Contraction Properties Research Articles

THE FIXED POINT ITERATIONS METHOD FOR THE CONTRACTION MAPPING

This paper studies the fixed point iterations method that considers the contraction mapping and one of its applications for the parameter re-estimation of the normal (Gaussian) distribution, where the presence of outliers is considered. In order to study the observed method Banach’s fixed point theorem is presented, where it is shown that the contraction property is directly related to the Jacobian of the observed mapping. Furthermore, convergence analysis is conducted in order to estimate the convergence order of the observed model.

Evaluating the effects of cement asphalt emulsion paste as a grouting material on the fatigue and thermal contraction properties of semi-flexible asphalt composite pavement

Semi-flexible asphalt (SFA) composite pavement is widely used in pavement engineering for its high load-bearing capacity, enhanced durability, impermeability, and resistance to fuel and oil spillage. However, its cracking resistance remains a concern, influenced by repeated vehicle loads and thermal contraction stresses. This study investigates the impact of cement asphalt emulsion paste as a grouting material on SFA’s fatigue and thermal contraction. SFA specimens were grouted with cement paste (CP) containing 20%, 40%, and 60% asphalt emulsion. These specimens were subjected to indirect tensile strength, resilient modulus, and fatigue tests, along with evaluation of thermal contraction behavior using coefficient of thermal contraction. Results indicated that adding asphalt emulsion to CP enhances the flexibility and ductility of SFA but reduces its indirect tensile strength and stiffness modulus. A mathematical model was introduced to predict the resilient modulus based on indirect tensile strength tests. The fatigue analysis demonstrated significant difference in fatigue resistance between SFA and AC16 materials. Incorporating asphalt emulsion also improved SFA’s thermal contraction behavior.

Inferring Covariance Structure from Multiple Data Sources via Subspace Factor Analysis

Factor analysis provides a canonical framework for imposing lower-dimensional structure such as sparse covariance in high-dimensional data. High-dimensional data on the same set of variables are often collected under different conditions, for instance in reproducing studies across research groups. In such cases, it is natural to seek to learn the shared versus condition-specific structure. Existing hierarchical extensions of factor analysis have been proposed, but face practical issues including identifiability problems. To address these shortcomings, we propose a class of SUbspace Factor Analysis (SUFA) models, which characterize variation across groups at the level of a lower-dimensional subspace. We prove that the proposed class of SUFA models lead to identifiability of the shared versus group-specific components of the covariance, and study their posterior contraction properties. Taking a Bayesian approach, these contributions are developed alongside efficient posterior computation algorithms. Our sampler fully integrates out latent variables, is easily parallelizable and has complexity that does not depend on sample size. We illustrate the methods through application to integration of multiple gene expression datasets relevant to immunology.

Abstract Mo121: Sarcomere activation biosensor reveals key functional differences in live cell active states between cardiac and skeletal muscle

The sarcomere is the functional unit of striated muscle contraction. Previous studies have provided valuable information about the sarcomeric proteins and modulators that are necessary for activation of contraction through inter-myofilament signaling. This work has revealed key differences in contraction kinetics and paradigms between cardiac, slow skeletal, and fast skeletal muscle. We seek here to expand these studies through the use of myofilament incorporated Förster Resonance Energy Transfer (FRET) fluorescent biosensor in live, intact muscle. This biosensor fuses fluorescent donor and acceptor proteins to the N- and C-terminals of fast skeletal and cardiac (slow) troponin C, respectively, and allows for the monitoring in real-time of the stepwise physiological mechanism of muscle sarcomere activation in an intact system which preserves significant features of the muscle, including excitation-contraction coupling and load. This biosensor has been designed and validated in both cardiac and skeletal muscle and using intact muscles from transgenic animals we have demonstrated FRET fluorescence in cardiac papillaries, extensor digitorum longus, and soleus muscles. This biosensor has shown unique sarcomere activation properties between cardiac and skeletal muscle, notably the emergence of a prolonged return to baseline of the FRET signal in loaded fast and slow skeletal muscle, which is evidence of a “primed state” of myofilament activation unique to skeletal muscles under load. Elucidation of the “primed state” of sarcomere activation is evidence of a transient memory of recent activity enabling the enhanced contraction properties of skeletal muscle. This finding advances previous understanding of skeletal muscle activation, including summation and tetanic contraction, which is not possible in cardiac muscle. The implementation of this biosensor provides a new approach to interrogate the essential physiological features of muscle sarcomere activation and contraction and adds a valuable new tool for small molecule and gene-based discoveries for muscle disease remediation.

Impact of lengthening velocity on the generation of eccentric force by slow-twitch muscle fibers in long stretches

After an initial increase, isovelocity elongation of a muscle fiber can lead to diminishing (referred to as Give in the literature) and subsequently increasing force. How the stretch velocity affects this behavior in slow-twitch fibers remains largely unexplored. Here, we stretched fully activated individual rat soleus muscle fibers from 0.85 to 1.3 optimal fiber length at stretch velocities of 0.01, 0.1, and 1 maximum shortening velocity, vmax, and compared the results with those of rat EDL fast-twitch fibers obtained in similar experimental conditions. In soleus muscle fibers, Give was 7%, 18%, and 44% of maximum isometric force for 0.01, 0.1, and 1 vmax, respectively. As in EDL fibers, the force increased nearly linearly in the second half of the stretch, although the number of crossbridges decreased, and its slope increased with stretch velocity. Our findings are consistent with the concept of a forceful detachment and subsequent crossbridge reattachment in the stretch’s first phase and a strong viscoelastic titin contribution to fiber force in the second phase of the stretch. Interestingly, we found interaction effects of stretch velocity and fiber type on force parameters in both stretch phases, hinting at fiber type-specific differences in crossbridge and titin contributions to eccentric force. Whether fiber type-specific combined XB and non-XB models can explain these effects or if they hint at some not fully understood properties of muscle contraction remains to be shown. These results may stimulate new optimization perspectives in sports training and provide a better understanding of structure–function relations of muscle proteins.

Deletion of Dux ameliorates muscular dystrophy in mdx mice by attenuating oxidative stress via Nrf2.

DUX4 has been widely reported in facioscapulohumeral muscular dystrophy, but its role in Duchenne muscular dystrophy (DMD) is unclear. Dux is the mouse paralog of DUX4. In Dux-/- mdx mice, forelimb grip strength test and treadmill test were performed, and extensor digitorum longus (EDL) contraction properties were measured to assess skeletal muscle function. Pathological changes in mice were determined by serum CK and LDH levels and muscle Masson staining. Inflammatory factors, oxidative stress, and mitochondrial function indicators were detected using kits. Primary muscle satellite cells were isolated, and the antioxidant molecule Nrf2 was detected. MTT assay and Edu assay were used to evaluate proliferation and TUNEL assay for cell death. The results show that the deletion of Dux enhanced forelimb grip strength and EDL contractility, prolonged running time and distance in mdx mice. Deleting Dux also attenuated muscle fibrosis, inflammation, oxidative stress, and mitochondrial dysfunction in mdx mice. Furthermore, Dux deficiency promoted proliferation and survival of muscle satellite cells by increasing Nrf2 levels in mdx mice.

Cold kiss still hot: limited temperature effects on envenomation performance in predatory strikes of a Japanese pit viper (Gloydius blomhoffii).

Understanding how environmental factors affect the performance of predators can provide profound insights into predator-prey interactions from evolutionary and ecological perspectives and the global distributional patterns of each taxon. Almost all venomous predators are ectotherms, with muscle contraction properties depending on temperature. For predators having venom transportation systems driven by muscle contraction, temperature may have quite large effects on envenomation performance for prey subjugation. Here, we used videography and enzyme-linked immunosorbent assay to examine thermal effects on envenomation kinematics and venom expenditure in predatory strikes of a venomous snake, the Mamushi Gloydius blomhoffii, to its main rodent prey at various body temperatures under both field and laboratory experimental conditions. Unexpectedly, we found that the thermal effects on envenomation performance are limited over nearly the entire ecologically relevant range of temperature (from 13.2°C to 26.2°C). Although temperature statistically significantly affected the mass of venom injected under field conditions, temperature explained only a minor proportion of the variation in venom expenditure. These findings suggest that the Mamushi is able to maintain prey subjugation performance across a wide range of temperatures, which is highly advantageous for ectothermic predators. Further studies should examine the underlying mechanisms of the limited thermal effects and their ubiquity across venomous predators.

Trajectory tracking PID passivity-based control of spacecraft formation flying around Sun-Earth L2 point in the port-Hamiltonian framework

Spacecraft formation flying for interferometric observations around the 2nd Lagrange point in the Sun-Earth system (SEL2) is currently focal point in deep space exploration research, which demands high precision in relative position control of spacecraft. This paper proposes the relative motion dynamics of satellite formations around the L2 point in the port-Hamiltonian framework, and establishes a high-precision nonlinear dynamics model. PID passivity-based control (PID-PBC) is widely used in engineering. However, existing methods of PID-PBC cannot address the trajectory tracking issues in port-Hamiltonian systems. Utilizing the contraction properties of the port-Hamiltonian system, this paper proposes the trajectory tracking PID-PBC (tPID-PBC) approach, effectively resolving trajectory tracking issues for formation dynamics around L2 point in port-Hamiltonian framework. The paper details explicit solutions of the Partial Differential Equations (PDE) for the tPID-PBC method and its controller structure, and references the trajectories of interferometric observation formations, to verify the method’s effectiveness through numerical simulation. The presented control approach is applicable across generic port-Hamiltonian systems, offering substantial theoretical value.

Approximation for the invariant measure with applications for jump processes (convergence in total variation distance)

In this paper, we establish an abstract framework for the approximation of the invariant probability measure for a Markov semigroup. Following Pagès and Panloup (2022) we use an Euler scheme with decreasing step (unadjusted Langevin algorithm). Under some contraction property with exponential rate and some regularization properties, we give an estimate of the error in total variation distance. This abstract framework covers the main results in Pagès and Panloup (2022) and Chen et al. (2023). As a specific application we study the convergence in total variation distance to the invariant measure for jump type equations. The main technical difficulty consists in proving the regularization properties — this is done under an ellipticity condition, using Malliavin calculus for jump processes.

Perjanjian Pinjam Meminjam Berdasarkan Pasal 1754 KUHperdata

Civil Law is a branch of law that regulates relationships between individuals or legal entities of a private nature. Civil Law regulates the rights and obligations of individuals or legal entities in the context of civil relationships, such as agreements, property ownership, legal responsibility, inheritance, marriage, divorce, and contracts. Civil Law usually applies in situations where there is a relationship between individuals or legal entities that stand as equal legal subjects. This is different from Public Law which regulates the relationship between individuals or legal entities and the state or government. Civil Law covers several important areas, including contract law, property law, inheritance law, family law, and labor law. In this area, Civil Law determines the rights and obligations of the parties involved, clarifies legal responsibilities, and provides a legal framework for resolving disputes. The general principles underlying Civil Law include freedom of contract, principles of justice, protection of personal rights, legal responsibility, legal certainty, and compensation for losses incurred as a result of violations or negligence.

Study on the influence of gap dependent error on the cryogenic permanent magnet undulator performance

The mass production of the first stage of HEPS (High Energy Photon Source) is approaching its final stage. 6 CPMUs (cryogenic permanent magnet undulators) have been manufactured, with four successfully finalizing the tuning of the magnetic field. To ensure radiation performance, HEPS's CPMUs enforce stringent phase error protocols. Moreover, the contraction properties at cryogenic temperature lead to a decrease in phase error after cooling. In the process of CPMU commissioning, a technique for forecasting the change of magnetic errors from room to cryogenic temperature was discovered and studied, as will be demonstrated in this paper.

The Brownian transport map

Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the Föllmer process, which pushes forward the Wiener measure onto probability measures on Euclidean spaces. Utilizing the tools of the Malliavin and stochastic calculus in Wiener space, we show that this Brownian transport map is a contraction in various settings where the analogous questions for optimal transport maps are open. The contraction properties of the Brownian transport map enable us to prove functional inequalities in Euclidean spaces, which are either completely new or improve on current results. Further and related applications of our contraction results are the existence of Stein kernels with desirable properties (which lead to new central limit theorems), as well as new insights into the Kannan–Lovász–Simonovits conjecture. We go beyond the Euclidean setting and address the problem of contractions on the Wiener space itself. We show that optimal transport maps and causal optimal transport maps (which are related to Brownian transport maps) between the Wiener measure and other target measures on Wiener space exhibit very different behaviors.

Positive Competitive Networks for Sparse Reconstruction.

We propose and analyze a continuous-time firing-rate neural network, the positive firing-rate competitive network (PFCN), to tackle sparse reconstruction problems with nonnegativity constraints. These problems, which involve approximating a given input stimulus from a dictionary using a set of sparse (active) neurons, play a key role in a wide range of domains, including, for example, neuroscience, signal processing, and machine learning. First, by leveraging the theory of proximal operators, we relate the equilibria of a family of continuous-time firing-rate neural networks to the optimal solutions of sparse reconstruction problems. Then we prove that the PFCN is a positive system and give rigorous conditions for the convergence to the equilibrium. Specifically, we show that the convergence depends only on a property of the dictionary and is linear-exponential in the sense that initially, the convergence rate is at worst linear and then, after a transient, becomes exponential. We also prove a number of technical results to assess the contractivity properties of the neural dynamics of interest. Our analysis leverages contraction theory to characterize the behavior of a family of firing-rate competitive networks for sparse reconstruction with and without nonnegativity constraints. Finally, we validate the effectiveness of our approach using a numerical example.

Optimal Contracts for Time-Inconsistent Consumers with Heterogeneous Beliefs

In many markets (e.g., cell phones, video games), firms offer menus of contracts that include some tariffs charging per-use prices above marginal cost and others below marginal cost. We term this puzzling phenomenon as two-sided deviations from marginal cost pricing and present a potential explanation based on two well-recognized consumer characteristics. The first one is that consumers’ actual consumptions may depart systematically from their initial plans (i.e., time-inconsistent preferences). In addition, consumers can be either sophisticated or naive in their beliefs about their time inconsistency (i.e., heterogenous beliefs). We characterize properties of the optimal contracts for a firm to screen the time-inconsistent consumers with heterogeneous beliefs. We articulate the conditions under which the optimal menu may account for two-sided deviations from marginal cost pricing. We also show that, contrary to intuition, a higher degree of time inconsistency may reduce firm profit and increase social welfare. Meanwhile, reducing consumer naivete may harm the society. Moreover, we confirm that our main results are robust to the presence of time-consistent consumers. This paper was accepted by Dmitri Kuksov, marketing. Funding: This work was supported by the Hunan Provincial Natural Science Foundation of China [Grant 2022JJ40102]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.02653 .

Considering momentum spillover effects via graph neural network in option pricing

AbstractTraditional options pricing relies on underlying asset volatility and contract properties. However, asset volatility is affected by the “lead–lag effects,” known as the “momentum spillover effect.” To address this, we propose a proxy measuring correlated options' influence based on maturity date. Findings indicate that 1‐day‐lagged proxy indicators positively impact option returns. Furthermore, to capture the dynamic effects of correlated options, we introduce a deep graph neural network‐based model (GNN‐MS). Empirical results on Shanghai Stock Exchange 50 exchange‐traded fund options reveal GNN‐MS significantly outperforms classics, enhancing root‐mean‐square error by at least 8.81%. This study provides novel insights into option pricing considering momentum spillover effects.

A simple gradation-state-dependent model for granular materials

This paper proposes a gradation-state-dependent constitutive model to capture the granular materials' mechanical behaviours considering the granular crushing's influence. Firstly, a gradation evolution law is developed to reflect the change in grain size distribution (GSD) with the growth of stress levels, and then, based on the evolution law, the elastic compliance matrix is modified to reflect the effects of particle breakage. Secondly, as the critical state line (CSL) exhibits gradation dependence, a novel method is developed to describe the family of CSLs under different fixed gradations. Subsequently, by combining the gradation evolution law with the CSL equation, the paper explains the steepening of the slope of the critical state line when the crushing is activated. With the improvement of CSL, the material's shear dilatancy and contraction properties are better reflected, assisting in establishing a plastic compliance matrix. Employing the derived elastic and plastic compliance matrix, the elastic–plastic model reflecting the influence of gradation and state effects is established and verified with a series of experimental and discrete element method (DEM) simulation results.

Quantitative estimates for Lévy driven SDEs with different drifts and applications

By partly invoking the refined basic coupling for the Lévy process, we establish quantitative estimates of distributions associated with two Lévy driven SDEs with different drifts, which are partially dissipative. This quantitative result is powerful not only to investigate the exponentially contractive property of distributions corresponding to partially dissipative McKean-Vlasov SDEs with jumps but also to handle the long time behavior of time-inhomogeneous SDEs with jumps. Our approach also works very well for two Lévy driven SDEs with different drift terms, which satisfy monotone and Lyapunov conditions. As important applications of the result in this aspect, under monotone and Lyapunov conditions, we obtain succinctly the exponential decay and the locally exponential contractivity as well as the exponential ergodicity for McKean-Vlasov SDEs driven by Lévy noises.

On the contraction properties for weak solutions to linear elliptic equations with 𝐿²-drifts of negative divergence

We show the existence and uniqueness as well as boundedness of weak solutions to linear elliptic equations with L 2 L^2 -drifts of negative divergence and singular zero-order terms which are positive. Our main target is to show the L r L^r -contraction properties of the unique weak solutions. Indeed, using the Dirichlet form theory, we construct a sub-Markovian C 0 C_0 -resolvent of contractions and identify it to the weak solutions. Furthermore, we derive an L 1 L^1 -stability result through an extended version of the L 1 L^1 -contraction property.

Legal Dogmatic Questions about the Impact of the European Union’s Digital Legislation on Hungarian Contract Law

The complexity and flexibility of contract law, and its ability to meet various social, economic and technical-technological needs, are indicated by a number of theories (approaches) that offer a new approach to the processing of contracts. Among the predominant theories one might include the following: overview of contracts from a constitutional and human rights approach2; deriving from this the contracts related to private and family life (intimate contracts)3; by connecting the concepts of contract law and property rights, exploring the specific characteristics of existing contracts4; filling the term "digital contract type" with content5; classification of different kinds of interconnection of contracts (complex contracts).6 The author dedicates the study to the topic of whether Hungarian contract law can meet the challenges created by digitalization, which have not yet been identified in all its details, and what are the critical points that require consideration and action as soon as possible. After the summary of the digital legislation of the European Union the author identifies the effects of digitalization in relation to the Hungarian contract law and the special contracts resulting from digitalization. Finally, the author makes de lege lata and de lege ferenda conclusions in light of this topic.

Variational Principles in Quaternionic Analysis with Applications to the Stationary MHD Equations

In this paper we aim to combine tools from variational calculus with modern techniques from quaternionic analysis that involve Dirac type operators and related hypercomplex integral operators. The aim is to develop new methods for showing geometry independent explicit global existence and uniqueness criteria as well as new computational methods with special focus to the stationary incompressible viscous magnetohydrodynamic equations. We first show how to specifically apply variational calculus in the quaternionic setting. To this end we explain how the mountain pass theorem can be successfully applied to guarantee the existence of (weak) solutions. To achieve this, the quaternionic integral operator calculus serves as a key ingredient allowing us to apply Schauder’s fixed point theorem. The advantage of the approach using Schauder’s fixed point theorem is that it is also applicable to large data since it does not require any kind of contraction property. These considerations will allow us to provide explicit iterative algorithms for its numerical solution. Finally to obtain more precise a-priori estimates one can use in the situations dealing with small data the Banach fixed point theorem which then also grants the uniqueness.