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We develop a model for contagion risks and optimal security investment in a directed network of interconnected agents with heterogeneous degrees, loss functions and security profiles. Our model generalizes much of contagion models in the literature; in particular the independent cascade model and the linear threshold model. We state various limit theorems on the final size of infected agents in the case of random networks with given vertex degrees for finite and infinite variance degree distributions. The results allow us to derive a resilience condition of the network to the infection of a large group of agents and quantify how contagion amplifies small shocks to the network. We show that when the degree distribution has infinite variance and, highly correlated in- and out-degrees, then even when agents have high thresholds, a sub-linear fraction of initially infected agents is enough to trigger the infection of a positive fraction. We also show how these results are sensitive to vertex and edge percolation (immunization). We then study the asymptotic Nash equilibrium and socially optimal security investment. In the asymptotic limit, agents' risk depends on all other agents' investment through an aggregate quantity, that we call network vulnerability. The limit theorems allow us to capture the impact of one class of agents' decision on the overall network vulnerability. Based on our results, the vulnerability is semi-analytic allowing for a tractable Nash equilibrium. We give sufficient conditions for investment in equilibrium to be monotone in the network vulnerability. When investment is monotone, we show that the (asymptotic) Nash equilibrium is unique. In the particular example of two types core-periphery agents, we exhibit a strong effect of the cost heterogeneity and in particular non-monotonous investment as a function of costs.

Fear of infection will limit economic activity Widespread testing alone will not solve this problem Targeted testing in concert with targeted subsidies will b

Here, we study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton–Jacobi–Bellman equations with convex Hamiltonians in the torus. This large-time limit solves the corresponding stationary problem, sometimes called the ergodic problem. This problem, however, has multiple viscosity solutions and, thus, a key question is which of these solutions is selected by the limit. Here, we provide a representation for the viscosity solution to the Cauchy problem in terms of generalized holonomic measures. Then, we use this representation to characterize the large-time limit in terms of the initial data and generalized Mather measures. In addition, we establish various results on generalized Mather measures and duality theorems that are of independent interest.

We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit, solutions are ill-defined due to divergences in the sum over infinite trajectories in the spectrum of D2-D0-brane bound states. We explore various prescriptions to make the sum well-defined, show that one of them reproduces the existing solution in the literature, and identify an alternative solution which is better behaved in a certain limit. Furthermore, we show that a suitable asymptotic expansion of the $\tau$ function reproduces the genus expansion of the topological string partition function for any small crepant resolution. As a by-product, we conjecture new integral representations for the triple sine function, similar to Woronowicz' integral representation for Faddeev's quantum dilogarithm., Comment: 25+14 pages; added proof for integral representation of the double sine function and a similar conjecture for the triple sine; version accepted for publication in Annales Henri Poincar\'e

Organisms acquire and use information from their environment to guide their behaviour. However, it is unclear whether this information quantitatively limits their performance at behavioural tasks. Here we relate information to the ability of Escherichia coli to navigate up chemical gradients, the behaviour known as chemotaxis. First, we derive a theoretical limit on the speed with which cells climb gradients, given the rate at which they acquire information. Next, we measure cells’ gradient-climbing speeds and the rate of information acquisition by their chemotaxis signalling pathway. We find that E. coli cells make behavioural decisions with much less than the one bit required to determine whether they are swimming up the gradient. Some of this information is irrelevant to gradient climbing, and some is lost in communication to behaviour. Despite these limitations, E. coli cells climb gradients at speeds within a factor of two of the theoretical bound. Thus, information can limit the performance of an organism, and sensory–motor pathways may have evolved to efficiently use information acquired from the environment. Information theory sets an upper limit on the ability of bacteria to navigate up chemical gradients. Experiments reveal that cells do so at speeds within a factor of two of the limit, suggesting they are selected to efficiently use information.

Radial jet drilling (RJD) technology has been applied to enhance the recovery of difficult-to-produce reserves by multiple horizontal micro-holes. The micro-hole length drilled by high-pressure water jets is of vital importance for the oil and gas recovery effect and is usually tens of meters long for applications in maturing oil fields in China. The water jets are generated by multiple orifices nozzle generally. Many studies focused on improving the self-propelled force generated by water jets to increase the micro-hole length. However, there are few researches on improving the micro-hole extension capacity in terms of optimizing the flexible hose that acts as the drill pipe in conventional drilling technology. This paper firstly studied the relationship between the flexible hose length and the micro-hole extension limit according to the analytical model to calculate the micro-hole extension limit. Then, the method to optimize the flexible hose length and the flow rate was developed aiming to obtain maximum micro-hole extension limit. The results show that the micro-hole extension limit decreases logarithmically with the increase in the flexible hose length under the condition that the takes the maximum value. The optimization model is applied by a field case and is proved to be effective to increase the micro-hole extension limit. This study is significant to improve the micro-hole extension capacity. Moreover, it provides a reference for the design of the hydraulics and selection of flexible hose for the RJD.

In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates near some curve evolving according to the binormal curvature flow, and conversely, that a curve moving this way can be realized in a suitable sense by some solution to the dispersive Ginzburg-Landau equation. Some partial results are known with rather strong symmetry assumptions. Our main theorems here provide affirmative answer to both conjectures under certain small curvature assumption. The results are valid for small but fixed material parameter in the equation, in contrast to the general practice to take this parameter to its zero limit. The advantage is that we can retain precise description of the vortex filament structure. The results hold on a long but finite time interval, depending on the curvature assumption., Comment: 26 pp

Naive Bayes (NB) was once awarded as one of the top 10 data mining algorithms, but the unreliable probability estimation and the unrealistic attribute conditional independence assumption limit its performance. To alleviate these two primary weaknesses simultaneously, instance and attribute weighting has been recently proposed. However, the existing approach learns instance and attribute weights separately, without considering their interactions at all, which restricts the performance of the learned model. Therefore, in this study, we propose a novel approach to learning instance and attribute weights collaboratively and call the resulting model collaboratively weighted naive Bayes (CWNB). In CWNB, we first learn the weight of each training instance iteratively based on its estimated posterior probability loss to make the prior and conditional probabilities more accurate, then we incorporate these two probabilities into the conditional log-likelihood (CLL) formula, and at last we search the optimal weight of each attribute by maximizing the CLL. Extensive experimental results show that CWNB significantly outperforms the standard NB and all the other existing state-of-the-art competitors.

Unsupervised subsequence outlier detection on multivariate time series (MTS) is a valuable problem in practice that can observably save the cost of labeling and provide interpretability in real applications. For the task, most of the classic methods are under two strong assumptions: (i) stationary MTS. it may have difficulty coping with the phenomenon of time drift. (ii) Attribute-level IIDness (independent and identically distributed), it may ignore the relationship between attribute when measuring the similarity between multivariate subsequences. The above assumptions limit the availability of existing methods in real scenarios. To address this issue, this paper introduces a novel coupled generalized local outlier detection model for MTS, which extends the traditional generalized local outlier detection model to cope with subsequence outlier detection tasks by incorporating a novel Non-IID similarity metric. Specifically, the proposed method mainly includes three aspects: (i) represents the MTS relationship in symbolic space which provides a lower complexity and satisfactory sensitivity. (ii) Proposes a Non-IID coupled similarity metric (TSDis) which considers the intrinsic intra-attribute and inter-attribute coupling between segments. (iii) Extends the traditional generalized local outlier detection model to handle subsequence outlier detection tasks by embedding Non-IID coupled similarity metric. Experimental results show the proposed method can utilize the potential characteristics of MTS effectively and stably. Meanwhile, it detects outliers more accurately than baseline approaches on 12 time-series datasets.

We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical assumptions, discuss the verification of these assumptions and illustrate our results by different examples (subshifts of finite type, Young towers, Sinai billiards, random matrix products), including situations of unbounded observables with integrability order arbitrarily close to the optimal moment condition required in the i.i.d. setting., Comment: 66 pages, 2 figures

In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field fulfills a Navier-slip condition, while the magnetic field satisfies the insulating condition. It is shown that the initial boundary value problem has a global weak solution for a general smooth domain. More importantly, for a flat domain, we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable.

When studying the Influence Maximization (IM) problem in social networks, it is found that the initial seed nodes selected by some heuristic algorithms have the characteristics of aggregation. This situation is called the rich club phenomenon of seed sets. Once the seed node is over-aggregated, it will limit the spread of influence. Therefore, analyzing the rich-club phenomenon is necessary for solving the IM problem. The paper proposes the rich club coefficient and reactivation rate to quantitatively analyze this phenomenon. The analysis mainly focuses on the relationship between the hop distance and the propagation probability. In addition, the relationship between the rich club phenomenon and the IM problem is also an aspect of concern. When dealing with the main aspects, a key problem needs to be solved, which is that the optimal range of hop is different under different propagation probabilities. To solve this problem, the Multi Hop Remove (MHR) algorithm is proposed, which is based on the independent cascade model. By the MHR algorithm, the hop range is determined under different propagation probabilities. According to our experimental results, the more serious the rich club phenomenon accumulates, the smaller the influence spread. To reduce the obstruction of this phenomenon, the multi-hop selection of seed nodes is a superior solution.

We investigate strong stability preserving (SSP) implicit-explicit (IMEX) methods for partitioned systems of differential equations with stiff and nonstiff subsystems. Conditions for order p and stage order $$q=p$$ q = p are derived, and characterization of SSP IMEX methods is provided following the recent work by Spijker. Stability properties of these methods with respect to the decoupled linear system with a complex parameter, and a coupled linear system with real parameters are also investigated. Examples of methods up to the order $$p=4$$ p = 4 and stage order $$q=p$$ q = p are provided. Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration, and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.

The logic $${\mathbb{L}}_\theta ^1$$ was introduced in [She12]; it is the maximal logic below $${{\mathbb{L}}_{\theta, \theta}}$$ in which a well ordering is not definable. We investigate it for θ a compact cardinal. We prove that it satisfies several parallels of classical theorems on first order logic, strengthening the thesis that it is a natural logic. In particular, two models are $${\mathbb{L}}_\theta ^1$$ -equivalent iff for some ω-sequence of θ-complete ultrafilters, the iterated ultrapowers by it of those two models are isomorphic. Also for strong limit λ>θ of cofinality $${\aleph _0}$$ , every complete $${\mathbb{L}}_\theta ^1$$ -theory has a so-called special model of cardinality λ, a parallel of saturated. For first order theory T and singular strong limit cardinal λ, T has a so-called special model of cardinality λ. Using “special” in our context is justified by: it is unique (fixing T and λ), all reducts of a special model are special too, so we have another proof of interpolation in this case.

Based on the first-order second-moment method, a comparative study on seismic fragility analysis with consideration of modeling uncertainty is carried out for a 12-story reinforced concrete frame structure under excitation with far-field and pulse-like near-field ground motions by using the multiple stripes analysis method. The sensitivity of the median fragility capacity of the building to fourteen parameters in the cases of three limit states (i.e., immediate occupancy, life safety, and collapse prevention) is analysed, and the effect of the selection of ground motion intensity measures on the determination of modeling uncertainty is investigated. Finally, the annual probabilities of exceeding each limit state with different confidence levels are calculated, and two methods, the mean estimates approach and the confidence interval method, are used to incorporate uncertainties. The results show that the characteristics of ground motions affect the sensitivity of the median capacity to the disturbance of structural parameters. The modeling uncertainty estimated in the near-field records is meaningfully less than that in the far-field records. Judging from this limited case study, the modeling uncertainty estimated may be underestimated by using an inefficient IM. The influence of the modeling uncertainty in the fragility analysis for each limit state cannot be ignored when using the confidence interval method.

At present, the deep learning super-resolution (SR) method has achieved excellent results, but it also faces problems such as large models, high computational cost, a large amounts of training data, and poor interpretability. However, traditional machine learning-based methods still have room for improvement in feature extraction and model structure. This paper constructs a gradient embedding cascade forest structure on the basis of random forest and proposes a limit gradient embedding cascaded forest SR (LGECFSR) model. In feature construction, we not only adopt the first-order gradient, the second-order gradient, and other features of the image but also fuse the information of the original LR image. In addition, image blocks of different sizes are used for training, which increases the model’s generalization ability. Compared with the state-of-the-art machine learning-based methods, our method achieves the best performance and the second-best computational speed. In addition, compared with some deep learning-based methods, our model has a similar reconstruction effect and the best computational speed. In detail, for some reconstruction tasks, the Multi-Adds of LGECFSR is one-tenth to one-4000th of that of some current models. However, the SR performance of LGECFSR is the same or slightly better than that of some current classical algorithms.

Tailor rolled blank (TRB) with graded thickness has shown great potential in the automobile field. Using traditional forming limit diagrams (FLDs) to evaluate TRB formability is challenging due to thickness variations. In this paper, a 3D forming limit surface (FLS) considering the influence of thickness was obtained. A numerical model was developed to predict final strains. Moreover, a forming margin was denoted and calculated to generate the forming limit margin field graph for quantitative evaluation of the TRB formability. Results showed that as the punch travel increased, the forming margin value decreased. As the travel changed from 35.2 mm to 37.4 mm, the corresponding forming margin value changed from 0.002 to −0.024. The formability declined, and the specimen eventually cracked on the thinner side. Besides, the deformation and strain paths predicted by simulation agreed well with those measured from formed part, which indicated that the final strains used in formability evaluation were reliable. The method was suitable for quantitative evaluation of the formability and predicting the cracking position in TRB forming.

The fundamental mission of a distribution network is to satisfy the customer demand by providing sufficient delivery capacity. However, the capacity of a distribution network is practically stochastic because of unexpected events, and moreover, the commodities may rot or be spoilt during delivery owing to inclement weather, traffic accidents, collisions, and so on, such that the intact commodity flow may not meet market demand. This paper focuses on the reliability of a multi-state distribution network (MSDN) with cost and spoilage characteristics, defined as the probability that the MSDN is able to distribute a sufficient quantity of goods to meet the market demand under delivery spoilage and budget limit considerations. A specific spoilage rate associated with each route is adopted to characterize the perishability of commodity flows, and the critical routes whose spoilage rate change has the biggest impact on network reliability are identified with the use of sensitivity analysis method. Apart from delivery cost, the cost involved with the disposal of spoilt goods is also incorporated into the reliability indicator. A minimal paths based algorithm is presented to calculate network reliability, together with an example to illustrate the procedure. A real fruit distribution network is accordingly discussed to demonstrate the utility of the algorithm and the managerial implication of network reliability.

We shall prove the validity of the Prandtl boundary layer expansion for the two-dimensional Navier-Stokes flows around the Rayleigh boundary layer, which is the first result verifying the stability of the formation of the boundary layer in the inviscid limit with respect to the perturbations in the Gevrey $$\frac{3}{2}$$ class.

The (2 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model. By using the long wave limit method and confining the conjugation conditions on the interrelated solitons, the general M-lump, high-order breather, and localized interaction hybrid solutions are investigated, respectively. Then we implement the numerical simulations to research their dynamical behaviors, which indicate that different parameters have very different dynamic properties and propagation modes of the waves. The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.

This study aims to propose state-of-the-art techniques in predicting and controlling slope stability in open-pit mines based on limit equilibrium analysis, artificial neural networks, and optimization algorithms. Accordingly, the simplified Bishop method was used to analyze the slope stability of an open-pit coal mine through the limit equilibrium analysis method. Various rock mass properties and the geometrical parameters of the slopes were considered, such as bench height, slope angle, unit weight, cohesion, and friction angle. Finally, 495 cases were analyzed to compute the factor of safety (FOS). Subsequently, the radial basis function neural network (RBFNN) model was applied to predict FOS. In order to optimize the RBFNN model, the brainstorm optimization (BSO) algorithm was applied to train the RBFNN model, named as BSO-RBFNN model. The genetic algorithm (GA)-RBFNN, RBFNN (without optimization), and multiple layers perceptron (MLP) neural network were also developed to predict FOS and compared with the proposed BSO-RBFNN model as part of the study. The results revealed that the optimization of the BSO algorithm and RBFNN model provided a state-of-the-art technique (i.e., BSO-RBFNN) for predicting and controlling slope stability with high accuracy (i.e., mean absolute error (MAE) = 0.047, root-mean-squared error (RMSE) = 0.057, determination coefficient (R2) = 0.929, variance accounted for (VAF) = 92.948), and reliability (i.e., absolute error of 5.89% for 80% of cases in practice). Comparisons also indicated that the proposed BSO-RBFNN model is the most dominant model for predicting slope stability in this study (i.e., MAEGA-RBFNN = 0.048, RMSEGA-RBFNN = 0.060, R2GA-RBFNN = 0.927, VAFGA-RBFNN = 92.534; MAERBFNN = 0.064, RMSERBFNN = 0.081, R2RBFNN = 0.925, VAFRBFNN = 89.189; MAEMLP = 0.065, RMSEMLP = 0.081, R2MLP = 0.873, VAFMLP = 85.724). Furthermore, the slope angle and bench height should be taken into account to control slope stability in practical engineering based on the proposed BSO-RBFNN model.

The paper deals with the limit behavior of a compound Poisson process with switching between a finite number of sequences of i.i.d. random variables. The switching is provided by Bernoulli’s random variables. Under suitable normalization, the limit process is a Brownian motion with switching variance.

We introduce notions of generalized $$\varepsilon $$ -quasi solutions to approximate set type solutions of set optimization problems. We study their properties, consistency and limit behavior as approximations to efficient and strict weak efficient solutions. Moreover, we prove an existence result for such solutions and a bound for their asymptotic cone. Finally, we obtain optimality conditions for them.

We prove a limit theorem on the convergence of mathematical expectations of functionals of sums of independent random variables to the Cauchy problem solution for the nonstationary Schr¨odinger equation with a symmetric fractional derivative operator of order $$ \upalpha\ \upepsilon \bigcup_{m=3}^{\infty}\left(m-1,m\right) $$ in the righthand side.

The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a job is determined by the processing time of its first operation. At any point in time, the total consumption of this additional resource cannot exceed a given limit (referred to as the storage capacity). The goal is to minimise the makespan, i.e. to minimise the time needed for the completion of all jobs. This problem is NP-hard in the strong sense. The paper analyses how the parameter - a lower bound on the storage capacity specified in terms of the processing times, affects the computational complexity.

We present a unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Polya and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemannian manifolds and derive the well-known Taikov and Hardy-Littlewood-Polya inequalities for functions defined on the d-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of another class. In addition, we establish sharp Solyar type inequalities for unbounded closed operators with closed range.

In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable $2D$ Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green's function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries., 69 pages. Minor revisions. Version accepted by Annales Henri Poincar\'e. arXiv admin note: substantial text overlap with arXiv:2006.04458

We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

Predictions of future water resources are essential for the strategic plans of any country especially in arid regions such as Saudi Arabia (SA). This paper presents a modeling study of the temporal annual rainfall variability over SA, evaluating the best model for future rainfall predictions and mapping spatiotemporal rainfall over SA. Common time series models of orders p and q such as autoregressive, AR(p), moving average, MA(q), and the combined autoregressive-moving average, ARMA(p,q), models are utilized. The models are applied to 28 metrological stations distributed over SA. Spatiotemporal statistical analysis of rainfall data is performed over a period between 1970 and 2012. The minimum and maximum fitted parameters of the models are φ1 = − 0.55, 0.46 for ARMA (1,0), θ1 = − 0.66, 0.17 for ARMA (0,1) and φ1 = − 0.84, 0.94, θ1 = − 0.87, 0.78 for ARMA (1,1), respectively. It has been shown that ARMA (1,0) is the best to model the temporal variability based on the Akaike information criterion (AIC), the correlation coefficient (R), and the root mean square error (RMSE). The Monte Carlo method is used to make future predictions (100 realizations) with the confidence levels (CIs) based on ARMA (1,0). Spatial distribution of the ensemble predictions and their CIs are presented graphically at the upper limit of 95%, 97.5%, and 99% and the lower limit of 5%, 2.5%, and 1% confidence, respectively, for the year 2030 to help decision-makers for future water resources planning of the country. Abha city has the highest annual rainfall prediction in 2030 (221 mm) with upper confidences (436, 533, and 643 mm) for 95%, 97.5%, and 99%, respectively. The prediction results indicate that the high mountainous areas (Asir and Taif) are expected to have more rainfall in the future than the rest of the regions in SA. The use of non-traditional water resources is the solution to future challenges.

The ‘limits of markets’ debate broadly concerns the question of when it is (im)permissible to have a market in some good. Markets can be of tremendous benefit to society, but many have felt that certain goods should not be for sale (e.g., sex, kidneys, bombs). Their sale is argued to be corrupting, exploitative, or to express a form of disrespect. In Markets without Limits, Jason Brennan and Peter Jaworski have recently argued to the contrary: For any good, as long as it is permissible to give it for free, then it is permissible to give it for money. Their thesis has led to a number of engaging objections, and I leverage recent work on the nature of feasibility within political philosophy to offer a new challenge.I argue that feasibility offers a constraint on which markets can be permissibly implemented. Though it may be possible to create a morally acceptable version of an otherwise repugnant market, some of these markets may be infeasible, and so we are not permitted to implement them. After laying out this challenge, I consider several replies. They concern the relevance of feasibility, and whether any markets really are infeasible. This provides an opportunity to explore the dangers of pursuing the infeasible and with markets generally. I conclude by considering what might lead us to pursue these markets despite their infeasibility, or how knowledge of infeasibility may prove useful regardless.

We study the homogenization of the evolutionary compressible Navier–Stokes–Fourier system in a bounded three-dimensional domain perforated with a large number of very tiny holes. We show that under suitable assumptions on the smallness and distribution of the holes the limit system remains the same in the unperforated domain. One of the main novelty in the paper consists in the treatment of the entropy inequality and thus the paper also improves the related result in the steady case from Lu and Pokorný (J Differ Equ 278:463–492, 2021).

This paper studies the stabilizability and stabilization of continuous-time systems in the presence of stochastic multiplicative uncertainties. The authors consider multi-input, multi-output (MIMO) linear time-invariant systems subject to multiple static, structured stochastic uncertainties, and seek to derive fundamental conditions to ensure that a system can be stabilized under a mean-square criterion. In the stochastic control framework, this problem can be considered as one of optimal control under state- or input-dependent random noises, while in the networked control setting, a problem of networked feedback stabilization over lossy communication channels. The authors adopt a mean-square small gain analysis approach, and obtain necessary and sufficient conditions for a system to be mean-square stabilizable via output feedback. For single-input, single-output (SISO) systems, the condition provides an analytical bound, demonstrating explicitly how plant unstable poles, nonminimum phase zeros, and time delay may impose a limit on the uncertainty variance required for mean-square stabilization. For MIMO minimum phase systems with possible delays, the condition amounts to solving a generalized eigenvalue problem, readily solvable using linear matrix inequality optimization techniques.

We analyze the stability of elastic systems composed of the shells of revolution with variable curvature and complex structures in the field of conservative axisymmetric loads of different nature. Within the framework of classical and refined theories of shells, we determine the limit and bifurcation critical values of the acting loads based on the geometrically nonlinear statement of the problem and a criterion of dynamic stability. To solve the corresponding nonlinear and eigenvalue problems, we propose to use a numerical-analytic approach based on their rational reduction to one-dimensional linear boundaryvalue problems in the meridional coordinate and their numerical solution by the discrete-orthogonalization method. We present test examples that confirm the applicability of the proposed procedure to the analyzed class of problems. The limit and bifurcation values of the critical loads in the shell system are analyzed depending on its geometric parameters.

In this work we show how it is possible to derive a new set of nudging equations, a tool still used in many data assimilation problems, starting from statistical physics considerations and availing ourselves of stochastic parameterizations that take into account unresolved interactions. The fluctuations used are thought of as Gaussian white noise with zero mean. The derivation is based on the conditioned Langevin dynamics technique. Exploiting the relation between the Fokker–Planck and the Langevin equations, the nudging equations are derived for a maximally observed system that converges towards the observations in finite time. The new nudging term found is the analog of the so called quantum potential of the Bohmian mechanics. In order to make the new nudging equations feasible for practical computations, two approximations are developed and used as bases from which extending this tool to non-perfectly observed systems. By means of a physical framework, in the zero noise limit, all the physical nudging parameters are fixed by the model under study and there is no need to tune other free ad-hoc variables. The limit of zero noise shows that also for the classical nudging equations it is necessary to use dynamical information to correct the typical relaxation term. A comparison of these approximations with a 3DVar scheme, that use a conjugate gradient minimization, is then shown in a series of four twin experiments that exploit low order chaotic models.

A partial-limit method is developed to understand solutions related to real eigenvalues for the Fokas–Lenells equation. By applying a partial-limit procedure to soliton solutions of the Fokas–Lenells equation, new multiple-pole solutions related to real repeated eigenvalues are obtained. For the envelop $$|u|^2$$ , the simplest solution corresponds to a real double eigenvalue, showing a solitary wave with algebraic decay. Two such solitons allow elastic scattering but asymptotically with zero phase shift. Single eigenvalue with higher multiplicity gives rise to rational solutions which contain an intrinsic parameter, live on a zero background, and have slowly changing amplitudes. The partial-limit procedure may be extended to other integrable systems and generate new solutions.

This study aims to show that the low bid price survey standard has lower limit price characteristics and analyzes the behavior of firms in the public procurement market where the lower price limit is set. This study uses regression analysis to investigate the effects of exogenously determined low-price survey standards and predetermined prices on the winning bid ratio, the number of participants, the participants’ bid ratio, the difference between the second-place price and the winning bid, the second bid, and the single bidder’s bid. The results show that the winning bid ratio increased with a rise in the low-price survey standard, thereby indicating that the low-price survey standard has the characteristics of a lower limit price. The results also suggest that the low-price survey standard causes oversupply, which encourages firms to carefully set prices higher than the lower price limit, and intensify competition at levels higher than the lower limit price.

Structural safety evaluation is a critical issue in the realm of civil engineering. It involves factors such as uncertainties, external loads, and structural damage after long-term service. Presently, real-time safety evaluation of structural resistance remains challenging for real-world structures. This study proposes a resistance updating model for reinforced concrete beams based on Bayesian inference. The measured static loads of six experimental beams were taken as the proof loads for assessing real-time safety, and a stiffness degradation coefficient (SDC) was developed to embody resistance reduction. The SDC was continuously updated based on the deflection monitoring data of the beams under the proof loads. Specifically, the beam resistances were defined as the random distributions, and their initial distributions were calculated according to the material properties of the beams. Then, the corresponding SDCs of each proof load were estimated. Based on the initial resistance distributions and the real-time SDCs, the iterative updating of the resistance distributions was carried out using Bayesian inference. Subsequently, the future reliability indices of these beams were inferred using the JC method, which utilized the updated resistance distributions and the assumed future load distributions. Finally, a reliability index evolution model was established to evaluate the safety of the experimental beams. The analysis results showed that the proposed method can effectively estimate the resistance to provide an upper limit of future loading. The proposed method is sensitive to the proposed SDC but insensitive to the initial distributions of the resistance.

This paper, based on an extended bi-directional evolutionary structural optimization method, proposes a design approach to minimize the maximum von Mises stress of continuum structures subject to both material use and casting constraints. The stress singularity phenomenon is avoided naturally by the technique of discrete variable of the bi-directional evolutionary structural optimization method. The maximum von Mises stress is approximated by the global p-norm stress aggregation approach, and the adjoint method is adopted to derive the sensitivity numbers. Both sensitivity numbers and topological variables are filtered to overcome the highly nonlinear stress behavior and stabilize the optimization procedure. A series of comparison studies have been conducted to validate the effectiveness and practicability of the method on several benchmark design problems. Both two and four parting directions are investigated in this paper. The examples exhibit significant difference in the final topologies for designs with casting constraints. The casting constraints limit the range of solutions to topology optimization problems. Designs with casting constraints seek to satisfy manufacturability of the optimized structure at the expense of structural strength performance. The study demonstrates the importance of strength criteria for the design of continuum structures under casting constraints.

Analytical study of ball vibration absorber behavior is presented in the paper. The dynamics of trajectories of a heavy ball moving without slipping inside a spherical cavity are analyzed. Following our previous work, where a similar system was investigated through various numerical simulations, research of the dynamic properties of a sphere moving in a spherical cavity was carried out by methods of analytical dynamics. The strategy of analytical investigation enabled definition of a set of special and limit cases which designate individual domains of regular trajectories. In order to avoid any mutual interaction between the domains along a particular trajectory movement, energy dissipation at the contact of the ball and the cavity has been ignored, as has any kinematic excitation due to cavity movement. A governing system was derived using the Lagrangian formalism and complemented by appropriate non-holonomic constraints of the Pfaff type. The three first integrals are defined, enabling the evaluation of trajectory types with respect to system parameters, the initial amount of total energy, the angular momentum of the ball and its initial spin velocity. The neighborhoods of the limit trajectories and their dynamic stability are assessed. Limit and transition special cases are investigated along with their individual elements. The analytical means of investigation enabled the performance of broad parametric studies. Good agreement was found when comparing the results achieved by the analytical procedures in this paper with those obtained by means of numerical simulations, as they followed from the Lagrangian approach and the Appell-Gibbs function presented in previous papers.

In a fully mechanized top coal caving mining process, the mechanical properties of the top coal deteriorate constantly, and the stability of the support is determined by the boundary position of the top coal entering the limit equilibrium state. Top coal flaking occurs more easily along the advancing direction owing to an increase in the distance of the boundary from the wall. Moreover, the strength of the coal seam is an important factor that determines the boundary position. The equation of the top coal limit equilibrium zone boundary, used in fully mechanized top coal caving mining, was determined based on the limit equilibrium theory, continuum damage mechanics, and the Hoek–Brown rock empirical strength criterion. Using the RFPA3D and UDEC numerical analysis methods, the effect of top coal strength on the mechanical behavior during the mining process was determined; and the space–time relationship between the top coal deformation failure, damage evolution, and boundary of the limit equilibrium zone was established. The results revealed that when the coal mass entered the limit equilibrium zone, accelerated crack development, accelerated damage, and axial unloading occurred. Moreover, an increase in the coal seam strength caused the boundary of the top coal limit equilibrium zone to be closer to the wall. By comparing the numerical results with the theoretical results, the overall trend was found to be consistent, allowing the verification of the rationality and reliability of the determination equation of the boundary position of the limit equilibrium zone.

We consider a nonlinear nonautonomous system of two ordinary differential equations with a stable fixed point and assume that the non-Hamiltonian part of the system tends to zero at infinity. We examine the asymptotic behavior of a two-parameter family of solutions that start from a neighborhood of the stable equilibrium. The proposed construction of asymptotic solutions is based on the averaging method and the transition in the original system to new dependent variables, one of which is the angle of the limit Hamiltonian system, and the other is the Lyapunov function for the complete system.

To reduce the adverse vibrations of buildings, tuned mass dampers (TMDs), which are the most representative passive control devices, have been widely used and studied in aerospace, machinery, civil engineering, and other fields for many years. Most scholars used to treat the TMD as a linear damper, but they show some nonlinear characteristics owing to the use of limit devices and large displacements. It is necessary to consider the nonlinear coefficient of the TMD when designing its parameters. In this study, the mass ratio of the TMD was optimized with considering the nonlinear coefficient of the TMD. The complex variable average method and multiscale method were used for analysis. A mass ratio interval was found on the “ε- N2” curve in which modulation response can occur, and then an analytical method for obtaining the optimal mass ratio of TMD was derived based on this phenomenon. The numerical results showed that taking the midpoint of this mass ratio interval as the optimal mass ratio can yield a better damping effect and robustness than using the traditional linear design method.

The process of press hardening is gaining importance in view of the increasing demand for weight reduction combined with higher crash safety in cars. An alternative to the established manganese-boron steel 22MnB5 is hot-formed martensitic chromium steels such as AISI 420C. Strengths of 1850 MPa and elongations of 12% are possible, exceeding those of 22MnB5. In industrial manufacturing, FE-simulation is commonly used in order to design car body parts cost-efficiently. Therefore, the characterization and the modeling of AISI 420C regarding flow stress, phase transformations as well as failure behavior are presented in this paper. Temperature-depended flow curves are determined, showing the low flow stress and hardening behavior at temperatures around 1000 °C. Cooling experiments are carried out, and a continuous cooling diagram is generated. Observed phases are martensite and retained austenite for industrial relevant cooling rates above 10 K/s. In addition, tests to investigate temperature-dependent forming limit curves are performed. As expected, the highest forming limit is reached at 1050 °C and decreases with falling temperature. Finally, a simulation model of a press-hardening process chain is set up based on the material behavior characterized earlier and compared to experimental values. The forming force, phase transformation and forming limit could be calculated with good agreement to the experiment.

There has been much research about regularizing optimal portfolio selections through $$\ell _1$$ norm and/or $$\ell _2$$ -norm squared. The common consensuses are (i) $$\ell _1$$ leads to sparse portfolios and there exists a theoretical bound that limits extreme shorting of assets; (ii) $$\ell _2$$ (norm-squared) stabilizes the computation by improving the condition number of the problem resulting in strong out-of-sample performance; and (iii) there exist efficient numerical algorithms for those regularized portfolios with closed-form solutions each step. When combined such as in the well-known elastic net regularization, theoretical bounds are difficult to derive so as to limit extreme shorting of assets. In this paper, we propose a minimum variance portfolio with the regularization of $$\ell _1$$ and $$\ell _2$$ norm combined (namely $$\ell _{1, 2}$$ -norm). The new regularization enjoys the best of the two regularizations of $$\ell _1$$ norm and $$\ell _2$$ -norm squared. In particular, we derive a theoretical bound that limits short-sells and develop a closed-form formula for the proximal term of the $$\ell _{1,2}$$ norm. A fast proximal augmented Lagrange method is applied to solve the $$\ell _{1,2}$$ -norm regularized problem. Extensive numerical experiments confirm that the new model often results in high Sharpe ratio, low turnover and small amount of short sells when compared with several existing models on six datasets.

The deterministic rate equation has been considered as an approximate description of the dynamics of the gene regulatory network, derived in the limit of vanishing stochastic fluctuations. When stochastic fluctuations are introduced, the stable fixed points of the deterministic equation usually turn into local maxima of the stationary distribution. Here, I consider a simple genetic regulatory network with a positive feedback and a cooperative binding, where the stationary distribution does not have a local minimum at a stable fixed point. I show that a transient peak appears at the stable fixed point instead, whose life-time grows exponentially as the stochastic fluctuation decreases. The result shows that the order of the limits is important for retrieving the deterministic dynamics.

This paper presents the probabilistic seismic demand and fragility analyses of a novel mid-rise large-span cassette structure. A newly designed nine-storey office building in Hunan, China, is selected, and its two different design schemes, namely, a traditional frame structure and a novel cassette structure, are examined using numerical models established on the basis of a shake table test. Based on probabilistic seismic theory, the appropriate intensity measures are firstly studied based on a set of 110 seismic records; and PGV and GeoSaavg, which consider the 3D characteristics of the structure, are selected. In addition, the uncertainty of earthquakes, including spectral characteristics, fault distance and input direction, are considered, and 25 seismic records recommended by the Federal Emergency Management Agency are selected. An incident angle interval of 22.5° is selected to consider the uncertainty in the input directions of real earthquakes. Incremental dynamic analyses are conducted, and the structural responses in every individual input direction as well as in all the directions are studied. Finally, probabilistic seismic fragility analysis is conducted, and the probabilities of exceeding different limit states of the frame and cassette structures is presented. Amongst the studies, the novel cassette design can not only achieve much larger span, but also shows a better, more stable seismic performance. Therefore, the cassette structure may be a better alternative in seismic design.

Generalized Kramers–Kronig (K–K) type dispersion relations and sum rules are derived in the static limit for the moments of the degenerate four wave mixing susceptibility. The degenerate nonlinear susceptibility is different from a typical use of the conventional K–K dispersion relations, which assume absence of complex poles of a function in the upper half of complex frequency plane, whereas degenerate susceptibility has simultaneous poles in both half planes. In the derivation of the generalized K–K relations the poles and their order are taken into account by utilization of the theorem of residues. The conventional K–K relations can be used to estimate the real and imaginary parts of the second and higher powers of the susceptibility as the effect of the poles is reduced due to a faster convergence of the dispersion relations. The present theory is directly applicable to higher order susceptibilities and can be used in testing of theoretical models describing the degenerate four wave mixing susceptibility in nonlinear optical and terahertz spectroscopy.