Beta Transformation Research Articles

Beta transformation of the Exponential-Gaussian distribution with its properties and applications

This study introduces a five-parameter continuous probability model named the Beta-Exponential-Gaussian distribution by extending the three-parameter Exponential-Gaussian distribution with the beta transformation method. The basic properties of the new distribution, including reliability measure, hazard function, survival function, moment, skewness, kurtosis, order statistics, and asymptotic behavior, are established. Using the acceptance-rejection algorithm, simulation studies are conducted. The new model is fitted to the simulated and real data sets, and its performance is reported. The Beta-Exponential-Gaussian distribution is found to be more flexible and has better performance in many aspects. It is suggested that the new distribution would be used in modeling data having skewness and bimodal distribution.

Adapting to the Dark: A Novel Adaptive Low Light Illumination Correction Algorithm for Video Sequences in Wireless Communications

The lower image quality and higher noise levels of low light images can have a substantial effect on wireless communication. Images typically have less brightness, less clarity, and more picture noise in low light situations. The precision and dependability of picture-based communication may be impacted by this decline in image quality. Low light levels can be detrimental to video chats since it becomes difficult for the camera to get clear pictures of the user's face. This may lead to decreased video quality, trouble with facial recognition, and a generally worse user experience when communicating over video. Low light illumination correction algorithms are frequently made to work quickly and effectively in order to enable real-time video-based wireless communication. Correcting uneven illumination or low light in images is crucial for various fields; as such images pose challenges for human recognition, computer vision algorithms, and multimedia algorithms. An adaptive illumination correction algorithm based on a simple log transformation approach enhanced by a hyperbolic beta transformation and a logarithmic image processing is presented in this research. It has an adaptive optimization function that adjusts itself based on the image’s illumination and reflectance. Low computation and minimal parameter optimization are the hallmarks of this method. A variety of illuminated images and video sequences from various datasets are used to evaluate the suggested adaptive illumination approach. This adaptive illumination approach's experimental findings are impressive compared to those produced using prior techniques. The results reveal that the proposed system can adapt to various image-based communication and surveillance video sequences taken under various illumination conditions.

Effects of Multistage Aging Treatment on the Microstructure and Mechanical Properties of α + β-Type Ti-6Al-7Nb Alloy

The influence of multistage heat treatments on the microstructure and mechanical properties of Ti-6Al-7Nb alloy used for functional structures was systematically studied. Cast Ti-6Al-7Nb alloy samples were subjected to hot forging, annealing, and multiple stages of heat treatments. The relationship between volume fraction of α-phase and the mechanical properties was investigated. Herein, multiple heat treatment steps were selected based on the dilatometric analysis, at the end of the beta transformation and the start of the beta transformation, followed by aging at low temperature, i.e., 500 °C. A higher volume fraction of α-phase leads to higher strength but lower ductility. The yield, ultimate tensile strengths, and ductility of the annealed alloy are 822 MPa, 1019 MPa, and 10%, respectively. The corresponding values for the alloy treated at 900 °C followed by WQ are 777 MPa, 932 MPa, and 16%, while the aged alloy has 879 MPa, 967 MPa, and 12%, respectively. A trade-off between strength and ductility was attained. Besides, the microstructural evolution of the studied conditions was also covered in depth.Graphical

Comparison of combination methods to create calibrated ensemble forecasts for seasonal influenza in the U.S.

The characteristics of influenza seasons vary substantially from year to year, posing challenges for public health preparation and response. Influenza forecasting is used to inform seasonal outbreak response, which can in turn potentially reduce the impact of an epidemic. The United States Centers for Disease Control and Prevention, in collaboration with external researchers, has run an annual prospective influenza forecasting exercise, known as the FluSight challenge. Uniting theoretical results from the forecasting literature with domain-specific forecasts from influenza outbreaks, we applied parametric forecast combination methods that simultaneously optimize model weights and calibrate the ensemble via a beta transformation and made adjustments to the methods to reduce their complexity. We used the beta-transformed linear pool, the finite beta mixture model, and their equal weight adaptations to produce ensemble forecasts retrospectively for the 2016/2017, 2017/2018, and 2018/2019 influenza seasons in the U.S. We compared their performance to methods that were used in the FluSight challenge to produce the FluSight Network ensemble, namely the equally weighted linear pool and the linear pool. Ensemble forecasts produced from methods with a beta transformation were shown to outperform those from the equally weighted linear pool and the linear pool for all week-ahead targets across in the test seasons based on average log scores. We observed improvements in overall accuracy despite the beta-transformed linear pool or beta mixture methods' modest under-prediction across all targets and seasons. Combination techniques that explicitly adjust for known calibration issues in linear pooling should be considered to improve probabilistic scores in outbreak settings.

Динамика формирования поглощённых доз в крови лабораторных животных от альфа-излучающих радионуклидов с последовательными распадами

Since the beginning of the XXI century, active research has begun on the development of fundamentally new radiopharmaceutical drugs based on alpha-emitting maternal radionuclides for radionuclide therapy of micro-tumors and metastases. The main difficulty in assessing the absorbed doses of internal irradiation of such drugs is to take into account the radiation loads from all daughter radionuclides of sequential decay with alpha and beta transformations. The aim of the work is to develop a methodology for calculating the accumulated and total absorbed doses in the blood of laboratory animals from alpha-emitting radionuclides with successive decays within the framework of the compartment modeling method. To test the developed methodology and calculate the dosimetric characteristics, the free isotope Ac-225, injected into the blood as part of its chloride Ac-225Cl3, and the osteotropic preparation Ac-225-KHEDP (monokalium salt of hydroxyethylidendiphosphonic acid) labeled with it were selected. Quantitative data on the bio-distribution of Ac-225-KHEDP and Ac-225Cl3 in the body of intact mice were used to identify the necessary parameters. Calculations of the dosimetric characteristics of two Ac-225-labeled drugs in the blood of intact mice showed that the values of accumulated absorbed doses monotonically increase from the moment of drug administration, reaching their limit values equal to the total absorbed doses by about 300 hours. Alpha-emitting parent and daughter radionuclides make the main contribution to the values of total absorbed doses. The contribution of daughter beta-emitting radionuclides is significantly less, therefore, they can be ignored when preliminary estimates of the total absorbed doses are made. When using Ac-225-KHEDP, all radiation loads on the blood are approximately 2.5 times less compared to Ac-225Cl3, which is explained by the higher blood clearance value for Ac-225-KHEDP. The results obtained indicate the prospects for further studies of 225Ac-KHEDP and the possibility of its clinical application for the treatment of skeletal metastases.

AN EXTENDED KATZ’S DISTRIBUTION OBTAINED BY THE BETA TRANSFORMATION FOR THE COUNT DATA

In this paper, we introduce an extension of the Katz distribution constructed by the beta transformation. This is a new three-parameter distribution for the analysis and modeling of count data, which we call the new extended Katz distribution. We will study the new distribution from a probabilistic and statistical point of view. We perform a comparison study with an other extension of the Katz distribution with two methods: graphical and goodness-of-fit comparisons. For goodness-of-fit, we have considered the real data and the parameters are estimated by the maximum likelihood method.

Correlation of the Corvis Biomechanical Factor with tomographic parameters in keratoconus.

To investigate the relationship between corneal biomechanics and keratoconus (KC) severity as described by tomographic parameters. University-based German ophthalmology department. Retrospective cross-sectional study. A total of 448 KC corneas of the Homburg Keratoconus Center and 112 healthy corneas (448+112 patients) were examined by Pentacam high-resolution and Corneal Visualization Scheimpflug Technology (Pentacam HR and Corvis ST). The KC population included a wide spectrum of disease severity based on Belin's ABCD classification. Linear regression analysis was performed between the linear term of the Corvis Biomechanical Index (CBI) (CBI beta) and the tomographic values anterior radius of curvature (ARC), posterior radius of curvature (PRC), and thinnest corneal thickness (TCT). A linear transformation of the CBI beta was performed to provide an intuitive scaling, which was referred to as the Corvis Biomechanical Factor (CBiF = -0.24294226 × CBI beta + 6.02). This scaling adjusted the CBI beta to the same scale as posterior corneal curvature (PRC). There was a high correlation of the CBI beta and its modification, the CBiF, with TCT (Pearson, r = -0.775), ARC (r = -0.835), and PRC (r = -0.839) in the KC population (P < .001). In the control corneas, the correlation between the CBI beta and ARC was weak (r = -0.216, P = .022), not significant (PRC, r = -0.146, P = .125), or moderate (TCT, r = -0.628, P < .001). The linear term of the CBI was highly associated with KC severity as defined by corneal tomography. The CBiF represents a new scale based on biomechanical characteristics in KC, which could serve as a basis for a biomechanical KC classification in the future.

Unique equilibrium states for some intermediate beta transformations

We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with [Formula: see text] having the property that the orbit of 0 is bounded away from 1.

Go‐for‐green policies: The role of finance and trade for sustainable development

AbstractThe relationship between carbon dioxide (CO2) emissions and income per capita (GDPpc) is widely discussed in the environmental literature, generally known as ‘Environmental Kuznets Curve (EKC)’. The study primarily contributes to the literature on the EKC by (a) focusing on a sample of less developed countries (LDCs), (b) controlling for per capita GDP scaled by a factor of two (in logs), (c) controlling for lagged per capita GDP squared (in logs), and (d) controlling for per capita GDP cubed (in logs). The effect of environmental regulation on trade and FDI inflows evaluates the ‘Pollution Haven Hypothesis (PHH)’ across nations. The extended version of the EKC (EV‐EKC) framework validates the population‐based emission, generally known as ‘IPAT hypothesis’ where (I) is measured by air pollution (i.e. CO2 emissions), (P) is measured by population growth, (A) is measured by GDPpc, and (T) is measured by FDI inflows, trade, and energy demand. The study selected a panel of 24 LICs for the period of 2002–2016 for robust inferences. The results supported the inverted U‐shaped EKC hypothesis under the new beta's transformation in panel econometric techniques. The results partially supported the ‘PHH’ where FDI inflows are significantly associated with the CO2 emissions; while trade openness is not statistically significant in the prescribed regression apparatus. Population growth decreases carbon emissions to support the ‘genius’ principle, which rejected the IPAT hypothesis, whereas energy demand increases carbon emissions across countries.

Two bifurcation sets arising from the beta transformation with a hole at 0

Given β∈(1,2], the β-transformation Tβ:x↦βx(mod1) on the circle [0,1) with a hole [0,t) was investigated by Kalle et al. (2019). They described the set-valued bifurcation set Eβ≔{t∈[0,1):Kβ(t′)≠Kβ(t)∀t′>t},where Kβ(t)≔{x∈[0,1):Tβn(x)≥t∀n≥0} is the survivor set. In this paper we investigate the dimension bifurcation set ℬβ≔{t∈[0,1):dimHKβ(t′)≠dimHKβ(t)∀t′>t},where dimH denotes the Hausdorff dimension. We show that if β∈(1,2] is a multinacci number then the two bifurcation sets ℬβ and Eβ coincide. Moreover we give a complete characterization of these two sets. As a corollary of our main result we prove that for β a multinacci number we have dimH(Eβ∩[t,1])=dimHKβ(t) for any t∈[0,1). This confirms a conjecture of Kalle et al. for β a multinacci number.

VCO‐less PLL control‐based voltage‐source converter for power quality improvement in distributed generation system

This paper presents the voltage-controlled oscillator (VCO) less phase-locked loop (PLL)-based control of voltage source converter. It is used in the distributed power generation system for improved power quality. This control extracts the fundamental component from the sensed load current using three phases to alpha–beta transformation without using VCO, unlike synchronous reference frame–PLL, where fundamental component extraction needs two transformations with the use of VCO. Owing to the absence of VCO in the proposed method, the computational burden of trigonometric operations is very less that results in a faster dynamic response under variable conditions. This characteristic makes it suitable for the distributed power generation system, where fast changes occur frequently. In this study, wind-based distributed generation system has been taken for study, which comprises of self-excited induction generator feeding non-linear load with varying electrical conditions. Using the proposed control, the reactive power compensation, harmonics reduction and load balancing are carried out in the system. In addition to it, neutral current compensation is also accomplished with the help of star–delta transformer connected at the load end. The system performances are investigated under steady state as well as in transient state and results are found satisfactory.

Mechanical and kinetic studies on the refractory fused silica of integrally cored ceramic mold fabricated by additive manufacturing

A refractory fused silica based integrally cored ceramic mold, the ceramic core with a ceramic mold shell in a single patternless construction, is fabricated by ceramic stereolithography of additive manufacturing. Refractory ceramic molds should satisfy the following restrictions such as similar strength to that of cast metal during solidification, thermal stability for dimensional accuracy, and easy removal of core after casting. Here, we report mechanical and transformation kinetic studies on the refractory fused silica of integrally cored ceramic mold. The flexural strength of sintered silica continually increases with higher density of better densification up to 11.4 MPa at 1300 °C, while it decreases from 11.3 MPa at 1350 °C to 4.6 MPa at 1500 °C. The degradation of the flexural strength is related to the larger amount of the cristobalite and microcracks generated by the abrupt contraction induced during the transformation of beta to alpha cristobalite. Given the quantitative x-ray diffraction study on transformation kinetics, an apparent activation energy Q is 674 ± 53 kJ/mol and the average time exponent 1.85, suggesting that the transformation kinetic is controlled by 1-dimensional interfacial growth.

Synthesis and characterisation of chitin from periwinkle (Tympanotonus fusatus (L.)) and snail (Lissachatina fulica (Bowdich)) shells

This study characterizes chitin extracted from bio-sources of snail and periwinkle using varied combinations of acid and alkali concentrations. A three level factorial design of experiment with alkali and acid concentrations was used. FTIR, XRD and SEM were used to investigate the structural changes after treatments. Results reveal that both alkali and acid concentrations significantly affect the development of the functional groups and their intensities in the extracted chitin. A certain combination of concentration of acid and alkali can be used to obtain chitin with high degree of order (Crystallinity Index (CrI)>0.9) and a degree of de-acetylation (DD>50%). This results in combined high crystallinity and degree of de-acetylation. The study also established that certain combination of acid and alkali concentrations could lead to alpha to beta transformation in chitin structure.

High-Temperature Oxidation Kinetics and Behavior of Ti–6Al–4V Alloy

Owing to the high-temperature reactivity of titanium, the oxidation and alloying of titanium during hot working processes is an important variable. The oxidation behavior of Ti–6Al–4V alloy in air was investigated at various temperatures between 850 and 1100 °C for different times. The oxidation kinetics were determined by isothermal oxidation weight gain experiments. The results showed that the oxidation kinetics approximately obeyed a parabolic law. The activation energy of oxidation was estimated to be 199 and 281 kJ mol−1 when temperature was above and below the beta transformation temperature (T β), respectively. A model to predict oxidation extent was established based on experimental observations. The oxide scales mainly consisted of TiO2 with a small amount of Al2O3 and TiVO4. The alpha case was defined as solid solution formed because of oxygen diffusion into the substrate. The difference in the morphology and the formation mechanism of the alpha case at different temperature ranges was mainly owing to the participation of the grain boundary and grain orientation of the nucleation site.

Momentum and Covered Calls Almost Everywhere

We examine times series momentum and covered call strategies through conventional representations across 10 asset classes. The performance of the two strategies generally outperform static buy and hold investments and they are classified as positive and negative autocorrelation factors. The tactical overlay of time series momentum and covered call strategies onto asset classes are considered beta transformations (of previous alpha). The two “beta” replacements of the underlying asset are incorporated into well established risk based allocation heuristics such as maximum diversification and equal risk contribution. The resulting portfolios show enhanced risk adjusted performance compared to the corresponding buy and hold investments. We designate this global tactical asset allocation framework as autocorrelation factor allocation, ACFA.

Liquid phase surface nitriding of Ti-6Al-4V pre-placed with chromium

In this study, liquid phase surface nitriding of Ti-6Al-4V was carried out by pre-placing of chromium powder on the substrate and subsequent Tungsten Inert Gas (TIG) surface melting. The effect of the application of low and high heat inputs on the microstructure, microhardness and wear resistance of the treated layers were studied. Surface alloying with chromium in a nitrogen containing atmosphere resulted in the formation of hard intermetallic compounds such as TiN, Cr2N and TiCr2. Moreover, the presence of beta stabilizer chromium together with the application of high heat input during surface treatment resulted in the presence of beta phase at room temperature. However, applying low heat input could not prevent transformation of beta to martensite. The hardness of the layers fabricated at high and low heat inputs were respectively 1050 and 1200 HV0.3 compared to average 280 HV0.3 for the as-received material. Liquid phase surface treatment of titanium at the aforementioned conditions improved the wear resistance. The lowest weight loss belonged to the specimen with the beta phase matrix. The formation of the fairly ductile bcc-β phase hindered crack nucleation during wear. The weight loss in this condition was 7 times lower than that of the base material.

Initial Rotor Position Estimation and Sensorless Control of SRM Based on Coordinate Transformation

Accurate estimation of the rotor position is essential for reliable start-up and sensorless control of switched reluctance motor drives. In this paper, a series of position estimation schemes based on phase inductance vector coordinate transformations are proposed. Using the rotating coordinate transformation and coordinate components normalization, the dc component and higher order harmonics of the normalized three-phase coordinate components can be eliminated effectively. According to the coordinate transformation theory, the rotating speed of the space vector is synchronized with the angular frequency of the three-phase inductance. Thus, through alpha–beta transformation, the synchronous rotating angle of the space vector and the rotor position can be estimated. Since the rotating angle can be arbitrary, it is possible to construct another coordinate system and find one of its normalized coordinate components that is perpendicular to the one in the former coordinate system. Based on the orthogonal coordinate transformation, the rotor position can also be estimated. Experiments have been implemented for verification. The proposed methods effectively solve the challenges in initial rotor position estimation and are also suitable for reliable sensorless starting under light-load conditions. However, these methods are not suitable for high-load driving–running conditions. To solve this problem, a combination of the phase current slope difference comparison-based method and the coordinate transformation-based method is developed in this paper. The experimental results verified the validity of this method. In addition, the proposed methods do not require additional hardware and complex computation, which simplifies the implementation.

Equidistribution from fractal measures

We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that the sequence x,nx,n^2 x,... equidistributes modulo 1. This condition is robust under C^1 coordinate changes, and it applies also when n is a Pisot number and equidistribution is understood with respect to the beta-map and Parry measure. As applications we obtain new results (and strengthen old ones) about the prevalence of normal numbers in fractal sets, and new results on measure rigidity, specifically completing Host's theorem to multiplicatively independent integers and proving a Rudolph-Johnson-type theorem for certain pairs of beta transformations.

Structure and properties of Cu-37%Zn alloy during quasi-spherical explosive loading

The relations between the parameters of loading by powerful convergent shock waves (such as high pressure 40-300 GPa, high-speed deformation 106-107 с-1, tensile stress 0.25-1.75 GPa at unloading and temperature 100-2500°С ) and structural changes (main of which are effects of localized deformation, beta–alpha–beta transformation, the melting and crystallization) in alloy Cu-37%Zn were investi-gated. The investigations were performed with ball samples with diameter 60 and 40 mm. The balls were subjected to the explosion of a spherical explosive charge 10 и 20 mm thick from the surface at twelve points spread uniformly over the charge’s surface. The calculated pressure was 40 и 70 GPa on a ball’s surface and 180 и 300 GPa at its center. A correlation between macrostructural and microstructural changes and the geometrical conditions of shock-wave loading according to various schemes has been found. Effects of the interaction of converging shock waves at loading by and the related phenomena of localization of plastic deformation and the fracture were studied. The initiation of the radial cracks in the spherical samples occurs where the tensile stresses at unloading begin to exceeds the dynamic yield strength of the material. It is determined, that in the spherical sample of brass this distance corresponds to a half of radius of the sample, and the value of the tensile stress is approximately 1.3 GPa, that is close to the spall dynamic strength of brass - 1.75 GPa and exceeds the ultimate static strength of brass by a factor of 5.

A family of non-sofic beta expansions

Let ${\it\beta}_{n}&gt;1$ be a root of $x^{n}-x-1$ for $n=4,5,\ldots$ ; we will prove that ${\it\beta}_{n}$ is not a Parry number, i.e., the associated beta transformation does not correspond to a sofic symbolic system. A generalization is shown in the last section.