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Featured Application: This study shows the validation of an effective methodology for determining the residual stresses of components obtained with a 3D-printed polymer such as PLA based on the DIC and the hole-drilling method. The hole-drilling method (HDM) is a common technique used for the determination of residual stresses, especially for metal alloy components, though also for polymers. This technique is usually implemented with strain gages, though other methods for determining the fields of displacements are quite mature, such as the use of digital image correlation (DIC). In the present paper, this combined methodology is applied to a 3D-printed PLA precurved specimen that is flattened in order to impose a bending distribution which can be considered known with a reasonable accuracy. The back-calculated stress distribution is in agreement with the expected (imposed) bending stress, however, a converging iterative procedure for obtaining the solution is introduced and discussed in the paper. [ABSTRACT FROM AUTHOR]

This work aims at reviewing the state of the art of the field of lexicographic multi/many-objective optimization. The discussion starts with a review of the literature, emphasizing the numerous application in the real life and the recent burst received by the advent of new computational frameworks which work well in such contexts, e.g., Grossone Methodology. Then the focus shifts on a new class of problems proposed and studied for the first time only recently: the priority-levels mixed-pareto-lexicographic multi-objective-problems (PL-MPL-MOPs). This class of programs preserves the original preference ordering of pure many-objective lexicographic optimization, but instantiates it over multi-objective problems rather than scalar ones. Interestingly, PL-MPL-MOPs seem to be very well qualified for modeling real world tasks, such as the design of either secure or fast vehicles. The work also describes the implementation of an evolutionary algorithm able to solve PL-MPL-MOPs, and reports its performance when compared against other popular optimizers. [ABSTRACT FROM AUTHOR]

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from modelling heavy tailed phenomena because it has a finite variance, even when it seems the most appropriate one to fit the data. In this work we provide for the first time a LogNormal distribution having a finite mean and a variance which converges to a well-defined infinite value. This is possible thanks to the use of Non-Standard Analysis. In particular, we have been able to obtain a Non-Standard LogNormal distribution, for which it is possible to numerically and experimentally verify whether the expected mean and variance of a set of generated pseudo-random numbers agree with the theoretical ones. Moreover, such a check would be much more cumbersome (and sometimes even impossible) when considering heavy tailed distributions in the traditional framework of standard analysis. [ABSTRACT FROM AUTHOR]

This work presents a generalized implementation of the infeasible primal-dual interior point method (IPM) achieved by the use of non-Archimedean values, i.e., infinite and infinitesimal numbers. The extended version, called here the non-Archimedean IPM (NA-IPM), is proved to converge in polynomial time to a global optimum and to be able to manage infeasibility and unboundedness transparently, i.e., without considering them as corner cases: by means of a mild embedding (addition of two variables and one constraint), the NA-IPM implicitly and transparently manages their possible presence. Moreover, the new algorithm is able to solve a wider variety of linear and quadratic optimization problems than its standard counterpart. Among them, the lexicographic multi-objective one deserves particular attention, since the NA-IPM overcomes the issues that standard techniques (such as scalarization or preemptive approach) have. To support the theoretical properties of the NA-IPM, the manuscript also shows four linear and quadratic non-Archimedean programming test cases where the effectiveness of the algorithm is verified. This also stresses that the NA-IPM is not just a mere symbolic or theoretical algorithm but actually a concrete numerical tool, paving the way for its use in real-world problems in the near future. [ABSTRACT FROM AUTHOR]

Photonics-based neural networks promise to outperform electronic counterparts, accelerating neural network computations while reducing power consumption and footprint. However, these solutions suffer from physical layer constraints arising from the underlying analog photonic hardware, impacting the resolution of computations (in terms of effective number of bits), requiring the use of positive-valued inputs, and imposing limitations in the fan-in and in the size of convolutional kernels. To abstract these constraints, in this paper we introduce the concept of Photonic-Aware Neural Network (PANN) architectures, i.e., deep neural network models aware of the photonic hardware constraints. Then, we devise PANN training schemes resorting to quantization strategies aimed to obtain the required neural network parameters in the fixed-point domain, compliant with the limited resolution of the underlying hardware. We finally carry out extensive simulations exploiting PANNs in image classification tasks on well-known datasets (MNIST, Fashion-MNIST, and Cifar-10) with varying bitwidths (i.e., 2, 4, and 6 bits). We consider two kernel sizes and two pooling schemes for each PANN model, exploiting 2 × 2 and 3 × 3 convolutional kernels, and max and average pooling, the latter more amenable to an optical implementation. 3 × 3 kernels perform better than 2 × 2 counterparts, while max and average pooling provide comparable results, with the latter performing better on MNIST and Cifar-10. The accuracy degradation due to the photonic hardware constraints is quite limited, especially on MNIST and Fashion-MNIST, demonstrating the feasibility of PANN approaches on computer vision tasks. [ABSTRACT FROM AUTHOR]

In this work, we describe the new command zonotope, which, by resorting to a geometry-based approach, provides a measure of productivity that fully accounts for the existing heterogeneity across firms within the same industry. The method we propose also enables assessment of the extent of multidimensional heterogeneity with applications to fields beyond that of production analysis. Finally, we detail the functioning of the software to perform the related empirical analysis, and we discuss the main computational issues encountered in its development. [ABSTRACT FROM AUTHOR]

Alpha-Theory was introduced in 1995 to provide a simplified version of Robinson's non-standard analysis which overcomes the technicalities of symbolic logic. The theory has been improved over the years, and recently it has been used also to solve practical problems in a pure numerical way, thanks to the introduction of algorithmic numbers. In this paper, we introduce Alpha-Theory using a novel axiomatic approach oriented towards real-world applications, to avoid the need to master mathematical logic and model theory. To corroborate the strong link of this Alpha-Theory axiomatization and scientific computations, we report numerical illustrative applications never carried out by means of non-standard numbers within a computer, i.e., the computation of the eigenvalues of a non-Archimedean matrix, some computations related to non-Archimedean Markov chains, and the Cholesky factorization of a non-Archimedean matrix. We also highlight the differences between our numerical routines and pure symbolic approaches: as expected, the former scales better when the dimension of the problem increases. [ABSTRACT FROM AUTHOR]

Linear programming is a very well known and deeply applied field of optimization theory. One of its most famous and used algorithms is the so called Simplex algorithm, independently proposed by Kantorovič and Dantzig, between the end of the 30s and the end of the 40s. Even if extremely powerful, the Simplex algorithm suffers of one initialization issue: its starting point must be a feasible basic solution of the problem to solve. To overcome it, two approaches may be used: the two-phases method and the Big-M method, both presenting positive and negative aspects. In this work we aim to propose a non-Archimedean and non-parametric variant of the Big-M method, able to overcome the drawbacks of its classical counterpart (mainly, the difficulty in setting the right value for the constant M). We realized such extension by means of the novel computational methodology proposed by Sergeyev, known as Grossone Methodology. We have validated the new algorithm by testing it on three linear programming problems. [ABSTRACT FROM AUTHOR]

This article concerns the study of mixed Pareto-lexicographic multiobjective optimization problems where the objectives must be partitioned in multiple priority levels (PLs). A PL is a group of objectives having the same importance in terms of optimization and subsequent decision making, while between PLs a lexicographic ordering exists. A naive approach would be to define a multilevel dominance relationship and apply a standard EMO/EMaO algorithm, but the concept does not conform to a stable optimization process as the resulting dominance relationship violates the transitive property needed to achieve consistent comparisons. To overcome this, we present a novel approach that merges a custom nondominance relation with the Grossone methodology, a mathematical framework to handle infinite and infinitesimal quantities. The proposed method is implemented on a popular multiobjective optimization algorithm (NSGA-II), deriving a generalization of it called by us PL-NSGA-II. We also demonstrate the usability of our strategy by quantitatively comparing the results obtained by PL-NSGA-II against other priority and nonpriority-based approaches. Among the test cases, we include two real-world applications: one 10-objective aircraft design problem and one 3-objective crash safety vehicle design task. The obtained results show that PL-NSGA-II is more suited to solve lexicographical many-objective problems than the general purpose EMaO algorithms. [ABSTRACT FROM AUTHOR]

With the arrival of the open-source RISC-V processor architecture, there is the chance to rethink Deep Neural Networks (DNNs) and information representation and processing. In this work, we will exploit the following ideas: i) reduce the number of bits needed to represent the weights of the DNNs using our recent findings and implementation of the posit number system, ii) exploit RISC-V vectorization as much as possible to speed up the format encoding/decoding, the evaluation of activations functions (using only arithmetic and logic operations, exploiting approximated formulas) and the computation of core DNNs matrix-vector operations. The comparison with the well-established architecture ARM Scalable Vector Extension is natural and challenging due to its closedness and mature nature. The results show how it is possible to vectorize posit operations on RISC-V, gaining a substantial speed-up on all the operations involved. Furthermore, the experimental outcomes highlight how the new architecture can catch up, in terms of performance, with the more mature ARM architecture. Towards this end, the present study is important because it anticipates the results that we expect to achieve when we will have an open RISC-V hardware co-processor capable to operate natively with posits. [ABSTRACT FROM AUTHOR]

Reconfigurable linear optical processors can be used to perform linear transformations and are instrumental in effectively computing matrix–vector multiplications required in each neural network layer. In this paper, we characterize and compare two thermally tuned photonic integrated processors realized in silicon-on-insulator and silicon nitride platforms suited for extracting feature maps in convolutional neural networks. The reduction in bit resolution when crossing the processor is mainly due to optical losses, in the range 2.3–3.3 for the silicon-on-insulator chip and in the range 1.3–2.4 for the silicon nitride chip. However, the lower extinction ratio of Mach–Zehnder elements in the latter platform limits their expressivity (i.e., the capacity to implement any transformation) to 75%, compared to 97% of the former. Finally, the silicon-on-insulator processor outperforms the silicon nitride one in terms of footprint and energy efficiency. [ABSTRACT FROM AUTHOR]

There are many natural phenomena that can best be described by the use of infinitesimal and infinite numbers (see e.g. [1,5,13,23]. However, until now, the Non-standard techniques have been applied to theoretical models. In this paper we investigate the possibility to implement such models in numerical simulations. First we define the field of Euclidean numbers which is a particular field of hyperreal numbers. Then, we introduce a set of families of Euclidean numbers, that we have called altogether algorithmic numbers, some of which are inspired by the IEEE 754 standard for floating point numbers. In particular, we suggest three formats which are relevant from the hardware implementation point of view: the Polynomial Algorithmic Numbers, the Bounded Algorithmic Numbers and the Truncated Algorithmic Numbers. In the second part of the paper, we show a few applications of such numbers. [ABSTRACT FROM AUTHOR]

This article focuses on the trends, opportunities, and challenges of novel arithmetic for deep neural network (DNN) signal processing, with particular reference to assisted- and autonomous driving applications. Due to strict constraints in terms of the latency, dependability, and security of autonomous driving, machine perception (i.e., detection and decision tasks) based on DNNs cannot be implemented by relying on remote cloud access. These tasks must be performed in real time in embedded systems on board the vehicle, particularly for the inference phase (considering the use of DNNs pretrained during an offline step). When developing a DNN computing platform, the choice of the computing arithmetic matters. Moreover, functional safe applications, such as autonomous driving, impose severe constraints on the effect that signal processing accuracy has on the final rate of wrong detection/decisions. Hence, after reviewing the different choices and tradeoffs concerning arithmetic, both in academia and industry, we highlight the issues in implementing DNN accelerators to achieve accurate and lowcomplexity processing of automotive sensor signals (the latter coming from diverse sources, such as cameras, radar, lidar, and ultrasonics). The focus is on both general-purpose operations massively used in DNNs, such as multiplying, accumulating, and comparing, and on specific functions, including, for example, sigmoid or hyperbolic tangents used for neuron activation. [ABSTRACT FROM AUTHOR]

With the advent of image processing and computer vision for automotive under real-time constraints, the need for fast and architecture-optimized arithmetic operations is crucial. Alternative and efficient representations for real numbers are starting to be explored, and among them, the recently introduced posit TM number system is highly promising. Furthermore, with the implementation of the architecture-specific mathematical library thoroughly targeting single-instruction multiple-data (SIMD) engines, the acceleration provided to deep neural networks framework is increasing. In this paper, we present the implementation of some core image processing operations exploiting the posit arithmetic and the ARM scalable vector extension SIMD engine. Moreover, we present applications of real-time image processing to the autonomous driving scenario, presenting benchmarks on the tinyDNN deep neural network (DNN) framework. [ABSTRACT FROM AUTHOR]

Prisoner's Dilemma (PD) is a widely studied game that plays an important role in Game Theory. This paper aims at extending PD Tournaments to the case of infinite, finite or infinitesimal payoffs using Sergeyev's Infinity Computing (IC). By exploiting IC, we are able to show the limits of the classical approach to PD Tournaments analysis of the classical theory, extending both the sets of the feasible and numerically computable tournaments. In particular we provide a numerical computation of the exact outcome of a simple PD Tournament where one player meets every other an infinite number of times, for both its deterministic and stochastic formulations. [ABSTRACT FROM AUTHOR]

This paper describes an optimal sampling approach to support glider fleet operators and marine scientists during the complex task of planning the missions of fleets of underwater gliders. Optimal sampling, which has gained considerable attention in the last decade, consists in planning the paths of gliders to minimize a specific criterion pertinent to the phenomenon under investigation. Different criteria (e.g., A, G, or E optimality), used in geosciences to obtain an optimum design, lead to different sampling strategies. In particular, the A criterion produces paths for the gliders that minimize the overall level of uncertainty over the area of interest. However, there are commonly operative situations in which the marine scientists may prefer not to minimize the overall uncertainty of a certain area, but instead they may be interested in achieving an acceptable uncertainty sufficient for the scientific or operational needs of the mission. We propose and discuss here an approach named sampling on-demand that explicitly addresses this need. In our approach the user provides an objective map, setting both the amount and the geographic distribution of the uncertainty to be achieved after assimilating the information gathered by the fleet. A novel optimality criterion, called Ah, is proposed and the resulting minimization problem is solved by using a Simulated Annealing based optimizer that takes into account the constraints imposed by the glider navigation features, the desired geometry of the paths and the problems of reachability caused by ocean currents. This planning strategy has been implemented in a Matlab toolbox called SoDDS (Sampling on-Demand and Decision Support). The tool is able to automatically download the ocean fields data from MyOcean repository and also provides graphical user interfaces to ease the input process of mission parameters and targets. The results obtained by running SoDDS on three different scenarios are provided and show that SoDDS, which is currently used at NATO STO Centre for Maritime Research and Experimentation (CMRE), can represent a step forward towards a systematic mission planning of glider fleets, dramatically reducing the efforts of glider operators. [ABSTRACT FROM AUTHOR]

This paper presents a method, based on classification techniques, for automatic detection and diagnosis of defects of rolling element bearings. The experimental data set consists of vibration signals recorded by four accelerometers on a mechanical device including rolling element bearings: the signals were collected both with all faultless bearings and after substituting one faultless bearing with an artificially damaged one. Four defects and, for one of them, three severity levels are considered. Classification accuracy higher than 99% was achieved in all the experiments performed on the vibration signals represented in the frequency domain, thus proving the high sensitivity of our method to different types of defects and to different degrees of fault severity. The degree of robustness of our method to noise is also assessed by analyzing how the classification performance varies with the signal-to-noise ratio and using statistical classifiers and neural networks. [ABSTRACT FROM PUBLISHER]

This paper presents a flexible and easy-to-use methodological approach to the forecasting of energy production in solar photovoltaic (PV) installations, using time series analysis and neural networks. The aim is to develop and validate a one day-ahead forecasting model by adopting an artificial neural network with tapped delay lines. The main novelty of our approach is the proposal of a general methodology, consisting of a sequence of steps to perform in order to find, based on heuristic criteria, the optimal structure of the neural network (particularly, number of hidden neurons and number of delay elements) and the best configuration of the neural predictor (namely, the training window width and the sampling frequency). The best experimental results have been obtained using as inputs the irradiation and the sampling hour to predict the daily accumulated energy. Considering a dataset of 15-minute measurements pertinent to one year, despite the presence of 77 missing days (scattered through the whole year in correspondence with system slowdown), we achieved seasonal mean absolute percentage errors ranging from a minimum of 12.2% of 26% than those obtained by the persistence method, a benchmark frequently used in this kind of applications. [ABSTRACT FROM AUTHOR]

The aim of this work is to report on an activity carried out during the 2010 Recognized Environmental Picture experiment, held in the Ligurian Sea during summer 2010. The activity was the first at-sea test of the recently developed decision support system (DSS) for operation planning, which had previously been tested in an artificial experiment. The DSS assesses the impact of both environmental conditions (meteorological and oceanographic) and non-environmental conditions (such as traffic density maps) on people and assets involved in the operation and helps in deciding a course of action that allows safer operation. More precisely, the environmental variables (such as wind speed, current speed and significant wave height) taken as input by the DSS are the ones forecasted by a super-ensemble model, which fuses the forecasts provided by multiple forecasting centres. The uncertainties associated with the DSS's inputs (generally due to disagreement between forecasts) are propagated through the DSS's output by using the unscented transform. In this way, the system is not only able to provide a traffic light map ( run/ not run the operation), but also to specify the confidence level associated with each action. This feature was tested on a particular type of operation with underwater gliders: the glider surfacing for data transmission. It is also shown how the availability of a glider path prediction tool provides surfacing options along the predicted path. The applicability to different operations is demonstrated by applying the same system to support diver operations. [ABSTRACT FROM AUTHOR]

This paper addresses oil spill detection from remotely sensed optical images. In particular, it focuses on the automatic classification of regions of interest (ROIs) in two classes, namely oil spills or look-alikes. Candidate regions and the corresponding boundaries have been manually identified from full resolution Moderate Resolution Imaging Spectroradiometer images, related to the Mediterranean Sea over the years 2008 and 2009. Then, a set of features has been extracted from each ROI, allowing to formulate the oil spill detection problem as a two-class classification task on the provided regions (i.e. using a supervised learning strategy). Since ROI classification is challenging, some desired characteristics for the classification algorithm are first identified, such as accuracy, robustness, etc. Then, a solution (called SVME) is provided: it is based on an ensemble of incremental/decremental cost-oriented Support Vector Machines, aggregated with the Receiving Operating Characteristic (ROC) convex hull method in the ROC space. Such a solution addresses all the desired characteristics. Finally, the results obtained on the collected dataset are shown. The importance of this study is the devising of a powerful classification technique that may have an impact on optical oil spill detection from space, especially if fused with satellite synthetic aperture radar data. Moreover, it is shown how the proposed system can be used as a decision support tool, to help a junior operator in making more reliable detections. [ABSTRACT FROM AUTHOR]

We adopted decision fusion techniques to develop a computer-aided detection (CAD) system for automatic detection of pulmonary nodules in low-dose CT images. Two distinct phases, aimed, respectively, at detecting volumes of interests (VOIs) within the CT scan, and at classifying VOIs into nodules and non-nodules, were considered. Three algorithms, namely thresholding, region growing and robust fuzzy clustering, were used as VOI detectors. For the classification phase, we built multi-classifier systems, which aggregate the decisions of three statistical classifiers, a neural network and a decision tree. Finally, the receiver operating characteristic convex hull method was used to build the final classifier, which results to be the aggregation of the best local behaviors of both classifiers and combiners. All the CAD modules were tested on CT scans analyzed by two expert radiologists. In the experiments, we achieved a sensitivity of 92.5% against a specificity of 83.5%. [ABSTRACT FROM AUTHOR]

In this work, we propose sequential non-negative least squares (S-NNLS), an efficient algorithm for the solution of a sequence of non-negative least squares problem, which is more efficient than its batch counterparts when data are collected sequentially. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The ocean color inverse problem consists of determining the concentrations of optically active constituents, such as chlorophyll, suspended particulate matter and colored dissolved organic matter, from remotely sensed multispectral measurements of the reflected sunlight back-scattered by the water body. In this paper, we approach this regression problem by using an evolutionary multi-objective algorithm, namely the (2+2) Modified Pareto Archived Evolutionary Strategy ((2+2)M-PAES), to optimize Takagi-Sugeno type (TS-type) fuzzy rule-based systems (FRBSs). Accuracy and complexity are the two competitive objectives to be simultaneously optimized. TS-type FRBSs are implemented as an artificial neural network; by training the neural network, the parameters of the fuzzy model are adjusted. In this way, the evolutionary optimization coarsely identifies the structure of the TS-type FRBSs, while the corresponding neural networks finely tune their parameters. As a result, a set of TS-type FRBSs with different trade-offs between accuracy and complexity is provided at the end of the optimization process. We show the effectiveness of our approach by comparing our results with those obtained on the ocean color inverse problem by other techniques recently proposed in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fuzzy logic-based approach which exploits remotely sensed multispectral measurements of the reflected sunlight to estimate the concentration of optically active constituents of the sea water. The relation between the concentrations of interest and the subsurface reflectances is modeled by a set of fuzzy rules extracted automatically from the data through a two-step procedure. First, a compact initial rule base is generated by projecting onto the input variables the clusters produced by a fuzzy clustering algorithm. Then, a genetic algorithm is applied to optimize the rules. Appropriate constraints maintain the semantic properties of the initial model during the genetic evolution. Results of the application of the fuzzy model obtained from data simulated with an ocean color model over the channels Of the Medium Resolution Imaging Spectrometer are shown and discussed. [ABSTRACT FROM AUTHOR]

Thanks to the advent of new technologies and higher real-time computational capabilities, the use of unmanned vehicles in the marine domain has received a significant boost in the last decade. Ocean and seabed sampling, missions in dangerous areas, and civilian security are only a few of the large number of applications which currently benefit from unmanned vehicles. One of the most actively studied topic is their full autonomy; i.e., the design of marine vehicles capable of pursuing a task while reacting to the changes of the environment without the intervention of humans, not even remotely. Environmental dynamicity may consist of variations of currents, the presence of unknown obstacles, and attacks from adversaries (e.g., pirates). To achieve autonomy in such highly dynamic uncertain conditions, many types of autonomous path planning problems need to be solved. There has thus been a commensurate number of approaches and methods to optimize this kind of path planning. This work focuses on game-theoretic approaches and provides a wide overview of the current state of the art, along with future directions. [ABSTRACT FROM AUTHOR]

This paper examines the statistical properties and the quality of the speed through water (STW) measurement based on data extracted from almost 200 container ships of Maersk Line's fleet for 3 years of operation. The analysis uses high-frequency sensor data along with additional data sources derived from external providers. The interest of the study has its background in the accuracy of STW measurement as the most important parameter in the assessment of a ship's performance analysis. The paper contains a thorough analysis of the measurements assumed to be related with the STW error, along with a descriptive decomposition of the main variables by sea region including sea state, vessel class, vessel IMO number and manufacturer of the speed-log installed in each ship. The paper suggests a semi-empirical method using a threshold to identify potential error in a ship's STW measurement. The study revealed that the sea region is the most influential factor for the STW accuracy and that 26 % of the ships of the dataset's fleet warrant further investigation. [ABSTRACT FROM AUTHOR]

In this study, an underwater image enhancement method based on local contrast correction (LCC) and multi-scale fusion is proposed to resolve low contrast and color distortion of underwater images. First, the original image is compensated using the red channel, and the compensated image is processed with a white balance. Second, LCC and image sharpening are carried out to generate two different image versions. Finally, the local contrast corrected images are fused with sharpened images by the multi-scale fusion method. The results show that the proposed method can be applied to water degradation images in different environments without resorting to an image formation model. It can effectively solve color distortion, low contrast, and unobvious details of underwater images. [ABSTRACT FROM AUTHOR]

Path planning is a key issue in the field of coastal ships, and it is also the core foundation of ship intelligent development. In order to better realize the ship path planning in the process of navigation, this paper proposes a coastal ship path planning model based on the optimized deep Q network (DQN) algorithm. The model is mainly composed of environment status information and the DQN algorithm. The environment status information provides training space for the DQN algorithm and is quantified according to the actual navigation environment and international rules for collision avoidance at sea. The DQN algorithm mainly includes four components which are ship state space, action space, action exploration strategy and reward function. The traditional reward function of DQN may lead to the low learning efficiency and convergence speed of the model. This paper optimizes the traditional reward function from three aspects: (a) the potential energy reward of the target point to the ship is set; (b) the reward area is added near the target point; and (c) the danger area is added near the obstacle. Through the above optimized method, the ship can avoid obstacles to reach the target point faster, and the convergence speed of the model is accelerated. The traditional DQN algorithm, A* algorithm, BUG2 algorithm and artificial potential field (APF) algorithm are selected for experimental comparison, and the experimental data are analyzed from the path length, planning time, number of path corners. The experimental results show that the optimized DQN algorithm has better stability and convergence, and greatly reduces the calculation time. It can plan the optimal path in line with the actual navigation rules, and improve the safety, economy and autonomous decision-making ability of ship navigation. [ABSTRACT FROM AUTHOR]

With increasing real-time constraints being put on the use of Deep Neural Networks (DNNs) by real-time scenarios, there is the need to review information representation. A very challenging path is to employ an encoding that allows a fast processing and hardware-friendly representation of information. Among the proposed alternatives to the IEEE 754 standard regarding floating point representation of real numbers, the recently introduced Posit format has been theoretically proven to be really promising in satisfying the mentioned requirements. However, with the absence of proper hardware support for this novel type, this evaluation can be conducted only through a software emulation. While waiting for the widespread availability of the Posit Processing Units (the equivalent of the Floating Point Unit (FPU)), we can already exploit the Posit representation and the currently available Arithmetic-Logic Unit (ALU) to speed up DNNs by manipulating the low-level bit string representations of Posits. As a first step, in this paper, we present new arithmetic properties of the Posit number system with a focus on the configuration with 0 exponent bits. In particular, we propose a new class of Posit operators called L1 operators, which consists of fast and approximated versions of existing arithmetic operations or functions (e.g., hyperbolic tangent (TANH) and extended linear unit (ELU)) only using integer arithmetic. These operators introduce very interesting properties and results: (i) faster evaluation than the exact counterpart with a negligible accuracy degradation; (ii) an efficient ALU emulation of a number of Posits operations; and (iii) the possibility to vectorize operations in Posits, using existing ALU vectorized operations (such as the scalable vector extension of ARM CPUs or advanced vector extensions on Intel CPUs). As a second step, we test the proposed activation function on Posit-based DNNs, showing how 16-bit down to 10-bit Posits represent an exact replacement for 32-bit floats while 8-bit Posits could be an interesting alternative to 32-bit floats since their performances are a bit lower but their high speed and low storage properties are very appealing (leading to a lower bandwidth demand and more cache-friendly code). Finally, we point out how small Posits (i.e., up to 14 bits long) are very interesting while PPUs become widespread, since Posit operations can be tabulated in a very efficient way (see details in the text). [ABSTRACT FROM AUTHOR]