Entropy

Dynamical systems like the one described by the three-variable Lorenz-63 model may serve as metaphors for complex natural systems such as climate systems. When these systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz-63 model by studying its trajectories initialized far away from the asymptotic attractor. Counterintuitively, these transient trajectories exhibit complex routes and, in particular, the sensitivity to initial conditions is akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium. Full article

Traditionally, the study of quantum key distribution (QKD) assumes an omnipotent eavesdropper that is only limited by the laws of physics. However, this is not the case for specific application scenarios such as the QKD over a free-space link. In this invited paper, we introduce the geometrical optics restricted eavesdropping model for secret key distillation security analysis and apply to a few scenarios common in satellite-to-satellite applications. Full article

The paper discusses issues concerning the occurrence of anomalies affecting the process of phase transitions. The considered issue was examined from the perspective of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything. The basis for the research was the Potts model in the context of IT networks. The author proposed the classification of anomalies in relation to the states of particular nodes in the network structure. Considered anomalies included homogeneous, heterogeneous, individual and cyclic disorders. The results of tests and simulations clearly showed the impact of anomalies on the phase transitions in the network structures. The obtained results can be applied in modelling the processes occurring in network structures, particularly in IT networks. Full article

Quality of service (QoS) requirements for live streaming are most required for video-on-demand (VoD), where they are more sensitive to variations in delay, jitter, and packet loss. Dynamic Adaptive Streaming over HTTP (DASH) is the most popular technology for live streaming and VoD, where it has been massively deployed on the Internet. DASH is an over-the-top application using unmanaged networks to distribute content with the best possible quality. Widely, it uses large reception buffers in order to keep a seamless playback for VoD applications. However, the use of large buffers in live streaming services is not allowed because of the induced delay. Hence, network congestion caused by insufficient queues could decrease the user-perceived video quality. Active Queue Management (AQM) arises as an alternative to control the congestion in a router’s queue, pressing the TCP traffic sources to reduce their transmission rate when it detects incipient congestion. As a consequence, the DASH client tends to decrease the quality of the streamed video. In this article, we evaluate the performance of recent AQM strategies for real-time adaptive video streaming and propose a new AQM algorithm using Long Short-Term Memory (LSTM) neural networks to improve the user-perceived video quality. The LSTM forecast the trend of queue delay to allow earlier packet discard in order to avoid the network congestion. The results show that the proposed method outperforms the competing AQM algorithms, mainly in scenarios where there are congested networks. Full article

We study the increase in per-sample differential entropy rate of random sequences and processes after being passed through a non minimum-phase (NMP) discrete-time, linear time-invariant (LTI) filter G. For LTI discrete-time filters and random processes, it has long been established by Theorem 14 in Shannon’s seminal paper that this entropy gain, $\left(G\right)$, equals the integral of $log\left|G\right|$. In this note, we first show that Shannon’s Theorem 14 does not hold in general. Then, we prove that, when comparing the input differential entropy to that of the entire (longer) output of G, the entropy gain equals $\left(G\right)$. We show that the entropy gain between equal-length input and output sequences is upper bounded by $\left(G\right)$ and arises if and only if there exists an output additive disturbance with finite differential entropy (no matter how small) or a random initial state. Unlike what happens with linear maps, the entropy gain in this case depends on the distribution of all the signals involved. We illustrate some of the consequences of these results by presenting their implications in three different problems. Specifically: conditions for equality in an information inequality of importance in networked control problems; extending to a much broader class of sources the existing results on the rate-distortion function for non-stationary Gaussian sources, and an observation on the capacity of auto-regressive Gaussian channels with feedback. Full article

This article considers the use of the entropy method in the optimization and forecasting of multimodal transport under conditions of risks that can be determined simultaneously by deterministic, stochastic and fuzzy quantities. This will allow to change the route of transportation in real time in an optimal way with an unacceptable increase in the risk at one of its next stages and predict the redistribution of the load of transport nodes. The aim of this study is to develop a mathematical model for the optimal choice of an alternative route, the best for one or more objective functions in real time. In addition, it is proposed to use this mathematical model to estimate the dynamic change in turnover through intermediate transport nodes, forecasting their loading over time under different conditions that also include long-term risks which are significant in magnitude. To substantiate the feasibility of the proposed mathematical model, the analysis and forecast of cargo turnover through the seaports of Ukraine are presented, taking into account and analysing the existing risks. Full article

Genome-wide expression study is a powerful genomic technology to quantify expression dynamics of genes in a genome. In gene expression study, gene set analysis has become the first choice to gain insights into the underlying biology of diseases or stresses in plants. It also reduces the complexity of statistical analysis and enhances the explanatory power of the obtained results from the primary downstream differential expression analysis. The gene set analysis approaches are well developed in microarrays and RNA-seq gene expression data analysis. These approaches mainly focus on analyzing the gene sets with gene ontology or pathway annotation data. However, in plant biology, such methods may not establish any formal relationship between the genotypes and the phenotypes, as most of the traits are quantitative and controlled by polygenes. The existing Quantitative Trait Loci (QTL)-based gene set analysis approaches only focus on the over-representation analysis of the selected genes while ignoring their associated gene scores. Therefore, we developed an innovative statistical approach, GSQSeq, to analyze the gene sets with trait enriched QTL data. This approach considers the associated differential expression scores of genes while analyzing the gene sets. The performance of the developed method was tested on five different crop gene expression datasets obtained from real crop gene expression studies. Our analytical results indicated that the trait-specific analysis of gene sets was more robust and successful through the proposed approach than existing techniques. Further, the developed method provides a valuable platform for integrating the gene expression data with QTL data. Full article

Text mining is applied to 510 articles on econophysics to reconstruct the lexical evolution of the discipline from 1999 to 2020. The analysis of the relative frequency of the words used in the articles and their “visualization” allow us to draw some conclusions about the evolution of the discipline. The traditional areas of research, financial markets and distribution of wealth, remain central, but they are flanked by other strands of research—production, currencies, networks—which broaden the discipline by pushing towards a dialectical application of traditional concepts and tools drawn from statistical physics. Full article

About a century ago, in the spirit of ancient atomism, the quantum of light was renamed the photon to suggest that it is the fundamental element of everything. Since the photon carries energy in its period of time, a flux of photons inexorably embodies a flow of time. Thus, time comprises periods as a trek comprises legs. The flows of quanta naturally select optimal paths (i.e., geodesics) to level out energy differences in the least amount of time. The corresponding flow equations can be written, but they cannot be solved. Since the flows affect their driving forces, affecting the flows, and so on, the forces (i.e., causes) and changes in motions (i.e., consequences) are inseparable. Thus, the future remains unpredictable. However, it is not all arbitrary but rather bounded by free energy. Eventually, when the system has attained a stationary state where forces tally, there are no causes and no consequences. Since there are no energy differences between the system and its surroundings, the quanta only orbit on and on. Thus, time does not move forward either but circulates. Full article

IIT includes commitments about the very nature of physical reality, a fact both highly unusual for an empirical theory within neuroscience, and surprisingly underappreciated within the literature. These commitments are intimately tied to the theory; they are not incidental. This paper demonstrates as much by raising certain objections in a “naive” way, and then exposing how the principled IIT responses would rely upon metaphysical positions. Along the way we draw on the IIT literature for support for these interpretations, but also point to a need for elaboration and clarification. Section 1 applies the Placement Argument in a way that leads to problem involving zombies, treated in Section 2. Section 3 frames the zombie problem as an apparent dilemma, and addresses that dilemma by drawing on claims in the IIT literature concerning physical reality. Section 4 raises a related dilemma and treats it in a way that dovetails with the treatment in Section 3 of physical reality. All of this underscores not just the breadth of IIT, but the relevance of this breadth to a full consideration of IIT’s merits. Full article

Stochastic spatio-temporal processes are prevalent across domains ranging from the modeling of plasma, turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by describing them as evolutionary processes on Hilbert spaces, and in doing so, derives a framework for spatio-temporal manipulation from fundamental thermodynamic principles. This approach yields a variational optimization framework for controlling stochastic fields. The resulting scheme is applicable to a wide class of spatio-temporal processes and can be used for optimizing parameterized control policies. Our simulated experiments explore the application of two forms of this approach on four stochastic spatio-temporal processes, with results that suggest new perspectives and directions for studying stochastic control problems for spatio-temporal systems. Full article

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts. Full article

There exists a natural trade-off in public key encryption (PKE) schemes based on ring learning with errors (RLWE), namely: we would like a wider error distribution to increase the security, but it comes at the cost of an increased decryption failure rate (DFR). A straightforward solution to this problem is the error-correcting code, which is commonly used in communication systems and already appears in some RLWE-based proposals. However, applying error-correcting codes to those cryptographic schemes is far from simply installing an add-on. Firstly, the residue error term derived by decryption has correlated coefficients, whereas most prevalent error-correcting codes with remarkable error tolerance assume the channel noise to be independent and memoryless. This explains why only simple error-correcting methods are used in existing RLWE-based PKE schemes. Secondly, the residue error term has correlated coefficients leaving accurate DFR estimation challenging even for uncoded plaintext. It can be found in the literature that a tighter DFR estimation can effectively create a DFR margin. Thirdly, most error-correcting codes are not well designed for safety considerations, e.g., syndrome decoding has a nonconstant time nature. A code good at error correcting might be weak under a variety of attacks. In this work, we propose a polar coding scheme for RLWE-based PKE. A relaxed “independence” assumption is used to derive an uncorrelated residue noise term, and a wireless communication strategy, outage, is used to construct polar codes. Furthermore, some knowledge about the residue noise is exploited to improve the decoding performance. With the parameterization of NewHope Round 2, the proposed scheme creates a considerable DRF margin, which gives a competitive security improvement compared to state-of-the-art benchmarks. Specifically, the security is improved by $28.8\%$, while a DFR of $2^{-149}$ is achieved a for code rate pf 0.25, $n=1024,q=$ 12,289, and binomial parameter $k=55$. Moreover, polar encoding and decoding have a quasilinear complexity $O\left(N{log}_{2}N\right)$ and intrinsically support constant-time implementations. Full article

We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases of quantum systems. The nicest thing about this framework is that we can characterize the properties of quantum codes by the properties of the group algebra. We show how it characterizes the properties of quantum codes as well as generates some new results about quantum codes. Full article

For finding colorectal polyps the standard method relies on the techniques and devices of colonoscopy and the medical expertise of the gastroenterologist. In case of images acquired through colonoscopes the automatic segmentation of the polyps from their environment (i.e., from the bowel wall) is an essential task within computer aided diagnosis system development. As the number of the publicly available polyp images in various databases is still rather limited, it is important to develop metaheuristic methods, such as fuzzy inference methods, along with the deep learning algorithms to improve and validate detection and classification techniques. In the present manuscript firstly a fuzzy rule set is generated and validated. The former process is based on a statistical approach and makes use of histograms of the antecedents. Secondly, a method for selecting relevant antecedent variables is presented. The selection is based on the comparision of the histograms computed from the measured values for the training set. Then the inclusion of the Rényi-entropy-based structural entropy and the spatial filling factor into the set of input variables is proposed and assessed. The beneficial effect of including the mentioned structural entropy of the entropies from the hue and saturation (H and S) colour channels resulted in 65% true positive and 60% true negative rate of the classification for an advantageously selected set of antecedents when working with HSV images. Full article

Wind erosion is the leading cause of soil degradation and air pollution in many regions of the world. As wind erosion is controlled by climatic factors, research on this phenomenon is urgently needed in soil and land management in order to better adapt to climate change. In this paper, the impact of wind erosion on the soil surface in relation to particle size distribution was investigated. Changes in percentage of sand, silt and clay fractions based on historical KPP data (1961–1970), LUCAS data base (2009), and field measurements (2016) were analysed in five cadastral areas impacted by wind erosion (Záhorie Lowlands, Slovakia). With the use of GIS tools, models of spatial distribution of sand, silt, clay and erodible fraction (EF) content were developed based on those measurements. Our findings proved that soil texture change driven by wind erosion could happen relatively quickly, and a significant proportion of soil fine particles may be carried away within a few years. The results indicate that the soil surface became much rougher over the period of more than 50 years, but also that the accumulation of fraction of the silt particles occurred in most of the areas affected by the erosive effect. Full article

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set. Full article

Achieving real-time inference is one of the major issues in contemporary neural network applications, as complex algorithms are frequently being deployed to mobile devices that have constrained storage and computing power. Moving from a full-precision neural network model to a lower representation by applying quantization techniques is a popular approach to facilitate this issue. Here, we analyze in detail and design a 2-bit uniform quantization model for Laplacian source due to its significance in terms of implementation simplicity, which further leads to a shorter processing time and faster inference. The results show that it is possible to achieve high classification accuracy (more than 96% in the case of MLP and more than 98% in the case of CNN) by implementing the proposed model, which is competitive to the performance of the other quantization solutions with almost optimal precision. Full article