Deterministic Variation Research Articles

An investigation of firm size distributions involving the growth functions

Following the ideas of prospect theory, a class of growth functions is used to characterize deterministic variations of firm size, which portrays the asymmetric efforts of the firm to achieve the desired size. Considering the differences in the ability of different firm size to cope with uncertainties, the Boltzmann equation for the evolution of firm size is constructed. Utilizing a suitable scaling limit, the Fokker–Planck equation is acquired and its explicit steady-state solution is derived. Our results illustrate that different choices of parameters in the growth function lead to various statistical laws for firm size, such as the Amoroso distribution, the lognormal distribution and Zipf’s law. Under certain conditions, inequality for the distribution of firm size decreases as firm size increases. The numerical analyses are presented to illustrate our results.

Effect of rotation speed fluctuation on rotor noise generation: A numerical and experimental study

The practical operations of rotors for unmanned aircraft systems can undergo time-varying rotation speeds due to various uncertainty factors. This work investigates the aeroacoustic effect of the rotor’s rotation speed fluctuation using both numerical and experimental approaches. The measured real-time angular speed signal reveals that a hovering rotor experiences highly deterministic rotation speed variations in one revolution, which are closely related to the motor property. Delayed detached eddy simulations are performed, and the fluctuating rotation speed is realized by controlling the mesh displacement at each time step. The results suggest that significant additional tones are produced at the excitation frequency and neighbour frequencies, even though the amplitudes of the rotation speed fluctuations at the dominant frequencies are much smaller than the mean rotation speed. By comparing the full signal to individual harmonic components, it is found that the phase difference between each mode is unimportant. Therefore, the total aeroacoustic effect can be regarded as a linear superposition of different harmonic components. Aeroacoustic source analysis is also performed to isolate the contribution of various source types and correlate the far-field noise with the near-field source distribution. The results show that the extra tonal noise is mostly dominated by the loading noise, with a weaker contribution from the thickness noise. The agreement between the experiments and the simulations indicates that the rotation speed fluctuation is likely responsible for the generation of middle-frequency tonal noise at harmonics of the blade passing frequency.

Synergistic and antagonistic effects of deterministic and stochastic cell-cell variations.

By diversifying, cells in a clonal population can together overcome the limits of individuals. Diversity in single-cell growth rates allows the population to survive environmental stresses, such as antibiotics, and grow faster than the undiversified population. These functional cell-cell variations can arise stochastically, from noise in biochemical reactions, or deterministically, by asymmetrically distributing damaged components. While each of the mechanisms is well understood, the effect of the combined mechanisms is unclear. To evaluate the contribution of the deterministic component we developed a mathematical model by mapping the growing population to the Ising model. To analyze the combined effects of stochastic and deterministic contributions we introduced the analytical results of the Ising-mapping into an Euler-Lotka framework. Model results, confirmed by simulations and experimental data, show that deterministic cell-cell variations increase near-linearly with stress. As a consequence, we predict that the gain in population doubling time from cell-cell variations is primarily stochastic at low stress but may cross over to deterministic at higher stresses. Furthermore, we find that while the deterministic component minimizes population damage, stochastic variations antagonize this effect. Together our results may help identifying stress-tolerant pathogenic cells and thus inspire novel antibiotic strategies.

Spectral analysis of solar-irradiance fluctuations

Solar-irradiance fluctuations possess a power-law spectrum with two different slopes in the intermediate (1/day <f<1/h) and high [1/h <f<1/(2 min)] frequency (f) regimes. This spectrum is a combination of a deterministic (latitude-dependent) variation of daylight duration and a stochastic component arising from various environmental attenuation factors. We propose a principled approach to decompose the solar-irradiance time series into the deterministic location-dependent clear sky and the stochastic environmental attenuation signals. Such decomposition permits one to systematically analyze the solar photovoltaic power-fluctuation spectra after accounting for the strong geographic dependence, failing which no baseline standard exists with which to compare spectra between disparate geographic locations. Our analysis for two different locations shows that the stochastic environmental factors determine the spectral power-law slope in the high-frequency range, while the deterministic clear-sky signal plays a role in the intermediate frequency range. We close by discussing its implications for solar photovoltaic power production, in particular, for the geographic smoothing of fluctuations. Published by the American Physical Society 2024

CHARACTERIZING SPINAL LOAD-DISPLACEMENT BEHAVIOUR USING REPRESENTATIVE COMPONENTS

AbstractObjectivesSpinal stiffness and flexibility terms are typically evaluated from linear regression of experimental data and are then assembled into 36-element matrices. Summarising in vitro test results in this manner is quick, computationally cheap and has the distinct advantage of outputting simple characteristic values which make it easy to compare results. However, this method disregards many important experimental features such as stiffening effects, neutral and elastic zones magnitudes, extent of asymmetry and energy dissipation (hysteresis). Alternatives to the linear least squares method include polynomials, separation of the load-displacement behaviour into the neutral and elastic zones using various deterministic methods and variations on the double sigmoid and Boltzmann curve fits. While all these methods have their advantages, none provide a comprehensive and complete characterisation of the load-displacement behaviour of spine specimens. In 1991, Panjabi demonstrated that the flexion-extension and mediolateral bending behaviour of functional spinal units could be approximated using the viscoelastic model consisting of a nonlinear spring in series with a linear Kelvin element. Nowadays viscoelastic models are mainly used to describe creep and stress relaxation, rather than for cyclic loading. The aim of this study was to conclusively prove the viscoelastic nature of spinal behaviour subject to cyclic loading. Being able to describe the behaviour of spine specimens using springs and dampers would yield characterising coefficients with recognisable physical meaning, thus providing an advantage over existing techniques.MethodsSix porcine isolated spinal disc specimens (ISDs) were tested under position and load control. Visual inspection of the load-displacement graphs from which the principal terms of the stiffness and flexibility matrices are derived suggest that the load-displacement behaviour could be idealised by a nonlinear spring system with damping. It was hypothesised that the contributions arising from non-linear spring-like behaviour and damping could be separated for each of the principal load-displacement graphs.ResultsThe principal elements from position and load control tests were plotted with load on the vertical axis and displacement on the horizontal axis, and a polynomial representing spring force was fitted to the data. This polynomial was subtracted from the experimental data. The remainder - representing damping force - was plotted against displacement and velocity and compared to idealised plots for different types of damping behaviour. Applying this reasoning to the six principal load-displacement plots obtained from stiffness and flexibility tests revealed that four of six exhibit behaviour which is a combination of a nonlinear hardening spring and viscous damper. However, for flexion-extension and mediolateral bending, the damping behaviour is more akin to coulomb damping with viscous influences, characterised by a steep central linear region and near horizontal regions at the extremes. These trends were common amongst all six specimens within the study sample size.ConclusionsThe unique approach described here has allowed the characterisation of the load-displacement behaviour of ISDs in terms of characteristic mass-spring-damper systems. This is an important development which allows experimental findings to be framed in terms of mechanical contributions to a given load-displacement behaviour.Declaration of Interest(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.

Inter-bacterial mutualism promoted by public goods in a system characterized by deterministic temperature variation

Mutualism is commonly observed in nature but not often reported for bacterial communities. Although abiotic stress is thought to promote microbial mutualism, there is a paucity of research in this area. Here, we monitor microbial communities in a quasi-natural composting system, where temperature variation (20 °C–70 °C) is the main abiotic stress. Genomic analyses and culturing experiments provide evidence that temperature selects for slow-growing and stress-tolerant strains (i.e., Thermobifida fusca and Saccharomonospora viridis), and mutualistic interactions emerge between them and the remaining strains through the sharing of cobalamin. Comparison of 3000 bacterial pairings reveals that mutualism is common (~39.1%) and competition is rare (~13.9%) in pairs involving T. fusca and S. viridis. Overall, our work provides insights into how high temperature can favour mutualism and reduce competition at both the community and species levels.

Variability in Plant–Herbivore Interactions

Plants and herbivores are remarkably variable in space and time, and variability has been considered a defining feature of their interactions. Empirical research, however, has traditionally focused on understanding differences in means and overlooked the theoretically significant ecological and evolutionary roles of variability itself. We review the literature with the goal of showing how variability-explicit research expands our perspective on plant–herbivore ecology and evolution. We first clarify terminology for describing variation and then review patterns, causes, and consequences of variation in herbivory across scales of space, time, and biological organization. We consider how incorporating variability improves existing hypotheses and leads to new ones. We conclude by suggesting future work that reports full distributions, integrates effects of variation across scales, describes nonlinearities, and considers how stochastic and deterministic variation combine to determine herbivory distributions.

Eddy Current Measurement of Chemiresistive Sensing Transients in Graphene-hBN Heterostructures.

The development of graphene-based electronic and gas sensing devices has motivated considerable research interest in the properties of graphene-hBN heterostructures. Eddy current measurements of the sheet conductance of graphene-hBN heterostructures show a relatively low conductance, as compared to results previously reported in the literature, all of which were obtained using contact-based measurement methods. Chemiresistive measurements of the graphene-hBN heterostructure response to oxygen adsorption, including hysteric effects under transient multicycle loading, show that the incremental sheet conductance responses of graphene and graphene-hBN sensors differ in sign. A transient, nonlinear, history dependent constitutive model of graphene-hBN response to oxygen adsorption distinguishes stochastic variations in material properties from deterministic variations in sensor performance. The deterministic variations are due to sensing process hysteresis, a phenomenon of central interest in the development of graphene-based sensor systems.

STEP AP 242 file-based automatic tolerance analysis of mechanical assembly using unified Jacobian Torsor Model and direct linearization method

ABSTRACT This work presents the approach and algorithms to develop a smart computer-aided tolerance analysis system that is capable of performing Unified Jacobian Torsor Model (UJTM) and Direct Linearization Method (DLM) based deterministic tolerance analysis on mechanical assemblies using the STEP AP 242 file data generated from the assembly 3D CAD model. The smart tolerance analysis system tested on two different CAD packages can automatically extract the B-rep data, tolerance data from the STEP AP 242 file and find the mating surface information to perform the tolerance analysis. The location of the STEP AP 242 file is given as the input into the developed smart system, and the final output is the deterministic variation in the functional requirement and the plot showing the percentage contribution of tolerance to the variation in functional requirement of the mechanical assembly. The capability of the developed smart system is validated against the two mechanical assembly case studies, and the results computed by the developed system are an exact match with the tolerance values calculated manually.

Estimation of requirements to signal parameters at V-shaped frequency distribution in mathematical model of multi-position transmitter system

This paper is a brief review of methods for electromagnetic radiation focusing using a multi-position system of radiators based on mutually consistent spatial-amplitude-phase-frequency control of radiated signals and limitations of their potentialities arising from various random fluctuations of signals and antenna parameters. The statistical study of influence of different random and deterministic variations of electrical and design parameters of the antennas, control systems of the radiated signals with V-shaped frequency distribution over the aperture of a multi-position radiating system on the peak power level, duration and repetition period of the focused pulses is carried out. The parameters of the space-amplitude-phase-frequency control law must be stable for a time equal to the average duration of the pulses at the output of the emitters when forming a single space-time pulse, and when forming a sequence of space-time pulses during this pack of space-time pulses. The requirements concerning accuracy and stability of parameters of the signals’ space-phase-frequency control law are considered. The analysis of the influence of various kinds of deviations from the given values of the parameters of the space-phase-frequency control law of emitted signals in the channels of a multi-position system of emitters during formation of space-time pulses sequences is carried out. It is shown that the influence of errors in the location of the phase centers of the emitters in the direction of radiation does not depend on the distance to the focusing point, but is significant and special measures are required to reduce them.

Hybrid control for combining model-based and model-free reinforcement learning

We develop an approach to improve the learning capabilities of robotic systems by combining learned predictive models with experience-based state-action policy mappings. Predictive models provide an understanding of the task and the dynamics, while experience-based (model-free) policy mappings encode favorable actions that override planned actions. We refer to our approach of systematically combining model-based and model-free learning methods as hybrid learning. Our approach efficiently learns motor skills and improves the performance of predictive models and experience-based policies. Moreover, our approach enables policies (both model-based and model-free) to be updated using any off-policy reinforcement learning method. We derive a deterministic method of hybrid learning by optimally switching between learning modalities. We adapt our method to a stochastic variation that relaxes some of the key assumptions in the original derivation. Our deterministic and stochastic variations are tested on a variety of robot control benchmark tasks in simulation as well as a hardware manipulation task. We extend our approach for use with imitation learning methods, where experience is provided through demonstrations, and we test the expanded capability with a real-world pick-and-place task. The results show that our method is capable of improving the performance and sample efficiency of learning motor skills in a variety of experimental domains.

Compact PUF Design With Systematic Biases Mitigation on Xilinx FPGAs

Physical unclonable functions (PUFs) are a strong and secure root source for identification and authentication applications. PUFs are especially valuable in FPGA-based systems because FPGA designs are vulnerable to intellectual property (IP) thefts and cloning, which PUFs protect against by generating random but device-specific bitstrings. Theoretically, the randomness of PUFs originates from variations in the manufacturing process. PUFs should be free of deterministic variation owing to the systematic bias among all chips of the same model. Correspondingly, one of the major challenges for FPGA-based PUFs is the difficulty of avoiding systematic bias between nominally matched delays in competing paths. In this paper, a deep investigation into the LUT structure on a Xilinx FPGA was conducted. Based on the investigation findings, a compact PUF design based on programmable look-up table paths is proposed. The proposed intertwined structure and the novel 2-phase, 2-pass scheme significantly reduced the impact of systematic biases in the Xilinx FPGA LUT. The proposed PUFs exploit random variations in LUTs, thus exhibiting very good uniformity and uniqueness among the generated bitstrings.

Hardware Topologies for Decentralized Large-Scale MIMO Detection Using Newton Method

Centralized Massive Multiple Input Multiple Output (MIMO) uplink detection techniques for baseband processing possess severe bottleneck in terms of interconnect bandwidth and computational complexity. This problem has been addressed in the current work by adapting the centralized Newton method for decentralized MIMO uplink detection leveraging several Base Station antenna clusters. The proposed decentralized Newton (DN) method achieves error-rate performance close to centralized Zero Forcing detector as compared to other decentralized techniques. Two hardware topologies, namely the ring and the star topologies, are proposed to assess and discuss the trade-off among interconnect bandwidth and throughput, in comparison with contemporary decentralized MIMO uplink detection techniques. As such the following findings are elaborated. On BS antenna cluster scaling for different MIMO system configurations, the ring topology provides high throughput at constant interconnect bandwidth, while the star topology provides lower latency with a deterministic variation in the hardware resource consumption. Due to strategic optimizations on the hardware implementation, additional user equipment can be allotted at a fractional increase in Field Programmable Gate Array resource consumption, improved energy efficiency, and increased transaction of bits per Joule. The ring topology can process additional subcarrier at a fractional increase in latency and improved system throughput.

Deterministic Choice Set Variation in Demand Estimation - with an Application to Consumption Rivalry in the EV Public Charging Market

Consumption rivalry generates variation in the choice sets individual decision-makers face. When such variation is not taken into account, biased estimates of demand result. Researchers however often lack exact information on temporal variation in product availability and necessarily limit themselves to imposing probabilistic consideration constraints. This paper instead uses deterministic constraints to incorporate information on the exact set of available alternatives at the time of choosing. In an application to the market for public charging infrastructure for electric vehicles I show how this improves predictions of individual choice and the aggregate demand estimates for local charging facilities.

Impact of Virtual Power Plants on Power System Short-Term Transient Response

This paper studies the impact of coordinated and non-coordinated frequency control of Virtual Power Plants (VPPs) on power system transients. A realistic modelling of the communication system within the VPP is also taken into account. The case study considers a modified version of the WSCC 9-bus test system with inclusions of a VPP with distributed generations and, discusses the performance of the coordinated frequency controller in the VPP. All simulations are performed considering both deterministic and stochastic variations of the wind and voltage-dependent loads.

Multi-Objective Optimal Allocation of Wireless Bus Charging Stations Considering Costs and the Environmental Impact

In recent years, due to environmental concerns, there has been an increasing desire to develop alternative solutions to traditional energy sources. Since transportation is a significant fossil-fuel consumer, the development of electric vehicles, especially buses, has the potential to reduce fossil-fuel use and thus provide a better living environment. The aim of the current work was to develop an optimal allocation model for designing a system-wide network of wireless bus charging stations. The main advantages of wireless charging are the need for a much smaller battery and the fact that the charging process may occur under both static and dynamic (in-motion) conditions. The suggested approach consisted of a multi-objective model that selected the locations for the charging stations while (a) minimizing the costs, (b) maximizing the environmental benefit, and (c) minimizing the number of charging stations. The problem was formulated as a multi-objective non-linear optimization model with both deterministic and stochastic variations. An efficient genetic algorithm was introduced to solve the problem. A test case was used to demonstrate the model; accordingly, the decision-maker was provided with a solution set from which the best fit solution could be selected.

Chance and necessity in the pleiotropic consequences of adaptation for budding yeast.

Mutations that a population accumulates during evolution in one (“home”) environment may cause fitness gains or losses in other conditions. Such pleiotropic fitness effects determine the evolutionary fate of the population in variable environments and can lead to ecological specialization. It is unclear how the pleiotropic outcomes of evolution are shaped by the intrinsic randomness of the evolutionary process and by the deterministic variation in selection pressures across environments. To address this question, we evolved 20 replicate populations of the yeast Saccharomyces cerevisiae in 11 laboratory environments and measured their fitness across multiple conditions. We found that evolution led to diverse pleiotropic fitness gains and losses, driven by multiple types of mutations. Approximately 60% percent of this variation is explained by a clone’s home environment and the most common parallel genetic changes, while about 40% is attributed to the stochastic accumulation of mutations whose pleiotropic effects are unpredictable. While populations typically specialized to their home environment, generalists also evolved in almost all conditions. Our results suggest that the mutations accumulating during evolution incur a variety of pleiotropic costs and benefits with different probabilities. Therefore, whether a population evolves towards a specialist or a generalist phenotype is heavily influenced by chance.

Dominant Tree Species Shape Soil Microbial Community via Regulating Assembly Processes in Planted Subtropical Forests

Understanding the ecological processes that regulate microbial community assembly in different habitats is critical to predict microbial responses to anthropogenic disturbances and environmental changes. Rubber (Hevea brasiliensis) and Eucalypt (Eucalyptus urophylla) plantations (thereafter RP and EP) are rapidly established at the expense of forests in tropical China, greatly affecting tropical soils and their processes. However, the assembly processes of soil microbial communities after forest conversions remain unclear. We investigated soil microbial communities’ attributes and quantified the portion of deterministic assembly variation in two RP (a 3- and a 5-year-old) and two EP (a 2- and a 4-year-old) in Southern China. Shannon and Faith’s Phylogenetic α-diversity of both bacterial and fungal communities were higher in RP than in EP, regardless of plantation age or soil depth (0–50 cm). Bacterial and fungal community structure was significantly different among the four plantations. The dominant microbial taxa in RP closely tracked the availability of nitrogen, phosphorus and potassium (K) while those in EP were closely related to the high total K content. Microbial co-occurrence networks in RP were more modular than those in EP, as governed by more keystone taxa that were strongly dependent on soil available nutrients. Environmental filtering imposed by soil nutrients heterogeneity contributed a considerable portion (33–47%) of bacterial assembly variation in RP, but much less (8–14%) in EP. The relative contribution of environmental selection on fungal assembly was also greater in RP than in EP. Our findings suggest that in RP clear microbial community patterns exist with respect to soil nutrients, whereas in EP microbial community assembly patterns are more stochastic and variable. The large variation in soil microbial community assembly patterns in EP could lead to fragile and unstable microbial-soil relationships, which may be one factor driving soil degradation in EP.

Systematic Meta-analysis Revealed an Association of PGC-1α rs8192678 Polymorphism in Type 2 Diabetes Mellitus.

Background Genome-wide association study (GWAS) provides an unprecedented opportunity to reveal substantial genetic contribution to type 2 diabetes mellitus (T2DM) and glycemic identification of allelic heterogeneity and population-specific genetic variants, yet it also faces difficulty due to the vast amount of potential confounding factors and limited availability of clinical data. To identify responsible susceptibility loci and genomic polymorphism for T2DM and glycemic traits, we have systematically investigated a genome-wide association study related to T2DM. Although GWAS has captured many common genetic variations, which are related to T2DM, each risk allele (RA) of single-nucleotide polymorphisms (SNPs) at these loci is not conclusive. Therefore, it is common to present a combination of several SNPs to infer T2DM risk, yet it is still insufficient to be deterministic. To streamline the identification of a deterministic genetic variation in T2DM, we developed this meta-analysis as a showcase to comprehensively identify the association between cumulative RAs and T2DM risk by combining different studies in reported literature and databases. After all, we identified that PGC-1α rs8192678 polymorphism can be considered as a potentially deterministic biomarker in T2DM risk. Previous studies have potentially linked PGC-1α rs8192678 polymorphism to type 2 diabetes mellitus (T2DM) risk, but the results remain inconsistent in different populations and are not conclusive. We developed a new meta-analysis approach to systematically identify the association between PGC-1α rs8192678 polymorphism and T2DM, and we have comprehensively assessed different ethnic groups to validate our findings. Methods We performed comprehensive information retrieval and knowledge discovery meta-analysis by searching extensively published literature and different electronic databases to acquire eligible studies for the above association study. We developed a method to use pooled odds ratios (ORs) and their corresponding 95% confidence intervals (CIs) in five genetic models (allelic, dominant, recessive, homozygous, and heterozygous genetic models) to identify the relationship among ethnicity subgroup analyses comprehensively. Results We identified 20 eligible studies consisting of 16,182 subjects (8,038 cases and 8,144 controls) in our meta-analysis. PGC-1α rs8192678 polymorphisms of all subjects showed a significant association with T2DM susceptibility under all genetic models: allelic (OR: 1.24, 95% CI: 1.13-1.35), dominant (OR: 1.27, 95% CI: 1.14-1.42), recessive (OR: 1.24, 95% CI: 1.14-1.36), homozygous (OR: 1.40, 95% CI: 1.20-1.64), and heterozygous (OR: 1.20, 95% CI: 1.06-1.35). In the subgroup analysis, we identified a significant association between PGC-1α rs8192678 polymorphism and T2DM in the Caucasian and Indian populations under all genetic models we investigated. This is the most comprehensive study of the subject to date. Conclusion Our development of meta-analysis revealed that the minor allele (A) carriers, especially AA genotype carriers, can lead to risk of T2DM in the Caucasian and Indian populations. This is the first report that such risk has been confirmed. Our finding shed new light into the genetic alteration in T2DM.

Determination of the Refractive Contribution to GPS Phase “Scintillation”

AbstractAs L‐band radio waves travel through the ionosphere, such as those transmitted by the Global Positioning System (GPS) satellites, changes in the electron density along the ray path may induce refractive and/or diffractive variations in the signal's phase; where refractive variations are deterministic and diffractive variations are stochastic. Typically, the refractive component of these variations is thought to be slow varying, associated with frequencies less than 0.1 Hz. Therefore, if the refractive contribution is assumed to be associated with frequencies less than 0.1 Hz, the frequencies greater than 0.1 Hz are then assumed and treated as diffractive. These variations are usually referred to as scintillation. In scintillation studies the deterministic refractive variations are very often ignored. We propose that rapid changes in the electron density, and therefore changes in the refractive index along the ray path of the GPS signal, can induce dominantly refractive variations at frequencies greater than 0.1 Hz. The increased drift speeds observed in the high‐latitude region create conditions suitable for these high‐frequency refractive variations; the GPS ray path will sweep through large‐scale irregularities at higher speeds, resulting in high‐frequency refractive variations. Using recent advances in GPS, most importantly an improved signal tracking technique, we present examples of rapid refractive variations in the GPS signal's phase. These high‐frequency variations are shown to be refractive using a combination of techniques, one adapted from a previous technique used for the low‐frequency refractive contributions and a new technique only possible with advances in GPS tracking.