Perturbations of embedded eigenvalues for the planar bilaplacian

Operators on unbounded domains may acquire eigenvalues that are embedded in the essential spectrum. Determining the fate of these embedded eigenvalues under small perturbations of the underlying operator is a challenging task, and the persistence properties of such eigenvalues is linked intimately to the multiplicity of the essential spectrum. In this paper, we consider the planar bilaplacian with potential and show that the set of potentials for which an embedded eigenvalue persists is locally an infinite-dimensional manifold with infinite codimension in an appropriate space of potentials

Persistence of embedded eigenvalues

We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < \infty we show that in favorable situations the set of small perturbations of a suitable Banach space which do not remove the eigenvalue form a smooth submanifold of co-dimension m

Privacy-Aware Load Balancing in Fog Networks: A Reinforcement Learning Approach

Fog Computing has emerged as a solution to support the growing demands of real-time Internet of Things (IoT) applications, which require high availability of these distributed services. Intelligent workload distribution algorithms are needed to maximize the utilization of such Fog resources while minimizing the time required to process these workloads. These load balancing algorithms are critical in dynamic environments with heterogeneous resources and workload requirements along with unpredictable traffic demands. In this paper, load balancing is provided using a Reinforcement Learning (RL) algorithm, which optimizes the system performance by minimizing the waiting delay of IoT workloads. Unlike previous studies, the proposed solution does not require load and resource information from Fog nodes, which makes the algorithm dynamically adaptable to possible environment changes over time. This also makes the algorithm aware of the privacy requirements of Fog service providers, who might like to hide such information to prevent competing providers from calculating better pricing strategies. The proposed algorithm is interactively evaluated on a Discrete-event Simulator (DES) to mimic a practical deployment of the solution in real environments. In addition, we evaluate the algorithm's generalization ability on simulations longer than what it was trained on, which, to the best of our knowledge, has never been explored before. The results provided in this paper show how our proposed approach outperforms baseline load balancing methods under different workload generation rates.Comment: 9 pages, 9 figures, 1 tabl

Protein Domain Linker Prediction: A Direction for Detecting Protein – Protein Interactions

Protein chains are generally long and consist of multiple domains. Domains are the basic of elements of protein structures that can exist, evolve and function independently. The accurate and reliable identification of protein domains and their interactions has very important impacts in several protein research areas. The accurate prediction of protein domains is a fundamental stage in both experimental and computational proteomics. The knowledge is an initial stage of protein tertiary structure prediction which can give insight into the way in which protein works. The knowledge of domains is also useful in classifying the proteins, understanding their structures, functions and evolution, and predicting protein-protein interactions (PPI). However, predicting structural domains within proteins is a challenging task in computational biology. A promising direction of domain prediction is detecting inter-domain linkers and then predicting the reigns of the protein sequence in which the structural domains are located accordingly. Protein-protein interactions occur at almost every level of cell function. The identification of interaction among proteins and their associated domains provide a global picture of cellular functions and biological processes. It is also an essential step in the construction of PPI networks for human and other organisms. PPI prediction has been considered as a promising alternative to the traditional drug design techniques. The identification of possible viral-host protein interaction can lead to a better understanding of infection mechanisms and, in turn, to the development of several medication drugs and treatment optimization. In this work, a compact and accurate approach for inter-domain linker prediction is developed based solely on protein primary structure information. Then, inter-domain linker knowledge is used in predicting structural domains and detecting PPI. The research work in this dissertation can be summarized in three main contributions. The first contribution is predicting protein inter-domain linker regions by introducing the concept of amino acid compositional index and refining the prediction by using the Simulated Annealing optimization technique. The second contribution is identifying structural domains based on inter-domain linker knowledge. The inter-domain linker knowledge, represented by the compositional index, is enhanced by the in cooperation of biological knowledge, represented by amino acid physiochemical properties. To develop a well optimized Random Forest classifier for predicting novel domain and inter-domain linkers. In the third contribution, the domain information knowledge is utilized to predict protein-protein interactions. This is achieved by characterizing structural domains within protein sequences, analyzing their interactions, and predicting protein interaction based on their interacting domains. The experimental studies and the higher accuracy achieved is a valid argument in favor of the proposed framework

Solving Traveling Salesman Problem for Large Spaces using Modified Meta-Optimization Genetic Algorithm

Traveling salesman problem also called TSP is defined to find the best shortest way between n cities such as nodes, customers, and branches etc. with known distances for traveling between each city on GPS, where the salesman leaves a location in the city, visits each of the cities just once and returns back to the origin of city where he started. The traveling salesman problem is one of the NP-hard problems (nondeterministic polynomial time) in optimization. It has a wide range of applications including distribution, planning, logistics, and it has been studied by researchers and academicians for so many years. In this paper, applied Meta-optimization genetic algorithm with neural networks is used to solve the TSP for finding all the best paths between all n cities. The meta-optimization genetic algorithm is good to find the way between all cities with low progress, less time, and compared with the TSP just using a genetic algorithm with the same parameters using the same map for the cities or nodes

Embedded eigenvalues for asymptotically periodic ODE systems

We investigate the persistance of embedded eigenvalues under perturbations of a certain self-adjoint Schr\"odinger-type differential operator in $L^2(\mathbb{R};\mathbb{R}^n)$, with an asymptotically periodic potential. The studied perturbations are small and belong to a certain Banach space with a specified decay rate, in particular, a weighted space of continuous matrix valued functions. Our main result is that the set of perturbations for which the embedded eigenvalue persists forms a smooth manifold with a specified co-dimension. This is done using tools from Floquet theory, basic Banach space calculus, exponential dichotomies and their roughness properties, and Lyapunov-Schmidt reduction. A second result is provided, where under an extra assumption, it can be proved that the first result holds even when the space of perturbations is replaced by a much smaller space, as long as it contains a minimal subspace. In the end, as a way of showing that the investigated setting exists, a concrete example is presented. The example itself relates to a problem from quantum mechanics and represents a system of electrons in an infinite one-dimensional crystal.Comment: 17 page

Effect of Openings on the Torsional Behavior of SCC Box Beams Under Monotonic and Repeated Loading

Repeated Torsional loading occurs in many concrete structures, such as offshore structures, freeways, multistory parking garages, and other structures; however, repeated torsional loading is still poorly understood. This study aims to investigate the effect of openings on the ultimate and cracking torques, angle of twist, and modes of failure of self-compacted R.C. box beams under monotonic and repeated loading. Two groups of eight half-scale box beams with different numbers of circular openings in the web with a diameter of about 30% of the hollow box dimension were investigated. The first group (I) included four beams: one was the control box beam without openings, whereas the rest of the beams were hollow with one, two, or three openings in the web tested under monotonic loading. The second group (II) consisted of the same details as the first one tested under repeated loading. The range of the repeated loading was about 30% and 60% of the ultimate load of the monotonic tests. The study showed that the cracking and ultimate torques and the angle of twist of the tested beams were significantly reduced due to openings in the web. Results revealed a more pronounced effect for monotonic loading, with a maximum reduction of 20% and 26.8% in cracking and ultimate torsional strength, respectively, compared to monotonic loading. Moreover, results revealed that repeated loading causes inelastic deformations in proportion to the number of loading cycles. Doi: 10.28991/CEJ-2023-09-09-015 Full Text: PD

Involving machine learning techniques in heart disease diagnosis: a performance analysis

Artificial intelligence is a science that is growing at a tremendous speed every day and has become an essential part of many domains, including the medical domain. Therefore, countless artificial intelligence applications can be seen in the medical domain at various levels, which are employed to enhance early diagnosis and prediction and reduce the risks associated with many diseases, including heart diseases. In this article, machine learning techniques (logistic regression, random forest, artificial neural network, support vector machines, and k-nearest neighbors) are utilized to diagnose heart disease from the Cleveland Clinic dataset got from the University of California Irvine machine learning (UCL) repository and Kaggle platform then create a comparison between the performance of these techniques. In addition, some literature related to machine learning and deep learning techniques that aim to provide reasonable solutions in monitoring, detecting, diagnosing, and predicting heart disease and how these technologies assist in making health decisions are reviewed. Ten studies are selected and summarized by the authors published between 2017 and 2022 are illustrated. After executing a series of tests, it is seen that the most profitable performance in diagnosing heart disease is the support vector machines, with a diagnostic accuracy of 96%. This article has concluded that these techniques play a significant and influential role in assisting physicians and health care workers in analyzing heart patients' data, making health decisions, and saving patients' lives