Generation Function Research Articles

Generic dijet soft functions at two-loop order: correlated emissions

We present a systematic algorithm for the perturbative computation of soft functions that are defined in terms of two light-like Wilson lines. Our method is based on a universal parametrisation of the phase-space integrals, which we use to isolate the singularities in Laplace space. The observable-dependent integrations can then be performed numerically, and they are implemented in the new, publicly available package SoftSERVE that we use to derive all of our numerical results. Our algorithm applies to both SCET-1 and SCET-2 soft functions, and in the current version it can be used to compute two out of three NNLO colour structures associated with the so-called correlated-emission contribution. We confirm existing two-loop results for about a dozen e+e− and hadron-collider soft functions, and we obtain new predictions for the C-parameter as well as thrust-axis and broadening-axis angularities.

Auditory Localization in Low-Bitrate Compressed Ambisonic Scenes

The increasing popularity of Ambisonics as a spatial audio format for streaming services poses new challenges to existing audio coding techniques. Immersive audio delivered to mobile devices requires an efficient bitrate compression that does not affect the spatial quality of the content. Good localizability of virtual sound sources is one of the key elements that must be preserved. This study was conducted to investigate the localization precision of virtual sound source presentations within Ambisonic scenes encoded with Opus low-bitrate compression at different bitrates and Ambisonic orders (1st, 3rd, and 5th). The test stimuli were reproduced over a 50-channel spherical loudspeaker configuration and binaurally using individually measured and generic Head-Related Transfer Functions (HRTFs). Participants were asked to adjust the position of a virtual acoustic pointer to match the position of virtual sound source within the bitrate-compressed Ambisonic scene. Results show that auditory localization in low-bitrate compressed Ambisonic scenes is not significantly affected by codec parameters. The key factors influencing localization are the rendering method and Ambisonic order truncation. This suggests that efficient perceptual coding might be successfully used for mobile spatial audio delivery.

Методология интеграции психологических служб силовых ведомств

The article is devoted to the problem of integration of individual psychological services of law enforcement agencies into a single, centrally controlled state structure. The study conducted a generalization of experience, analysis of statistical data on the organization of psychological support, work with personnel, information and analytical materials; the study of the legal framework of the organization of psychological support and the activities of psychologists of various law enforcement agencies, as well as functional and cost analysis. The novelty of the material is that according to the results of the study, the conceptual basis for the creation of an integrated psychological service is determined by us through the continuum "specificity of functions – universality of functions". The implementation of the generic (common) functions of psychologists (of virtually all activities on work with the personnel) is displayed in the new organizational structure (Federal interagency integrated psychological service). Specific functions (in the total volume of measures about 10 %) are assigned (remain, as before) to departmental psychologists. Level-regional organization of the new integrated structure takes into account the peculiarities of professional activities of all law enforcement agencies. Such innovation will allow to achieve saving of the Federal budget more than 5 % from the amount of funds allocated for the maintenance of psychologists of all power structures of the Russian Federation, to exclude duplication of similar actions, to increase density and quality of psychological work, to improve the social and legal status of psychologists.

Fashion cycle dynamics induced by agents' heterogeneity for generic bell-shaped attractiveness functions

ABSTRACTWe extend the exchange economy evolutionary discrete-time model with heterogeneous agents introduced in ‘Fashion cycle dynamics in a model with endogenous discrete evolution of heterogeneous preferences’, by A. Naimzada and M. Pireddu, appeared in Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 055907 (2018), by considering generic bell-shaped attractiveness functions for the two groups of agents, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. The reproduction level of a group is related to its attractiveness degree, which depends on its social visibility level, determined by the consumption choices of the agents in that group. We investigate the asymptotic heterogeneity among agents, finding that the global dynamics may differ according to the chosen functional form for the attractiveness. Nonetheless, the model is still able to reproduce the recurrent dynamic behaviour typical of the fashion cycle.

Maximum likelihood estimation based on Newton-Raphson iteration for the bivariate random effects model in test accuracy meta-analysis.

A bivariate generalised linear mixed model is often used for meta-analysis of test accuracy studies. The model is complex and requires five parameters to be estimated. As there is no closed form for the likelihood function for the model, maximum likelihood estimates for the parameters have to be obtained numerically. Although generic functions have emerged which may estimate the parameters in these models, they remain opaque to many. From first principles we demonstrate how the maximum likelihood estimates for the parameters may be obtained using two methods based on Newton–Raphson iteration. The first uses the profile likelihood and the second uses the Observed Fisher Information. As convergence may depend on the proximity of the initial estimates to the global maximum, each algorithm includes a method for obtaining robust initial estimates. A simulation study was used to evaluate the algorithms and compare their performance with the generic generalised linear mixed model function glmer from the lme4 package in R before applying them to two meta-analyses from the literature. In general, the two algorithms had higher convergence rates and coverage probabilities than glmer. Based on its performance characteristics the method of profiling is recommended for fitting the bivariate generalised linear mixed model for meta-analysis.

Hierarchy Theorems for Testing Properties in Size-Oblivious Query Complexity

Focusing on property testing tasks that have query complexity that is independent of the size of the tested object (i.e., depends on the proximity parameter only), we prove the existence of a rich hierarchy of the corresponding complexity classes. That is, for essentially any function $$q : (0, 1] \rightarrow \mathbb{N}$$ , we prove the existence of properties for which $$\epsilon$$ -testing has query complexity $$\Theta(q(\Theta(\epsilon)))$$ . Such results are proved in three standard domains that are often considered in property testing: generic functions, adjacency predicates describing (dense) graphs, and incidence functions describing bounded-degree graphs. These results complement hierarchy theorems of Goldreich, Krivelevich, Newman, and Rozenberg (Computational Complexity, 2012), which refer to the dependence of the query complexity on the size of the tested object, and focus on the case that the proximity parameter is set to some small positive constant. We actually combine both flavors and get tight results on the query complexity of testing when allowing the query complexity to depend on both the size of the object and the proximity parameter.

Vibrational response of a MRI gradient coil cylinder to time-harmonic Lorentz-force excitations: An exact linear elastodynamic model for shielded longitudinal gradient coils

• A simple linear elastodynamic model of a shielded longitudinal gradient coil (GC) is introduced. • The model is used to investigate the frequency response of a typical whole-body GC cylinder. • The frequency response is governed by the Fourier decomposition of the spatial current density. • The widths of all structural resonances are decreased when shielding currents are present. • Numerical results are consistent with available in-situ experimental data and numerical models. The reduction of gradient coil (GC) vibration continues to be a challenging problem in the optimization of magnetic resonance imaging systems. A key deficiency for passive reduction strategies is that, under realistic thick-shell conditions, there are no existing mathematical models that can provide reliable theoretical predictions about the parametrical behaviors of the vibration response. In this paper, we introduce a simple linear elastodynamic model of a shielded longitudinal GC that can serve as a baseline theoretical model for studying the steady-state linear vibration response of an undamped GC cylinder under the condition that only the Z-coil windings are excited by Lorentz forces . The exact three-dimensional theory of linear elasticity is used to formulate the model, and hence, there are no built-in geometrical constraints. An exact closed-form solution for the steady-state displacement field of the GC cylinder is given, and the solution is then used to numerically investigate the frequency response of a typical whole-body GC cylinder. A core prediction of the model is that the frequency response is essentially governed by the Fourier decomposition of a dimensionless “profile function” that specifies how the current density varies along the GC cylinder axis. An interesting corollary is that generally the same set of resonant modes are excited independent of how the currents are spatially distributed. The model also predicts that the widths of all resonances are substantially decreased when shielding currents are present. Numerical results obtained using generic profile functions are found to be remarkably consistent with available in-situ experimental data and existing numerical models. The model is therefore well-suited for parametric studies of the steady-state linear vibration response assuming that Z-coil windings are excited exclusively.

Attaining the Ultimate Precision Limit in Quantum State Estimation

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator’s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, called D-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.

On unified stability for a class of chemostat model with generic growth rate functions: Maximum yield as control goal

A unified criterion for stability is dealt for a class of chemostat model which includes a generic growth rate function representing substrate, biomass, and product inhibitions. The stability criterion is unified at sense that the growth kinetic rate takes a general form into the vector field and includes both the maintenance coefficient and the death rate parameters. Sufficient conditions are provided for multiplicity of the steady states. In addition, from a local analysis, an expression is proposed as a unified criterion for the local stability and for local bifurcations existence. Hence, a control design relies the unified criterion to account local stability and bifurcation with independence of the specific growth rate governing a chemostat. The criterion is based on partial derivatives which allows us to reduce the calculation needed to determine the equilibrium point stability and the bifurcation points existence. Analytical features of the chemostat were investigated when the maximum of productivity was set as the control objective. Results are illustrated through bifurcation diagrams for the specific growth rate models and parameter values reported in the scientific literature, and with examples for which the maximum of productivity is structurally stable. In this sense, the unified criterion is a tool for the formulation of the extremum seeking problem as well. Finally, some examples for applicability of the results are shown for chemostat that might be governed by different growth rates.

A General Equilibrium Evolutionary Model with Generic Utility Functions and Generic Bell-Shaped Attractiveness Maps, Generating Fashion Cycle Dynamics

We propose a discrete-time exchange economy evolutionary model, in which two groups of agents are possibly characterized by heterogeneous preference structures. With respect to the classical Walrasian framework, in our setting the definition of equilibrium, in addition to utility functions and endowments, depends also on population shares, which affect the market clearing conditions. We prove that, despite such difference with the standard framework, for every economy and for each population shares there exists at least one equilibrium and we show that, for all population shares, generically in the set of the economies, equilibria are finite and regular. We then introduce the dynamic law governing the evolution of the population shares, and we investigate the existence and the stability of the resulting stationary equilibria. More precisely, we assume that the reproduction level of a group is related to its attractiveness degree, which depends on the social visibility level, determined by the consumption choices of the agents in that group. The attractiveness of a group is described via a generic bell-shaped map, increasing for low visibility levels, but decreasing when the visibility of the group exceeds a given threshold value, due to a congestion effect. Thanks to the combined action of the price mechanism and of the share updating rule, the model may reproduce the recurrent dynamic behavior typical of the fashion cycle, presenting booms and busts in the agents’ consumption choices, and in the groups’ attractiveness and population shares. We illustrate the emergence of fashion cycle dynamics in the case of Stone-Geary utility functions, which generalize the Cobb-Douglas utility functions, and for different formulations of the attractiveness maps, already considered in the literature.

Patella tendon moment arm function considerations for human vastus lateralis force estimates

In vivo muscle forces are typically estimated using literature-based or subject-specific moment arms (MAs) because it is not possible to measure in vivo muscle forces non-invasively. However, even subject-specific muscle-tendon MAs vary across contraction levels and are impossible to determine at high contraction levels without techniques that use ionized radiation. Therefore, different generic MA functions are often used to estimate in vivo muscle forces, which may alter force predictions and the shape of the muscle’s force-length relationship. The aim of this study was to examine the influence of different literature-based patella tendon MA functions on the vastus lateralis (VL) force-angle relationship. Participants (n = 11) performed maximum voluntary isometric knee extension contractions at six knee flexion angles, ranging from 40° to 90°. To estimate in vivo VL muscle force, the peak knee extension torque at each joint angle was multiplied by the VL’s physiological cross-sectional area (PCSA) relative to the quadriceps’ PCSA (34%) and then divided by the angle-specific patella tendon MA for 19 different functions. Maximum VL force was significantly different across MA functions (p ≤ 0.039) and occurred at different knee flexion angles. The shape of the VL force-angle relationship also differed significantly (p < 0.01) across MA functions. According to the maximum force generated by VL based on its literature-derived PSCA, only the VL force-angle relationships estimated using geometric imaging-based MA functions are feasible across the knee angles studied here. We therefore recommend that an average of these MA functions is calculated to estimate quadriceps muscle forces if subject-specific MAs cannot be determined.

Influence of the noise on DFT-based sine-wave frequency and amplitude estimators

This paper analyses the effect of wide-band noise on the accuracy of generic sine-wave frequency and amplitude estimators based on Discrete Fourier Transform (DFT) samples located closely to the spectrum peak. A cosine window is adopted to reduce the influence on the estimated parameters of spectral leakage from the negative frequency component. Closed-form expressions for the estimator variances are derived. Moreover, the variance of a frequency estimator expressed as a ratio of generic linear functions of DFT sample modules is specifically investigated. It is also shown that the same frequency estimation accuracy can be achieved when complex-valued DFT samples are considered. The derived expressions are verified on a specific sine-wave frequency estimator and a related amplitude estimator, using both simulation and experimental results.

Bifurcation structures in a 2D exponential diffeomorphism with Allee effect

An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.

The changes of quality of life and their correlations with psychosocial factors following surgery among women with breast cancer from the post-surgery to post-treatment survivorship

ObjectivesThis 14-month study aimed to examine the changes of quality of life following breast cancer surgery and associations of such changes with depression and anxiety levels, and protective factors (attachment styles in close relationship, and meaning in life) based on positive psychology theory. Materials and methodsWomen with breast cancer were recruited within one week of completion of breast cancer surgery. They were asked to complete several questionnaires to measure the generic and breast cancer specific quality of life, depression and anxiety levels, attachment styles in close relationship, and meaning in life. Assessments were performed at baseline (T0), T1 (the 2nd month), T2 (the 5th month), T3 (the 8th month), and T4 (the 14th month). ResultsWhile the generic functions of quality of life improve after surgery, no significant changes of the breast-specific functions were found during the 14-month follow up period. While physical, role, and social functions improved immediately after surgery, the improvements of emotional and cognitive functions began to occur at the 5th and the 8th months after surgery. Depressive symptoms predicted almost all general and breast-specific QOL functions and symptoms. Avoidant and anxious attachment styles were associated with the negative scores for breast-specific functions and symptoms. ConclusionBreast-specific functions, in particular body image and sexual function, remain unchanged with the passage of time following surgery. A psychological rehabilitation program aiming to reduce depressive symptoms and enhance secure attachment styles in close relationships needs to be established immediately following surgery and continue through the post-treatment survivorship stages.

Ventriloquist Illusion Produced With Virtual Acoustic Spatial Cues and Asynchronous Audiovisual Stimuli in Both Young and Older Individuals.

Ventriloquist illusion, the change in perceived location of an auditory stimulus when a synchronously presented but spatially discordant visual stimulus is added, has been previously shown in young healthy populations to be a robust paradigm that mainly relies on automatic processes. Here, we propose ventriloquist illusion as a potential simple test to assess audiovisual (AV) integration in young and older individuals. We used a modified version of the illusion paradigm that was adaptive, nearly bias-free, relied on binaural stimulus representation using generic head-related transfer functions (HRTFs) instead of multiple loudspeakers, and tested with synchronous and asynchronous presentation of AV stimuli (both tone and speech). The minimum audible angle (MAA), the smallest perceptible difference in angle between two sound sources, was compared with or without the visual stimuli in young and older adults with no or minimal sensory deficits. The illusion effect, measured by means of MAAs implemented with HRTFs, was observed with both synchronous and asynchronous visual stimulus, but only with tone and not speech stimulus. The patterns were similar between young and older individuals, indicating the versatility of the modified ventriloquist illusion paradigm.

Exploring the thermodynamic criteria for responsive adsorption processes.

We describe a general model to explore responsive adsorption processes in flexible porous materials. This model combines mean field formalism of the osmotic potential, classical density functional theory of adsorption in slit pore models and generic potential functions which represent the Helmholtz free energy landscape of a porous system. Using this model, we focus on recreating flexible adsorption phenomena observed in prototypical metal-organic frameworks, especially the recently discovered effect of negative gas adsorption (NGA). We identify the key characteristics required for the model to generate unusual adsorption processes and subsequently employ an extensive parametric study to outline conditions under which gate-opening and NGA are observed. This powerful approach will guide the design of responsive porous materials and the discovery of entirely new adsorption processes.

Generic colourful tori and inverse spectral transform for Hankel operators

This paper explores the regularity properties of an inverse spectral transform for Hilbert--Schmidt Hankel operators on the unit disc. This spectral transform plays the role of action-angles variables for an integrable infinite dimensional Hamiltonian system -- the cubic Szeg\"o equation. We investigate the regularity of functions on the tori supporting the dynamics of this system, in connection with some wave turbulence phenomenon, discovered in a previous work and due to relative small gaps between the actions. We revisit this phenomenon by proving that generic smooth functions and a G $\delta$ dense set of irregular functions do coexist on the same torus. On the other hand, we establish some uniform analytic regularity for tori corresponding to rapidly decreasing actions which satisfy some specific property ruling out the phenomenon of small gaps.

Wood Lathe Machine Analysis Using Taguchi Robust Method

This paper presents the use of Taguchi method in investigating the use of a wood lathe machine (turning operations) in dynamic systems for obtaining the optimum cutting parameters. Two generic functions characterize the woodturning process: The specific energy of cutting is connected linearly with the power of cutting and with the quantity of the cut. These parameters have been measured on the basis of the cutting depth and the rotational cutting speed. The optimization of the rough woodturning relies upon the ratios of dynamic signal to noise and the sensitivities that tolerate superior performance and efficiency.

Technological support systems for teachers

This paper categorises the functional scope of 66 technological support systems for teachers and we aim to evaluate the systems’ potential to provide support that fits teachers’ occupational demands. Descriptions of system functions were subjected to structured content analysis. Based on two classification schemes derived from literature, we classified the generic functions of the reviewed systems and assessed their applicability to different areas of teachers’ professional activity. Our results demonstrate that data- and document-management functions are much more common than functions that promote collaboration and communication or functions that provide decision-making support. Cross classifications with different areas of teachers’ professional activities revealed that the mentioned system functions predominantly serve to facilitate administrative work and organisational tasks before, during and after instructional units. Systems that support making justified pedagogical and diagnostic decisions by providing options to purposefully analyse and display content- and student-related information are currently rare.

Developing an Optimal Class of Generic Sixteenth-Order Simple-Root Finders and Investigating Their Dynamics

Developed here are sixteenth-order simple-root-finding optimal methods with generic weight functions. Their numerical and dynamical aspects are investigated with the establishment of a main theorem describing the desired optimal convergence. Special cases with polynomial and rational weight functions have been extensively studied for applications to real-world problems. A number of computational experiments clearly support the underlying theory on the local convergence of the proposed methods. In addition, to investigate the relevant global convergence, we focus on the dynamics of the developed methods, as well as other known methods through the visual description of attraction basins. Finally, we summarized the results, discussion, conclusion, and future work.