Short Time Limit Research Articles

Analytical study of the time-fractional Smoluchowski coagulation equation in light of different integrodifferential operators

AbstractThis article presents the derivation of the fractional Smoluchowski coagulation equation via the variational principles technique. We use the variational iteration method to solve the Caputo-type fractional coagulation equation. Furthermore, we analyze the time-fractional coagulation equation using the homotopy perturbation transform approach, considering three different fractional operators: Caputo, Caputo-Fabrizio, and Atangana-Baleanu. Our findings demonstrate that the solutions for the total number of particles during coagulation align well with existing literature, particularly in the short time limit. Additionally, we examine the impact of the time-fractional order on the dynamics of particle coagulation for each fractional operator.

Prioritizing drug targets by perturbing biological network response functions.

Therapeutic interventions are designed to perturb the function of a biological system. However, there are many types of proteins that cannot be targeted with conventional small molecule drugs. Accordingly, many identified gene-regulatory drivers and downstream effectors are currently undruggable. Drivers and effectors are often connected by druggable signaling and regulatory intermediates. Methods to identify druggable intermediates therefore have general value in expanding the set of targets available for hypothesis-driven validation. Here we identify and prioritize potential druggable intermediates by developing a network perturbation theory, termed NetPert, for response functions of biological networks. Dynamics are defined by a network structure in which vertices represent genes and proteins, and edges represent gene-regulatory interactions and protein-protein interactions. Perturbation theory for network dynamics prioritizes targets that interfere with signaling from driver to response genes. Applications to organoid models for metastatic breast cancer demonstrate the ability of this mathematical framework to identify and prioritize druggable intermediates. While the short-time limit of the perturbation theory resembles betweenness centrality, NetPert is superior in generating target rankings that correlate with previous wet-lab assays and are more robust to incomplete or noisy network data. NetPert also performs better than a related graph diffusion approach. Wet-lab assays demonstrate that drugs for targets identified by NetPert, including targets that are not themselves differentially expressed, are active in suppressing additional metastatic phenotypes.

A high-efficiency method for simultaneous quantitation of bioactive gibberellins in Litchi chinensis using UHPLC-QQQ-MS/MS

Gibberellins (GAs) are a group of phytohormones that have profound and diverse effects on plant growth and development. Within this group, bioactive GAs, including GA1, GA3, GA4, and GA7, play a particularly significant role in regulating these processes. Lychee (Litchi chinensis Sonn.) is a tropical fruit tree native to southern China. Optimization of rapid and precise methods for analyzing bioactive GAs in lychee is crucial to enhance our understanding of the underlying physiological mechanisms of fruit and flower development and to explore its potential industrial applications in this fruit tree. In this study, we developed a high-efficiency method for simultaneous quantitation of bioactive GAs in lychee using ultra-high performance liquid chromatography coupled with triple quadrupole tandem mass spectrometry (UHPLC-QQQ-MS/MS). Ultimately, this method was effectively utilized to quantify the bioactive GAs in various tissues of lychee, including fruits, seeds, and flowers. The developed method exhibited satisfactory recoveries and precision, as well as short chromatographic run time and low limits of detection and quantitation of bioactive GAs in lychee. This protocol provides a valuable method for the characterization of physiological roles and molecular mechanism of GAs in lychee.

A general method for the estimation of moments of substitution number in molecular evolution

The random variable ‘substitution number’ N t , i.e.the number of mutations that have accumulated in a sequence under neutral evolution during a time t, is a cornerstone of the field of molecular evolution. We show here that a complete solution of the moments of this random variable can be obtained explicitly by recurrence, using a simple matrix shift method. This result leads to simple expressions for both the short and long time limits of the moments that can be computed directly from the substitution matrix used to model the neutral evolution. The method developed here is also used to compute the moments of the complementary variable, T n , the time it takes to accumulate n mutations. The method we develop here necessitates only elementary operations on the substitution matrix and does not involve spectral decomposition.

Active oscillatory associative memory

Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that the nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.

Influence phase of a dS observer. Part I. Scalar exchange

Inspired by real-time computations in AdS black holes, we propose a method to obtain the influence phase of a cosmological observer by calculating the on-shell action on a doubled spacetime geometry. The influence phase is the effective action for an open system: for a dS static patch observer coupled to a scalar field it incorporates the radiation reaction due to the bulk fields and their dS Hawking radiation. For a general extended source in dS, we describe how to account for finite size effects. In the long-time limit, we get a Markovian open quantum system susceptible to cosmological fluctuations, whereas the short-time limit reproduces the worldline theory of flat-space radiation reaction. We also present a fully covariantised form for the cubic corrections to the radiation reaction in even spacetime dimensions, including Hubble contributions, and find an intriguing recursive structure across dimensions.

A fast and specific near‐infrared fluorescent probe for hydrogen sulfide detection in aquaculture freshwater

AbstractThe content of Hydrogen sulfide (H2S) is one of the most important indicators of aquaculture water quality monitoring, which has a profound impact on the survival of aquatic animals and the income of aquaculture. Therefore, it's of great significance to develop an accurate and convenient detection method for the detection of hydrogen sulfide in aquaculture. Herein, using 2,4‐dinitrophenyl (DNP) ether as the detection group, a novel near‐infrared (NIR) fluorescent probe, X‐NO2, based on the hemicyanine fluorophore, was designed and synthesized for H2S detection in aquaculture. Accompanied by a noticeable color change from purple to blue, the probe X‐NO2 shows strong fluorescence at 685 nm when H2S mediates the thiolysis of DNP ether and release X‐OH. In 10 % DMSO‐PBS (pH=7.4,10 mM,v/v), the probe X‐NO2 shows high selectivity to H2S than other anions and some somebiologicalthiols, and strong anti‐interference capacity. Probe X‐NO2 also has short response time (within 3 min) and low detection limit (65 nM) towards H2S and has a stable performance over a wide pH range (6‐9) in hydrogen sulfide monitoring system. Moreover, probe X‐NO2 was used to determine the H2S levels in real water samples from aquaculture accurately and conveniently, which shows a good application prospect in the future.

Enzymatic cleaving of entangled DNA rings drives scale-dependent rheological trajectories.

DNA, which naturally occurs in linear, ring, and supercoiled topologies, frequently undergoes enzyme-driven topological conversion and fragmentation in vivo, enabling it to perform a variety of functions within the cell. In vitro, highly concentrated DNA polymers form entanglements that yield viscoelastic properties dependent on the topologies and lengths of the DNA. Enzyme-driven alterations of DNA size and shape therefore offer a means of designing active materials with programmable viscoelastic properties. Here, we incorporate multi-site restriction endonucleases into dense DNA solutions to linearize and fragment circular DNA molecules. We pair optical tweezers microrheology with differential dynamic microscopy and single-molecule tracking to measure the linear and nonlinear viscoelastic response and transport properties of entangled DNA solutions over a wide range of spatiotemporal scales throughout the course of enzymatic digestion. We show that, at short timescales, relative to the relaxation timescales of the polymers, digestion of these 'topologically-active' fluids initially causes an increase in elasticity and relaxation times followed by a gradual decrease. Conversely, for long timescales, linear viscoelastic moduli exhibit signatures of increasing elasticity. DNA diffusion, likewise, becomes increasingly slowed, in direct opposition to the short-time behavior. We hypothesize that this scale-dependent rheology arises from the population of small DNA fragments, which increases as digestion proceeds, driving self-association of larger fragments via depletion interactions, giving rise to slow relaxation modes of clusters of entangled chains, interspersed among shorter unentangled fragments. While these slow modes likely dominate at long times, they are presumably frozen out in the short-time limit, which instead probes the faster relaxation modes of the unentangled population.

Wavelet representation of hardcore bosons

We consider the one-dimensional Tonks–Girardeau gas with a space-dependent potential out of equilibrium. We derive the exact dynamics of the system when divided into n boxes and decomposed into energy eigenstates within each box. It is a representation of the wave function that is a mixture between real space and momentum space, with basis elements consisting of plane waves localized in a box, giving rise to the term ‘wavelet’. Using this representation, we derive the emergence of generalized hydrodynamics in appropriate limits without assuming local relaxation. We emphasize that a generalized hydrodynamic behaviour emerges in a high-momentum and short-time limit, in addition to the more common large-space and late-time limit, which is akin to a semi-classical expansion. In this limit, conserved charges do not require numerous particles to be described by generalized hydrodynamics. We also show that this wavelet representation provides an efficient numerical algorithm for a complete description of the out-of-equilibrium dynamics of hardcore bosons.

Extremal statistics for a one-dimensional Brownian motion with a reflective boundary

In this work, we investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant D) during a time interval 0,t in the presence of a reflective boundary at the origin, when starting from a positive position x0. We first obtain the distribution P(M|x0,t) of the maximum displacement M and its expectation 〈M〉. In the short-time limit, i.e., t≪td where td=x02/D is the diffusion time from the starting position x0 to the reflective boundary at the origin, the particle behaves like a free Brownian motion without any boundaries. In the long-time limit, t≫td, 〈M〉 grows with t as 〈M〉∼t, which is similar to the free Brownian motion, but the prefactor is π/2 times of the free Brownian motion, embodying the effect of the reflective boundary. By solving the propagator and using a path decomposition technique, we then obtain the joint distribution P(M,tm|x0,t) of M and the time tm at which this maximum is achieved, from which the marginal distribution P(tm|x0,t) of tm is also obtained. For t≪td, P(tm|x0,t) looks like a U-shaped attributed to the arcsine law of free Brownian motion. For t equal to or larger than order of magnitude of tm, P(tm|x0,t) deviates from the U-shaped distribution and becomes asymmetric with respect to t/2. Moreover, we compute the expectation 〈tm〉 of tm, and find that 〈tm〉/t is an increasing function of t. In two limiting cases, 〈tm〉/t→1/2 for t≪td and 〈tm〉/t→(1+2G)/4≈0.708 for t≫td, where G≈0.916 is the Catalan’s constant. Finally, we analytically compute the statistics of the last time tℓ the particle crosses the starting position x0 and the occupation time to spent above x0. We find that 〈tℓ〉/t→1/2 in the short-time and long-time limits, and reaches its maximum at an intermediate value of t. The fraction of the occupation time 〈to〉/t is a monotonic function of t, and tends towards 1 in the long-time limit. All the theoretical results are validated by numerical simulations.

Magnetic porous carbon material derived from imine-linked covalent organic frameworks for magnetic solid phase extraction of trace chlorine-containing herbicides in soil

Here, imine-linked covalent organic frameworks coated Fe3O4 microspheres were fabricated and employed as the self-template to prepare magnetic porous carbon material. The magnetic solid phase extraction (MSPE) performance of such magnetic covalent organic frameworks derived porous carbons (CMCOFs) were studied for the first time, and the improved MSPE performance was verified. The variations of chemical and material properties in the carbonization processes were studied, and it was found that the CMCOFs carbonated at 400°C exhibited highest adsorption efficiencies for chlorine-containing herbicides due to the formation of nitrile components at this stage. The CMCOFs retained high adsorption efficiencies (above 90 %) to chlorine-containing herbicides at wide pH range (3–12) and high salt concentration. The CMCOFs-based MSPE coupled with HPLC technique was in good potential for analysis of trace chlorine-containing herbicides in soil samples. Under the optimized conditions, this approach displayed short extraction and elution time (5 and 8 min) and low limits of detection (0.35–5.5 ng/mL) for chlorine-containing herbicides. The recoveries of spiked analytes and the relative standard deviations in real soil samples were 81.86 %–110.9 % and less than 5.92 %, respectively. This study provides an efficient method for the analysis of trace chlorine-containing herbicides in complex samples, as well as give some inspiration on material modulation by controlled carbonization to achieve improved sorption performances.

Ideology, Information, and Social Welfare Preferences

Research shows that Americans have a generally poor understanding of welfare programs. Providing information about such programs has the potential to shape public preferences, but we argue that such effects may differ based on the content of the information and its correspondence with existing ideological beliefs. Using original survey experiments embedded in the Cooperative Congressional Election Study and through Amazon’s Mechanical Turk, we analyze how the relationship of ideology with welfare programs varies in response to different types of negative information about the program, and different descriptions of policy design. We find that information about inadequate benefits has a larger negative impact on welfare support for liberals than for conservatives but that both liberals and conservatives may be equally concerned about fraud and inefficiency. Other information about policy design has the expected conditional effect: state (as opposed to federal) funding and short time limits for benefits are more appealing to conservatives than liberals.

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings.

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Frequency-dependent diffusion kurtosis imaging in the human brain using an oscillating gradient spin echo sequence and a high-performance head-only gradient

Measuring the time/frequency dependence of diffusion MRI is a promising approach to distinguish between the effects of different tissue microenvironments, such as membrane restriction, tissue heterogeneity, and compartmental water exchange. In this study, we measure the frequency dependence of diffusivity (D) and kurtosis (K) with oscillating gradient diffusion encoding waveforms and a diffusion kurtosis imaging (DKI) model in human brains using a high-performance, head-only MAGNUS gradient system, with a combination of b-values, oscillating frequencies (f), and echo time that has not been achieved in human studies before. Frequency dependence of diffusivity and kurtosis are observed in both global and local white matter (WM) and gray matter (GM) regions and characterized with a power-law model ∼Λ*fθ. The frequency dependences of diffusivity and kurtosis (including changes between fmin and fmax, Λ, and θ) vary over different WM and GM regions, indicating potential microstructural differences between regions. A trend of decreasing kurtosis over frequency in the short-time limit is successfully captured for in vivo human brains. The effects of gradient nonlinearity (GNL) on frequency-dependent diffusivity and kurtosis measurements are investigated and corrected. Our results show that the GNL has prominent scaling effects on the measured diffusivity values (3.5∼5.5% difference in the global WM and 6∼8% difference in the global cortex) and subsequently affects the corresponding power-law parameters (Λ, θ) while having a marginal influence on the measured kurtosis values (<0.05% difference) and power-law parameters (Λ, θ). This study expands previous OGSE studies and further demonstrates the translatability of frequency-dependent diffusivity and kurtosis measurements to human brains, which may provide new opportunities to probe human brain microstructure in health and disease.

The influence of irrelevant emotionally negative stimuli on early and late retrospective metacognitive judgements.

It is well established that negative emotions influence a range of cognitive processes. How these emotions influence the metacognitive judgement individuals make about their own performance and whether this influence is similar depending on the conditions under which metacognition is assessed, however, is far less understood. The primary aim of this study was to determine whether exposure to emotional stimuli could influence metacognitive judgements made under short or long time constraints. A total sample of 144 young adults (aged 18-35 years) was recruited and asked to complete an arithmetic strategy selection task under emotional or neutral condition. Following each strategy selection trial, participants also provided a retrospective confidence judgement (RCJ). Both strategy selection and RCJ were collected under short or long time constraints (1,500 vs. 2,500 ms for strategy selection and 800 vs. 1,500 ms for RCJ). In addition to replicating previous findings showing lower rates of better strategy selection under negative emotions compared with neutral condition, an effect of negative stimuli on the accuracy of participants' confidence judgements was found, but only if participants had a short time limit to make their second-level evaluation. Such findings are consistent with the hypothesis that exposure to emotional stimuli disturbs early, but not late metacognitive processes and have important implications to further our understanding of the role of emotions on metacognition.

Large deviations of the interface height in the Golubović-Bruinsma model of stochastic growth.

We study large deviations of the one-point height H of a stochastic interface, governed by the Golubović-Bruinsma equation, ∂_{t}h=-ν∂_{x}^{4}h+(λ/2)(∂_{x}h)^{2}+sqrt[D]ξ(x,t), where h(x,t) is the interface height at point x and time t and ξ(x,t) is the Gaussian white noise. The interface is initially flat, and H is defined by the relation h(x=0,t=T)=H. We focus on the short-time limit, T≪T_{NL}, where T_{NL}=ν^{5/7}(Dλ^{2})^{-4/7} is the characteristic nonlinear time of the system. In this limit typical, small fluctuations of H are unaffected by the nonlinear term, and they are Gaussian. However, the large-deviation tails of the probability distribution P(H,T) "feel" the nonlinearity already at short times, and they are non-Gaussian and asymmetric. We evaluate these tails using the optimal fluctuation method (OFM). The lower tail scales as -lnP(H,T)∼H^{5/2}/T^{1/2}. It coincides with its analog for the Kardar-Parisi-Zhang (KPZ) equation, and we point out to the mechanism of this universality. The upper tail scales as -lnP(H,T)∼H^{11/6}/T^{5/6}, it is different from the upper tail of the KPZ equation. We also compute the large deviation function of H numerically and verify our asymptotic results for the tails.

Research on Detection of Ultra-Low Concentration Anthrax Protective Antigen Using Graphene Field-Effect Transistor Biosensor.

Protective antigen (PA) is an important biomarker for the early diagnosis of anthrax, and the accurate detection of protective antigen under extremely low concentration conditions has always been a hot topic in the biomedical field. To complete the diagnosis of anthrax in a timely manner, it is necessary to detect PA at extremely low concentrations, as the amount of PA produced in the early stage of anthrax invasion is relatively small. Graphene field-effect transistor (Gr-FET) biosensors are a new type of material for preparing biosensors, with the advantages of a short detection time and ultra-low detection limit. The effect of different concentrations of diluents on the affinity of PA monoclonal antibodies was determined via an ELISA experiment. Combined with the Debye equation, 0.01 × PBS solution was finally selected as the diluent for the experiment. Then, a PA monoclonal antibody was selected as the bio-recognition element to construct a Gr-FET device based on CVD-grown graphene, which was used to detect the concentration of PA while recording the response time, linear range, detection limit, and other parameters. The experimental results showed that the biosensor could quickly detect PA, with a linear range of 10 fg/mL to 100 pg/mL and a detection limit of 10 fg/mL. In addition, the biosensor showed excellent specificity and repeatability. By constructing a Gr-FET device based on CVD-grown graphene and selecting a PA monoclonal antibody as the bio-recognition element, a highly sensitive, specific, and repeatable Gr-FET biosensor was successfully prepared for detecting extremely low concentrations of anthrax protective antigen (PA). This biosensor is expected to have a wide range of applications in clinical medicine and biological safety monitoring.

Atomically Thin 2D TiO2 Nanosheets with Ligand Modified Surface for Ultra-sensitive Humidity Sensor

As a kind of two-dimensional (2D) nanostructured materials, metal oxide nanosheets (MONS) are attractive and promising humidity sensing materials due to their considerable surface area, good charge carrier transportation, and designable surface functional groups properties. Nevertheless, the ultra-thin MONS modified with active functional groups for humidity sensing are still rare. As a proof of concept, the atomically thin TiO2 nanosheets with high surface area and electron-donating amino groups are prepared by a structure-maintained post-ligand modification strategy. The fabricated TiO2-based sensors demonstrate superior humidity sensing performance with high response, short response time, narrow hysteresis, and ultra-low theoretical limit of detection of about 15 ppm. Additionally, the possible mechanism is proposed from the AC complex impedance measurements and DC instantaneous reverse polarity experiments. This work provides a possible path for developing the high-performance 2D nanostructured metal oxides-based humidity materials through the surface chemical method.

Mathematical modeling of anomalous diffusive behavior in transdermal drug-delivery including time-delayed flux concept

Molecular transport through a composite multilayer membrane is a central process in transdermal drug delivery (TDD). Classical Fickean approach treats skin as a pseudo-homogenous membrane, while in reality skin is highly heterogeneous system as shown in basic physiological research. Particle transport across such systems shows anomalous diffusive behavior that is described by fractional models. These models don't consider experimentally observed dependence of particle transport nature on time scale. The possible way of inclusion of that observation in model of transdermal transport is presented in this paper. The generalized fractional models of the spectral functions of the concentration profile and the cumulative amount of the drug absorbed through the bloodstream are derived. The derived model predicts resonances in concentration profile and larger cumulative amount of the drug in both the short-time limit and the long-time limit, which can have significant physiological implications.

Short-Time Behavior in Arithmetic Asian Option Price Under a Stochastic Volatility Model with Jumps

In this paper, we study the short-time behavior of the arithmetic average of Asian option price (AOP) derived from a general class of the stochastic volatility model with jumps. The AOP that rarely has explicit expression can reduce the volatility in the option price because of the average of the underlying asset price over the time interval. We consider the future average process in the model which is a non-adapted process. By using the Malliavin calculus operators, we get a non-adapted Itô formula, and also a decomposition formula of the option price in the model. We apply the decomposition formula to find the short-time limit of the arithmetic AOP and the implied volatility.