Tumor growth and population modeling in a toxicant-stressed random environment.

When examining some factors that contribute to the growth or decline of a population or tumor, it is essential to consider a random hypothesis. By analyzing the effects of stress on a population (or volume of tumor growth) in a random environment, we develop stochastic models describing the dynamics of the population (or tumor growth) based on random adjustments to the population's intrinsic growth rate, carrying capacity, and harvesting efforts (or tumor treatments). Apart from the models' ability to capture fluctuations, the availability of a shape parameter in the models gives it the flexibility to describe a variety of population/tumor data with different shapes. The distribution of the stressed population size with or without harvesting (or treatments) is derived and used to calculate the maximum expected amount of harvests that can be taken from the population without depleting resources in the long run (or the minimum amount of chemotherapy needed to cause shrinkage or eradication of a tumor). The work done is applied to analyze tumor growth using published data comprising of the volume of breast tumor obtained by orthotopically implanting LM2-[Formula: see text] cells into the right inguinal mammary fat pads of 6- to 8-week-old female Severe Combined Immuno-Deficient mice.

Statistical evaluation of tongue capability with visual feedback.

BACKGROUND: Analysis of tongue movement would benefit from a reference showcasing healthy tongue capability. We aimed to develop a reference of tongue capability and evaluated the role of visual feedback on the expression of movement. METHODS: Using a wireless tracking intraoral wearable device, we composed probability distributions of the tongue tip as subjects were asked to explore the entire sensing surface area. Half of the 32 subjects received live visual feedback of the location of the center of the tongue tip contact. RESULTS: We observed that the visual feedback group was 51.0% more consistent with each other in the position domain, explored 21.5% more sensing surface area, and was 50.7% more uniformly distributed. We found less consistent results when we evaluated velocity and acceleration. CONCLUSION: Visual feedback best established a healthy capability reference which can be used for designing new interfaces, quantifying tongue ability, developing new diagnostic and rehabilitation techniques, and studying underlying mechanisms of tongue motor control.

Evidence of a Proximity Effect in a (AgI)x - C(1-x) Mixture Using a Simulation Model Based on Random Variable Theory.

Silver iodide is a prototype compound of superionic conductors that allows ions to flow through its structure. It exhibits a first-order phase transition at 420 K, characterized by an abrupt change in its ionic conductivity behavior, and above this temperature, its ionic conductivity increases by more than three orders of magnitude. Introducing small concentrations of carbon into the silver iodide structure produces a new material with a mixed conductivity (ionic and electronic) that increases with increasing temperature. In this work, we report the experimental results of the ionic conductivity as a function of the reciprocal temperature for the (AgI)x - C(1-x) mixture at low carbon concentrations (x = 0.99, 0.98, and 0.97). The ionic conductivity behavior as a function of reciprocal temperature was well fitted using a phenomenological model based on a random variable theory with a probability distribution function for the carriers. The experimental data show a proximity effect between the C and AgI phases. As a consequence of this proximity behavior, carbon concentration or temperature can control the conductivity of the (AgI)x - C(1-x) mixture.

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics.

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.

Not All Probability Density Functions Are Tomograms.

This paper delves into the significance of the tomographic probability density function (pdf) representation of quantum states, shedding light on the special classes of pdfs that can be tomograms. Instead of using wave functions or density operators on Hilbert spaces, tomograms, which are the true pdfs, are used to completely describe the states of quantum systems. Unlike quasi-pdfs, like the Wigner function, tomograms can be analysed using all the tools of classical probability theory for pdf estimation, which can allow a better quality of state reconstruction. This is particularly useful when dealing with non-Gaussian states where the pdfs are multi-mode. The knowledge of the family of distributions plays an important role in the application of both parametric and nonparametric density estimation methods. We show that not all pdfs can play the role of tomograms of quantum states and introduce the conditions that must be fulfilled by pdfs to be "quantum".

A Color- and Geometric-Feature-Based Approach for Denoising Three-Dimensional Cultural Relic Point Clouds.

In the acquisition process of 3D cultural relics, it is common to encounter noise. To facilitate the generation of high-quality 3D models, we propose an approach based on graph signal processing that combines color and geometric features to denoise the point cloud. We divide the 3D point cloud into patches based on self-similarity theory and create an appropriate underlying graph with a Markov property. The features of the vertices in the graph are represented using 3D coordinates, normal vectors, and color. We formulate the point cloud denoising problem as a maximum a posteriori (MAP) estimation problem and use a graph Laplacian regularization (GLR) prior to identifying the most probable noise-free point cloud. In the denoising process, we moderately simplify the 3D point to reduce the running time of the denoising algorithm. The experimental results demonstrate that our proposed approach outperforms five competing methods in both subjective and objective assessments. It requires fewer iterations and exhibits strong robustness, effectively removing noise from the surface of cultural relic point clouds while preserving fine-scale 3D features such as texture and ornamentation. This results in more realistic 3D representations of cultural relics.

Noise-induced dynamics in a single species model with Allee effect driven by correlated colored noises.

In this paper, a single species model with Allee effect driven by correlated colored noises is proposed and investigated. The stationary probability density of the model is obtained using the approximative Fokker-Planck equation, and its shape is discussed in detail. P-bifurcation and noise-induced bistability are explored, followed by the observation of noise-enhanced stability through mean first passage time analysis. Our findings demonstrate that: (i) noise can induce P-bifurcation, causing the structure of a stationary probability distribution to shift from unimodal to monotonic under positive correlation and switch from unimodal to bimodal under negative correlation; (ii) correlation time promotes population growth, leading to a higher probability of large population size and delaying the extinction process; (iii) noise-enhanced stability induced by multiplicative noise depends on both additive noise and correlation time, while it always exists for additive noise.

Distributions of energy imparted to a micro-volume by secondary charged fragments of nuclear interactions in space radiation field.

The field of cosmic radiation at low-Earth orbit (LEO) has a complex composition. It always contains a component of secondary charged particles, formed by the products of nuclear interactions of the primary high-energy radiation with the nuclei of spacecraft's shielding material, electronic components and biological matter on board. Generation of this secondary radiation can be observed in some track detectors in the form of "stars" formed by tracks-fragments with a common vertex. The energy absorbed by the medium in the region adjacent to the interaction vertex can reach abnormally high values because of its intersection by several particle fragments. In the present paper, a methodology is considered to calculate the energy imparted by such fragments to a spherical sensitive volume in an aqueous medium. The energy distributions for three fragment events were calculated for different positions of the vertex relative to the spherical volume. The obtained data were analyzed and were compared with the distribution for a uniform fluence of secondary particles. It was shown that as the fragmentation vertex approaches the boundary of the sensitive micro-volume, the probability of events with anomalously high energy transfers, higher than the energies from single fragments, increases. The method can be applied to calculate absorbed energy distributions from secondary radiation in media of different elemental composition than that used in the present work. In the future, it is of interest to apply the method for example to study the energy imparted from secondary fragments to a silicon medium, to quantify the number of single event upsets in electronic components.

Optimization of sowing date for spring maize in China's loess plateau based on presowing temperature and soil water content.

BACKGROUND: The sowing date of spring maize in China's Loess Plateau is often restricted by the presowing temperature and soil water content (SWC). The effective measurement of the effects of presowing temperature and SWC on the sowing date is a major concern for agricultural production in this region. In this paper, we considered the average daily air temperature of ˃10 °C in the 7 days before sowing. The Decision Support System for Agrotechnology Transfer (DSSAT) model was used to simulate a spring maize yield under distinct combinations of SWC and sowing date for 51 years (1970-2020). Subsequently, through the cumulative probability distribution function, the contribution of presowing SWC to the spring maize yield was quantified, and the optimal sowing date of spring maize in each production location was determined. RESULTS: The results revealed that the daily average temperature of ˃10 °C for 7 days consecutively can be used effectively as the basis for the simulation of spring maize sowing date. The presowing SWC affected the spring maize yield but did not change the optimal sowing date. When the SWC of each study site is about 70% of the field capacity, Wenshui and Yuanping can properly delay sowing, and Lin county can sow early to obtain a higher yield. CONCLUSION: This study provides an effective approach for optimizing presowing soil moisture management and the sowing date of spring maize in the semiarid regions of the Loess Plateau. © 2023 Society of Chemical Industry.

Probability Distributions Describing Qubit-State Superpositions.

We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.

Quantum Oscillator at Temperature T and the Evolution of a Charged-Particle State in the Electric Field in the Probability Representation of Quantum Mechanics.

A short review constructing the probability representation of quantum mechanics is given, and examples of the probability distributions describing the states of quantum oscillator at temperature T and the evolution of quantum states of a charged particle moving in the electric field of an electrical capacitor are considered. Explicit forms of time-dependent integrals of motion, linear in the position and momentum, are used to obtain varying probability distributions describing the evolving states of the charged particle. Entropies corresponding to the probability distributions of initial coherent states of the charged particle are discussed. The relation of the Feynman path integral to the probability representation of quantum mechanics is established.

Causality Analysis with Information Geometry: A Comparison.

The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction of one process based on the knowledge of another process at an earlier time. However, they have their own limitations, e.g., in applications to nonlinear, non-stationary data, or non-parametric models. In this study, we propose an alternative approach to quantify causality through information geometry that overcomes such limitations. Specifically, based on the information rate that measures the rate of change of the time-dependent distribution, we develop a model-free approach called information rate causality that captures the occurrence of the causality based on the change in the distribution of one process caused by another. This measurement is suitable for analyzing numerically generated non-stationary, nonlinear data. The latter are generated by simulating different types of discrete autoregressive models which contain linear and nonlinear interactions in unidirectional and bidirectional time-series signals. Our results show that information rate causalitycan capture the coupling of both linear and nonlinear data better than GC and TE in the several examples explored in the paper.

Virtual walks inspired by a mean-field kinetic exchange model of opinion dynamics.

We propose two different schemes of realizing a virtual walk corresponding to a kinetic exchange model of opinion dynamics. The walks are either Markovian or non-Markovian in nature. The opinion dynamics model is characterized by a parameter [Formula: see text] which drives an order disorder transition at a critical value [Formula: see text]. The distribution [Formula: see text] of the displacements [Formula: see text] from the origin of the walkers is computed at different times. Below [Formula: see text], two time scales associated with a crossover behaviour in time are detected, which diverge in a power law manner at criticality with different exponent values. [Formula: see text] also carries the signature of the phase transition as it changes its form at [Formula: see text]. The walks show the features of a biased random walk below [Formula: see text], and above [Formula: see text], the walks are like unbiased random walks. The bias vanishes in a power law manner at [Formula: see text] and the width of the resulting Gaussian function shows a discontinuity. Some of the features of the walks are argued to be comparable to the critical quantities associated with the mean-field Ising model, to which class the opinion dynamics model belongs. The results for the Markovian and non-Markovian walks are almost identical which is justified by considering the different fluxes. We compare the present results with some earlier similar studies. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Meta-analysis Using Flexible Random-effects Distribution Models.

BACKGROUND: In meta-analysis, the normal distribution assumption has been adopted in most systematic reviews of random-effects distribution models due to its computational and conceptual simplicity. However, this restrictive model assumption is possibly unsuitable and might have serious influences in practices. METHODS: We provide two examples of real-world evidence that clearly show that the normal distribution assumption is explicitly unsuitable. We propose new random-effects meta-analysis methods using five flexible random-effects distribution models that can flexibly regulate skewness, kurtosis and tailweight: skew normal distribution, skew t-distribution, asymmetric Subbotin distribution, Jones-Faddy distribution, and sinh-arcsinh distribution. We also developed a statistical package, flexmeta, that can easily perform these methods. RESULTS: Using the flexible random-effects distribution models, the results of the two meta-analyses were markedly altered, potentially influencing the overall conclusions of these systematic reviews. CONCLUSION: The restrictive normal distribution assumption in the random-effects model can yield misleading conclusions. The proposed flexible methods can provide more precise conclusions in systematic reviews.

Prediction of probability distributions of molecular properties: towards more efficient virtual screening and better understanding of compound representations.

Various in silico approaches to predict activity and properties of chemical compounds constitute nowadays the basis of computer-aided drug design. While there is a general focus on the predictions of values, mathematically more appropriate is the prognosis of probability distributions, which offers additional possibilities, such as the evaluation of uncertainty, higher moments, and quantiles. In this study, we applied the Hierarchical Correlation Reconstruction approach to assess several ADMET properties of chemical compounds. It uses multiple linear regression to independently assess multiple moments, which are then finally combined into predicted probability distribution. The method enables inexpensive selection of compounds with properties nearly certain to fall into the particular range during virtual screening and automatic rejection of predictions characterized by high rate of uncertainty; however, unlike to the currently used virtual screening methods, it focuses on the prediction of the property distribution, not its actual value. Moreover, the presented protocol enables detection of structural features, which should be carefully considered when optimizing compounds towards particular property, as well as it provides deeper understanding of the examined compound representations.

Broadband and Efficient Envelope Amplifier for Envelope Elimination and Restoration/Envelope Tracking Higher-Efficiency Power Amplifiers.

Increasing the efficiency of transmitters, as the largest consumers of energy, is relevant for any wireless communication devices. For higher efficiency, a number of methods are used, including envelope tracking and envelope elimination and restoration. Increasing the bandwidth of used frequencies requires expanding envelope modulators bandwidth up to 250-500 MHz or more. The possibility of using amplifiers with input signal quantization (AISQ), as an alternative to the most common hybrid envelope tracking modulators, is considered. An approach has been developed for optimizing AISQ characteristics according to the criterion of minimum loss when amplifying modern telecommunication signals with Rayleigh envelope distribution. The optimal quantization levels are determined and the energy characteristics of AISQ are calculated. AISQ loss power is shown to decrease by 1.66 times with two-level quantization, by 2.4 times with three-level quantization, and by a factor of 3.0-3.7 for four-five quantization levels compared to a class B amplifier. With these parameters, AISQ becomes competitive with respect to hybrid envelope tracking modulators but does not have electromagnetic interference from the pulse width modulation (PWM) path.

Regional frequency analysis of drought severity and duration in Karkheh River Basin, Iran using univariate L-moments method.

Drought is one of the natural disasters that causes a great damage to human life and natural ecosystems. The main differences are in the gradual effect of drought over a relatively long period, impossibility of accurately determining time of the beginning and end of drought, and geographical extent of the associated effects. On the other hand, lack of a universally accepted definition of drought has added to the complexity of this phenomenon. In the last decade, due to increasing frequency of drought in Iran and reduction of water resources, its consequences have become apparent and have caused problems for planners and managers. So in this research, regional frequency analysis using L-moments methods was performed to investigate severity and duration of Standardized Precipitation Index (SPI), Standardized Evapotranspiration Index (SEI), Standardized Runoff Index (SRI), and Standardized Soil Moisture Index (SSI) and to study of meteorological, agricultural, and hydrological droughts in Karkheh River Basin in Iran. Using K-means clustering method, basin was divided into four homogeneous areas. Uncoordinated stations in each cluster were removed. The best regional distribution function was selected for each homogeneous region, and it was found that Pearson type (3) has the highest fit on the data set in the basin. Based on Hosking and Wallis heterogeneity test, Karkheh Basin with H1 < 1 was identified as acceptable homogeneous in all clusters. The results showed that hydrological drought occurs with a very short time delay in Karkheh River Basin after the meteorological drought, and two indicators show meteorological and hydrological drought conditions well. Agricultural drought occurs after meteorological and hydrological drought, respectively, and its severity and duration are less than the other indicators. Meteorological, hydrological, and agricultural droughts do not occur at the same time in all of the years. In general, the SPI drought index shows the most severe droughts compared with the other three indices. By this way, in 5- to 20-year return period with severity of 3SPI and in 20- to 100-year return period with severity of 7SPI, region IV or the western and northwestern areas of the basin has been affected by severe meteorological drought. By using the regional standardized quantities, it is possible to estimate the probability of drought in any part of the catchment that does not have sufficient data for hydrological studies.

Generalized Householder Transformations.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. The dichotomy is modulated by allowing more than one negative eigenvalue or by abandoning binaries altogether, yielding generalized operator-valued arguments for contextuality. We also discuss a form of contextuality by the variation of the functional relations of the operators, in particular by additivity.

On the Mortality of Companies.

Using data from both the US and UK we examine the survival and mortality of companies in both the early stage or start-up and mature phases. The shape of the mortality curve is broadly similar to that of humans. Even small single cellular organisms such as rotifers have a similar shape. The mortality falls in the early stages in a hyperbolic manner until around 20-30 years when it begins to rise broadly according to the Gompertz exponential law. To explain in simple terms these features we adapt the MinMax model introduced by the authors elsewhere to explain the shape of the human mortality curve.

Contextuality, Complementarity, Signaling, and Bell Tests.

This is a review devoted to the complementarity-contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable's outcome on the experimental context; on the system-apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr's contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling-for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of "pure contextuality" from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell-Dzhafarov-Kujala inequalities.