Probability Distribution Function Research Articles

Monotonicity of the RG flow in an emergent dual holography of a worldsheet nonlinear σ model

Based on the renormalization group (RG) flow of worldsheet bosonic string theory, we construct an effective holographic dual description of the target space theory identifying the RG scale with the emergent extra dimension. This results in an effective dilaton-gravity-gauge theory, analogous to the low-energy description of bosonic M theory. We argue that this holographic dual effective field theory is nonperturbative in the α′ expansion, where a class of string quantum fluctuations are resummed to all orders. To investigate the monotonicity of the RG flow of the target space metric in the emergent spacetime, we consider entropy production along the RG flow. We construct a microscopic entropy functional based on the probability distribution function of the holographic dual effective field theory, regarded as Gibbs- or Shannon-type entropy. Given that the Ricci flow represents the 1-loop RG flow equation of the target space metric for the 2D nonlinear sigma model, and motivated by Perelman’s proof of the monotonicity of Ricci flow, we propose a Perelman’s entropy functional for the holographic dual effective field theory. This entropy functional is also nonperturbative in the α′ expansion, and thus, generalizes the 1-loop result to the all-loop order. Furthermore, utilizing the equivalence between the Hamilton-Jacobi equation and the local RG equation, we suggest that the RG flow of holographic Perelman’s entropy functional is the Weyl anomaly. This eventually reaffirms the monotonicity of RG flow for the emergent target spacetime but in a nonperturbative way. Interestingly, we find that the microscopic entropy production rate can be determined by integrating the rate of change of the holographic Perelman’s entropy functional over all possible metric configurations along the flow. Published by the American Physical Society 2025

DeepDISC-photoz: Deep Learning-Based Photometric Redshift Estimation for Rubin LSST

Photometric redshifts will be a key data product for the Rubin Observatory Legacy Survey of Space and Time (LSST) as well as for future ground and space-based surveys. The need for photometric redshifts, or photo-zs, arises from sparse spectroscopic coverage of observed galaxies. LSST is expected to observe billions of objects, making it crucial to have a photo-z estimator that is accurate and efficient. To that end, we present DeepDISC photo-z, a photo-z estimator that is an extension of the DeepDISC framework. The base DeepDISC network simultaneously detects, segments, and classifies objects in multi-band coadded images. We introduce photo-z capabilities to DeepDISC by adding a redshift estimation Region of Interest head, which produces a photo-z probability distribution function for each detected object. On simulated LSST images, DeepDISC photo-z outperforms traditional catalog-based estimators, in both point estimate and probabilistic metrics. We validate DeepDISC by examining dependencies on systematics including galactic extinction, blending and PSF effects. We also examine the impact of the data quality and the size of the training set and model. We find that the biggest factor in DeepDISC photo-z quality is the signal-to-noise of the imaging data, and see a reduction in photo-z scatter approximately proportional to the image data signal-to-noise. Our code is fully public and integrated in the RAIL photo-z package for ease of use and comparison to other codes at https://github.com/LSSTDESC/rail_deepdisc

Performance evaluation of wireless node positioning over α − η − μ fading channel

Abstract The increasing demand for diverse services, ubiquitous coverage, and device-oriented point-to-point communications necessitates a focus on user mobility in characterizing the wireless channel environment. This study addresses the random waypoint mobility (RWP) model, where users follow a zigzag path between waypoints, causing significant fluctuations in perceived signal power. Recognizing the critical role of mobility-driven channel modelling in optimizing network infrastructure, this paper evaluates user mobility in non-linear and non-line-of-sight (NLOS) scenarios, leveraging the α-η-μ fading distribution. We derive a closed-form expression for the probability distribution function (PDF) by integrating the RWP mobility model with the α-η-μ fading channel. The study explores path loss exponent variations under different node positioning dimensions (1D, 2D, and 3D). The novel RWP-modelled α-η-μ composite fading channel PDF is then used to quantify performance metrics, including outage performance and bit error rate (BER) in communication systems, particularly in the context of evolving to 5 G networks. Additionally, this work considers dynamic node mobility in various distributions such as one-sided Gaussian, exponential, Nakagami-m (with its discrete version Chi), Rayleigh, and Weibull. The obtained results from the derived expressions are rigorously validated through Monte Carlo simulations.

Modeling and Performance Analysis of Task Offloading of Heterogeneous Mobile Edge Computing Networks

Mobile edge computing architecture (MEC) can provide users with low latency services by integrating computing, storage and processing capabilities near users and data sources. As such, there has been intense interest in this topic, especially in single-server and homogeneous multi-server scenarios. The impact of network heterogeneity and load fluctuations is ignored, and the performance evaluation system relies too much on statistical mean indicators, ignoring the impact of real-time indicators. In this paper, we propose a new heterogeneous edge computing network architecture composed of multi-core servers with varying transmission power, computing capabilities and waiting queue length. Since it is necessary to evaluate and analyze the service performance of MEC to guarantee Quality of Service (QoS), we design some indicators by solving the probability distribution function of response time, such as average task offloading delay, immediate service probability and blocking probability. By analyzing the impact of bias factors and network parameters associated with MEC servers on network performance, we provide insights for MEC design, deployment and optimization.

Optimal Probability Distribution Function and Plotting Position for Annual Maximum Flood in Mahanadi River System, India

In the present work, optimum probability distribution function and plotting position of annual maximum flood series data obtained for Mahanadi River system has been analysed. For the analysis, 25 to 45 years of data obtained from Nineteen gauging stations of Mahanadi river system have been considered. Different commonly used probability distribution functions have been tested for their applicability at all the nineteen gauging stations individually. They are Generalised Extreme Value (GEV), Generalised Pareto (GP), Log-Pearson III (LP III), Normal, Log normal (LN), Log-Logistic (LL), Log-Logistic 3P(LL-3P), Log normal 3P(LN-3P), Pareto (P) and Gumbel max method. A comparison of the results obtained using these distributions has been done with the Weibull, Hazen & California plotting positions. From the results, the Generalised Pareto (GP) probability distribution provided best results followed by GEV and Log Pearson Type III. The goodness of fit tests namely Kolmogorov-Smirov (KS), Anderson-Darling (AD), and Chi squared (CS) tests has been done to assess the best performing probability distribution. The annual maximum flow observed are compared well with the predicted annual maximum flow for the return period of 5, 10, 20, 25, 30, 35 and 45 years. The results obtained are promising and can be used for design and development of water resources projects in Mahanadi river system.

Multi-scale geometrical Lagrangian statistics of heavy impurities in drift wave turbulence

Abstract We investigate the behavior of heavy impurities in edge plasma turbulence by analyzing their trajectories using the Hasegawa–-Wakatani model. Through direct numerical simulations, we track ensembles of impurity particles over hundreds of eddy turnover times within statistically steady turbulent flows. Assuming that heavy impurities lag behind the flow, a novel derivation of relaxation time of heavy impurities is proposed. Our results reveal that heavy impurities can cluster within turbulence. We provide multi-scale geometrical Lagrangian statistics of heavy impurities trajectories. To quantify directional changes, we analyze the scale-dependent curvature angle, along with the influence of the Stokes number on the mean curvature angles and the probability distribution function of curvature angles.

Microscopic fluctuations in the spreading fronts of circular wetting liquid droplets.

We study numerically the kinetic roughening properties of the precursor fronts of nonvolatile liquid droplets spreading on solid substrates, for the case of circular droplets, more frequently addressed in experiments. To this end, we perform kinetic Monte Carlo (kMC) simulations of a lattice gas model whose kinetic roughening behavior has been recently assessed in a band geometry [J. M. Marcos et al., Phys. Rev. E 105, 054801 (2022)2470-004510.1103/PhysRevE.105.054801]. We compare the scaling behaviors of the spreading fronts obtained for the two geometries, in view of the occurrence of, for example, different universality subclasses for different growth geometries for the related important Kardar-Parisi-Zhang (KPZ) universality class. For circular droplets, we obtain that the average front position increases (sub)diffusively as R∼t^{δ}, where δ≲1/2 shows a stronger dependence on the conditions considered for temperature and substrate wettability than in band geometry. In spite of this, front fluctuations for circular droplets behave qualitatively similar to those seen for band geometries, with kinetic roughening exponent values which similarly depend on temperature T but become T-independent for sufficiently high T. Circular droplets also display intrinsic anomalous scaling with different values of the roughness exponent at short and large length scales, and fluctuations statistics which are close to the Tracy-Widom probability distribution function that applies in the corresponding KPZ universality subclass, now the one expected for interfaces with an overall circular symmetry.

Sensitivity Analysis of Distribution Network Reconfiguration Optimization for Electric Vehicle and Renewable Distributed Generator Integration

Distribution networks have faced significant efficiency and reliability challenges, balancing the recent integration of electric vehicles (EVs) and renewable distributed generators (DGs). This study proposes a reconfiguration optimization of the distribution system by adjusting the status of switches within the network. This approach aims to minimize power losses and enhance overall operational efficiency. To model the variability of wind and solar DGs, probability distribution functions (PDFs) are employed, which allow for a more accurate representation of their performance. Additionally, stochastic models and Monte Carlo Simulation (MCS) are utilized to generate various scenarios that reflect real-world conditions, including the charging and discharging behaviors of EVs. A sensitivity analysis is conducted to evaluate the effectiveness of our proposed reconfiguration strategy across different levels of EV and DG penetration.

Impact of activity time stochasticity on critical paths and their completion probabilities in construction projects

Accurate planning and project control activities are essential in ensuring the timely completion of construction projects. Even though the classical scheduling techniques like Gantt charts, critical path method (CPM), program evaluation and review technique (PERT), etc., are well-designed and can effectively support construction scheduling functions, they do not account for the variability in activity times arising out of the random/stochastic nature of the activities involved. The study utilizes a simulation-based approach to identify the impact of variability in activity time durations on critical paths and on the probability of timely completion of construction projects. The effectiveness of four different probability distribution functions, namely uniform, triangular, bound exponential, and unbound exponential, in capturing the stochasticity of activity times in construction projects was also evaluated as part of the study. A MATLAB-based simulation framework was developed to sample random durations of project activities and compute various project scheduling parameters based on PERT assumptions. Activity time variability was introduced in the network by extending pessimistic time (tp) by up to 50%. Observation in the study suggests that for projects that experience delays during execution, allocating additional resources to the preassigned critical path may not always be effective in addressing these delays. Instead, dynamic corrective measures (time extensions, resource allocation, etc.) that consider all possible scenarios of project completion and can account for any possible changes in critical path due to the incurred delay may be adopted to ensure a higher probability of project completion within the revised schedule. Exponential bounded distribution was found to provide a more realistic estimate of project completion time with a high probability of timely completion of construction projects. The study also suggests exponential unbound distribution to be effective in simulating worst-case scenarios encountered in construction projects. Future research could validate this approach on real projects and use machine learning to automate scheduling adjustments for delays.

Enhanced statistical approach for urban groundwater flooding risk assessment

This study introduces a novel Groundwater Flooding Risk Assessment (GFRA) model to evaluate risks associated with groundwater flooding (GF), a globally significant hazard often overshadowed by surface water flooding. GFRA utilizes a conditional probability function considering critical factors, including topography, ground slope, and land use-recharge to generate a risk assessment map. Additionally, the study evaluates the return period of GF events (GFRP) by fitting annual maxima of groundwater levels to probability distribution functions (PDFs). Approximately 57% of the pilot area falls within high and critical GF risk categories, encompassing residential and recreational areas. Urban sectors in the north and east, containing private buildings, public centers, and industrial structures, exhibit high risk, while developing areas and agricultural lands show low to moderate risk. This serves as an early warning for urban development policies. The Generalized Extreme Value (GEV) distribution effectively captures groundwater level fluctuations. According to the GFRP model, about 21% of the area, predominantly in the city’s northeast, has over 50% probability of GF exceedance (1 to 2-year return period). Urban outskirts show higher return values (> 10 years). The model’s predictions align with recorded flood events (90% correspondence). This approach offers valuable insights into GF threats for vulnerable locations and aids proactive planning and management to enhance urban resilience and sustainability.

Hidden social and emotional competencies in autism spectrum disorders captured through the digital lens

Background/objectivesThe current deficit model of autism leaves us ill-equipped to connect with persons on the spectrum, thus creating disparities and inequalities in all aspects of social exchange in which autistic individuals try to participate. Traditional research models also tend to follow the clinical definition of impairments in social communication and emotions without offering personalized therapeutic help to autistic individuals. There is a critical need to redefine autism with the aim of co-adapting and connecting with this exponentially growing sector of society. Here, we hypothesize that there are social and emotional competencies hidden in the movements’ nuances that escape the naked eye. Further, we posit that we can extract such information using highly scalable means such as videos from smartphones.MethodsUsing a phone/tablet app, we recorded brief face videos from 126 individuals (56 on the spectrum of autism) to assess their facial micro-motions during several emotional probes in relation to their resting state. We extracted the micro-movement spikes (MMSs) from the motion speed along 68 points of the OpenFace grid and empirically determined the continuous family of probability distribution functions best characterizing the MMSs in a maximum likelihood sense. Further, we analyzed the action units across the face to determine their presence and intensity across the cohort.ResultsWe find that the continuous Gamma family of probability distribution functions describes best the empirical face speed variability and offers several parameter spaces to automatically classify participants. Unambiguous separation at rest denotes marked differences in stochastic patterns between neurotypicals and autistic individuals amenable to further separate autistic individuals according to the required level of support. Both groups have comparable action units present during emotional probes. They, however, operate within parameter ranges that fall outside our perceptual umwelt and, as such, do not meet our expectations from prior experiences. We cannot detect them.ConclusionsThis work offers new methods to detect hidden facial features and begin the path of augmenting our perception to include those signatures of the autism spectrum that can enhance our capacity for social interactions, communication, and emotional support to meet theirs.

Hydrodynamic simulations of the Disc of Gas Around Supermassive black holes (HDGAS) -II; The transition from neutral atomic to molecular gas phases

Abstract We use HDGAS hydrodynamic simulations to study the impact of active galactic nucleus (AGN) feedback on the conversion of atomic-gas to molecular-gas within the circumnuclear-disc (CND) of a typical AGN-dominated galaxy. The comparison of CI, CII, and CO line intensities and their ratios in the HDGAS post-processing radiative-transfer analysis reveals the complex interplay between AGN-activity, cold molecular gas properties, and the physical processes governing the evolution of star-formation in galaxies. Our results demonstrate that the CI/CO intensity ratio serves as a reliable indicator of the atomic-to-molecular gas transition. We present the probability distribution function (PDF) and abundance trends of various metal species related to molecular H2 gas, highlighting differences in clumpiness and intensity maps between AGN feedback and NoAGN models. The profile of the integrated intensity (moment-0) maps shows that the AGN-feedback model exhibits a lower CI/CO intensity ratio in the vicinity of the supermassive black hole (< 50 pc), indicating a smaller atomic-gas abundance and the presence of positive AGN-feedback. Our simulations have successfully predicted the presence of faint-CO emissions extending to larger radii from the galactic center. We also explore the relationships between CII/CO and CI/CII intensity ratios, as well as the ratios versus CO intensity, which provides insights into the ‘CO-dark’ issues. One notable feature in the later time-scale of the AGN model is the presence of a ‘CO-dark’ region, where the intensity of CO emission ($\rm I_{CO}$) is depleted relative to the H2 column density ($N_{\rm H_2}$) compared to the NoAGN model.

Do lumbar spine kinematics contribute to individual low back pain development in habitual sitting?

This study explored differences in activities and spine kinematics by transient low back pain status throughout a week of their usual office work. Using a 100-mm visual-analogue scale, twenty participants were classified as non-pain (NPD) and pain developers (PD; ≥10 mm). Tri-axial accelerometers measured sitting time and thorax, pelvis, and lumbar spine angles. Amplitude probability distribution functions were constructed for postures and movements. PD (n = 6) exhibited increases in pain daily, with partial or complete recovery overnight and full recovery over the weekend, hence pain did not accumulate. PD sat more than NPD (n = 14), exhibited decreased peak posterior pelvic tilt (10°) and thorax inclination (8°), and tended to demonstrate less frequent spine movements. To decrease the risk of pain with sitting, reducing seated time, reclining on the seatback, and promoting seated movements should be recommended. With habitual exposures, small differences between pain groups could suggest a pathway to sitting-related back pain over time. Practitioner Summary: The biomechanical link between habitual sitting and low back pain remains unclear. Activity, spine kinematics, and pain ratings were collected throughout a week of individuals’ seated work at their own workstation. Small differences between those with and without transient low back pain could suggest a pathway to sitting-related back pain.

Universal and non-universal large deviations in critical systems

Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large nn limit, and Monte Carlo simulations, we investigate universal rare events of critical O(n)O(n) systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cramér’s series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics. We also discuss the ubiquity of this power-law corrections to the leading compressed-exponential decay in these tails in and out-of-equilibrium.

Carbon Emission Minimization through Real-time Economic Dispatch

<p>Conventional electrical power systems often prioritize economic gain over environmental protection, which can lead to negative environmental consequences, such as emissions from thermal power plants. In recent years, there has been significant research and investment aimed at addressing the challenges posed by both environmental restrictions and economic dispatch. This study introduces the Black Widow Optimization (BWO) technique to optimize the integration of Renewable Energy Sources (RES) in the context of effective economic dispatch. The BWO algorithm is inspired by the unique mating behaviors of black widow spiders, where cannibalism plays a crucial role in the process. To achieve faster convergence, the BWO removes species with poor fitness from the population. Compared to other optimization algorithms, BWO offers several advantages, including early convergence and the ability to achieve higher fitness values. To assess the performance of the proposed approach, we applied it to various test cases, including a 10-unit generator system, the IEEE 30-bus system, and the real-time 62-bus Indian Utility System (IUS), which incorporates RES output. The results show that, in comparison to other contemporary algorithms, the BWO method significantly reduces fuel costs, as demonstrated by both the Probability Distribution Function (PDF) and the Cumulative Distribution Function (CDF).</p>

The multi-dimensional halo assembly bias can be preserved when enhancing halo properties with HALOSCOPE

Over $90$% of dark matter haloes in cosmological simulations have unresolved properties. This can hinder the dynamical range of simulations and result in systematic biases when modelling cosmological tracers. Current methods for enhancing unresolved haloes cannot preserve the multi-dimensional assembly bias found in simulations. We aim to more precisely determine unresolved structural and dynamical halo properties while preserving the correlations with environment and halo assembly bias found in simulations. We have developed a machine learning technique that uses multi-variate conditional probability distribution functions. This method ensures that correlations among various halo properties, as well as their dependence on the local environment, are preserved. In this work, we trained with a high-resolution (HR) simulation and used it to better determine the properties (concentration, spin, and two shape parameters) of unresolved dark matter haloes in an eight times lower resolution simulation. is able to recover the multi-dimensional halo assembly bias, that is, the correlations of different combinations of halo properties with the large-scale environment, measured in the HR simulation. This is achieved by including the linear halo-by-halo bias and tidal anisotropy in the set of input training parameters. by design, also recovers the joint distribution of the halo properties. To study how resolution effects propagate into the clustering of model galaxies, we generated catalogues of central galaxies using two implementations of the assembly bias in a halo occupation distribution model. The clustering of central model galaxies is improved by a factor of three at $0.009<k ( when the unresolved haloes are enhanced with hs. Our method can preserve the multi-dimensional halo assembly bias when trained using the local environment of haloes. can improve the accuracy of cosmological tracer catalogues produced with approximate methods when many realisations are needed.

RFID Antenna Deployment Model and Anti-Collision Algorithms to Enhance Vehicle Toll System Efficiency

This paper proposes a standard applications of Radio Frequency Identification (RFID) system to manage vehicles at electronic toll gate system without compromising the vehicle speed. The existing electronic toll gate system has low latency as each car needs to wait in a queue for passing the gate. Installation of reader antenna at each lane makes the system expensive. We propose a two-ray ground model for using minimal reader antenna to define required antenna height and downtilt angle to cover the total gate area. We estimate that reader antenna at a height of 15 m and 45.4° downtilit angle are required for optimal signal reception from the car at a distance of 35–38 m. Modified Pulse Protocol algorithm is suggested for mitigating reader collision and increase throughput and utilization of the system by 14.71% and 15.2% respectively. The probability distribution function of the contention window is modified to triangular function. The M-ary Trimming Q-tree protocol is suggested to resolve the tag collision by trimming the idle nodes from the query tree, which reduces identification time. The total time slot decreases with higher elements, and the total throughput also increases to 98%. The “no-lane” strategy established a fast, efficient and cost effective vehicle toll collection system.

Probability distributions of the order parameter of the O(N) model.

We study the probability distribution function (PDF) of the order parameter of the three-dimensional O(N) model at criticality using the functional renormalization group. For this purpose, we generalize the method introduced by Balog etal. [Phys. Rev. Lett. 129, 210602 (2022)0031-900710.1103/PhysRevLett.129.210602] to the O(N) model. We study the large N limit, as well as the cases N=2 and N=3 at the level of the local potential approximation (LPA), and compare our results to Monte Carlo simulations. We compute the entire family of universal scaling functions, obtained in the limit where the system size L and the correlation length of the infinite system ξ_{∞} diverge, with the ratio ζ=L/ξ_{∞} constant. We also generalize our results to the approach of criticality from the low-temperature phase where another infinite family of universal PDF exists. We find that the LPA describes very well the functional form of the family of PDFs, once we correct for a global amplitude of the (logarithm of the) PDF and of ζ.

Generalization of the central limit theorem to critical systems: Revisiting perturbation theory.

The central limit theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group in the case of the three-dimensional Ising model [Balog et al., Phys. Rev. Lett. 129, 210602 (2022)10.1103/PhysRevLett.129.210602]. It has been shown in that article that there exists an entire family of universal PDFs parameterized by ζ=lim_{L,ξ_{∞}→∞}L/ξ_{∞} which is the ratio of the system size L to the bulk correlation length ξ_{∞} with both the thermodynamic limit and the critical limit being taken simultaneously. We show how these PDFs or, equivalently, the rate functions which are their logarithm, can be systematically computed perturbatively in the ε=4-d expansion. We determine the whole family of universal PDFs and show that they are in good qualitative agreement with Monte Carlo data. Finally, we conjecture on how to significantly improve the quantitative agreement between the one-loop and the numerical results.

Research on Unmanned Aerial Vehicle Path Planning for Carbon Emission Monitoring of Land-Side Heavy Vehicles in Ports

Climate change makes it necessary to implement precise carbon dioxide reduction measures, and establishing a port carbon dioxide emission inventory has become a key step in port management.However, the establishment of a port carbon emission inventory, while crucial for the execution of environmental policies, currently lacks effective monitoring and path planning schemes to support this process. To address these issues, we propose a path planning scheme for port-based carbon emission monitoring. The scheme analyzes the factors affecting the effectiveness of the scheme and establishes a hierarchy of these factors to optimize the monitoring path. Furthermore, a multi-objective path planning mathematical model is established in this article, introducing the optimal goals of economic and environmental costs to achieve the overall path planning objectives. Lastly, this paper focuses on the initial path planning problem of drone monitoring and proposes an improved A* algorithm (IEHA). The algorithm improves the search method of child nodes by eliminating nodes that collide with obstacles, thereby reducing the threat of path collisions. At the same time, the evaluation function is improved by introducing the average value and Gaussian distribution probability function into the heuristic function, enhancing the reliability of the evaluation function, reducing the length of the optimal path, and improving operational efficiency. In the simulation experiment results, the proposed algorithm outperforms A*, ACO, and IEA algorithms in optimizing path length, reducing collision points to ensure path safety, and robustness. This indicates that the proposed algorithm can effectively improve the path planning performance of drones in port carbon dioxide emission monitoring, providing an effective technical means for port carbon dioxide emission monitoring.