Effective task scheduling algorithm in cloud computing with quality of service alert bees and grey wolf optimization

Quality-based services are an indicative factor in providing a meaningful measure. These measures allow labeling for upcoming targets with a numerical comparison with a valid mathematical proof of reading and publications. By obtaining valid designs, organizations put this measure into the flow of technology development operations to generate higher profits. Since the conditions were met from the inception of cloud computing technology, the market was captured heavily by providing support through cloud computing. With the increase in the use of cloud computing, the complexity of data has also increased greatly. Applying natural theory to cloud technology makes it a fruit cream. Natural methods often come true, because survival depends on the live events and happenings, so using it in real life as well as any communication within technology will always be reliable. The numerical results are also showing a better value by comparing the optimization method. Finally, the paper introduces an adaptation theory with effective cloudsim coding of honey bees and grey wolf in conjunction with their natural life cycle for solving task scheduling problems. Using adapted bees improved the results by 50% compared with the original bees and secondly by honeybees and grey wolf improved 60%.

Formal Verification of CHAP PPP authentication Protocol for Smart City/Safe City Applications.

A smart city is a technologically advanced metropolitan region with several connected devices that collects data using various electronic technologies, voice activation methods, and sensors. The information obtained from the data is utilised to efficiently manage assets, resources, and services; in turn, the data is used to enhance operations throughout the city. Achieving security for smart cities is one of the major challenges as the number of connected devices increases the vulnerability also increases. The security of a smart city system depends on the reliability of the security protocols used by the security systems. To design and develop a highly secure system for a smart city the security protocols used must be highly reliable. To prove the reliability of a security protocol the validation technique is not desirable because of its several drawbacks, these drawbacks can be overcome using the formal verification technique which provides the mathematical proof for its correctness. In this work, The Challenge-Handshake Authentication Protocol Point-to-Point (CHAP PPP) which is more commonly used in PPP authentication of smart cities is formally verified using the well-known verification technique known as the model checking technique. The Scyther model checker is the tool used to build the abstract security protocol model.

Extension of the Wittrick-Williams Algorithm for Free Vibration Analysis of Hybrid Dynamic Stiffness Models Connecting Line and Point Nodes

This paper extends the Wittrick-Williams (W-W) algorithm for hybrid dynamic stiffness (DS) models connecting any combinations of line and point nodes. The principal novelties lie in the development of both the DS formulation and the solution technique in a sufficiently systematic and general manner. The parent structure is considered to be in the form of two dimensional DS elements with line nodes, which can be connected to rigid/spring point supports/connections, rod/beam point supports/connections, and point connections to substructures. This is achieved by proposing a direct constrain method in a strong form which makes the modeling process straightforward. For the solution technique, the W-W algorithm is extended for all of the above hybrid DS models. No matrix inversion is needed in the proposed extension, making the algorithm numerically stable, especially for complex built-up structures. A mathematical proof is provided for the extended W-W algorithm. The proposed DS formulation and the extended W-W algorithm are validated by the FE results computed by ANSYS. This work significantly extends the application scope of the DS formulation and the W-W algorithm in a methodical and reliable manner, providing a powerful eigenvalue analysis tool for beam-plate built-up structures.

Different Testing Results on SVM with Double Penalty Parameters

The Support Vector Machine proposed by Vapnik is a generalized linear classifier which makes binary classification of data based on the supervised learning. SVM has been rapidly developed and has derived a series of improved and extended algorithms, which have been applied in pattern recognition, image recognition, etc. Among the many improved algorithms, the technique of regulating the ratio of two penalty parameters according to the ratio of the sample quantities of the two classes has been widely accepted. However, the technique has not been verified in the way of rigorous mathematical proof. The experiments based on USPS sets in the study were designed to test the accuracy of the theory. The optimal parameters of the USPS sets were found through the grid-scanning method, which showed that the theory is not accurate in any case because there is absolutely no linear relationship between ratios of penalty parameters and sample sizes.

A regularized shallow-water waves system with slip-wall boundary conditions in a basin: theory and numerical analysis

The simulation of long, nonlinear dispersive waves in bounded domains usually requires the use of slip-wall boundary conditions. Boussinesq systems appearing in the literature are generally not well-posed when such boundary conditions are imposed, or if they are well-posed it is very cumbersome to implement the boundary conditions in numerical approximations. In the present paper a new Boussinesq system is proposed for the study of long waves of small amplitude in a basin when slip-wall boundary conditions are required. The new system is derived using asymptotic techniques under the assumption of small bathymetric variations, and a mathematical proof of well-posedness for the new system is developed. The new system is also solved numerically using a Galerkin finite-element method, where the boundary conditions are imposed with the help of Nitsche’s method. Convergence of the numerical method is analysed, and precise error estimates are provided. The method is then implemented, and the convergence is verified using numerical experiments. Numerical simulations for solitary waves shoaling on a plane slope are also presented. The results are compared to experimental data, and excellent agreement is found.

On Euclid and the Genealogy of Proof

I argue for an interpretation of Euclid’s postulates as principles grounding the science of measurement. Euclid’s Elements can then be viewed as an application of these basic principles of measurement to what I call general measurements—that is, metric comparisons between objects that are only partially specified. As a consequence, rather than being viewed as a tool for the production of certainty, mathematical proof can then be interpreted as the tool with which such general measurements are performed. This gives, I argue, a more satisfying story of the origin of proof in Ancient Greece, and of the status of Euclid’s postulates.

Service Function Chaining with Deterministic Fault Tolerance in Optical Edge Networks

<p>In the upcoming 5G-and-beyond era, ultra-reliable low-latency communication (URLLC) services will be ubiquitous in edge networks. To improve network performance and quality of service (QoS), URLLC services could be delivered via a sequence of software-based network functions, also known as service function chains (SFCs). Towards reliable SFC delivery, it is imperative to incorporate deterministic fault tolerance during SFC deployment. However, deploying an SFC with deterministic fault tolerance is challenging because the protection mechanism needs to consider protection against physical/virtual network failures and hardware/software failures jointly. Against multiple and diverse failures, this work investigates how to effectively deliver an SFC in optical edge networks with deterministic fault tolerance while minimizing wavelength resource consumption. We introduce a protection augmented graph, called <i>k</i>-connected service function slices layered graph (KC-SLG), protecting against <i>k</i>-1 fiber link failures and <i>k</i>-1 server failures. We formulate a novel problem called deterministic-fault-tolerant SFC embedding and propose an effective algorithm, called most candidate first SF slices layered graph embedding (MCF-SE). MCF-SE employs two proposed techniques: <i>k</i>-connected network slicing (KC-NS) and <i>k</i>-connected function slicing (KC-FS). Through thorough mathematical proof, we show that KC-NS is <i>2</i>-approximate. For KC-FS, we demonstrate that <i>k</i> = 3 provides the best cost-efficiency. Our experimental results also show that the proposed MCF-SE achieves deterministic-fault-tolerant service delivery and performs better than the schemes directly extended from existing work regarding survivability and average cost-efficiency.</p>

Service Function Chaining with Deterministic Fault Tolerance in Optical Edge Networks

<p>In the upcoming 5G-and-beyond era, ultra-reliable low-latency communication (URLLC) services will be ubiquitous in edge networks. To improve network performance and quality of service (QoS), URLLC services could be delivered via a sequence of software-based network functions, also known as service function chains (SFCs). Towards reliable SFC delivery, it is imperative to incorporate deterministic fault tolerance during SFC deployment. However, deploying an SFC with deterministic fault tolerance is challenging because the protection mechanism needs to consider protection against physical/virtual network failures and hardware/software failures jointly. Against multiple and diverse failures, this work investigates how to effectively deliver an SFC in optical edge networks with deterministic fault tolerance while minimizing wavelength resource consumption. We introduce a protection augmented graph, called <i>k</i>-connected service function slices layered graph (KC-SLG), protecting against <i>k</i>-1 fiber link failures and <i>k</i>-1 server failures. We formulate a novel problem called deterministic-fault-tolerant SFC embedding and propose an effective algorithm, called most candidate first SF slices layered graph embedding (MCF-SE). MCF-SE employs two proposed techniques: <i>k</i>-connected network slicing (KC-NS) and <i>k</i>-connected function slicing (KC-FS). Through thorough mathematical proof, we show that KC-NS is <i>2</i>-approximate. For KC-FS, we demonstrate that <i>k</i> = 3 provides the best cost-efficiency. Our experimental results also show that the proposed MCF-SE achieves deterministic-fault-tolerant service delivery and performs better than the schemes directly extended from existing work regarding survivability and average cost-efficiency.</p>

A Novel Portfolio Based on Interval-Valued Intuitionistic Fuzzy AHP with Improved Combination Weight Method and New Score Function

The classical Analytic Hierarchy Process (AHP) requires an exact value to compare the relative importance of two attributes, but experts often can not obtain an accurate assessment of every attribute in the decision-making process, there are always some uncertainty and hesitation. Compared with classical AHP, our new defined interval-valued intuitionistic fuzzy AHP has accurately descripted the vagueness and uncertainty. In decision matrix, the real numbers are substituted by fuzzy numbers. In addition, each expert will make different evaluations according to different experiences for each attribute in the subjective weighting method, which neglects objective factors and then generates some deviations in some cases. This paper provides two ways to make up for this disadvantage. On the one hand, by combining the interval-valued intuitionistic fuzzy AHP with entropy weight, an improved combination weighting method is proposed, which can overcome the limitations of unilateral weighted method only considering the objective or subjective factors. On the other hand, a new score function is presented by adjusting the parameters, which can overcome the invalidity of some existing score functions. In theory, some theorems and properties for the new score functions are given with strictly mathematical proof to validate its rationality and effectiveness. In application, a novel fuzzy portfolio is proposed based on the improved combination weighted method and new score function. A numerical example shows that these results of our new score function are consistent with those of most existing score functions, which verifies that our model is feasible and effective.

Language Constraints in Constructing Arguments for Mathematical Proofs

A learning trajectory for constructing mathematical proof has been developed. The trajectory is to provide the students with a step-by-step procedure in constructing arguments for proving mathematical statements. However, in proving activities, the students were found to encounter difficulties in completing a deductive axiomatic argument constituting an accepted mathematical proof. An investigation has been conducted to explore the problems the students experienced in constructing proofs. It was found that they faced language constraints in constructing mathematical arguments. They encountered challenges in how to correctly express the mathematical statements in their constructed proofs.