We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

The use of risk measures such as the Value at Risk (VaR) or Tail Conditional Expectation (TCE) is required by the Basel Committee on Banking Supervision in determining a bank’s risk profile. However, both measures can be shown to have shortcomings in the information that they provide to regulators and investors. In this paper we present an introduction to risk measure calculations before demonstrating the weaknesses of these measures. Through the exploration of specific cases we show how familiar yet differing risk profiles have identical values for combinations of these measures. From this evidence we recommend that a sequence of several risk measures should be used to give a more accurate representation of the risk contained on banking balance sheet.

In this article, our main purpose is to establish a new extension of Mittag-Leffler function by using the known extended beta function $\mathbf{B}_{\omega}(a,b;p)$ introduced in [1]. It led to a novel extension of the applicability of Mittag-Leffler function that introduced them as distributions defined for a specific set of functions. We also, investigate some of its important properties, namely recursion relation, Mellin transform and differential formulas.

Lately, the Critical Pathway(CP) of Electronic Medical Record(EMR) is used to the guideline for a treatment in the public hospital. We propose a healthcare promotion service using disease pattern with lifestyle risk factors. We classify a medical historical patient data with disease codes with lifestyle risk factors (hypertension, diabetes, smoking, overweight, excessive alcohol intake, and low physical activity) to make the lifestyle risk factors through the classification. We finally make the clusters of disease code with lifestyle risk factors using the medical historical data based on EMR's electronic discharge summary data. As the result of that, we do a healthcare recommending service based on the disease pattern with lifestyle risk. We can build a medical help desk of a public hospital to support people as we check into the public hospital; how to get the procedure of curing, the desired curing clinical method for the healthcare promotion service by each disease code, and how to be better our healthcare. We evaluate the performance of the proposed system by experimenting with the datasets collected at the medical center to measure performance and report some experimental results.

Let be a power function $f_{r,M}(s)$ defined for every $s$ within the finite set $M$ as follows $$f_{r,M}(s)= \begin{cases} s^r, \ &s\in M,\\ 0, \ &\mathrm{otherwise}. \end{cases} $$ Let a discrete convolution of $f_{r,M}(s)$ be denoted as follows $\mathrm{Conv}_{r,M}[n]=(f_{r,M}*f_{r,M})[n]$. Let a real coefficients $A_{m,j}$ be given by the following recurrence $$ A_{m,j} = \begin{cases} 0, & \mathrm{if } \ j<0 \ \mathrm{or } \ j>m, \\ (2j+1)\binom{2j}{j} \sum_{d=2j+1}^{m} A_{m,d} \binom{d}{2j+1} \frac{(-1)^{d-1}}{d-j} B_{2d-2j}, & \mathrm{if } \ 0 \leq j < m, \\ (2j+1)\binom{2j}{j}, & \mathrm{if } \ j=m. \end{cases} $$ In this paper we show that for every $n>0$ the following odd-power identities involving coefficients $A_{m,j}$ and convolution transform $\mathrm{Conv}_{r,M}[n]$ hold $$ \begin{split} n^{2m+1}+1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{N}}[n],\\ n^{2m+1}-1&=\sum_{r=0}^{m}A_{m,r}\mathrm{Conv}_{r,\mathbb{Z}_{>0}}[n],\\ n^{2m+1}&=\sum_{r=0}^{m}A_{m,r}\sum_{k=1}^{n} k^r(n-k)^r\\ &=\sum_{r=0}^{m}A_{m,r}\sum_{k=0}^{n-1} k^r(n-k)^r. \end{split} $$

Runtime verification (RV) is a lightweight approach to detecting temporal errors of system at runtime. It confines the verification on observed trajectory which avoids state explosion problem.To predict the future violation, some work proposed the predictive RV which uses the information from models or static analysis. But for software whose models and codes cannot be obtained, or systems running under uncertain environment, these predictive methods cannot take effect. Meanwhile, RV in general takes multi-valued logic as the specification languages, for example the " true, false and inconclusive" in three-valued semantics. They cannot give accurate quantitative description of correctness when "inconclusive" is encountered. We in this paper present a RV method which learns probabilistic model of system and environment from history traces and then generates probabilistic runtime monitor to quantitatively predict the satisfaction of temporal property at each runtime state. In this approach, Hidden Markov Model (HMM) is firstly learned and then transformed to Discrete Time Markov Chain (DTMC). To construct incremental monitor, the monitored LTL property is translated into Deterministic Rabin Automaton (DRA). The final probabilistic monitor is obtained by generating the product of DTMC and DRA, and computing the probabilities for each state. With such method, one can give early warning once the probability of correctness is lower than pre-defined threshold, and have the chance to do adjustment in advance. The method has been implemented and experimented on real UAS (Unmanned Aerial Vehicle) simulation platform.

The purpose of this study is to ascertain the effect of weight setting of objectives on displacement and implementation difficulty in slot allocation model. Therefore, a linear integer programming model including three kinds of evaluation objectives with different weights is designed to compare and analyze displacement and implementation difficulty. Test results show that the difficulty of implementation can be significantly reduced to a certain extent by weight setting with a little increase of displacement under the condition of specific capacity setting. In addition, whether the movements are listed in order of descending priority or not has a great impact on displacement and implementation difficulty in the model. Capacity is surely a key factor affecting displacement and implementation difficulties. This study contributes to proposing an index of implementation difficulty for comparing and selecting suitable weights of evaluation objectives which can help decision makers to upgrade slot allocation policies.

Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

This paper proposes a preference neural network (PNN) to address the problem of indifference preferences orders with new activation function. PNN also solves the Multi-label ranking problem, where labels may have indifference preference orders or subgroups are equally ranked. PNN follows a multi-layer feedforward architecture with fully connected neurons. Each neuron contains a novel smooth stairstep activation function based on the number of preference orders. PNN inputs represent data features and output neurons represent label indexes. The proposed PNN is evaluated using new preference mining dataset that contains repeated label values which have not experimented before. PNN outperforms five previously proposed methods for strict label ranking in terms of accurate results with high computational efficiency.

Integrated information theory (IIT) proposes a measure of integrated information (Φ) to capture the level of consciousness for a physical system in a given state. Unfortunately, calculating Φ itself is currently only possible for very small model systems, and far from computable for the kinds of systems typically associated with consciousness (brains). Here, we consider several proposed measures and computational approximations, some of which can be applied to larger systems, and test if they correlate well with Φ. While these measures and approximations capture intuitions underlying IIT and some have had success in practical applications, it has not been shown that they actually quantify the type of integrated information specified by the latest version of IIT. In this study, we evaluated these approximations and heuristic measures, based not on practical or clinical considerations, but rather based on how well they estimate the Φ values of model systems. To do this, we simulated networks consisting of 3–6 binary linear threshold nodes randomly connected with excitatory and inhibitory connections. For each system, we then constructed the system’s state transition probability matrix (TPM), as well as its state transition matrix (STM) over time for all possible initial states. From these matrices, we calculated, approximations to Φ, and measures based on state differentiation, state entropy, state uniqueness, and integrated information. All measures were correlated with Φ in a state dependent and state independent manner. Our findings suggest that Φ can be approximated closely in small binary systems by using one or more of the readily available approximations (r > 0.95), but without major reductions in computational demands. Furthermore, Φ correlated strongly with measures of signal complexity (LZ, r_s = 0.722), decoder based integrated information (Φ*, r_s = 0.816), and state differentiation (D1, r_s = 0.827), on the system level (state independent). These measures could allow for efficient estimation of Φ on a group level, or as accurate predictors of low, but not high, Φ systems. While it’s uncertain whether the results extend to larger systems or systems with other dynamics, we stress the importance that measures aimed at being practical alternatives to Φ are at a minimum rigorously tested in an environment where the ground truth can be established.

In the neuroscience research field, specific for medical imaging analysis, how to mining more latent medical information from big medical data is significant for us to find the solution of diseases.  In this review, we focus on neuroimaging data that is functional Magnetic Resonance Imaging (fMRI) which non-invasive techniques, it already becomes popular tools in the clinical neuroscience and functional cognitive science research. After we get fMRI data, we actually have various software and computer programming that including open source and commercial,  it's very hard to choose the best software to analyze data. What's worse,  it would cause final result imbalance and unstable when we combine more than software together, so that's why we want to make a pipeline to analyze data. On the other hand, with the growing of machine learning, Python has already become one of very hot and popular computer programming. In addition, it is an open source and dynamic computer programming,  the communities, libraries and contributors fast increase in the recent year. Through this review, we hope that can make neuroimaging data analysis more easy, stable and uniform base the one platform system.

Over the past few years, the importance of video surveillance in securing the national critical infrastructure has significantly increased, whose applications include detecting failures and anomalies. Accompanied by video proliferation is the increasing number of attacks against surveillance systems. Among the attacks, false frame injection (FFI) attacks that replay video frames from a previous recording to mask the live feed has the highest impact. While many attempts have been made to detect FFI frames using features from the video feeds, video analysis is computationally too intensive to be deployed on-site for real-time false frame detection. In this paper, we investigate the feasibility of FFI attacks on compromised surveillance systems at the edge and propose an effective technique to detect the injected false video and audio frames by monitoring the surveillance feed using the embedded Electrical Network Frequency (ENF) signals. An ENF operates at a nominal frequency of 60 Hz/50 Hz based on its geographical location and maintains a stable value across the entire power grid interconnection with minor fluctuations. For surveillance system video/audio recordings connected to the power grid, the ENF signals are embedded. The time-varying nature of the ENF component is used as a forensic application for authenticating the surveillance feed. The paper highlights the ENF signal collection from a power grid creating a reference database and ENF extraction from the recordings using conventional short-time Fourier Transform and spectrum detection for robust ENF signal analysis in the presence of noise and interference caused in different harmonics. The experimental results demonstrate the effectiveness of ENF signal detection and/or abnormalities for FFI attacks.

In this paper, we study the weighted reproducing kernels. We introduce a generalization of weighted reproducing property and extend it to relative reproducing property on Banach spaces. This generalization will develop the parallel computing and it can be used as a base of parallel learning for machines especially in the case that there are non-homogenous weighted hypothesis. This methods formulate learning and estimation problems in a relative reproducing kernel Banach space (RRKBS) of functions defined on the data domain, expanded in terms of a kernel.

ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid. ARBTools was developed for simulations of magnetic molecular traps, in which the magnitude, gradient and vector components of a magnetic field are required. Numerical integrators for solving particle trajectories are included, but the core interpolator can be used for any scalar or vector field. The only additional system requirements are NumPy.

In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension for the sake of simplicity. The underlying finite volume scheme is conservative and it is accurate up to the second order in space. The main novelty consists in the motion of the grid. This new dynamic aspect can be used to resolve better the areas with high solution gradients or any other special features. No interpolation procedure is employed, thus an unnecessary solution smearing is avoided. Thus, our method enjoys excellent conservation properties. The resulting grid is completely redistributed according the choice of the so-called monitor function. Several more or less universal choices of the monitor function are provided. Finally, the performance of the proposed algorithm is illustrated on several examples stemming from the simple linear advection to the simulation of complex shallow water waves. We believe that the techniques described in our paper can be beneficially used to model tsunami wave propagation and run-up.

During the exploration of the surrounding environment, the brain links together external inputs, giving rise to perception of a persisting object.  During imaginative processes, the same object can be recalled in mind even if it is out of sight.   Here, topological theory of shape provides a mathematical foundation for the notion of persistence perception.  In particular, we focus on ecological theories of perception, that account for our knowledge of world objects by borrowing a concept of invariance in topology.  We show how a series of transformations can be gradually applied to a pattern, in particular to the shape of an object, without affecting  its invariant properties, such as boundedness of parts of a visual scene. High-level representations of objects in our environment are mapped to simplified views (our interpretations) of the objects, in order to construct a symbolic representation of the environment.  The representations can be projected continuously to an environmental object that we have seen and continue to see, thanks to the mapping from shapes in our memory to shapes in Euclidean space.

Robotic path planning is a field of research which is gaining traction given the broad domains of interest to which path planning is an important systemic requirement; the aim being to optimise the efficacy of robotic movements in a defined operational environment. For example, robots have been employed in many domains including: cleaning robots (such as vacuum cleaners), automated paint spraying robots, window cleaning robots, forest monitoring robots, agricultural robots (often driven using satellite and geostationary positional satellite data). Additionally, mobile robotic systems have been utilised in disaster areas and locations hazardous to humans (such as war zones in mine clearance). The coverage path planning problem describes an approach which is designed to determine the path that traverses all points in a defined operational environment while avoiding static and dynamic (moving) obstacles. In this paper we present our proposed Smooth-STC model, the aim of the model being to identify an optimal path, avoid all obstacles, prevent (or at least minimise) backtracking, and maximise the coverage in any defined operational environment. The experimental results in a simulation show that, in uncertain environments, our proposed smooth STC method achieves an almost absolute coverage rate and demonstrates improvement when measured against alternative conventional algorithms.

Digital Evidence is considered as an important type of evidence in many legal cases. Many legislations have dedicated laws to the collection, handling and admissibility of digital evidence. New technologies and new devices are rapidly being developed, which creates new sources of digital evidence. This presents a challenge to law enforcement agencies and digital investigators to stay up to date with the rapid development in the digital field. This paper discusses a relatively new source of digital evidence which is the evidence extracted from Wearable devices. A Fitbit fitness tracker is one of the most common wearable devices used by many people today. This paper presents a case study whereby data extracted from a Fitbit was used as a digital evidence. The admissibility and the challenges of using Wearables as digital evidence is also discussed.

A non-Newtonian fluid model is used to investigate the two-dimensional pulsatile blood flow through a tapered artery with a stenosis. The mixed convection effects of heat and mass transfer are also taken into account. By applying non-dimensionalization and radial coordinate transformation, we simplify the system in a tube. Under the finite difference scheme, numerical solutions are calculated for velocity, temperature concentration, resistance, impedance, wall shear stress and shearing stress at the stenosis throat. Finally, Quantitative analysis is carried out.

Steganography is the branch of cryptology that deals with concealing information inside another information. it’s prefer over cryptography as it hides a message inside another innocent looking message, while cryptography shows scrambled message that might arouse attention of an attacker, however the challenges in steganography is the modification of carrier that causes some abnormalities which is detectable and often the methods are not optimize. This paper presents a novel approach in cryptography and steganography, which utilizes mathematical concept of bits combination to optimize time of transmission using sets of multiple transmitter, and receiver’s addresses where each abstractly represents a bits combination without itself modified. In addition, the paper introduces a concept of dynamical clockwise and anti-clockwise rotation of bits combination over addresses after every transmission to reinforce resistivity against steganalysis.

Several specific types of generalized compactness of generalized topological spaces have been defined, investigated and related to compactness in ordinary topological spaces from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized compactness in a generalized topological space is reported herein as a starting point for more generalized classes.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

We present smooth approximations to $ \vert{x} \vert $ using sigmoid functions. In particular $ x\,erf(x/\mu) $ is proved to be better smooth approximation for $ \vert{x} \vert $ than $ x\,tanh(x/\mu) $ and $ \sqrt{x^2 + \mu} $ with respect to accuracy. To accomplish our goal we also provide sharp hyperbolic bounds for error function.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

Designing motion representations for the problem of 3D human action recognition from skeleton sequences is an important yet challenging task. An effective representation should be robust to noise, invariant to viewpoint changes and result in a good performance with low-computational demand. Two main challenges in this task include how to efficiently represent spatio-temporal patterns of skeletal movements and how to learn their discriminative features for classification task. This paper presents a novel skeleton-based representation and a deep learning framework for 3D action recognition using RGB-D sensors. We propose to build an action map called SPMF (Skeleton Posture-Motion Feature), which is a compact image representation built from skeleton poses and their motions. An Adaptive Histogram Equalization (AHE) algorithm is then applied on the SPMF to enhance their local patterns and form an enhanced action map, namely Enhanced-SPMF. For learning and classification tasks, we exploit Deep Convolutional Neural Networks based on the DenseNet architecture to learn directly an end-to-end mapping between input skeleton sequences and their action labels via the Enhanced-SPMFs. The proposed method is evaluated on four challenging benchmark datasets, including both individual actions, interactions, multiview and large-scale datasets. The experimental results demonstrate that the proposed method outperforms previous state-of-the-art approaches on all benchmark tasks, whilst requiring low computational time for training and inference.

Although Shannon mutual information has been widely used, its effective calculation is often difficult for many practical problems, including those in neural population coding. Asymptotic formulas based on Fisher information sometimes provide accurate approximations to the mutual information but this approach is restricted to continuous variables because the calculation of Fisher information requires derivatives with respect to the encoded variables. In this paper, we consider information-theoretic bounds and approximations of the mutual information based on Kullback--Leibler divergence and Rényi divergence. We propose several information metrics to approximate Shannon mutual information in the context of neural population coding. While our asymptotic formulas all work for discrete variables, one of them has consistent performance and high accuracy regardless of whether the encoded variables are discrete or continuous. We performed numerical simulations and confirmed that our approximation formulas were highly accurate for approximating the mutual information between the stimuli and the responses of a large neural population. These approximation formulas may potentially bring convenience to the applications of information theory to many practical and theoretical problems.

Age-in-place can reduce the progress of dementia syndrome and improve the quality of life of the sufferers and their families. This work proposes an innovative information home support system to be established at the houses of people suffering from dementia. The main innovation of the system are its transparent character that overcomes the need for training of the sufferer, as well as the exploitation of a well-known technique for dementia, namely music therapy. It addresses the need of people suffering from dementia as well as their familiars to be recognized by them and have better interaction and collaboration. The system offers a ubiquitous recognition system, just by using smart devices like smart-phones or smart-wristbands. When a familiar person is detected in the house, then a sound file is reproduced on smart speakers placed in the house, in order to trigger the memory, based on the principles of music therapy. The system reproduced the appropriate time at 100% of the cases and the benefits of music therapy are evident daily. To the best of the authors' knowledge, this is the first system of its kind ever reported in the literature.

In financial time series modelling and forecasting, combining ARMA and GARCH models tend to produce superior and reliable models for volatility persistence, half-life volatility and backtesting (application of model in real life). In Nigeria, banking stocks are mostly traded because of its potential benefits to investors. This study modelled and forecasted the Guaranty Trust (GT) Bank daily stock returns from January 2^nd 2001 to May 8^th 2017 data set collected from a secondary source. The ARMA-GARCH models, persistence, half-life and backtesting were used to analysed the collected data using student t and skewed student t distributions, and the analyses are carried out R environment using rugard and performanceAnaytics Packages. The study revealed that using the lowest information criteria values only could be misleading rather we added the use of backtesing. The ARMA(1,1)-GARCH(1,1) models fitted exhibited high persistency in the daily stock returns while the days it takes for mean-reverting of the models ranges from 5 days to 100 days but unfortunately the models failed backtesting. The results further revealed ARMA(1,1)-eGARCH (2,2) model with student t distribution provides a suitable model for evaluating the GT bank stock returns among the competing models while it takes less than 30 days for the persistence volatility to return back to its average value of the stock returns. This study recommended that researchers should adopt backtesting approach while fitting GARCH models while GT bank stocks investor should be assured that no matter the fluctuations in the stock market, the GT bank stock returns has the ability to returns to its mean price return.

This article will provide an overview on internet of things (IoT), 5G communication System and Distributed Clouds. The basic concepts and benefits will be briefly presented, along with current standardization activities. In a nutshell, but the research will focus on relating internet of things, 5G and Distributed Cloud Computing.

The speech entailed in human voice comprises essentially para-linguistic information used in many voice-recognition applications. Gender voice-recognition is considered one of the pivotal parts to be detected from a given voice, a task that involves certain complications. In order to distinguish gender from a voice signal, a set of techniques have been employed to determine relevant features to be utilized for building a model from a training set. This model is useful for determining the gender (i.e, male or female) from a voice signal. The contributions are involved in two folds: (i) providing analysis information about well-known voice signal features using a prominent dataset, (ii) studying various machine learning models of different theoretical families to classify the voice gender, and (iii) using three prominent feature selection algorithms to find promisingly optimal features for improving classification models. Experimental results show the importance of sub-features over others, which are vital for enhancing the efficiency of classification models performance. Experimentation reveals that the best recall value is equal to 99.97%; 99.7% of two models of Deep Learning (DL) and Support Vector Machine (SVM) and with feature selection the best recall value is 100% for SVM techniques.

This paper considers estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the Log--Huber loss function which is resistant to outliers and useful to find robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of Bayesian risk function with themselves as well as the usual plug-in density ratio estimators. Some applications such as classification and divergence function estimation are addressed.

In this paper, we introduce the bicomplex Tetranacci and Tetranacci-Lucas quaternions. Moreover, we present Binet's formulas, generating functions, and the summation formulas for those bicomplex quaternions.

In this paper, we study the convergence of new implicit iterations dealing with n-tupled fixed point results for nonlinear contractive-like mappings on W-hyperbolic metric spaces. Herein, we demonstrate that our newly implicit iteration schemes have faster rate of convergence than implicit S-iteration process, implicit Ishikawa and Mann type iteration processes. Furthermore, a numerical simulation to improve our theoretical results is obtained.

Matiyasevich's theorem states that there is no algorithm to decide whether or not a given Diophantine equation has a solution in non-negative integers. Smorynski's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. We prove: (1) Smorynski's theorem easily follows from Matiyasevich's theorem, (2 ) Hilbert's Tenth Problem for Q has a negative solution if and only if the set of all Diophantine equations with a finite number of rational solutions is not recursively enumerable.

In this paper we use Toeplitz quantization to extend in a very natural way Kostant's theorem for the group $SU(m)$ to the group of symplectomorphisms of the unit sphere and we also give another proof of the infinite dimensional version of Schur and Horn theorem for the sphere based on Schur and Horn theorem for Hermitian matrices.

In standard construction of hyperrational numbers using ultra-power we assume that the ultralter is selective. It makes possible toassign real value to any nite hyperrational number. So, we can consider hyperrational numbers with selective ultralter as extension of traditional real numbers. Also proved the existence of strictly monotonic or stationary representing sequence for any hyperrational number.

In the past few decades, probabilistic interpretations of brain functions have become widespread in cognitive science and neuroscience. In particular, the free energy principle and active inference are increasingly popular theories of cognitive functions that claim to offer a unified understanding of life and cognition within a general mathematical framework derived from information and control theory, and statistical mechanics. However, we argue that if the active inference proposal is to be taken as a general process theory for biological systems, it is necessary to understand how it relates to existing control theoretical approaches routinely used to study and explain biological systems. For example, recently, PID control has been shown to be implemented in simple molecular systems and is becoming a popular mechanistic explanation of behaviours such as chemotaxis in bacteria and amoebae, and robust adaptation in biochemical networks. In this work, we will show how PID controllers can fit a more general theory of life and cognition under the principle of (variational) free energy minimisation when using approximate linear generative models of the world. This more general interpretation provides also a new perspective on traditional problems of PID controllers such as parameter tuning as well as the need to balance performances and robustness conditions of a controller. Specifically, we then show how these problems can be understood in terms of the optimisation of the precisions (inverse variances) modulating different prediction errors in the free energy functional.

This paper proposes a smart system of virus detection that can classify a file as benign or malware with high accuracy detection rate. The approach is based on the aspects of the artificial immune system and the deep learning technique. The first stage is data extraction to create the main feature set. In the second stage, the Artificial Immune Network (aiNet) is used to build a clonal generation of malware detectors and improve the accuracy of unknown virus detection rate. Then they are trained with a deep belief network model to evaluate the performance of the system. As a result, our method can achieve a high detection rate of 98.86% on average with a very low false positive rate.

In the article, by applied the concept of strongly convex function and one known identity, we establish several Ostrowski type inequalities involving conformable fractional integrals. As applications, some new error estimations for the midpoint formula are provided as well.

Deep learning has taken over - both in problems beyond the realm of traditional, hand-crafted machine learning paradigms as well as in capturing the imagination of the practitioner sitting on top of petabytes of data. While the public perception about the efficacy of deep neural architectures in complex pattern recognition tasks grows, sequentially up-to-date primers on the current state of affairs must follow. In this review, we seek to present a refresher of the many different stacked, connectionist networks that make up the deep learning architectures followed by automatic architecture optimization protocols using multi-agent approaches. Further, since guaranteeing system uptime is fast becoming an indispensable asset across multiple industrial modalities, we include an investigative section on testing neural networks for fault detection and subsequent mitigation. This is followed by an exploratory survey of several application areas where deep learning has emerged as a game-changing technology - be it anomalous behavior detection in financial applications or financial time-series forecasting, predictive and prescriptive analytics, medical imaging, natural language processing or power systems research. The thrust of this review is on outlining emerging areas of application-oriented research within the deep learning community as well as to provide a handy reference to researchers seeking to embrace deep learning in their work for what it is: statistical pattern recognizers with unparalleled hierarchical structure learning capacity with the ability to scale with information.

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In this review paper, we present a pellucid proof of how x tanh(x/µ) approximates |x|and is better than  √x² +µ  when we are concernedwith accuracy.  

We examine the extensions of the basic arithmetical operations of addition and multiplication on the natural numbers into higher-rank hyper-operations also on the natural numbers. We go on to define the concepts of prime and composite numbers under these hyper-operations and derive some results about factorisation, resulting in fundamental theorems analogous to the Fundamental Theorem of Arithmetic.

Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing.  This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.   

We present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for the involutive uninorm logic IUL is proved. Then the standard completeness of IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.

Our method for density elimination is generalized to the non-commutative substructural logic GpsUL∗. Then the standard completeness of HpsUL∗follows as a lemma by virtue of previous workbyMetcalfeandMontagna. This result shows that HpsUL∗ is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis.

With the increase of the Artificial Neural Network (ANN), machine learning has taken a forceful twist in recent times. One of the most spectacular kinds of ANN design is the Convolutional Neural Network (CNN). The Convolutional Neural Network (CNN) is a technology that mixes artificial neural networks and up to date deep learning strategies. In deep learning, Convolutional Neural Network is at the center of spectacular advances. This artificial neural network has been applied to several image recognition tasks for decades and attracted the eye of the researchers of the many countries in recent years as the CNN has shown promising performances in several computer vision and machine learning tasks. This paper describes the underlying architecture and various applications of Convolutional Neural Network.

This paper aims at tackling with the task of fusion feature from images and its corresponding point clouds for 3D object detection in autonomous driving scenarios basing on AVOD, an Aggregate View Object Detection network. The proposed fusion algorithms fuse features targeted from Bird’s Eye View (BEV) LIDAR point clouds and its corresponding RGB images. Differs in existing fusion methods, which are simply the adoptions of concatenation module, element-wise sum module or element-wise mean module, our proposed fusion algorithms enhance the interaction between BEV feature maps and its corresponding images feature maps by designing a novel structure, where single level feature maps and another utilizes multilevel feature maps. Experiments show that our proposed fusion algorithm produces better results on 3D mAP and AHS with less speed loss comparing to existing fusion method used on the KITTI 3D object detection benchmark.

We give a topological condition for a generic sliced space to be globally hyperbolic, without any hypothesis on the lapse function, shift function and spatial metric.

We report on an exploratory study conducted at a graduate school in Sweden with a humanoid robot, Baxter. First, we describe a list of potentially useful capabilities for a robot teaching assistant derived from brainstorming and interviews with faculty members, teachers, and students. These selected capabilities consist of reading, greeting, alerting, remote operation, clarification, and motion. Second, we present feedback on how the robot's capabilities, demonstrated in part with the Wizard of Oz approach, were perceived, and iteratively adapted over the course of several lectures, using the \EP tool. Third, we discuss observations and findings regarding the capabilities and the development process. Our findings suggest that using a social robot as a teaching assistant is promising using the chosen capabilities. We find that personalizing the capabilities and the role of embodiment are important topics to be considered in future work.

This paper has two major parts. In the first part histogram equalization for the image enhancement was implemented without using the built-in function in MATLAB. Here, at first, a color image of a rat was chosen and the image was transformed into a grayscale image. After this conversion, histogram equalization was implemented on the grayscale image. Later on, in the same image for each RGB channel, histogram equalization was implemented to observe the effect of histogram equalization on each channel. In the end, the histogram equalization was implemented to this specific color image of a rat. In the second part, for the grayscale image in part 1, the desired histogram of another colored image of a rat was introduced and histogram specification was implemented on the original colored image.

In recent years, CPU caches have revealed themselves as one of the most powerful sources of information leakage. This information leakage affects any implementation whose memory accesses, to data or instructions, depend on sensitive information such as private keys. In most cases, side-channel cache attacks do not require any specific permission and just need access to a shared cache. This fact, combined with the spread of cloud computing, where the infrastructure is shared between different customers, have made these attacks quite popular. In this paper, we present a novel approach to exploit the information obtained from the CPU cache. First, we introduce a non-access attack that provides a 97\% reduction in the number of encryptions required to obtain a 128-bit AES key. Next, this attack is adapted and extended in what we call the encryption-by-decryption cache attack or EBD, to obtain a 256-bit AES key. When EBD is applied to AES-256, we are able to obtain the 256 bits of the key with less than 10000 encryptions. These results make EBD, to the best of our knowledge, the first practical attack on AES-256 and also demonstrate that AES-256 is only about 3 times more complex to attack than AES-128 via cache attacks. In both cases the target is the AES T-table-based implementation, and we also demonstrate that our approach works in a cross-VM scenario.

Estimation and planning play a vital role in the construction of an autonomous navigation framework. However, these problems are often considered separately, while planning gives robot a free-collision path towards the desired goal, estimation algorithm presents the executed trajectory in the sense that it has to be closed to the ground truth path as much as possible. Recently, a unified probabilistic framework, which supports solving these problems simultaneously, dubbed STEAP has been proposed. Nevertheless, its current version is only designated for an omni wheels robot, which allows robot to move and turn in vertical direction. Differential drive robot, on the other hand, though limited to move along only one direction, has been used in various situations due to its flexibility and lower cost in hardware designing. Thus, in this extension, our aim is to control a differential drive robot via STEAP. Moreover, in a more complicated environment such as labyrinth or maze, the original STEAP sometimes fails to find a path. Indeed, this problem is mainly caused by the poor initialization and the non-linearity in optimizer constraints. In our implementation, instead of dealing with these constraints, we employ a global planner algorithm such as Dijkstra or RRT to treat STEAP as an effective local planner module that focus on following the global path. Consequently, the experimental results show that the extended STEAP not only able to navigate a differential drive robot but also in a more complicated and unstructured environment.

Komlos conjecture is about the existing of a universal constant K such that for all dimension n and any collection of vectors (V_1 ) ⃗ ,…,(V_n ) ⃗ ∈R^n with ‖(V_i ) ⃗ ‖_2≤1 , there are weights ε_i∈{-1,1} in such that ‖∑_(i=1)^n▒〖ϵ_i (V_i ) ⃗ 〗‖_∞≤K(n)≤K. In this paper, the constant K(n) is evaluated for n≤5 to be K(2)=√2, K(3)=(√2+√11)/3, K(4)=√3, and K(5)=(4+√142)/9. For higher dimension, the function f(n)=√(n-⌈〖 log〗_2 (2^(n-1)⁄n)⌉ ) is found to be the lower bound for the constant K(n), from where it can be concluded that the Komlos conjecture is false i.e., the universal constant K=max┬(‖(V_i ) ⃗^* ‖_2≤1)⁡min┬(ε_i=±1)⁡〖‖∑_(i=1)^n▒〖ϵ_i (V_i ) ⃗^* 〗‖_∞ 〗 does not exsit because of lim┬(n→∞)⁡〖K(n)≥lim┬(n→∞)⁡√(log⁡(n)-1)=+∞〗.

In this paper, at first, a color image of a car is taken. Then the image is transformed into a grayscale image. After that, the motion blurring effect is applied to that image according to the image degradation model described in equation 3. The blurring effect can be controlled by a and b components of the model. Then random noise is added in the image via Matlab programming. Many methods can restore the noisy and motion blurred image; particularly in this paper Inverse filtering as well as Wiener filtering are implemented for the restoration purpose. Consequently, both motion blurred and noisy motion blurred images are restored via Inverse filtering as well as Wiener filtering techniques and the comparison is made among them.

Thresholding is considered as a statistical-decision making theory which can lessen the average error incurred in allocating pixels to two or more groups. The traditional Bayes decision rule can be applied with the prior knowledge of the Probability Density Function (PDF) of each class. It is surmised that a threshold resulting in the best class separation is the optimal one. In this paper, Otsu’s thresholding for image segmentation has been implemented. The well-known Otsu’s method is to learn a threshold that can maximize the between-class variance or equivalently make light of the within-class variance of the entire image. At first, a color image of a tree is taken. After that, the image is transformed into a grayscale image. Then in the first part, two-level thresholding is conducted, and later on, three-level thresholding is also applied. Again, two-level thresholding, as well as three level thresholding, are also applied to some other images. Finally, the comparison is made between two level thresholding and three level thresholding

In this work, we establish some new Hermite-Hadamard type inequalities for convex functions via conformable fractional integral. Moreover, we show that through the conformable fractional integral we can find some new Hermite-Hadamard type inequalities for convex functions via the classical integrals.

The aim of this research work was to provide model for predicting stock volatility in Nigeria Stock market. To achieve this, monthly data for Nigerian stock exchange, Exchange rate, Share index and inflation rate was collected for a period of January 1990 to December 2016.The descriptive statistics revealed these variables to exhibit volatility as a characteristics of financial time –varying series. DCC Model was fitted, were the coefficients for all the parameters and that of the correlation-Targeting (rho_21) are both negative and positive and tend very close to 1 and -1, indicating that high persistence in the conditional variances. The Model DCC, satisfied the properties of a good model of conditional mean and variance of the confidential Interval (C.I) of 1 and -1, that is, the conditional variances are finites and their series are strictly stationary. This therefore implies that the Nigerian Stock Exchange, Exchange rate, share index and Inflation rate will experience a non-steady shock in the Stock market. However Each of these variables have different length of recovery (volatility half- life)  ranging from 1.5month, 6.5months, 6months to 2,4months   for stock exchange, exchange rate, share index and inflation rate respectively. By implication, the volatility of these variables had a long memory, persistence and mean-reverting.

Clustering is an important task in data mining that has become more challenging due to the ever-increasing size of available datasets. To cope with these big data scenarios, a high-performance clustering approach is required. Sparse grid clustering is a density-based clustering method that uses a sparse grid density estimation as its central building block. The underlying density estimation approach enables the detection of clusters with non-convex shapes and without a predetermined number of clusters. In this work, we introduce a new distributed and performance-portable variant of the sparse grid clustering algorithm that is suited for big data settings. Our compute kernels were implemented in OpenCL to enable portability across a wide range of architectures. For distributed environments, we added a manager-worker scheme that was implemented using MPI. In experiments on two supercomputers, Piz Daint and Hazel Hen, with up to 100 million data points in a 10-dimensional dataset, we show the performance and scalability of our approach. The dataset with 100 million data points was clustered in 1198s using 128 nodes of Piz Daint. This translates to an overall performance of 352TFLOPS. On the node-level, we provide results for two GPUs, Nvidia's Tesla P100 and the AMD FirePro W8100, and one processor-based platform that uses Intel Xeon E5-2680v3 processors. In these experiments, we achieved between 43% and 66% of the peak performance across all compute kernels and devices, demonstrating the performance portability of our approach.

E-commerce businesses employ recommender models to assist in identifying a personalized set of products for each visitor. To accurately assess the recommendations’ influence on customer clicks and buys, three target areas—customer behavior, data collection, user-interface —will be explored for possible sources of erroneous data. Varied customer behavior misrepresents the recommendations’ true influence on a customer due to the presence of B2B interactions and outlier customers. Non-parametric statistical procedures for outlier removal are delineated and other strategies are investigated to account for the effect of a large percentage of new customers or high bounce rates. Subsequently, in data collection we identify probable misleading interactions in the raw data, propose a robust method of tracking unique visitors, and accurately attributing the buy influence for combo products. Lastly, user-interface issues discuss the possible problems caused due to the recommendation widget’s positioning on the e-commerce website and the stringent conditions that should be imposed when utilizing data from the product listing page. This collective methodology results in an exact and valid estimation of the customer’s interactions influenced by the recommendation model in the context of standard industry metrics such as Click-through rates, Buy-through rates, and Conversion revenue.

In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs, due to the flexibility with respect to geometry and high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focus towards localized radial basis function approximations, as the local meshless method is proposed here. The local meshless procedures is used for spatial discretization whereas for temporal discretization different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation using regular and irregular domains.

The aim of this work is to study generalizations of the notion of mean. Kolmogorov proposed a generalization based on an improper integral with a decay rate for the tail probabilities. This weak or Kolmogorov mean relates to the Weak Law of Large Numbers in the same way that the ordinary mean relates to the Strong Law. We propose a further generalization, also based on an improper integral, called the doubly weak mean, applicable to heavy-tailed distributions such as the Cauchy distribution and the other symmetric stable distributions, We also consider generalizations arising from Abel-Feynman type mollifiers that damp the behavior at infinity and alternative formulations of the mean in terms of the cumulative distribution and the characteristic function.

We study the effectiveness of various machine learning techniques, including artificial neural networks, support vector machine, logistic regression, K-nearest neighbors, decision tree and Naive Bayesian, for detecting and mitigating power jamming attacks in optical networks. Our study shows that artificial neural network is the most accurate in detecting out-of-band power jamming attacks in optical networks. To further mitigating the power jamming attacks, we apply a new resource reallocation scheme that utilizes the statistical information of attack detection accuracy, and propose a resource reallocation algorithm to lower the probability of successful jamming of lightpaths. Simulation results show that higher the accuracy of detection, lower is the likelihood of jamming a lightpath.

IoT is a new communication paradigm that gains a very high importance in the past few years. This communication paradigm supports various heterogeneous applications in many fields and with the dramatic increase of the number of sensor devices, it becomes a demand. Designing IoT networks faces many challenges that include security, massive traffic, high availability, high reliability and energy constraints. Thus, new communication technologies and paradigms should be deployed for IoT networks to overcome these challenges and achieve high system performance. Distributed computing techniques (e.g. fog and MEC), software defined networking (SDN), network virtualization and blockchain are common recent paradigms that should be deployed for IoT networks, either combined or individually, to achieve the main requirements of the IoT networks at a high system performance. Fog computing is a form of edge computing that has been developed to provide the computing capabilities (e.g. storage and processing) at the edge of the access network. Employing Fog computing in IoT networks, as an intermediate layer between IoT devices and the remote cloud, becomes a demand to make use of the edge computing benefits. In this work, we provide a framework for the IoT system structure that employs an edge computing layer of Fog nodes controlled and managed by SDN network with the blockchain technology to achieve a high level of security for latency sensitive IoT applications. The proposed system employs SDN network with distributed controllers and distributed OpenFlow switches; these switches are enabled with limited computing and processing capabilities.  Furthermore, a data offloading algorithm is developed to allocate different processing and computing tasks to the distributed OpenFlow switches with available resources. Moreover, a traffic model is proposed to model and analyze the traffic among different parts of the network. The proposed work achieves various benefits to the IoT network, such as the latency reduction, security improvement and high efficiency of resources utilization. The proposed algorithm is simulated and also the proposed system is experimentally tested over a developed testbed to validate the proposed structure. Experimental results show that the proposed system achieves higher efficiency in terms of latency, security and resource utilization.

The present reality of the Nigerian economy is the fact that inflation has remained unabated in spite of all exchange rate measures that have been adopted by the monetary authority. This calls for investigation into the extent to which exchange rate impact on inflation in Nigeria. The research paper examined the impact of exchange rate depreciation on inflation in Nigeria for the period 1981–2017, using Auto Regressive Distributed Lag (ARDL) Bounds Test Cointegration Procedure. The research shows that inflation rate in Nigeria is highly susceptible to lagged inflation rate, exchange rate, lagged exchange rate, lagged broad money, and lagged gross domestic product at 5% level of significance. A long run relationship was also found to exist between inflation rate, gross domestic product and general government expenditure, indicating that the model has a self-adjusting mechanism for correcting any deviation of the variables from equilibrium. Therefore, this study concludes that exchange rate is an important tool to manage inflation in the country; thus, this paper recommends that policies that have direct influence on inflation as well as exchange rate policies that would checkmate inflation movement in the country, should be used by the Central Bank of Nigeria. Also, monetary growth and import management policies should be put in place to encourage domestic production of export commodities, which are currently short-supplied. In addition, policy makers should not rely on this instrument totally to control inflation, but should use it as a complement to other macro-economic policies.

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered a new class of orthogonal polynomials on the real line. One of these is a four-parameter polynomial with a discrete spectrum. Another that appeared while solving a Heun-type equation has a mix of continuous and discrete spectra. Based on these results and on our recent study of the solution space of an ordinary differential equation of the second kind with four singular points, we introduce a modification of the hypergeometric polynomials in the Askey scheme. Up to now, all of these polynomials are defined only by their three-term recursion relations and initial values. However, their other properties like the weight function, generating function, orthogonality, Rodrigues-type formula, etc. are yet to be derived analytically. This is an open problem in orthogonal polynomials.

In this paper, we look at how Artificial Swarm Intelligence can evolve using evolutionary algorithms that try to minimize the sensory surprise of the system. We will show how to apply the free-energy principle, borrowed from statistical physics, to quantitatively describe the optimization method (sensory surprise minimization), which can be used to support lifelong learning. We provide our ideas about how to combine this optimization method with evolutionary algorithms in order to boost the development of specialized Artificial Neural Networks, which define the proprioceptive configuration of particular robotic units that are part of a swarm. We consider how optimization of the free-energy can promote the homeostasis of the swarm system, i.e. ensures that the system remains within its sensory boundaries throughout its active lifetime. We will show how complex distributed cognitive systems can be build in the form of hierarchical modular system, which consists of specialized micro-intelligent agents connected through information channels. We will also consider the co-evolution of various robotic swarm units, which can result in development of proprioception and a comprehensive awareness of the properties of the environment. And finally, we will give a brief outline of how this system can be implemented in practice and of our progress in this area.

Timely detection of surface damages on wind turbine blades is imperative for minimising downtime and avoiding possible catastrophic structural failures. With recent advances in drone technology, a large number of high-resolution images of wind turbines are routinely acquired and subsequently analysed by experts to identify imminent damages. Automated analysis of these inspection images with the help of machine learning algorithms can reduce the inspection cost, thereby reducing the overall maintenance cost arising from the manual labour involved. In this work, we develop a deep learning based automated damage suggestion system for subsequent analysis of drone inspection images. Experimental results demonstrate that the proposed approach could achieve almost human level precision in terms of suggested damage location and types on wind turbine blades. We further demonstrate that for relatively small training sets advanced data augmentation during deep learning training can better generalise the trained model providing a significant gain in precision.

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

This paper predict and effectively control the temperature distribution of the steady-state and transient states of anisotropic four-layer composite materials online, knowing the density, specific heat, heat conductivity and thickness of the composite materials. Based on the transfer function, a mathematical model was established to study the dynamic characteristics of heat transfer of the composite materials. First of all, the Fourier heat transfer law was used to establish a one-dimensional Fourier heat conduction differential equation for each composite layer, and the Laplace transformation was carried out to obtain the system function. Then the approximate second-order transfer function of the system was obtained by Taylor expansion, and the Laplace inverse transformation was carried out to obtain the transfer function of the whole system in the time domain. Finally, the accuracy of the simplified analytical solutions of the first, second and third order approximate transfer functions was compared with computer simulation. The results showed that the second order approximate transfer functions can describe the dynamic process of heat transfer better than others. The research on the dynamic characteristics of heat transfer in the composite layer and the dynamic model of heat transfer in composite layer proposed in this paper have a reference value for practical engineering application. It can effectively predict the temperature distribution of composite layer material and reduce the cost of experimental measurement of heat transfer performance of materials.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

In most econometrics literature, the Autoregressive Distributed Lag (ARDL) model is often applied in many economic analyses to study short and long run relationships. This is because ARDL model can deal with economic variables that are integrated of different order (I(0), I(1) or combination of both) and also it is robust where there is single long-run relationship between the underlying variables in a simple sample size. This study applied the ARDL model to examine the contributions of commercial Banks to GDP growth in Nigeria. To achieve this, annual data covering 1981 to 2015 for loans and advances, savings, lending rates and GDP of Financial Institutions were collected from CBN bulletin. The ADF test revealed that the variables are I(1) except for lending rate which was of I(0) order. The ARDL(1,1,1,2) model revealed that loans and advances, and lending rates are significantly positively related to GDP in Nigeria but savings was not significant in the model. The model revealed some evidence of short run relationships while the ecm(-1) was -0.6156 (P-value=0.0038<0.05) which means that the rate of the speed of adjustment to equilibrium is 61.56% annually. The estimated model is free from serial correlation, multicollinearity, heteroscedasticity while the model is stable and the residuals are normally distributed. The study recommends that savings and savings culture should be encouraged in Nigeria since economic theory states that savings and investment are related in any economic development.

We derive a concentration inequality for the uncertainty in stratied random sampling. Minimising this inequality leads to an iterated online method for choosing samples from the strata. The inequality is versatile and considers a range of factors including: the data ranges, weights, sizes of the strata, as well as the number of samples taken, the estimated sample variances and whether strata are sampled with or without replacement. We evaluate the improvement this method reliably offers against other methods over sets of synthetic data, and also in approximating the Shapley value of cooperative games. The method is seen to be competitive with the performance of perfect Neyman sampling, even without prior information on strata variances. We supply a multidimensional extension of our inequality and discuss some future applications.

The dark proteome as we define it, is the part of the proteome where 3D structure has not been observed either by homology modeling or by experimental characterization in the protein universe. From the 550.116 proteins available in Swiss-Prot (as of July 2016) 43.2% of the Eukarya universe and 49.2% of the Virus universe are part of the dark proteome. In Bacteria and Archaea, the percentage of the dark proteome presence is significantly less, with 12.6% and 13.3% respectively. In this work, we present the map of the dark proteome in Human and in other model organisms. The most significant result is that around 40%- 50% of the proteome of these organisms are still in the dark, where the higher percentages belong to higher eukaryotes (mouse and human organisms). Due to the amount of darkness present in the human organism being more than 50%, deeper studies were made, including the identification of ‘dark’ genes that are responsible for the production of the so-called dark proteins, as well as, the identification of the ‘dark’ organs where dark proteins are over represented, namely heart, cervical mucosa and natural killer cells. This is a step forward in the direction of the human dark proteome.

The geometry of Poincare disk itself is interpreted without any mapping to dierent spaces. Our approach might be one of the shortest and is intended for educational contribution.

Multispectral remote sensing data may contain component images which are heavily corrupted by noise and pre-filtering (denoising) procedure is often applied to enhance these component images. To do this, one can use reference images – component images having relatively high quality and which are similar to the image subject to pre-filtering. Here we study the following problems: how to select component images that can be used as references (e.g., for the Sentinel multispectral remote sensing data) and how to perform the actual denoising. We demonstrate that component images of the same resolution as well as component images of a better resolution can be used as references. Examples of denoising of real-life images demonstrate high efficiency of the proposed approach.

In this paper we define a continuous wavelet transform of a Schwartz tempered distribution $f \in S^{'}(\mathbb R^n)$ with wavelet kernel $\psi \in S(\mathbb R^n)$ and derive the corresponding wavelet inversion formula interpreting convergence in the weak topology of $S^{'}(\mathbb R^n)$. It turns out that the wavelet transform of a constant distribution is zero and our wavelet inversion formula is not true for constant distribution, but it is true for a non-constant distribution which is not equal to the sum of a non-constant distribution with a non-zero constant distribution.

Multigranulation is a new approach to the Rough Set Theory, where several separability relationships are used to obtain different granulations of the universe. The Multigranulation starts from the existence of different contexts or subsets of features to characterize the objects of the universe. In this paper, a method for the generation of contexts from the construction of similarity relations is proposed.The proposed solution was evaluated in an international database using the KNN classifier. It was also applied in the solution of a real problem in Civil Engineering specifically in Traffic Engineering, the contexts generated from the proposal used to determine the features of higher incidence in the service level of the road. The results achieved both in the international database and in the proposed application demonstrate the applicability of the proposed method.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}

An SIRS (Susceptible–Infected–Removed-Susceptible) mathematical model for the transmission dynamics of the Transfusion–Transmitted Malaria (TTM) model with optimal control pair u₁(t) and u₂(t) was developed and studied in this research work. The model Transfusion–Transmitted Malaria disease–free equilibrium and endemic equilibriums points were determined. The model exhibited two equilibriums; disease-free and endemic equilibrium. It is shown that the disease–free equilibrium was locally asymptotically stable if the associated basic reproduction numbers R₀ is less than unity while the disease persists if R₀ is greater than unity. The global stability of the Transfusion–Transmitted Malaria model at the disease-free equilibrium was established using the comparison method. The optimality system was derived and an optimal control model of blood screening and drug treatment for the Transfusion–Transmitted Malaria model was investigated. Conditions for the optimal control were considered using Pontryagin’s Maximum Principle and solved numerically using the Forward and Backward Finite Difference Method (FBDM). Numerical results obtained are in perfect agreement with our analytical results.

The violation of privacy, others people or personal, is a very current problem, which concerns not only on the web but also in private life. In the years 1990 it was expected that nowadays, that any routine operation was carried out "manually", and it would be performed through mobile phones or personal computers. The problem pertains the distribution network that allows to share and bring together information and as result the network becomes unsafe, if subjected to attacks. Nowaday we put personal information on web because otherwise we are seen as “weak”. This work aims to measure and analyze how much information are shared by users of a pre-established social network and it is carried out through a set of algorithms techniques of machine learning.

We investigate the exact travelling wave solutions of the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations, appear in nonlinear optics, using simple ansatz approach. We use the Painlevé and traveling wave transformations to convert the mentioned nonlinear equations into nonlinear ordinary differential equations. Then, the simple ansatz approach has been employed to procure wave solutions, in terms of bright, singular soliton and trigonometric functions, for the Tzitzéica-Dodd–Bullough–Mikhailov (TDBM) and Tzitzéica-type (TT) equations. The study shows that the simple ansatz approach is straightforward and easy to implement for solving nonlinear problems.

As e-commerce services and Internet technology have rapidly developed in recent years, many services and applications integrating these technologies can now be completed online. These commercial activities include online auctions, online ticketing and online payments. The client shops from the store online, andthe store delivers the goods to the client. The goods can be divided into digital products without entities, as well as actual entities. If it is a physical product, the store will deliver the package to the client through itslogistics. However, there have been many cases of switched goods purchased by clients in recent years. Earlier, some scholars proposed a security mechanism with a subliminal channel for E-cash and digital content. Only the sender and the receiver would know that the secret information was hidden in the signature. So the privacy of this subliminal message couldbe ensured. We apply this concept to the logistics environment to design secure logistics architecture with subliminal messages. The client can check the subliminal message of the received package, and know whether the package has been switched by malicious people. In addition, the proposed scheme also applies sensor technology;the client can check the GPS location, the temperature and humidity at any time during the delivery process. So intelligent logisticswouldthereby be achieved. This paper proposes an intelligent and secure package sensoring logistics system based on a subliminal channel. The proposed architecture uses the related mechanisms tosolve the problems of a logistics system, including how to achieve mutual authentication, data integrity, anti-switch package, package location and status tracing, resisting replay attacks, forward and backward secrecy, and non-repudiation issues.

Security is a major topic in recent researchers, and finding new methods deliver was the motivations for this research to emphasize and as an awareness to browsers developers to handle images with more care and to enhance exploit detection technology in the browser, as this paper proves that hackers now can attack users with just an image.

Many various using of this new-born fuzzy model for solving real-world problems and urgent requirements involve introducing new concept for analyzing the situations which leads to solve them by proper, quick and ecient method based on statistical data. This gap between the model and its solution cause that we introduce nikfar domination in neutrosophic graphs as creative and eective tool for studying a few selective vertices of this model instead of all ones by using special edges. Being special selection of these edges aect to achieve quick and proper solution to these problems. Domination hasn't ever been introduced. So we don't have any comparison with another denitions. The most used graphs which have properties of being complete, empty, bipartite, tree and like stu and they also achieve the names for themselves, are studied as fuzzy models for getting nikfar dominating set or at least becoming so close to it. We also get the relations between this special edge which plays main role in doing dominating with other special types of edges of graph like bridges. Finally, the relation between this number with other special numbers and characteristic of graph like order are discussed.

We introduce a new variation on the domination theme which we call nikfar domination as reducing waste of time in transportation planning. We determine the nikfar domination number  v for several classes of fuzzy graphs. The bounds is obtained for it. We prove both of the Vizing's conjecture and the Grarier-Khelladi's conjecture are monotone decreasing fuzzy graph property for nikfar domination. We obtain Nordhaus-Gaddum (NG) type results for these parameters. Finally, we discuss about nikfar dominating set of a fuzzy tree by using the bridges and -strong edges equivalence.

This research proposed in this paper focuses on gathering evidence from devices with Windows 10 operating systems in order to discover and collect artifacts left by cloud storage applications that suggest their use even after the deletion of the Google client application. We show where and what type of data remnants can be found using our analysis which can be used as evidence in a digital forensic investigations.

Fast 3D reconstruction with semantic information on road scenes is of great requirements for autonomous navigation. It involves issues of geometry and appearance in the field of computer vision. In this work, we propose a method of fast 3D semantic mapping based on the monocular vision. At present, due to the inexpensive price and easy installation, monocular cameras are widely equipped on recent vehicles for the advanced driver assistance and it is possible to acquire semantic information and 3D map. The monocular visual sequence is used to estimate the camera pose, calculate the depth, predict the semantic segmentation, and finally realize the 3D semantic mapping by combination of the techniques of localization, mapping and scene parsing. Our method recovers the 3D semantic mapping by incrementally transferring 2D semantic information to 3D point cloud. And a global optimization is explored to improve the accuracy of the semantic mapping in light of the spatial consistency. In our framework, there is no need to make semantic inference on each frame of the sequence, since the mesh data with semantic information is corresponding to sparse reference frames. It saves amounts of the computational cost and allows our mapping system to perform online. We evaluate the system on naturalistic road scenes, e.g., KITTI and observe a significant speed-up in the inference stage by labeling on the mesh.

Supplier selection is one of the most important multi criteria decision making (MCDM) problems for decision makers in competitive market. Organizations of today’s world are seeking new ways to reduce negative effects of their organizations to the environment and to reach a greener system. At this point, green supplier selection concept has gained great importance with its ability on incorporating environmental or green criteria into the classical supplier selection practices. Therefore, in this study, it is aimed at proposing a multi-phase MCDM model based on Best-Worst Method (BWM) and interval type-2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS). A case study in a plastic injection molding facility in Turkey is performed to show the applicability of the proposed integrated methodology. The paper ensures insights into the decision making, methodology, and managerial implications. Results of the case study are examined and suggestions for future research are provided.

The authors intend to establish new oscillation criteria for a class of generalized third order functional difference equation of the form \begin{equation}{\label{eq01}} \Delta_{\ell}\left(a_2(n)\left[\Delta_{\ell}\left(a_1(n)\left[\Delta_{\ell}z(n)\right]^{\beta_1}\right)\right]^{\beta_2}\right)+q(n)f(x(g(n)))=0, ~~n\geq n_0, \end{equation} where $z(n)=x(n)+p(n)x(\tau(n))$. We also present sufficient conditions for the solutions to converges to zero. Suitable examples are presented to validate our main results.

Reverse-order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse-order laws for a matrix product AB is (AB)^(i,...,j) = B^(i,...,j)A^(i,...,j), where (·)^i,...,j denotes an {i,...,j}-generalized inverse of matrix. Because {i,...,j}-generalized inverse of a general matrix is not necessarily unique, the relationships between both sides of the reverse-order law can be divided into four situations for consideration. In this article, we first introduce a linear mixed model y = ABβ + Aγ + ε, present two least-squares  methodologies to estimate the fixed parameter vector in the model, and describe the connections between the two least-squares estimators and the reverse-order laws for generalized inverses of the matrix product AB. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of B^(i,...,j)A^(i,...,j), as well as necessary and sufficient conditions for B^(i,...,j)A^(i,...,j) to be invariant with respect to the choice of A^(i,...,j) and B^(i,...,j). We then present a unied approach to the 512 set inclusion problems {(AB)^(i,...,j) ⊇ {B^(i,...,j)A^(i,...,j)}for the eight commonly-used types of generalized inverses of A, B, and AB using the block matrix representation method (BMRM), matrix equation method (MEM), and matrix rank method (MRM), where {(·)^(i,...,j)} denotes the collection of all {i,...,j}-generalized inverse of a matrix.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

Indoor navigation systems must deal with absence of GPS signals, since they are only available in outdoor environments. Therefore, indoor systems have to rely upon other techniques for positioning users. Recently various indoor navigation systems have been designed and developed to help visually impaired people. In this paper an overview of some existing indoor navigation systems for visually impaired people are presented and they are compared from different perspectives. The evaluated techniques are ultrasonic systems, RFID-based solutions, computer vision aided navigation systems, ans smartphone-based applications.

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized fractional differential and integral operators is demonstrated and discussed.

In the paper, a fully discrete compact difference scheme with $O(\tau^{2}+h^{4})$ precision is established by considering the numerical approximation of the one-dimensional Allen-Cahn equation. The numerical solutions satisfy discrete maximum principle under reasonable step ratio and time step constraint is proved. And the energy stability for the fully discrete scheme is investigated. An example is finally presented to show the effectiveness of scheme.

The aim of this article is to extend the local as well as the semi-local convergence analysis of multi-point iterative methods using center Lipschitz conditions in combination with our idea, of the restricted convergence region. It turns out that this way a finer convergence analysis for these methods is obtained than in earlier works and without additional hypotheses. Numerical examples favoring our technique over earlier ones completes this article.