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Introduction/purpose: Studying the dynamics of the mutual influence of supply and demand is relevant in connection with the financial losses that arise due to uncertainty in demand and forecast errors. The work aims to build a mathematical model of the dynamics of this interaction for the market of one product. Methods: The paper proposes a mathematical model of the states of the supply-demand system, within the framework of which the processes occurring in this system are considered from the perspective of the methodology of economic synergetics. The mathematical model of dynamics has the form of a system of two differential equations with quadratic nonlinearity. Results: The use of the proposed model to reproduce various dynamic states of market self-regulation processes made it possible to identify the hierarchy of transition from stable dynamic regimes to unstable ones with the appearance of corresponding bifurcations. The main attention was paid to studying the behavior of the system at the boundaries of the stability region. Conclusion: The existence of a saddle-node bifurcation of limit cycles has been revealed, which suggests the appearance of stable self-oscillations in the case of a "soft" cycle and unstable ones in the case of a "hard" cycle. When studying a bifurcation of codimension two - "double zero" - special dynamic structures were discovered, determined by the properties of global bifurcations. This type of behavior is characterized by self-oscillations with a low frequency, which gives rise to the so-called "ultra-long waves" of the economic state.

Many emerging applications, such as factory automation, electric power distribution, and intelligent transportation systems, require multicast Ultra-Reliable Low-Latency Communications (mURLLC). Since 3GPP Release 17, 5G systems natively support multicast functionality, including multicast Hybrid Automatic Repeat Request and various feedback schemes. Although these features can be promising for mURLLC, the specifications and existing studies fall short in offering guidance on their efficient usage. This paper presents the first comprehensive system-level evaluation of mURLLC, leveraging insights from 3GPP specifications. It points out (i) how mURLLC differs from traditional multicast broadband wireless communications, and (ii) which approaches to provide mURLLC require changing the paradigm compared with the existing solutions. Finally, the paper provides recommendations on how to satisfy strict mURLLC requirements efficiently, i.e., with low channel resource consumption, which increases the capacity of 5G systems for mURLLC. Simulation results show that proper configuration of multicast mechanisms and the corresponding algorithms for mURLLC traffic can reduce resource consumption up to three times compared to the baseline solutions proposed for broadband multicast traffic, which significantly increases the system capacity.

Abstract Individuals at Clinical High Risk for Psychosis (CHR-P) demonstrate heterogeneity in clinical profiles and outcome features. However, the extent of neuroanatomical heterogeneity in the CHR-P state is largely undetermined. We aimed to quantify the neuroanatomical heterogeneity in structural magnetic resonance imaging measures of cortical surface area (SA), cortical thickness (CT), subcortical volume (SV), and intracranial volume (ICV) in CHR-P individuals compared with healthy controls (HC), and in relation to subsequent transition to a first episode of psychosis. The ENIGMA CHR-P consortium applied a harmonised analysis to neuroimaging data across 29 international sites, including 1579 CHR-P individuals and 1243 HC, offering the largest pooled CHR-P neuroimaging dataset to date. Regional heterogeneity was indexed with the Variability Ratio (VR) and Coefficient of Variation (CV) ratio applied at the group level. Personalised estimates of heterogeneity of SA, CT and SV brain profiles were indexed with the novel Person-Based Similarity Index (PBSI), with two complementary applications. First, to assess the extent of within-diagnosis similarity or divergence of neuroanatomical profiles between individuals. Second, using a normative modelling approach, to assess the ‘normativeness’ of neuroanatomical profiles in individuals at CHR-P. CHR-P individuals demonstrated no greater regional heterogeneity after applying FDR corrections. However, PBSI scores indicated significantly greater neuroanatomical divergence in global SA, CT and SV profiles in CHR-P individuals compared with HC. Normative PBSI analysis identified 11 CHR-P individuals (0.70%) with marked deviation (>1.5 SD) in SA, 118 (7.47%) in CT and 161 (10.20%) in SV. Psychosis transition was not significantly associated with any measure of heterogeneity. Overall, our examination of neuroanatomical heterogeneity within the CHR-P state indicated greater divergence in neuroanatomical profiles at an individual level, irrespective of psychosis conversion. Further large-scale investigations are required of those who demonstrate marked deviation.

Abstract Omniphobic and icephobic twin-scale surfaces based on the “urchin”-like fluorinated Al2O3 particles are presented. Combined effect of hierarchical topography and fluorination supplied to the surfaces omniphobic and icephobic properties. The study of the stability of the Cassie wetting state is reported. High apparent contact angles were accompanied with the low contact angle hysteresis and high stability of the Cassie air trapping wetting state. Time delay of the ice crystallization as high as $$88\pm 5$$ 88 ± 5 min was established when compared to the ice formation on flat aluminum and non-fluorinated “urchin”-like surfaces. Crystallized water droplets formed on the reported nano-structured surfaces were easily blown out by the air jet with the velocity of $$v=3.0\pm 1.0$$ v = 3.0 ± 1.0 m/s, (which is markedly lower than that common for exploitation of aircrafts and turbines). Heated “urchin”-like surfaces completely restored their omniphobic and icephobic surfaces after thawing. Qualitative analysis of water freezing is supplied.

Предметом досліджень статті є виродження першої форми при моногармонійній зміні коефіцієнта форми та за умови, коли частота пульсації «форм» коливань досягає другої парціальної частоти. Метою є оцінка можливості виродження i-ої форми коливань при різних законах зміни збуджуючого впливу та аналіз даного явища. Завдання дослідження полягають у побудові принципів оцінки впливу високочастотних пульсацій параметрів системи на вільні коливання останньої. Застосовувані методи: описання динамічних моделей диференційними рівняннями; частотний аналіз; формування амплітудно-частотних характеристик. Отримані результати: для динамічної моделі з певними показниками приводу та веденої ланки визначено, що при гармонійній зміні функції руху з частотою пульсації, що перевищує одиницю при співвідношенні коефіцієнтів демпфування більше одиниці спостерігається ефект виродження першої форми коливань, в результаті чого частота коливань веденої ланки практично відповідає другій формі. Практична значущість роботи полягає у побудові моделі формування частотних характеристик динамічної моделі при високочастотній пульсації параметрів останньої. Для виявлення цих ефектів доводиться відмовлятися від традиційних уявлень про малість інерційних складових, викликаних нестаціонарністю форм коливань.

A common limitation of neuroimaging studies is their small sample sizes. To overcome this hurdle, the Enhancing Neuro Imaging Genetics through Meta-Analysis (ENIGMA) Consortium combines neuroimaging data from many institutions worldwide. However, this introduces heterogeneity due to different scanning devices and sequences. ENIGMA projects commonly address this heterogeneity with random-effects meta-analysis or mixed-effects mega-analysis. Here we tested whether the batch adjustment method, ComBat, can further reduce site-related heterogeneity and thus increase statistical power. We conducted random-effects meta-analyses, mixed-effects mega-analyses and ComBat mega-analyses to compare cortical thickness, surface area and subcortical volumes between 2897 individuals with a diagnosis of schizophrenia and 3141 healthy controls from 33 sites. Specifically, we compared the imaging data between individuals with schizophrenia and healthy controls, covarying for age and sex. The use of ComBat substantially increased the statistical significance of the findings as compared to random-effects meta-analyses. The findings were more similar when comparing ComBat with mixed-effects mega-analysis, although ComBat still slightly increased the statistical significance. ComBat also showed increased statistical power when we repeated the analyses with fewer sites. Results were nearly identical when we applied the ComBat harmonization separately for cortical thickness, cortical surface area and subcortical volumes. Therefore, we recommend applying the ComBat function to attenuate potential effects of site in ENIGMA projects and other multi-site structural imaging work. We provide easy-to-use functions in R that work even if imaging data are partially missing in some brain regions, and they can be trained with one data set and then applied to another (a requirement for some analyses such as machine learning).