In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has connections with biased walks on digraphs. Within this framework, we introduce a space-time generalization of the Poisson process as a strictly increasing walk with discrete Mittag-Leffler jumps subordinated to a (continuous-time) fractional Poisson process. We call this process ‘space-time Mittag-Leffler process’. We derive explicit formulae for the state probabilities which solve a Cauchy problem with a Kolmogorov-Feller (forward) difference-differential equation of general fractional type. We analyze a “well-scaled” diffusion limit and obtain a Cauchy problem with a space-time convolution equation involving Mittag-Leffler densities. We deduce in this limit the ‘state density kernel’ solving this Cauchy problem. It turns out that the diffusion limit exhibits connections to Prabhakar general fractional calculus. We also analyze in this way a generalization of the space-time fractional Mittag-Leffler process. The approach of construction of good Laplacian generator functions has a large potential in applications of space-time generalizations of the Poisson process and in the field of continuous-time random walks on digraphs.

Deep neural networks are hegemonic approaches to many machine learning areas, including natural language processing (NLP). Thanks to the availability of large corpora collections and the capability of deep architectures to shape internal language mechanisms in self-supervised learning processes (also known as "pre-training"), versatile and performing models are released continuously for every new network design. But these networks, somehow, learn a probability distribution of words and relations across the training collection used, inheriting the potential flaws, inconsistencies and biases contained in such a collection. As pre-trained models have found to be very useful approaches to transfer learning, dealing with bias has become a relevant issue in this new scenario. We introduce bias in a formal way and explore how it has been treated in several networks, in terms of detection and correction. Also, available resources are identified and a strategy to deal with bias in deep NLP is proposed.

Nonparametric density estimation for nonnegative data is considered in a situation where a random sample is not directly available but the data are instead observed from the length-biased sampling. Due to the boundary bias problem of the location-scale kernel, the approach in this paper is an application of asymmetric kernel. Two nonparametric density estimators are proposed. The mean integrated squared error, strong consistency, and asymptotic normality of the estimators are investigated. Some simulations illustrate the finite sample performance of the estimators.

For a fiber optic gyroscope, thermal deformation of the fiber coil can introduce additional ther-mal-induced phase errors, commonly referred to as thermal errors. Thermal error compensation techniques are effective means of addressing this issue. The principle behind these techniques involves real-time sensing of thermal errors and correcting them within the output signal. Since it is challenging to directly separate thermal errors from the output signal of the fiber optic gyro-scope, it is necessary to predict thermal errors based on temperature. To establish a mathematical model between temperature and thermal errors, this paper measured synchronized data of phase errors and angular velocity for the fiber coil under different temperature conditions and aimed to model it using data-driven methods. Due to the difficulty of conducting tests and the limited number of data samples, an algorithm called TD-model modeling is proposed to address the issue of overfitting, which can reduce the model's generalization ability. First, a theoretical analysis of the phase errors caused by thermal deformation of the fiber coil is performed. Subsequently, the critical parameters, such as the thermal expansion coefficient, are determined, and a theoretical model is established. Finally, the theoretical analysis model is incorporated as a regularization term and combined with the test data to jointly participate in the regression of model coefficients. Through experimental comparative analysis, it is shown that, relative to ordinary regression models, the TD-model effectively mitigates overfitting caused by the limited number of samples, leading to a 58% improvement in predictive accuracy.

This study applied the principal-agent model to interpret the impact of routine biased technological change (RBTC) on the structure of employment relations. RBTC increases the proportion of routine tasks in work activities, due to their fixed procedural nature, routine tasks reduce uncertainties in the principal-agent problem. Employers, being able to predict work contingencies and to verify employee efforts, find the benefit of offering standard labor contracts is reduced, thereby increasing the ratio of non-standard employment. This study applied logistic regression based on the Program for the International Assessment of Adult Competencies (PIAAC) survey data to verify this framework. The results indicated that with each standard deviation increased in routine task intensity, the odds ratio of non-standard employment increased by 13.6%. This effect was heterogeneous in various institutional contexts. This study expends the toolkit for analyzing employment relations problems, and extends the scope of RBTC to employment relations.

This article presents a self balanced multistage DC-DC step-up converter for photovoltaic applications. Proposed converter topology is designed for unidirectional power transfer and provides a doable solution for photovoltaic applications where voltage is required to be stepped up without magnetic components (Transformer-less and Inductor-less). The output voltage obtained from renewable sources will be low and must be stepped up by using a DC-DC converter for photovoltaic applications. K diodes and K capacitors along with two semiconductor control switch are used in the K-stage proposed converter to obtain an output voltage which is (K+1) times the input voltage. The conspicuous features of proposed topology are i) Magnetic components free (Transformer-less and Inductor-less). ii) Continuous input current iii) Low voltage rating semiconductor devices and capacitors iv) Modularity v) Easy to add a higher number of levels to increase voltage gain vi) Only two control switches with alternating operation and simple control. The proposed converter is compared with recent existing transformer-less and Inductor-less power converter in term of voltage gain, number of devices and cost. The application of proposed circuit is discussed in detail. The proposed converter has been designed with rated power of 60W, input voltage is 24V, output voltage is 100V and switching frequency is 100 kHz. The performance of the converter is verified through experimental and simulation results.

G protein-coupled receptors (GPCRs) play a key role in many cellular signaling mechanisms, and must select among multiple coupling possibilities in a ligand-specific manner in order to carry out a myriad of functions in diverse cellular contexts. Much has been learned about the molecular mechanisms of ligand-GPCR complexes from Molecular Dynamics (MD) simulations. However, to explore ligand-specific differences in the response of a GPCR to diverse ligands, as is required to understand ligand bias and functional selectivity, necessitates creating very large amounts of data from the needed large-scale simulations. This becomes a Big Data problem for the high dimensionality analysis of the accumulated trajectories. Here we describe a new machine learning (ML) approach to the problem that is based on transforming the analysis of GPCR function-related, ligand-specific differences encoded in the MD simulation trajectories into a representation recognizable by state-of-the-art deep learning object recognition technology. We illustrate this method by applying it to recognize the pharmacological classification of ligands bound to the 5-HT2A and D2 subtypes of class A GPCRs from the serotonin and dopamine families. The ML-based approach is shown to perform the classification task with high accuracy, and we identify the molecular determinants of the classifications in the context of GPCR structure and function. This study builds a framework for the efficient computational analysis of MD Big Data collected for the purpose of understanding ligand-specific GPCR activity.

In this paper we perform numerous numerical studies for the problem of low-rank matrix completion. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. However, we also find that the length of the confidence intervals revealed by the de-biased estimator for an entry is absolutely shorter than the length of the considered credible interval. These suggest further theoretical studies on the estimation error and the concentration for Bayesian methods as they are being quite limited up to present.

G protein-coupled receptors (GPCRs) are critical drug targets. GPCRs convey signals from the extracellular to the intracellular environment through G proteins. There is evidence that some ligands that bind to the GPCRs activate different downstream signaling pathways. G protein activation or -arrestin biased signaling involves ligands binding to receptors and stabilizing conformations that trigger a specific pathway. Molecular dynamics (MD) simulations are especially valuable for obtaining detailed mechanistic information, including identification of allosteric sites and understanding modulators' interactions between receptors and ligands. Here, we highlight recent simulation studies and methods used to study biased G protein-coupled receptor signaling and their conformational dynamics. We also highlight applications of MD simulations to drug discovery.

Ensembles of Species Distribution Models (SDMs) represent the geographic ranges of pathogen vectors by combining alternative analytical approaches and merging information on vector occurrences with more extensive environmental data. Biased collection data impact SDMs, regardless of the target species but no studies have compared the differences in the distributions predicted by the ensemble models when different sampling frameworks are used for the same species. We compared Ensemble SDMs for two important Ixodid tick vectors, Amblyomma americanum and Ixodes scapularis in mainland Florida, USA, when inputs were either convenience samples of ticks, or collections obtained using the standard protocols promulgated by the U.S. Centers for Disease Control and Prevention. The Ensemble SDMs for the convenience samples and standard surveys showed only a slight agreement (Kappa = 0.060, A. americanum; 0.053, I. scapularis). Convenience sample SDMs indicated A. americanum and I. scapularis should be absent from 34.5% and 30.9% of the state where standard surveys predicted the highest likelihood of occurrence of the respective vectors. Ensemble models from standard surveys predicted 81.4% and 72.5% (A. americanum and I. scapularis) of convenience sample sites. Omission errors by standard survey SDMs, of the convenience collections, frequently were associated with adjacency to at least one SDM or errors in geocoding algorithms that failed to correctly locate convenience samples. These geocoding errors emphasize commonly overlooked needs to explicitly evaluate and improve data quality for vector survey data used in spatial models.

The separation of sister chromatids during anaphase is the culmination of mitosis and one of the most strikingly beautiful examples of cellular movement. It consists of two distinct processes: Anaphase A, the movement of chromosomes toward spindle poles via shortening of the connecting fibers, and anaphase B, separation of the two poles from one another via spindle elongation. I focus here on anaphase A chromosome-to-pole movement. The chapter begins by summarizing classical observations of chromosome movements, which support the current understanding of anaphase mechanisms. Live cell fluorescence microscopy studies showed that poleward chromosome movement is associated with disassembly, or ‘melting’ of the kinetochore-attached microtubule fibers that link chromosomes to poles. Microtubule-marking techniques established that kinetochore-fiber disassembly often occurs through a ‘pac-man’ mechanism, where tubulin subunits are lost from kinetochore-attached plus ends and the kinetochore appears to consume its microtubule track as it moves poleward. In addition, kinetochore-fiber disassembly in many cells occurs partly through ‘flux’, where the microtubules flow continuously toward the poles and tubulin subunits are lost from minus ends. Molecular mechanistic models for how load-bearing attachments are maintained to disassembling microtubule ends, and how the forces are generated to drive pac-man and flux-based movements, are discussed.

Opioid analgesics have been used for more than 5,000 years and remain the principal pain medications prescribed today. Although morphine is considered the gold standard for pain relief, this µ-opioid receptor (MOP)-selective agonist provides only moderate relief for many chronic pain conditions and promotes several unwanted effects that can adversely affect patient quality-of-life, prevent adherence to treatment or generate addiction. In addition to the lack of progress in the development of better analgesics, there have been no significant breakthroughs to date that have addressed side effects mentioned above. Fortunately, a better understanding of opioid pharmacology has restored hope for the development of better and safer pain medications. In this review, we describe how clinically approved opioids were initially characterized as biased ligands and what impact this approach could have on clinical practice. We also looked at the preclinical and clinical development of MOP biased agonists, with an emphasis on the oliceridine story, as the first specifically designed biased painkiller. Moreover, we explore the discrepancies between ligands with low intrinsic efficacy and those with biased properties. Finally, we examine the rationale behind biased ligand development during the opioid crisis era.

Opioid analgesics are effective pain therapeutics but cause various adverse effects and addiction. For safer pain therapy, biased opioid agonists selectively target distinct m opioid receptor (MOR) conformations, while the potential of biased opioid antagonists has been neglected. Agonists convert a dormant receptor form (MOR-m) to a ligand-free active form (MOR-m*), which mediates MOR signaling. Moreover, MOR-m converts spontaneously to MOR-m* (basal signaling). Persistent upregulation of MOR-m* has been invoked as a hallmark of opioid dependence. Contrasting interactions with both MOR-m and MOR-m* can account for distinct pharmacological characteristics of inverse agonists (naltrexone), neutral antagonists (6b-naltrexol), and mixed opioid agonist-antagonists (buprenorphine). Upon binding to MOR-m*, naltrexone but not 6b-naltrexol suppresses MOR-m*signaling. Naltrexone blocks opioid analgesia non-competitively at MOR-m*with high potency, whereas 6BN must compete with agonists at MOR-m, accounting for ~100-fold lower in vivo potency. Buprenorphine’s bell-shaped dose-response curve may also result from opposing effects on MOR-m and MOR-m*. In contrast, we find that 6b-naltrexol potently prevents dependence, below doses affecting analgesia or causing withdrawal, possibly binding to MOR conformations relevant to opioid dependence. We propose that 6b-naltrexol is a biased opioid antagonist modulating opioid dependence at low doses, opening novel avenues for opioid pain therapy and use management.