial intelligence and machine learning for the policymaking process, reinforcement machine learning techniques for the Internet of Things (IoT) data analytics, expert systems in finance, FinTech, and within big data ecosystems. [ABSTRACT FROM AUTHOR]

The excessive emission of greenhouse gases leads to abnormal climate change. Under this background, China puts forward the dual carbon target. In this paper, we use the analytic hierarchy process to determine the important influencing factor of carbon emissions. Next, we establish a delayed differential equation model of carbon emission-absorption under the influence of China's urbanization. We analyze the existence and stability of the positive equilibrium. Finally, we determine the ranges of parameters and study the impact of urbanization on China's dual carbon target through numerical simulations. The numerical simulation also shows that the system may have globally asymptotically stable equilibrium. Through the simulation results, we conclude whether the dual carbon target of China can be achieved by the scheduled time and give some suggestions that could be taken to achieve this target. The projected results provide some guidance for policy adjustments and also have practical significance in protecting the ecological environment. [ABSTRACT FROM AUTHOR]

In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the Störmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value. [ABSTRACT FROM AUTHOR]

in this paper, we study cellular neural networks with almost periodic variable coefficients and time-varying delays. By using the existence theorem of almost periodic solution for general functional differential equations, introducing many real parameters and applying the Lyapunov functional method and the technique of Young inequality, we obtain some sufficient conditions to ensure the existence, uniqueness, and global exponential stability of almost periodic solution. The results obtained in this paper are new, useful, and extend and improve the existing ones in previous literature. [ABSTRACT FROM AUTHOR]

In this paper, several simple and new conditions are presented to ensure existence, uniqueness and global exponential robust stability of the equilibrium point of neural networks with delays by using contraction mapping principle, homeomorphism property and Lyapunov method. The conditions given in this paper are easy to verify and apply, and the obtained results improve and extend to those in the literature. In addition, two examples are given to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

With the help of the dynamics model of the integration of AI and the management of college civic education, this paper investigates the integration of artificial intelligence and civic education in three directions: application specification, application design, and application practice. Using differential equations to represent the non-linear dynamics equations of the system and by means of differential solutions, the evolution mechanism of AI education application and integration is projected in this paper. The integration of AI and college civic education is explored through empirical analysis and comparative analysis. The results show that the average value of the comprehensive score of the three directions in the sample colleges and universities is 77.5828, which is in the bare integration stage, and the integration degree in the “formulation” path is the best, which is 85.698, and is in the complete integration stage. The students in the experimental class of the sample universities scored better than the control class without AI integration in civic education. There were no students with scores below 60, and there were 32 more students than the control class in the 90–100 segment.

Once an active distribution network of a cyber-physical system is in alert state, it is vulnerable to cross-domain cascading failures. It is necessary to transit the state of an active distribution network of cyber-physical system from an alert state to a normal state using a preventive control policy against cross-domain cascading failures. In fact, it is difficult to construct and analyze a preventive control policy via theoretical analysis methods or physical experimental methods. The theoretical analysis methods may not be accurate due to approximated models, and the physical experimental methods are expensive and time consuming for building prototypes. This paper presents a preventive control policy construction method based on a deep deterministic policy gradient idea (shorted as PCMD) to generate and optimize a preventive control policy with Artificial Intelligence (AI) technologies. It adopts the reinforcement learning technique to make full use of the available historical data to overcome the problems of high cost and low accuracy. Firstly, a preventive control model is designed based on the finite automaton theory, which can guide the data collection and learning policy selection. The control model considers the voltage stability, frequency stability, current overload prevention, and the control cost reduction as a feedback variable, without the specific power flow equations and differential equations. Then, after enough training, a local optimal preventive control policy can be constructed under the comparability condition among a fitted action-value function and a fitted policy function. The constructed preventive control policy contains some control actions to achieve a low cost and in accord with the principle of shortening a cross-domain cascading failures propagation sequence as far as possible. The PCMD is more flexible and closer to reality than the theoretical analysis methods and has a lower cost than the physical experimental methods. To evaluate the performance of the proposed method, an experimental case study, China Electric Power Research-Cyber-Physical System (shorted as CEPR-CPS), which comes from China Electric Power Research Institute, is carried out. The result shows that the effectiveness of preventive control policy construction with the PCMD is better than most current methods, such as the multi-agent method in terms of reducing the number of failure nodes and avoiding the state space explosion. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of mean square exponential stability of stochastic Cohen- Grossberg neural networks (SCGNN), whose state variables are described by stochastic nonlinear integrodifferential equations. With the help of Lyapunov function, stochastic analysis technique, and inequality techniques, some novel sufficient conditions on mean square exponential stability for SCGNN are given. Furthermore, we also establish some sufficient conditions for checking exponential stability for Cohen-Grossberg neural networks with unbounded distributed delays. [ABSTRACT FROM AUTHOR]

This paper studies multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories. [ABSTRACT FROM AUTHOR]

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of these networks to be stable. The main contribution of the paper is that Lyapunov function and singularly perturbed technique are combined to access several new stable properties of different time-scales neural networks. Exponential stability and asymptotic stability are obtained by sector and bound conditions. Compared to other papers, these conditions are simpler. Numerical examples are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In designing the adaptive controllers, the Lyapunov theory can be used as a powerful tool that can prevent the system from facing unstable situations. By satisfying its condition, the desired controller can be obtained. Compare to other chaotic control methods, The controller based on the above mentioned method is particularly simple and practical, with no need for a precise system model. Having the system dimension is solely enough for this controller. The main purpose of this paper is to investigate the capability of this control method by applying it in some chaotic systems and demonstrating its rapid success rate in stabilizing the fixed unstable point of these systems and also comparing it with the state feedback controller. [ABSTRACT FROM AUTHOR]

In this paper, two kinds of stochastic differential equations with piecewise constant arguments are investigated. Sufficient conditions for the existence of the square-mean S-asymptotically ω -periodic solutions of these two type equations are derived where ω is an integer. Then, the global asymptotic stability for one of them is considered by using the comparative approach. In order to show the theoretical results, we give two examples. [ABSTRACT FROM AUTHOR]

To balance the supply and demand in China's beef market, beef consumption must be scientifically and effectively forecasted. Beef consumption is affected by many factors and is characterized by gray uncertainty. Therefore, gray theory can be used to forecast the beef consumption, In this paper, the structural defects and unreasonable parameter design of the traditional gray model are analyzed. Then, a new gray model termed, EGM(1,1,r), is built, and the modeling conditions and error checking methods of EGM(1,1,r) are studied. Then, EGM(1,1,r) is used to simulate and forecast China’s beef consumption. The results show that both the simulation and prediction precisions of the new model are better than those of other gray models. Finally, the new model is used to forecast China’s beef consumption for the period from 2019–2025. The findings will serve as an important reference for the Chinese government in formulating policies to ensure the balance between the supply and demand for Chinese beef. [ABSTRACT FROM AUTHOR]

Recently, the synchronization issue in chaotic systems has become a hot topic in nonlinear dynamics and has aroused great interest among researchers due to the theoretical significance and potential applications. In this paper, complete periodic synchronization is considered for the delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution, a novel control method is presented by using differential inclusions theory, nonsmooth Lyapunov method and linear matrix inequality (LMI) approach. Based on a newly obtained necessary and sufficient condition, several criteria are derived to ensure the global asymptotical stability of the error system, and thus the response system synchronizes with the drive system. Moreover, the estimation gains are obtained. With these new and effective methods, complete synchronization is achieved. Simulation results are given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a hyperchaotic RTD-based cellular neural network is proposed and its hyperchaotic dynamics is demonstrated. The Lyapunov exponents spectrum is presented, and some typical Lyapunov exponents are calculated in a range of parameters. Several important phase portraits are presented as well. [ABSTRACT FROM AUTHOR]

In this paper, global synchronization of linearly coupled neural network (NN) systems with time-varying coupling is investigated. The dynamical behavior of the uncoupled system at each node is general, which can be chaotic or others; the coupling configuration is time varying, i.e., the coupling matrix is not a constant matrix. Based on Lyapunov function method and the specific property of Householder transform, some criteria for the global synchronization are obtained. By these criteria, one can verify whether the coupled system with time-varying coupling is globally synchronized, which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration. Finally, two simulations are given to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Aggregation plays a central role as a means of combining all opinions that are expressed by group members in a group decision support system (GDSS). In this paper, we propose a new r-ASA (Aggregation based on Situation Assessment) algorithm to reflect a decision situation in the aggregation process. Al- though some research findings showed the importance of cultural factors in GDSS, most of them did not present how to implement cultural factors in GDSS. To handle this problem, we present a proposal for reflecting status differentials in GDSS. It may be used to reflect cultural differences in GDSS design. It is a further step toward the integration of cultural factors into existing GDSS design. [ABSTRACT FROM AUTHOR]

In this paper, we present a class of delayed parabolic neural networks (DPNN) with variable coefficients. Some sufficient conditions for the global exponential stability of the DPNN with variable coefficients are derived by a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of DPNN with variable coefficients. [ABSTRACT FROM AUTHOR]

This paper focuses on the development of a Petri-fuzzy-neural-network (PFNN) control for an indirect field-oriented linear-induction-motor (LIM) drive. First, an indirect field-oriented mechanism for a LIM drive is derived to preserve the decoupling control characteristic. Then, the concept of a Petri net (PN) is incorporated into a traditional FNN (TFNN) to form a new type of PFNN framework for alleviating the computation burden. Moreover, the supervised gradient descent method is used to develop the online training algorithm for the PFNN. In order to guarantee the convergence of tracking error, analytical methods based on a discrete-type Lyapunov function are proposed to determine the varied learning rates of the PFNN. With the proposed PFNN control system, the mover position of the controlled LIM drive possesses the advantages of good transient control performance and robustness to uncertainties for the tracking of periodic reference trajectories. In addition, the effectiveness of the proposed control scheme is verified by both numerical simulations and experimental results. Furthermore, the superiority of the proposed PFNN control system is indicated in comparison with the TFNN control system. [ABSTRACT FROM AUTHOR]

In recent years, a recurrent neural network called projection neural network was proposed for solving monotone variational inequalities and related convex optimization problems. In this paper, we show that the projection neural network can also be used to solve pseudomonotone variational inequalities and related pseudoconvex optimization problems. Under various pseudomonotonicity conditions and other conditions, the projection neural network is proved to be stable in the sense of Lyapunov and globally convergent, globally asymptotically stable, and globally exponentially stable. Since monotonicity is a special case of pseudomononicity, the projection neural network can be applied to solve a broader class of constrained optimization problems related to variational inequalities. Moreover, a new concept, called componentwise pseudomononicity, different from pseudomononicity in general, is introduced. Under this new concept, two stability results of the projection neural network for solving variational inequalities are also obtained. Finally, numerical examples show the effectiveness and performance of the projection neural network. [ABSTRACT FROM AUTHOR]

This paper presents a new class of chaotic and hyperchaotic low dimensional cellular neural networks modeled by ordinary differential equations with some simple connection matrices. The chaoticity of these neural networks is indicated by positive Lyapunov exponents calculated by a computer. [ABSTRACT FROM AUTHOR]

In the present paper the question of global asymptotic stability of a class of impulsive delayed cellular neural networks with dynamical thresholds is considered. The main results are obtained by means of piecewise continuous Lyapunov functions. The Razumikhin technique is used. [ABSTRACT FROM AUTHOR]

Lab-on-a-chip (LoC) systems can be functionally decomposed into their basic operating devices. Common devices are mixers, reactors, injectors, and separators. In this paper, the injector device is modeled using artificial neural networks (NNs) trained with finite element simulations of the underlying mass transport partial differential equations (PDEs). This technique is used to map the injector behavior into a set of analytical performance functions parameterized by the system's physical variables. The injector examples shown are the cross, the double-tee, and the gated-cross. The results are four orders of magnitude faster than numerical simulation and accurate with mean square errors (MSEs) on the order of 10-4. The resulting NN training data compare favorably with experimental data from a gated-cross injector found in the literature. [ABSTRACT FROM AUTHOR]

In a previous paper [1], the self-trapping network (STN) was introduced as more biologically realistic than attractor neural networks (ANNs) based on the Ising model. This paper extends the previous analysis of a one-dimensional (1-D) STN storing a single memory to a model that stores multiple memories and that possesses generalized sparse connectivity. The energy, Lyapunov function, and partition function derived for the 1-D model are generalized to the case of an attractor network with only near-neighbor synapses, coupled to a system that computes memory overlaps. Simulations reveal that 1) the STN dramatically reduces intra-ANN connectivity without severly affecting the size of basins of attraction, with fast self-trapping able to sustain attractors even in the absence of intra-ANN synapses; 2) the basins of attraction can be controlled by a single free parameter, providing natural attention-like effects; 3) the same parameter determines the memory capacity of the network, and the latter is much less dependent than a standard ANN on the noise level of the system; 4) the STN serves as a useful memory for some correlated memory patterns for which the standard ANN totally fails; 5) the STN can store a large number of sparse patterns; and 6) a Monte Carlo procedure, a competitive neural network, and binary neurons with thresholds can be used to induce self-trapping. [ABSTRACT FROM AUTHOR]

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high- order Hopfleld-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained. [ABSTRACT FROM AUTHOR]

This paper compares two indirect adaptive neu- rocontrollers, namely a multilayer perceptron neurocontroller (MLPNC) and a radial basis function neurocontroller (RBFNC) to control a synchronous generator. The different damping and transient performances of two neurocontrollers are compared with those of conventional linear controllers, and analyzed based on the Lyapunov direct method. [ABSTRACT FROM AUTHOR]

With the development of multi-/many-core processors, applications need to be written as parallel programs to improve execution efficiency. For data-intensive applications that use multiple threads to read/write files simultaneously, an I/O sub-system can easily become a bottleneck when too many of these types of threads exist; on the contrary, too few threads will cause insufficient resource utilization and hurt performance. Therefore, programmers must pay much attention to parallelism control to find the appropriate number of I/O threads for an application. This paper proposes a parallelism control mechanism named IOPA that can adjust the parallelism of applications to adapt to the I/O capability of a system and balance computing resources and I/O bandwidth. The programming interface of IOPA is also provided to programmers to simplify parallel programming. IOPA is evaluated using multiple applications with both solid state and hard disk drives. The results show that the parallel applications using IOPA can achieve higher efficiency than those with a fixed number of threads. [ABSTRACT FROM AUTHOR]

In this article, the properties of solutions of Hadamard fractional differential equations are investigated on an infinite interval. The equations are subject to integral and discrete boundary conditions. A new proper compactness criterion is introduced in a unique space. By applying the monotone iterative technique, we have obtained two positive solutions. And, an error estimate is also shown at the end. This study innovatively uses a monotonic iterative approach to study Hadamard fractional boundary-value problems containing multiple fractional derivative terms on infinite intervals, and it enriches some of the existing conclusions. Meanwhile, it is potentially of practical significance in the research field of computational fluid dynamics related to blood flow problems and in the direction of the development of viscoelastic fluids. [ABSTRACT FROM AUTHOR]

Researchers often use theoretical models which provide a relatively simple, yet concise and effective way of modelling various phenomena. However, it is a well-known fact that the more complex the model, the more complex the mathematical description is. For this reason, theoretical models generally avoid large complexity and aim for the simplest possible definition, which although makes models mathematically more manageable, in practice it also often leads to sub-optimal performance. Furthermore, the data collected during the observations usually contain confounding factors, for which a simple theoretical model can not be prepared. Overall, mathematical models are usually too rigid and sophisticated, and therefore cannot really deal with sudden changes in the environment. The application of artificial intelligence, however, provides a good opportunity to develop complex models that can combine the basic capabilities of the theoretical models with the ability to learn more complex relationships. It has been shown [16] that with neural networks, we can build such models that can approximate mathematical functions. Trained artificial neural networks are thus able to behave like theoretical models developed for different fields, while still retaining their overall flexibility, which guarantees an overall better performance in a complex real-world environment. The aim of our study is to show our notion that we can create an architecture using neural networks, which is able to approximate a given theoretical model, and then further improve it with the help of real data to suit the real world and its various aspects better. In order to validate the functionality of the architecture developed by us, we have selected a simple theoretical model, namely the Kermack-McKendrick one [4] as the base of our research. This is an SIR [2] model, which is a relatively simple compartmental epidemic model, based on differential equations that can be used well for infections that spread very similarly to influenza or COVID. However, on one hand, the SIR model relies too heavily on its parameters, with slight changes in them leading to drastic overall changes of the S, I and R curves, and on the other hand, the simplicity of the SIR model distorts its accuracy in many cases. In our paper, by using the SIR model, we will show that the architecture described above can be a valid approach to modeling the spread of a given disease (such as influenza or COVID-19). To this end, we detail the accuracy of our models with different settings and configurations and show that it performs better than both a simple mathematical model and a plain neural network with randomly initialized weights. [ABSTRACT FROM AUTHOR]

This paper presents basic definitions and challenges/opportunities from different perspectives to study and control water cycle impacts on society and vice versa. The wider and increased interactions and their consequences such as global warming and climate change, and the role of complex institutional- and governance-related socioeconomic-environmental issues bring forth new challenges. Hydrology and integrated water resources management (IWRM from the viewpoint of an engineering planner) do not exclude in their scopes the study of the impact of changes in global hydrology from societal actions and their feedback effects on the local/global hydrology. However, it is useful to have unique emphasis through specialized fields such as hydrosociology (including the society in planning water projects, from the viewpoint of the humanities) and sociohydrology (recognizing the large-scale impacts society has on hydrology, from the viewpoint of science). Global hydrological models have been developed for large-scale hydrology with few parameters to calibrate at local scale, and integrated assessment models have been developed for multiple sectors including water. It is important not to do these studies with a silo mindset, as problems in water and society require highly interdisciplinary skills, but flexibility and acceptance of diverse views will progress these studies and their usefulness to society. To deal with complexities in water and society, systems modeling is likely the only practical approach and is the viewpoint of researchers using coupled human–natural systems (CHNS) models. The focus and the novelty in this paper is to clarify some of these challenges faced in CHNS modeling, such as spatiotemporal scale variations, scaling issues, institutional issues, and suggestions for appropriate mathematical tools for dealing with these issues. [ABSTRACT FROM AUTHOR]

For analysis of physical properties of different materials, rectangular porous fins are used to examine the heat transformation through a system. In this paper, a metaheuristic is combined with neural computing modelling to study the effects of temperature changes in a porous fin model. Cuckoo search algorithm is used as an efficient optimization technique to find the best weights to reduce the mean squared error in the required temperature profile. The governing partial differential equation is converted into a non-linear ordinary differential equation subject to certain boundary conditions. Two individual cases, of silicon nitride ( Si 3 N 4 ) and Aluminium (Al), are considered. In the proposed procedure, the Cuckoo Search(CS) algorithm is combined with the artificial neural network (ANN), namely CS-ANN, to solve the differential equations and obtain solutions with better accuracy. [ABSTRACT FROM AUTHOR]

Gaussian mixtures (i.e. linear combinations of multivariate Gaussian probability densities) appear in numerous applications due to their universal ability to approximate multimodal probability distributions. Finding the modes (maxima) of a Gaussian mixture is a fundamental problem arising in many practical applications such as machine learning and digital image processing. In this paper, we propose a computationally efficient method for finding a significant mode of the Gaussian mixture. Such a mode represents an area of large probability, and it often coincides with the global mode of the mixture. The proposed method uses a Gaussian convolution in order to remove undesired local maxima of the Gaussian mixture and preserve its underlying structure. The transformation between the maximizers of the smoothed Gaussian mixture and the original one is formulated as a differential equation. A robust trust region method for tracing the solution curve of this differential equation is described. Our formulation also allows mixtures with negative weights or even negative values, which occur in some applications related to machine learning or quantum mechanics. The applicability of the method to mode-finding of Gaussian kernel density estimates obtained from experimental data is illustrated. Finally, some numerical results are given to demonstrate the ability of the method to find significant modes of Gaussian mixtures and kernel density estimates. [ABSTRACT FROM AUTHOR]

The exponential stability of a class of stochastic fuzzy cellular neural networks with distributed delays is investigated in this paper. By using analytic methods such as Lyapunov functional, Itô's formula, inequality techniques and non-negative semimartingale convergence theorem, the sufficient conditions guaranteeing the almost sure and mean square exponential stability of its equilibrium solution are respectively obtained. For illustration, an example is given to show the feasibility of results. [ABSTRACT FROM AUTHOR]

Abstract: The discrete delayed Hopfield neural networks is an extension of the discrete Hopfield neural networks. In this paper, the convergence of discrete delayed Hopfield neural networks is mainly studied, and some results on the convergence are obtained by using Lyapunov function. Several new sufficient conditions for the delayed networks converging towards a limit cycle with period at most 2 are proved in parallel updating mode. Also, some conditions for the delayed networks converging towards a limit cycle with 2-period are investigated in parallel updating mode. All results established in this paper extend the previous results on the convergence of both the discrete Hopfield neural networks, and the discrete delayed Hopfield neural networks in parallel updating mode. [Copyright &y& Elsevier]

In this paper, several sufficient conditions are established for the global asymptotic stability of recurrent neural networks with multiple time-varying delays. The Lyapunov--Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed in our investigation. The results are shown to be generalizations of some previously published results and are less conservative than existing results. The present results are also applied to recurrent neural networks with constant time delays. [ABSTRACT FROM AUTHOR]

For most applications, analog electrical circuit implementations of continuous-valued neural networks have been abandoned in favor of digital simulations. This is not surprising, as both precision and accuracy can be more easily ensured in digital computers. Still, because they use far fewer transistors and support components, analog circuits can still be orders of magnitude smaller than their digital simulations. In some application, like micro-robotics and embedded control, one might be willing to tolerate less accuracy and precision for the size and power benefits. One would not under any condition, however, tolerate significant behavioral mismatches between the differential equation and electrical circuit forms of the neural networks in question. In this paper, we will present a design for an analog neural computer that embodies the commonly used continuous time recurrent neural network. We will show that the computer possesses excellent behavioral congruence to the differential equation form even in the presence of significant practical compromises. We will also discuss the implications of this work for both practical Commercial, Off-The-Shelf (COTS) and Application-Specific Integrated Circuit (ASIC) devices. [ABSTRACT FROM AUTHOR]

Abstract: Many algorithms have been suggested for the shape-from-shading problem, and some years have passed since the publication of the survey paper by Zhang et al. [R. Zhang, P.-S. Tsai, J.E. Cryer, M. Shah, Shape from shading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence 21 (8) (1999) 690–706]. In this new survey paper, we try to update their presentation including some recent methods which seem to be particularly representative of three classes of methods: methods based on partial differential equations, methods using optimization and methods approximating the image irradiance equation. One of the goals of this paper is to set the comparison of these methods on a firm basis. To this end, we provide a brief description of each method, highlighting its basic assumptions and mathematical properties. Moreover, we propose some numerical benchmarks in order to compare the methods in terms of their efficiency and accuracy in the reconstruction of surfaces corresponding to synthetic, as well as to real images. [Copyright &y& Elsevier]

In this paper, we are concerned with two interesting problems in the dynamics of neural networks. What connection topology will prohibit chaotic behavior in a continuous time neural network (NN). To what extent is a continuous time neural network (NN) described by continuous ordinary differential equations simple enough yet still able to exhibit chaos? We study these problems in the context of the classical neural networks with three neurons, which can be described by three-dimensional autonomous ordinary differential equations. We first consider the case where there is no direct interconnection between the first neuron and the third neuron. We then discuss the case where each pair of neurons has a direct connection. We show that the existence of the directed loop in connection topology is necessary for chaos to occur. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative to partial differential equations (PDE5) for solving problems in computer vision based on evolutive heat transfer. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a purely mathematical process. Instead of using the PDE, we propose to use the global heat principle and to decompose it into basic laws. We show that some of these laws admit an exact global version since they arise from conservative principles. We also show that the assumptions made about the other basic laws can be made wisely, taking into account knowledge about the problem and the domain. The numerical scheme is derived in a straightforward way from the modeled problem, thus providing a physical explanation for each step in the solution. The advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it, allowing changing the application to a great number of problems. We apply the scheme to two applications: image denoising and inpainting which are modeled with heat transfer. For denoising, we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion. [ABSTRACT FROM AUTHOR]