Original Problem Research Articles

Energy-Efficient Resource Optimization for IRS-Assisted VLC-Enabled Offshore Communication System

In this paper, a downlink energy efficiency maximization problem is investigated in an intelligent reflective surface (IRS)-assisted visible light communication system. In order to extend wireless communication coverage of the onshore base station, an IRS mounted on a unmanned aerial vehicle (UAV) is introduced to assist an onshore lighthouse with simultaneously providing remote ship users wireless communication services and illumination. Aiming to maximizing the energy efficiency of the proposed system, a resource allocation problem is formulated as the ratio of the achievable system sum rate to the total power consumption under the constraints of the user’s data requirement and transmit power budget. Due to the non-convexity of the proposed problem, the Dinkelbach method and mean-square error (MSE) method are adopted to turn the non-convex origin problem into two equivalent problems, namely transmit beamforming and reflected phase shifting. The Lagrangian method and semidefinite relaxation technique are used to obtain the closed-form solutions of these two subproblems. Accordingly, an alternative optimization-based resource allocation scheme is proposed to obtain the optimal system energy efficiency. The simulation results show that the proposed scheme performs better in terms of energy efficiency over benchmark schemes.

H. Bergson on the Problem of Origin of Life

Henri Bergson’s conjectures about the origin of life avoid providing a solution to the problem, and yet he did make some suggestions. A close reading of his texts reveals the philosopher’s implicit assumption of an origin of life on Earth through natural processes. This paper is concerned with the concept of an élan, and focuses on the evolution of this philosophical concept in Bergson’s thought. The argument divides the élan from its constant companion, vital, in order to highlight its non-spiritual aspect which applies to what that Bergson described as “physiological life.” I emphasize that élan has a history, and that there must have been a moment when an élan began. Finally, the argument moves from élan’s history/origin to life’s history/origin.

Downlink Scheduler for Delay Guaranteed Services Using Deep Reinforcement Learning

In this paper, we propose a novel scheduling scheme to guarantee per-packet delay in single-hop wireless networks for delay-critical applications. We consider several classes of packets with different delay requirements, where high-class packets yield high utility after successful transmission. Considering the correla-tionship of delays among competing packets, we apply a delay-laxity concept and introduce a new output gain function for scheduling decisions. Particularly, the selection of a packet takes into account not only its output gain but also the delay-laxity of other packets. In this context, we formulate a multi-objective optimization problem aiming to minimize the average queue length while maximizing the average output gain under the constraint of guaranteeing per-packet delay. However, due to the uncertainty in the environment (e.g., time-varying channel conditions and random packet arrivals), it is difficult and often impractical to solve this problem using traditional optimization techniques. We develop a deep reinforcement learning (DRL)-based framework to solve it. Specifically, we decompose the original optimization problem into a set of scalar optimization subproblems and model each of them as a partially observable Markov Decision Process (POMDP). We then resort to a Double Deep Q Network (DDQN)-based algorithm to learn an optimal scheduling policy for each subproblem, which can overcome the large-scale state space and reduce Q-value overestimation. Simulation results show that our proposed DDQN-based algorithm outperforms the conventional Q-learning algorithm in terms of reward and learning speed. In addition, our proposed scheduling scheme can achieve significant reductions in average delay and delay outage drop rate compared to other benchmark schemes.

Energy-Efficiency Optimization With Model Convexification for Wireless Ad Hoc Networks With Multi-Packet Reception Capability

Energy efficiency is a significant requirement of resource management and design optimization in information networks. In this work, we propose an iterative fractional programming framework embedded with a distributed primal-dual extra-gradient projection algorithm, which addresses a wide class of the energy-efficiency optimization problems in wireless ad hoc networks with full-duplex radios and multi-packet reception capability. Specifically, we propose a model convexification mechanism by joining an affine transformation and an exponential transformation into the nonlinear fractional programming, which enables us to deal with the challenge arising from the complexity and non-convex structure of the original problem. With the model convexification, we can map the non-convex power control space into a convex space and equivalently derive a sequence of convex subproblems, which relaxes the convexity assumption widely adopted in the existing literature. We further propose a distributed primal-dual algorithm based on extra-gradient projection to solve the convex subproblem at each iteration of the fractional programming. The convergence of the proposed iterative fractional programming and the distributed optimization method is theoretically proven. Numerical results also verify the proposed method and demonstrate its superior performance over other representative distributed and centralized schemes in terms of achieving global energy efficiency.

Nonzero Degree-Based Multiobjective Cooperative Coevolutionary for Block Sparse Recovery

Block sparse signals have the characteristics of nonzero values concentrated as blocks. Therefore, block sparse recovery requires recovering the original signal from the observed signal and the measurement matrix, where the recovered error should be small and the signal satisfies the block sparsity. In this paper, block sparse recovery is solved as a multiobjective problem (MOP) and the recovery error, sparsity, and the block number of the recovered signal are considered as the conflicting objectives. Furthermore, the dimensionality of real block sparse signals is often too large, which increases the difficulty of recovery. Cooperative coevolutionary (CC) can effectively alleviate the curse of dimensionality in block sparse recovery. In addition, block sparsity causes zero and nonzero variables in the signal to form natural clusters, which is similar to the decomposition and cooperation of subproblems in CC. Therefore, CC is used in the algorithm to solve the block sparse MOP and decomposes the original problem into different subproblems. Each subproblem has a defined nonzero degree that can be combined with the proposed adaptive operator to adaptively adjust the way of generating new solutions of subproblem, which encourages the complete solution to have block sparsity. For the increased number of function evaluations (FEs) caused by the decomposition, a new list-inquiry evaluation is designed to avoid repeated evaluation. Finally, the experimental results on simulated data and real data have demonstrated the effectiveness of the proposed algorithm.

Analysis on a High Accuracy Fully Implicit Solution for Strong Nonlinear Diffusion Problem - Convergence, Stability, and Uniqueness

Some fundamental properties are analyzed for a fully implicit finite difference (FIFD) solution of conservative strong nonlinear diffusion problem. The scheme is constructed by combining a second-order backward difference temporal discretization and a central finite difference spatial discretization, and therefore highly nonlinear. Theoretical analysis is carried out under a coercive condition according with the diffusion feature of the strong nonlinear diffusion model. Benefiting from the boundedness estimates of the FIFD solution itself and its first- and second-order spatial difference quotients, some novel argument techniques are developed to overcome the difficulties coming from the nonlinear approximation for the strong nonlinear conservative diffusion operator. Consequently, it is proved rigorously that the FIFD scheme is unconditionally stable, its solution is unique and convergent to the exact solution of the original problem with second-order space-time accuracy. Numerical examples are provided to confirm its advantages on precision and efficiency over its first-order time accurate counterpoint.

Inducing Clusters Deep Kernel Gaussian Process for Longitudinal Data

We consider the problem of predictive modeling from irregularly and sparsely sampled longitudinal data with unknown, complex correlation structures and abrupt discontinuities. To address these challenges, we introduce a novel inducing clusters longitudinal deep kernel Gaussian Process (ICDKGP). ICDKGP approximates the data generating process by a zero-mean GP with a longitudinal deep kernel that models the unknown complex correlation structure in the data and a deterministic non-zero mean function to model the abrupt discontinuities. To improve the scalability and interpretability of ICDKGP, we introduce inducing clusters corresponding to centers of clusters in the training data. We formulate the training of ICDKGP as a constrained optimization problem and derive its evidence lower bound. We introduce a novel relaxation of the resulting problem which under rather mild assumptions yields a solution with error bounded relative to the original problem. We describe the results of extensive experiments demonstrating that ICDKGP substantially outperforms the state-of-the-art longitudinal methods on data with both smoothly and non-smoothly varying outcomes.

Abnormality and Strict-Sense Minimizers That Are Not Extended Minimizers

We consider a constrained optimal control problem and an extension of it, in which the set of strict-sense trajectories is enlarged. Extension is a common procedure in optimal control used to derive necessary and sufficient optimality conditions for the original problem from the extended one, which usually admits a minimizer and has a more regular structure. However, this procedure fails if the two problems have different infima. Therefore, it is relevant to identify such situations. Following on from earlier work by Warga but adopting perturbation techniques developed in nonsmooth analysis, we investigate the relation between the occurrence of an infimum gap and the abnormality of necessary conditions. For the notion of a local minimizer based on control distance and an extension, including the impulsive one, we prove that (i) a local extended minimizer that is not a local minimizer of the original problem, and (ii) a local strict-sense minimizer that is not a local minimizer of the extended problem both satisfy the extended maximum principle in abnormal form. The main novelty is result (ii), as until now, it has only been shown that a strict-sense minimizer that is not an extended minimizer is abnormal for an ‘averaged version’ of the maximum principle.

Transfer learning for metamaterial design and simulation

Abstract We demonstrate transfer learning as a tool to improve the efficacy of training deep learning models based on residual neural networks (ResNets). Specifically, we examine its use for study of multi-scale electrically large metasurface arrays under open boundary conditions in electromagnetic metamaterials. Our aim is to assess the efficiency of transfer learning across a range of problem domains that vary in their resemblance to the original base problem for which the ResNet model was initially trained. We use a quasi-analytical discrete dipole approximation (DDA) method to simulate electrically large metasurface arrays to obtain ground truth data for training and testing of our deep neural network. Our approach can save significant time for examining novel metasurface designs by harnessing the power of transfer learning, as it effectively mitigates the pervasive data bottleneck issue commonly encountered in deep learning. We demonstrate that for the best case when the transfer task is sufficiently similar to the target task, a new task can be effectively trained using only a few data points yet still achieve a test mean absolute relative error of 3 % with a pre-trained neural network, realizing data reduction by a factor of 1000.

A novel surface-derivative-free of jumps AIIM with triangulated surfaces for 3D Helmholtz interface problems

Triangular surface-based 3D IIM (Immersed Interface Method) algorithms face major challenges due to the need to calculate surface derivative of jumps. This paper proposes a fast, easy-to-implement, surface-derivative-free of jumps, augmented IIM (AIIM) with triangulated surfaces for 3D Helmholtz interface problems for the first time, which combines the simplified AIIM with domain decomposed and embedding techniques. The computational domain is divided into sub-domains along the interface and the solutions of sub-domains are continuously extended into larger regular domains by embedding. The jumps in normal derivative of solution along the interfaces in the extended domains are introduced as unknowns to impose the original jump relations. The original problem is simplified into Helmholtz interface problems with constant coefficients by coupling them with the augmented equation, which is then solved using fast simplified AIIM. This approach eliminates the need to compute surface derivatives of jumps, making implementation of 3D IIM based on triangulated surfaces fairly simple. Numerical results demonstrate that the algorithm is efficient and can achieve the overall second-order accuracy.

Lyapunov-Schmidt reduction in the study of bifurcation of periodic travelling wave solutions of a perturbed (1 + 1)−dimensional dispersive long wave equation

In this paper, the Lyapunov-Schmidt reduction is used to investigate the bifurcation of periodic travelling wave solutions of a perturbed (1+1)−dimensional dispersive long wave equation. We demonstrate that the bifurcation equation corresponding to the original problem is supplied by a nonlinear system of two cubic algebraic equations. As the bifurcation parameters change, this system has only one, three, or five regular real solutions. The linear approximation of the solutions to the main problem has been discovered.

DELEUZE AND INFINITE REPRESENTATION: CONTRADICTION VERSUS SUFFICIENT REASON

The relationship between Deleuze and Hegel and Deleuze’s obvious anti-Hegelianism manifests itself mainly in the Difference-in-Itself section of Difference and Repetition. The issue in this first part of Difference and Repetition consists of the critique of traditional metaphysics as a system of representation. Traditional metaphysics tries to represent existing things, instead of problemtising their genesis. It presents them by making them organized and suitable for the human eye. Traditional philosophy does this by subordinating difference to identity. Ultimately, for philosophy, difference is merely a means to guarantee the structure of the representational system based on identity and on harmony. However, Deleuze’s philosophy is a system of thought about the origin of the existence of things. Here, difference becomes the constitutive element. At this point, our aim will be to reveal the general structure of various representational systems. Our first subject will be Aristotle’s Organic Representational system, in which the limit of beings is well determined. After this system, we will move on to the infinite representational system, where the purpose of the limit is not the restriction but to enable the finite to pass beyond itself. According to Deleuze, the Philosophical systems that are similar to the latter are exemplified by Hegel and Leibniz. Essentially, in this section, Deleuze shows himself to be on the side of Leibniz and criticizes Hegelian dialectics. This criticism here shows that individual and unconscious creation is the basic question at the core of Deleuze’s system, which is based on the problem of origin. Deleuze’s aim is to build a system of philosophy based on Leibnizian philosophy, purified from old metaphysics defects and a reinterpretation of Kantian experience.

Fitness as the organismal performance measure guiding adaptive evolution.

A long-standing problem in evolutionary theory is to clarify in what sense (if any) natural selection cumulatively improves the design of organisms. Various concepts, such as fitness and inclusive fitness, have been proposed to resolve this problem. In addition, there have been attempts to replace the original problem with more tractable questions such as whether a given gene or trait is favoured by selection. Here we ask what theoretical properties the concept fitness should possess to encapsulate the improvement criterion required to talk meaningfully about adaptive evolution. We argue that natural selection tends to shape phenotypes based on the causal properties of individuals, and that this tendency is therefore best captured by a fitness concept that focusses on these properties. We highlight a fitness concept which meets this role under broad conditions, but requires adjustments in our conceptual understanding of adaptive evolution. These adjustments combine elements of Dawkinsian gene selectionism and Egbert Leigh's "parliament of genes".

On mathematical problems of two-coefficient inverse problems of ultrasonic tomography

This paper proves the theorem of uniqueness for the solution of a coefficient inverse problem for the wave equation in (with two unknown coefficients: speed of sound and absorption. The original nonlinear coefficient inverse problem is reduced to an equivalent system of two uniquely solvable linear integral equations of the first kind with respect to the sound speed and absorption coefficients. Estimates are made, substantiating the multistage method for two unknown coefficients. These estimates show that given sufficiently low frequencies and small inhomogeneities, the residual functional for the nonlinear inverse problem approaches a convex one. This solution method for nonlinear coefficient inverse problems is not linked to the limit approach as frequency tends to zero, but assumes solving the inverse problem using sufficiently low, but not zero, frequencies at the first stage. For small inhomogeneities that are typical, for instance, for medical tasks, carrying out real experiments at such frequencies does not present major difficulties. The capabilities of the method are demonstrated on a model inverse problem with unknown sound speed and absorption coefficients. The method effectively solves the nonlinear problem with parameter values typical for tomographic diagnostics of soft tissues in medicine. A resolution of approximately 2 mm was achieved using an average sounding pulse wavelength of 5 mm.

Robust Transceiver Design for Correlated MIMO Interference Channels in the Presence of CSI Errors under General Power Constraints

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Chains with Connections of Diffusion and Advective Types

The local dynamics of a system of oscillators with a large number of elements and with diffusive- and advective-type couplings containing a large delay are studied. Critical cases in the problem of the stability of the zero equilibrium state are singled out, and it is shown that all of them have infinite dimensions. Applying special methods of infinite normalization, we construct quasinormal forms, namely, nonlinear boundary value problems of the parabolic type, whose nonlocal dynamics determine the behavior of the solutions of the initial system in a small neighborhood of the equilibrium state. These quasinormal forms contain either two or three spatial variables, which emphasizes the complexity of the dynamical properties of the original problem.

A sublinear functional based approximated equivalence to optimality and duality for multiobjective programming in complex spaces

In this paper, we introduce a new approximation approach for a class of multiobjective programming problems in complex spaces and their duals. Using a sublinear functional, an approximated problem is constructed at a given feasible solution of the original problem. The equivalence between the solution of the considered multiobjective complex programming problem and its approximated problem is established by deriving the sufficiency theorem under the F-convexity assumption. An example showing this equivalence is also presented. Further, corresponding to the approximated problem, the Mond–Weir and Wolfe-type approximated dual problems are formulated. The duality results for the Mond–Weir and Wolfe-type dual problems are derived using the duality results established for the approximated Mond–Weir and Wolfe-type dual problems, respectively. The importance of the optimality conditions and proposed approximation approach is highlighted in a blind equalization problem in a communication system.

Sum-Rate Maximization Scheme for Multi-RIS-Assisted NOMA Uplink Systems

Sum-Rate Maximization Scheme for Multi-RIS-Assisted NOMA Uplink Systems

Interpreting correlations in stress‐dependent permeability, porosity, and compressibility of rocks: A viewpoint from finite strain theory

AbstractCharacteristics of stress‐dependent properties of rocks are commonly described by empirical laws. It is crucial to establish a universal law that connects rock properties with stress. The present study focuses on exploring the correlations among permeability, porosity, and compressibility observed in experiments. To achieve this, we propose a novel finite strain‐based dual‐component (FS‐DC) model, grounded in the finite strain theory within the framework of continuum mechanics. The FS‐DC model decomposes the original problem into the rock matrix and micro‐pores/cracks components. The deformation gradient tensor is utilized to derive the constitutive relations. One of the novelties is that the stress‐dependent variables are calculated in the current configuration, in contrast to the reference configuration used in small deformation theory. The model has only a few number of parameters, each with specific physical interpretations. It can be reduced to existing models with appropriate simplifications. Then, model performance is examined against experimental data, including permeability, porosity, compressibility, volumetric strain and specific storage. It proves that the variations of these properties are effectively described by the proposed model. Further analysis reveals the effect of pores/cracks parameters. The validity of the FS‐DC model is examined across a broad range of pressures. The results show that rock properties at high confining pressures (300 MPa) differ from those observed under relatively low pressures (200 MPa). This disparity can be attributed to inelastic behaviors of micro‐structure, wherein the rock skeleton undergoes permanent deformation and breakage.

To Charge In-Flight or Not: A Comparison of Two Parallel Hybrid Electric Aircraft Configurations via Optimal Control

This study examines two configurations for parallel hybrid electric aircraft, one with a mechanical connection between the engines and the electric motors and the other without. A previously proposed power allocation algorithm in the context of aircraft energy management is applied to these two configurations for a 19-seat conceptual hybrid electric aircraft. The original optimal control problem is then transformed into a finite-dimensional optimization, and the second-order sufficient conditions for the global optimality of the obtained solution are validated. This is followed by a sensitivity analysis of the fuel consumption to the initial aircraft weight and flight duration. Simulation and theoretical results clarify the limited benefits of charging the battery in-flight for this class of hybrid electric aircraft for the purpose of reducing fuel consumption and CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> emissions.