RESUMEN

Nanobubbles are sub- micron-sized gas entities that find applications in a wide  range of scientific fields. Typically, they are thought to  diffuse according to Brownian motion. We report the  existence of self-propelled motion of oxygen bulk  nanobubbles in ultrapure water at body temperature.  Their motion, to a large extent, is self-affine; there are  different scaling exponents along the x- and y-axes as  well as for the lateral displacement. We use fractal  analysis, and we calculate the structure function, the  normalised velocity autocorrelation function, the  skewness, and the kurtosis. All descriptors attest the  existence of a quasi-Gaussian stochastic process, which  is classified as fractional Brownian motion. More than 50 \% of the trajectories along the x-axis follow  superdiffusion, while this amount drops to 30 \% for  motion along the y-axis as a result of the asymmetry of  the field of view.

RESUMEN

This study presents a computational investigation of a stochastic Zika virus along with optimal control model using the Legendre spectral collocation method (LSCM). By accumulation of stochasticity into the model through the proposed stochastic differential equations, we appropriating the random fluctuations essential in the progression and disease transmission. The stability, convergence and accuracy properties of the LSCM are conscientiously analyzed and also demonstrating its strength for solving the complex epidemiological models. Moreover, the study evaluates the various control strategies, such as treatment, prevention and treatment pesticide control, and identifies optimal combinations that the intervention costs and also minimize the proposed infection rates. The basic properties of the given model, such as the reproduction number, were determined with and without the presence of the control strategies. For R 0 < 0 , the model satisfies the disease-free equilibrium, in this case the disease die out after some time, while for R 0 > 1 , then endemic equilibrium is satisfied, in this case the disease spread in the population at higher scale. The fundamental findings acknowledge the significant impact of stochastic phonemes on the robustness and effectiveness of control strategies that accelerating the need for cost-effective and multi-faceted approaches. In last the results provide the valuable insights for public health department to enabling more impressive mitigation of Zika virus outbreaks and management in real-world scenarios.

Asunto(s)

RESUMEN

In this paper, we propose a new Bayesian adaptive design, score-goldilocks design, which has the same algorithmic idea as goldilocks design. The score-goldilocks design leads to a uniform formula for calculating the probability of trial success for different endpoint trials by using the normal approximation. The simulation results show that the score-goldilocks design is not only very similar to the goldilocks design in terms of operating characteristics such as type 1 error, power, average sample size, probability of stop for futility, and probability of early stop for success, but also greatly saves the calculation time and improves the operation efficiency.

RESUMEN

Mastering the self-organization of nanoparticle morphologies is pivotal in soft matter physics and film growth. Silicon dioxide (SiO2) nanoparticles are an archetypical model of nanomotor in soft matter. Here, the emphasis is on the self-organizing behavior of SiO2 nanoparticles under extreme conditions. It is unveiled that manipulating the states of the metal substrate profoundly dictates the motion characteristics of SiO2 nanoparticles. This manipulation triggers the emergence of intricate morphologies and distinctive patterns. Employing a reaction-diffusion model, the fundamental roles played by Brownian motion and Marangoni-driven motion in shaping fractal structures and radial Turing patterns are demonstrated, respectively. Notably, these radial Turing patterns showcase hyperuniform order, challenging conventional notions of film morphology. These discoveries pave the way for crafting non-equilibrium morphological materials, poised with the potential for self-healing, adaptability, and innovative applications.

RESUMEN

Tool wear prediction is of great significance in industrial production. Current tool wear prediction methods mainly rely on the indirect estimation of machine learning, which focuses more on estimating the current tool wear state and lacks effective quantification of random uncertainty factors. To overcome these shortcomings, this paper proposes a novel method for predicting cutting tool wear. In the offline phase, the multiple degradation features were modeled using the Brownian motion stochastic process and a SVR model was trained for mapping the features and the tool wear values. In the online phase, the Bayesian inference was used to update the random parameters of the feature degradation model, and the future trend of the features was estimated using simulation samples. The estimation results were input into the SVR model to achieve in-advance prediction of the cutting tool wear in the form of distribution densities. An experimental tool wear dataset was used to verify the effectiveness of the proposed method. The results demonstrate that the method shows superiority in prediction accuracy and stability.

RESUMEN

Desert ants stand out as some of the most intriguing insect navigators, having captured the attention of scientists for decades. This includes the structure of walking trajectories during goal approach and search behaviour for the nest and familiar feeding sites. In the present study, we analysed such trajectories with regard to changes in walking direction. The directional change of the ants was quantified, i.e. an angle θ between trajectory increments of a given arclength λ was computed. This was done for different length scales λ, according to our goal of analysing desert ant path characteristics with respect to length scale. First, varying λ through more than two orders of magnitude demonstrated Brownian motion characteristics typical of the random walk component of search behaviour. Unexpectedly, this random walk component was also present in - supposedly rather linear - approach trajectories. Second, there were small but notable deviations from a uniform angle distribution that is characteristic of random walks. This was true for specific search situations, mostly close to the (virtual) goal position. And third, experience with a feeder position resulted in straighter approaches and more focused searches, which was also true for nest searches, albeit to a lesser extent. Taken together, these results both verify and extend previous studies on desert ant path characteristics. Of particular interest are the ubiquitous Brownian motion signatures and specific deviations thereof close to the goal position, indicative of unexpectedly structured search behaviour.

Asunto(s)

RESUMEN

Swarm robots are frequently preferred for the exploration of harsh environments and search and rescue operations. This study explores the factors that influence the movement strategies of autonomous robot swarms and their impact on swarm distribution in the field, employing simulation-based analysis. The research consists of two parts: initially, robots undergo free-fall as passive entities, followed by a phase where they employ predefined movement strategies from their fall positions. The study aims to investigate how the initial position and related parameters affect movement characteristics and the ultimate swarm distribution. To achieve this objective, four parameters-radius, height, mass, and the Coefficient of Restitution-were identified, each assigned three different values. The study observes the effects of these parameters on robot motion, considering motion strategies such as Random Walk, Levy Walk, Markov Process, and Brownian Motion. Results indicate that increasing parameter values induce changes in the position values of the free-falling swarm in the first part, which is the initial position for the second part, influencing movement strategies in diverse ways. The outcomes are analyzed concerning the radial and angular spread of the robots. Radial spread measures how far swarm elements spread from their initial positions, while angular spread indicates how homogeneously the robots are distributed according to the polar angle. The study comprehensively investigates how the movement strategies of autonomous robot swarms are impacted by parameters and how these effects manifest in the results. The findings are anticipated to enhance the effective utilization of autonomous robot swarms in exploration missions.

Asunto(s)

RESUMEN

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov-Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.

RESUMEN

We propose an adaptive sequential testing procedure for the selection and testing of multiple treatment options, such as dose/regimen, different drugs, sub-populations, endpoints, or a mixture of them in a seamlessly combined phase II/III trial. The selection is to be made at the end of phase 2 stage. Unlike in many of the published literature, the selection rule is not required to be to "select the best", and does not need to be pre-specified, which provides flexibility and allows the trial investigators to use any efficacy and safety information/criteria, or surrogate or intermediate endpoint to make the selection. Sample size and power calculations are provided. The calculations have been confirmed to be accurate by simulations. Interim analysis can be performed after the selection, sample size can be modified if the observed efficacy deviates from the assumed. Inference after the trial, including p-value, median unbiased point estimate and confidence intervals, are provided. By applying a dominance theorem, the procedure can be applied to normal, binary, Poisson, negative binomial distributed endpoints and time-to-event endpoints, and a mixture of these distributions (in trials involving endpoint selection).

RESUMEN

Desert ants stand out as some of the most intriguing insect navigators, having captured the attention of scientists for decades. This includes the structure of walking trajectories during goal approach and search behaviour for the nest and familiar feeding sites. In the present study, we analysed such trajectories with regard to changes in walking direction. The directional change of the ants was quantified, i.e. an angle θ between trajectory increments of a given arclength λ was computed. This was done for different length scales λ, according to our goal of analysing desert ant path characteristics with respect to length scale. First, varying λ through more than two orders of magnitude demonstrated Brownian motion characteristics typical of the random walk component of search behaviour. Unexpectedly, this random walk component was also present in - supposedly rather linear - approach trajectories. Second, there were small but notable deviations from a uniform angle distribution that is characteristic of random walks. This was true for specific search situations, mostly close to the (virtual) goal position. And third, experience with a feeder position resulted in straighter approaches and more focused searches, which was also true for nest searches, albeit to a lesser extent. Taken together, these results both verify and extend previous studies on desert ant path characteristics. Of particular interest are the ubiquitous Brownian motion signatures and specific deviations thereof close to the goal position, indicative of unexpectedly structured search behaviour.

Asunto(s)

RESUMEN

Tracing fast nanopore-translocating analytes requires a high-frequency measurement system that warrants a temporal resolution better than 1 µs. This constraint may practically shift the challenge from increasing the sampling bandwidth to dealing with the rapidly growing noise with frequencies typically above 10 kHz, potentially making it still uncertain if all translocation events are unambiguously captured. Here, a numerical simulation model is presented as an alternative to discern translocation events with different experimental settings including pore dimension, bias voltage, the charge state of the analyte, salt concentration, and electrolyte viscosity. The model allows for simultaneous analysis of forces exerting on a large analyte cohort along their individual trajectories; these forces are responsible for the analyte movement leading eventually to the nanopore translocation. Through tracing the analyte trajectories, the Brownian force is found to dominate the analyte movement in electrolytes until the last moment at which the electroosmotic force determines the final translocation act. The mean dwell time of analytes mimicking streptavidin decreases from ≈6 to ≈1 µs with increasing the bias voltage from ±100 to ±500 mV. The simulated translocation events qualitatively agree with the experimental data with streptavidin. The simulation model is also helpful for the design of new solid-state nanopore sensors.

RESUMEN

When writing down a Langevin equation for the time evolution of a "system" in contact with a thermal bath, one typically makes the implicit (and often tacit) assumption that the thermal environment is in equilibrium at all times. Here, we take this assumption as a starting point to formulate the problem of a system evolving in contact with a thermal bath from the perspective of the bath, which, since it is in equilibrium, can be described by the microcanonical ensemble. We show that the microcanonical ensemble of the bath, together with the Hamiltonian equations of motion for all the constituents of the bath and system together, give rise to a Langevin equation for the system evolution alone. The friction coefficient turns out to be given in terms of auto-correlation functions of the interaction forces between the bath particles and the system, and the Einstein relation is recovered. Moreover, the connection to the Fokker-Planck equation is established.

RESUMEN

Designing clinical trials for emerging infectious diseases such as COVID-19 is challenging because information needed for proper planning may be lacking. Pre-specified adaptive designs can be attractive options, but what happens if a trial with no such design needs to be modified? For example, unexpectedly high efficacy (approximately 95%) in two COVID-19 vaccine trials might cause investigators in other COVID-19 vaccine trials to increase the number of interim analyses to allow earlier stopping for efficacy. If such a decision is based solely on external data, there are no issues, but what if internal trial data by arm are also examined? Fortunately, the conditional error principle of Müller and Schäfer (2004) can be used to ensure no inflation of the type 1 error rate, even if no interim analyses were planned. We study the properties, including limitations, of this method. We provide a shiny app to evaluate changes in timing of interim analyses in response to outcome data by arm in clinical trials.

Asunto(s)

RESUMEN

The cerebrovascular system is characterized by parameters such as arterial blood pressure (ABP), cerebral perfusion pressure (CPP), and cerebral blood flow velocity (CBFV). These are regulated by interconnected feedback loops resulting in a fluctuating and complex time course. They exhibit fractal characteristics such as (statistical) self-similarity and scale invariance which could be quantified by fractal measures. These include the coefficient of variation, the Hurst coefficient H, or the spectral exponent α in the time domain, as well as the spectral index ß in the frequency domain. Prior to quantification, the time series has to be classified as either stationary or nonstationary, which determines the appropriate fractal analysis and measure for a given signal class. CBFV was characterized as a nonstationary (fractal Brownian motion) signal with spectral index ß between 2.0 and 2.3. In the high-frequency range (>0.15 Hz), CBFV variability is mainly determined by the periodic ABP variability induced by heartbeat and respiration. However, most of the spectral power of CBFV is contained in the low-frequency range (<0.15 Hz), where cerebral autoregulation acts as a low-pass filter and where the fractal properties are found. Cerebral vasospasm, which is a complication of subarachnoid hemorrhage (SAH), is associated with an increase in ß denoting a less complex time course. A reduced fractal dimension of the retinal microvasculature has been observed in neurodegenerative disease and in stroke. According to the decomplexification theory of illness, such a diminished complexity could be explained by a restriction or even dropout of feedback loops caused by disease.

Asunto(s)

RESUMEN

Upconverting nanoparticles are essential in modern photonics due to their ability to convert infrared light to visible light. Despite their significance, they exhibit limited brightness, a key drawback that can be addressed by combining them with plasmonic nanoparticles. Plasmon-enhanced upconversion has been widely demonstrated in dry environments, where upconverting nanoparticles are immobilized, but constitutes a challenge in liquid media where Brownian motion competes against immobilization. This study employs optical tweezers for the three-dimensional manipulation of an individual upconverting nanoparticle, enabling the exploration of plasmon-enhanced upconversion luminescence in water. Contrary to expectation, experiments reveal a long-range (micrometer scale) and moderate (20%) enhancement in upconversion luminescence due to the plasmonic resonances of gold nanostructures. Comparison between experiments and numerical simulations evidences the key role of Brownian motion. It is demonstrated how the three-dimensional Brownian fluctuations of the upconverting nanoparticle lead to an "average effect" that explains the magnitude and spatial extension of luminescence enhancement.

RESUMEN

Homeostatic, circadian and ultradian mechanisms play crucial roles in the regulation of sleep. Evidence suggests that ratios of low-to-high frequency power in the electroencephalogram (EEG) spectrum indicate the instantaneous level of sleep pressure, influenced by factors such as individual sleep-wake history, current sleep stage, age-related differences and brain topography characteristics. These effects are well captured and reflected in the spectral exponent, a composite measure of the constant low-to-high frequency ratio in the periodogram, which is scale-free and exhibits lower interindividual variability compared to slow wave activity, potentially serving as a suitable standardization and reference measure. Here we propose an index of sleep homeostasis based on the spectral exponent, reflecting the level of membrane hyperpolarization and/or network bistability in the central nervous system in humans. In addition, we advance the idea that the U-shaped overnight deceleration of oscillatory slow and fast sleep spindle frequencies marks the biological night, providing somnologists with an EEG-index of circadian sleep regulation. Evidence supporting this assertion comes from studies based on sleep replacement, forced desynchrony protocols and high-resolution analyses of sleep spindles. Finally, ultradian sleep regulatory mechanisms are indicated by the recurrent, abrupt shifts in dominant oscillatory frequencies, with spindle ranges signifying non-rapid eye movement and non-spindle oscillations - rapid eye movement phases of the sleep cycles. Reconsidering the indicators of fundamental sleep regulatory processes in the framework of the new Fractal and Oscillatory Adjustment Model (FOAM) offers an appealing opportunity to bridge the gap between the two-process model of sleep regulation and clinical somnology.

Asunto(s)

RESUMEN

We record and analyze the movement patterns of the marsupial Didelphis aurita at different temporal scales. Animals trajectories are collected at a daily scale by using spool-and-line techniques and, with the help of radio-tracking devices, animals traveled distances are estimated at intervals of weeks. Small-scale movements are well described by truncated Lévy flight, while large-scale movements produce a distribution of distances which is compatible with a Brownian motion. A model of the movement behavior of these animals, based on a truncated Lévy flight calibrated on the small scale data, converges towards a Brownian behavior after a short time interval of the order of 1 week. These results show that whether Lévy flight or Brownian motion behaviors apply, will depend on the scale of aggregation of the animals paths. In this specific case, as the effect of the rude truncation present in the daily data generates a fast convergence towards Brownian behaviors, Lévy flights become of scarce interest for describing the local dispersion properties of these animals, which result well approximated by a normal diffusion process and not a fast, anomalous one. Interestingly, we are able to describe two movement phases as the consequence of a statistical effect generated by aggregation, without the necessity of introducing ecological constraints or mechanisms operating at different spatio-temporal scales. This result is of general interest, as it can be a key element for describing movement phenomenology at distinct spatio-temporal scales across different taxa and in a variety of systems.

RESUMEN

We introduce a modified spatial Λ-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective population density. We derive an analytical formula for the expected number of shared haplotype segments between two individuals depending on their sampling locations. This formula involves the transition density of a skew diffusion which appears as a scaling limit of the ancestral lineages of individuals in this model. We then show that this formula can be used to infer the dispersal parameters and the effective population density of both regions, using a composite likelihood approach, and we demonstrate the efficiency of this method on a range of simulated data sets.

Asunto(s)

RESUMEN

Nanofluid is a specially crafted fluid comprising a pure fluid with dispersed nanometer-sized particles. Incorporation these nanoparticles into pure fluid results in a fluid with improved thermal properties in comparison of pure fluid. The enhanced properties of nanofluids make them highly sought after, in diverse applications, consisting of coolant of devices, heat exchangers, and thermal solar systems. In this study hybrid nanofluid consisting of copper, alumina and titanium nanoparticles on a curved sheet has investigated with impact of chemical reactivity, magnetic field and Joule heating. The leading equations have converted to normal equations by using appropriate set of variables and has then evaluated by homotopy analysis method. The outcomes are shown through Figures and Tables and are discussed physically. It has revealed in this study that Cu-nanofluid flow has augmented velocity, temperature, and volume fraction distributions than those of Al2O3-nanofluid and TiO2-nanofluid. Also, the Cu-nanofluid flow has higher heat and mass transfer rates than those of Al2O3-nanofluid and TiO2-nanofluid.

RESUMEN

In this study, the computational analysis of entropy generation optimization for synthetic cilia regulated ternary hybrid Jeffery nanofluid (Ag-Au-TiO2/PVA) flow through a peristaltic vertical channel with swimming motile Gyrotactic microorganisms is investigated. Understanding the intricate interaction of multiple physical phenomena in biomedical applications is essential for optimizing entropy generation and advancing microfluidic systems. The characteristics of nanofluid are explored for the electroosmotic MHD fluid flow in the presence of thermophoresis and Brownian motion, viscous dissipation, Ohmic heating and chemical reaction. Using the appropriate transformations, a set of ordinary differential equations are created from the governing partial differential equations. The resulting ODEs are numerically solved using the shooting technique using BVP5C in MATLAB after applying the long-wavelength and low Reynolds number approximation. The velocity, temperature, concentration, electroosmosis, and microorganism density profiles are analyzed graphically for different emerging parameters. Graphical investigation of engineering interest quantities like heat transfer rate, mass transfer rate, skin friction coefficient, and entropy generation optimization are also presented. It is observed that the rate of mass transfer increases for increasing thermophoretic parameter, while reverse effect is noted for Brownian motion parameter, Schmidt number, and chemical reaction number. The outcomes of present study can be pertinent in studying Cilia properties of respiratory tract, reproductive system, and brain ventricles.