Probability Distribution Of Position Research Articles

Field theory of active chiral hard disks: a first-principles approach to steric interactions

A first-principles approach for active chiral hard disks is presented, that explicitly accounts for steric interactions on the two-body level. We derive an effective one-body equation for the joint probability distribution of positions and angles of the particles. By projecting onto the angular modes, we write a hierarchy for the lowest hydrodynamic modes, i.e. particle density, polarisation, and nematic tensor. Introducing dimensionless variables in the equations, we highlight the assumptions, which—though inherent—are often included implicit in typical closure schemes of the hierarchy. By considering different regimes of the Péclet number, the well-known models in active matter can be obtained through our consideration. Explicitly, we derive an effective diffusive description and by going to higher orders in the closure scheme, we show that this first-principles approach results in the recently introduced Active Model B +, a natural extension of the Model B for active processes. Remarkably, here we find that chirality can change the sign of the phenomenological activity parameters.

High-precision two- and three- dimensional atom localization in a microwave and radio-frequency driven Δ∇ system

We introduce a new approach for precise and high-resolution two-dimensional (2D) and three-dimensional (3D) atom localization in a four-level Δ∇ atomic system driven by microwave (M) and radio frequency (R) fields. In the proposed work, additional microwave and radio-frequency fields are utilized for an efficient control of the localization precision. Due to the spatially varying atom-field interaction, the probe susceptibility become position dependent and therefore, one can directly ascertain the position probability distribution of an atom by analyzing the probe spectra. The phase-sensitive property of the atomic system plays a significant role in substantially reducing the uncertainty associated with atom position measurements. We have studied the system behavior through the analysis of dressed states, which forms the basis for its physical interpretation. The increase in precision for measuring the atom’s position is a result of interference between one-photon excitation and the phase-dependent three-photon excitation arising from the closed interacting contour within the laser-driven atomic system, as demonstrated through both numerical calculations and qualitative analyses. The findings indicate that precise sub-wavelength atom localization can be attained by appropriately adjusting the system parameters. Also, the optimal adjustment of these parameters can lead to 100% probability of locating the atom at a particular position within 2D and 3D subspaces.

Indoor position estimation using angle of arrival measurements: An efficient multi-anchor approach with outlier rejection

This paper addresses the inherent nonlinear problem in indoor position estimation utilizing Angle of Arrival (AoA) measurements. We investigate the influence of deployment geometry on system performance through both analytical methods and Monte-Carlo simulations, shedding light on the limitations of single and multi-anchor setups and underscoring the imperative for advanced multi-anchor localization methods. In response to this problem, we propose a multi-anchor solution with outlier rejection that efficiently considers the nonlinearity of the model. For each anchor, our approach approximates the probability distribution of the node position by leveraging a geometrically-derived unscented transformation of AoA estimates. The approximations are then integrated into a majority voting scheme, effectively eliminating outliers induced by multipath or other adverse effects. To derive the final enhanced position estimate, Bayesian inference is applied to fuse the selected information. Finally, the efficacy of the solution is validated conducting a comparative analysis against commonly used approaches in a real-world Bluetooth indoor localization system. The results obtained solely from high-level angular measurements underscore the practicality, robustness and high accuracy of the proposal.

Intrinsic Versus Wind‐Forced Great Whirl Non‐Seasonal Variability

AbstractThe Great Whirl (GW) is a quasi‐permanent anticyclonic eddy that appears every summer monsoon offshore of the Somalia upwelling. The annual cycle of the GW is well described, but deviations from its mean seasonal cycle (hereafter non‐seasonal variability) have been less explored. Satellite observations reveal that the leading mode of summer non‐seasonal sea‐level variability in this region is associated with ∼100‐km northward or southward GW shifts from its climatological position. Northward shifts are associated with a stronger GW, and two cold, productive coastal upwelling wedges at 5°N and 10°N. Southward shifts are associated with a weaker GW, no wedge at 5°N and a single stronger‐than‐usual cold and productive wedge at 10°N. An eddy‐permitting (25‐km resolution) 50‐member ensemble ocean simulation reproduces this GW variability well. It indicates that the non‐seasonal GW variability has a short ∼20 days timescale intrinsic component, associated with the GW interaction with mesoscale eddies, and a lower‐frequency, ∼100 days externally forced component. Intrinsic variability dominates at both subseasonal (two thirds of the variance) and interannual timescales (57% of the variance). The externally forced signal results from shifts in the probability distribution of the subseasonal GW position (e.g., more likely northward than southward shifted instantaneous GW positions over a season). The mechanism for this external forcing is not entirely clear, but it appears to be related to the Rossby wave response to offshore wind stress curl forcing, which evolves into a north‐south dipole that projects onto the GW variability pattern.

Bidirectional Semi-supervised Dual-branch CNN for Robust 3D Reconstruction of Stereo Endoscopic Images via Adaptive Cross and Parallel Supervisions.

Semi-supervised learning via teacher-student network can train a model effectively on a few labeled samples. It enables a student model to distill knowledge from the teacher's predictions of extra unlabeled data. However, such knowledge flow is typically unidirectional, having the accuracy vulnerable to the quality of teacher model. In this paper, we seek to robust 3D reconstruction of stereo endoscopic images by proposing a novel fashion of bidirectional learning between two learners, each of which can play both roles of teacher and student concurrently. Specifically, we introduce two self-supervisions, i.e., Adaptive Cross Supervision (ACS) and Adaptive Parallel Supervision (APS), to learn a dual-branch convolutional neural network. The two branches predict two different disparity probability distributions for the same position, and output their expectations as disparity values. The learned knowledge flows across branches along two directions: a cross direction (disparity guides distribution in ACS) and a parallel direction (disparity guides disparity in APS). Moreover, each branch also learns confidences to dynamically refine its provided supervisions. In ACS, the predicted disparity is softened into a unimodal distribution, and the lower the confidence, the smoother the distribution. In APS, the incorrect predictions are suppressed by lowering the weights of those with low confidence. With the adaptive bidirectional learning, the two branches enjoy well-tuned mutual supervisions, and eventually converge on a consistent and more accurate disparity estimation. The experimental results on four public datasets demonstrate our superior accuracy over other state-of-the-arts with a relative decrease of averaged disparity error by at least 9.76%.

Stochastic Quantum Probability and Subatomic Particle Experiment Design

This article is the third of a trilogy of articles on the nature of probability in quantum mechanics. The first article [1] began by noting that superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into the position probability density of an atomic particle, which happens nowhere else in probability theory. It went on to also note that there is an unexplained coincidence in quantum mechanics in that the interference term in the squared amplitude of superposed wavefunctions gives the squared amplitude the form of a variance of a sum of correlated random variables and went on to examine whether there could be an archetypical variable, in the Platonic sense of true form, behind quantum probability that would reconcile quantum probability with classic probability. This examination found such a variable, which can encompass both local and nonlocal quantum events. The second article [2] provided evidence that quantum probability has such a stochastic nature. This evidence was based on the number of electrons that need to be sent through a two-slit interferometer to gain a clear pattern of self-interference, which when compared with the number that would be expected to be sufficient in order for the position probability distribution of the self-interference wavefunction to take clear shape suggests that there is more variability present than that described by the formulation of quantum mechanics, which implies the presence of an underlying and as yet unrecognized physical process. This final article completes the trilogy by considering how a key aspect of experimental design would be affected by the increased variability that would be present if quantum probability is itself stochastic in the manner suggested in the previous two articles.

A unified transform method for general robust property of probabilistic Boolean control networks

This article proposes a unified transform method for general robust property of probabilistic Boolean control networks (PBCNs). Here, the general robust property of PBCNs means any given robust property of any given PBCN with probability one. Specifically, the method is that the investigation on any given robust property of any given PBCN with probability one can be equivalently transformed into the investigation on the given robust property of the corresponding Boolean control network (BCN). Note that the PBCN has time-varying probability distribution and the property can be set according to the needs of specific problems. As an application of the method, we study the robust set stabilization with probability one of PBCNs with positive time-varying probability distribution. We derive the results through a discussion of the robust set stabilization of the corresponding BCNs. Also, we characterize all of the time-optimal robust set stabilizers of the PBCNs. A reduced disturbed PBCN model of the lac operon in the Escherichia coli is provided to show the effectiveness of the achieved results.

Calculation Method for Initial Discharge Formation Parts of Live Line Worker Based on Leader Discharge Theory

For the initial attachment parts of the human body discharge under live working conditions of transmission lines, this paper proposes a calculation method suitable for any working posture and tower type based on the leader discharge theory. By simulating the formation of the leader channel, the minimum background field for the initiation of the stable leader in various parts of the human body is calculated, and the probability distribution of the initial discharge attachment position on the body surface of the worker is obtained. The results show that the stable transformation of the secondary corona to the leader channel at the tip of the human body is a precondition for this part to become an attachment point of the discharge; In the process of the worker entering the equipotential, affected by the entering direction and posture, the parts with a large curvature such as the hands and feet are likely to become the initial discharge attachment position; Due to the shielding effect from the limbs, the rear part of the worker has a low probability of becoming the initial discharge attachment position. The purpose of this research is to explore an effective method for identifying the discharge location of a live line worker, and to strengthen the protection of workers from the electric field. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Ground Risk Estimation of Unmanned Aerial Vehicles Based on Probability Approximation for Impact Positions with Multi-Uncertainties

In this paper, a methodology to assess ground risk with multi-uncertainties is introduced, which is associated with a major unmanned aerial vehicle (UAV) in-flight incident. In the assessment model, random factors are taken into account including uncertainty in the drag force, uncertainty in the UAV velocity, and the random effects of local wind. The probability distribution of impact positions is first estimated by using a second-order drag model with probabilistic assumptions regarding the least well-known parameters. Then, an approach for modeling and estimating the ground risks is presented, in which the ground casualties are set as the safety index. In the multifactor risk estimation model, ground casualty areas covered by the UAVs’ debris are determined. Correspondingly, the probability of fatal injuries to people is derived by addressing the protection effects, impact energy, and energy threshold a person can sustain. Further, four kinds of sheltering effects are defined. Finally, the affected area on the ground is partitioned into six zones, taking into consideration the density and distribution of the local population. Case studies are conducted for fixed-wing and rotary-wing UAVs. Risk levels on the ground are obtained and compared with the widely accepted target safety level of manned aircrafts.

Statistical Analysis of Rainfall Data: A Case Study of Georgetown, Guyana

Rainfall is a key component for designing of many engineering projects, including canals, bridges, culverts, and road drainage systems. This research will provide useful information to water resource planners, farmers, and urban engineers for analysis of water availability and for building appropriate engineering structures. In order to calculate the appropriate input value for the design and analysis of engineering structures as well as for crop planning, a thorough statistical study is required. The Botanical Gardens raingauge station in Georgetown was selected for analysis as Georgetown experiences frequent floods. The mean, standard deviation and coefficient of variation, skewness and kurtosis of monthly and annual rainfall for a 30 year period were analyzed. According to the computed data, the rainfall pattern is unpredictable, as demonstrated by the coefficient of variation. The variability in rainfall for May, June and July are (38%, 35% and 37%) respectively are much lower than the other months. An analysis of the average monthly rainfall data shows a bi-modal yearly rainfall pattern. Various plotting position formulae and probability distribution functions were used to analyze the return period of the yearly rainfall. It was determined that the Chegodayev technique provides the best fit distribution for yearly rainfall data using the plotting position method, whilst the Gumbel’s Extreme Distribution yields the highest value for rainfall for various return periods using the probabilistic methods. Chegodayev technique also provides the best fit annual one day maximum rainfall for the plotting position methods The Chegodayev technique projects that rainfall for 5, 10, 50, 100 and 150 year return period are 2668.31 mm, 3024.23 mm, 3850.65 mm 4206.56 mm and 4414.76 mm whilst Gumbel’s Extreme Distribution projects rainfall of 2761.54 mm, 3090.30 mm, 3813.85 mm, 4119.73 mm and 4298.10 mm respectively for the same periods. It should be noted that the result from the plotting position formulae are usually good for small extrapolations as errors increases with the amount of extrapolations.

Nonlinear effective dynamics of a Brownian particle in magnetized plasma

An effective description is presented for a Brownian particle in a magnetized plasma. In order to systematically capture various corrections to linear Langevin equation, we construct effective action for the Brownian particle, to quartic order in its position. The effective action is first derived within nonequilibrium effective field theory formalism, and then confirmed via a microscopic holographic model consisting of an open string probing magnetic fifth-dimensional anti--de Sitter (${\mathrm{AdS}}_{5}$) black brane. For practical usage, the non-Gaussian effective action is converted into Fokker-Planck-type equation, which is an Euclidean analog of Schr\"odinger equation and describes time evolution of probability distribution for particle's position and velocity.

Active particles driven by competing spatially dependent self-propulsion and external force

We investigate how the competing presence of a nonuniform motility landscape and an external confining field affects the properties of active particles. We employ the active Ornstein-Uhlenbeck particle (AOUP) model with a periodic swim-velocity profile to derive analytical approximations for the steady-state probability distribution of position and velocity, encompassing both the Unified Colored Noise Approximation and the theory of potential-free active particles with spatially dependent swim velocity recently developed. We test the theory by confining an active particle in a harmonic trap, which gives rise to interesting properties, such as a transition from a unimodal to a bimodal (and, eventually multimodal) spatial density, induced by decreasing the spatial period of the self propulsion. Correspondingly, the velocity distribution shows pronounced deviations from the Gaussian shape, even displaying a bimodal profile in the high-motility regions. We thus show that the interplay of two relatively simple physical fields can be employed to generate complex emerging behavior.

Report of Evidence That Quantum Probability Is Itself Stochastic

This report covers work since a previous article on quantum probability. It provides evidence that quantum probability has a stochastic nature. This evidence is based on the number of electrons that need to be sent through a twoslit interferometer to gain a clear pattern of self-interference, which when compared with the number that would be expected to be sufficient in order for the position probability distribution of the self-interference wavefunction to take clear shape suggests that there is more variability present than that described by the formulation of quantum mechanics, which implies the presence of an underlying and as yet unrecognized physical process.

Stochastic emulation of quantum algorithms

Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two qubits at the same time. The former aspect renders the direct classical simulation of quantum algorithms difficult. Here we introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares these basic properties of quantum mechanical states needed for a quantum algorithm. Discretization of the positions allows one to represent the quantum mechanical state of n bit qubits by 2(n bit + 1) classical stochastic bits. Based on this, we demonstrate many-particle interference and representation of pure entangled quantum states via derivatives of probability distributions and find the universal set of stochastic maps that correspond to the quantum gates in a universal gate set. We prove that the propagation via the stochastic map built from those universal stochastic maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state with the corresponding quantum algorithm, leading to an automated translation of a quantum algorithm to a stochastic classical algorithm. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of the emulation.

Operational Theories in Phase Space: Toy Model for the Harmonic Oscillator.

We show how to construct general probabilistic theories that contain an energy observable dependent on position and momentum. The construction is in accordance with classical and quantum theory and allows for physical predictions, such as the probability distribution for position, momentum, and energy. We demonstrate the construction by formulating a toy model for the harmonic oscillator that is neither classical nor quantum. The model features a discrete energy spectrum, a ground state with sharp position and momentum, an eigenstate with a nonpositive Wigner function as well as a state that has tunneling properties. The toy model demonstrates that operational theories can be a viable alternative approach for formulating physical theories.

Dynamics of active particles with space-dependent swim velocity.

We study the dynamical properties of an active particle subject to a swimming speed explicitly depending on the particle position. The oscillating spatial profile of the swim velocity considered in this paper takes inspiration from experimental studies based on Janus particles whose speed can be modulated by an external source of light. We suggest and apply an appropriate model of an active Ornstein Uhlenbeck particle (AOUP) to the present case. This allows us to predict the stationary properties, by finding the exact solution of the steady-state probability distribution of particle position and velocity. From this, we obtain the spatial density profile and show that its form is consistent with the one found in the framework of other popular models. The reduced velocity distribution highlights the emergence of non-Gaussianity in our generalized AOUP model which becomes more evident as the spatial dependence of the velocity profile becomes more pronounced. Then, we focus on the time-dependent properties of the system. Velocity autocorrelation functions are studied in the steady-state combining numerical and analytical methods derived under suitable approximations. We observe a non-monotonic decay in the temporal shape of the velocity autocorrelation function which depends on the ratio between the persistence length and the spatial period of the swim velocity. In addition, we numerically and analytically study the mean square displacement and the long-time diffusion coefficient. The ballistic regime, observed in the small-time region, is deeply affected by the properties of the swim velocity landscape which induces also a crossover to a sub-ballistic but superdiffusive regime for intermediate times. Finally, the long-time diffusion coefficient decreases as the amplitude of the swim velocity oscillations increases because the diffusion is mainly determined by those regions where the particles are slow.

Numerical Study of Duffing Nonlinearity in the Quantum Dot Embedded Nanomechanical Resonator

Geometry, electrostatics, and single-electron tunneling contribute to the nonlinearity in the quantum dot embedded nanomechanical resonator, while “Duffing term” is a kind of mathematics describing the third-order nonlinearity of the system as a whole. We study theoretically the influence of a variation of a mathematical parameter Fuffing term on the actual physical effect. The position probability distribution, the average current, and the displacement fluctuation spectrum with the different Duffing parameter and electromechanical coupling are obtained through numerically calculating the Fokker Planck equation. The mechanical bistability has been described by these quantities under different electromechanical coupling and Duffing parameters. We conclude that the nonlinearities of the nanotube resonator contribute to the mechanical bistability, which induces the asymmetry of the position probability distribution, compresses the current, and softens or stiffens the mechanical resonance frequency as the same as the electromechanical coupling to use it in mechanical engineering.

Temperature and friction-induced tunable current reversal, anomalous mobility and diffusions

Abstract We numerically investigate the transport properties and dynamic relaxation of a classical inertia Brownian particle in a biased periodic potential under the action of friction and thermal fluctuations. The both fluctuations may be related to friction, thus they may be correlated with each other. We mainly focus on how particle’s transport and dynamic relaxation are affected by fluctuations and the correlation between them. It is unexpected that the combinations of them can tune transport of the particle, including current reversal, and anomalous mobility and diffusions. These results are explained via the stationary probability distributions, which suggest that the bias of the potential can lead to a transition between unimodal and bimodal stationary probability distributions of particle’s velocity. To understand the physical mechanism of these findings, we present dynamic relaxations, namely, the transient probability distributions of velocity and position. These distributions suggest that the motion of the particle is not only related to systematic parameters, but also sensitive to the initial conditions. Our findings may be potentially helpful for research on various transport of the particle and on similar circuits, such as particle separation, Josephson junctions, the phase-locked loops, etc.

Three-state quantum walk on the Cayley Graph of the Dihedral Group

The finite dihedral group generated by one rotation and one reflection is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the dihedral group. Considering the characteristics of the elements in the dihedral group, we propose a model of three-state discrete-time quantum walk (DTQW) on the Caylay graph of the dihedral group with Grover coin. We derive analytic expressions for the position probability distribution and the long-time limit of the return probability starting from the origin. It is shown that the localization effect is governed by the size of the underlying dihedral group, coin operator and initial state. We also numerically investigate the properties of the proposed model via the probability distribution and the time-averaged probability at the designated position. The abundant phenomena of three-state Grover DTQW on the Caylay graph of the dihedral group can help the community to better understand and to develop new quantum algorithms.

Molecular motor traffic with a slow binding site

We discuss how the presence of a slow binding site in molecular motor traffic gives rise to defect-induced ”traffic jams” that have properties different from those of the well-studied boundary-induced jams that originate from an imbalance between initiation and termination. To this end we analyze in detail the stationary distribution of a lattice gas model for traffic of molecular motors with a defect. In particular, we obtain analytically the exact spatial distribution of motors, the probability distribution of the random position of the molecular traffic jam and we report unexpected spatial anticorrelations between local molecular motor densities near the defect.