Strong Solutions Research Articles

Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domains

We study strong core and Pareto-optimal solutions for multiple partners matching problem under lexicographic preference domains from a computational point of view. The restriction to the two-sided case is called stable many-to-many matching problem and the general one-sided case is called stable fixtures problem. We provide an example to show that the strong core can be empty even for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. On the positive side, we give efficient algorithms for finding a near feasible strong core solution and for finding a fractional matching in the strong core of fractional matchings. In contrast with the NP-hardness result for the stable fixtures problem, we show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems. Finally, we show that for reverse-lexicographic preferences the strong core is always non-empty in the many-to-many case.

Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations

Abstract Relying on the pathwise uniqueness property, we prove existence of the strong solution of a one-dimensional reflected stochastic delay equation driven by a mixture of independent Brownian and fractional Brownian motions. The difficulty is that on the one hand we cannot use the fixed-point and contraction mapping methods because of the stochastic and pathwise integrals, and on the other hand the non-continuity of the Skorokhod map with respect to the norms considered.

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In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation driven by a highly irregular vector field and study the effect of this noise on such dynamical systems. We employ a new method to prove existence and uniqueness of global strong solutions, where classical methods fail because of the “roughness” and non-Markovianity of the driving process. In addition, we prove the rather remarkable property that such solutions are infinitely many times classically differentiable with respect to the initial condition in spite of the vector field being discontinuous. The technique used in this article corresponds, in a certain sense, to the Nash–Moser iterative scheme in combination with a new concept of “higher order averaging operators along highly fractal stochastic curves”. This approach may provide a general principle for the study of regularization by noise effects in connection with important classes of partial differential equations.

HyperFast: Instant Classification for Tabular Data

Training deep learning models and performing hyperparameter tuning can be computationally demanding and time-consuming. Meanwhile, traditional machine learning methods like gradient-boosting algorithms remain the preferred choice for most tabular data applications, while neural network alternatives require extensive hyperparameter tuning or work only in toy datasets under limited settings. In this paper, we introduce HyperFast, a meta-trained hypernetwork designed for instant classification of tabular data in a single forward pass. HyperFast generates a task-specific neural network tailored to an unseen dataset that can be directly used for classification inference, removing the need for training a model. We report extensive experiments with OpenML and genomic data, comparing HyperFast to competing tabular data neural networks, traditional ML methods, AutoML systems, and boosting machines. HyperFast shows highly competitive results, while being significantly faster. Additionally, our approach demonstrates robust adaptability across a variety of classification tasks with little to no fine-tuning, positioning HyperFast as a strong solution for numerous applications and rapid model deployment. HyperFast introduces a promising paradigm for fast classification, with the potential to substantially decrease the computational burden of deep learning. Our code, which offers a scikit-learn-like interface, along with the trained HyperFast model, can be found at https://github.com/AI-sandbox/HyperFast.

Optimizing precision agriculture: Bayesian-enhanced papaya (Carica papaya L.) fruit disease classification via cubic SVM and ResNet-101 deep features

With the rise of the fruit processing industry, machine learning and image processing have become necessary for quality control and monitoring of fruits. Recently, strong vision-based solutions have emerged in farming industries that make inspections more accurate at a much lower cost. Advanced deep learning methods play a key role in these solutions. In this study, we built an image-based framework that uses the ResNet-101 CNN model to identify different types of papaya fruit diseases with minimal training data and processing power. A case study to identify commonly encountered papaya fruit diseases during harvesting was used to support the results of the suggested methodology. A total of 983 images of both healthy and defective papaya were considered during the experiment. In this study, we initially used the ResNet-101 CNN model for classification and then combined the deep features drawn out from the activation layer (fc1000) of the ResNet-101 CNN along with a multi-class Support Vector Machine (SVM) to classify papaya fruit defect detection. After comparing the performance of both approaches, it was found that Cubic SVM is the best classifier using the deep feature of ResNet-101 CNN, achieved with an accuracy of 99.5% and an area under the curve (AUC) of 1 without any classification error. The findings of this experiment reveal that the ResNet-101 CNN with the cubic SVM model can categorize good, diseased, and defective papaya pictures. Moreover, the suggested model executed the task in a greater way in terms of the F1- Score (0.99), sensitivity (99.50%), and precision (99.71%). The present work not only assists the end user in determining the type of disease but also makes it possible for them to take corrective measures during farming.

Strong solutions to the 3D full compressible magnetohydrodynamic flows

In this paper, we deal with the strong solutions to the full compressible magnetohydrodynamic flows in a domain Ω⊆R3. We prove the local existence and unique of strong solution under three different types of boundary conditions provided that the initial data satisfies a natural compatibility condition. The initial density of such a strong solution is allowed to contain vacuum states. Compared to the classical compressible MHD, the key issue in the limit passage is to obtain the a priori estimates of the absolute temperature, some new estimate ideas are introduced to estimate these results.

Strong stabilization of damped nonlinear Schrödinger equation with saturation on unbounded domains

We consider the damped nonlinear Schrödinger equation with saturation: i.e., the complex evolution equation contains in its left hand side, besides the potential term V(x)u, a nonlinear term of the form iμu(t,x)/|u(t,x)| for a given parameter μ>0 (arising in optical applications on non-Kerr-like fibers). In the right hand side we assume a given forcing term f(t,x). The important new difficulty, in contrast to previous results in the literature, comes from the fact that the spatial domain is assumed to be unbounded. We start by proving the existence and uniqueness of weak and strong solutions according the regularity of the data of the problem. The existence of solutions with a lower regularity is also obtained by working with a sequence of spaces verifying the Radon-Nikodým property. Concerning the asymptotic behavior for large times we prove a strong stabilization result. For instance, in the one dimensional case we prove that there is extinction in finite time of the solutions under the mere assumption that the L∞-norm of the forcing term f(t,x) becomes less than μ after a finite time. This presents some analogies with the so called feedback bang-bang controls v (here v=−iμu/|u|+f).

An AI-Enabled Blockchain Algorithm: A Novel Approach to Counteract Blockchain Network Security Attacks

INTRODUCTION: In this research, we present a novel method for strengthening the security of blockchain networks through the use of AI-driven technology. Blockchain has emerged as a game-changing technology across industries, but its security flaws, particularly in relation to Sybil and Distributed Denial of Service (DDoS) attacks, are a major cause for worry. To defend the blockchain from these sophisticated attacks, our research centres on creating a strong security solution that combines networks of Long Short-Term Memory (LSTM) and Self-Organizing Maps (SOM).
 OBJECTIVES: The main goal of this project is to create and test an AI-driven blockchain algorithm that enhances blockchain security by utilising LSTM and SOM networks. These are the objectives that the research hopes to achieve: In order to assess the shortcomings and weaknesses of existing blockchain security mechanisms. The goal is to create a new approach that uses LSTM sequence learning and SOM pattern recognition to anticipate and stop security breaches. In order to see how well this integrated strategy works in a simulated blockchain setting against different types of security risks.
 METHODS: The methods used in our study are based on social network analysis. A combination of support vector machines (SOM) for pattern recognition and long short-term memory (LSTM) networks for learning and event sequence prediction using historical data constitutes the methodology. The steps involved in conducting research are: The current state of blockchain security mechanisms is examined in detail. Creating a virtual blockchain and incorporating the SOM+LSTM algorithm.
 Putting the algorithm through its paces in order to see how well it detects and defends against different security risks.
 RESULTS: Significant enhancements to blockchain network security are the primary outcomes of this study. Important results consist of: Using the SOM+LSTM technique, we were able to increase the detection rates of possible security risks, such as Sybil and DDoS attacks. Enhanced reaction times when compared to conventional security techniques for attack prediction and prevention. Demonstrated ability of the algorithm to adapt and learn from new patterns of attacks, assuring long-term sustainability.
 CONCLUSION: This paper's findings highlight the efficacy of enhancing blockchain security through the integration of artificial intelligence technologies such as LSTM and SOM networks. In addition to improving blockchain technology's detection and forecasting capabilities, the SOM+LSTM algorithm helps advance the platform toward greater security and reliability. This study provides a solid answer to the increasing worries about cyber dangers in the modern era and opens the door to more sophisticated AI uses in blockchain security.

Implicit direct time integration of the heat conduction problem in the Method of Matched Sections

The paper is devoted to further elaboration of the Method of Matched Sections as a new branch of finite element method in application to the transient 2D temperature problem. The main distinction of MMS from conventional FEM consist in that the conjugation is provided between the adjacent sections rather than in the nodes of the elements. Important feature is that method is based on approximate strong form solution of the governing differential equations called here as the Connection equations. It is assumed that for each small rectangular element the 2D problem can be considered as the combination of two 1D problems – one is x-dependent, and another is y-dependent. Each problem is characterized by two functions – the temperature, , and heat flux . In practical realization for rectangular finite elements the method is reduced to determination of eight unknowns for each element – two unknowns on each side, which are related by the Connection equations, and requirement of the temperature continuity at the center of element. Another salient feature of the paper is an implementation of the original implicit time integration scheme, where the time step became the parameter of shape function within the element, i.e. it determines the behavior of the Connection equations. This method was early proposed by first author for number of 1D problem, and here in first time it is applied for 2D problems. The number of tests for rectangular plate exhibits the remarkable properties of this “embedded” time integration scheme with respect to stability, accuracy, and absence of any restrictions as to increasing of the time step.

Global existence and exponential decay of the 2D density‐dependent Bénard system with vacuum in bounded domain

In this paper, an initial boundary value problem of the 2D incompressible Bénard system is concerned. The global existence of a unique strong solution is established by the energy method and a key logarithmic interpolation inequality. In particular, the exponential decay rates for the gradients of velocity and temperature field are obtained.

Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions

We consider incompressible Navier–Stokes equations in a bounded 2D domain, complete with the so-called dynamic slip boundary conditions. Assuming that the data are regular, we show that weak solutions are strong. As an application, we provide an explicit upper bound of the fractal dimension of the global attractor in terms of the physical parameters. These estimates comply with analogous results in the case of Dirichlet boundary condition.

Advancement in automation of co-extrusion collagen casings

Co extrusion sausage technology has been a game changer in the industry as it has transformed the traditional way of filling meat betters into premade casings (e.g., synthetic materials such as cellulose or natural casings) to producing the casings on top of the meat batter as it comes out of the stuffer. This allows full automation of the process (working 24/7) with lower waste, while also increasing food safety standards. The main material used is collagen which today is extracted from a limited type of beef hides. It is then treated with a strong alkaline solution, to breakdown some of the original structures, and later with a strong acid to allow swelling of the resulting suspension. The application of the collagen gel requires special equipment to line up the collagen fibers in such a way that they provide the strength and elasticity during the cooking operation (meat expends during cooking) and later provide the consumer with the characteristics bit/“snap” similar to natural casings. Understanding the interactions between the chemical and physical properties of collagen is essential in obtaining good results. During production it is important that the collagen is quickly dried and crosslinked so the shape of the product will not be modified. This requires special large horizontal dryers and a unit to apply liquid smoke (source of aldehydes for crosslinking). Currently most systems are built for large capacity production, and therefore require large investment, however the industry is working on developing smaller and more flexible units for future use.

3D printing of melatonin-loaded esophageal stents for treatment of corrosive esophagitis

Corrosive esophagitis (CE) is a severe disease caused by accidental or suicidal ingestion of corrosive chemical agents, leading to serious esophageal stenosis or fibrosis. However, the effective and safe treatment of CE is lacking. Here, a melatonin esophagus stent (MES) was prepared using the stereolithography three-dimensional (3D) printing technology with melatonin, polyethylene glycol diacrylate (PEGDA), polyethylene glycol (PEG) 400, and other additives. The MESs with the Roman columns, caduceus, Pagoda, and mace morphologies were designed and printed, respectively. Pagoda MESs exhibited good mechanical properties, retained in the esophagus for more than 24 h, and showed rapid melatonin release. MESs had high in vitro and in vivo safety. More importantly, the implanted MES was broken down into fragments in the gastrointestinal tract and then completely evacuated from the rat body. The CE rat model was established by injecting a strong alkaline solution into the esophagus. The Pagoda MES was conveniently implanted at the injury position, which remarkably alleviated the CE symptoms, reduced inflammation, and prevented esophagus stenosis and fibrosis. 3D-printed Pagoda MESs hold promise for the treatment of CE.

Ti3AlC2 MAX Phase: A surprising candidate material for highly selective and efficient gold recovery from strong acid solutions

Given the scarcity of natural gold sources and associated mining challenges, the recovery of gold from secondary sources, such as electronic equipment waste (e-waste), becomes imperative. E-waste is typically treated with aqua regia to obtain highly acidic gold-containing solutions, which are subsequently processed by various methods to recover gold. Gold recovery materials offer numerous benefits but often exhibit insufficient selectivity, efficiency, and cost-effectiveness. To address this problem, we herein used a nonmodified pristine Ti-Al-C MAX phase (Ti3AlC2) to realize the one-pot room-temperature recovery of gold from highly acidic solutions (pH < 1) in the form of easily collectable bulky ball-shaped Au0 aggregates. High gold selectivity (Kd = 2.03 × 106 mL/g) and extraction efficiency (∼99 %) were observed even in the presence of interfering metal ions (Pd2+, Pt4+, Co2+, Ni2+, Cu2+, Zn2+), and the maximum gold extraction capacity (>6000 mg/g) surpassed that of previously reported gold recovery materials. The recovered gold was highly pure (>90 mass%) and contained minimal amounts of the original MAX phase, which obviated the need for intensive postpurification. The results of instrumental analyses suggested that gold recovery relied on electron transfer, similar to cementation, and primarily involved the reduction of solution-phase Au3+ to Au0via electron transfer from the Ti and Al of Ti3AlC2. Thus, our work demonstrates the significant potential of pristine Ti3AlC2 for the energy-efficient recovery of gold from highly acidic solutions and paves the way for the efficient valorization of e-waste.

The Cauchy problem for an inviscid and non-diffusive Oldroyd-B model in two dimensions

A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by Elgindi and Rousset (2015) where the global existence and uniqueness of the strong solution were established for arbitrarily large initial data. As pointed out by Bhave et al. (1991), since the diffusion coefficient is significantly smaller than other effects, it is interesting to study the non-diffusive model. In the present work, we obtain the global-in-time existence and uniqueness of the strong solution to the non-diffusive model with small initial data by deriving some uniform regularity estimates and taking vanishing diffusion limits. In addition, the large time behavior of the solution is studied and the optimal time-decay rates for each order of spatial derivatives are obtained. The main challenges focus on the lack of dissipation and regularity effects of the system and on the slower decay in the two-dimensional settings. A combination of the spectral analysis and the Fourier splitting method is adopted.

Vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg equations with slip boundary condition

In this paper, we investigate the vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg (NSK) equations in a three-dimensional horizontally periodic strip domain, in which the velocity of the fluid is supplemented with slip boundary condition and the gradient of density with Dirichlet boundary condition on the boundary. We prove that there exists an positive constant T0 independent on the capillarity and viscosity coefficients, such that the incompressible NSK equations have a unique strong solution on [0,T0] and the solution is uniformly bounded in H3. Based on the uniform estimates, we further give the convergence rate in H1 from the solutions of the incompressible NSK equations to the solution of the inhomogeneous incompressible Euler equations as the capillarity and viscosity coefficients go to zero simultaneously.

Removal of Pb(II), Cu(II), and Ag(I) from aqueous solutions using biochar derived by P-enriched water hyacinth

ABSTRACT A new synthesis was developed to prepare engineered biochar derived from phosphorous-rich water hyacinth. The statistical analysis indicated a significant correlation between P content and the removal rates of Pb (II), Cu (II), and Ag (I), revealing the pivotal role of enrich P in the biochar for heavy metals (HM) removal. SEM-EDX, XRD and FTIR analyses validated the presence of P functional groups on the surface of P-biochar. Batch experiments showed that the strong acidic initial solution negatively affected the adsorption of HM ions, and a similar negative impact was observed during Cu (II) adsorption under the high ionic strength conditions. Competitive adsorption experiment confirmed P-biochar’s resilience against competing metal ions during the adsorption of HM ions. Pb (II) and Ag (I) adsorption were primarily governed by precipitation/reduction, along with complexation reactions involving P functional groups. Cu (II) adsorption was dominated by complexation between Cu (II) and P functional groups.

Global existence of the strong solution to the climate dynamics model with topography effects and phase transformation of water vapor

This study investigates a climate dynamics model that incorporates topographical effects and the phase transformation of water vapor. The system comprises the Navier–Stokes equations, the temperature equation, the specific humidity equation, and the water content equation, all adhering to principles of energy conservation. Applying energy estimation methods, the Helmholtz–Weyl decomposition theorem, and the Brezis–Wainger inequality, we derive high-order a priori estimates for state functions. Subsequently, based on the initial data assumptions V0 ∈ H4(Ω), T0′,q0,mw0∈H2(Ω), we can prove that a strong solution to this system exists globally in time and establish the uniqueness of the global strong solution.

Optimal decay-in-time rates of solutions to the Cauchy problem of 3D compressible magneto-micropolar fluids

This paper focuses on the long time behavior of the solutions to the Cauchy problem of the three-dimensional compressible magneto-micropolar fluids. More precisely, we aim to establish the optimal rates of temporal decay for the highest-order spatial derivatives of the global strong solutions by the method of decomposing frequency. Our result can be regarded as the further investigation of the one in (Wei, Guo and Li in J. Differ. Equ. 263:2457–2480, 2017), in which the authors only provided the optimal rates of temporal decay for the lower-order spatial derivatives of the perturbations of both the velocity and the micro-rotational velocity.

Well-posedness for the stochastic Landau–Lifshitz–Bloch equation with helicity

We consider the stochastic Landau–Lifshitz–Bloch equation with helicity term driven by a real-valued Wiener process. We show the existence of a weak martingale solution, followed by pathwise uniqueness of the obtained solution, culminating into the existence of a strong solution using the theory of Yamada and Watanabe.