A Complexity Reduction Method for VVC Intra Prediction Based on Statistical Analysis and SAE-CNN

Compared with High Efficiency Video Coding (HEVC), the latest video coding standard Versatile Video Coding Standard (VVC), due to the introduction of many novel technologies and the introduction of the Quad-tree with nested Multi-type Tree (QTMT) division scheme in the block division method, the coding quality has been greatly improved. Due to the introduction of the QTMT scheme, the encoder needs to perform rate–distortion optimization for each division mode during Coding Unit (CU) division, so as to select the best division mode, which also leads to an increase in coding time and coding complexity. Therefore, we propose a VVC intra prediction complexity reduction algorithm based on statistical theory and the Size-adaptive Convolutional Neural Network (SAE-CNN). The algorithm combines the establishment of a pre-decision dictionary based on statistical theory and a Convolutional Neural Network (CNN) model based on adaptively adjusting the size of the pooling layer to form an adaptive CU size division decision process. The algorithm can make a decision on whether to divide CUs of different sizes, thereby avoiding unnecessary Rate–distortion Optimization (RDO) and reducing coding time. Experimental results show that compared with the original algorithm, our suggested algorithm can save 35.60% of the coding time and only increases the Bjøntegaard Delta Bit Rate (BD-BR) by 0.91%.

Statistical Theory of Helical Twisting in Nematic Liquid Crystals Doped with Chiral Nanoparticles

A molecular field theory of the cholesteric ordering in nematic nanocomposites doped with chiral nanoparticles was developed taking into consideration chiral dispersion interaction between rod-like nanoparticles. It was shown that the inverse pitch of the cholesteric helical structure is proportional to the anisotropy of the effective polarizability and the anisotropy of the effective gyration tensor of a nanoparticle in the nematic host. The theory enables one to predict the helical sense inversion induced by a change of the low-frequency dielectric susceptibility of the nematic host phase. The components of the high-frequency effective polarizability and the effective optical activity of a gold rod-like nanoparticle in a particular nematic solvent were calculated numerically.

Large Number of Rare Events: Diversity Analysis in Multiple Choice Questionnaires and Related Topics

<p>The statistical analysis of a large number of rare events, (LNRE), which can also be called statistical theory of diversity, is the subject of acute interest both in statistical theory and in numerous applications. A careful eye will quickly see the presence of a large number of very rare objects almost everywhere: large numbers of rare species in ecosystems, large numbers of rare opinions in any opinion pool, large numbers of small admixtures in any solution and large numbers of rare words in any text are only few examples. In studying such objects, the interest for mathematical statisticians lies in the fact that most of the frequencies are small and, therefore, difficult to deal with. It is not immediately clear how one should be able to derive consistent and reliable inference from a large number of such frequencies. In this thesis we study the diversity of questionnaires with multiple answers. It has been demonstrated that this is a particular model of LNRE theory. In our analysis, the theories of large deviation, contiguity and Edgeworth expansion were employed, and limit theorems have been established.</p>

Large Number of Rare Events: Diversity Analysis in Multiple Choice Questionnaires and Related Topics

<p>The statistical analysis of a large number of rare events, (LNRE), which can also be called statistical theory of diversity, is the subject of acute interest both in statistical theory and in numerous applications. A careful eye will quickly see the presence of a large number of very rare objects almost everywhere: large numbers of rare species in ecosystems, large numbers of rare opinions in any opinion pool, large numbers of small admixtures in any solution and large numbers of rare words in any text are only few examples. In studying such objects, the interest for mathematical statisticians lies in the fact that most of the frequencies are small and, therefore, difficult to deal with. It is not immediately clear how one should be able to derive consistent and reliable inference from a large number of such frequencies. In this thesis we study the diversity of questionnaires with multiple answers. It has been demonstrated that this is a particular model of LNRE theory. In our analysis, the theories of large deviation, contiguity and Edgeworth expansion were employed, and limit theorems have been established.</p>

Failure Detection in Eucalyptus Plantation Based on UAV Images

The information of the locations and numbers of failures is crucial to precise management of new afforestation, especially during seedling replanting in young forests. In practice, foresters are more accustomed to determining the locations of failures according to their rows than based on their geographical coordinates. The relative locations of failures are more difficult to collect than the absolute geographic coordinates which are available from an orthoimage. This paper develops a novel methodology for obtaining the relative locations of failures in rows and counting the number of failures in each row. The methodology contains two parts: (1) the interpretation of the direction angle of seedlings rows on an unmanned aerial vehicle (UAV) orthoimage based on the probability statistical theory (called the grid-variance (GV) method); (2) the recognition of the centerline of each seedling rows using K-means and the approach to counting failures in each row based on the distribution of canopy pixels near the centerline of each seedling row (called the centerline (CL) method). The experimental results showed that the GV method can accurately interpret the direction angle of rows (45°) in an orthoimage and the CL method can quickly and accurately obtain the numbers and relative locations of failures in rows. The failure detection rates in the two experimental areas were 91.8% and 95%, respectively. These research findings can provide technical support for the precise cultivation of planted seedling forests.

Applications of Flory’s Statistical Theory to Ionic Liquids in the Extended Pressure Range and at Different Temperatures

Introduction: Flory’s statistical theory (FST) for the first time, has been applied successfully to two pure ionic liquids, [C3mim][NTf2] and [C5mim][NTf2] over an extended range of pressure (0.10 – 59.9) MPa and at different temperatures (298.15 – 333.15) K . Methods: : Density and sound speed data have been employed to compute a number of useful and important properties of these ionic liquids in the light of FST. Using Flory parameters (P*, T*, V*, P̃, T̃, Ṽ) the expression for the surface tension (σ) has been deduced in the form σ = σ* σ᷉ (Ṽ), σ* and σ᷉ (Ṽ) being the characteristic and reduced values of surface tension. Since the experimental σ of liquids is not known, the validity of FST has been tested by calculating u using four different u-ρ- σ correlations, namely Auerbach (1948), Altenberg (1950) Singh et al (1997) and Modified Auerbach (2016). Results: A number of useful and important properties of ionic liquids, under the varying physical conditions, have been deduced and compared with the observed ones with quite satisfactory agreement. Such properties include Pint, van der Waals constants (a & b), parachor [P], Eötvas constant (kB), energy (∆EV) and heat of vaporization (∆HV), cohesive energy density (ced), polarity index (n) and solubility parameter (δ). Conclusion: Thus the validity of FST to two ionic liquids under the present study, has been confirmed.

STATISTICAL THEORY AND ANALYSIS IN BIOASSAY

Statistical Theory and Analysis in Bioassay is a seven-chapter monograph tailored essentially to meet the needs of graduate students, practitioners, and researchers in the fields of medicine, pharmacology, biosciences/life sciences, and related fields that employs the tools of biostatistics in bioassays and analysis. In this wise, we have taken time to discuss in detail relevant topics; principles, methods, and applications. Practice exercises are also included where necessary. The earlier chapters gave background information, definition of terms, purpose, types, structure, and relative potency in bioassay. An important theorem, Fieller’s theorem is proved in detail with illustrative examples. The last two chapters are on dose-response relationship, fitting in parallel-line assays and estimation. We are convinced that this monograph will meet the expectations of the readers while constructive criticisms that will improve another edition will be appreciated.