Activation Functions are crucial parts of the Deep Learning Artificial Neural Networks. From the Biological point of view, a neuron is just a node with many inputs and one output. A neural network consists of many interconnected neurons. It is a “simple” device that receives data at the input and provides a response. The function of neurons is to process and transmit information; the neuron is the basic unit in the nervous system. Carly Vandergriendt (2018) stated the human brain at birth consists of an estimated 100 billion Neurons. The ability of a machine to mimic human intelligence is called Machine Learning. Deep Learning Artificial Neural Networks was designed to work like a human brain with the aid of arbitrary choice of Non-linear Activation Functions. Currently, there is no rule of thumb on the choice of Activation Functions, “Try out different things and see what combinations lead to the best performance”, however, sincerely; the choice of Activation Functions should not be Trial and error. Jamilu (2019) proposed that Activation Functions shall be emanated from AI-ML-Purified Data Set and its choice shall satisfy Jameel’s ANNAF Stochastic and or Deterministic Criterion. The objectives of this paper are to propose instances where Deep Learning Artificial Neural Networks are SUPERINTELLIGENT. Using Jameel’s ANNAF Stochastic and or Deterministic Criterion, the paper proposed four classes where Deep Learning Artificial Neural Networks are Superintelligent namely; Stochastic Superintelligent, Deterministic Superintelligent, and Stochastic-Deterministic 1^st and 2^nd Levels Superintelligence. Also, a Normal Probabilistic-Deterministic case was proposed.

Most studies modelling population mobility and the spread of infectious diseases, particularly using meta-population-multi-patched models, tend to focus on theoretical properties and numerical simulations of such models. There is relatively scanty literature published on fit, inference and uncertainty quantification on epidemic models with population mobility. In this research, we have used three estimation techniques to solve an inverse problem and quantify its uncertainty on a human mobility-based multi-patched epidemic model, using mobile phone sensing data and COVID-19 confirmed positive cases in Hermosillo, Mexico. First, we have utilized a Brownian bridge model using mobile phone GPS data to estimate residence and mobility parameters of the epidemic model. In the second step, we have estimated the optimal model epidemiological parameters by deterministically inverting the model using a Darwinian inspired evolutionary algorithm (EA) known as the genetic algorithm (GA). The third part of the analysis involves performing inference and uncertainty quantification on the epidemic model using two Bayesian Monte Carlo sampling methods: t-walk and Hamiltonian Monte Carlo (HMC). The results show that the estimated model parameters and incidence adequately fit the observed daily COVID-19 incidence in Hermosillo. Moreover, the estimated parameters from HMC result into large credible intervals, improving their coverage for the observed and predicted daily incidences. We also observe improved predictions when using multi-patch model with mobility against the single-patch model.

This paper proposes a novel deterministic methodology for estimating the optimal sampling frequency (SF) of water quality monitoring systems. The proposed methodology is based on employing two-dimensional contaminant transport simulation models to determine the minimum SF considering all the potential changes in the boundary conditions of a water body. A two-dimensional contaminant transport simulation model (RMA4) was implemented to estimate the distribution patterns of the total dissolved solids (TDS) within the Al-Hammar Marsh in the southern part of Iraq for 30 cases of potential boundary conditions. Using geographical information system (GIS) tools, a spatiotemporal analysis approach was applied to the results of the RMA4 model to determine the minimum SF of the monitoring stations with an accuracy level of detectable change in TDS concentration (ALC) of 5%, 10% and 15%. The proposed methodology specified a minimum and maximum SF for each monitoring station (MS) that ranged between 12 and 33 times per year, respectively. Additionally, increasing the ALC to 10% and 15% increase the minimum SF for some MSs by approximately 18% and 21%, respectively. However, the proposed methodology includes all the potential values and cases of boundary conditions, which increases the certainty of monitoring the system and the efficiency of the SF schedule. Moreover, the proposed methodology can be effectively applied to all types of surface water resources.

We study the deterministic dynamics of N point particles moving at constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback-control on the particles, inverting the horizontal component of their velocities, when their number in the channel exceeds a fixed threshold. Such a bounce--back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed both for rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.

The robust control of high precision electromechanical systems, such as micropositioners, is challenging in terms of the inherent high nonlinearity, the sensitivity to external interference, and the complexity of accurate identification of the model parameters. To cope with these problems, this work investigates a disturbance observer-based deep reinforcement learning control strategy to realize high robustness and precise tracking performance. Reinforcement learning has shown great potential as optimal control scheme, however, its application in micropositioning systems is still rare. Therefore, embedded with the integral differential compensator (ID), deep deterministic policy gradient (DDPG) is utilized in this work with the ability to not only decrease the state error but also improves the transient response speed. In addition, an adaptive sliding mode disturbance observer (ASMDO) is proposed to further eliminate the collective effect caused by the lumped disturbances. The sterling performance is revealed with intensive tracking simulation experiments and demonstrates the improvement in the accuracy and response time of the controller.

A detailed literature review is performed in this study to address solutions for the full-body design and control of an aerial manipulator. Deep Reinforcement Learning methods are growing to be utilized recently to cope with various uncertainties. The pros and cons of these theories will be explained as well as introducing the advantages of Fuzzy Reinforcement Learning methods. State-of-the-Art, possible challenges, potential approaches, and a summary of desired precision devices are discussed in this study.

Air sampling using vortex air samplers combined with species specific amplification of pathogen DNA, was carried out over two years in four or five locations in the Salinas Valley of California. The resulting time series data for the abundance of pathogen DNA trapped per day displayed complex dynamics with features of both deterministic (chaotic) and stochastic dynamics. Methods of nonlinear time series analysis developed for the reconstruction of low dimensional attractors provided new insights into the complexity of the pathogen abundance data, but also indicated that practicality may limit the capacity for definitively classifying the dynamics of air borne plant pathogen inoculum. Over the two years of the study five location/year combinations were classified as having stochastic linear dynamics and four were not. Calculation of entropy values for either the number of pathogen DNA copies or for a binary string indicating the pathogen abundance data were increasing or not, revealed (1) some robust differences in the dynamics between seasons that were not obvious in the time series data themselves, and also (2) that the series were almost all at their theoretical maximum entropy value when considered from the simple perspective of whether instantaneous change along the sequence is positive or not.

With correct dynamic system parameters (embodied in self-awareness statements), a controller can provide precise signals for tracking desired state trajectories. If dynamic system parameters are initially guessed incorrectly, a learning method may be used to find the correct parameters. In the deterministic artificial intelligence method, self-awareness statements are formed as mathematical expressions of the governing physics. When the nonlinear, coupled expressions are precisely parameterized as the product of known matrix components and unknown victrix (i.e., a regression form) tracking errors may be projected onto the known matrix to update the unknown victrix in an optimal form (in a two-norm sense). In this work, a modified learning method is proposed and proved to have global convergence of both state error and parameter estimation error. The modified learning method is compared with those in the prequels using simulation experiments of three-dimensional rigid body dynamic rotation motion. The modified approach is two magnitudes better than the methods in the prequels in terms of state error convergence.

This article analyses entropy changes triggered by specific events in deterministic and indeterministic systems. Article considers a simple model consisting of water in a cuvette, an ice cube in the device above the cuvette and a random number generator (RNG) that controls the probability of dropping the ice into water. Article introduces the entropic potential Z(T, A) of an event A occurred in a system R at the moment Т₀, which describes the influence of the event A to the entropy of the system R in the future (for the moments T>Т₀). The entropic potential of an event Z(T,A) can be calculated as the difference between the mathematical expectations of entropy of the system R for the moment T (T>Т₀) made immediately before and immediately after the event A as Z(T, A) = Ŝ_T(Т₀+dT) - Ŝ_T(Т₀-dT). Article also presents examples of calculations of the entropic potentials of events in indeterministic systems with different probabilities of events. Since real-life systems are mostly indeterministic, the entropic potentials of events in real-life usually have non-zero values. The entropic potentials of the events "useful" for the system are negative, and entropic potentials of the events "harmful" for the system are positive.

Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.

The Universe, rather than being homogeneous, displays an almost infinite topological genus, because it is punctured with a countless number of gravitational vortexes, i.e., black holes. Starting from this view, we aim to show that the occurrence of black holes is constrained by geometric random walks taking place during cosmic inflationary expansion. At first, we introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, which describes three-dimensional cosmic random walks. In case of nonlinear 3D paths, trajectories in an expanding Universe can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to separate cosmic structures (standing for matter/energy), spaced out by empty areas (constituted by black holes and dark matter). These procedures allow us to describe the topology of an universe of infinite genus, to assess black hole formation in terms of infinite Betti numbers, to highlight how non-linear random walks might provoke gravitational effects also in absence of mass/energy, and to propose a novel interpretation of Beckenstein-Hawking entropy: it is proportional to the surface, rather than the volume, of a black hole, because the latter does not contain information.

The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.

Integrating numerous renewable resources has been extensively researched and studied to create a dependable energy system. This study investigated the best techno-economical hybrid energy system configuration while using hydrogen energy to keep the system's energy balanced. Additionally, this study aims to determine the best hybrid system configuration for the location under investigation. A novel technique of DBM (Deterministic Balanced Method) was introduced to determine the total annual energy output for the project's lifetime. This approach is used to contrast the outcomes of other HOMER software tools. Then, using HOMER, it is possible to confirm the sizing optimization results for the suggested method by comparing the power ratings and yearly energy output. A detailed comparison between our proposed method and HOMER Pro has been conducted for validation and verification. Our method has been rigorously tested in various hybrid off-grid energy systems, ensuring its applicability and reliability across different scenarios and configurations. The results of our study indicate a high degree of similarity between the proposed approach and HOMER pro for computing annual energy power for the studied energy systems. Specifically, our analysis revealed that the difference between the approaches was within a range of 5%, indicating a high level of consistency and reliability in our method. These findings suggest that our approach can be confidently applied to determine the appropriate size of hybrid energy systems accurately. Overall, our study provides valuable insights into the development of effective sizing methodologies for hybrid energy systems. After considering the amount of solar radiation and wind speed gathered by global weather data platforms like NASA and METEONORM, this paper has also included a real case study of the Cairo International Airport's hybrid renewable energy production systems. To guarantee the viability of this study, the system design was founded on an actual load that was researched and simulated. A cluster of distributed networks was finally proposed to use the excess energy and enable energy conversion processes to be used in industry and transportation applications.

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

In the era of electrification and artificial intelligence, direct current motors are widely utilized with numerous innovative adaptive and learning methods. Traditional methods utilize model-based algebraic techniques with system identification, such as recursive least squares, extended least squares, and autoregressive moving averages. The new method known as deterministic artificial intelligence asserts physical-based process dynamics to achieve target trajectory tracking. There are two common autonomous trajectory generation algorithms: sinusoidal function and Pontryagin's based generation algorithm. This thesis aims to simulate model-following and deterministic artificial intelligence methods using sinusoidal and Pontryagin's methods and compare their performance difference when following challenging step function slew maneuver.

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, adaptive and learning methods are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a method in which the controller is designed to adapt the system with parameters which vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model & measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. Deterministic artificial intelligence, a learning-based approach that uses the process dynamics defined by physics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive & learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output & the reference trajectory and the standard deviation of the error. The first order-hold method of discretization and surprisingly large sample time of seven tenths of a second yields over sixty percent improvement over the results presented in the prequel literature.

Classical k-ratio models, e.g. ZAF and phi(rho z), used in electron probe microanalysis (EPMA) assume a homogeneous or multi-layered material structure, which essentially limits the spatial resolution of EPMA to the size of the interaction volume where characteristic x-rays are produced. We present a new model for characteristic x-ray emission that avoids assumptions on the material structure to not restrict the resolution of EPMA a-priori. Our model bases on the spherical harmonic (PN) approximation of the Boltzmann equation for electron transport in continuous slowing down approximation. PN models have a simple structure, are hierarchical in accuracy and well-suited for efficient adjoint-based gradient computation, which makes our model a promising alternative to classical models in terms of improving the resolution of EPMA in the future. We present results of various test cases including a comparison of the PN model to a minimum entropy moment model as well as Monte-Carlo (MC) trajectory sampling, a comparison of PN-based k-ratios to k-ratios obtained with MC, a comparison with experimental data of electron backscattering yields as well as a comparison of PN and Monte-Carlo based on characteristic X-ray generation in a three-dimensional material probe with fine structures.

Several mathematicians and physicists are working all over the globe to get a unified theory. However, most of them are discarding Einstein’s view at the very first step of their theories. This article provides a brief non-mathematical introduction on this. Also, on the basis of Koga’s theory we point out two reasons which might have caused Einstein’s failure to get a unified theory.

We discuss the generation of various reproduction ratios or numbers to monitor the outbreak of Covid-19 or other epidemics and examine the effects of intervention/relaxation measures. A detailed SEIR algorithm is described for their computation, with applications given to the current Covid-19 outbreak in several countries in America (Argentina, Brazil, Mexico, US) and Europe (France, Italy, Spain and UK). The corresponding matlab script, complete and ready to use, is provided for free downloading.

Accurate and reliable project cost estimates are fundamental to achieve successful municipal capital improvement (CIP) programs. Engineering cost estimates typically represent critical information for key decision makers to authorize and efficiently allocate the necessary funds for construction, budgeting, to generate a request for proposals, contract negotiations, scheduling, etc. for these reasons, cost estimators are using different estimating methods and approaches that allow for required levels of accuracy. As the project’s scope becomes more detailed and the potential risks are identified and/or the project design stage progresses these cost estimates are revised and updated. In this paper, the most common project cost estimation methods and approaches were collected and categorized into two main groups of (1) probabilistic and (2) deterministic methods. Under these groups overall ten different methods were identified and discussed addressing their requirements, advantages, and shortcomings, including the potential risk that can positively or negatively affect the project’s cost outcome. This paper will be a good resource for professionals who are in budget development and/or are seeking to a better understanding of different methods in determining an appropriate base cost margin and produce a meaningful and reliable project cost estimate.

This study determines the threshold for the computational rate of actuator motor controllers for unmanned underwater vehicles necessary to accurately follow discontinuous square wave commands. Motors must track challenging square-wave inputs, and identification of key computational rates permit application of deterministic artificial intelligence (D.A.I.) to achieve tracking to a machine-precision degree of accuracy in direct comparison to other state-of-art approaches. All modeling approaches are validated in MATLAB simulations where the motor process is discretized at varying step-sizes (inversely proportional to computational rate). At a large step-size (fast computational rate), discrete D.A.I. shows a mean error more than three times larger than that of a ubiquitous model-following approach. Yet, at a smaller step size (slower computational rate), the mean error decreases by a factor of 10, only three percent larger than that of continuous D.A.I. Hence, the performance of discrete D.A.I. is critically affected by the sampling period for discretization of the system equations and computational rate. Discrete D.A.I. should be avoided when small step-size discretization is unavailable. In fact, continuous D.A.I. has surpassed all modeling approaches which makes it the safest and most viable solution to future commercial applications in unmanned underwater vehicles.

This manuscript compares deterministic artificial intelligence to model following control applied to DC motor control, including evaluation of the threshold computation rate to let unmanned underwater vehicles correctly follow the challenging discontinuous square wave command signal. The approaches presented in the main text are validated in MATLAB®, where the motor process is discretized at multiple step sizes, which is inversely proportional to the computation rate. The performance is evaluated by the error mean and standard deviation. With a large step size, discrete deterministic artificial intelligence shows a larger error mean than the model-following self-turning regulator approach (benchmark selection). However, the performance gets optimized with the step size decreased. The error mean is close to the continuous deterministic artificial intelligence when the step size is reduced to 0.2 seconds, which means that the computation rate and the sampling period restrict discrete deterministic artificial intelligence. In that case, the continuous deterministic artificial intelligence is the most feasible and reliable selection for future applications on unmanned underwater vehicles since it is superior to all the approaches with multiple computation rates.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

The Van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Because of its chaotic nature, controlling, or forcing, the behavior of a Van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two Van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the Van der Pol oscillator. Deterministic AI (DAI) is an adaptive feedback control method that leverages the known physics of the Van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of DAI employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error (MAE) between the target trajectory and the response oscillator trajectory over time. RLS with exponential forgetting (RLS-EF) had the lowest MAE overall, with a 2.46% reduction in error. However, another method was notable. Least Mean Squares with normalized gradient adaptation (LMS-NG) had worse initial error in the first 10% of the simulation, but after that point had consistently better performance. We found that over the last 90% of the simulation, DAI with LMS-NG had a 48.7% reduction in MAE compared to feedforward alone.