Multifractal Company Market: An Application to the Stock Market Indices

Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects.

Optimal Control of Uniformly Heated Granular Fluids in Linear Response

We present a detailed analytical investigation of the optimal control of uniformly heated granular gases in the linear regime. The intensity of the stochastic driving is therefore assumed to be bounded between two values that are close, which limits the possible values of the granular temperature to a correspondingly small interval. Specifically, we are interested in minimising the connection time between the non-equilibrium steady states (NESSs) for two different values of the granular temperature by controlling the time dependence of the driving intensity. The closeness of the initial and target NESSs make it possible to linearise the evolution equations and rigorously—from a mathematical point of view—prove that the optimal controls are of bang-bang type, with only one switching in the first Sonine approximation. We also look into the dependence of the optimal connection time on the bounds of the driving intensity. Moreover, the limits of validity of the linear regime are investigated.

Understanding Dilated Mathematical Relationship between Image Features and the Convolutional Neural Network’s Learnt Parameters

Deep learning, in general, was built on input data transformation and presentation, model training with parameter tuning, and recognition of new observations using the trained model. However, this came with a high computation cost due to the extensive input database and the length of time required in training. Despite the model learning its parameters from the transformed input data, no direct research has been conducted to investigate the mathematical relationship between the transformed information (i.e., features, excitation) and the model’s learnt parameters (i.e., weights). This research aims to explore a mathematical relationship between the input excitations and the weights of a trained convolutional neural network. The objective is to investigate three aspects of this assumed feature-weight relationship: (1) the mathematical relationship between the training input images’ features and the model’s learnt parameters, (2) the mathematical relationship between the images’ features of a separate test dataset and a trained model’s learnt parameters, and (3) the mathematical relationship between the difference of training and testing images’ features and the model’s learnt parameters with a separate test dataset. The paper empirically demonstrated the existence of this mathematical relationship between the test image features and the model’s learnt weights by the ANOVA analysis.

Forest Fire Detection via Feature Entropy Guided Neural Network

Forest fire detection from videos or images is vital to forest firefighting. Most deep learning based approaches rely on converging image loss, which ignores the content from different fire scenes. In fact, complex content of images always has higher entropy. From this perspective, we propose a novel feature entropy guided neural network for forest fire detection, which is used to balance the content complexity of different training samples. Specifically, a larger weight is given to the feature of the sample with a high entropy source when calculating the classification loss. In addition, we also propose a color attention neural network, which mainly consists of several repeated multiple-blocks of color-attention modules (MCM). Each MCM module can extract the color feature information of fire adequately. The experimental results show that the performance of our proposed method outperforms the state-of-the-art methods.

Cooperative Spectrum Sensing Based on Multi-Features Combination Network in Cognitive Radio Network

cognitive radio, as a key technology to improve the utilization of radio spectrum, acquired much attention. Moreover, spectrum sensing has an irreplaceable position in the field of cognitive radio and was widely studied. The convolutional neural networks (CNNs) and the gate recurrent unit (GRU) are complementary in their modelling capabilities. In this paper, we introduce a CNN-GRU network to obtain the local information for single-node spectrum sensing, in which CNN is used to extract spatial feature and GRU is used to extract the temporal feature. Then, the combination network receives the features extracted by the CNN-GRU network to achieve multifeatures combination and obtains the final cooperation result. The cooperative spectrum sensing scheme based on Multifeatures Combination Network enhances the sensing reliability by fusing the local information from different sensing nodes. To accommodate the detection of multiple types of signals, we generated 8 kinds of modulation types to train the model. Theoretical analysis and simulation results show that the cooperative spectrum sensing algorithm proposed in this paper improved detection performance with no prior knowledge about the information of primary user or channel state. Our proposed method achieved competitive performance under the condition of large dynamic signal-to-noise ratio.

Inferring a Property of a Large System from a Small Number of Samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.

Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time, Configuration Entropy and Optimal Spatial Dimension

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.

Security Analysis of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution Systems in Complex Communication Environments

Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system.

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.

Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.