Large-scale Limit Research Articles

Renormalisation group methods for effective epidemiological models

Epidemiological models describe the spread of an infectious disease within a population. They capture microscopic details on how the disease is passed on among individuals in various different ways, while making predictions about the state of the entirety of the population. However, the type and structure of the specific model considered typically depend on the size of the population under consideration. To analyse this effect, we study a family of effective epidemiological models in space and time that are related to each other through scaling transformations. Inspired by a similar treatment of diffusion processes, we interpret the latter as renormalisation group transformations, both at the level of the underlying differential equations and their solutions. We show that in the large scale limit, the microscopic details of the infection process become irrelevant, safe for a simple real number, which plays the role of the infection rate in a basic compartmental model.

The Essence of the Right to Property under Art 1 of Protocol 1 to the echr: An Inviolable Core or a Purely Symbolic Concept? Cases from Central and Eastern Europe revisited

Abstract It is inherent to the fundamental right to property that far from being absolute, the owners’ rights may be limited in the general interest. As exemplified recently by unprecedented closures of restaurants and other businesses due to the covid-19 pandemic, also large-scale and far-reaching limitations are broadly deemed justified. The outer boundary of these limitations appears to be the essence of the right, which may not be impinged upon. Yet, both this very term and its scope are fiercely contested. This article, thus, revisits the “essence” of a fundamental right in the context of the European Convention on Human Rights. Drawing on the example of the right to property under Art 1 of Protocol 1 (P1-1) to the echr, this contribution expounds the prevailing approaches to the essence of fundamental rights and highlights the discrepancies between the formally adopted absolute approach to the essence as a purportedly inviolable core and the relative understanding of this concept which sees it as part of the fair-balance test. As the ECtHR case law makes room for virtually any interference with P1-1 including expropriation without any compensation, it will be argued that an untouchable or pre-established essence is not a concept attributable to the right to property under the Convention. It is maintained, however, that the limited scope of the essence is consistent with the underlying principles of the Convention as well as the intrinsic social function of private property.

PEGylation Can Effectively Strike a Balance in siRNA Delivery Performances of Guanidinylated Linear Synthetic Polypeptides with Potential Use for Transcriptional Gene Silencing.

The prevailing design philosophy for polymeric vectors delivering siRNA is rooted in the post-transcriptional gene silencing (PTGS) mechanism. Yet, the transcriptional gene silencing (TGS) mechanism offers a potentially more durable silencing effect, which necessitates efficient siRNA delivery into the nucleus. However, it remains a challenge for the polymeric vectors to efficiently deliver siRNA into the nucleus. We have explored guanidinylated cyclic synthetic polypeptides (GCSPs) to enhance the nuclear delivery of siRNA, but an increased cytotoxicity and difficulty in producing the GCSPs on a large scale limit their utility. Herein, we simply prepare PEGylated guanidinylated linear synthetic polypeptides (PGLSPs) exhibiting improved membrane penetration, direct siRNA transport to the nucleus, reduced toxicity, high cellular uptake, and mitigation of protein corona formation. The PEGylation can effectively balance the vector's nuclear delivery capacity with other critical aspects of performances for siRNA delivery. Therefore, the PGLSPs hold promise as TGS-based delivery vectors, offering potential for future therapeutic applications.

Leveraging digital twins for improved orthopaedic evaluation and treatment.

The purpose of this article is to explore the potential of digital twin technologies in orthopaedics and to evaluate how their integration with artificial intelligence (AI) and deep learning (DL) can improve orthopaedic evaluation and treatment. This review addresses key applications of digital twins, including surgical planning, patient-specific outcome prediction, augmented reality-assisted surgery and simulation-based surgical training. Existing studies on digital twins in various domains, including engineering, biomedical and orthopaedics are reviewed. We also reviewed advancements in AI and DL relevant to digital twins. We focused on identifying key benefits, challenges and future directions for the implementation of digital twins in orthopaedic practice. The review highlights that digital twins offer significant potential to revolutionise orthopaedic care by enabling precise surgical planning, real-time outcome prediction and enhanced training. Digital twins can model patient-specific anatomy using advanced imaging techniques and dynamically update with real-time data, providing valuable insights during surgery and postoperative care. However, challenges such as the need for large-scale data sets, technological limitations and integration issues must be addressed to fully realise these benefits. Digital twins represent a promising frontier in orthopaedic research and practice, with the potential to improve patient outcomes and enhance surgical precision. To enable widespread adoption, future research must focus on overcoming current challenges and further refining the integration of digital twins with AI and DL technologies. Level V.

Approach to stationarity for the KPZ fixed point with boundaries

Current fluctuations for the one-dimensional totally asymmetric exclusion process (TASEP) connected to reservoirs of particles, and their large scale limit to the KPZ fixed point in finite volume, are studied using exact methods. Focusing on the maximal current phase for TASEP, corresponding to infinite boundary slopes for the KPZ height field, we obtain for general initial condition an exact expression for the late time correction to stationarity, involving extreme value statistics of Brownian paths. In the special cases of stationary and narrow wedge initial conditions, a combination of Bethe ansatz and numerical conjectures alternatively provide fully explicit exact expressions.

Convergence rate analysis in limit theorems for nonlinear functionals of the second Wiener chaos

This paper analyzes the distribution distance between random vectors from the analytic wavelet transform of squared envelopes of Gaussian processes and their large-scale limits. For Gaussian processes with a long-memory parameter below 1/2, the limit combines the second and fourth Wiener chaos. Using a non-Stein approach, we determine the convergence rate in the Kolmogorov metric. When the long-memory parameter exceeds 1/2, the limit is a chi-distributed random process, and the convergence rate in the Wasserstein metric is determined using multidimensional Stein’s method. Notable differences in convergence rate upper bounds are observed for long-memory parameters within (1/2,3/4) and (3/4,1).

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.

Prediction research on the contribution degree of solar energy to the coefficient of heating performance of carbon dioxide heat pump

The carbon dioxide heat pump (CDHP) offers efficient heating over a wide temperature range, but its heating energy efficiency under low-temperature conditions decreases obviously due to a correlation with the evaporation temperature, limiting the widespread use of CDHP in cold regions. To address this, we implemented a passive solar house with short-term heat storage capacity to raise the evaporation temperature and studied it by experimental and theoretical analysis. We introduced the concept of contribution degree (K) of solar energy to the heating performance coefficient of CDHP. The prediction models for the evaporation temperature, heating performance coefficient, and K were constructed gradually. The study optimized the operation mode of solar-assisted CDHP using the evaporation temperature partition theory and presented a method to calculate the limit distribution range of K. The result shows that the order of importance level of the significant items on evaporation temperature was ambient temperature (Ta) > direct solar irradiance on the inclined surface (Gb) > scattering solar irradiance on the inclined surface (Gr) > GḃTa > Ta2 > Gb2. The predicted limit distribution range of K was [0.00, 8.17]. The study optimized the operation mode of solar-assisted CDHP into three categories. It was observed that K changes positively with any single variable according to the law of a composite function composed of a natural exponential function and a quadratic function. Our study suggests a feasible development direction and offers a new theoretical and engineering basis for overcoming the large-scale application limitations of CDHP in cold regions.

Thermal vortex ring: vortex-dynamics analysis of a high-resolution simulation

A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by $s^n$ with $n=-1$ , 0, 1, where $s$ is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with $n=-1$ ). Analysis of the budget supports this description.

On the performance evaluation of distributed join-idle-queue load balancing with and without token withdrawals

Distributed Join-Idle-Queue load balancing is known to achieve vanishing waiting times in the large-scale limit provided that the number of dispatchers remains fixed, while the number of servers tends to infinity. When the number of dispatchers m scales to infinity together with the number of servers n, such that r=n/m remains fixed, the large-scale performance of Join-Idle-Queue load balancing is less clear as waiting times no longer vanish.In this paper we first discuss some existing mean field models for distributed Join-Idle-Queue load balancing with r=n/m fixed and explain why the well-known model introduced in Lu et al. (2011) is not exact in the large-scale limit. The inexactness is caused by mixing two variants of distributed Join-Idle-Queue load balancing: a variant with and one without token withdrawals. Next we introduce mean field models for Join-Idle-Queue load balancing with and without token withdrawals, where an idle server places a token at a dispatcher with the shortest among d randomly chosen dispatchers.The introduced mean field models in case of token withdrawals imply that for phase type distributed service times and a total job arrival rate of λn<n, the response time of a job corresponds to that in a standard M/PH/1 queue with load λq0. The value of q0 can be determined numerically and depends on λ,r and d, but not on the job size distribution (apart from its mean). This simple behavior is lost if token withdrawals do not take place. For the models without withdrawals we develop fast numerical algorithms to determine the performance. We present simulation experiments that suggest that the unique fixed point of the introduced mean field models provides exact results in the large-scale limit.

Ni/Fe2O3 Mott-Schottky heterointerface engineering and phosphate doping synergistically refining d-band center for efficient oxygen evolution reaction

Developing highly effective non-precious metal-based electrocatalysts is pivotal to overcome unfavorable slow kinetics of oxygen evolution reaction (OER) and large-scale application limitations of noble metals. Herein, a dual-modulation strategy of anion incorporation and Mott-Schottky heterointerface engineering was adopted to synthesize phosphate-doped Ni/Fe2O3 heterostructure (Pi-Ni/Fe2O3). Experimental combined theoretical calculations evident that the strong coupling between Ni and Fe2O3 leads to the redistributed electron and charge at the heterointerface and the reduction of bandgap, and adjusts electronic density of state around active centers into the bargain. Moreover, phosphate incorporation can reduce the probability of anti-bond filling, and serve as proton acceptors to form hydrogen bonds for stabilizing *OOH intermediates. Heterostructure formation and phosphate doping induce the upshift of d-band center of Pi-Ni/Fe2O3, giving lower energy barrier toward OER compared with Fe2O3 and Ni. Consequently, the above merits endow Pi-Ni/Fe2O3 with outstanding OER performance to deliver 10 mA cm−2 at an overpotential of 263 mV, as well as superior electrocatalytic performance for overall water splitting. This study not only reveals the synergistic effect of Schottky heterogeneous interface and phosphate doping, but also sheds light on advancing high-efficiency catalysts from the perspective of proton receptor modification and interface engineering.

Review of microbial fuel cell from a techno-economic perspective

This review presents a techno-economic analysis of microbial fuel cells (MFCs) in the domain of generating sustainable energy and treating wastewater with the aim of attracting investors through research and development for residential and commercial applications. The operation principles and various MFC types, along with their advantages and disadvantages, are thoroughly considered. The efficiency of various MFC types is considered to present appropriate options for commercial applications. However, large-scale integrations face substantial financial limitations owing to the reluctance of investors. This review explores the cost-benefit balance associated with the operation of an MFC system. For encouraging investors, different cost variables, such as the initial investment, operating costs, potential electricity generation, and waste treatment capacity, are thoroughly considered. These variables are placed on the spectrum of a cost-benefit analysis to vitalize the economic feasibility of the MFC technology in various scenarios, considering an order of financial variables. MFC development at an optimized cost is the pivotal pre-requisite to secure a competitive advantage over conventional sources of energy with carbon emissions. Thus, this study is expected to prompt decision-makers to adopt the MFC technology at the commercial level.

Neuronal connected burst cascades bridge macroscale adaptive signatures across arousal states

The human brain displays a rich repertoire of states that emerge from the microscopic interactions of cortical and subcortical neurons. Difficulties inherent within large-scale simultaneous neuronal recording limit our ability to link biophysical processes at the microscale to emergent macroscopic brain states. Here we introduce a microscale biophysical network model of layer-5 pyramidal neurons that display graded coarse-sampled dynamics matching those observed in macroscale electrophysiological recordings from macaques and humans. We invert our model to identify the neuronal spike and burst dynamics that differentiate unconscious, dreaming, and awake arousal states and provide insights into their functional signatures. We further show that neuromodulatory arousal can mediate different modes of neuronal dynamics around a low-dimensional energy landscape, which in turn changes the response of the model to external stimuli. Our results highlight the promise of multiscale modelling to bridge theories of consciousness across spatiotemporal scales.

Large Scale Limit of the Observed Galaxy Power Spectrum.

The large scale limit of the galaxy power spectrum provides a unique window into the early Universe through a possible detection of scale dependent bias produced by primordial non Gaussianities. On such large scales, relativistic effects could become important and be confused for a primordial signal. In this Letter we provide the first consistent estimate of such effects in the observed galaxy power spectrum, and discuss their possible degeneracy with local primordial non Gaussianities. We also clarify the physical differences between the two signatures, as revealed by their different sensitivity to the large scale gravitational potential. Our results indicate that, while relativistic effects could easily account for 10% of the observed power spectrum, the subset of those with a similar scale dependence to a primordial signal can be safely ignored for current galaxy surveys, but it will become relevant for future observational programs.

Performance of Load Balancers With Bounded Maximum Queue Length in Case of Non-Exponential Job Sizes

In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in the large-scale limit. However, these policies have thus far only been studied in case of exponential job sizes. As job sizes are more variable in real systems, we investigate how the performance of these policies (and in particular the value of these bounds) is impacted by the job size distribution. We present a unified analysis which can be used to compute the bound on the queue length in case of phase-type distributed job sizes for four load balancing policies. We find that in most cases, the bound on the maximum queue length can be expressed in closed form. In addition, we obtain job size (in)dependent bounds on the expected response time. Our methodology relies on the use of the cavity process. That is, we conjecture that the cavity process captures the behaviour of the real system as the system size grows large. For each policy, we illustrate the accuracy of the cavity process by means of simulation.

Waves in a Stochastic Cell Motility Model

In Bhattacharya et al. (Sci Adv 6(32):7682, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied at two levels. The microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction–diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction–diffusion system, or chemical Langevin equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction–diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

A Particle System with Mean-Field Interaction: Large-Scale Limit of Stationary Distributions

We consider a system consisting of n particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle “jumps forward” at some time points, with the instantaneous rate of jumps given by a decreasing function of the particle’s location quantile within the current state (empirical distribution). Previous work on this model established, under certain conditions, the convergence, as [Formula: see text], of the system random dynamics to that of a deterministic mean-field model (MFM), which is a solution to an integro-differential equation. Another line of previous work established the existence of MFMs that are traveling waves, as well as the attraction of MFM trajectories to traveling waves. The main results of this paper are: (a) We prove that, as [Formula: see text], the stationary distributions of (recentered) states concentrate on a (recentered) traveling wave; (b) we obtain a uniform across n moment bound on the stationary distributions of (recentered) states; and (c) we prove a convergence-to-MFM result, which is substantially more general than that in previous work. Results (b) and (c) serve as “ingredients” of the proof of (a), but also are of independent interest.

Augmented bilinear network for incremental multi-stock time-series classification

Deep Learning models have become dominant in tackling financial time-series analysis problems, overturning conventional machine learning and statistical methods. Most often, a model trained for one market or security cannot be directly applied to another market or security due to differences inherent in the market conditions. In addition, as the market evolves over time, it is necessary to update the existing models or train new ones when new data is made available. This scenario, which is inherent in most financial forecasting applications, naturally raises the following research question: How to efficiently adapt a pre-trained model to a new set of data while retaining performance on the old data, especially when the old data is not accessible? In this paper, we propose a method to efficiently retain the knowledge available in a neural network pre-trained on a set of securities and adapt it to achieve high performance in new ones. In our method, the prior knowledge encoded in a pre-trained neural network is maintained by keeping existing connections fixed, and this knowledge is adjusted for the new securities by a set of augmented connections, which are optimized using the new data. The auxiliary connections are constrained to be of low rank. This not only allows us to rapidly optimize for the new task but also reduces the storage and run-time complexity during the deployment phase. The efficiency of our approach is empirically validated in the stock mid-price movement prediction problem using a large-scale limit order book dataset. Experimental results show that our approach enhances prediction performance as well as reduces the overall number of network parameters.

Building Spacetime from Effective Interactions Between Quantum Fluctuations

We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity (GR) in vacuum regions. This is an investigation of a possible scenario of spacetime emergence from quantum interactions directly in the spacetime, and of how effective quantum behaviour might provide a useful link between detailed properties of quantum interactions and GR. The quantum fluctuations are assumed to entangle sufficiently for a cohesive spacetime to form, so that their effective properties can be described relative to a D-dimensional reference frame. To obtain the desired features of a smooth metric with a vanishing Ricci tensor, the quantum fluctuations are modelled as Gaussian probability distributions, with a shape set relative to the interactions coming from the surroundings. At small scales, the propagation through the spacetime is modelled by a Gaussian random walk.

Plasmonic Coupling of Au Nanoclusters on a Flexible MXene/Graphene Oxide Fiber for Ultrasensitive SERS Sensing.

High sensitivity, good signal repeatability, and facile fabrication of flexible surface enhanced Raman scattering (SERS) substrates are common pursuits of researchers for the detection of probe molecules in a complex environment. However, fragile adhesion between the noble-metal nanoparticles and substrate material, low selectivity, and complex fabrication process on a large scale limit SERS technology for wide-ranging applications. Herein, we propose a scalable and cost-effective strategy to a fabricate sensitive and mechanically stable flexible Ti3C2Tx MXene@graphene oxide/Au nanoclusters (MG/AuNCs) fiber SERS substrate from wet spinning and subsequent in situ reduction processes. The use of MG fiber provides good flexibility (114 MPa) and charge transfer enhancement (chemical mechanism, CM) for a SERS sensor and allows further in situ growth of AuNCs on its surface to build highly sensitive hot spots (electromagnetic mechanism, EM), promoting the durability and SERS performance of the substrate in complex environments. Therefore, the formed flexible MG/AuNCs-1 fiber exhibits a low detection limit of 1 × 10-11 M with a 2.01 × 109 enhancement factor (EFexp), signal repeatability (RSD = 9.80%), and time retention (remains 75% after 90 days of storage) for R6G molecules. Furthermore, the l-cysteine-modified MG/AuNCs-1 fiber realized the trace and selective detection of trinitrotoluene (TNT) molecules (0.1 μM) via Meisenheimer complex formation, even by sampling the TNT molecules at a fingerprint or sample bag. These findings fill the gap in the large-scale fabrication of high-performance 2D materials/precious-metal particle composite SERS substrates, with the expectation of pushing flexible SERS sensors toward wider applications.