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While the linear Pearson correlation coefficient represents a well-established normalized measure to quantify the inter-relation of two stochastic variables X and Y, it fails for multidimensional variables, such as Cartesian coordinates. Avoiding any assumption about the underlying data, the mutual information I(X, Y) does account for multidimensional correlations. However, unlike the normalized Pearson correlation, it has no upper bound (I ∈ [0, ∞)), i.e., it is not clear if say, I = 0.4 corresponds to a low or a high correlation. Moreover, the mutual information (MI) involves the estimation of high-dimensional probability densities (e.g., six-dimensional for Cartesian coordinates), which requires a k nearest-neighbor algorithm, such as the estimator by Kraskov et al. [Phys. Rev. E 69, 066138 (2004)]. As existing methods to normalize the MI cannot be used in connection with this estimator, a new approach is presented, which uses an entropy estimation method that is invariant under variable transformations. The algorithm is numerically efficient and does not require more effort than the calculation of the (un-normalized) MI. After validating the method by applying it to various toy models, the normalized MI between the Cα-coordinates of T4 lysozyme is considered and compared to a correlation analysis of inter-residue contacts. [ABSTRACT FROM AUTHOR]

We introduce a general definition of a quantum committor in order to clarify reaction mechanisms and facilitate control in processes where coherent effects are important. With a quantum committor, we generalize the notion of a transition state to quantum superpositions and quantify the effect of interference on the progress of the reaction. The formalism is applicable to any linear quantum master equation supporting metastability for which absorbing boundary conditions designating the reactant and product states can be applied. We use this formalism to determine the dependence of the quantum transition state on coherences in a polaritonic system and optimize the initialization state of a conical intersection model to control reactive outcomes, achieving yields of the desired state approaching 100%. In addition to providing a practical tool, the quantum committor provides a conceptual framework for understanding reactions in cases when classical intuitions fail. [ABSTRACT FROM AUTHOR]

We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01 cm s−1) than for methylamine (0.069 ± 0.006 cm s−1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005 cm s−1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration. [ABSTRACT FROM AUTHOR]

Objective: This study aimed to compare the maximum and rapid force production of Spanish football players and explore the differences between age group and level of competition. Methods: A cross-sectional study was developed to evaluate the peak force (PF), relative PF, and rate of force development over 250 ms (RFD0−250) during the isometric midthigh pull between groups of football players based on age group (senior vs junior) and level of competition (national vs regional). Using a portable isometric rig, 111 football players performed 2 isometric midthigh-pull trials on a force plate. Two-way analysis of variance with Bonferroni post hoc correction was applied, and statistical significance was set at P ≤.05. The PF, relative PF, and RFD0−250 0, 25, 50, 75, and 100 percentiles were also calculated and descriptively reported, separated by age group and level of competition. Results: The analysis of variance revealed a significant main effect of the level of competition for the PF (P <.001), relative PF (P =.003), and RFD0−250 (P <.001). There was a significant main effect of age group for the PF (P <.001). There was a significant interaction effect of the age group × level of competition for relative PF (P =.014). National players were stronger than regional players on the PF and RFD0−250 (P <.001). Senior players were stronger than junior players for the PF (P <.001). Conclusions: Maximum and rapid force production are crucial for Spanish football players as they progress in both level of competition and age group. Practitioners should encourage young football players to prioritize strength development to improve their athletic performance. [ABSTRACT FROM AUTHOR]

Several types of dynamics at stationarity can be described in terms of a Markov jump process among a finite number N of representative sites. Before dealing with the dynamical aspects, one basic problem consists in expressing the a priori steady-state occupation probabilities of the sites. In particular, one wishes to go beyond the mere black-box computational tools and find expressions in which the jump rate constants appear explicitly, therefore allowing for a potential design/control of the network. For strongly connected networks admitting a unique stationary state with all sites populated, here we express the occupation probabilities in terms of a formula that involves powers of the transition rate matrix up to order N − 1. We also provide an expression of the derivatives with respect to the jump rate constants, possibly useful in sensitivity analysis frameworks. Although we refer to dynamics in (bio)chemical networks at thermal equilibrium or under nonequilibrium steady-state conditions, the results are valid for any Markov jump process under the same assumptions. [ABSTRACT FROM AUTHOR]

Purpose: This study aimed to investigate the peak performance characteristics of the world top-8 swimmers and the key factors involved in the journey toward achieving better peak performance. Methods: The results of the world top-8 swimmers from 2001 to 2022 were collected from the World Aquatics performance database. Progression to peak performance was tracked with individual quadratic trajectories (1191 cases). Utilizing k-means clustering to group competitive feature variables, this study investigated key developmental factors through a binary logistic regression model, using the odds ratio (OR) to represent whether a factor was favorable (OR > 1) or unfavorable (OR < 1). Results: Significant differences (P <.001) in the peak age between men (23.54/3.80) and women (22.31/4.60) were noticed, while no significant differences (P >.05) in the peak-performance window for both sexes appeared. Peak performance occurred at later ages for the sprint for both sexes, and women had a longer duration in peak-performance window for sprint (P <.05). Peak-performance occurred at later ages for the breaststroke and butterfly for both sexes (P <.05). Binary logistic regression revealed that high first-participation performance (OR = 1.502), high major-competition performance (OR = 4.165), early first-major-competition age (OR = 1.441), participation frequency above 4 times/year in both phase 2 (4.3–8.0 times/y, OR = 3.940; 8.1–20.0 times/y, OR = 5.122) and phase 3 (4.1–7.5 times/y: OR = 5.548; 7.7–15.0 times/y: OR = 7.526), and a career length of 10 years or more (10–15 y, OR = 2.102; 16–31 y, OR = 3.480) were favorable factors for achieving better peak performance. Conclusions: Peak performance characteristics varied across sex, swimming stroke, and race distance in the world top-8 swimmers. Meanwhile, the research indicated that certain specific developmental factors were key conditions for the world top-8 swimmers to achieve better peak performance in the future. [ABSTRACT FROM AUTHOR]

Purpose: This study aimed to cross-validate a recently proposed equation for the prediction of maximal oxygen uptake ( V ˙ O 2 max) in cycling exercise by using the average power output normalized by the body mass from a 5-minute time trial (RPO5-min) as the independent variable. Further, the study aimed to update the predictive equation using Bayesian informative prior distributions and meta-analysis. Methods: On different days, 49 male cyclists performed an incremental graded exercise test until exhaustion and a 5-minute time trial on a stationary cycle ergometer. We compared the actual V ˙ O 2 max with the predicted value obtained from the RPO5-min, using a modified Bayesian Bland–Altman agreement analysis. In addition, this study updated the data on the linear regression between V ˙ O 2 max and RPO5-min, by incorporating information from a previous study as a Bayesian informative prior distribution or via meta-analysis. Results: On average, the predicted V ˙ O 2 max using RPO5-min underestimated the actual V ˙ O 2 max by −6.6 mL·kg–1·min–1 (95% credible interval, −8.6 to −4.7 mL·kg–1·min–1). The lower and upper 95% limits of agreement were −17.2 (−22.7 to −12.3) and 3.8 (−1.0 to 9.5) mL·kg–1·min–1, respectively. When the current study's data were analyzed using the previously published data as a Bayesian informative prior distribution, the accuracy of predicting sample means was found to be better when compared with the data combined via meta-analyses. Conclusions: The proposed equation presented systematic bias in our sample, in which the prediction underestimated the actual V ˙ O 2 max. We provide an updated equation using the previous one as the prior distribution, which could be generalized to a greater audience of cyclists. [ABSTRACT FROM AUTHOR]

Purpose: This study analyzed the sequences of actions in professional men and women padel players to identify common game patterns. Methods: The sample comprised 17,557 stroke-by-stroke actions (N = 1640 rallies) of the championship World Padel Tour. Multistep Markov chains were used to calculate the conditional probabilities of occurrence of actions during the rally. Results: Results revealed that men's and women's padel is mainly defined by 36 patterns constituting 55% and 63% of all actions in the game, respectively, with the 10 most common sequences accounting for 42% to 45% of the game. There were recurrent technical–tactical actions with specific offensive and defensive functions that were constantly reiterated during the rallies. In men, the use of smash, volley, bandeja, direct, back wall, back-wall lobs, and direct lobs followed a foreseeable pattern up to 8 lags, whereas women described predictable interactions for volley, bandeja, direct, lobs, and direct lobs up to 5 lags and for smash and back wall up to 4 lags. Conclusions: The ability of padel players to recall these patterns and enhance their anticipation skills may potentially improve their performance. These findings contribute to a better knowledge of professional padel game dynamics while providing coaches and players with useful information to optimize training and decision-making strategies. [ABSTRACT FROM AUTHOR]

This study focuses on the stochastic modelling and analysis of a serial production network consisting of two manufacturing stations operating under a make-to-stock inventory policy. The outcome is a single type of product and every manufacturing station includes a machine and an output buffer. Both machines are gradually deteriorating during their operation. Deterioration results in a reduced production rate. Continuous-time Markov chain was used to model all the possible states the network transits over time due to the occurrence of certain events, such as client arrival, deterioration failure, production or repair completion. The structure of the Markov chain was thoroughly studied providing useful information, supporting the effort of numerical solving to determine the steady-state probabilities enabling the calculation of useful performance metrics like equipment availability, down time, idle time, utilisation and average inventory. Through a series of numerical experiments, the behaviour of the serial production network was examined while alternating its parameters. Interesting conclusions emerged regarding the factors affecting the operation of such production systems subjected to gradual deterioration. [ABSTRACT FROM AUTHOR]

The paper presents an analytical model for travel time evaluation in double-deep, triple-deep, quadruple-deep and fivefold-deep tier-captive shuttle-based storage and retrieval system (SBS/RS). Under the assumption of the deepest location rule for the storage process and the nearest neighbour rule for the retrieval process, the expressions for single-command and dual-command cycle times of the shuttle vehicle and elevator are developed, from which the SBS/RS performance can be estimated. The model based on the probability theory enables the evaluation of all individual times that make up the cycle times and assessment of the average number of totes relocated during a retrieval process. Special attention is devoted to the modelling of the relocation of totes which block access to the requested tote during the retrieval process. The validity of the analytical model is examined via the developed simulation model. The given case study shows that the proposed analytical travel time model results match the results of the simulation model. The presented modelling strategy could be applied to bigger system racking depths following the same modelling logic. [ABSTRACT FROM AUTHOR]

Purpose: As a multidisciplined combat sport, relationships between external and internal training loads and intensities of mixed martial arts (MMA) have not been described. The aim of this study was to determine the external loads and intensities of MMA training categories and their relationship to internal loads and intensities. Methods: Twenty MMA athletes (age = 23.3 [5.3] y, mass = 72.1 [7.2] kg, stature = 171.5 [8.4] cm) were observed for 2 consecutive weeks. Internal load and intensity (session rating of perceived exertion [sRPE]) were calculated using the Foster RPE for the session overall (sRPE-training load [TL]) and segmented RPE (segRPE-TL) for each training category: warm-up, striking drills, wrestling drills, Brazilian jiujitsu (BJJ) drills, striking sparring, wrestling sparring, BJJ sparring, and MMA sparring. External load and intensity were measured via Catapult OptimEye S5 for the full duration of each session using accumulated Playerload (PLdACC) and PLdACC per minute (PLdACC·min−1). Differences in loads between categories and days were assessed via Bayesian analysis of variance (BF10 ≥ 3). Predictive relationships between internal and external variables were calculated using Bayesian regression. Results: Session overall sRPE-TL = 448.6 (191.1) arbitrary units (AU); PLdACC = 310.6 (112) AU. Category segRPE-TL range = 33.8 (22.6) AU (warm-up) to 122.8 (54.6) AU (BJJ drills). Category PLdACC range = 44 (36.3) AU (warm-up) to 125 (58.8) AU (MMA sparring). Neither sRPE-TL nor PLdACC changed between days. PLdACC was different between categories. Evidence for regressions was strong-decisive except for BJJ drills (BF10 = 7, moderate). R2 range =.50 to.77, except for warm-up (R2 =.17), BJJ drills (R2 =.27), BJJ sparring (R2 =.49), and session overall (R2 =.13). Conclusions: While MMA training categories may be differentiated in terms of external load, overall session external load does not change within or between weeks. Resultant regression equations may be used to appropriately plan MMA technical/tactical training loads. [ABSTRACT FROM AUTHOR]

We spell out the paradigm of exact conditioning as an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-based scoring known from languages such as Stan. We study exact conditioning in the cases of discrete and Gaussian probability, presenting prototypical languages for each case and giving semantics to them. We make use of categorical probability (namely Markov and CD categories) to give a general account of exact conditioning, which avoids limits and measure theory, instead focusing on restructuring dataflow and program equations. The correspondence between such categories and a class of programming languages is made precise by defining the internal language of a CD category. [ABSTRACT FROM AUTHOR]

In response to a financial crisis, many organizations adjust their pay systems to reduce labor costs. In this research, we focus on the use of delayed pay (the postponement of employees' contractual compensation) and examine its effect on employee voluntary turnover outcomes. In a field study (Study 1) with data collected from the executive managers of 129 Chinese hotels experiencing a financial crisis caused by coronavirus disease 2019 (COVID‐19), we find a positive relationship between delayed pay and the voluntary turnover rate at the organizational level. In addition, this relationship becomes weaker when delayed pay consists of a larger proportion of pay‐for‐performance (PFP). We then conduct an experiment (Study 2) to extend our theoretical framework to the individual level, establish causality, and examine the underlying mechanism. The results show that the perceived negative instrumentality of stay (i.e., expected economic losses associated with staying in an organization) explains why individuals intend to leave organizations adopting delayed base pay but not delayed PFP. We further replicate these findings in a critical incident technique study (Study 3). We also discuss the theoretical and practical implications of these findings. [ABSTRACT FROM AUTHOR]

The probability of inserting, without overlap, a hard spherical particle of diameter σ in a hard-sphere fluid of diameter σ0 and packing fraction η determines its excess chemical potential at infinite dilution, μex(σ, η). In our previous work [R. L. Davidchack and B. B. Laird, J. Chem. Phys. 157, 074701 (2022)], we used Widom's particle insertion method within molecular dynamics simulations to obtain high precision results for μex(σ, η) with σ/σ0 ≤ 4 and η ≤ 0.5. In the current work, we investigate the behavior of this quantity at small σ. In particular, using the inclusion-exclusion principle, we relate the insertion probability to the hard-sphere fluid distribution functions and thus derive the higher-order terms in the Taylor expansion of μex(σ, η) at σ = 0. We also use direct evaluation of the excluded volume for pairs and triplets of hard spheres to obtain simulation results for μex(σ, η) at σ/σ0 ≤ 0.2247 that are of much higher precision than those obtained earlier with Widom's method. These results allow us to improve the quality of the small-σ correction in the empirical expression for μex(σ, η) presented in our previous work. [ABSTRACT FROM AUTHOR]

The three body fragmentation of methane dication has been studied using the technique of cold target recoil ion momentum spectroscopy. The process is initiated by impact of energetic Ar9+ ions on neutral methane and the data is subsequently collected in coincidence with Ar8+ projectile. By analysing the dissociation channels leading to (H + H+ + CH 2 + ) and (H + H 2 + + CH+) fragments, it is concluded that these fragments are formed in a sequential manner via formation of molecular intermediates CH 3 + and CH 2 + respectively. It is shown that these molecular intermediates carry a few eVs as their internal energies, part of which is released when they emit an H-atom with the open possibility that the final detected fragments may still be internally excited. This was accomplished by analysing the two-steps of the sequential process in their own native frames. For a molecular system having three-dimensional structure, our results prove to be an ideal example to highlight the importance of using native frames for correct interpretation of the obtained results. Our results indicate that the dissociation of methane dication can be a major source of production of H-atoms in addition to H+ fragments with the probability of the two being of similar order. [ABSTRACT FROM AUTHOR]

In this paper, we examine a supply chain consisting of a supplier with capital constraint and multiple retailers with no working capital. The retailers can get either trade credit from the supplier or loan from banks. All the retailers are differentiated by their credit scores, which measure the possibility that they default. We show that when the retailer's default probability is high compared with the marginal cost, the retailer cannot get financial support. If the retailers only get money from banks, the more reliable a retailer is, the higher the wholesale price the supplier may charge him. We also find out that the supplier has the motivation to provide trade credit even when the retailers can get money from banks. And no matter where the retailers get money from, when the initial capital is a little insufficient, the supplier will reduce the quantity of the products provided to all retailers. As the initial capital becomes less, the supplier will cut off all the supply to the lowest-score retailer first no matter whether the supplier undertakes the default risk or not. In other words, when the retailers are heterogeneous, for supplier, it is not always the more retailers, the better. [ABSTRACT FROM AUTHOR]

The returning probability (RP) theory, a rigorous diffusion-influenced reaction theory, enables us to analyze the binding process systematically in terms of thermodynamics and kinetics using molecular dynamics (MD) simulations. Recently, the theory was extended to atomistically describe binding processes by adopting the host–guest interaction energy as the reaction coordinate. The binding rate constants can be estimated by computing the thermodynamic and kinetic properties of the reactive state existing in the binding processes. Here, we propose a methodology based on the RP theory in conjunction with the energy representation theory of solution, applicable to complex binding phenomena, such as protein–ligand binding. The derived scheme of calculating the equilibrium constant between the reactive and dissociate states, required in the RP theory, can be used for arbitrary types of reactive states. We apply the present method to the bindings of small fragment molecules [4-hydroxy-2-butanone (BUT) and methyl methylthiomethyl sulphoxide (DSS)] to FK506 binding protein (FKBP) in an aqueous solution. Estimated binding rate constants are consistent with those obtained from long-timescale MD simulations. Furthermore, by decomposing the rate constants to the thermodynamic and kinetic contributions, we clarify that the higher thermodynamic stability of the reactive state for DSS causes the faster binding kinetics compared with BUT. [ABSTRACT FROM AUTHOR]

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data. [ABSTRACT FROM AUTHOR]

Purpose: This study aimed to determine the effects of a field-based priming session on perceptual, physiological, and performance responses in female rugby sevens athletes. Methods: Thirteen highly trained female rugby sevens players (age: 20.7 [2.0] y; height: 169.3 [4.8] cm; weight: 68.8 [7.9] kg) completed either a 20-minute field-based priming session or a control condition. Perceptual, physiological, and performance variables were collected at baseline (PRE) and 5 (POST5), 30 (POST30), and 120 minutes (POST120) postintervention. Data were analyzed using Bayesian mixed effects models. Results: The priming protocol had a larger increase in mental readiness (maximum a posteriori [MAP] = 20, 95% high-density intervals [HDI] = −4 to 42, probability of direction [PD]% = 95, % in region of practical equivalence [ROPE] = 9.7), physical readiness (MAP = 20.1, 95% HDI = −4.6 to 42.1, PD% = 93, % in ROPE = 10.6), and testosterone (MAP = 14.9, 95% HDI = 0.5 to 27.7, PD% = 98, % in ROPE = 5.6) than the control POST30. Cognitive performance decreased POST120 in the priming condition for congruent (MAP = 0.02, 95% HDI = −0.06 to 0.00, PD% = 95, % in ROPE = 6.4) and incongruent tasks (MAP = 0.00, 95% HDI = −0.07 to 0.00, PD% = 98, % in ROPE = 3.2) when compared with the control. Conclusions: Perceptual and physiological markers improved POST30 in the priming condition. Findings indicate that perceptual and physiological responses to priming were not coupled with performance improvements. Priming was not accompanied by perceptual, physiological, or performance improvements at POST120. [ABSTRACT FROM AUTHOR]

We consider the problem of analyzing spin-flip qubit gate operation in the presence of Random Telegraph Noise (RTN). Our compressive approach is the following. By using the Feynman disentangling operators method, we calculate the spin-flip probability of qubit driven by different kinds of composite pulses, e.g., Constant pulse (C-pulse), Quantum Well pulse (QW-pulse), and Barrier Potential pulse (BP-pulse) in the presence of RTN. When composite pulses and RTN act in the x-direction and z-direction respectively, we calculate the optimal time to achieve perfect spin-flip probability of qubit. We report that the highest fidelity of spin-flip qubit can be achieved by using C-pulse, followed by BP-pulse and QW-pulse. For a more general case, we have tested several pulse sequences for achieving high fidelity quantum gates, where we use the pulses acting in different directions. From the calculations, we find that high fidelity of qubit gate operation in the presence of RTN is achieved when QW-pulse, BP-pulse, and C-pulse act in the x-direction, y-direction, and z-direction, respectively. We extend our investigations for multiple QW and BP pulses while choosing the C-pulse amplitude constant in the presence of RTN. The results of calculation show that 98.5 % fidelity can be achieved throughout the course of RTN that may be beneficial for quantum error correction. [ABSTRACT FROM AUTHOR]

We report an algorithm based on renormalization to compute the probability that a particular state, or set thereof, is visited along the first passage or transition paths between two endpoint states of a finite Markov chain. The procedure is numerically stable and does not require dense storage of the transition matrix. [ABSTRACT FROM AUTHOR]

We investigate the implications of recovering real-world conditional expectation of return functions using options on the S&P 500 index and Treasury bond futures. First, we construct estimates of the probability of disasters, defined as higher than 6%, 5%, or 4% equity market declines over option expiration cycles. This measure of disaster probability forecasts realized disasters. Second, we employ options on the futures of the 10- and 30-year Treasury bonds to construct estimates for the expected return of bond futures. These measures display forecasting ability for subsequent futures returns beyond the level, slope, and curvature variables extracted from the yield curve. [ABSTRACT FROM AUTHOR]

Continuous time Bayesian networks (CTBNs) represent a class of stochastic processes, which can be used to model complex phenomena, for instance, they can describe interactions occurring in living processes, social science models or medicine. The literature on this topic is usually focused on a case when a dependence structure of a system is known and we are to determine conditional transition intensities (parameters of a network). In the paper, we study a structure learning problem, which is a more challenging task and the existing research on this topic is limited. The approach, which we propose, is based on a penalized likelihood method. We prove that our algorithm, under mild regularity conditions, recognizes a dependence structure of a graph with high probability. We also investigate properties of the procedure in numerical studies. [ABSTRACT FROM AUTHOR]

Subsampling is a practical strategy for analyzing vast survival data, which are progressively encountered across diverse research domains. While the optimal subsampling method has been applied to inferences for Cox models and parametric accelerated failure time (AFT) models, its application to semi‐parametric AFT models with rank‐based estimation have received limited attention. The challenges arise from the non‐smooth estimating function for regression coefficients and the seemingly zero contribution from censored observations in estimating functions in the commonly seen form. To address these challenges, we develop optimal subsampling probabilities for both event and censored observations by expressing the estimating functions through a well‐defined stochastic process. Meanwhile, we apply an induced smoothing procedure to the non‐smooth estimating functions. As the optimal subsampling probabilities depend on the unknown regression coefficients, we employ a two‐step procedure to obtain a feasible estimation method. An additional benefit of the method is its ability to resolve the issue of underestimation of the variance when the subsample size approaches the full sample size. We validate the performance of our estimators through a simulation study and apply the methods to analyze the survival time of lymphoma patients in the surveillance, epidemiology, and end results program. [ABSTRACT FROM AUTHOR]

Summary Probability weights have been widely used in addressing selection bias arising from a variety of contexts. Common examples of probability weights include sampling weights, missing data weights, and propensity score weights. Frequency weights, which are used to control for varying variabilities of aggregated outcomes, are both conceptually and analytically different from probability weights. Popular software such as R, SAS and STATA support both types of weights. Many users, including professional statisticians, become bewildered when they see identical estimates, but different standard errors and p$$ p $$‐values when probability weights are treated as frequency weights. Some even completely ignore the difference between the two types of weights and treat them as the same. Although a large body of literature exists on each type of weights, we have found little, if any, discussion that provides head‐to‐head comparisons of the two types of weights and associated inference methods. In this paper, we unveil the conceptual and analytic differences between the two types of weights within the context of parametric and semi‐parametric generalised linear models (GLM) and discuss valid inference for each type of weights. To the best of our knowledge, this is the first paper that looks into such differences by identifying the conditions under which the two types of weights can be treated the same analytically and providing clear guidance on the appropriate statistical models and inference procedures for each type of weights. We illustrate these considerations using real study data. [ABSTRACT FROM AUTHOR]

Summary This work presents an approach to control a type of stochastic cascade nonlinear systems, which involve external disturbances and nonlinear terms. The external disturbances under the consideration are not measurable and regarded as extended states. The proposed method addresses the problem of unmeasured states and external disturbances by introducing an extended state observer (ESO). Based on the above work, a new stochastic nonlinear system including ESO is established. To ensure the stability and boundedness of the system, an adaptive output feedback controller is designed by using stochastic integrated input‐to‐state stability and backstepping design technique. This controller guarantees that all the states remain almost surely bounded and globally asymptotically stable in probability. Simulation experiments are conducted to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

ABSTRACT With the widespread worldwide adoption of location‐based service technologies, accurate and reliable driving trajectories have become crucial. However, because of the inherent deficiencies of sensor devices, accurate road matching results may not always be obtained directly from trajectory data, which poses a challenge for many location and trajectory based services. Existing map‐matching techniques mainly focus on high‐sampling‐rate trajectory data while paying relatively less attention to low‐frequency trajectory data. Low‐sampling‐rate trajectory data have greater matching difficulties than high‐sampling‐rate data owing to the limited available information. Moreover, in the case of signal loss or interference, the accuracy of map‐matching algorithms can decrease significantly for low‐sampling‐rate data. To achieve accurate map‐matching results for low‐sampling‐rate trajectory data, this study proposes a map‐matching algorithm based on probability interpolation. First, the trajectory data are denoised to eliminate redundant trajectory points. Second, the concept of the probability truth value is introduced to handle the relationship between the interpolated virtual points and actual sampled trajectory points accurately. A higher probability truth value indicates a higher confidence level of the interpolation. Third, the denoised trajectory data are interpolated and a probability truth value is assigned based on the interpolation accuracy. Finally, a comprehensive probability composed of the probability truth value, emission probability, and transition probability is used to determine the correctly matched road segments. Experimental results on real trajectory datasets demonstrated that the proposed algorithm outperformed several advanced algorithms in terms of accuracy and performance. [ABSTRACT FROM AUTHOR]

Deep learning has enabled breakthroughs in automated diagnosis from medical imaging, with many successful applications in ophthalmology. However, standard medical image classification approaches only assess disease presence at the time of acquisition, neglecting the common clinical setting of longitudinal imaging. For slow, progressive eye diseases like age-related macular degeneration (AMD) and primary open-angle glaucoma (POAG), patients undergo repeated imaging over time to track disease progression and forecasting the future risk of developing a disease is critical to properly plan treatment. Our proposed Longitudinal Transformer for Survival Analysis (LTSA) enables dynamic disease prognosis from longitudinal medical imaging, modeling the time to disease from sequences of fundus photography images captured over long, irregular time periods. Using longitudinal imaging data from the Age-Related Eye Disease Study (AREDS) and Ocular Hypertension Treatment Study (OHTS), LTSA significantly outperformed a single-image baseline in 19/20 head-to-head comparisons on late AMD prognosis and 18/20 comparisons on POAG prognosis. A temporal attention analysis also suggested that, while the most recent image is typically the most influential, prior imaging still provides additional prognostic value. [ABSTRACT FROM AUTHOR]

Understanding the data and reaching accurate conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have been widely used for this purpose in various fields. One critically important yet less explored aspect is capturing and analyzing uncertainties in the data and model. Proper quantification of uncertainty helps to provide valuable information to obtain accurate diagnosis. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, various novel deep learning techniques have been proposed to deal with such uncertainties and improve the performance in decision making. [ABSTRACT FROM AUTHOR]

Analysis of integrated data often requires record linkage in order to join together the data residing in separate sources. In case linkage errors cannot be avoided, due to the lack a unique identity key that can be used to link the records unequivocally, standard statistical techniques may produce misleading inference if the linked data are treated as if they were true observations. In this paper, we propose methods for categorical data analysis based on linked data that are not prepared by the analyst, such that neither the match‐key variables nor the unlinked records are available. The adjustment is based on the proportion of false links in the linked file and our approach allows the probabilities of correct linkage to vary across the records without requiring that one is able to estimate this probability for each individual record. It accommodates also the general situation where unmatched records that cannot possibly be correctly linked exist in all the sources. The proposed methods are studied by simulation and applied to real data. [ABSTRACT FROM AUTHOR]

Anabolic androgenic steroids (AAS) are traditionally used for the treatment/control of various diseases; however, they are being used for non-therapeutic and indiscriminate purposes to enhance sports performance and physical appearance. This study aimed to assess the prevalence and associated factors of AAS use among professional CrossFit® competitors. We conducted an observational cross-sectional survey in which an anonymous questionnaire was applied to professional CrossFit® athletes. The prevalence of AAS usage was 33.3%. Most users were male (74.2%), aged between 30 and 39 years (51.6%), with completed higher education (83.9%), and had been training for more than 5 years (77.4%); the primary motivation for AAS use was performance enhancement (77.4%). Individuals who were older (p < 0.05) and more experienced in competitions (p < 0.01) are more likely to use AAS. Testosterone was the most employed AAS (71.0%); CrossFit® athletes typically used an average of 2 different AAS. The majority of users had notably sought advice from a physician (74.2%), and AAS were acquired from either drugstores (80.6%) or through illicit channels (29.0%). Moreover, 61.3% of AAS users reported experiencing adverse effects. Our results demonstrated a higher prevalence of AAS users among professional competitors in CrossFit® compared to the general population; older age and greater experience in official competitions were decisive factors for a greater inclination toward AAS use. A significant percentage of athletes seek drugs through illegal channels. Despite the majority of users experiencing adverse effects, athletes report satisfaction with use, believing that the benefits still outweigh the drawbacks. [ABSTRACT FROM AUTHOR]

We consider a continuous-time two-dimensional risk model, in which the claims from the two lines of insurance businesses satisfy an extensive asymptotic independence structure and the stochastic return is driven by a geometric Lévy process. Under a mild technical condition regarding the Laplace exponent of the Lévy process, we obtain explicit asymptotic expansions for both finite-time and infinite-time ruin probabilities when the claim sizes have regularly varying distributions. [ABSTRACT FROM AUTHOR]

We provide Bayesian inference in the context of Least Median of Squares and Least Trimmed Squares, two well-known techniques that are highly robust to outliers. We apply the new Bayesian techniques to linear models whose errors are independent or AR and ARMA. Model comparison is performed using posterior model probabilities, and the new techniques are examined using Monte Carlo experiments as well as an application to four portfolios of asset returns. [ABSTRACT FROM AUTHOR]

Abstract.In this article, by means of Rosenthal-type inequality, we study the complete convergence and strong law of large numbers for weighted sums of m-widely accpetable random variables under sub-linear expectations, which extend some existing results in classical probability space. As applications, we investigate the complete consistency and strong consistency of weighted estimators in nonparametric regression models under sub-linear expectations. In addition, we provide some simulation studies to verify the finite sample performance of the theoretical results. [ABSTRACT FROM AUTHOR]

Background: Patient-centered care aims to prevent disease and promote well-being by actively involving patients in treatment and decision-making that is based on respecting the patients and their families. However, no scales have been developed to assess patient-centered care from the nurse's perspective. This study aimed to develop a scale to measure nurses' level of patient-centered communication and confirm its validity and reliability. Methods: A methodological cross-sectional study was adopted to develop and validate the Patient-Centered Communication Scale (PCCS). The items were developed through a literature review and online interviews with nurses. Content validity was assessed by experts and the content validity index was calculated. A pretest of the questionnaire was conducted with 10 clinical nurses. To evaluate the factor structure and internal consistency reliability, the PCCS was administered online to 325 nurses in South Korea. Data were analyzed using descriptive statistics, explanatory factor analysis (EFA), and confirmatory factor analysis (CFA). Results: The final instrument consisted of 12 items and three factors: (1) information sharing, (2) patient-as-person, and (3) therapeutic alliance. EFA revealed a distinct three-factor structure, explaining 59.0% of the total variance. CFA confirmed the adequacy of the model fit and validated the inclusion of the final items. The Cronbach's alpha values ranged from 0.60 to 0.77, indicating acceptable internal consistency. Convergent validity was evidenced by the correlation between the PCCS and a measure of interpersonal communication competence. Conclusions: The 12-item PCCS showed good reliability, construct validity, and convergent validity. The scale has utility for measuring the level of patient-centered communication skills in nurses. [ABSTRACT FROM AUTHOR]

Background: Compassion fatigue in nursing interns contributes to career indecision and worsens the nursing shortage. While work environment and psychological factors are well-studied, the ethical dimension remains unexplored. Understanding these mechanisms, particularly the role of moral courage, is essential for designing interventions to combat compassion fatigue and address the workforce crisis. This study investigates the influence of moral courage on compassion fatigue among Chinese nursing interns, focusing on the mediating roles of moral sensitivity and professional identity. Methods: A quantitative, cross-sectional study was conducted in accordance with the STROBE guidelines. We used the convenience sampling method to recruit 467 nursing interns from four public junior colleges in Hunan Province, China in February, 2024. Data were collected using Compassion Fatigue Short Scale, Moral Courage Scale, Revised Moral Sensitivity Questionnaire, and Professional Identity Scale. Data analyses were conducted using SPSS 22.0 and Amos 21.0. Results: The modified model exhibited a good fit (χ2/df = 3.437, AGFI = 0.928, IFI = 0.984, TLI = 0.976, CFI = 0.984, NFI = 0.977, RMSEA = 0.072). Moral sensitivity positively influenced both moral courage and professional identity, while professional identity negatively impacted compassion fatigue. Importantly, the effect of moral courage on compassion fatigue was entirely mediated by moral sensitivity and professional identity (β = -0.114, P = 0.001). Conclusion: This study suggests that moral courage in nursing interns mitigates compassion fatigue through the combined mediating effects of moral sensitivity and professional identity. Ethics education programs fostering moral courage, moral sensitivity, and professional values in nursing students could be crucial in alleviating compassion fatigue. [ABSTRACT FROM AUTHOR]

Background: The Geriatrics Health Behavior Questionnaire (GHBQ) is essential for assessing health-related behaviors among older adults populations. This study focuses on the translation, cultural adaptation, and psychometric evaluation of the Arabic version of the GHBQ to ensure its relevance and accuracy for Arabic-speaking older adults individuals. Methods: This cross-sectional study was conducted at the Cairo University Educational Hospital's outpatient clinic. The GHBQ was translated and culturally adapted through a systematic process, including initial translation, back-translation, expert review, and pilot testing. The psychometric properties of the Arabic-translated GHBQ were evaluated using a sample of 200 older adults Arabic-speaking participants. Reliability was assessed using Cronbach's alpha (α) and Intraclass Correlation Coefficient (ICC). Validity was evaluated through Content Validity Index (CVI), Exploratory Factor Analysis (EFA), and Confirmatory Factor Analysis (CFA). Results: The Arabic GHBQ demonstrated excellent reliability with Cronbach's alpha values ranging from 0.74 to 0.87 across subscales and ICC values confirming reproducibility (ICC = 0.82). The CVI indicated strong content validity (average CVI = 0.91). EFA revealed a five-factor structure, explaining 72% of the variance, with all factor loadings exceeding 0.60. CFA supported the questionnaire's structure with fit indices meeting recommended criteria: χ²/df = 2.05, NFI = 0.92, TLI = 0.94, GFI = 0.90, SRMR = 0.05, AIC = 140.35, and BIC = 160.22. Criterion validity was confirmed through significant correlations with established health behavior measures (r = 0.63, p < 0.001). Conclusions: The culturally adapted Arabic version of the GHBQ is a reliable and valid tool for assessing health behaviors in the older adults population in Egypt. This instrument can aid healthcare providers in identifying and addressing health behaviors, ultimately improving the well-being of this demographic. Future research should focus on expanding the sample and comparing the GHBQ with other similar tools used in Arabic-speaking populations. [ABSTRACT FROM AUTHOR]

Accurately estimating the duration of freeway incidents can enhance emergency management practices and reduce the likelihood of secondary incidents. To investigate the mechanisms through which key factors influence incident duration, this study sorted out the characteristics and variables of the incident duration on a special freeway in Zhejiang Province, that is, the ring road, and developed a latent class accelerated hazard model. Heterogeneity was incorporated into the model. Three distributions (Weibull, Log-normal, and Log-logistic) were compared, and the Log-logistic distribution exhibited superior performance. The analysis revealed two distinct latent classes: Latent Class 1 and Class 2, had class membership probability of 0.53 and 0.47, respectively, with a total of 11 variables being statistically significant at the 0.05 significance level. It is worth noting that, some neglected explanatory variables are discussed in depth in this study. For example, the mechanism of which specific lane is closed has an impact on the incident duration, rather than a general discussion of the number of lane closures. Furthermore, the way in which the driver involved in the incident reports to the police has a significant impact on the duration of incidents. Notably, potential heterogeneity and its influencing mechanism are captured in the model. Additionally, by predicting class membership using posterior probabilities, it was determined that most data points were more likely to belong to Class 1, and the incident duration primarily ranged between 0 and 60 minutes. These findings are helpful to reduce the duration of incidents on ring-roads and freeways in China, and provide theoretical support for the formulation of freeway incident management and treatment policies. [ABSTRACT FROM AUTHOR]

Summary Among the variety of statistical intervals, highest‐density regions (HDRs) stand out for their ability to effectively summarise a distribution or sample, unveiling its distinctive and salient features. An HDR represents the minimum size set that satisfies a certain probability coverage, and current methods for their computation require knowledge or estimation of the underlying probability distribution or density f$$ f $$. In this work, we illustrate a broader framework for computing HDRs, which generalises the classical density quantile method. The framework is based on neighbourhood measures, that is, measures that preserve the order induced in the sample by f$$ f $$, and include the density f$$ f $$ as a special case. We explore a number of suitable distance‐based measures, such as the k$$ k $$‐nearest neighbourhood distance, and some probabilistic variants based on copula models. An extensive comparison is provided, showing the advantages of the copula‐based strategy, especially in those scenarios that exhibit complex structures (e.g. multimodalities or particular dependencies). Finally, we discuss the practical implications of our findings for estimating HDRs in real‐world applications. [ABSTRACT FROM AUTHOR]

The cGAS-STING pathway is a pivotal element of the innate immune system, recognizing cytosolic DNA to initiate the production of type I interferons and pro-inflammatory cytokines. This study investigates the alterations of the cGASSTING signaling components in the cortex and hippocampus of mice aged 24 and 108 weeks. In the cortex of old mice, an increase in the dsDNA sensor protein cGAS and its product 2030-cGAMP was observed, without corresponding activation of downstream signaling, suggesting an uncoupling of cGAS activity from STING activation. This phenomenon may be attributed to increased dsDNA concentrations in the EC neurons, potentially arising from nuclear DNA damage. Contrastingly, the hippocampus did not exhibit increased cGAS activity with aging, but there was a notable elevation in STING levels, particularly in microglia, neurons and astrocytes. This increase in STING did not correlate with enhanced IRF3 activation, indicating that brain inflammation induced by the cGAS-STING pathway may manifest extremely late in the aging process. Furthermore, we highlight the role of autophagy and its interplay with the cGAS-STING pathway, with evidence of autophagy dysfunction in aged hippocampal neurons leading to STING accumulation. These findings underscore the complexity of the cGASSTING pathway's involvement in brain aging, with regional variations in activity and potential implications for neurodegenerative diseases. [ABSTRACT FROM AUTHOR]

In order to reduce the probability of leakage and improve detection accuracy, multiple radar equipment is required to perform multiple detections on the same airspace. Due to the overlap of airspace, there are multiple local tracks reported by various radar equipment that belong to the same target. The local tracks reported by each radar require track fusion to form a system track, and track association is a prerequisite for track fusion. This paper proposes a multi-target and multi-sensor track association analysis method, which can distinguish whether local tracks come from the same target and associate local tracks with the same target, providing conditions for track fusion to form system tracks. This method divides track association into two steps: Coarse association and fine association, which greatly improves the accuracy of track association. [ABSTRACT FROM AUTHOR]

In this paper, a two-layer network model featuring inherent community structures is introduced to examine the interplay between awareness transmission and epidemic spreading. The model incorporates an unaware-aware-unaware (UAU) framework within the informational upper layer, shaped by community structures, and a susceptible-infected-susceptible (SIS) paradigm within the epidemic lower layer. The role of individual self-awareness is also considered, with the hypothesis that individuals spontaneously become aware of the disease when the local awareness rate in their vicinity exceeds a predetermined threshold. The epidemic threshold is delineated through the application of the microscopic Markov chain approach (MMCA). Findings indicate that the individual self-awareness mechanism impacts epidemic thresholds in a dual-phase manner, with distinct high and low threshold stages. It is observed that when the community structure remains static, fluctuations in the transmission probability of awareness — whether intra-community or inter-community — do not significantly influence the threshold or the ultimate scale of the epidemic. Analysis suggests that a denser community structure, along with increased inter-community connectivity, facilitates the spread of awareness and effectively suppresses the propagation of the epidemic. [ABSTRACT FROM AUTHOR]

Sinking accidents can cause catastrophic losses in human, economic resources and environmental damage. Sinking accidents are one of the most common maritime accidents that occur in Indonesia. Therefore, this study aims to analyze the cause-and-effect probability of ship sinkings in Indonesian waters. Bayesian Network method and accident factor level are used to analyze the causal factors of ship sinking accidents. The results found that the Loss of Stability of the vessel is the most sensitive node. An additional take from the investigated sinking is that half of the accidents occurred on passenger vessels, and ships over 25 years old are prone to sinking due to corrosion and lack of proper maintenance. While 70.5% of accident caused by human error that is majorly triggered by unsafe acts. The real-case analysis also performed in this study reveals that eliminating Human Error and ship’s associated factors can reduce the probability of sinking by 17.2%. [ABSTRACT FROM AUTHOR]

When planning abundance surveys, the impact of search intensity on the quality of the density estimates is rarely considered. We constructed a time‐budget modeling framework for abundance surveys using principles from optimal foraging theory. We link search intensity to the number of sample units surveyed, searcher detection probability, the number of detections made, and the precision of the estimated population density. This framework allowed us to determine how a searcher should behave to produce optimized density estimates. Using data collected from quadrat and removal surveys of zebra mussels (Dreissena polymorpha) in central Minnesota, we applied this framework to evaluate potential improvements. We found that by tuning searcher behavior, density estimates from removal surveys of zebra mussels could be improved by up to 60% in some cases, without changing the overall survey time. Our framework also predicts a critical population density where the best survey method switches from removal surveys at low densities to quadrat surveys at high densities, consistent with past empirical work. In addition, we provide simulation tools to apply this form of analysis to a number of other commonly used survey designs. Our results provide insights into how to improve the performance of many survey methods in high‐density environments by either tuning searcher behavior or decoupling the estimation of population density and detection probability. [ABSTRACT FROM AUTHOR]

ABSTRACT Wind‐blown sand movements induce desertification and cause various environmental problems. This study investigates the rebound probability of sand particles during sand transport. The widely used rebound probability models are essentially empirical and the mechanism that generates non‐rebounding particles remains unclear. By tracking the grain–bed collision process of impact particles in steady‐state sand flows, it was observed that non‐rebounding particles undergo repetitive collisional momentum losses within the rheological layer of the sand bed. Therefore, rebound probability models based on the incident velocity and angle cannot realistically describe rebound probability. Furthermore, the rheological sand bed produces numerous rebound particles with a coefficient of restitution above 1.0, converting the normal distribution of the coefficient of restitution into a lognormal distribution pattern with considerably larger variances. The new insights into aeolian rebounds gained through this study are expected to reduce the uncertainties in sand flux predictions. [ABSTRACT FROM AUTHOR]

Summary We propose a novel empirical likelihood (EL) approach for ranked set sampling (RSS) that leverages the ranking structure and information of the RSS. Our new proposal suggests constraining the sum of the within‐stratum probabilities of each rank stratum to 1/H$$ 1/H $$, where H$$ H $$ is the number of rank strata. The use of the additional constraints eliminates the need of subjective weight selection in unbalanced RSS and facilitates a seamless extension of the method for balanced RSS to unbalanced RSS. We apply our new proposal to testing one sample population mean and evaluate its performance through a numerical study and two real‐world data sets, examining obesity from body fat data and symmetry of dental size from human tooth size data. We further consider the extension of the proposed EL method to jackknife EL. [ABSTRACT FROM AUTHOR]

Background: Acute and complete unilateral vestibular deafferentation induces a significant change in ipsilateral vestibuloocular reflex gain, making the patient unable to stabilize gaze during active or passive head movements. This inability creates the illusion that the visual environment is moving, resulting in persistent visual discomfort during rapid angular or linear acceleration of the head. This is known as oscillopsia. Our objective was to understand if the spontaneous sensation of oscillopsias after complete unilateral vestibular deafferentation by vestibular neurotomy at 5 days (D5) and at 3 months (M3) is correlated with the loss of vestibuloocular reflex gain and dynamic visual acuity. Methods: Retrospective cohort study was conducted in an otolaryngology tertiary care center (2019-2022) on patients with complete unilateral vestibular loss by vestibular neurotomy. They were divided into 2 groups according to the presence (group G1) or absence (group G2) of a spontaneous complaint of oscillopsia assessed at M3. Severity of oscillopsias evaluated by Oscillopsia Severity Questionnaire. Vestibuloocular reflex gain based on video head impulse test (vHIT) and the dynamic visual acuity were measured for each group at D5 and M3. Categorical variables were compared using χ2 test and quantitative variables using the nonparametric Wilcoxon-Mann-Whitney test. Results: All patients have a complete vestibular deafferentation at D5 and M3. At D5 (G1 = 8 patients, G2 = 5 patients), there is no significant difference for ipsilateral and contralateral vestibuloocular reflex gains and dynamic visual acuity losses. The Oscillopsia Severity Questionnaire was 2.68 ± 1.03 in G1 and 1.23 ± 1.03 in G2 (P <.05). At M3 (G1 = 9 patients, G2 = 6 patients), there is no significant difference between groups for epidemiologic and clinical data and for vestibuloocular reflex and dynamic visual acuity losses. The Oscillopsia Severity Questionnaire was 2.10 ± 0.63 in G1 and 1.24 ± 0.28 in G2 (P <.05). Conclusions: The spontaneous disabling sensation of oscillopsia after complete unilateral vestibular loss is well assessed by the Oscillopsia Severity Questionnaire but cannot be explained by objective vestibular tests assessing vestibuloocular reflex gain (vHIT) or dynamic visual acuity loss at D5 or M3. Further studies are needed to measure the sensation of oscillopsia under real-life conditions and to identify the factors responsible for its persistence. Trial registration: Retrospectively registered. [ABSTRACT FROM AUTHOR]

Let R be a finite commutative ring. In this paper, we consider the probability that the product of randomly chosen three elements of R is zero, which we denote by zp3(R). First we obtain bounds for zp3(R) for various classes of rings and then show that for any ring R with identity zp3(R) ≤ 7 8. Finally, we characterize all commutative rings R with identity with certain range of zp3(R). [ABSTRACT FROM AUTHOR]

We demonstrate that the assembly pathway method underlying assembly theory (AT) is an encoding scheme widely used by popular statistical compression algorithms. We show that in all cases (synthetic or natural) AT performs similarly to other simple coding schemes and underperforms compared to system-related indexes based upon algorithmic probability that take into account statistical repetitions but also the likelihood of other computable patterns. Our results imply that the assembly index does not offer substantial improvements over existing methods, including traditional statistical ones, and imply that the separation between living and non-living compounds following these methods has been reported before. [ABSTRACT FROM AUTHOR]