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The purpose of this paper is to establish some fixed point results for a pair of fuzzy dominated mappings satisfying contractive conditions on closed ball in multiplicative metric space. Some new fixed point results with graphic contraction on closed ball for a pair of fuzzy graph dominated mappings on multiplicative metric space have been established. Furthermore, we find a unique common solution for a system of non linear Voltera type integral equations and lastly we give an application to ensure the existence of common bounded solution of a functional equation in dynamic programming.

As other authors have been very interested in the topic of fixed points, we have obtained some results in this study that emphasize the importance of the fixed point theory. Kannan described a more general contraction than the Banach contraction that took its name and later Reich generalized this contraction further in metric spaces. In this paper, we have introduced some new contractions called Reich type γ-contraction and Kannan type γ-contraction which are generalization of γ-contraction and we have obtained some fixed point results for Reich type γ-contraction in non-Archimedean fuzzy metric spaces. We have presented a result about Kannan type-contraction. Furtermore, we have established an example about our main result.

Origami has been proved as a valuable tool to develop deployable, multifunctional, and tunable devices for diverse engineering applications. Inspired by the Kresling origami, this article presents a soft pneumatic actuator with vacuum control to realize the compound motion of twist and contraction. The twist direction varies as the crease angle changes and it offers pure contraction after combining two actuators with reverse creases. Our actuator can lift 180 folds of its weight and achieve the contraction ratio of 47%, while the response time is below 0.3 s. The origami-based actuator can realize an adjustable bistable property, leading to the possibility for external stimulus detection and mechanical memory devices, where the sensitivity can be regulated by the initial vacuum pressure. Through several actuators, we demonstrate the reconfigurable crawling robots capable of worm-like creep, alternating-step locomotion as well as obstacle detection. After activating all the actuators, the four-actuator robot with two working modes is validated to perform agilely for confined space navigation, showing our actuator has the potential in soft robotics applications.

We develop two generalizations of contraction theory, namely, semi-contraction and weak contraction theory. First, using the notion of semi-norm, we propose a geometric framework for semi-contraction theory. We introduce matrix semi-measures and characterize their properties. We show that the spectral abscissa of a matrix is the infimum over weighted semi-measures. For dynamical systems, we use the semi-measure of their Jacobian to characterize the contractivity properties of their trajectories. Second, for weakly contracting systems, we prove a dichotomy for the asymptotic behavior of their trajectories and novel sufficient conditions for convergence to an equilibrium. Third, we show that every trajectory of a doubly-contracting system, i.e., a system that is both weakly and semi-contracting, converges to an equilibrium point. Finally, we apply our results to various important network systems including affine averaging and affine flow systems, continuous-time distributed primal-dual algorithms, and networks of diffusively-coupled dynamical systems. For diffusively-coupled systems, the semi-contraction theory leads to a sufficient condition for synchronization that

We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally when considering deletion and contraction operations on graphs on surfaces. We give a description of each class in terms of coloured ribbon graphs. We then identify a universal deletion-contraction invariant (i.e., a `Tutte polynomial') for each class. We relate these to graph polynomials in the literature, including the Bollob\'as--Riordan, Krushkal, and Las Vergnas polynomials, and give state-sum formulations, duality relations, deleton-contraction relations, and quasi-tree expansions for each of them., Comment: This is the authors accepted manuscript / version of record with an unfortunate typo corrected on p24

This letter develops an adaptive actuator failure compensation method for nonlinear systems with unmatched parametric uncertainty based on contraction metrics. The proposed method, which is constructed by benefiting from the recent achievements on contraction metrics based adaptive control techniques, ensures the closed-loop stability and asymptotic tracking of the desired trajectory in the presence of actuator failures. In particular, a sufficient convex condition is derived for constructing a valid metric, by which a quadratic program-based controller is obtained to determine the inputs of the actuators. The introduced method is more general than the common adaptive actuator failure compensation methods, as it does not require the system to have an identical relative degree for all inputs and be transformable into the parametric strick-feedback or feedback linearization form. Besides, it can be enriched with learning-based algorithms and common robust modifications. Simulation results are presented to verify the effectiveness of the proposed controller.

This letter presents the contraction-based control of switched nonlinear systems to time varying references under dwell time conditions. The overall approach is to study the differential dynamics of switched subsystems, using switched contraction metrics, for a corresponding switched nonlinear system, and use properties of the Riemannian energy to draw conclusions on the incremental stability of the collective dynamics. The result is the formulation of conditions on the switching signal that guarantee contraction of the overall system with a specified contraction rate. Reference-independent synthesis and implementation details for a novel switched contraction-based tracking controller, based on the proposed framework, are also provided. An illustrative example is presented to demonstrate the proposed approach.

Twisted and Coiled Artificial Muscles (TCAMs) are lightweight actuators providing high power/weight ratio, and can substitute heavy electromagnetic motors and pneumatic artificial muscles in applications that require low weight and high contractile work. In this letter we present a robust and adaptive output feedback control strategy for electro-thermally actuated TCAMs. The controller adjusts the voltage applied to the TCAM in order to match desired muscles contraction/expansion. The proposed controller compensates for disturbances and uncertainties in the TCAM’s dynamic model. The robustness and stability analysis of the controller takes into account a digital implementation of the control algorithms. Performance are derived in terms of the sampling time of the CPU and the sensors available. The efficacy of the controller is validated through experimental tests.

McKibben artificial muscles, comprised of an expandable bladder wrapped in a double-helix-braided sheath, have the ability to generate forces without restricting motion to occur exclusively along the direction of actuation. This makes them attractive for a variety of applications including soft, wearable, and biomimetic robots. Despite their advantages, the theoretical maximum contraction ratio of McKibben muscles is only 36.3\%, which restricts the range of motion of the systems they actuate. This work introduces a novel ‘chain-link actuator’ that exploits the bending stiffness of McKibben muscles to achieve contraction ratios of more than 50\%. A static model that captures the relationship between pressure, displacement, and force is presented and validated on several real chain-link actuator systems.

In the present paper, we introduce the notion of generalize FR-contraction and establish some fixed point results for such mappings, which extend and generalize the result of Alam and Imdad (J. Fixed Point Theory & Appl., 17(4) (2015), 693-702), Sawangsup et al. (J. Fixed Point Theory, 2016 (2016), 1-15) and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not necessary condition for existence of fixed point in relational metric spaces. We also derive some N-order fixed point theorems from our main results. As an application of our main result, we find a solution of a certain class of nonlinear matrix equations.

In the present paper, we proved a common fixed-point theorem for two-hybrid pair of non-self mappings satisfying a generalized $(F, \xi, \eta) $- contraction condition under joint common limit range property in weak partial $b$- metric spaces. Our result is a generalization of many works available in metric space setting. An example and application to the integral equation are given to support the results proved in this paper.

A reduced-order model of a converter-dominated microgrid system may not resemble its full-order system associated with uncertainties. This paper aims to provide a singular perturbation-based contraction framework for model order reduction in converter-dominated uncertain microgrid systems. For this purpose, the concerned microgrid system is modeled as a generalized multi-timescale system, and certain sufficient conditions are derived such that convergence between the trajectories of the uncertain full-order and the corresponding reduced-order model can be guaranteed. The contraction theory-based strategy also provides explicit parameter-dependent expressions for quantifying discrepancies. The derived results are utilized to analyze the inverter-based microgrid system?s convergence behavior and obtain uncertainty bounds on its parameters. Further, the effects of modeling uncertainties and different loading conditions on the reduced-order model?s validity are also discussed. It is observed that for any uncertainty associated with the microgrid parameters that are within the bounds of checkable conditions, the states of the reduced-order microgrid model converge to that of the uncertain full-order system. Further, it is also shown that the obtained discrepancy expressions are more precise than state of the art.

Flow dynamics associated with open-channel confluences are highly three-dimensional (3D) with significant velocity gradients in the contraction zone downstream of junctions. The main objective of the present study was to investigate the impact of discharge ratio and junction angle on the non-uniformity of the velocity distribution within the contraction zone. A one-dimensional (1D) theoretical model and a 3D numerical model were developed to establish the relationships of the maximum values of energy and momentum correction coefficients ( α m and β m ) with discharge ratio (q) and junction angle (θ). The expressions of α m and β m were determined in terms of q and cosθ with the 1D theoretical model, and the constants were determined through regression analysis with the computed results from the 3D numerical model. The expressions show that α m and β m increased with an increase in junction angle or a decrease in discharge ratio due to the improved three-dimensionality of the flow structure. The expressions of α m and β m determined from the present study are consistent with the existing findings with θ = 90°.

The aim of this paper is to assess the stress concentration zone (SCZ) of a circular smooth specimen at an early stage. Following the detection of the stress concentration zone, the specimen residual life was calculated and compared to the experimental result. Uniaxial loading on the servo-hydraulic testing machine was used for the laboratory testing. The stress concentration tester was used to detect the SCZ on the specimen, based on spontaneous surface micro magnetic signals on the ferromagnetic surface. In addition, cyclic testing for fatigue characteristics was conducted at 70% and 75% of ultimate tensile stress (UTS). The results indicated that the estimated residual life for the 70% UTS was nearly identical to the experimental value, based on two magnetic parameters, i.e, Kmax and the contraction value. Meanwhile, the estimated residual life for the 75% UTS was equivalent to the experimental findings. The minimum and maximum error values for life estimation using both parameters were 0.47% and 24.35%, respectively, for the contraction value. The correlation value, R2, between the estimated life using MMM and experimental life was 0.95, showing good estimation. All the estimated life data using this method was distributed within the range of a 95% to 90% confidence interval. Hence, the proposed method can be used to predict the fatigue life of ferromagnetic components through magnetic flux leakage signals, especially in the stress concentration region.

The fixed point results for Chatterjea type contraction in the setting of Complete metric space exists in literature. Taking this approach forward Karapinar gave the concept of cyclic Chatterjea contraction mappings. Fan also worked on these cyclic mappings in a new setting of quasi-partial b-metric space. Motivated by the work of these researchers, we have introduced the notion of $qp_{b}$-cyclic Chatterjea contractive mappings and established fixed point results on them. The aim of this paper is to use an interpolative approach in the framework of quasi-partial b-metric space and to prove existence and uniqueness of fixed point theorem for $qp_{b}$-interpolative Chatterjea contraction mappings. The results are affirmed with applications based on them.

The paper presents design, fabrication, characterization and experimental verification of a new sensing method (soft optical sensing) for pneumatic artificial muscle (PAM) actuators. Soft optical waveguides are designed and fabricated using the proposed modified stiffness concept for soft sensors. The design of the sensor allows us to measure both contraction and force of a PAM actuator under loaded conditions. This proposed method makes it possible to have a highly sensitive actuator system with linear contraction sensing. The sensorized PAMs are supposed to work in high-pressure applications with the ability to be used repeatedly without significant degradation in signal quality. To characterize and validate the proposed method, two PAM actuators make use of two separately designed test systems to plot and model the characteristic curves. Finally, the validation for control is provided using measured sensor data as feedback to the controller.

In a previously published paper, a model for the nonlinear acoustic response of an area contraction including bias flow was presented. The model's prediction for the zero-driving resistance grew progressively worse as the steady-flow Mach number increased. This trend suggests that the forward loss coefficients should depend on the steady Mach number. This letter provides an empirical fitting of this Mach number dependence, along with additional validation data for the model. These additional validation data corroborate the model's prediction that the nonlinear impedance is frequency independent. This letter additionally provides an experimental methodology for determining the characteristic length with sample results.

We address counting and optimization variants of multicriteria global min-cut and size-constrained min-k-cut in hypergraphs. 1) For an r-rank n-vertex hypergraph endowed with t hyperedge-cost functions, we show that the number of multiobjective min-cuts is O(r2^{tr}n^{3t-1}). In particular, this shows that the number of parametric min-cuts in constant rank hypergraphs for a constant number of criteria is strongly polynomial, thus resolving an open question by Aissi, Mahjoub, McCormick, and Queyranne [Aissi et al., 2015]. In addition, we give randomized algorithms to enumerate all multiobjective min-cuts and all pareto-optimal cuts in strongly polynomial-time. 2) We also address node-budgeted multiobjective min-cuts: For an n-vertex hypergraph endowed with t vertex-weight functions, we show that the number of node-budgeted multiobjective min-cuts is O(r2^{r}n^{t+2}), where r is the rank of the hypergraph, and the number of node-budgeted b-multiobjective min-cuts for a fixed budget-vector b ∈ ℝ^t_+ is O(n²). 3) We show that min-k-cut in hypergraphs subject to constant lower bounds on part sizes is solvable in polynomial-time for constant k, thus resolving an open problem posed by Queyranne [Guinez and Queyranne, 2012]. Our technique also shows that the number of optimal solutions is polynomial. All of our results build on the random contraction approach of Karger [Karger, 1993]. Our techniques illustrate the versatility of the random contraction approach to address counting and algorithmic problems concerning multiobjective min-cuts and size-constrained k-cuts in hypergraphs.

In this paper, an adaptive modified weak Galerkin (AMWG) method is considered to solve second-order elliptic problem. Under the assumption of a penalty parameter, by showing reliability of error estimator, comparison of solutions and reduction of error estimator, the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops, is proved to be a contraction, namely, the adaptive algorithm is convergent. Numerical experiments are implemented to support the theoretical results.

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.

A combined numerical/experimental technique has been applied to study the semi-solid contraction behavior of aluminum alloys. The semi-solid contraction coefficients of A319, B206, 1350, as well as strontium-modified A356 were calculated using a coupled thermal-stress model to simulate the temperature and displacement of T-shaped castings produced with each alloy. The simulation results show good agreement between the predicted results and experimental data confirming the validity of the methodology for specifying the semi-solid contraction. The technique has been used successfully to present a comprehensive analysis of the semi-solid contraction behavior of the investigated aluminum alloys, as well as useful material property data for macro-scale models of casting processes.

This paper is aimed at acquainting with a new Kannan F -expanding type mapping by the approach of Wardowski in the complete metric space. We establish some fixed point results for Kannan F -expanding type mapping and F -contractive type mappings which satisfy F -contraction conditions. Additionally, some new results are given which generalize several results present in the literature. Moreover, some applications and examples are provided to show the practicality of our results.

While presenting a combinatorial point of view to the class of equistable graphs, Miklavic and Milanic pointed out the inclusions among the classes of equistable, general partition and triangle graphs. Orlin conjectured that the first two classes were equivalent, but in 2014, Milanic and Trotignon showed that the three classes are all distinct, leading to the following hierarchy: general partition graphs ⊂ equistable graphs ⊂ triangle graphs. In this paper, we solve an open problem from Anbeek et al. (1997) by showing that all the above classes are equivalent when restricted to planar graphs. Additionally, we present short proofs on some structural properties of the general partition, equistable and triangle classes. In particular, we show that the general partition and triangle classes are both closed under the operations of substitution, induction and contraction of modules which allow us to recover several results in the literature.

This article studies the contraction issue for stochastic switched impulsive systems (SSISs). The notion of almost sure contraction is proposed for SSISs. By using the first variation, the almost sure contraction is equivalent to the almost sure exponential stability of the virtual dynamics of SSISs. By It $\hat{\text{o}}$ 's formula and martingale theory, criteria on almost sure contraction are established for SSISs. The contraction criteria are also derived by the Lyapunov-like function method. All the criteria of contraction are expressed via the conditions of impulse frequency (I.F.). It is shown that these criteria via I.F. are more general and less restrictive than those reported for subclasses of SSISs. Finally, two examples are given to illustrate the effectiveness of the results.

This paper addresses the exploitation of vector based contraction theory to synchronize the motion of agents in multiagent systems. The convergence analysis of the agents using this theory provides a flexible frame as the components of a vector distance norm follow less stringent conditions than classical contraction analysis. The key feature is that it encompasses the formulation of some comparison system, as a result, the problem of convergence analysis of a complex multiagent system reduces to the convergence analysis of a much simpler comparison system. Hence, despite the nonlinearities, the methods of designing consensus controls remain simple as compared to the existing literature. We address four different cases: 1) consensus of third‐order dynamics multiagent systems subjected to acceleration and input constraints; 2) consensus of multiagent systems with heterogeneous nodes under communication imperfections; 3) synchronization of multiagent systems with connected and disconnected switching topologies; 4) synchronization in networked systems with time‐varying couplings. Moreover, an effective synchronization control scheme for a class of multiagent systems with underactuated agent dynamics is developed using the method of aggregation of comparison systems. Finally, simulation results are illustrated that show the validity of the mathematical results.

Backpressure prediction for flow-through monoliths (FTMs) and particulate filters (PFs) has been investigated. Backpressure data for model validation was measured as a function of part length by progressively shortening the parts. The experimental setup has fixed pressure at the inlet and zero exit pressure change, so varying the length of an FTM is equivalent to measuring the pressure along the channels, enabling separation of along-channel and entrance contributions to backpressure. With PFs, the PF becomes a partial PF after the first cut; testing in both orientations doubles the available data. Full and partial PFs are governed by the same differential equations, so this partial PF data can be used to validate the balance equations of a full PF. CFD results for a channel with an upstream contraction were also used for model validation. Equations for predicting the pressure drop due to flow contraction into the part are developed and validated. How to combine equations for pressure drop due to flow contraction and that along channels to give an accurate backpressure prediction for an FTM is considered. The length-varying technique enables different models proposed for PFs to be discriminated against. An approach for including the effect of developing flow in PFs is proposed; this includes a definition for dimensionless length for PFs, which is validated against literature CFD results.

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

In this manuscript, we introduce orthogonal $$(\tau ,F_{ST})$$ -contraction mappings in the framework of orthogonal metric space and establish some sufficient conditions for the existence of a solution for such class of mappings using Picard–Jungck sequences. Some nontrivial examples are also illustrated to show the usability of the results.

In this paper, we establish fixed point theorems for α - F -convex contraction mappings in b -metric space and prove the existence and uniqueness of fixed points for such mappings. Our result extends and generalizes comparable results in the existing literature. Finally, we provide an example in support of our main finding.

Kinodynamic planning of tensegrity robots is a thorny problem, and there are few works that have been reported on this subject, especially for tensegrity manipulators. In this study, a symplectic instantaneous optimal control (IOC) method for the obstacle-avoiding kinodynamic planning of a spinal tensegrity manipulator driven by sliding cables is first developed. This tensegrity mechanism can imitate the basic operations of the humanoid spine, such as bending, scoliosis, contraction and rotation. The actuation of sliding cables is treated as the kinematic constraints of the system inspired by the concept of multibody dynamics, so that a general dynamic model of the sliding cable-driven tensegrity robots is constructed by differential algebraic equations (DAEs). Subsequently, based on the discrete variational principle and Lagrange–d’Alembert principle, an IOC planner coupled with a symplectic penalty iteration is proposed to solve the kinodynamic planning problem of DAE systems. The proposed algorithm provides a novel unified control framework for the kinodynamic planning of tensegrity manipulators with fewer sliding cable actuators. A suboptimal collision-free path with input saturation can be planned in a complex dynamic environment where the target or the obstacles are moving. Finally, certain numerical experiments on the kinodynamic planning of a spinal tensegrity manipulator are carried out to demonstrate the effectiveness and advantages of the proposed symplectic IOC approach.

Mechanically compliant systems have become one of the major concerns in robotics recently. Along with advanced control techniques, various designs of compliant actuators have been steadily proposed for taking advantages of shock absorption, low reflected inertia, and capability of energy storage. One of the well-known examples is a series elastic actuator (SEA) composed of an elastic element and a force transmission mechanism connected in series. Most transmission mechanisms in SEAs use gears that show inherent limitations of backlash and non-backdrivability. While twisted string actuators (TSAs) have been proposed to address the issues of gearboxes, they have narrow speed ranges and relatively short stroke lengths. To overcome these drawbacks, we propose a twisted elastic rotary-rail actuator (TERRA) that can generate elastic contraction motions. The proposed actuator employs a structure of a double-stranded helix for effectively converting rotation to linear contraction as well as allowing for elasticity. The TERRA shows advantages of stability, efficiency, and portability.

According to Lorentz transformations, for a stationary observer, time in a moving inertial reference frame slows down, while the linear dimensions are reduced. While the first effect was observed more than 80 years ago, the second one has not been directly observed so far. The modified Duguay method is proposed in this paper for measuring the Lorentz contraction of a moving body length using the propagation of light pulses in an optical liquid medium. Three variants of the measurement scheme are considered: with a 'light square' in an optical medium, with a 'light ruler' in two optical media with different refractive indices, and with two relativistic electron bunches in a vacuum. It is shown that the classical effect of compression of spatial intervals between light pulses in an optical medium, which was not considered earlier, considerably reduces the measurement accuracy. It is also shown that the distortion of the sides of a light square oriented orthogonal to the movement direction caused by the different delays of light from different parts of a moving body also reduces the measurement accuracy of the light square method.

This study proposes a novel artificial muscle based on a pouch-type actuator with a contraction ratio amplification mechanism (CRAM). The CRAM places the final length of the pouch-type actuator into a secondary direction, while the main direction is used only for contraction purpose. Thus, the contraction ratio is substantially increased. The interaction process model between the pouch-type actuator and the mechanism is developed through the principle of virtual work, allowing us to select the adequate parameters so that the contraction ratio of the pouch-type actuator improves up to 48.3%. This improvement is 1.372 times that of the original pouch-type actuator. The output characterization is tested to verify the virtual work model of the process. Moreover, a capacitance-based displacement sensor with low root-mean-square error is built and placed in the actuator. The sensor does not increase the complexity of the system and has high repeatability and linearity. The overall functionality of the sensor is verified through sinusoidal and square-wave tracking experiments employing closed-loop control. Finally, a preliminary upper-limb-assisting test verifies that the actuator can reduce 17.48% of the muscle effort. In sum, this artificial muscle with good performance provides a design reference and alternative for wearable applications.

The purpose of this paper is to introduce a new iterative algorithm to approximate the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Also, we show that our proposed iterative algorithm converges weakly and strongly to the fixed points of almost contraction mappings and generalized α-nonexpansive mappings. Furthermore, it is proved analytically that our new iterative algorithm converges faster than one of the leading iterative algorithms in the literature for almost contraction mappings. Some numerical examples are also provided and used to show that our new iterative algorithm has better rate of convergence than all of S, Picard-S, Thakur and M iterative algorithms for almost contraction mappings and generalized α-nonexpansive mappings. Again, we show that the proposed iterative algorithm is stable with respect to T and data dependent for almost contraction mappings. Some applications of our main results and new iterative algorithm are considered. The results in this article are improvements, generalizations and extensions of several relevant results existing in the literature.

This letter presents a novel tube-type pneumatic helical actuator generating complex 3-dimensional torsional motions. Inspired by the molecular structure of DNA, this actuator is fabricated by combining two helical contraction actuators, introduced in our previous research, in parallel and covered by a sleeve. By controlling the air pressure and top rotation angle of each helical actuator, this double helical actuator can realize bidirectional screwing, curving, and mixture of screwing and curving in a 3-dimensional space. Qualitative working principles of these patterns are analyzed, and two mathematical models are introduced to estimate the helical diameter change in one motion and coordinate change of the tip point in another motion according to the air pressure. The models were validated through experiments. Finally, taking advantage of its shape-controllable features with a vast range of workspace, the effectiveness as an application to a flexible manipulator for inspection in narrow spaces is investigated and its validity is experimentally verified.

In this work, we design new type of projection methods to solve the split feasibility problem. We prove the convergence theorems under some mild conditions. Finally, we give some applications to compressed sensing and image restoration. Numerical results show that our methods can outperform related algorithms in the literature.

Many modular robots and active matter platforms are inspired by natural aggregates of single-celled organisms that exhibit complex emergent behaviors far beyond the capability and range of individuals. These behaviors stem primarily from short range chemical and mechanical interactions. Past work has focused largely on wireless communication akin to chemicals, however, physical interactions require a shift from rigid to soft, durable robots capable of inducing and measuring strain. Here, we present a platform to support such studies. The hardware consists of stand-alone, soft, pneumatic robots capable of radial expansion and contraction. The robots are cheap and fast to produce; they have 3 directional strain sensors, and 6 magnet pairs to loosely couple with their neighbors. We characterize force profiles, sensors, elastic modulus, magnetic interaction, as well as exploratory aggregate motions. Finally, we demonstrate their ability to synchronize, locomote, and fracture in a complimentary quasi-static simulator, with a coupled oscillator model, and discuss evaluation metrics. We hope that this platform will serve to further insights on how simple physical interactions between locally informed agents may lead to complex emergent behaviors.

The aim of this paper is to define fuzzy contraction in the context of complex valued extended b -metric space and prove fuzzy fixed-point results. Our results improve and extend certain recent results in literature. Moreover, we discuss an illustrative example to highlight the realized improvements. As application, we derive fixed-point results for multivalued mappings in the setting of complex valued extended b -metric space.

The augmented Lagrangian method (ALM) provides a benchmark for solving the canonical convex optimization problem with linear constraints. The direct extension of ALM for solving the multiple-block separable convex minimization problem, however, is proved to be not necessarily convergent in the literature. It has thus inspired a number of ALM-variant algorithms with provable convergence. This paper presents a novel parallel splitting method for the multiple-block separable convex optimization problem with linear equality constraints, which enjoys a larger step size compared with the existing parallel splitting methods. We first show that a fully Jacobian decomposition of the regularized ALM can contribute a descent direction yielding the contraction of proximity to the solution set; then, the new iterate is generated via a simple correction step with an ignorable computational cost. We establish the convergence analysis for the proposed method, and then demonstrate its numerical efficiency by solving an application problem arising in statistical learning.

In this note, we define Meir-Keeler contraction in S b -metric spaces. Further, by adding the concept of α -admissible mappings, we define generalized α s -Meir-Keeler contraction and used it for examining the existence and uniqueness of fixed points. Various results are also given as a consequence of our results.

In this paper, some new accelerated iterative schemes are proposed to solve the variational inequality problem with a pseudomonotone and uniformly continuous operator in real Hilbert spaces. Strong...

We develop an algorithmic framework for contracting tensor networks and demonstrate its power by classically simulating quantum computation of sizes previously deemed out of reach. Our main contribution, index slicing, is a method that efficiently parallelizes the contraction by breaking it down into much smaller and identically structured subtasks, which can then be executed in parallel without dependencies. We benchmark our algorithm on a class of random quantum circuits, achieving greater than 105 times acceleration over the original estimate of the simulation cost. We then demonstrate applications of the simulation framework for aiding the development of quantum algorithms and quantum error correction. As tensor networks are widely used in computational science, our simulation framework may find further applications. An efficient method for parallelizing the contraction of tensor networks pushes the boundaries for the classical simulation of quantum computation, and aids the development of quantum algorithms and hardware.

We present the concept of α , k , θ , φ -contractive multivalued mappings in b -metric spaces and prove some fixed point results for these mappings in this study. Our results expand and refine some of the literature’s findings in fixed point theory.

Through this work, we analyze the structure of extended Gb-metric spaces and show a fundamental lemma for sequence convergence within the same metric. We also propose the new notion of generalized geraghty type Θ-berinde contraction mappings and demonstrate several fixed point theorems for these mappingsin the sense of extended Gb-metric spaces. Eventually, the existence result for solutions of a Fredholm integral equation is furnished to show the efficacy of the technique developed.

This article proposes a hybrid control scheme synthesizing fuzzy approximate Q -iteration algorithm and discrete-time terminal-like sliding mode control for deploying tethered space robot, which is modeled as a deterministic Markov decision process. The existence of a switching condition allows FQ-iteration algorithm and terminal-like sliding surface constituting an optimal sliding mode control, and the fuzzy logic approximation is employed to improve the efficiency of optimization. Under arbitrary switching, the sliding mode reaching law works to compress the contraction of sliding surface variable. Simulation results verify the analyses on contraction of fuzzy approximate Q -iteration for optimal sliding mode control, the stability of reduced-order system yielded by the proposed discrete-time terminal-like sliding surface, and existence of switching condition.

We use mathematical modeling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semiflexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility. Exploiting this, we use repeated simulations of disordered networks to confirm that both protein friction and actin filament bending are required for contraction. We then use simulations of elementary two-filament systems to show that filament bending flexibility can facilitate contraction on the microscopic scale. Finally, we show that actin filament turnover is necessary to sustain contraction and prevent filament aggregation. Simulations with and without turnover also exhibit contractile pulses. However, these pulses are aperiodic, suggesting that periodic pulsation can only arise because of additional regulatory mechanisms or more complex mechanical behavior. Refereed/Peer-reviewed

In this paper, firstly, we introduce some new generalizations of $ F- $contraction, $ F- $Suzuki contraction, and $ F- $expanding mappings. Secondly, we prove the existence and uniqueness of the fixed points for these mappings. Finally, as an application of our main result, we investigate the existence of a unique solution of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order (1, 2).