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Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in an unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often nontrivial. Here, we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic-to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In a similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection/classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical subdomains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in a statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data. [ABSTRACT FROM AUTHOR]

Introduction: Intraindividual variability across a battery of neuropsychological tests (IIV-dispersion) can reflect normal variation in scores or arise from cognitive impairment. An alternate interpretation is IIV-dispersion reflects reduced engagement/invalid test data, although extant research addressing this interpretation is significantly limited. Method: We used a sample of 97 older adult (mean age: 69.92), predominantly White (57%) or Black/African American (34%), and predominantly cis-gender male (87%) veterans. Examinees completed a comprehensive neuropsychological battery, including measures of reduced engagement/invalid test data (a symptom validity test [SVT], multiple performance validity tests [PVTs]), as part of a clinical evaluation. IIV-dispersion was indexed using the coefficient of variance (CoV). We tested 1) the relationships of raw scores and "failures" on SVT/PVTs with IIV-dispersion, 2) the relationship between IIV-dispersion and validity/neurocognitive disorder status, and 3) whether IIV-dispersion discriminated the validity/neurocognitive disorder groups using receiver operating characteristic (ROC) curves. Results: IIV-dispersion was significantly and independently associated with a selection of PVTs, with small to very large effect sizes. Participants with invalid profiles and cognitively impaired participants with valid profiles exhibited medium to large (d =.55–1.09) elevations in IIV-dispersion compared to cognitively unimpaired participants with valid profiles. A non-significant but small to medium (d =.35–.60) elevation in IIV-dispersion was observed for participants with invalid profiles compared to those with a neurocognitive disorder. IIV-dispersion was largely accurate at differentiating participants without a neurocognitive disorder from invalid participants and those with a neurocognitive disorder (areas under the Curve [AUCs]=.69–.83), while accuracy was low for differentiating invalid participants from those with a neurocognitive disorder (AUCs=.58–.65). Conclusions: These preliminary data suggest IIV-dispersion may be sensitive to both neurocognitive disorders and compromised engagement. Clinicians and researchers should exercise due diligence and consider test validity (e.g. PVTs, behavioral signs of engagement) as an alternate explanation prior to interpretation of intraindividual variability as an indicator of cognitive impairment. [ABSTRACT FROM AUTHOR]

The Lindley distribution is useful in a wide variety of fields, such as biology and astronomy. Many generalizations of the Lindley distribution have been introduced in the literature, with various motivations. Inspired by the concept of superstatistics in nonequilibrium statistical mechanics, we introduce here a novel generalization of the Lindley distribution, by regarding its shape parameter as a stochastic variable. This procedure is particularly well motivated in astronomy applications, since this parameter may fluctuate over a large spatiotemporal scale. By appealing to the central limit theorem, two families of distributions are constructed, associated with additive and multiplicative random processes. We discuss in detail these distributions, we study their asymptotic behavior, and compute their moments. We briefly discuss their possible use in astronomy, biology, and elsewhere. [ABSTRACT FROM AUTHOR]

Quark–Gluon plasma driven by the strong force is subject to the conservativeness of the baryon number, net electric charge, strangeness, etc. However, the fluctuations around their mean values at specific temperatures and chemical potentials can provide viable signals for the production of Quark–Gluon plasma. These fluctuations can be captured theoretically as moments of different orders in the expansion of pressure or the thermodynamic potential of the system under concern. Here, we look for possible explanations in the methodologies used for capturing them by using the framework of the Polyakov–Nambu–Jona-Lasinio (PNJL) model under the 2 + 1 flavor consideration with mean-field approximation. The various quantities thus explored can act to signify meaningfully near the phase transitions. Justifications are also made for some of the quantities capable of serving necessarily under experimental scenarios. Additionally, variations in certain quantities are also made for the different collision energies explored in the high-energy experiments. Rectification of the quantitative accuracy, especially in the low-temperature hadronic sector, is of prime concern, and it is also addressed. It was found that most of the observables stay in close proximity with the existing lattice QCD results at the continuum limit, with some artifacts still remaining, especially in the strange sector, which needs further attention. [ABSTRACT FROM AUTHOR]

Introduction: Lebrikizumab is a novel monoclonal antibody with established efficacy in patients with moderate-to-severe atopic dermatitis (AD) in multiple Phase 3 trials. One of the ultimate treatment goals for patients with moderate-to-severe AD is to achieve stable disease control without concern for planning future life events. Methods: In ADvocate1 and ADvocate2, lebrikizumab-treated patients meeting the protocol-defined response criteria at Week 16 were re-randomized 2:2:1 to receive lebrikizumab every 2 weeks (Q2W), lebrikizumab every 4 weeks (Q4W), or placebo Q2W (lebrikizumab withdrawal) for 36 additional weeks. In this post hoc analysis, we evaluated the proportions of patients with no or minimal fluctuations of efficacy during the 36-week maintenance period and plotted individual patient trajectories. We defined no or minimal fluctuations as achieving and maintaining the defined endpoint (≥ 75% improvement in the Eczema Area and Severity Index [EASI 75], ≥ 90% improvement in EASI, Pruritus Numeric Rating Scale [NRS] ≥ 4-point improvement, or Pruritus NRS ≥ 3-point improvement) for ≥ 80% of the study visits. If patients used rescue medication, discontinued treatment, or transferred to the escape arm, data collected at or after the event were imputed as non-response. Results: The proportions of lebrikizumab responders who maintained EASI 75 with no or minimal fluctuations were 70.8% (lebrikizumab Q2W), 71.2% (lebrikizumab Q4W), and 60.0% (lebrikizumab withdrawal). Of the patients with baseline Pruritus NRS ≥ 4 and who achieved ≥ 4-point improvement at Week 16, 66.1% (lebrikizumab Q2W), 62.7% (lebrikizumab Q4W), and 55.2% (lebrikizumab withdrawal) maintained ≥ 4-point Pruritus NRS improvement with no or minimal fluctuations. Conclusions: Patients who met the response criteria at Week 16 and continued treatment with lebrikizumab Q2W or Q4W demonstrated a stable response with no or minimal fluctuations of efficacy in measures of skin and itch up to Week 52. Clinical Trial Registration: NCT04146363 (ADvocate1) and NCT04178967 (ADvocate2). Plain Language Summary: Atopic dermatitis, also known as atopic eczema (or just eczema), is a common skin disease that causes itchy, dry skin. Patients with eczema are often unsure of when disease flares will happen, even while receiving treatment. In two global studies, ADvocate1 and ADvocate2, lebrikizumab improved the signs and symptoms of moderate-to-severe eczema after 16 weeks of treatment. Most of these patients also saw improvement up to 52 weeks. We wanted to know if patients continued to feel better between Week 16 and Week 52. Patients who responded to lebrikizumab after 16 weeks were given lebrikizumab every 2 weeks, lebrikizumab every 4 weeks, or placebo every 2 weeks. We tested how many patients experienced stable response to therapy, which we said was maintaining the same level of improvement on skin signs and itch symptoms for at least 80% of study visits from Week 16 to Week 52. In patients treated with lebrikizumab every 2 weeks or every 4 weeks, we saw that about seven of every ten patients maintained a stable response in skin improvement and about six of every ten patients maintained stable response in itch symptoms. In patients who stopped lebrikizumab therapy, six out of every ten patients maintained a stable skin improvement and more than five of every ten patients maintained a stable improvement in itch symptoms. In ADvocate1 and ADvocate2, most lebrikizumab-treated patients showed a stable response over time on skin and itch with dosing every 2 weeks or every 4 weeks. [ABSTRACT FROM AUTHOR]

Background: Children's cognitive performance fluctuates across multiple timescales. However, fluctuations have often been neglected in favour of research into average cognitive performance, limiting the unique insights into cognitive abilities and development that cognitive variability may afford. Preliminary evidence suggests that greater variability is associated with increased symptoms of neurodevelopmental disorders, and differences in behavioural and neural functioning. The relative dearth of empirical work on variability, historically limited due to a lack of suitable data and quantitative methodology, has left crucial questions unanswered, which the CODEC (COgnitive Dynamics in Early Childhood) study aims to address. Method: The CODEC cohort is an accelerated 3-year longitudinal study which encompasses 600 7-to-10-year-old children. Each year includes a 'burst' week (3 times per day, 5 days per week) of cognitive measurements on five cognitive domains (reasoning, working memory, processing speed, vocabulary, exploration), conducted both in classrooms and at home through experience sampling assessments. We also measure academic outcomes and external factors hypothesised to predict cognitive variability, including sleep, mood, motivation and background noise. A subset of 200 children (CODEC-MRI) are invited for two deep phenotyping sessions (in year 1 and year 3 of the study), including structural and functional magnetic resonance imaging, eye-tracking, parental measurements and questionnaire-based demographic and psychosocial measures. We will quantify developmental differences and changes in variability using Dynamic Structural Equation Modelling, allowing us to simultaneously capture variability and the multilevel structure of trials nested in sessions, days, children and classrooms. Discussion: CODEC's unique design allows us to measure variability across a range of different cognitive domains, ages, and temporal resolutions. The deep-phenotyping arm allows us to test hypotheses concerning variability, including the role of mind wandering, strategy exploration, mood, sleep, and brain structure. Due to CODEC's longitudinal nature, we are able to quantify which measures of variability at baseline predict long-term outcomes. In summary, the CODEC study is a unique longitudinal study combining experience sampling, an accelerated longitudinal 'burst' design, deep phenotyping, and cutting-edge statistical methodologies to better understand the nature, causes, and consequences of cognitive variability in children. Trial registration: ClinicalTrials.gov - NCT06330090 [ABSTRACT FROM AUTHOR]

Background Objectives Methods Results Conclusions Parkinson's disease (PD) is a progressive neurodegenerative disorder characterized by motor and non‐motor symptoms, primarily because of the impairment of dopaminergic neurons. Long‐term use of levodopa, the standard PD treatment, often results in fluctuating therapeutic effects and dyskinesia, necessitating alternative therapies.This review aims to synthesize current insights and clinical experiences with foslevodopa‐foscarbidopa, focusing on its pharmacokinetics, efficacy, and safety profile, to evaluate its potential in transforming PD therapy.A systematic literature search was conducted up to November 2023 using databases PubMed, Web of Science, and Cochrane Library. The search yielded eight eligible articles, including pharmacological studies, case reports, observational studies, and controlled trials. No language restrictions were applied.Foslevodopa and foscarbidopa, as prodrugs of levodopa and carbidopa, exhibited excellent chemical stability and solubility, facilitating continuous subcutaneous infusion. Clinical trials demonstrated that these prodrugs maintain stable levodopa levels, thereby addressing the limitations of oral levodopa therapy. Phase 1 and 3 studies indicated significant improvements in motor function and quality of life in advanced PD patients. However, a higher incidence of treatment‐emergent adverse events, mainly infusion site reactions, was observed compared to oral therapies.Foslevodopa‐foscarbidopa emerges as a promising alternative for advanced PD treatment, offering sustained symptom control. Its efficacy in managing motor fluctuations and dyskinesia makes it a viable option in the PD therapeutic spectrum. Future research should focus on long‐term safety, economic impact, and broader accessibility. Foslevodopa‐foscarbidopa is now commercially distributed in many countries in Europe and in Japan. [ABSTRACT FROM AUTHOR]

Translation abstract Air entraining concrete with superabsorbent polymers (SAP) – Part 3: robustness to fluctuations in raw materials and ambient conditionsThe production of the required artificially introduced air void content in fresh concrete poses a major challenge under certain practical construction conditions. Fluctuating properties in the air void content can lead to increased rejection of deliveries as well as to poor concrete properties. The influences on air void formation and stability are manifold and result from concrete technology, production‐related and environmental conditions. The robustness of superabsorbent polymers (SAP) against practical variations for the introduction of an artificial air void system into hardened concrete is still relatively unknown. Building on the previous parts 1 (fresh concrete properties) and 2 (hardened concrete properties), this article describes and discusses systematic investigations into the robustness of LP concretes with both superabsorbent polymers and classic LP formers to fluctuations in the starting materials or ambient conditions (temperature). The experimental results show that superabsorbent polymers (SAP) in concrete react very robustly to such practical construction influences with regard to the introduction of artificial air voids and the resulting frost resistance. [ABSTRACT FROM AUTHOR]

The Pólya urn is the most representative example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose almost sure (a.s.) time-limit is not random any more. In this work, in the stream of previous recent works, we introduce a new family of (finite size) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one component-wise, one collective) are tuned through (possibly) two different rates. In special cases, these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead to limits which may be random or not. Different parameter regimes need to be considered. We state two kind of results. First, we study the time-asymptotic and show that L2 and a.s. convergence always holds. Moreover, all the components share the same time-limit (so called synchronization phenomenon). We study the nature of the limit (random/deterministic) according to the parameters' regime considered. Second, we study fluctuations by proving central limit theorems. Scaling coefficients vary according to the regime considered. This gives insights into many different rates of convergence. In particular, we identify the regimes where synchronization is faster than convergence toward the shared time-limit. [ABSTRACT FROM AUTHOR]

Four decades since the concept of polyamorphism was introduced by [L. S. Palatnik (1909–1994), Fiz. Nizk. Temp. 25, 400 (1909)], numerous investigations proved its presence in a broad variety of nonmagnetic short-range ordered materials, like structural, metallic, a-metallic, inorganic molecule, orientational, electron glasses, water, ice, carbons, and others. It was manifested by phase transitions between amorphous states as a function of the quench condition and under compression, mediated by long-wave fluctuations of an order parameter. There has been much recent discussion given to the phenomenon of polyamorphism where distinct, different states of amorphous liquids and solids are observed as a function of density. The outstanding contribution of the recently late [A. Sella, et al. (1956–2022), Nat. Mater. 21, 490 (2022)],2 in the field should be recognized here. Underlying this phenomenon is the possibility of a first-order liquid-liquid phase transition driven by the density and entropy differences between the two amorphous phases. Magnetic boost of multilayer graphene under pressure was also recently discovered. Their famous spin counterparts, such as spin liquid, spin ice, and spin glass have been less studied at this end despite numerous similarities, registered so far. Taking that in mind, for further polyamorphism platform development, we demonstrate the signatures of phase transition in spin glass, driven by a magnetic field, and eventually, a novel type of polyamorphism, the spin-glass one. [ABSTRACT FROM AUTHOR]

We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model. Statistical representation of the aggregate: conditional average. [ABSTRACT FROM AUTHOR]

Abstract Introduction Lebrikizumab is a novel monoclonal antibody with established efficacy in patients with moderate-to-severe atopic dermatitis (AD) in multiple Phase 3 trials. One of the ultimate treatment goals for patients with moderate-to-severe AD is to achieve stable disease control without concern for planning future life events. Methods In ADvocate1 and ADvocate2, lebrikizumab-treated patients meeting the protocol-defined response criteria at Week 16 were re-randomized 2:2:1 to receive lebrikizumab every 2 weeks (Q2W), lebrikizumab every 4 weeks (Q4W), or placebo Q2W (lebrikizumab withdrawal) for 36 additional weeks. In this post hoc analysis, we evaluated the proportions of patients with no or minimal fluctuations of efficacy during the 36-week maintenance period and plotted individual patient trajectories. We defined no or minimal fluctuations as achieving and maintaining the defined endpoint (≥ 75% improvement in the Eczema Area and Severity Index [EASI 75], ≥ 90% improvement in EASI, Pruritus Numeric Rating Scale [NRS] ≥ 4-point improvement, or Pruritus NRS ≥ 3-point improvement) for ≥ 80% of the study visits. If patients used rescue medication, discontinued treatment, or transferred to the escape arm, data collected at or after the event were imputed as non-response. Results The proportions of lebrikizumab responders who maintained EASI 75 with no or minimal fluctuations were 70.8% (lebrikizumab Q2W), 71.2% (lebrikizumab Q4W), and 60.0% (lebrikizumab withdrawal). Of the patients with baseline Pruritus NRS ≥ 4 and who achieved ≥ 4-point improvement at Week 16, 66.1% (lebrikizumab Q2W), 62.7% (lebrikizumab Q4W), and 55.2% (lebrikizumab withdrawal) maintained ≥ 4-point Pruritus NRS improvement with no or minimal fluctuations. Conclusions Patients who met the response criteria at Week 16 and continued treatment with lebrikizumab Q2W or Q4W demonstrated a stable response with no or minimal fluctuations of efficacy in measures of skin and itch up to Week 52. Clinical Trial Registration NCT04146363 (ADvocate1) and NCT04178967 (ADvocate2).

Abstract Background Children’s cognitive performance fluctuates across multiple timescales. However, fluctuations have often been neglected in favour of research into average cognitive performance, limiting the unique insights into cognitive abilities and development that cognitive variability may afford. Preliminary evidence suggests that greater variability is associated with increased symptoms of neurodevelopmental disorders, and differences in behavioural and neural functioning. The relative dearth of empirical work on variability, historically limited due to a lack of suitable data and quantitative methodology, has left crucial questions unanswered, which the CODEC (COgnitive Dynamics in Early Childhood) study aims to address. Method The CODEC cohort is an accelerated 3-year longitudinal study which encompasses 600 7-to-10-year-old children. Each year includes a ‘burst’ week (3 times per day, 5 days per week) of cognitive measurements on five cognitive domains (reasoning, working memory, processing speed, vocabulary, exploration), conducted both in classrooms and at home through experience sampling assessments. We also measure academic outcomes and external factors hypothesised to predict cognitive variability, including sleep, mood, motivation and background noise. A subset of 200 children (CODEC-MRI) are invited for two deep phenotyping sessions (in year 1 and year 3 of the study), including structural and functional magnetic resonance imaging, eye-tracking, parental measurements and questionnaire-based demographic and psychosocial measures. We will quantify developmental differences and changes in variability using Dynamic Structural Equation Modelling, allowing us to simultaneously capture variability and the multilevel structure of trials nested in sessions, days, children and classrooms. Discussion CODEC’s unique design allows us to measure variability across a range of different cognitive domains, ages, and temporal resolutions. The deep-phenotyping arm allows us to test hypotheses concerning variability, including the role of mind wandering, strategy exploration, mood, sleep, and brain structure. Due to CODEC’s longitudinal nature, we are able to quantify which measures of variability at baseline predict long-term outcomes. In summary, the CODEC study is a unique longitudinal study combining experience sampling, an accelerated longitudinal ‘burst’ design, deep phenotyping, and cutting-edge statistical methodologies to better understand the nature, causes, and consequences of cognitive variability in children. Trial registration ClinicalTrials.gov - NCT06330090

The relevance of the topic presented in the article is determined primarily by the current foreign policy situation, namely the hybrid war unleashed by the collective West against the Russian Federation, a significant component of which are the so-called nonkinetic wars: informational, organizational, mental, cognitive, etc. In the article, the author focuses specifically on cognitive wars, which are the least studied in the social sciences. Hence, the main purpose of the article is to consider possible methodological foundations for the analysis of cognitive wars in the context of the high turbulence of the world order and the growing dynamics of digital transformations in the economy, politics, and social spheres. As the core of such a methodology, the author suggests considering social synergetics, the key postulates of which are openness, non-linearity of self-development, and the nonequilibrium nature of systems of various natures, which are most consistent with the current context of public relations. Special attention is paid to the role of the system of spiritual and moral values, or the social value basis, in ensuring the stability of the political system and effective counteraction to cognitive aggression. The author revealed its main functions, such as ensuring communicative effectiveness, overcoming the social atomization of modern society, and ensuring the cognitive stability of society by increasing resistance to cognitive and mental aggression.

Background: We performed an analysis of a large intensive care unit electronic database to provide preliminary estimates of various blood pressure parameters in patients with acute stroke receiving intravenous (IV) antihypertensive medication and determine the relationship with in-hospital outcomes. Methods: We identified the relationship between pre-treatment and post-treatment systolic blood pressure (SBP) and heart rate (HR)–related variables and in-hospital mortality and acute kidney injury in patients with acute stroke receiving IV clevidipine, nicardipine, or nitroprusside using data provided in the Medical Information Mart for Intensive Care (MIMIC) IV database. Results: A total of 1830 patients were treated with IV clevidipine (n = 64), nicardipine (n = 1623), or nitroprusside (n = 143). The standard deviations [SDs] of pre-treatment SBP (16.3 vs. 13.7, p ≤ 0.001) and post-treatment SBP (15.4 vs. 14.4, p = 0.004) were higher in patients who died compared with those who survived, particularly in patients with intracerebral hemorrhage (ICH). The mean SBP was significantly lower post treatment compared with pre-treatment values for clevidipine (130.7 mm Hg vs. 142.5 mm Hg, p = 0.006), nicardipine (132.8 mm Hg vs. 141.6 mm Hg, p ≤ 0.001), and nitroprusside (126.2 mm Hg vs. 139.6 mm Hg, p ≤ 0.001). There were no differences in mean SDs post treatment compared with pre–treatment values for clevidipine (14.5 vs. 13.5, p = 0.407), nicardipine (14.2 vs. 14.6, p = 0.142), and nitroprusside (14.8 vs. 14.8, p = 0.997). The SDs of pre-treatment and post-treatment SBP were not significantly different in patients with ischemic stroke treated with IV clevidipine, nicardipine, or nitroprusside or for patients with ICH treated with IV clevidipine or nitroprusside. However, patients with ICH treated with IV nicardipine had a significantly higher SD of post-treatment SBP (13.1 vs. 14.2, p = 0.0032). Conclusions: We found that SBP fluctuations were associated with in-hospital mortality in patients with acute stroke. IV antihypertensive medication reduced SBP but did not reduce SBP fluctuations in this observational study. Our results highlight the need for optimizing therapeutic interventions to reduce SBP fluctuations in patients with acute stroke. [ABSTRACT FROM AUTHOR]

The study aims to analyze the availability of renewable freshwater resources and their spatiotemporal distribution in the Eastern Region of Kosovo (ERK). As a crucible resource for agricultural, industrial, and commercial activities, water scarcity will lead to water shortages. Kosovo is a landlocked country, and ERK is the most important region for industrial activities (coal, mines) and agricultural use (plains). Located in continental climate conditions, surrounded by middle to high-altitude mountains, the region does not have a favorable spatio-temporal distribution of freshwaters. The determination of the water resources is based on the amount of surface runoff, which being divided per capita, gives indications of the water resources of a region (catchment). For our aims, main river discharge and population statistics are used to analyze the spatiotemporal distribution and availability of renewable freshwater in ERK. Falkenmark Freshwater Indicator with 1.483 m³/capita/year shows that ERK lies under water scarcity, and existing water reservoirs offer low security for water withdrawals, and further reservoirs would prevent water scarcity in the region.

In 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\unicode{x2124}$ : in this model, the probability that the walk moves from a point of $\unicode{x2124}$ to a given neighbor depends on the number of previous crossings of the directed edge from the initial point to the target, called the local time of the edge. Tóth and Vető found that this model exhibited very peculiar behavior, as the process formed by the local times of all the edges, evaluated at a stopping time of a certain type and suitably renormalized, converges to a deterministic process, instead of a random one as in similar models. In this work, we study the fluctuations of the local times process around its deterministic limit, about which nothing was previously known. We prove that these fluctuations converge in the Skorokhod $M_1$ topology, as well as in the uniform topology away from the discontinuities of the limit, but not in the most classical Skorokhod topology. We also prove the convergence of the fluctuations of the aforementioned stopping times. [ABSTRACT FROM AUTHOR]

An analysis of the features of measurements and correction of phase distortions in optical waves propagating in the atmosphere at various levels of turbulence was performed. It is shown that with increasing intensity fluctuations, the limiting capabilities of phase correction decrease, and the phase of an optical wave that has passed through a turbulence layer consists of two components: potential and vortex. It was found that even in the region of weak fluctuations there is an overlap of spectral filtering functions for intensity and phase fluctuations. Areas of turbulence inhomogeneities have been identified that will have mutual influence and negatively affect the operation of the phase meter. It is noted that correlation functions, both phase and intensity, are less susceptible to this compared to structural functions. The results of experimental studies on the reconstruction of the wavefront of laser radiation distorted by atmospheric turbulence using a Shack–Hartmann wavefront sensor during vignetting and central screening of the entrance pupil in the optical system are presented. Studies have been carried out on the propagation of laser radiation along a horizontal atmospheric path for various levels of turbulence. The results are analyzed in terms of Zernike polynomials. [ABSTRACT FROM AUTHOR]

Struts of a superconducting YBa2Cu3Oy (YBCO) foam prepared by the infiltration growth method on the base of commercial polyurethane foams were extracted from the bulk, and thoroughly characterized concerning the microstructure and the magnetoresistance, measured by the four-point technique. Optical microscopy, electron microscopy, electron backscatter diffraction and atomic force microscopy observations indicate a unique microstructure of the foam struts which shows a large amount of tiny Y2BaCuO5 (Y-211) particles (with diameters between 50 and 100 nm) being enclosed in channel-like grain boundaries between the YBCO grains and a one-of-a-kind surface of the struts covered with Ba3Cu5Oy-particles. The resistance data obtained at temperatures in the range 4.2 K ≤ T ≤ 150 K (applied magnetic fields ranging from 0 to 7 T) were analyzed in the framework of the fluctuation-induced conductivity (FIC) approach using the models of Aslamazov–Larkin (AL) and Lawrence–Doniach (LD). The resulting FIC curves reveal the presence of five distinct fluctuation regimes, namely, the short-wave (SWF), one-dimensional (1D), two-dimensional (2D), three-dimensional (3D), and critical (CR) fluctuation domains. The analysis of the FIC data enable the coherence length in the direction of the c-axis at zero-temperature ( ξ c (0) ), the irreversibility field ( B irr ), the upper critical magnetic field ( B c 2 ), the critical current density at T = 0 K ( J c (0) ) and several other parameters describing the the material's superconducting properties to be determined. The present data reveal that the minuscule Y-211 particles found along the YBCO grain boundaries alter the excess conductivity and the fluctuation behavior as compared to conventional YBCO samples, leading to a quite high value for J c (0) for a sample with a non-optimized pinning landscape. [ABSTRACT FROM AUTHOR]

In this article, we study the fluctuations of the empirical occupa)tion measures of servers around their mean-field limit in a large system of heterogeneous processor sharing servers. It is assumed that there are M different servers grouped by their speeds and that the total number of servers is N. In particular, we study the sensitivity of the fluctuations to arrival rate parameters at the diffusion scale. The job arrival process is assumed to be Poisson with rate N(λ − β/√N ) and the job lengths are assumed to be exponentially distributed with unit mean. On arrival, a finite number of servers from each group are selected and the destination server depends on the server occupancy normalized to their speeds and pre-defined thresholds, referred to as the Join-Below-Threshold scheme. We derive Functional Central Limit Theorems (FCLTs) for the fluctuations that enable us to estimate the error of the mean field approximations to the empirical measures associated with a system with N servers. We then use these results to show mean response time for finite systems can be approximated by the response time given by the mean-field limit and the error isO( 1/√N ) for which the constants can be precisely calculated. [ABSTRACT FROM AUTHOR]

Stochastic models of synaptic plasticity must confront the corrosive influence of fluctuations in synaptic strength on patterns of synaptic connectivity. To solve this problem, we have proposed that synapses act as filters, integrating plasticity induction signals and expressing changes in synaptic strength only upon reaching filter threshold. Our earlier analytical study calculated the lifetimes of quasi-stable patterns of synaptic connectivity with synaptic filtering. We showed that the plasticity step size in a stochastic model of spike-timing-dependent plasticity (STDP) acts as a temperature-like parameter, exhibiting a critical value below which neuronal structure formation occurs. The filter threshold scales this temperature-like parameter downwards, cooling the dynamics and enhancing stability. A key step in this calculation was a resetting approximation, essentially reducing the dynamics to one-dimensional processes. Here, we revisit our earlier study to examine this resetting approximation, with the aim of understanding in detail why it works so well by comparing it, and a simpler approximation, to the system's full dynamics consisting of various embedded two-dimensional processes without resetting. Comparing the full system to the simpler approximation, to our original resetting approximation, and to a one-afferent system, we show that their equilibrium distributions of synaptic strengths and critical plasticity step sizes are all qualitatively similar, and increasingly quantitatively similar as the filter threshold increases. This increasing similarity is due to the decorrelation in changes in synaptic strength between different afferents caused by our STDP model, and the amplification of this decorrelation with larger synaptic filters. [ABSTRACT FROM AUTHOR]

Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with insights from information geometry theory. Focusing on linear Langevin systems, we use model predictive control online optimisation capabilities to determine the system inputs that minimise deviations from the geodesic of the information length over time, ensuring dynamics with minimum "geometric information variability". We validate our methodology through numerical experimentation on the Ornstein–Uhlenbeck process and Kramers equation, demonstrating its feasibility. Furthermore, in the context of the Ornstein–Uhlenbeck process, we analyse the impact on the entropy production and entropy rate, providing a physical understanding of the effects of minimum information variability control. [ABSTRACT FROM AUTHOR]

Experimental results of daily counting under a microscope for 30 days of prokaryotic cells in preparations from soil samples when stained with different specific dyes and published results on daily counting of bacteria in soil using different methods are presented. The FITC dye, which stains the entire set of bacterial cells, revealed a wavelike dynamics of cell numbers with different numbers of oscillations in the form of peaks in all experiments. Using the SFDA dye, which detects only living, metabolically active cells, wavelike dynamics were also revealed, but their oscillating number was significantly less. The reliability of oscillations and differences in cell numbers when using different dyes were confirmed statistically by harmonic analysis. The wavelike dynamics of living, metabolically active cells is a consequence of the cycles of growth and death of bacterial cells and short-term trophic succession in the microbial community. External disturbing influences did not affect the manifestation of wavelike population dynamics, either in the population of living cells or in the total number of cells. The phenomenon of wavelike dynamics of nonliving bacterial cells and their numerical superiority is explained by the fact that cells, losing viability, lyse and disintegrate not immediately after dying, but with some delay in time. This leads to the accumulation and permanent superiority of the pool of dead cells when microscopically counting the total number of bacteria in the soil and explains the discrepancy in bacterial numbers between different counting methods. The presented experimental and published material will serve as a substantiation for microbiologists and biotechnologists of the need to control the dynamics of the numbers of introduced populations and communities of microorganisms into the natural environment, as well as a source of knowledge for the successful management of natural microbial communities. [ABSTRACT FROM AUTHOR]

Abstract 2D materials have important fundamental properties allowing for their use in many potential applications, including quantum computing. Various Van der Waals materials, including Tungsten disulfide (WS2), have been employed to showcase attractive device applications such as light emitting diodes, lasers and optical modulators. To maximize the utility and value of integrated quantum photonics, the wavelength, polarization and intensity of the photons from a quantum emission (QE) must be stable. However, random variation of emission energy, caused by the inhomogeneity in the local environment, is a major challenge for all solid-state single photon emitters. In this work, we assess the random nature of the quantum fluctuations, and we present time series forecasting deep learning models to analyse and predict QE fluctuations for the first time. Our trained models can roughly follow the actual trend of the data and, under certain data processing conditions, can predict peaks and dips of the fluctuations. The ability to anticipate these fluctuations will allow physicists to harness quantum fluctuation characteristics to develop novel scientific advances in quantum computing that will greatly benefit quantum technologies.

2D materials have important fundamental properties allowing for their use in many potential applications, including quantum computing. Various Van der Waals materials, including Tungsten disulfide (WS2), have been employed to showcase attractive device applications such as light emitting diodes, lasers and optical modulators. To maximize the utility and value of integrated quantum photonics, the wavelength, polarization and intensity of the photons from a quantum emission (QE) must be stable. However, random variation of emission energy, caused by the inhomogeneity in the local environment, is a major challenge for all solid-state single photon emitters. In this work, we assess the random nature of the quantum fluctuations, and we present time series forecasting deep learning models to analyse and predict QE fluctuations for the first time. Our trained models can roughly follow the actual trend of the data and, under certain data processing conditions, can predict peaks and dips of the fluctuations. The ability to anticipate these fluctuations will allow physicists to harness quantum fluctuation characteristics to develop novel scientific advances in quantum computing that will greatly benefit quantum technologies. [ABSTRACT FROM AUTHOR]

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on Gibbs states whose edge overlap values with a reference state fall within a specified range. Using this metastate we show that, in any dimension, the variance of free energy difference fluctuations between pure states within a single mixed Gibbs state with multiple edge overlap values diverges linearly with the volume. We discuss some implications of these results. [ABSTRACT FROM AUTHOR]

A method for assessing the state of formed elements based on the dielectric characteristics of a blood suspension is considered. A design of a fluctuation dielectric Fourier spectrometer (FDFS) is proposed, with the help of which it is possible to estimate the distribution of the formed blood elements according to their membrane state. As an illustration, experiments to assess the functional state of patients with coronary heart disease and an experiment on the effect of ascitic Ehrlich carcinoma on laboratory mice are described. It is shown that by using the proposed spectrometer, it is possible to obtain express estimates of changes in blood characteristics during diseases and to identify the dynamics of pathological processes in animals with ascitic Ehrlich carcinoma. [ABSTRACT FROM AUTHOR]

"Chases and Escapes" is a classical mathematical problem. Recently, we proposed a simple extension, called "Group Chase and Escape," where one group chases another. This extension bridges the traditional problem with the current interest in studying collective motion among animals, insects, and cars. In this presentation, I will introduce our fundamental model and explore its intricate emergent behaviors. In our model, each chaser approaches the nearest escapee, while each escapee moves away from its closest chaser. Interestingly, despite the absence of communication within each group, we observe the formation of aggregate patterns. Furthermore, the effectiveness of capture varies as we adjust the ratio of chasers to escapees, which can be attributed to a group effect. I will delve into how these behaviors manifest in relation to various parameters, such as densities. Moreover, we have explored different expansions of this basic model. First, we introduced fluctuations, where players now make errors in their step directions with a certain probability. We found that a moderate level of fluctuations improves the efficiency of catching. Second, we incorporated a delay in the chasers' reactions to catch their targets. This distance-dependent reaction delay can lead to highly complex behaviors. Additionally, I will provide an overview of other groups' extensions of the model and the latest developments in this field. [ABSTRACT FROM AUTHOR]

An analytical model is developed for calculating the temperature in fretting, taking account of velocity fluctuations and surface shear, so as to assess the temperature stress and thermal expansion at the contact spot. The adhesion and slipping zones in preliminary displacement are shown. The apparatus for dynamic study of fretting is described. [ABSTRACT FROM AUTHOR]

Low-resolution coarse-grained (CG) models provide remarkable computational and conceptual advantages for simulating soft materials. In principle, bottom-up CG models can reproduce all structural and thermodynamic properties of atomically detailed models that can be observed at the resolution of the CG model. This review discusses recent progress in developing theory and computational methods for achieving this promise. We first briefly review variational approaches for parameterizing interaction potentials and their relationship to machine learning methods. We then discuss recent approaches for simultaneously improving both the transferability and thermodynamic properties of bottom-up models by rigorously addressing the density and temperature dependence of these potentials. We also briefly discuss exciting progress in modeling high-resolution observables with low-resolution CG models. More generally, we highlight the essential role of the bottom-up framework not only for fundamentally understanding the limitations of prior CG models but also for developing robust computational methods that resolve these limitations in practice. [ABSTRACT FROM AUTHOR]

Objectives: Cognitive fluctuations are a core clinical feature of dementia with Lewy bodies (DLB), but their contribution to the everyday functioning difficulties evident DLB are not well understood. The current study evaluated whether intraindividual variability across a battery of neurocognitive tests (intraindividual variability-dispersion) and daily cognitive fluctuations as measured by informant report are associated with worse daily functioning in DLB. Methods: The study sample included 97 participants with consensus-defined DLB from the National Alzheimer's Coordinating Center (NACC). Intraindividual variability-dispersion was measured using the coefficient of variation, which divides the standard deviation of an individual's performance scores across 12 normed neurocognitive indices from the NACC neuropsychological battery by that individual's performance mean. Informants reported on daily cognitive fluctuations using the Mayo Fluctuations Scale (MFS) and on daily functioning using the functional activities questionnaire (FAQ). Results: Logistic regression identified a large univariate association of intraindividual variability-dispersion and presence of daily cognitive fluctuations on the MFS (Odds Ratio = 73.27, 95% Confidence Interval = 1.38, 3,895.05). Multiple linear regression demonstrated that higher intraindividual variability-dispersion and presence of daily cognitive fluctuations as assessed by the MFS were significantly and independently related to worse daily functioning (FAQ scores). Conclusions: Among those with DLB, informant-rated daily cognitive fluctuations and cognitive fluctuations measured in the clinic (as indexed by intraindividual variability-dispersion across a battery of tests) were independently associated with poorer everyday functioning. These data demonstrate ecological validity in measures of cognitive fluctuations in DLB. [ABSTRACT FROM AUTHOR]

Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical principles. However, a proposed interpretation could shed light on the inherent principle behind the creation of fractals. This is the multiscale thermodynamic perspective, which states that an increase in external energy could initiate energy transport mechanisms that facilitate the dissipation or release of excess energy at different scales. Within this framework, it is revealed that power law patterns, and to a lesser extent, fractals, can emerge as a geometric manifestation to dissipate energy in response to external forces. In this context, the exponent of these power law patterns (thermodynamic fractal dimension D ) serves as an indicator of the balance between entropy production at small and large scales. Thus, when a system is more efficient at releasing excess energy at the microscopic (macroscopic) level, D tends to increase (decrease). While this principle, known as Principium luxuriæ, may sound promising for describing both multiscale and complex systems, there is still uncertainty about its true applicability. Thus, this work explores different physical, astrophysical, sociological, and biological systems to attempt to describe and interpret them through the lens of the Principium luxuriæ. The analyzed physical systems correspond to emergent behaviors, chaos theory, and turbulence. To a lesser extent, the cosmic evolution of the universe and geomorphology are examined. Biological systems such as the geometry of human organs, aging, human brain development and cognition, moral evolution, Natural Selection, and biological death are also analyzed. It is found that these systems can be reinterpreted and described through the thermodynamic fractal dimension. Therefore, it is proposed that the physical principle that could be behind the creation of fractals is the Principium luxuriæ, which can be defined as "Systems that interact with each other can trigger responses at multiple scales as a manner to dissipate the excess energy that comes from this interaction". That is why this framework has the potential to uncover new discoveries in various fields. For example, it is suggested that the reduction in D in the universe could generate emergent behavior and the proliferation of complexity in numerous fields or the reinterpretation of Natural Selection. [ABSTRACT FROM AUTHOR]

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This study aims to analyze fluctuations and disparity in broiler and carcass prices before, during, and after COVID-19 pandemic in five broiler-producing regions in Indonesia, including North Sumatra, West Java, Central Java, East Java, and South Sulawesi. Weekly data series were used to analyze fluctuations and disparity before (2017–February 2020), during (March 2020–2022), and after (January–June 2023) COVID-19 pandemic. Furthermore, Coefficient of variation (CV) and convergence models were also used during the analysis. The results showed that broiler price fluctuations in the five study areas were categorized as “medium” before and during pandemic. After pandemic, the majority of the areas were in the “low” category, except for South Sulawesi province, where CV was 10.02%. Carcass price fluctuations were categorized as “low” and “moderate” before and during COVID-19 pandemic. After the viral outbreak, all the provinces investigated in this study were classified as “low”. This indicated that the variability in carcass price decreased across all provinces after pandemic. The coefficient value of β1 was less than 1 indicating that broiler and carcass price did not show significant disparity between regions at all periods. The primary drivers of fluctuations and disparity were related to production and availability factors, and the government played a role in maintaining stability in producing areas.

The irradiation variations caused by cloud changes can cause rapid power fluctuations in large photovoltaic (PV) plants. The increased PV power share of the grid adversely affects the quality of power and the reliability of the power supply. Energy storage systems (ESSs)are often used to mitigate power fluctuations in the grid through various control algorithms. These algorithms create an ESS power reference that opposes the variations of the PV and reduces them to an acceptable value. Despite their everyday use, there have been few performance comparisons among the various methods, especially battery status, and the battery can operate in several systems with various smoothing methods. The paper aims to analyze the ramp-rate and step-rate control methods for smoothing solar PV fluctuations based on the irradiation profiles in a DC microgrid (MG) environment. The battery in the system operates as a continuous energy application, and a supercapacitor (SC) is used to remove transients in the battery system. The combined battery-SC coordinated system improves the performance of the DC microgrid system. The battery cycle analysis and depth are conducted using the well-established Coulomb counting technique. MATLAB/Simulink validates the simulation results, and the OP-5700 HIL test bench conducts real-time results.

Quark–Gluon plasma driven by the strong force is subject to the conservativeness of the baryon number, net electric charge, strangeness, etc. However, the fluctuations around their mean values at specific temperatures and chemical potentials can provide viable signals for the production of Quark–Gluon plasma. These fluctuations can be captured theoretically as moments of different orders in the expansion of pressure or the thermodynamic potential of the system under concern. Here, we look for possible explanations in the methodologies used for capturing them by using the framework of the Polyakov–Nambu–Jona-Lasinio (PNJL) model under the 2 + 1 flavor consideration with mean-field approximation. The various quantities thus explored can act to signify meaningfully near the phase transitions. Justifications are also made for some of the quantities capable of serving necessarily under experimental scenarios. Additionally, variations in certain quantities are also made for the different collision energies explored in the high-energy experiments. Rectification of the quantitative accuracy, especially in the low-temperature hadronic sector, is of prime concern, and it is also addressed. It was found that most of the observables stay in close proximity with the existing lattice QCD results at the continuum limit, with some artifacts still remaining, especially in the strange sector, which needs further attention.

Visual working memory (VWM) plays an important role during visual search, with some theories suggesting an equivalence between working memory representations and guidance from attentional templates. However, recent work has shown that participants can also use ‘negative templates’, the foreknowledge of distractor-features stored in VWM, to guide attention away from distractors during visual search. These negative templates must also be represented in working memory, but the question remains whether the quality of the working memory representations underlying negative and positive templates are similar, in spite of their opposite impacts on attention. In this study, participants (N = 33) engaged in a visual search task for a shape-defined target after receiving a positive cue (target color), negative cue (distractor color) or neutral cue (non-informative). In 20% of the trials, a color-wheel probe was presented instead of a search array to measure the quality of the cue representation stored in VWM. Our results revealed that participants were more likely to guess in response to neutral cues than negative cues. Yet, the comparison between positive and negative cues showed no significant differences. However, we found no difference in memory precision for the three cue types. More interestingly, the more the VWM quality is boosted by the negative cue, the greater the ability to guide attention away from distractors. Such a pattern of results might map to recent evidence of between-individuals differences in utilization of negative cues. These findings highlight the distinction between attentional templates and simple maintenance in working memory.

Simultaneous observations of radioactivity fluctuations from the natural isotope 40K were carried out in Moscow and Ulyanovsk. It was found that the changes in the counting rate from sources in these geographical points were not simultaneous, but were synchronized according to local solar time. Based on this observation and considering that radioactivity fluctuations correlated with body temperature rhythms, a method for short-term prediction of ultradian rhythms of animal activity has been developed and confirmed. An analysis of the consistency of the dynamics of the intensity of decay fluctuations and daily growth rates of an L-929 cell culture was also carried out. It was found that the highest correlation coefficient was recorded when the indicator of proliferative activity of the culture was compared with the intensity of decay fluctuations taken over the previous day. Thus, based on data on fluctuations in the radioactive decay of 40K, which are an indicator of the biotropic factor of the environment, it is possible to make short-term forecasts of ultradian and infradian biological rhythms. [ABSTRACT FROM AUTHOR]

Consideration of future consequences (CFC) was originally proposed to be a stable personality trait that describes the degree to which individuals consider the immediate versus distant results of their actions. Recent studies debate whether CFC fluctuates over short periods of time and whether it is a domain-specific construct. The present study aims to explore the fluctuation of CFC scale scores over a weekly interval and explore how this variability is associated with three relevant outcomes. For this purpose, the general CFC scale was adapted to three domain-specific scales: health, academic, and work. A total of 737 adults (Mage = 36.58, SD = 14.73) participated and completed the questionnaires over eight waves of data collection separated by one week. The results indicate that CFC scale scores fluctuates at weekly intervals. Healthy eating, academic engagement, and innovation at work at the intra-individual level were associated with fluctuations in the corresponding domain-specific scales over and above the general CFC scale. The results suggest that CFC is, to some extent, variable within short periods of time. Furthermore, we found evidence in favour of the reliability and validity of all CFC scales in Spanish used in this study. These findings may be useful for public policies that depend on people's future orientation. [ABSTRACT FROM AUTHOR]

Several vital processes in crop canopies and their microclimate, such as canopy photosynthesis and transpiration, are affected by fluctuations in irradiance, here called lightflecks. These lightflecks occur both in the field and inside greenhouses, although their dynamics may be different, due to an absence of wind in the greenhouse. When modelling plant and climate processes, these dynamic conditions are often ignored. The current study reports (1) high frequency (i.e. 1s interval) observations of lightflecks inside a greenhouse during several months and (2) a quantification of the effect of these lightflecks on leaf-level photosynthesis, transpiration and energy balance in rose by comparing results from a dynamic and a steady-state biophysical model. We found that lightflecks in the greenhouse were short, typically < 5s. Increasing complexity in irradiance fluctuation patterns (i.e. from very artificial to measured time series) reduced the difference between dynamic and steady-state simulations, e.g. for photosynthesis this difference decreased from 50% to 5%; for water-use efficiency the difference decreased from 70% to 5%. The relative contribution of the increase in light sum and fewer delayed responses by compensating drops in light level through additional light supply on plant processes was different. For example, photosynthesis was equally affected by both the increase in light sum and fewer delayed responses (i.e. 19% and 15% respectively), whereas water-use efficiency was mostly a result of less delayed plant responses (i.e. 9% compared to 1%). Our results demonstrate that lightflecks occur frequently in the greenhouse, and have strong effects on crop photosynthesis, water-use efficiency, and microclimate conditions. • High frequency radiation measurements reveal rapid light fluctuations in greenhouses. • Most lightflecks in the greenhouse are shorter than 5 s. • Using artificial lightflecks might overestimate dynamic plant response consequences. • Compensating light drops through supplementary light increases water-use efficiency. [ABSTRACT FROM AUTHOR]

We consider nonstationary diffusion in a medium with random traps-sinks. We study the self-averaging of the mean-square displacement (MSD) of the ensemble of N particles in the fluctuational long-time limit. We demonstrate that MSD of survivors is self-averaging with respect to the number of engaged particles N and is strongly non-self-averaging with respect to time t. To measure MSD of survivors with required accuracy at the required time of observation t 0 , the initial number of particles N 0 must be exponentially large in t 0 . Any N 0 , whatever large, will be insufficient at long enough time. In the formulation, when all particles, both survivors and trapped ones, contribute to MSD, we find self-averaging in N and non-strong non-self-averaging over t. [ABSTRACT FROM AUTHOR]