Spatiotemporal Research Articles

TVGCN: Time-varying graph convolutional networks for multivariate and multifeature spatiotemporal series prediction.

Spatiotemporal (ST) graph modeling has garnered increasing attention recently. Most existing methods rely on a predefined graph structure or construct a single learnable graph throughout training. However, it is challenging to use a predefined graph structure to capture dynamic ST changes effectively due to evolving node relationships over time. Furthermore, these methods typically utilize only the original data, neglecting external temporal factors. Therefore, we put forward a novel time-varying graph convolutional network model that integrates external factors for multifeature ST series prediction. Firstly, we construct a time-varying adjacency matrix using attention to capture dynamic spatial relationships among nodes. The graph structure adapts over time during training, validation, and testing phases. Then, we model temporal dependence by dilated causal convolution, leveraging gated activation unit and residual connection. Notably, the prediction accuracy is enhanced through the incorporation of embedding absolute time and the fusion of multifeature. This model has been applied to three real-world multifeature datasets, achieving state-of-the-art performance in all cases. Experiments show that the method has high accuracy and robustness when applied to multifeature and multivariate ST series problems.

Space–time characterization of ultrashort laser pulses: A perspective

The characterization of ultrashort laser pulses has significantly advanced beyond the standard spatial and temporal diagnostics to now include sophisticated spatio-temporal measurement techniques. In this perspective, we provide an overview of the current state of space–time characterization, discussing the theoretical foundations of ultrashort laser pulses, the various measurement techniques and their design trade-offs, and the challenges and opportunities for future development. We explore the extension of these techniques to different wavelength regimes and delve into the unique challenges posed by the characterization of polarization-structured beams. The potential for data-driven analysis to enhance the information extracted from the measurements is highlighted, along with the need for direct measurement of previously inaccessible field components, such as the longitudinal electric field in tightly focused beams. As these diagnostic tools continue to evolve, we anticipate a future where the intricate space–time structure of light can be analyzed on a routine basis, opening up new frontiers in ultrafast science and technology.

TC-Match: Fast Time-Constrained Continuous Subgraph Matching

Continuously monitoring structural patterns in streaming graphs is a critical task in many real-time graph-based applications. In this paper, we study the problem of time-constrained continuous subgraph matching (shorted as TCSM) over streaming graphs. Given a query graph Q with timing order constraint and a data graph stream G , TCSM aims to report all incremental matches of Q in G for each update of G , where a match should obey both structure constraint (i.e., isomorphism) and timing order constraint of Q. Although TCSM has a wide range of applications, such as cyber-attack detection and credit card fraud detection, we note that this problem has not been well addressed. The state-of-the-art bears the limitations of high index space cost and intermediate result maintenance cost. In this paper, we propose TC-Match, an effective approach to TCSM. First, we design a space and time cost-effective index CSS, which is essentially a k -partite graph structure where a node corresponds to an edge in G. By carefully creating links between nodes, we can encapsulate into CSS the partial embedding and timing order information between edges in G. We theoretically show that CSS has polynomial space and construction time complexities. Second, based on the property of CSS, we develop an efficient incremental matching algorithm with an effective node merging optimization. Extensive experiments show that TC-Match can achieve up to 3 orders of magnitude query performance improvement over the baseline methods, and meanwhile the memory consumption is reduced by 48.7%-86.7%.

Enhanced Spatio-Temporal Modeling for Rainfall Forecasting: A High-Resolution Grid Analysis

Rainfall serves as a lifeline for crop cultivation in many agriculture-dependent countries including India. Being spatio-temporal data, the forecasting of rainfall becomes a more complex and tedious process. Application of conventional time series models and machine learning techniques will not be a suitable choice as they may not adequately account for the complex spatial and temporal dependencies integrated within the data. This demands some data-driven techniques that can handle the intrinsic patterns such as non-linearity, non-stationarity, and non-normality. Space–Time Autoregressive Moving Average (STARMA) models were highly known for its ability to capture both spatial and temporal dependencies, offering a comprehensive framework for analyzing complex datasets. Spatial Weight Matrix (SWM) developed by the STARMA model helps in integrating the spatial effects of the neighboring sites. The study employed a novel dataset consisting of annual rainfall measurements spanning over 50 (1970–2019) years from 119 different locations (grid of 0.25 × 0.25 degree resolution) of West Bengal, a state of India. These extensive datasets were split into testing and training groups that enable the better understanding of the rainfall patterns at a granular level. The study findings demonstrated a notable improvement in forecasting accuracy by the STARMA model that can exhibit promising implications for agricultural management and planning, particularly in regions vulnerable to climate variability.

Full Diversity Space Time Codes for Next Generation Wireless Sensor Networks

For the next generation of wireless sensor networks, this research paper proposes two distinguished, robust space-time codes with low complexity and full diversity. The channel is constructed using Quasi-deterministic radio channel generation (Quadriga), which pursues a geometric stochastic model. This paper discusses an uplink perspective on an industrial communication system. A master node design with four distributed antennas is suggested. Two antennas are available on slave nodes, where the proposed space time coding can be used. Additionally, zero-forcing (ZF) and minimum mean squared error (MMSE)-based low-complexity decoders are designed. The proposed codes outperform the Alamouti code under identical circumstances, according to simulation data. The simulation results show that a coding gain of about 5dB in comparison to Alamouti code is achieved. A high coding gain is attained, which results in a more reliable transmission, according to the bit error rate (BER). This research paper significantly contributes to the standardization of the next-generation wireless sensor networks.

Synchronization transition in space–time chaos in the presence of quenched disorder

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in the presence of quenched disorder in coupling. The disorder is identical in both replicas. We study one-dimensional, two-dimensional, and globally coupled logistic and tent maps. We observe a clear second-order transition with new exponents. The order parameter decays as t−δ and δ depends on the map and its parameters. The asymptotic order parameter for Δ distance from a critical point grows as Δβ with β∼δ. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from those of the multiplicative noise universality class. However, it does not depend on dimensionality in the cases studied if the transition is continuous.

Modulating electronic structure and exposed surface area of Cu-based catalysts by Pd doping for enhanced CO2 hydrogenation to methanol

The development of efficient catalysts for CO2 hydrogenation to methanol holds great significance in addressing environmental concerns and sustainable energy production. In this study, a series of Cu/ZnO (CZ) catalysts doped with Pd, Pt, and Ru were investigated to unravel the role of Cu electronic structure in this process. Surprisingly, it was found that the introduction of Pd and Pt led to the formation of an electron-rich Cu site due to partial electron transfer, which greatly enhanced CO2 activation. Furthermore, the electronic effects of Pd and Cu allowed the 2Pd/CZ catalyst having the smallest Cu crystallite sizes and highest exposed Cu surface area. This offered the unique advantage of constructing the rich Cu-ZnO interface; thus, significantly enhanced the methanol synthesis activity. Utilizing this phenomenon, a series of Pd/CZ catalysts were synthesized by adjusting the amount of Pd incorporation, all of which exhibited excellent methanol synthesis performance. Notably, the 2Pd/CZ catalyst demonstrated the highest CH3OH STY (space–time yield) of 0.52 g·g−1·h−1. This work provides valuable insights into the design of highly efficient catalytic materials for CO2 hydrogenation to methanol.

Torricelli’s Law in Fractal Space–Time Continuum

A new formulation of Torricelli’s law in a fractal space–time continuum is developed to compute the water discharge in fractal reservoirs. Fractal Torricelli’s law is obtained by applying fractal continuum calculus concepts using local fractional differential operators. The model obtained can be used to describe the behavior of real flows, considering the losses in non-conventional reservoirs, taking into account two additional fractal parameters α and β in the spatial and temporal fractal continuum derivatives, respectively. This model is applied to the flows in reservoirs with structures of three-dimensional deterministic fractals, such as inverse Menger sponge, Sierpinski cube, and Cantor dust. The results of the level water discharge H(t) are presented as a curve series, showing the impact and influence of fluid flow in naturally fractured reservoirs that posses self-similar properties.

From Schrödinger equation to tempered distribution space on Minkowski chronotope and Schwartz Linear Algebra

In this paper, we propose a rational and almost obliged path leading us from the most natural assumption regarding the SchrÅNodinger wave functions (wave functions classically belonging to the domain of the classic Schrödinger equation) to the space of tempered distributions defined upon the Minkowski space time. It’s extremely natural to consider the space E of complex valued smooth functions as the natural domain of the Schrödinger equation, as it was the obvious implicit assumption of any partial differential equation with constant coefficients at the time of Schrödinger himself. The orthodox Born interpretation of the normalized wave functions and the intervention of von Neumann (a Hilbert‘s pupil) have deviated the straightforward understanding of that domain towards the unnecessary and unnatural Hilbert space L2. The Hilbert space of square integrable functions is clearly incompatible with any partial differential equation, which would require at least Sobolev Spaces to live in; unfortunately, the inner product of the Sobolev space H2 is not good for quantum mechanics and the de Broglie solutions of the Schrödinger equation do not belong to L2. We show in this article that moving inside the very good space E - and finally inside the huge tempered distribution space S′ - represents the first framework in which any desirable property of the key characters and actors of basic Quantum Mechanics is satisfied.

Kink, Dark, Bright, and Singular Optical Solitons to the Space–Time Nonlinear Fractional (41)-Dimensional Davey–Stewartson–Kadomtsev–Petviashvili Model+

The new types of exact solitons of the space–time fractional nonlinear (4+1)-dimensional Davey–Stewartson–Kadomtsev–Petviashvili (DSKP) model are achieved by applying the unified technique and modified extended tanh-expansion function technique. A novel definition of the fractional derivative known as the truncated M-fractional derivative is also used. This model describes both the non-elastic and elastic interactions between internal waves. This model is used to represent intricate nonlinear phenomena like shallow-water waves, plasma physics, and others. The obtained results are in the form of kink, singular, bright, periodic, and dark solitons. The observed results are verified and represented by 2D and 3D graphs. The observed results are not present in the literature due to the use of fractional derivatives. The impact of the truncated M-fractional derivative on the observed results is also represented by graphs. Hence, our observed results are fruitful for the future study of these models. The applied techniques are simple, fruitful, and reliable in solving the other models in applied mathematics.

Higher-order derivative of local times for space–time anisotropic Gaussian random fields

Let X={X(t),t∈RN} be a centered space–time anisotropic Gaussian random field values in Rd. Under some general conditions, the existence and smoothness (in the sense of Meyer-Watanabe) of the higher-order derivative of the local times of X(t) are studied. Moreover, we show that the derivatives of the local time of X(t) is jointly continuous on Rd×[0,1]N. The existing results on local times of fractional Brownian motion and other Gaussian random fields are extended to higher-order derivative of local times of more general space–time anisotropic Gaussian random fields.

On high-order schemes for the space-fractional conservative Allen–Cahn equations with local and local–nonlocal operators

In this study, we focus on two fractional conservative Allen–Cahn equations with a nonlocal space-independent operator (called the RSLM operator) and a local–nonlocal space–time dependent operator (called the BBLM operator), respectively. Recently, scholars have found that the fractional Allen–Cahn equation is better than the classical equation for describing the interface thickness. Subsequently, the fractional conservative Allen–Cahn equation was used for conservative fluid dynamics. We find that two fractional conservative Allen–Cahn equations both hold the mass conservation, energy stability, and maximum bound principle. In this study, we construct second- and third-order numerical algorithms for two fractional conservative Allen–Cahn equations, and prove the mass conservation and energy decrease laws for them. To our knowledge, for the conservative Allen–Cahn equation, there are only a few works for high-order schemes with proof of their energy stability. We then present several numerical examples whose results show that the convergence orders of the numerical solutions reach the second- and third-order in time as expected. We also simulate some phase transition behaviors to be mass conservative and energy stable, as described by the fractional conservative Allen–Cahn equations, and have some interesting discoveries. It is found that the BBLM formulation can better maintain small features, but the RSLM formulation is better at capturing the profile of the interface. We also compare two fractional conservation equations with the fractional Cahn–Hilliard equation, whose changes are similar to those of the RSLM formulation. In particular, we propose the variable-step BDF2 and BDF3 methods, and prove the mass conservation and energy stability under a time-ratio constraint.

Exploring Gauss Bonnet gravity in the realm of Tolman–Kuchowicz spacetime

This study reveals the implication of charge within the framework of [Formula: see text] gravity models by considering the Tolman–Kuchowicz space–time. The use of the Bardeen model to describe the fundamental characteristics of the external geometry is an important aspect of current findings. Moreover, for the qualitative analysis, we compare all the parameters involved in the selected metric potentials with Bardeen’s model. We apply this analysis to the stars [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We study all the necessary characteristics of stellar structures, such as energy density and pressure progression, equation of state parameters, equilibrium conditions, mass–radius ratio, adiabatic index, and energy conditions. A thorough graphical analysis is provided to establish the viability of the considered [Formula: see text] models. It is important to emphasize that our acquired solutions are physically acceptable.

Darboux and generalized Darboux transformations for the fractional integrable derivative nonlinear Schrödinger equation

Analytical methods provide crucial mathematical insights into the stable solitary waves hidden in nonlinear phenomena. The nonlinear Schrödinger (NLS) equation is one of the most important typical integrable soliton models. From a mathematical perspective, the essence of the celebrated derivative NLS (DNLS) equation’s difference from the classical NLS equation lies in its cubic potential being differentiated once by the spatial variable and multiplied by the imaginary unit, which leads to the former having some characteristics that the latter cannot have. This paper extends the DNLS equation to the fractional integrable case with conformable derivative operators, and uses Darboux transformations (DTs) and generalized DT (GDT) to solve it exactly. Specifically, Lax pairs generating the fractional DNLS equation are first given. Based on the given Lax pairs, then the n-fold DTs and GDT for the fractional DNLS equation are derived. Some special exact solutions of the fractional DNLS equation are further obtained by employing the derived n-fold DTs and GDT. Finally, several novel space–time structures and dynamical evolutions of the obtained exact solutions are analyzed. This paper reveals through the DT and GDT methods that the double power-law fractional orders in the exact solutions of the fractional DNLS equation can be used to dominate the variable velocity propagation and anomalous diffusion in fractional dimensional media at different geometric scales.

A conservative Allen–Cahn model for a hydrodynamics coupled phase-field surfactant system

In this study, we develop a model for a binary fluid–surfactant system utilizing a coupling of two kinds conservative Allen–Cahn type equations and the Navier–Stokes equations. To ensure mass conservation, we incorporate hybrid Lagrange multipliers into the two Allen–Cahn type equations. Specifically, for the concentration variable, a global correction using a time-dependent Lagrange multiplier is utilized, while for the binary fluid variable, a space–time dependent Lagrange multiplier is applied to minimize the impact of dynamics of motion by mean curvature. We propose a linear second order scheme for practical solution of the model. Computational tests demonstrate that the proposed model is effective for the binary fluid–surfactant system and is capable of preserving the small features of interfaces.

Superdiffusive planar random walks with polynomial space–time drifts

We quantify superdiffusive transience for a two-dimensional random walk in which the vertical coordinate is a martingale and the horizontal coordinate has a positive drift that is a polynomial function of the individual coordinates and of the present time. We describe how the model was motivated through an heuristic connection to a self-interacting, planar random walk which interacts with its own centre of mass via an excluded-volume mechanism, and is conjectured to be superdiffusive with a scale exponent 3/4. The self-interacting process originated in discussions with Francis Comets.

Case study: analysing the progression of artificial lighting in Gauteng Province over a decade using spatio-temporal analysis

ABSTRACT Services related to generating and distributing electrical power are essential to economic growth and development. This study investigates the temporal patterns of night-time light (NTL) recorded by the Visible Infrared Imaging Radiometer Suite (VIIRS) on orbiting satellites. The time series data covers the years 2012 through 2022. The findings show that the year-on-year changes in lighting are quite small. Most major cities’ luminosity has diminished, whereas smaller cities have remained relatively constant. Using statistical approaches, this study located areas of hot and cold spots of NTL trends across Gauteng Province using a space–time cube. By using space–time cubes, it is possible to visualise how phenomena evolve over time and space. The most worrying is the diminishing hot spot located at the economic powerhouse of South Africa, Johannesburg. The study also used three-dimensional visualisation to comprehend better the underlying patterns represented by each hot spot. This dataset makes it possible to determine where urban sprawl occurs in the province, as they are characterised by new, consecutive, and sporadic hot spots. By looking at spatiotemporal dynamic changing patterns, it is easy to find complex patterns that change over time and space and provide valuable information for NTL.

Polarization-Dependent Formation of Extremely Compressed Femtosecond Wave Packets and Supercontinuum Generation in Fused Silica

Previous studies of formation of extremely compressed wave packets during femtosecond filamentation in the region of anomalous group velocity dispersion in solid dielectrics mostly considered the case of linearly polarized laser pulses. However, recent results suggest potential applications of polarization state manipulation for ultrafast laser writing of optical structures in bulk solid-state media. In the present work, evolution of radiation polarization parameters during formation of such extreme wave packets at the pump wavelength of 1900 nm in fused silica is studied numerically on the basis of the carrier-resolved unidirectional pulse propagation equation (UPPE). It was revealed that initial close-to-circular polarization leads to higher intensity of the anti-Stokes wing in the spectrum of the generated supercontinuum. Numerical simulations indicate a complex, space–time variant polarization state, and the resulting spatiotemporal electric field distribution exhibits a strong dependence on the initial polarization of the femtosecond pulse. At the same time, electric field polarization tends to linear one in the region with the highest field strength regardless of the initial parameters. The origin of this behavior is attributed to the properties of the supercontinuum components generation during filament-induced plasma formation.

Noether symmetry in new extended modified f(R,G,T) theory of gravity

This study is dedicated to investigate the Noether symmetry approach in a newly introduced gravitational theory known as [Formula: see text] gravity, where [Formula: see text] is the function of Ricci scalar [Formula: see text], trace of energy–momentum tensor [Formula: see text], and the Gauss–Bonnet invariant term [Formula: see text]. The Noether symmetry approach plays a supportive role in generating models and then determining the exact solutions by using the conserved quantities. For this purpose, the flat Friedmann–Robertson–Walker space–time is selected to observe cosmic evolution. The set of partial differential equations is calculated in the background [Formula: see text] modified theory gravity. We further examine the four different [Formula: see text] gravity models and calculate the conserved quantities to investigate the exact solutions. The three models show the increasing behavior of the cosmic scale factor that supports the expansion of universe. In fourth model, we are able to get the corresponding conserved quantity only and it is anticipated that this model will also support the expansion of universe.

Reusable MIL-100(Fe)-polyacrylonitrile-TiO2 nanofiber webs for adsorption and decomposition of toluene

Due to rapid industrialization and urbanization, addressing the pressing issue of environmental pollution, particularly indoor air quality, demands innovative solutions. Volatile organic compounds (VOCs), notably toluene, are prevalent indoor pollutants that necessitate effective adsorption and removal strategies due to their adverse health impacts. Here, we propose a novel method for crafting a multifunctional air-filter membrane capable of simultaneous toluene adsorption and photocatalytic degradation across diverse light conditions, thus facilitating the development of a reusable air filtration system. This study outlines the successful synthesis of an air filter membrane by illustrating the in-situ growth of MIL-100(Fe) particles on polyacrylonitrile (PAN) nanofibers loaded with TiO2 nanoparticles, resulting in the formation of a PTF membrane. The PTF membrane exhibits an exceptional toluene adsorption efficiency of 98 % and a high toluene capacity of 383.94 mg g−1 (4.166 mmol/g), with a corresponding partition coefficient (PC) of 38.39 L/g ± 1.41. Notably, its design enables functionality, demonstrating impressive photocatalytic degradation efficiencies of 62.3 %, 71.3 %, and 80.2 % under UV, visible, and combined UV–visible light, respectively. This high efficiency is attributed to the PTF membrane’s reduced bandgap and enhanced light-absorption capabilities. Under the combined light conditions, the PTF membrane achieved the highest space–time yield (STY) of 0.197 mol/g/h and the highest reaction kinetic rate for toluene degradation, determined to be 6.34 × 10-8, surpassing the performance observed under individual UV and visible light sources. Moreover, the regeneration cycle of the PTF membrane demonstrates minimal efficiency loss, ensuring prolonged performance. The developed PTF membranes demonstrate notable stability and resilience even under the most extreme humid conditions, suggesting their strong potential for future applications in air filtration. This innovative approach offers a straightforward and environmentally friendly method for fabricating metal–organic framework (MOF)-based photocatalytic filters tailored to indoor VOC purification systems. This study is expected to significantly advance efforts aimed at improving and managing air quality, thereby fostering a healthier and more sustainable environment.