Unique Solution Research Articles

BUNNI: Learning Repair Actions in Rule-driven Data Cleaning

In this work, we address the challenging and open problem of involving non-expert users in the data repairing problem as first-class citizens. Despite a large number of proposals that have been devoted to cleaning data from the point of view of expert users (IT staff and data scientists), there is a lack of studies from the perspective of non-expert ones. Given a set of available data quality rules, we exploit machine learning techniques to guide the user to identify the dirty values for each violation and repair them. We show that with a low user effort, it is possible to identify the values in tuples that can be trusted and the ones that are most likely errors. We show experimentally how this machine learning approach leads to a unique clean solution with high quality in scenarios where other approaches fail.

Conceptual design of visible spectroscopy diagnostics for DTT

The project of the Visible Spectroscopy diagnostics for the Z eff radial profile measurement and for the divertor visible imaging spectroscopy, designed for the new tokamak DTT (Divertor Tokamak Test), is presented. To deal with the geometrical constraints of DTT and to minimize the diagnostics volume inside the access port, an integrated and compact solution hosting the two systems has been proposed. The Z eff radial profile will be evaluated from the Bremsstrahlung radiation measurement in the visible spectral range, acquiring light along ten Lines of Sight (LoS) in the upper part of the poloidal plane. The plasma emission will be focused on optical fibers, which will carry it to the spectroscopy laboratory. A second equipment, with a single toroidal LoS crossing the plasma centre and laying on the equatorial plane, will measure the average Z eff on a longer path, minimizing the incidental continuum spectrum contaminations by lines/bands emitted from the plasma edge. The divertor imaging system is designed to measure impurity and main gas influxes, to monitor the plasma position and kinetics of impurities, and to follow the plasma detachment evolution. The project aims at obtaining the maximum coverage of the divertor region. The collected light can be shared among different spectrometers and interferential filter devices placed outside the torus hall to easily change their setup. The system is composed of two telescopes, an upper and a lower one, allowing both a perpendicular and a tangential view of the DTT divertor region. This diagnostic offers a unique and compact solution designed to cope the demanding constraints of this next-generation tokamak fusion devices, integrating essential tools for wide-ranging impurity characterization and versatile investigation of divertor physics.

An analytical study on the influence of magnetic field-dependent viscosity on viscous and ohmic dissipative second-grade fluid boundary layers

This article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Complexiton, complex multiple kink soliton and the rational wave solutions to the generalized (3 + 1)-dimensional kadomtsev-petviashvili equation

Some new exact solutions of the generalized (3 + 1)-dimensional Kadomtsev-Petviashvili equation (KPE) are explored in this study. Firstly, the resonant multiple soltion solutions (RMSs) are discussed via employing the linear superposition principle and weight algorithm. Then, by introducing pairs of the conjugate parameters to the RMSs, the complexiton solutions including the non-singular complexiton and singular complexiton solutions are extracted. In addition, the complex multiple kink soliton solutions are also probed by employing the bilinear approach. Finally, we investigate the rational wave solutions via the test function method and symbolic computation. By choosing the appropriate parameters, the graph descriptions of the derived solutions are presented to show the dynamical properties. The outcomes of this work are desirous to bring some new perspective to the study of the complexiton, complex solutions and rational wave solutions to the other PDEs.

Relation-Preserving Functional Contractions Involving a Triplet of Auxiliary Functions with an Application to Integral Equations

This article addresses certain fixed-point results in a metric space equipped with a locally transitive binary relation under a functional contraction containing three auxiliary functions. The findings proved herein enrich and improve a number of existing results. In order to prove the credibility of our findings, an illustrative example is provided. Making use of our findings, we study the genuineness of the unique solution to a Fredholm integral equation.

On the sparsity of synthetic control method

ABSTRACT Synthetic Control Method (SCM) is a popular approach for causal inference in panel data, where the optimal weights for control units are often sparse. But the sparsity of SCM has received little attention in the literature except Abadie (2021), which explores the sparsity from the perspective of predictor space. In this paper, we make three contributions. First, we show that if there is a unique solution, then the number of positive weights is upper-bounded by the number of covariates. Second, we offer a simple alternative explanation about the sparsity of SCM from the perspective of parameter space. Third, we conduct a meta-analysis of empirical studies using SCM in the literature, which shows that the sparsity of SCM decreases with the relative number of covariates. A practical implication is that if the number of positive weights exceeds the number of covariates, there are multiple solutions and possibly unstable weights.

Computational and analytical analysis of integral-differential equations for modeling avoidance learning behavior

AbstractThis work emphasizes the computational and analytical analysis of integral-differential equations, with a particular application in modeling avoidance learning processes. Firstly, we suggest an approach to determine a unique solution to the given model by employing methods from functional analysis and fixed-point theory. We obtain numerical solutions using the approach of Picard iteration and evaluate their stability in the context of minor perturbations. In addition, we explore the practical application of these techniques by providing two examples that highlight the thorough analysis of behavioral responses using numerical approximations. In the end, we examine the efficacy of our suggested ordinary differential equations (ODEs) for studying the avoidance learning behavior of animals. Furthermore, we investigate the convergence and error analysis of the proposed ODEs using multiple numerical techniques. This integration of theoretical and practical analysis enhances the domain of applied mathematics by providing important insights for behavioral science research.

Third Order Dynamical Systems for the Sum of Two Generalized Monotone Operators

AbstractIn this paper, we propose and analyze a third-order dynamical system for finding zeros of the sum of two generalized operators in a Hilbert space $$\mathcal {H}$$ H . We establish the existence and uniqueness of the trajectories generated by the system under appropriate continuity conditions, and prove exponential convergence to the unique zero when the sum of the operators is strongly monotone. Additionally, we derive an explicit discretization of the dynamical system, which results in a forward–backward algorithm with double inertial effects and larger range of stepsize. We establish the linear convergence of the iterates to the unique solution using this algorithm. Furthermore, we provide convergence analysis for the class of strongly pseudo-monotone variational inequalities. We illustrate the effectiveness of our approach by applying it to structured optimization and pseudo-convex optimization problems.

Investigating the ability of PINNs to solve Burgers’ PDE near finite-time blowup

Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated Partial Differential Equations (PDEs) numerically while offering an attractive trade-off between accuracy and speed of inference. A particularly challenging aspect of PDEs is that there exist simple PDEs which can evolve into singular solutions in finite time starting from smooth initial conditions. In recent times some striking experiments have suggested that PINNs might be good at even detecting such finite-time blow-ups. In this work, we embark on a program to investigate this stability of PINNs from a rigorous theoretical viewpoint. Firstly, we derive error bounds for PINNs for Burgers’ PDE, in arbitrary dimensions, under conditions that allow for a finite-time blow-up. Our bounds give a theoretical justification for the functional regularization terms that have been reported to be useful for training PINNs near finite-time blow-up. Then we demonstrate via experiments that our bounds are significantly correlated to the ℓ2 -distance of the neurally found surrogate from the true blow-up solution, when computed on sequences of PDEs that are getting increasingly close to a blow-up.

Improved weighted nuclear norm with total variation for removing multiplicative noise

This paper introduces an improved weighted nuclear norm with a total variation model tailored for removing multiplicative noise. The model incorporates a weight matrix to regularize the residual matrix, effectively leveraging image redundancy to differentiate various statistical properties of the noise. Since there is no guarantee of a unique solution, the model is reformulated as a linear equality constraint problem and decomposed into two subproblems. These are addressed by using the alternating direction method of multipliers and the split Bregman method, respectively. In addition, each alternative update step has a closed-form and convergent solution. After obtaining the denoised image in the log-domain, the recovered image is given by using the exponential function and bias correction. Experimental evaluations demonstrate the efficacy of our algorithms in enhancing image restoration quality.

Intrinsically Decoupled Coordination Chemistries Enable Quasi-Eutectic Electrolytes with Fast Kinetics toward Enhanced Zinc-Ion Capacitors.

Eutectic electrolytes show potential beyond conventional low-concentration electrolytes (LCEs) in zinc (Zn)-ion capacitors (ZICs) yet suffer from high viscosity and sluggish kinetics. Herein, we originally develop an intrinsically decoupling strategy to address these issues, producing a novel electrolyte termed "quasi-eutectic" electrolyte (quasi-EE). Joint experimental and theoretical analyses confirm its unique solution coordination structure doped with near-LCE domains. This enables the quasi-EE well inherit the advanced properties at deep-eutectic states while provide facilitated kinetics as well as lower energy barriers via a vehicle/hopping-hybridized charge transfer mechanism. Consequently, a homogeneous electroplating pattern with much enhanced Sandꞌs time is achieved on the Zn surface, followed by a twofold prolonged service-life with drastically reduced concentration polarization. More encouragingly, the quasi-EE also delivers increased capacitance output in ZICs, which is elevated by 12.4%-144.6% compared to that before decoupling. Furthermore, the pouch cell with a cathodic mass loading of 36.6 mg cm-2 maintains competitive cycling performances over 600 cycles, far exceeding other Zn-based counterparts. This work offers fresh insights into eutectic decoupling and beyond.

Inverse kinematics solution and control method of 6-degree-of-freedom manipulator based on deep reinforcement learning

The advent of Industry 4.0 has significantly promoted the field of intelligent manufacturing, which is facilitated by the development of new technologies are emerging. Robot technology and robot intelligence methods have rapidly developed and been widely applied. Manipulators are widely used in industry, and their control is a crucial research topic. The inverse kinematics solution of manipulators is an important part of manipulator control, which calculates the joint angles required for the end effector to reach a desired position and posture. Traditional inverse kinematics solution algorithms often face the problem of insufficient generalization, and iterative methods have challenges such as large computation and long solution time. This paper proposes a reinforcement learning-based inverse kinematics solution algorithm, called the MAPPO-IK algorithm. The algorithm trains the manipulator agent using the MAPPO algorithm and calculates the difference between the end effector state of the manipulator and the target posture in real-time by designing a reward mechanism, while considering Gaussian distance and cosine distance. Through experimental comparative analysis, the feasibility, computational efficiency, and superiority of this reinforcement learning algorithm are verified. Compared with traditional inverse kinematics solution algorithms, this method has good generalization and supports real-time computation, and the obtained result is a unique solution. Reinforcement learning algorithms have better adaptability to complex environments and can handle different sudden situations in different environments. This algorithm also has the advantages of path planning, intelligent obstacle avoidance, and other advantages in dynamically processing complex environmental scenes.

Internal sites of actuation and activation in thin elastic films and membranes of finite thickness.

Functionalized thin elastic films and membranes frequently feature internal sites of net forces or stresses. These are, for instance, active sites of actuation, or rigid inclusions in a strained membrane that induce counterstress upon externally imposed deformations. We theoretically analyze the geometry of isotropic, flat, thin, linearly elastic films or membranes of finite thickness, laterally extended to infinity. At the mathematical core of such characterizations are the fundamental solutions for localized force and stress singularities associated with corresponding Green's functions. We derive such solutions in three dimensions and place them into the context of previous two-dimensional calculations. To this end, we consider both no-slip and stress-free conditions at the top and/or bottom surfaces. We provide an understanding for why the fully free-standing thin elastic membrane leads to diverging solutions in most geometries and compare these situations to the truly two-dimensional case. A no-slip support of at least one of the surfaces stabilizes the solution, which illustrates that the divergences in the fully free-standing case are connected to global deformations. Within the aforementioned framework, our results are important for associated theoretical characterizations of thin elastic films, whether supported or free-standing, and of membranes subject to internal or external forces or stresses.

Existence and uniqueness of well-posed fractional boundary value problem.

In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer's fixed point theorem. To show the results applicability some examples are presented. The basic mathematical concept of well-posed fractional boundary value issues is investigated in this study. It dives into the existence and uniqueness of these difficulties, offering light on the conditions that allow for both practical and singular solutions. This study contributes to a better knowledge of fractional calculus and its applications in a variety of scientific and technical areas, giving significant insights for both scholars and practitioners.

On optical soliton solutions of the higher-order Lakshmanan-Porsezian-Daniel model having the cubic-quintic-septic law in the presence of spatio-temporal and chromatic dispersion

The higher-order Lakshmanan-Porsezian-Daniel equation (LPDE) with the cubic-quintic-septic (CQS) law having spatiotemporal and chromatic dispersion terms (STD-CD) is examined to derive new optical soliton solutions. To accomplish this aim, we operated on a simple version of the new extended auxiliary equation method (SAEM26). The optical soliton solutions of the LPDE with CQS as well as STD-CD are constructed in detail. Moreover, 3D-surface, contour, and 2D plots are presented for the bright and periodic singular soliton solutions. Additionally, the effects of diverse model parameters on the bright soliton structure are surveyed, and these effects are displayed with 2D graphics. The findings established in this work can positively contribute to research in nonlinear optics, while the SAEM26 can be effectively applied to similar nonlinear models.

Novel analytic solutions of strain wave model in micro-structured solids

Abstract In this article, the modified extended direct algebraic method is implemented to investigate the strain wave model that governs the wave propagation in micro-structured solids. The proposed method provides many new exact traveling wave solutions with certain free parameters. Exact solutions are extremely important in interpreting the inner structures of the natural phenomena. Solitary and other wave solutions are provided for this model, such as bright solitary solutions, dark solitary solutions, singular solitary solutions, singular-dark combo solitary solutions. Also, periodic solutions and Jacobi elliptic function solutions are presented. To show the physical characteristics of the raised solutions, the graphical illustration of some solutions is presented.

Ethosome: An Innovative Perspective of Drug Delivery.

Ethosome offers a unique solution to the challenges faced by conventional drug delivery systems. In comparison to traditional liposomes and other nanocarriers, ethosomes exhibit a unique ability to improve drug absorption, overcoming a major limitation in the Transdermal Drug Delivery System. Their soft and flexible nano-vesicular structure facilitates faster permeation, resulting in significantly higher transdermal flux. This scientific investigation effectively traverses the changing landscape of ethosomes as an innovative drug delivery system. By conducting a thorough comparative analysis, we uncover the distinct characteristics that set them apart from other nanocarriers, offering insights into their distinct advantages. The study also includes a detailed analysis of the variables that have a complex impact on performance, elucidating transport mechanisms and addressing advanced facets pivotal for refined drug delivery strategies. This comprehensive overview highlights ethosomes as a future of medicine, offering a promising future for the safe and effective treatment of diverse diseases, impacting numerous lives.

Optimizing Advanced Trauma Life Support (ATLS®) to Maximize Readiness.

The Army utilizes Individual Critical Task Lists (ICTLs) to track and ensure competency and deployment readiness of its medical service members. ICTLs are the various skills and procedures that the Army has deemed foundational for each area of concentration (AOC)/military occupational specialty (MOS). While many ICTLs involve the patient care that military medical providers regularly provide, some procedures are not as commonly performed. This, when coupled with lower patient volume at military treatment facilities (MTF), poses a challenge for maintaining skill competency and deployment readiness. Fort Campbell's Blanchfield Army Community Hospital (BACH) has created a holistic and unique solution to meet many of these standardized requirements and support a ready medical force. By optimizing the Advanced Trauma Life Support (ATLS®) course curriculum to facilitate ICTL completion, BACH has increased its ICTL completion rates, ATLS® course exposure, and streamlined training requirements. The purpose of this article is to describe this best practice and suggest its applicability to other MTFs. By cross-referencing the ATLS® course curriculum and appendices with ICTLs, BACH has augmented ATLS® course certification with the additional completion of 12 ICTLs. This new approach not only increases ICTL completion, but also increases ATLS® curriculum exposure to medical providers, such as Registered Nurses or Nurse Practitioners, who would not typically take ATLS®. Since starting this new approach in April 2021, 73 military medical personnel have completed the ATLS® course at BACH, with 24 different medical specialties represented. A total of 361 ICTLs have been completed with specific ICTL completion counts ranging from 13 to 48. Each ICTL tested was completed 100% of its annual requirement. ATLS® is a mandatory joint interoperability standard for military physicians and it is also an Army ICTL for many AOCs/MOSs. Only counting completion of this course as one ICTL is a missed opportunity for the time spent by Army medical providers and limits the exposure of ATLS® to select AOCs/MOSs. This optimized and novel approach has been successful at BACH, suggesting its applicability at other MTFs that serve as ATLS® testing sites.

High-performance PVDF/PVB blend membranes with tailored sponge-like structure and antifouling properties for beer filtration

Currently limited research reported the design of microfiltration (MF) membranes specially for handling complex food processing streams such as rough beer. This study aimed to address this knowledge gap by tailoring for the first time a new class of polyvinylidene fluoride/poly(vinyl butyral) (PVDF/PVB) blend MF membrane with highly controllable pore structure and improved anti-fouling properties, and demonstrate its potential in real rough beer filtration. Combining an unconventional nonsolvent thermally induced phase separation (NTIPS) method and a unique quinary dope solution (i.e., PVDF/PVB/PVP/DMAc/MgCl2) with lower critical solution temperature (LCST) feature, the roles of PVB content and coagulation temperature were investigated in terms of pore structure characteristics and hydrophilicity. Although both the control PVDF membrane M0 without PVB and M6 with optimal 6.0 % PVB achieved similar turbidity removal (98–100 %), M6 exhibited enhanced permeance ranging from 27 % to 12 % with increasing simulated feed complexity from containing dextran only, yeast only to yeast/dextran mixture. The contribution of fouling of these key beer components was analyzed, indicating that the co-existence of yeast and dextran significantly aggravated fouling. Combining with membrane autopsy, in real rough beer filtration M6 showed permeance of 26.7 L·m−2·h−1·bar−1 at 1 bar that was ∼70 % higher than M0. Although with ∼50 % less irreversible fouling than M0, water cleaning implemented on M6 only recovered 62.5 % of flux. The simultaneous investigations on alkaline cleaning and operating pressure found that: a reasonably low pressure seemed favorable, e.g., 63.6 L·m−2·h−1·bar−1 at 0.2 bar, achieving up to flux recovery of ∼91 % with only ∼10 % contributed by irreversible fouling. Overall this study offers a facile yet practical strategy to tailor membranes for beer filtration, serving as an inspiration for designing future membrane processes for treating complex food processing and industry waste streams.

Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects

This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model’s solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus.