Unique Measure Research Articles

Integral-Type Representations for the Subdifferential of Suprema

AbstractAn integral-like representation is provided for the $$\varepsilon $$ ε -subdifferential of the supremum of an arbitrary family of convex functions. Our characterizations are expressed through appropriate discrete sums performed on the data functions $$f_{t}$$ f t ’s together with specific singular measures operating on them. Moreover, as long as the underlying space is a reflexive Banach space or a separable normed space, we substitute these additional measures with related limits that involve the data functions. All the objects involved in our characterizations rely intrinsically on the data functions that are (almost) active at the reference point.

Exponential mixing for singular skew-products

Abstract We study skew-products of the form ( x , u ) ↦ ( f x , u + φ ( x ) ) where f is a non-uniformly expanding map on a manifold X and φ : X → S 1 is piecewise C 1 . If the systems satisfies mild assumptions (in particular singular behaviour of ϕ is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map.

The impact of an organized physical activity program on the health indicators of students from differ-ent cultural groups in second chance school setting

The primary objective of this research was to assess the impact of a structured physical activity program on the health indicators of adult students attending a multicultural Second Chance School (SCS). The study encompassed a total of 62 SCS students aged 19 to 57, who were divided into two groups: experimental and control. The intervention program consisted of two sessions per week spanning 20 weeks, with each session lasting 60 minutes. The exercise intensity ranged from 65% to 85% of HRmax and included various activities such as aerobics, weight exercises, dumbbell routines, and hiking. Measurements were taken at both the commencement and conclusion of the organized physical activity program. Specialized equipment, including a wall-mounted stadiometer, precision scales, a unique tape measure, an automated sphygmomanometer, and the DXA machine, was employed for data collection. Data analysis involved ANOVA variance analyses, descriptive statistics, and T-Tests utilizing the SPSS software. The results revealed a statistically significant primary influence attributed to the 'measurement' factor (p<.001) across all health indicators, except for total BMD and total BMC, when comparing the experimental and control groups. In terms of gender disparities, men exhibited higher measurements in body mass, fat-free mass, belly size, and blood pressure, while women displayed greater fat mass and total body fat. To conclude, the intervention program had a positive impact on improving the health indicators of adult SCS students. Future research endeavors should explore the implementation of Physical Activity programs in other SCSs throughout Greece. Keywords: Adult Students; Health Indicators; Organized Physical Activity; Second Chance Schools

Cognitive Computing Method Based on Decoding Psychological Emotional States

The current artificial intelligence is constrained to passively executing human command control. It cannot perceive, learn, and guide itself. Furthermore, the majority of these systems are unable to comprehend the human psychological cognitive state or emotional intention actively. To enhance the universality and generalization ability of existing emotion recognition methods, a psychological emotion state decoding method combining singular spectrum analysis and entropy measure is designed based on an electroencephalography signal. This method is developed to empower the cognitive computing system with the ability to perceive emotions. The entropy measure is accelerated by the vector dissimilarity criterion. Finally, dynamic sample entropy model learning is used to realize the cognitive calculation of psychological and emotional state recognition. The results demonstrated that the computational efficiency of the proposed decoding algorithm was significantly improved. The average recognition accuracy of positive and negative emotional states reached 82.78±16.22. The best recognition accuracy of the proposed electroencephalography emotion recognition method was 84.64%. The proposed electroencephalography emotion recognition method demonstrated an accuracy of 64.15% in recognizing cross-individual positive, neutral, and negative emotional states. The proposed emotion recognition method shows better universality and generalization performance, and can effectively identify people's psychological and emotional states.

Reassessing the Functional Significance of Blood Oxygen Level Dependent Signal Variability.

BOLD signal variability (SDBOLD) has emerged as a unique measure of the adaptive properties of neural systems that facilitate fast, stable responding, based on claims that SDBOLD is independent of mean BOLD signal (meanBOLD) and is a powerful predictor of behavioral performance. We challenge these two claims. First, the apparent independence of SDBOLD and meanBOLD may reflect the presence of deactivations; we hypothesize that although SDBOLD may not be related to raw meanBOLD, it will be linearly related to "absolute" meanBOLD. Second, the observed relationship between SDBOLD and performance may be an artifact of using fixed-length trials longer than RTs. Such designs provide opportunities to toggle between on- and off-task states, and fast responders likely engage in more frequent state-switching, thereby artificially elevating SDBOLD. We hypothesize that SDBOLD will be higher and more strongly related to performance when using such fixed-length trials relative to self-paced trials that terminate upon a response. We test these two hypotheses in an fMRI study using blocks of fixed-length or self-paced trials. Results confirmed both hypotheses: (1) SDBOLD was robustly related with absolute meanBOLD, and (2) toggling between on- and off-task states during fixed-length trials reliably contributed to SDBOLD. Together, these findings suggest that a reappraisal of the functional significance of SDBOLD as a unique marker of cognitive performance is warranted.

Sticky Brownian motions on star graphs

AbstractThis paper is concerned with the construction of Brownian motions and related stochastic processes in a star graph, which is a non-Euclidean structure where some features of the classical modeling fail. We propose a probabilistic construction of the Sticky Brownian motion by slowing down the Brownian motion when in the vertex of the star graph. Later, we apply a random change of time to the previous construction, which leads to a trapping phenomenon in the vertex of the star graph, with characterization of the trap in terms of a singular measure $$\varPhi $$ Φ . The process associated to this time change is described here and, moreover, we show that it defines a probabilistic representation of the solution to a heat equation type problem on the star graph with non-local dynamic conditions in the vertex that can be written in terms of a Caputo-Džrbašjan fractional derivative defined by the singular measure $$\varPhi $$ Φ . Extensions to general graph structures can be given by applying to our results a localisation technique.

Infinite-Volume Gibbs States of the Generalized Mean-Field Orthoplicial Model

The generalized mean-field orthoplicial model is a mean-field model on a space of continuous spins on Rn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^n$$\\end{document} that are constrained to a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional ℓ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ell _1$$\\end{document}-sphere, equivalently a scaled (n-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n-1)$$\\end{document}-dimensional orthoplex, and interact through a general interaction function. The finite-volume Gibbs states of this model correspond to singular probability measures. In this paper, we use probabilistic methods to rigorously classify the infinite-volume Gibbs states of this model, and we show that they are convex combinations of product states. The predominant methods utilize the theory of large deviations, relative entropy, and equivalence of ensembles, and the key technical tools utilize exact integral representations of certain partition functions and locally uniform estimates of expectations of certain local observables.

Does being a responsible bank pay off? Evidence from the COVID-19 pandemic

We investigate whether banks’ initial responses during the first wave of the COVID-19 pandemic in supporting their customers, communities, and governments were perceived as value-enhancing by investors. Using a unique responsible banking measure for a sample of the largest US and European commercial banks, we find a negative relationship between responsible bank behavior and stock market performance, particularly in the first wave of the pandemic. We also find that riskier banks were affected more negatively if they behaved responsibly. Overall, our findings show that banks’ responsible behavior during a crisis reduces, or at best is not relevant to, shareholder value.

Scaling Limit of Multi-Type Invariant Measures via the Directed Landscape

Abstract This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar–Parisi–Zhang (KPZ) class. We identify a set of sufficient hypotheses for convergence of multi-type invariant measures of last-passage percolation (LPP) models to the stationary horizon (SH), which is the unique multi-type stationary measure of the KPZ fixed point. Our limit theorem utilizes conditions that are expected to hold broadly in the KPZ class, including convergence of the scaled last-passage process to the directed landscape. We verify these conditions for the six exactly solvable models whose scaled bulk versions converge to the directed landscape, as shown by Dauvergne and Virág. We also present a second, more general, convergence theorem with future applications to polymer models and particle systems. Our paper is the first to show convergence to the SH without relying on information about the structure of the multi-type invariant measures of the prelimit models. These results are consistent with the conjecture that the SH is the universal scaling limit of multi-type invariant measures in the KPZ class.

Unfolding dynamics in the perception of interior vehicle acoustics via continuous evaluation procedure (CEP)

The evaluation of a soundscape is a challenging task as the object of study is not a stationary event of sensation but rather a dynamic and complex scene stretching over a specific period. To do justice to the time dimension in such acoustic scenes, we utilized the Continuous Evaluation Procedure (CEP). Extending common standard instruments asking participants for a singular integral at the end of the sound experience (e.g., on a rating scale), the participants in this study were enabled to continuously evaluate the evolving acoustic scene of accelerating electrified vehicles (EVs) using CEP. With the increasing electrification of powertrains in the automotive industry, acoustic engineers face the challenge of defining innovative sounds using the availabilities of now low-noise emission platforms of EVs that deviate in their noise profiles from familiar but technologically outdated internal combustion engine vehicles (ICEVs), which have defined the general sound schemes for more than a century. To capture dynamic aspects in the quality perception of powertrain noise in EVs, we asked 37 participants to evaluate acoustic recordings of different vehicles in varying acceleration modes in a high-quality three-dimensional (3D) acoustic simulator. Thereby, we revealed much more detailed and time-dependent quality aspects, which do not come forth in an integral singular measure (ISM) where all impressions experienced during the ongoing acoustic scene are blended together. We, therefore, propagate the systematic application of the CEP method when it comes to the qualitative evaluation of transient acoustic scenes. CEP opens the great opportunity to unfold, detect, and analyze dynamic effects in soundscapes and noise profiles, but of any kind of acoustic signal.

Stability analysis of a stochastic port-Hamiltonian car-following model

Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model class is a generalisation of classical car-following approaches, including the optimal velocity model of Bando et al (1995 Phys. Rev. E 51 1035), the full velocity difference model of Jiang et al (2001 Phys. Rev. E 64 017101), and recent stochastic following models based on the Ornstein–Uhlenbeck process. In contrast to traditional models where the interaction is totally asymmetric (i.e. depending only on the speed and distance to the predecessor), the port-Hamiltonian car-following model also depends on the distance to the follower. We determine the exact stability condition of the finite system with N vehicles and periodic boundaries. The stable system is ergodic with a unique Gaussian invariant measure. Other properties of the model are studied using numerical simulation. It turns out that the Hamiltonian component improves the flow stability and reduces the total energy in the system. Furthermore, it prevents the problematic formation of stop-and-go waves with oscillatory dynamics, even in the presence of stochastic perturbations.

Are Wearable Photoplethysmogram-Based Heart Rate Variability Measures Equivalent to Electrocardiogram? A Simulation Study.

Traditional electrocardiography (ECG)-derived heart rate variability (HRV) and photoplethysmography (PPG)-derived "HRV" (termed PRV) have been reported interchangeably. Any potential dissociation between HRV and PRV could be due to the variability in pulse arrival time (PAT; time between heartbeat and peripheral pulse). This study examined if PRV is equivalent to ECG-derived HRV and if PRV's innate error makes it a high-quality measurement separate from HRV. ECG data from 1084 subjects were obtained from the PhysioNet Autonomic Aging dataset, and individual PAT dispersions for both the wrist (n = 42) and finger (n = 49) were derived from Mol et al. (Exp Gerontol. 2020; 135: 110938). A Bayesian simulation was constructed whereby the individual arrival times of the PPG wave were calculated by placing a Gaussian prior on the individual QRS-wave timings of each ECG series. The standard deviation (σ) of the prior corresponds to the PAT dispersion from Mol et al. This was simulated 10,000 times for each PAT σ. The root mean square of successive differences (RMSSD) and standard deviation of N-N intervals (SDNN) were calculated for both HRV and PRV. The Region of Practical Equivalence bounds (ROPE) were set a priori at ± 0.2% of true HRV. The highest density interval (HDI) width, encompassing 95% of the posterior distribution, was calculated for each PAT σ. The lowest PAT σ (2.0 SD) corresponded to 88.4% within ROPE for SDNN and 21.4% for RMSSD. As the σ of PAT increases, the equivalence of PRV and HRV decreases for both SDNN and RMSSD. The HDI interval width increases with increasing PAT σ, with the HDI width increasing at a higher rate for RMSSD than SDNN. For individuals with greater PAT variability, PRV is not a surrogate for HRV. When considering PRV as a unique biometric measure, SDNN may have more favorable measurement properties than RMSSD, though both exhibit a non-uniform measurement error.

Do global extreme hazards and related attention lead to financial risks in the shipping market?

ABSTRACT This paper investigates the impacts of extreme hazards on the shipping market in terms of freight rates. We develop a unique measure of abnormal freight rate occurred in the period of extreme hazard by introducing the concept of abnormal return in the finance field and find that such impacts of extreme hazards tend to be positive. The impacts are attributed to systematic risks in the shipping market due to increasing costs and decreasing supply. We observe similar associations between individuals’ attention to hazards and freight rates, which are related to stakeholders’ expectations and thus cause non-systematic risks in the shipping market. Unlike the systematic risk, which has short-term effects on the freight rates and starts to fade in three months, the non-systematic risks caused by attention is long-lived. Stakeholders require higher premium for higher systematic and non-systematic risks in the shipping market. The impacts of extreme hazards and attention remain positive when the hazards are associated with the shipping market, non-Asia market, environmental pollution, and seasonal effects. Our results are robust when considering alternative measures of freight rates, potential endogeneity of COVID-19 and macroeconomic conditions. We provide stakeholders with suggestions on pricing, environmental protection, decision-making and market-forecasting.

Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups

We provide a general expression of the Haar measure—that is, the essentially unique translation-invariant measure—on a p-adic Lie group. We then argue that this measure can be regarded as the measure naturally induced by the invariant volume form on the group, as it happens for a standard Lie group over the reals. As an important application, we next consider the problem of determining the Haar measure on the p-adic special orthogonal groups in dimension two, three and four (for every prime number p). In particular, the Haar measure on SO(2,Qp)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SO}(2,\\mathbb {Q}_p)$$\\end{document} is obtained by a direct application of our general formula. As for SO(3,Qp)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SO}(3,\\mathbb {Q}_p)$$\\end{document} and SO(4,Qp)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SO}(4,\\mathbb {Q}_p)$$\\end{document}, instead, we show that Haar integrals on these two groups can conveniently be lifted to Haar integrals on certain p-adic Lie groups from which the special orthogonal groups are obtained as quotients. This construction involves a suitable quaternion algebra over the field Qp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {Q}_p$$\\end{document} and is reminiscent of the quaternionic realization of the real rotation groups. Our results should pave the way to the development of harmonic analysis on the p-adic special orthogonal groups, with potential applications in p-adic quantum mechanics and in the recently proposed p-adic quantum information theory.

Establishing the psychological impact of congenital upper limb differences on parents and families.

The aim of this prospective study was to report the psychological experiences of parents caring for children with a congenital upper limb difference and to compare these to population norms. Contributing factors were explored, including access to support and coping strategies. Finally, parents with a congenital upper limb difference themselves were compared to those without. Data recorded included demographics, a validated wellbeing and family impact measure, a unique measure of emotions experienced and exploratory questions. Wellbeing and family impact scores were significantly lower than populations norms. Mothers experienced significantly more negative emotions than fathers. There was no significant different between parents with and without a congenital upper limb difference. Of the parents, 68% felt there should be improved access to psychological support. This demonstrates that parents of children with congenital upper limb differences have unique psychological experiences and needs. They may benefit from specialist psychological support and further research is needed.Level of evidence: III.

What’s the difference between measures of wellbeing, quality of life, resilience, and coping? An umbrella review and concept map of 155 measures of positive mental health

The multitude of definitions, models, and measures of positive mental health has hindered academic precision and therefore the ongoing scientific evolution of this important area. This umbrella review aimed to synthesize the theoretical landscape of positive mental health, by reviewing measures that were designed to capture overarching, multi-dimensional concepts of positive and adaptive states of mental health (i.e., wellbeing, quality of life, and resilience/coping), and interrogating their underlying dimensions (e.g., vitality, autonomy) and design features (e.g., response scales, item valence). Our search identified 155 measures of positive mental health with a total of 410 constituent dimensions. Using thematic analysis, we consolidated these 410 original dimensions into a set of 21 themes. These themes were transformed into a concept map to illustrate their inter-relationship with the overarching concepts of positive mental health as identified in this review. Our results point to a lack of consensus on the underlying dimensions and measurement approaches for investigating positive mental health, with singular measures failing to capture its breadth, resulting in an unwieldy situation for ongoing scientific inquiry.

Critical Gaussian multiplicative chaos for singular measures

Given d≥1, we provide a construction of the random measure – the critical Gaussian Multiplicative Chaos – formally defined as e2dXdμ where X is a log-correlated Gaussian field and μ is a locally finite measure on Rd. Our construction generalizes the one performed in the case where μ is the Lebesgue measure. It requires that the measure μ is sufficiently spread out, namely that for μ almost every x we have ∫B(x,1)μ(dy)|x−y|deρlog1|x−y|<∞, where ρ:R+→R+ can be chosen to be any lower envelope function for the 3-Bessel process (this includes ρ(x)=xα with α∈(0,1/2)). We prove that three distinct random objects converge to a common limit which defines the critical GMC: the derivative martingale, the critical martingale, and the exponential of the mollified field. We also show that the above criterion for the measure μ is in a sense optimal.

On a localization-in-frequency approach for a class of elliptic problems with singular boundary data

We consider a class of nonhomogeneous elliptic equations in the half-space with critical singular boundary potentials and nonlinear fractional derivative terms. The forcing terms are considered on the boundary and can be taken as singular measure. Employing a functional setting and approach based on localization-in-frequency and Littlewood–Paley decomposition, we obtain results on solvability, regularity, and symmetry of solutions.

Delivery and Delivery Frequency

Vaginal delivery is preferred given that morbidity and mortality associated with operative caesarean section have increased over time. Caesarean section is a unique measure of preserving the health and life of the mother or fetus, but the global rise in its frequency is alarming. Medical caesarean section is an effective method of reducing maternal and perinatal mortality. Any method of delivery for women with a history of caesarean section carries risks. Today, it is extremely necessary to assess the frequency of unreasonable delivery tactics, namely the frequency of unreasonable antenatal cesarean section, unsuccessful attempts at vaginal delivery, the frequency of delivery with severe complications for the mother and/or newborn. In general, 951 births occurred in the Kyrgyz Scientific Center for Human Reproduction in 2016, in 2017 (2193) the number of births increased by +130.6%, in 2018 (2638) by +20.3%, in 2019 the decline was −15.9%, in 2020 the number of births increased again (2808) by +26.5%, 2021 (3543) by +26.1% and 2022 (3231) cases of childbirth decreased by −8.8%. Analysis of delivery methods in women admitted to the Center for Human Reproduction in Bishkek showed in the years studied the predominance of vaginal deliveries over cesarean sections from 2.4 times to 3.0 times. Over time, cases of vaginal delivery tended to decrease against the background of an increase in cases of cesarean sections in 2018 and 2020-2022, with the exception of 2017 and 2019.

Asymptotic Analysis for the Generalized Langevin Equation with Singular Potentials

We consider a system of interacting particles governed by the generalized Langevin equation (GLE) in the presence of external confining potentials, singular repulsive forces, as well as memory kernels. Using a Mori–Zwanzig approach, we represent the system by a class of Markovian dynamics. Under a general set of conditions on the nonlinearities, we study the large-time asymptotics of the multi-particle Markovian GLEs. We show that the system is always exponentially attractive toward the unique invariant Gibbs probability measure. The proof relies on a novel construction of Lyapunov functions. We then establish the validity of the small-mass approximation for the solutions by an appropriate equation on any finite-time window. Important examples of singular potentials in our results include the Lennard–Jones and Coulomb functions.