Entropy

Assuming that the energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm’s quantum potential and the Madelung equation are obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics do admit a classical interpretation based on non-locality. Here, we generalize this approach imposing a finite speed of propagation of any perturbation, thus determining a covariant formulation of the Madelung equation. Full article

When traditional super-resolution reconstruction methods are applied to infrared thermal images, they often ignore the problem of poor image quality caused by the imaging mechanism, which makes it difficult to obtain high-quality reconstruction results even with the training of simulated degraded inverse processes. To address these issues, we proposed a thermal infrared image super-resolution reconstruction method based on multimodal sensor fusion, aiming to enhance the resolution of thermal infrared images and rely on multimodal sensor information to reconstruct high-frequency details in the images, thereby overcoming the limitations of imaging mechanisms. First, we designed a novel super-resolution reconstruction network, which consisted of primary feature encoding, super-resolution reconstruction, and high-frequency detail fusion subnetwork, to enhance the resolution of thermal infrared images and rely on multimodal sensor information to reconstruct high-frequency details in the images, thereby overcoming limitations of imaging mechanisms. We designed hierarchical dilated distillation modules and a cross-attention transformation module to extract and transmit image features, enhancing the network’s ability to express complex patterns. Then, we proposed a hybrid loss function to guide the network in extracting salient features from thermal infrared images and reference images while maintaining accurate thermal information. Finally, we proposed a learning strategy to ensure the high-quality super-resolution reconstruction performance of the network, even in the absence of reference images. Extensive experimental results show that the proposed method exhibits superior reconstruction image quality compared to other contrastive methods, demonstrating its effectiveness. Full article

Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how the heterogeneous character of adaptive couplings influences the emergence of new scenarios in the collective behavior of networks. Within the framework of a two-population network of coupled phase oscillators, we analyze the role of various factors of heterogeneous interaction, such as the rules of coupling adaptation and the rate of their change in the formation of various types of coherent behavior of the network. We show that various schemes of heterogeneous adaptation lead to the formation of transient phase clusters of various types. Full article

We introduce a new family of quantum distances based on symmetric Csiszár divergences, a class of distinguishability measures that encompass the main dissimilarity measures between probability distributions. We prove that these quantum distances can be obtained by optimizing over a set of quantum measurements followed by a purification process. Specifically, we address in the first place the case of distinguishing pure quantum states, solving an optimization of the symmetric Csiszár divergences over von Neumann measurements. In the second place, by making use of the concept of purification of quantum states, we arrive at a new set of distinguishability measures, which we call extended quantum Csiszár distances. In addition, as it has been demonstrated that a purification process can be physically implemented, the proposed distinguishability measures for quantum states could be endowed with an operational interpretation. Finally, by taking advantage of a well-known result for classical Csiszár divergences, we show how to build quantum Csiszár true distances. Thus, our main contribution is the development and analysis of a method for obtaining quantum distances satisfying the triangle inequality in the space of quantum states for Hilbert spaces of arbitrary dimension. Full article

The discontinuous Galerkin spectral element method (DGSEM) is a compact and high-order method applicable to complex meshes. However, the aliasing errors in simulating under-resolved vortex flows and non-physical oscillations in simulating shock waves may lead to instability of the DGSEM. In this paper, an entropy-stable DGSEM (ESDGSEM) based on subcell limiting is proposed to improve the non-linear stability of the method. First, we discuss the stability and resolution of the entropy-stable DGSEM based on different solution points. Second, a provably entropy-stable DGSEM based on subcell limiting is established on Legendre–Gauss (LG) solution points. Numerical experiments demonstrate that the ESDGSEM-LG scheme is superior in non-linear stability and resolution, and ESDGSEM-LG with subcell limiting is robust in shock-capturing. Full article

Real-world objects are usually defined in terms of their own relationships or connections. A graph (or network) naturally expresses this model though nodes and edges. In biology, depending on what the nodes and edges represent, we may classify several types of networks, gene–disease associations (GDAs) included. In this paper, we presented a solution based on a graph neural network (GNN) for the identification of candidate GDAs. We trained our model with an initial set of well-known and curated inter- and intra-relationships between genes and diseases. It was based on graph convolutions, making use of multiple convolutional layers and a point-wise non-linearity function following each layer. The embeddings were computed for the input network built on a set of GDAs to map each node into a vector of real numbers in a multidimensional space. Results showed an AUC of 95% for training, validation, and testing, that in the real case translated into a positive response for 93% of the Top-15 (highest dot product) candidate GDAs identified by our solution. The experimentation was conducted on the DisGeNET dataset, while the DiseaseGene Association Miner (DG-AssocMiner) dataset by Stanford’s BioSNAP was also processed for performance evaluation only. Full article

Lightweight block ciphers are normally used in low-power resource-constrained environments, while providing reliable and sufficient security. Therefore, it is important to study the security and reliability of lightweight block ciphers. SKINNY is a new lightweight tweakable block cipher. In this paper, we present an efficient attack scheme for SKINNY-64 based on algebraic fault analysis. The optimal fault injection location is given by analyzing the diffusion of a single-bit fault at different locations during the encryption process. At the same time, by combining the algebraic fault analysis method based on S-box decomposition, the master key can be recovered in an average time of 9 s using one fault. To the best of our knowledge, our proposed attack scheme requires fewer faults, is faster to solve, and has a higher success rate than other existing attack methods. Full article

Price, Cost and Income (PCI) are distinct economic indicators intrinsically linked to the values they denote. These observables take center stage in the multi-criteria decision-making process that enables economic agents to convey subjective utilities of market-exchanged commodities objectively. The valuation of these commodities heavily relies on PCI-based empirical observables and their supported methodologies. This valuation measure’s accuracy is critical, as it influences subsequent decisions within the market chain. However, measurement errors often arise due to inherent uncertainties in the value state, impacting economic agents’ wealth, particularly when trading significant commodities such as real estate properties. This paper addresses this issue by incorporating entropy measurements into real estate valuation. This mathematical technique adjusts and integrates triadic PCI estimates, improving the final stage of appraisal systems where definitive value decisions are crucial. Employing entropy within the appraisal system can also aid market agents in devising informed production/trading strategies for optimal returns. The results from our practical demonstration indicate promising implications. The entropy’s integration with PCI estimates significantly improved the value measurement’s precision and reduced economic decision-making errors. Full article

Entropy density behavior poses many problems when we study non-equilibrium situations. In particular, the local equilibrium hypothesis (LEH) has played a very important role and is taken for granted in non-equilibrium problems, no matter how extreme they are. In this paper we would like to calculate the Boltzmann entropy balance equation for a plane shock wave and show its performance for Grad’s 13-moment approximation and the Navier–Stokes–Fourier equations. In fact, we calculate the correction for the LEH in Grad’s case and discuss its properties. Full article

The subject of this research is the evaluation of electric cars and the choice of car that best meets the set research criteria. To this end, the criteria weights were determined using the entropy method with two-step normalization and a full consistency check. In addition, the entropy method was extended further with q-rung orthopair fuzzy (qROF) information and Einstein aggregation for carrying out decision making under uncertainty with imprecise information. Sustainable transportation was selected as the area of application. The current work compared a set of 20 leading EVs in India using the proposed decision-making model. The comparison was designed to cover two aspects: technical attributes and user opinions. For the ranking of the EVs, a recently developed multicriteria decision-making (MCDM) model, the alternative ranking order method with two-step normalization (AROMAN), was used. The present work is a novel hybridization of the entropy method, full consistency method (FUCOM), and AROMAN in an uncertain environment. The results show that the electricity consumption criterion (w = 0.0944) received the greatest weight, while the best ranked alternative was A7. The results also show robustness and stability, as revealed through a comparison with the other MCDM models and a sensitivity analysis. The present work is different from the past studies, as it provides a robust hybrid decision-making model that uses both objective and subjective information. Full article

This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive vector fields (RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the distances and velocities among the agents is designed to scale the RVFs adequately. It is shown that when the agents are at risk of collision, the distances among them are always greater than the safety distance. Numerical simulations and a comparison with a repulsive potential function (RPF) illustrate the agents’ performance. Full article

Can free agency be compatible with determinism? Compatibilists argue that the answer is yes, and it has been suggested that the computer science principle of “computational irreducibility” sheds light on this compatibility. It implies that there cannot, in general, be shortcuts to predict the behavior of agents, explaining why deterministic agents often appear to act freely. In this paper, we introduce a variant of computational irreducibility that intends to capture more accurately aspects of actual (as opposed to apparent) free agency, including computational sourcehood, i.e., the phenomenon that the successful prediction of a process’ behavior must typically involve an almost-exact representation of the relevant features of that process, regardless of the time it takes to arrive at the prediction. We argue that this can be understood as saying that the process itself is the source of its actions, and we conjecture that many computational processes have this property. The main contribution of this paper is technical, in that we analyze whether and how a sensible formal definition of computational sourcehood is possible. While we do not answer the question completely, we show how it is related to finding a particular simulation preorder on Turing machines, we uncover concrete stumbling blocks towards constructing such a definition, and demonstrate that structure-preserving (as opposed to merely simple or efficient) functions between levels of simulation play a crucial role. Full article

This paper considers coherent states for the representation of Weyl commutation relations over a field of p-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proven that the bases of coherent states corresponding to different lattices are mutually unbiased, and that the operators defining the quantization of symplectic dynamics are Hadamard operators. Full article

We propose a scheme for the generation of photons from a vacuum via time-modulation of a quantum system indirectly coupled to the cavity field through some ancilla quantum subsystem. We consider the simplest case when the modulation is applied to an artificial two-level atom (we call ‘t-qubit’, that can be located even outside the cavity), while the ancilla is a stationary qubit coupled via the dipole interaction both to the cavity and t-qubit. We find that tripartite entangled states with a small number of photons can be generated from the system ground state under resonant modulations, even when the t-qubit is far detuned from both the ancilla and the cavity, provided its bare and modulation frequencies are properly adjusted. We attest our approximate analytic results by numeric simulations and show that photon generation from vacuum persists in the presence of common dissipation mechanisms. Full article

This paper focuses on the adaptive control problem of a class of uncertain time-delay nonlinear cyber-physical systems (CPSs) with both unknown time-varying deception attacks and full-state constraints. Since the sensors are disturbed by external deception attacks making the system state variables unknown, this paper first establishes a new backstepping control strategy based on compromised variables and uses dynamic surface techniques to solve the disadvantages of the huge computational effort of the backstepping technique, and then establishes attack compensators to mitigate the impact of unknown attack signals on the control performance. Second, the barrier Lyapunov function (BLF) is introduced to restrict the state variables. In addition, the unknown nonlinear terms of the system are approximated using radial basis function (RBF) neural networks, and the Lyapunov–Krasovskii function (LKF) is introduced to eliminate the influence of the unknown time-delay terms. Finally, an adaptive resilient controller is designed to ensure that the system state variables converge and satisfy the predefined state constraints, all signals of the closed-loop system are semi-globally uniformly ultimately bounded under the premise that the error variables converge to an adjustable neighborhood of origin. The numerical simulation experiments verify the validity of the theoretical results. Full article

Analyzing deep neural networks (DNNs) via information plane (IP) theory has gained tremendous attention recently to gain insight into, among others, DNNs’ generalization ability. However, it is by no means obvious how to estimate the mutual information (MI) between each hidden layer and the input/desired output to construct the IP. For instance, hidden layers with many neurons require MI estimators with robustness toward the high dimensionality associated with such layers. MI estimators should also be able to handle convolutional layers while at the same time being computationally tractable to scale to large networks. Existing IP methods have not been able to study truly deep convolutional neural networks (CNNs). We propose an IP analysis using the new matrix-based Rényi’s entropy coupled with tensor kernels, leveraging the power of kernel methods to represent properties of the probability distribution independently of the dimensionality of the data. Our results shed new light on previous studies concerning small-scale DNNs using a completely new approach. We provide a comprehensive IP analysis of large-scale CNNs, investigating the different training phases and providing new insights into the training dynamics of large-scale neural networks. Full article

Ensuring the privacy and secrecy of digital medical images has become a pressing issue as a result of the quick development of smart medical technology and the exponential growth in the quantity of medical images transmitted and stored in networks. The lightweight multiple-image encryption approach for medical images that is suggested in this research can encrypt/decrypt any number of medical photos of varied sizes with just one encryption operation and has a computational cost that is similar to encrypting a single image. The plaintext images with different sizes are filled at the right and bottom of the image to ensure that the size of all plaintext images is uniform; then, all the filled images are stacked to obtain a superimposed image. The initial key, which is generated using the SHA-256 technique, is then used as the starting value of the linear congruence algorithm to create the encryption key sequence. The cipher picture is then created by encrypting the superimposed image with the encryption key and DNA encoding. The algorithm can be made even more secure by implementing a decryption mechanism that decrypts the image independently in order to reduce the possibility of information leaking during the decryption process. The outcomes of the simulation experiment demonstrate the algorithm’s strong security and resistance to interference such as noise pollution and lost image content. Full article

Over the past decades, many machine-learning- and artificial-intelligence-based technologies have been created to deduce biometric or bio-relevant parameters of speakers from their voice. These voice profiling technologies have targeted a wide range of parameters, from diseases to environmental factors, based largely on the fact that they are known to influence voice. Recently, some have also explored the prediction of parameters whose influence on voice is not easily observable through data-opportunistic biomarker discovery techniques. However, given the enormous range of factors that can possibly influence voice, more informed methods for selecting those that may be potentially deducible from voice are needed. To this end, this paper proposes a simple path-finding algorithm that attempts to find links between vocal characteristics and perturbing factors using cytogenetic and genomic data. The links represent reasonable selection criteria for use by computational by profiling technologies only, and are not intended to establish any unknown biological facts. The proposed algorithm is validated using a simple example from medical literature—that of the clinically observed effects of specific chromosomal microdeletion syndromes on the vocal characteristics of affected people. In this example, the algorithm attempts to link the genes involved in these syndromes to a single example gene (FOXP2) that is known to play a broad role in voice production. We show that in cases where strong links are exposed, vocal characteristics of the patients are indeed reported to be correspondingly affected. Validation experiments and subsequent analyses confirm that the methodology could be potentially useful in predicting the existence of vocal signatures in naïve cases where their existence has not been otherwise observed. Full article