Function Of Dimensions Research Articles

Mitigate Wormhole Attack and Blackhole Attack Using Elliptic Curve Cryptography in MANET.

Numerous network can be connected by using the mobile ad hoc network. It can have security attacks like the worm hole, denial of service attack, jellyfish and also the blackhole. During this they take a path which is the shortest for the place where it has to reach. During sending of message two types of attacks are generally seen such as the blackhole attack and the wormhole attack. In this research we have tried to focus on two major attacks such as the black hole and the worm hole attack. In this we have used two types of protocol such as the AODV whose other name is SWBAODV and the scalable-dynamic elliptic curve cryptography. During the use the prime numbers are selected at random. We can also choose certain specific prime number. Moreover the security level does not depend on the size of the key. Keeping A as worm hole and B as the black hole we have made a two dimensional vector function named as F [A, B]. Two types of study is done by us in our research such as the with attack and without attack. In case of no attack study we have shown graphically using the AODV and the in case of attack we have given it as the BAODV and also the WAODV. Here we have applied a specific method SWBAODV to our selected attack case. The results were found to be interesting for the case of, packet delivery ratio and end to end delay was near 188.40 on comparing it with the BAODV and the WAODV. It has shown 51.38% more value compared to the BAODV and WAODV. There has been a drastic fall in the value of delay and it reached to a 63.2 for BAODV to WAODV. The other two things which we have discussed here is the consumption of energy and the overhead routing. The results in case of SWBAODV were good compared with the consumption of energy and save about 73.52% with the attacked case and around 69.35% with the routing done on the BAODV and WAODV. From our study we were able to say that it will give protection to the (MANET).

Deriving equations from sensor data using dimensional function synthesis

We present a new method for deriving functions that model the relationship between multiple signals in a physical system. The method, which we call dimensional function synthesis , applies to data streams where the dimensions of the signals (e.g., length, mass, etc.) are known. The method comprises two phases: a compile-time synthesis phase and a subsequent calibration using sensor data. We implement dimensional function synthesis and use the implementation to demonstrate efficiently summarizing multimodal sensor data for two physical systems using 90 laboratory experiments and 10,000 synthetic idealized measurements. The results show that our technique can generate models in less than 300 ms on average across all the physical systems we evaluated. This is a marked improvement when compared to an average of 16 s for training neural networks of comparable accuracy on the same computing platform. When calibrated with sensor data, our models outperform traditional regression and neural network models in inference accuracy in all the cases we evaluated. In addition, our models perform better in training latency (up to 1096X improvement) and required arithmetic operations in inference (up to 34X improvement). These significant gains are largely the result of exploiting information on the physics of signals that has hitherto been ignored.

Bowel stiffness associated with histopathologic scoring of stenosis in patients with Crohn's disease

Background and aims: Intestinal stenosis is a common complication of Crohn's Disease (CD). Stenosis is associated with alteration of bowel mechanical properties. This study aims to quantitate the mechanical properties of the intestinal stenosis and to explore associations between histology and mechanical remodeling at stenotic intestinal sites in CD patients. Methods: Intestinal segments from stenotic sites were studied in vitro from 19 CD patients. A luminal catheter with a bag was used to stepwise pressurize the intestinal segments from 0-100 cmH2O with 10 cmH2O increments. B-mode ultrasound images were obtained at the narrowest part of the stenosis at each pressure level and morphometric parameters were obtained from ultrasound images. The mechanical behavior of the stenotic tissue were characterized by using an isotropic three dimensional strain energy function in Demiray model form, the mechanical constants were obtained by fitting the model to the recorded intraluminal pressure and the inner radius of the stenotic segment of the small bowel. Grading scores were used for histological analysis of inflammation, fibrosis, muscular hypertrophy and adipocyte proliferation in the intestinal layers. The collagen area fraction in intestinal layers was also calculated. Associations between histological and the mechanical constants (stiffness) were analyzed. Results: Chronic inflammation was mainly located in mucosa whereas fibrosis was found in submucosa. The mechanical remodeling was performed with changed mechanical constants ranged between 0.35-13.68kPa. The mechanical properties changes were associated mainly with chronic inflammation, fibrosis and combination of inflammation and fibrosis (R>0.69, P<0.001). Furthermore, the mechanical properties correlated with the collagen fraction in submucosa and muscular layers (R>0.53, P<0.05). Conclusions: We quantitated the intestinal stenosis stiffness. Associations were found between bowel mechanical remodeling and histological changes at the stenotic site in CD patients. Statement of significanceAlthough intestinal ultrasonography, CT and MRI can be used to diagnose Crohn's Disease (CD)-associated bowel strictures, these techniques may not have sufficient accuracy and resolution to differentiate predominantly inflammatory strictures from predominantly fibrotic strictures. The present study aims to quantitate the mechanical remodeling of intestinal stenosis and to explore the associations between histological parameters and mechanical properties at the intestinal stenotic sites in CD patients. For the first time, we quantitatively demonstrated that the mechanical properties of the intestinal wall in CD stenosis are associated with the chronic inflammation, fibrosis and collagen fraction in the intestinal layers. The results of this study may facilitate design and development of artificial biomaterials for gastrointestinal organs. The potential clinical implication of this study is that the histological characteristics in patients with CD can be predicted clinically by means of inflammation and fibrosis assessment in conjunction with tissue stiffness measurement.

The loss surfaces of neural networks with general activation functions

The loss surfaces of deep neural networks have been the subject of several studies, theoretical and experimental, over the last few years. One strand of work considers the complexity, in the sense of local optima, of high dimensional random functions with the aim of informing how local optimisation methods may perform in such complicated settings. Prior work of Choromanska et al (2015) established a direct link between the training loss surfaces of deep multi-layer perceptron networks and spherical multi-spin glass models under some very strong assumptions on the network and its data. In this work, we test the validity of this approach by removing the undesirable restriction to ReLU activation functions. In doing so, we chart a new path through the spin glass complexity calculations using supersymmetric methods in random matrix theory which may prove useful in other contexts. Our results shed new light on both the strengths and the weaknesses of spin glass models in this context.

Accelerated grey wolf optimization for global optimization problems

Grey Wolf Optimizer (GWO) belongs to the family of swarm intelligence and population-based algorithm which mimics the social behaviors of gray wolf packs. Due to its ease and viability, various researchers from different domains applied GWO to solve their research problems. However, GWO ought to have solid yet adjusted strengthening and broadening procedure to upgrade its execution. This paper introduces a novel SI algorithm, namely Accelerated gray Wolf Optimization (AGWO) which incorporates the enhanced hierarchy into GWO technique. Firstly, we introduce a mathematical model to strengthen the local and global search process. Then, we propose a diversity measure to eradicate the local confinement and to keep perfect balance between intensification and diversification process. Further, parameter tuned strategy is incorporated to speed up the convergence rate. The proposed methodology is experimented using MATLAB and tested with twenty-three mathematical benchmark problems (such as unimodal, multimodal and fixed dimensional multimodal functions). The search capability of the AGWO is compared with the generic GWO and various state-of-art swarm intelligence algorithms. Empirical results expose that AGWO provides better performance as per the standard deviation, best value and convergence curve compared to other algorithms. The sensitivity study of the proposed AGWO algorithm provides better results for 19 benchmark functions out of 23 benchmark functions in terms of minimal computation time and better convergence rate.

Optimisation of complex integration contours at higher order

We continue our study of contour deformation as a practical tool for dealing with the sign problem using the d-dimensional Bose gas with non-zero chemical potential as a toy model. We derive explicit expressions for contours up to the second order with respect to a natural small parameter and generalise these contours to an ansatz for which the evaluation of the Jacobian is fast (O(1)). We examine the behaviour of the various proposed contours as a function of space-time dimensionality, the chemical potential, and lattice size and geometry and use the mean phase factor as a measure of the severity of the sign problem. In turns out that this method leads to a substantial reduction of the sign problem and that it becomes more efficient as space-time dimensionality is increased. Correlations among contributions to Im 〈S〉 play a key role in determining the mean phase factor and we examine these correlations in detail.

A conjugate gradient method for distributed optimal control problems with nonhomogeneous Helmholtz equation

A conjugate gradient algorithm with strong Wolfe-Powell line search for distributed optimal control problem is proposed. The optimal system has been discussed in [1]. The proposed algorithm is employed to solve the problem in infinite dimensional function space. With low complexity, it is suitable for large-scale problem. The sufficient descent condition of conjugate gradient and the existence of iterative step are proved. The algorithm also has global convergence property and linear convergence rate. At last, numerical experiments are presented to illustrate the efficiency and the convergence rate of the proposed algorithm.

Global sensitivity analysis of riveting parameters based on a random sampling-high dimensional model representation

The riveting process involves numerous parameters and complex problems, such as contact phenomena and material nonlinearity; therefore, it is challenging to accurately control the deformation of riveted parts by adjusting the riveting parameters. Therefore, this paper proposes a global sensitivity analysis method to determine the effects of riveting parameters on the maximum deformation of aeronautical thin-wall structures (ATWS). Considering the correlation among variables, the riveting parameters are used as input variables and the maximum deformations of ATWS are used as the output response to establish a high-precision second-order random sampling-high dimensional model representation response function. The structure and correlative sensitivity analysis method is then used to analyze the response function, and an importance ranking of the input variables is obtained to provide guidance for designs that reduce the riveting deformation of thin-walled plates.

Existence of $ \mathcal{D}- $pullback attractor for an infinite dimensional dynamical system

&lt;p style='text-indent:20px;'&gt;At the very beginning of the theory of finite dynamical systems, it was discovered that some relatively simple systems, even of ordinary differential equations, can generate very complicated (chaotic) behaviors. Furthermore these systems are extremely sensitive to perturbations, in the sense that trajectories with close but different initial data may diverge exponentially. Very often, the trajectories of such chaotic systems are localized, up to some transient process, in some subset of the phase space, the so-called strange attractors. Such subset have a very complicated geometric structure. They accumulate the nontrivial dynamics of the system.&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;For a distributed system, whose time evolution is usually governed by partial differential equations (PDEs), the phase space X is (a subset of) an infinite dimensional function space. We will thus speak of infinite dimensional dynamical systems. Since the global existence and uniqueness of solutions has been proven for a large class of PDEs arising from different domains as Mechanics and Physics, it is therefore natural to investigate whether the features, in particular the notion of attractor, obtained for dynamical systems generated by systems of ODEs generalizes to systems of PDEs.&lt;/p&gt;&lt;p style='text-indent:20px;'&gt;In this paper we give a positive aftermath by proving the existence of pullback &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ \mathcal{D} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-attractor. The key point is to find a bounded family of pullback &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ \mathcal{D} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-absorbing sets then we apply the decomposition techniques and a method used in previous works to verify the pullback &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ w $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-&lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ \mathcal{D} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-limit compactness. It is based on the concept of the Kuratowski measure of noncompactness of a bounded set as well as some new estimates of the equicontinuity of the solutions.&lt;/p&gt;

Regularized derivative interpolation for two dimensional band-limited functions

In this paper, the ill-posedness of Derivative Interpolation is discussed and a regularized Partial Derivative Interpolation for band-limited signals is presented in the two dimensional case. The convergence of the regularized Derivative Interpolation is studied and compared with Derivative Interpolation using the Shannon sampling theorem.

Compressing the time series of five dimensional distribution function data from gyrokinetic simulation using principal component analysis

Phase space structures are extracted from the time series of five dimensional distribution function data computed by the flux-driven full-f gyrokinetic code GT5D. Principal component analysis (PCA) is applied to reduce the dimensionality and the size of the data. Phase space bases in (φ,v∥,w) and the corresponding spatial coefficients (poloidal cross section) are constructed by PCA, where φ, v∥, and w, respectively, mean the toroidal angle, the parallel velocity, and the perpendicular velocity. It is shown that 83% of the variance of the original five dimensional distribution function can be expressed with 64 principal components, i.e., the compression of the degrees of freedom from 1.3×1012 to 1.4×109. One of the important findings—resulting from the detailed analysis of the contribution of each principal component to the energy flux—deals with avalanche events, which are found to be mostly driven by coherent structures in the phase space, indicating the key role of resonant particles. Another advantage of the proposed analysis is the decoupling of 6D (1D time and 5D phase space) data into the combinations of 3D data which are visible to the human eye.

Static Response Analysis of Uncertain Structures With Large-Scale Unknown-But-Bounded Parameters

This paper proposes an interval finite element method based on function decomposition for structural static response problems with large-scale unknown-but-bounded parameters. When there is a large number of uncertain parameters, it will lead to the curse of dimensionality. The existing Taylor expansion-based methods, which is often employed to deal with large-scale uncertainty problems, need the sensitivity information of response function to uncertain parameters. However, the gradient information may be difficult to obtain for some complicated structural problems. To overcome this drawback, univariate decomposition expression (UDE) and bivariate decomposition expression (BDE) are deduced by the higher-order Taylor series expansion. The original structure function with [Formula: see text]-dimensional interval parameters is decomposed into the sum of several low-dimensional response functions by UDE or BDE, each of which has only one or two interval parameters while the other interval parameters are replaced by their midpoint values. Therefore, solving the upper and lower bounds of the [Formula: see text]-dimensional function can be converted into solving those of the one- or two-dimensional functions, which savethe calculation costs and can be easily implemented. The accuracy and efficiency of the new method are verified by three numerical examples.

The Additive Generators of &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt;-Dimensional Overlap Functions

In this paper, we introduce the concepts of additive generators and additive generator pair of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We mainly discuss the conditions under which an n-dimensional overlap function can be expressed in terms of its generator pair.

A New Approach Method of Crossover Process Based On Genetic Algorithm Using High Dimensional Benchmark Functions

A New Approach Method of Crossover Process Based On Genetic Algorithm Using High Dimensional Benchmark Functions

A Supervised Learning Approach Involving Active Subspaces for an Efficient Genetic Algorithm in High-Dimensional Optimization Problems

In this work, we present an extension of genetic algorithm (GA) which exploits the supervised learning technique called active subspaces (AS) to evolve the individuals on a lower-dimensional space. In many cases, GA requires in fact more function evaluations than other optimization methods to converge to the global optimum. Thus, complex and high-dimensional functions can end up extremely demanding (from the computational point of view) to be optimized with the standard algorithm. To address this issue, we propose to linearly map the input parameter space of the original function onto its AS before the evolution, performing the mutation and mate processes in a lower-dimensional space. In this contribution, we describe the novel method called ASGA, presenting differences and similarities with the standard GA method. We test the proposed method over $n$-dimensional benchmark functions---Rosenbrock, Ackley, Bohachevsky, Rastrigin, Schaffer N. 7, and Zakharov---and finally we apply it to an aeronautical shape optimization problem.

Constructions of &amp;lt;i&amp;gt;n&amp;lt;/i&amp;gt;-Dimensional Overlap Functions Based on Bivariate Overlap Functions

In this paper, we firstly introduce some new results on overlap functions and n-dimensional overlap functions. On the other hand, in a previous study, Gómez et al. presented some open problems. One of these open problems is “to search the construction of n-dimensional overlapping functions based on bi-dimensional overlapping functions”. To answer this open problem, in this paper, we mainly introduce one construction method of n-dimensional overlap functions based on bivariate overlap functions. We mainly use the conjunction operator ∧ to construct n-dimensional overlap functions based on bivariate overlap functions and study their basic properties.

Efficient Construction of Tensor Ring Representations from Sampling

In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least squares (ALS). Since the function has size exponential in $d$, where $d$ is the number of dimensions, we propose an efficient sampling scheme to obtain $O(d)$ important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has fewer parameters than the tensor-train format and also better respects the structure of the original function.

First-order differentiability properties of a class of equality constrained optimal value functions with applications

In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to the parameter. Target applications are nonconvex objective functions with equality constraints arising in optimal control and shape optimisation. The theorem makes use of the averaged adjoint approach in conjunction with the variational approach of Kunisch, Ito and Peichl. We provide two examples of our abstract result: (a) a shape optimisation problem involving a semilinear partial differential equation which exhibits infinitely many solutions, (b) a finite dimensional quadratic function subject to a nonlinear equation.

The Optimal Shape Parameter for the Least Squares Approximation Based on the Radial Basis Function

The radial basis function (RBF) is a class of approximation functions commonly used in interpolation and least squares. The RBF is especially suitable for scattered data approximation and high dimensional function approximation. The smoothness and approximation accuracy of the RBF are affected by its shape parameter. There has been some research on the shape parameter, but the research on the optimal shape parameter of the least squares based on the RBF is scarce. This paper proposes a way for the measurement of the optimal shape parameter of the least squares approximation based on the RBF and an algorithm to solve the corresponding optimal parameter. The method consists of considering the shape parameter as an optimization variable of the least squares problem, such that the linear least squares problem becomes nonlinear. A dimensionality reduction is applied to the nonlinear least squares problem in order to simplify the objective function. To solve the optimization problem efficiently after the dimensional reduction, the derivative-free optimization is adopted. The numerical experiments indicate that the proposed method is efficient and reliable. Multiple kinds of RBFs are tested for their effects and compared. It is found through the experiments that the RBF least squares with the optimal shape parameter is much better than the polynomial least squares. The method is successfully applied to the fitting of real data.

Three dimensional Green function in cylindrical coordinates: application to the Aharonov–Bohm effect of double arc-slits

The object of this paper is the generalization of the theoretical calculation of the probability density of finding a charged particle crossing the double arc-slit in the presence of the vector potential. The explicit derivations is carried out in cylindrical coordinates for the Green functions for the underlying problem corresponding to a particle in free magnetic field, for a quantized as well as a non-quantized flux. The discussion in this paper will be limited to the uniform wavefunction of each particle on the surfaces of double arc-slits.