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Tuft disentanglement involves the principal actions of opening and carding, which are essential processing in textile technology. In this article, tuft disentanglement is modeled as fiber withdrawal considering the fiber interactions within the tuft. Based on the reasonable tuft model, the kinematic constraints were constructed in the disentanglement considering the carding essence and fiber interactions. Combined with the dynamic equation, the state of the fibers can be solved as a linear complementarity problem due to the complementarity in the fiber interactions. The withdrawal forces verified the simulations, which capture the qualitative features of experiments. Also, the effect of the withdrawal parameters on disentanglement was studied. The simulation results showed that the withdrawal forces increased with increasing withdrawal velocities and decreasing gauge lengths. The simulation results are consistent with the experiments. The proposed computational framework can be extended for predicting the mechanical behaviors of other random fibrous materials involving fiber interactions. [ABSTRACT FROM AUTHOR]

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study. [ABSTRACT FROM AUTHOR]

Vietnam's agricultural exports to China have remained strong, with the country maintaining its position as the top destination for Agri-products. This article primarily utilizes the Revealed Comparative Advantage (RCA) Index, and Trade Complementarity (TC) index to examine the trade comparative advantage, and the complementary of twenty major agricultural products between China and Vietnam from 2012 to 2021. The study results showed that Vietnam and China frequently exchange agricultural products. Vietnam has more stronger competitiveness than China in terms of agricultural products. China's exports to Vietnam were highly complementary to Vietnam's imports in category 0 whiles Vietnam's exports to China showed strong complementarity with China's imports in category 2. This paper analyzes the complementarity and comparative advantages of agricultural trade between China and Vietnam, and proposes informed suggestions for policy-making to promote agricultural trade between the countries. The proposed suggestions aim to expand agricultural trade between the two countries, reduce the trade imbalance, and achieve mutual benefit and win-win results. [ABSTRACT FROM AUTHOR]

We evaluate the temporal complementarity in daily averages between wind and solar power potential in Chile using Spearman's correlation coefficient. We used hourly wind speed and solar radiation data for 176 geographic points from 2004 to 2016. The results allow us to identify four zones: Zone A1 on the coast and in the valleys in the north of Chile between latitudes 18° S and 36° S, with moderate positive correlation; Zone A2 in the north Andes between latitudes 25° S and 33° S, with weak negative correlation; Zone B in the center-south part of the country between latitudes 36° S and 51° S with moderate negative correlation; and Zone C in the south, between latitudes 51° S and 55° S with null or weak positive correlation. On the one hand, the interannual analysis shows that Zone A1 keeps uniform correlation values with negative asymmetry, i.e., higher correlation values. On the other hand, there is positive asymmetry in most of the years in Zone A2, i.e., lower (or negative) values of correlation. Zone B shows an interannual oscillation of the median correlation, while Zone C shows a larger dispersion in the interannual results. Significance analysis shows that 163 out of the 176 points are statistically significant, while Zones A1, A2, and B have significant correlations, with Zone C being marginally significant. The results obtained are relevant information for further studies on the location of hybrid generation facilities. We expect our methodology to be instrumental in Chile's energetic transition to a 100% renewable generation matrix. [ABSTRACT FROM AUTHOR]

Open Source Software (OSS) has become an increasingly important knowledge asset in modern economies. However, the economic impact of OSS on countries' GDP is ambivalent due to its public good character. Using a cross-country panel from 2000 to 2018, including 25 of the largest EU countries plus the USA, Japan, Korea, Canada, China, Norway, and Switzerland, matching OSS commits to GitHub to macroeconomic data provided by the OECD, our results confirm the dual nature of OSS. On the one hand, the open-access character creates great learning potential by providing a commonly accessible productive resource for all countries. On the other hand, it creates outward-directed spillovers associated with own OSS contributions. Accordingly, on average, we find that countries experience an increase in GDP when the world stock of OSS grows. However, smaller countries experience a decline in GDP resulting from their own contributions due to knowledge spillovers. The net effect is nonetheless positive. If no country contributed to OSS development, GDP for the average country would be 2.2% lower in the long run. Moreover, the losses associated with unintended spillovers are lower for countries with a higher R&D and patenting intensity. Based on our findings, we derive implications for policies and regulations concerning OSS. [ABSTRACT FROM AUTHOR]

In this paper, the simplified modulus-based matrix splitting iteration method was extended to solve the nonlinear complementarity problem, and the convergence conditions were presented from the spectral radius and the matrix norm. Then, for the special cases of this method, we provided some concrete convergence conditions as well as the quasi-optimal parameter matrix. Moreover, some numerical examples were illustrated to show the validity of the convergence results. [ABSTRACT FROM AUTHOR]

Restoration projects are increasingly widespread and many promote habitat succession and the diversity and abundance of faunal communities. These positive effects on biodiversity and abundance may extend to enhancing the ecological functioning and resilience of previously degraded ecosystems, but this is rarely quantified. This study surveyed a 200‐ha restoring coastal wetland and three control wetlands in the Maroochy River, eastern Australia to compare the effects of wetland restoration on the consumption of carrion and the biodiversity, abundance, and functional diversity of functionally important fish and crustaceans. Carrion consumption by fish and crustaceans was measured every 6 months from spring 2017 until spring 2021 for nine events using a combination of baited cameras and scavenging assays. We found restoration improved rates of carrion consumption and the biodiversity, functional diversity, and abundance of scavenger species. Despite positive effects on the diversity of scavengers and carrion consumption, the abundance of two species, longfin eels (Anguilla reinhardtii) and mud crabs (Scylla serrata), was the most important predictors of carrion consumption rates. The spatial distribution of carrion consumption was concentrated in areas with high saltmarsh extent, moderate to high mangrove extent, and high salinity, which also resembled the distribution of both longfin eels and mud crabs. We show that restoration can promote the rates of key ecological functions but that increases to functions are likely to be characterized by low functional redundancy and greater complementarity. Therefore, maintaining or increasing the abundance of functionally important species should become a key objective in future restoration projects. [ABSTRACT FROM AUTHOR]

As a natural extension of the tensor complementarity problem, the vertical tensor complementarity problem VTCP has important research value. In this paper, we get some properties of the solution of the VTCP. Furthermore, we focus on investigating the global error bound for the VTCP with the type VP tensor set. We define two positively homogeneous operators by the type VP tensor set and obtain two global error bounds of the VTCP through the positively homogeneous operators. [ABSTRACT FROM AUTHOR]

In this paper, by applying the accelerated technique and relaxation two-sweep strategy to the modulus-based matrix splitting iteration method, we establish the accelerated relaxation two-sweep modulus-based matrix splitting method. The proposed method contains the accelerated modulus-based matrix splitting and the generalized accelerated modulus-based matrix splitting methods presented recently as special cases. Compared with some existing methods, the proposed method can use more information during each iteration, which may lead to higher computational efficiency. We investigate the convergence properties of the new method, and prove that it is convergent under certain assumptions. Also, for the accelerated relaxation two-sweep modulus-based accelerated overrelaxation method, we analyze the convergence regions of the parameters in detail. Numerical examples are offered to show that the proposed method is efficient and performs better than the generalized accelerated modulus-based matrix splitting one in actual implementation. [ABSTRACT FROM AUTHOR]

For the large and sparse linear complementarity problem, we provide a family of new accelerated modulus-based iteration methods in this article. We provide some sufficient criteria for the convergence analysis when the system matrix is a \(P\)-matrix or an \(H_+\)-matrix. In addition, we provide some numerical examples of the different parameters to illustrate the efficacy of our proposed methods. These methods help us reduce the number of iterations and the time required by the CPU, which improves convergence performance.

The subject of the study is the contact interaction of deformable elements of linear complementarity problem (LCP). To solve the linear complementarity problem, the Lemke method with the introduction of an increasing parameter of external loading is used. The proposed approach solves the degenerated matrix in a finite number of steps, while the dimensionality of the problem is limited to the area of contact. To solve the problem, the initial table of the Lemke method is generated using the contact matrix of stiffness and the contact load vector. The unknowns in the problem are mutual displacements and interaction forces of contacting pairs of points of deformable solids. The proposed approach makes it possible to evaluate the change in working schemes as the parameter of external load increases. The features of the proposed formulation of the problem are shown, the criteria for stopping the stepwise process of solving such problems are considered. Model examples for the proposed algorithm are given. The algorithm has shown its efficiency in application, including for complex model problems. Recommendations on the use of the proposed approach are given.

In this paper, we study the existence, uniqueness, and stability of solutions to the pricing problem of European continuous-installment options under the regime-switching model based on a numerical approach. For this, we consider a two-state continuous-time Markov chain for the regime-switching model and a one-dimensional finite element method for the numerical scheme. Under our proposed model and the installment option feature for the option holder to continue paying installments until maturity and receive payoff or to stop installments and terminate the contract, the valuation problem has been formulated as coupled partial differential equations (CPDE) with free boundaries. For this problem, we obtained some appropriate assumptions for the model parameters to prove that the pricing problem has unique solutions under the regime-switching model. We also illustrated some proven theorems to show the stability of solutions with a numerical approach. Finally, some numerical examples are considered to show the performance of the obtained theoretical results through numerical implementations. [ABSTRACT FROM AUTHOR]

Semantic segmentation of human images is a research hotspot in the field of computer vision. At present, the semantic segmentation models based on U-net generally lack the ability to capture the spatial information of images. At the same time, semantic incompatibility exists because the feature maps of encoder and decoder are directly connected in the skip connection stage. In addition, in low light scenes such as at night, it is easy for false segmentation and segmentation accuracy to appear. To solve the above problems, a portrait semantic segmentation method based on dual-modal information complementarity is proposed. The encoder adopts a double branch structure, and uses a SK-ASSP module that can adaptively adjust the convolution weights of different receptor fields to extract features in RGB and gray image modes respectively, and carries out cross-modal information complementarity and feature fusion. A hybrid attention mechanism is used in the jump connection phase to capture both the channel and coordinate context information of the image. Experiments on human matting dataset show that the PA and MIoU coefficients of this algorithm model reach 96.58% and 94.48% respectively, which is better than U-net benchmark model and other mainstream semantic segmentation models. [ABSTRACT FROM AUTHOR]

In this paper, we present a new nonsmooth Newton-type algorithm for solving the generalized complementarity problem based on its reformulation as a system of nonlinear equations using a one-parametric family of complementarity functions. We demonstrate, under suitable hypotheses, that this algorithm converges locally and q-quadratically. In addition, we show numerical experiments that allow us to see the good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This work seeks to demonstrate how light pollution impacts fishing activities, including catch rates and the profits of fishermen. Our goal is to examine how light pollution affects the fishing dynamics of sardines and anchovies in the Casablanca-Rabat region of Morocco, within a bioeconomic framework involving these two marine populations. In this article, we show that our model is well posed by studying the positivity and the boundedness of our system, and then we show the local stability of the interior equilibrium point. Then, we move on to calculating the fishing effort that maximizes fishermen’s profits and catches under two main constraints: The influence of light pollution on the sustained viability of the sardine and anchovy populations. Using data reported by the National Fisheries Research Institute (INRH), we obtain detailed results in numerical simulations. [ABSTRACT FROM AUTHOR]

This paper explores the complementarity effect of information technology (IT) and workplace organization (WO) on firms' productivity, but it also provides evidence of the differential effect of two of the main IT systems: Enterprise Resource Planning (ERP) and Customer Relationship Management (CRM). To do this, I use a sample of more than 1,600 large Spanish firms for the period 2006-2009. I find evidence supporting the hypothesis that IT and WO are complementary. I also find that the use of CRM seems to interact better with WO to enhance productivity. Finally, results are consistent when analyzing manufacturing and services firms separately, although evidence for complementarity is strong for services. [ABSTRACT FROM AUTHOR]

In this paper, a relaxed two-step modulus-based matrix synchronous multisplitting iteration method for solving the linear complementarity problems is constructed. The convergence conditions of the proposed method are analyzed with the convergence range of the relaxation parameters. Some parallel numerical experiments under OpenACC framework are given to show that the proposed method can accelerate the convergence rate of the existing method significantly. [ABSTRACT FROM AUTHOR]

The operator splitting method has been effectively applied to jump-diffusion models, and it is also easy to implement because the differential and complementarity restrictions are decoupled and solved separately. Despite their ubiquity, these operator-splitting approaches for jump-diffusion models have no stability and error analysis. In this direction, we performed a priori stability analysis for the implicit–explicit backward difference operator splitting techniques (IMEX-BDF-OS). After the stability analysis, we established the error estimates for IMEX-BDF1-OS and IMEX-BDF2-OS techniques. To validate the theoretical results, numerical evidence of the pricing of American options under Kou's and Merton's jump-diffusion models has been shown. [ABSTRACT FROM AUTHOR]

Attributed network embedding aims to extract latent features of complex networks from structural topology and node attributes. Existing embedding models either use two separate learning processes to capture the complementarity of network topology and node attributes, or one process to capture their consistency. However, it is rare to simultaneously consider the complementarity and consistency of the network topology and node attributes in a single model, and network noise is often ignored. To address these issues, an unsupervised adversarial enhanced attributed network embedding model is proposed in this paper, called AEANE. The model firstly designs a novel feature extractor to simultaneously learn the consistency and complementarity features of node attributes and network topology, aiming to capture more accurate and comprehensive features. Secondly, a noisy version of the feature extractor is constructed as a fake feature generator to quickly generate more unseen fake features, aiming to simulate network noise and construct two game players. Finally, a novel adversarial auto-encoder network is designed, which integrates the auto-encoder network and the generative adversarial network into a single network, aiming to quickly learn robust node embedding and tolerate network noise. Experiments on four publicly available datasets and three analysis tasks demonstrate the advantages of our AEANE model. [ABSTRACT FROM AUTHOR]

Let M n be the space of real matrices of order n. The sign-real spectral radius ξ : M n → R + , introduced in a 1997 paper by S.M. Rump, intervenes for instance in the problem of estimating the componentwise distance to singularity. The function ξ has also a bearing in the analysis of generalized absolute value equations and linear complementarity problems. Although ξ is not a norm, it is at least absolutely homogeneous and continuous. Furthermore, ξ is invariant under transposition, permutation similarity, and a few other linear isomorphisms on M n. A matrix A ∈ M n is called sign-real expansive if ξ (A) ≥ 1. Let Ω n be the set of such matrices. The purpose of this work is to discover new properties of the function ξ and to explore in detail the structure of the set Ω n. [ABSTRACT FROM AUTHOR]

We study quitting games and introduce an alternative notion of strategy profiles—absorption paths. An absorption path is parametrized by the total probability of absorption in past play rather than by time, and it accommodates both discrete-time aspects and continuous-time aspects. We then define the concept of sequentially 0-perfect absorption paths, which are shown to be limits of ε -equilibrium strategy profiles as ε goes to 0. We establish that all quitting games that do not have simple equilibria (that is, an equilibrium where the game terminates in the first period or one where the game never terminates) have a sequentially 0-perfect absorption path. Finally, we prove the existence of sequentially 0-perfect absorption paths in a new class of quitting games. [ABSTRACT FROM AUTHOR]

Linear complementarity problems are fundamental in various mathematical fields, and it is widely recognized that these problems have a unique solution if and only if the matrix related to them is a P-matrix. However, determining whether a matrix is a P-matrix can be extremely challenging or even impossible, especially for large matrices. In this paper, we present a method for establishing the existence and uniqueness of the solution to linear complementarity problems without the need for P-matrix verification. [ABSTRACT FROM AUTHOR]

The article interrogates the complementarity of agrarian trade between the Czech Republic and Albania, Bosnia and Herzegovina, Montenegro, North Macedonia and Serbia applying the Trade Complementarity Index. Analyzing the last decade, the results indicate two-way complementarity of agrarian trade between the Czech Republic and North Makedonia and Montenegro. Due to the changes in the exports and import structure during the period under scrutiny, Serbia and Albania have also become complementary to the agrarian trade of the Czech Republic and vice versa. The Czech Republic's agrarian exports are also complementary to Bosnia and Herzegovina's agrarian imports. Generally, the results support the ongoing liberalization process between the EU and the Western Balkans and the rationale for the cooperation of the Czech Republic with Western Balkan countries and taking advantage of existing economic resources in the segment of agrarian products. However, results also indicate existing barriers to developing more intensive agrarian trade between the Czech Republic and countries of the Western Balkans. [ABSTRACT FROM AUTHOR]

This paper is concerned with the modeling of power dissipation due to friction and its relation with wear estimation in wheel–rail contact. Wear is a complex multi-scale and multi-physical phenomenon appearing in rolling contact. Wear is generated by high contact stress and the work of friction forces. This phenomenon leads to the appearing of the worn material in the form of wear debris between contacting surfaces. In contact models, wear is usually described in terms of the wear depth function. This function modifies the gap between the contacting bodies as well as the shape of the surfaces of the wheel and rail in contact. In this paper, besides the wear depth function, the dissipated energy, rather than the contact stress, is taken into account to evaluate the wear impact on rail or wheel surfaces. The dissipated energy allows us to more precisely evaluate the wear debris amount as well as the depth of wear and its distribution along the contact interface. A two-dimensional rolling contact problem with frictional heat flow is considered. The elasto-plastic deformation of the rail is considered. This contact problem is governed by a coupled system of mechanical and thermal equations in terms of generalized stresses, displacement and temperature. The finite element method is used to discretize this problem. A discretized system of equations with nonpenetration and friction conditions is transformed and formulated as a nonlinear complementarity problem. The generalized Newton method is applied to numerically solve this mechanical subproblem. The Cholesky method is used to find the solution of the heat-conductive problem. The dissipated power is evaluated based on the resultant force and slip at a reference point. Numerical results including the distribution of slip velocity, power factor and wear rate are provided and discussed. [ABSTRACT FROM AUTHOR]

With the advent of large-scale datasets, significant advancements have been made in image semantic segmentation. However, the annotation of these datasets necessitates substantial human and financial resources. Therefore, the focus of research has shifted towards few-shot semantic segmentation, which leverages a small number of labeled samples to effectively segment unknown categories. The current mainstream methods are to use the meta-learning framework to achieve model generalization, and the main challenges are as follows. (1) The trained model will be biased towards the seen class, so the model will misactivate the seen class when segmenting the unseen class, which makes it difficult to achieve the idealized class agnostic effect. (2) When the sample size is limited, there exists an intra-class gap between the provided support images and the query images, significantly impacting the model's generalization capability. To solve the above two problems, we propose a network with prototype complementarity characteristics (PCNet). Specifically, we first generate a self-support query prototype based on the query image. Through the self-distillation, the query prototype and the support prototype perform feature complementary learning, which effectively reduces the influence of the intra-class gap on the model generalization. A standard semantic segmentation model is introduced to segment the seen classes during the training process to achieve accurate irrelevant class shielding. After that, we use the rough prediction map to extract its background prototype and shield the background in the query image by the background prototype. In this way, we obtain more accurate fine-grained segmentation results. The proposed method exhibits superiority in extensive experiments conducted on the PASCAL- 5 i and COCO- 20 i datasets. We achieve new state-of-the-art results in the few-shot semantic segmentation task, with an mIoU of 71.27% and 51.71% in the 5-shot setting, respectively. Comprehensive ablation experiments and visualization studies show that the proposed method has a significant effect on small-sample semantic segmentation. [ABSTRACT FROM AUTHOR]

We concentrate on the general form of the weighted complementarity problem, which serves as a generalization of the nonlinear complementarity problem and finds extensive applications in various fields, including economics, sciences, engineering, atmospheric chemistry, and multibody dynamics. We introduce a novel Fischer-Burmeister-based one-parameter smoothing complementarity function. The WCP is then reformulated as a smoothing system of equations, and a new smoothing Newton method is devised to solve the problem efficiently on the new one-parameter smoothing complementarity function. To ensure global convergence, we introduce a new line search rule. The new method exhibits both global and local quadratic convergence properties under appropriate conditions, as demonstrated through several numerical experiments that confirm its effectiveness and stability. [ABSTRACT FROM AUTHOR]

We consider initial–boundary value problems for homogeneous parabolic systems with coefficients satisfying the double Dini condition with zero initial conditions in a semibounded plane domain with nonsmooth lateral boundary. The method of boundary integral equations is used to prove a theorem on the unique classical solvability of such problems in the space of functions that are continuous together with their first spatial derivative in the closure of the domain. An integral representation of the obtained solutions is given. It is shown that the condition for the solvability of the posed problems considered in the paper is equivalent to the well-known complementarity condition. [ABSTRACT FROM AUTHOR]

This paper focuses on the classification problem of multi-view data, aiming to improve the classification accuracy of current algorithms on multi-view data. Previous multi-view classification algorithms are usually based on exploiting the complementarity of different views and fusing features from different views. A representative category is the graph-based method, which builds a graph matrix for each view, and then fuses the graph matrices of different views to obtain a unified graph. These methods have the following problems: firstly, the graph matrix is simply based on sample similarity usually; secondly, the learned graph matrix does not change dynamically; thirdly, the weight of the graph representation matrix for a single view cannot be learned in the unified graph matrix. Therefore, this paper designs a Two-step classification algorithm based on Dynamic Graph-ELM, called TSDGELM. In the TSDGELM, the dynamic Graph-ELM is used to obtain the graph representation matrix of each view to save the local neighbor information of the data, and then a joint graph learning algorithm is designed based on the GBS (Graph-Based System) mechanism to fuse the graph matrix of the single-view, and finally the united graph is input into the classifier. To evaluate the effectiveness of the proposed method in this work, we conduct a series of experiments on eight datasets, and the results demonstrate the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

We present a sufficient condition for monotonicity of the nonlinear nonsmooth system generated by Fischer–Burmeister function associated with nonlinear complementarity problem. Based on the presented condition, the nonlinear complementarity problem considered in this paper is equivalently formulated to a nonsmooth monotone system. We then propose a modified multivariate spectral gradient projection method for the resulting system, and establish the global convergence without smoothness and Lipschitz condition. Preliminary numerical experiments show that, compared to some existing methods, the proposed method is effective. [ABSTRACT FROM AUTHOR]

The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.

This paper investigates the impact of product interrelatedness (substitutability and complementarity) on decision optimisation in a distribution channel consisting of a manufacturer and a retailer. The retailer purchases the manufacturer's product and retails it with another product as a bundle. The retailer decides the bundling strategy as a choice between full mixed bundling, partial mixed bundling, and pure bundling. Based on analytical models, we reveal how the degree of substitutability and complementarity influences the channel members' optimal bundling decisions. Considering substitutes, the retailer benefits from partial mixed bundling only when the substitutability is sufficiently high; otherwise, full mixed bundling dominates. The partial mixed bundling strategy outperforms full mixed bundling for the manufacturer when the substitutability is relatively high, but when it is not, full mixed bundling is better. Considering complements, the retailer will choose pure bundling as its optimal bundling strategy along with increasing complementarity. Otherwise, the retailer benefits from the partial mixed bundling with decreasing complementarity. The pure bundling strategy always improves the manufacturer's profit by expanding market demand significantly. [ABSTRACT FROM AUTHOR]

This article proposes a novel equilibrium finite element method (EFEM) for equilibrated solution of frictional contact problem. The development of such EFEM is mainly two‐fold. On the one hand, the traction‐based equilibrium element is employed to construct the discrete equilibrated stress field. This equilibrium element, using edge tractions as basic variables, is found straightforward to deal with the friction and contact constraints on the contact surface. On the other hand, the Coulomb frictional contact problem is recast into a linear complementarity problem (LCP), with which the algebraic complementarity formulation can be obtained with the help of the constructed equilibrated stress field. A remarkable property of the proposed EFEM is that the equilibrated solution, in conjunction with the compatible solution of the traditional FEM, can provide reliable error estimation for frictional contact within the framework of dual analysis. Numerical examples are finally conducted to see the performance and the ability to reliable error estimation of the proposed EFEM. [ABSTRACT FROM AUTHOR]

The early Earth, devoid of the protective stratospheric ozone layer, must have sustained an ambient prebiotic physicochemical medium intensified by the co-existence of shortwave UV photons and very low energy electrons (vLEEs). Consequently, only intrinsically stable molecules against these two co-existing molecular destructors must have proliferated and thereby chemically evolved into the advanced molecules of life. Based on this view, we examined the stability inherent in nucleobases and their complementary pairs as resistance to the molecular damaging effects of shortwave UV photons and vLEEs. This leads to the conclusion that nucleobases could only proliferated as their complementary pairs under the unfavorable prebiotic conditions on early Earth. The complementary base pairing not only enhances but consolidates the intrinsic stability of nucleobases against short-range UV photons, vLEEs, and possibly many as-yet-unknown deleterious agents co-existed in the prebiotic conditions of the early Earth. In short, complementary base pairing is a manifestation of chemical evolution in the unfavorable prebiotic medium created by the absence of the stratospheric ozone layer. Shortwave UV photons and very low energy electrons (vLEEs) are thought to be unfavorable prebiotic conditions on early Earth which can destroy unstable molecules. Here, the authors propose that nucleobases in their complementary pairs can enhance and consolidate the intrinsic stability of nucleobases against shortwave UV photons and vLEEs and promote their proliferation. [ABSTRACT FROM AUTHOR]

We complete previous results about the incompressible limit of both the n -dimensional (n ≥ 3) compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous works, in this limit, we derive the weak form of a geometric free boundary problem of Hele-Shaw type, also called congested flow. In particular, we are able to take into account the unsaturated zone, and establish the complementarity relation which describes the limit pressure by a degenerate elliptic equation. Not only our analysis uses a completely different framework than previous approaches, but we also establish two novel uniform estimates in L 3 of the pressure gradient and in L 1 for the time derivative of the pressure. We also prove regularity à la Aronson-Bénilan. Furthermore, for the Hele-Shaw problem, we prove the uniqueness of solutions, meaning that the incompressible limit of the PKS model is unique. In addition, we establish the corresponding incompressible limit of the stationary state for the PKS model with a given mass, where, different from the case of PKS model, we obtain the uniform bound of pressure and the uniformly bounded support of density. [ABSTRACT FROM AUTHOR]

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

We numerically and experimentally demonstrate a terahertz metadevice consisting of split-ring resonators (SRRs) present within square metallic rings. This device can function as a dual-band polarization converter by breaking the symmetry of SRRs. Under x-polarized incidence, the metastructure is able to convert linearly polarized (LP) light into a left-hand circular-polarized (LCP) wave. Intriguingly, under y-polarized incidence, frequency-dependent conversion from LP to LCP and right-hand circular-polarized (RCP) states can be achieved at different frequencies. Furthermore, reconfigurable LCP-to-LP and RCP-to-LP switching can be simulated by integrating the device with patterned graphene and changing its Fermi energy. This dual-band and multi-state polarization control provides an alternative solution to developing compact and multifunctional components in the terahertz regime. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an optimal control problem with a crucial ODE constraint involving a terminal stochastic LCP and its discrete approximation using the relaxation, the sample average approximation (SAA), and the implicit Euler time-stepping scheme. We show the existence of feasible solutions and optimal solutions to the optimal control problem and its discrete approximation under the condition that the expectation of the stochastic matrix in the stochastic LCP is a Z-matrix or an adequate matrix. Moreover, we prove that the solution sequence generated by the discrete approximation converges to a solution of the original optimal control problem with probability 1 by the repeated limits in the order of ∊ ↓ 0, v → ∞, and h ↓ 0, where ∊ is the relaxation parameter, v is the sample size, and h is the mesh size. We also provide asymptotics of the SAA optimal value and error bounds of the time-stepping method. A numerical example is used to illustrate the existence of optimal solutions, the discretization scheme, and error estimation. [ABSTRACT FROM AUTHOR]

Urban function evolution (UFE) has become more and more complex in emerging cities. However, insufficient theoretical support exists for the visual expression of the spatial correlation between UFE patterns. In order to fill this gap, we use the 2013 and 2022 Point-of-Interest (POI) data of Shenzhen city to implement the funtion2vec model based on the node2vec model and urban tree theory. In this model, we first divide UFE patterns into three categories: Function Replace (FR), Function Newly Added (FNA), and Function Vanishing (FV). Then, we calculate the correlation between those UFE patterns using their functional vectors, resulting in a graph structure representing the urban function evolution network (UFEN). Based on our case study, we obtained the following conclusions: (1) From 2013 to 2022, the UFE in Shenzhen was primarily dominated by FR (89.44%). (2) FV and FNA exhibit a long-tailed distribution, adhering to the 20–80 law. (3) Through the UFEN based on FR, healthcare services are well suited to form mutual complementarities with other functions; science, education, and cultural services demand a higher complementarity with other functions; administrative offices exhibit a strong diversity in their evolutionary patterns; and the integration of transportation hubs with other functions results in a significantly deviating urban function evolution from its original pattern. The above conclusions suggest that function2vec can well express UFE in emerging cities by adding spatial correlation in UFE. [ABSTRACT FROM AUTHOR]

In this paper, an error bound for linear complementarity problems of strong S DD1 matrices is given. By properties of S DD1 matrices, a new subclass of P-matrices called S DD1-B is presented, which contains B-matrices. A new error bound of linear complementarity problems for S DD¹-B is also provided, which improves the corresponding results. Numerical examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study the Schur complement problem of S-SOB matrices, and prove that the Schur complement of S-Sparse Ostrowski-Brauer (S-SOB) matrices is still in the same class under certain conditions. Based on the Schur complement of S-SOB matrices, some upper bound for the infinite norm of S-SOB matrices is obtained. Numerical examples are given to certify the validity of the obtained results. By using the infinity norm bound, an error bound is given for the linear complementarity problems of S -SOB matrices. [ABSTRACT FROM AUTHOR]

In this paper, we apply the ideas of modulus methods to the problem of non-negatively constrained image restoration based on total variation (TV) regularization and present a modulus iteration method for this problem. The proposed method has the potential to effectively handle non-negative constraint for image restoration. We prove the convergence of the proposed method. Experimental results show that the proposed method is feasible and effective. The results in peak signal-to-noise ratio (PSNR) and relative error obtained by using our proposed method are better than the corresponding results obtained by some state-of-the-art methods in most cases. [ABSTRACT FROM AUTHOR]

In this paper, by transforming the vertical linear complementarity problem (VLCP) as a certain absolute value equation, we design a class of modulus-based matrix splitting iteration methods for solving the VLCP. The convergence properties of the proposed methods are discussed in depth. By making use of some numerical experiments, we confirm the efficiency of the proposed methods. Numerical results show that the proposed methods are superior to the classical modulus-based matrix splitting iteration methods. [ABSTRACT FROM AUTHOR]

Let A be an n x n real matrix. The piecewise linear equation system z -- A|z| = b is called an absolute value equation (AVE). It is well known to be equivalent to the linear complementarity problem. Unique solvability of the AVE is known to be characterized in terms of a generalized Perron root called the sign-real spectral radius of A. For mere, possibly nonunique, solvability no such characterization exists. We narrow this gap in the theory. That is, we define the concept of the aligned spectrum of A and prove, under some mild genericity assumptions on A, that the mapping degree of the piecewise linear function FA : ℝn → ℝn,z ↦ z -- A |z| is congruent to (k + 1) mod 2, where k is the number of aligned values of A which are larger than 1. We also derive an exact--but more technical--formula for the degree of FA in terms of the aligned spectrum. Finally, we derive the analogous quantities and results for the linear complementarity problem. [ABSTRACT FROM AUTHOR]

We develop a projection recurrent neural network (RNN) to obtain the solution of the shortest path problem (SPP). Our focus on the paper is to give a compact single-layer structure RNN model to solve the SPP. To present the RNN model, we utilise a mixed linear complementarity problem (MLCP). Moreover, the developed RNN is proved to be globally stable. Finally, some numerical simulations are stated to show the performance of the presented approach. We compare the results with some other methods. [ABSTRACT FROM AUTHOR]

By reformulating the nonlinear complementarity problem into a system of nonsmooth equations, we proposed a two-step smoothing Levenberg-Marquardt method with global convergence in this paper, where not only one step but also an approximate step is computed at each iteration. Under local error bound condition, the local convergence result of the present algorithm is also obtained. Finally, numerical experiments illustrate the effectiveness of the present method when compare it with one-step smoothing Levenberg-Marquardt methods. [ABSTRACT FROM AUTHOR]