Dimensions Research Articles

Designing a Multitemporal Analysis of Land Use Changes and Vegetation Indices to Assess the Impacts of Severe Forest Fires Before Applying Control Measures

Forest fires represent a significant intersection between nature and society, often leading to the loss of natural resources, soil nutrients, and economic opportunities, as well as causing desertification and the displacement of communities. Therefore, the objective of this work is to analyze the multitemporal conditions of a sixth-generation forest fire through the use and implementation of tools such as remote sensing, photointerpretation with geographic information systems (GISs), thematic information on land use, and the use of spatial indices such as the Normalized Difference Vegetation Index (NDVI), the Normalized Burned Ratio (NBR), and its difference (dNBR) with satellite images from Sentinel-2. To improve our understanding of the dynamics and changes that occurred due to the devastating forest fire in Los Guájares, Granada, Spain, in September 2022, which affected 5194 hectares and had a perimeter of 150 km, we found that the main land use in the study area was forest, followed by agricultural areas which decreased from 1956 to 2003. We also observed the severity of burning, shown with the dNBR, reflecting moderate–low and moderate–high levels of severity. Health and part of the post-fire recovery process, as indicated by the NDVI, were also observed. This study provides valuable information on the spatial and temporal dimensions of forest fires, which will favor informed decision making and the development of effective prevention strategies.

To evaluate the divine proportion on silhouette photographs of skeletal class I bimaxillary protrusion cases treated with first premolar extraction- An in-vitro study

Objectives: The aim of the study is to assess the divine proportion of soft tissues seen in bimaxillary protrusion cases and compare this proportion on pre-treatment and post-treatment Silhouette photographs of skeletal (Sk) Class I bimaxillary protrusion patients treated by premolars extraction. Material and Methods: This research was conducted on 50 samples of pre-treatment along with post-treatment outline form photographs of Sk Class I bimaxillary protrusion patients aged 18–30 years in an orthodontics and dentofacial orthopedics department. The samples had an equal distribution with 25 males and females. All profile photos with Class I bimaxillary protrusion were converted into silhouette form. To assess the divine proportion in patient profiles, each silhouette photograph was marked by five anatomic landmarks, which were as follows: Soft-tissue nasion (N), trichion (Tr), subnasale (Sn), stomion (St), and a soft-tissue menton (Me) which was followed by the measurement of six linear dimensions; ratios were measured as R1, R2, R3, R4, and R5. These ratios of the patient’s profile, both before and after the treatment, were then compared to find out the soft-tissue alterations that have taken place in patients having Class I bimaxillary protrusion corrected by the first four premolars extraction. Results: The findings indicate that all post-treatment proportions in males indicated highly noticeable changes in contrast to pre-treatment ratios. However, females revealed highly noticeable differences in R1, R2, and R4 ratios, statistically evident differences were shown by R3 and R5 ratios in contrast to ratios before the treatment. Thus, the proportions appeared to be closer to the divine proportion. Conclusion: The results showed that all the ratios were found to be closer to divine proportion, and thus, premolars extraction in cases with convex facial form does help us to achieve esthetically pleasing faces.

Establishment of a locally adaptive allele in multidimensional continuous space.

Local adaptation is widely seen when species adapt to spatially heterogeneous environments. Although many theoretical studies have investigated the dynamics of local adaptation using two-population models, there remains a need to extend the theoretical framework to continuous space settings, reflecting the real habitats of species. In this study, we use a multidimensional continuous space model and mathematically analyze the establishment process of local adaptation, with a specific emphasis on the relative roles of mutation and migration. First, the role of new mutations is evaluated by deriving the establishment probability of a locally adapted mutation using a branching process and a diffusion approximation. Next, the contribution of immigrants from a neighboring region with similar environmental conditions is considered. Theoretical predictions of the local adaptation rate agreed with the results of Wright-Fisher simulations in both mutation-driven and migration-driven cases. Evolutionary dynamics depend on several factors, including the strength of migration and selection, population density, habitat size, and spatial dimensions. These results offer a theoretical framework for assessing whether mutation or migration predominantly drives convergent local adaptation in spatially continuous environments in the presence of patchy regions with similar environmental conditions.

The beach: tourism tax competition along the Italian coasts

AbstractThis paper investigates how tourism taxes are used by municipalities to attract tourists. We analyze how municipalities compete among each other, explicitly accounting for the spatial dimension. This paper provides a novel contribution to the literature on tax competition by explicitly modeling and testing the spatial dimension. First, we present a spatial model of tax competition, which is an adoption of the Hotelling model of imperfect competition in the linear city. We find that tax rates are strategic complements, as a change in taxes of one town will lead to a similar change of tax rates in neighboring towns. Second, we test the model with data from tourism taxes along the Italian coastline. We find that towns on the Tyrrhenian coast loose tourists to municipalities in the (south)east, if those reduce their tourism tax rate, and compete by lowering their own tax rates with respect to towns in the (north)west. We do not find similar behavior along the Adriatic coast.

Weakly Compressible Approximation of the Taylor–Green Vortex Solution

ABSTRACTThe Taylor–Green vortex represents an exact solution of the Navier–Stokes equations in . In this work, an approximation of this solution in two spatial dimensions is proposed for weakly compressible flows. These flows are characterized by small compressibility (or, equivalently, by a small Mach number) and are often employed in computational fluid dynamics to approximate the behaviour of incompressible Newtonian fluids. In this framework, the proposed solution is expected to be a useful benchmark for numerical solvers that implement the weakly compressibility approximation. To this end, some numerical examples are reported in the final section of this work.

How Digital Innovation Ecosystems Facilitate Low-Carbon Transformation of the Economy Based on a Dynamic Qualitative Comparative Analysis

The digital innovation ecosystem is an important driving force for building a modern economic development system. It is of great significance to explore the multiple configuration paths of digital innovation ecosystems affecting the development of the low-carbon transformation of the economy to facilitate the green and sustainable development of the economy. We have found through our research that the types of configuration that lead to the development of a high-level low-carbon economy are ‘subjects-resource-environment linkage’ and ‘subjects-environment driven’. The former is the key configuration path that leads to the development of a high-level low-carbon economy. In both models, a high-level digital environment is the core condition that facilitates the development of a high-level low-carbon economic transformation. Moreover, in the spatial dimension, there is a significant difference in the types of configuration that achieve low-carbon economic transformation in the eastern, central, and western regions of China. The findings of this study reveal how the three major subsystems of the digital innovation ecosystem synergistically affect the low-carbon transformation of the economy. It not only helps to improve the relevant theories, but also brings certain references for improving the ‘synergy’ between low-carbon development and economic growth.

Processes and controls of regional floods over eastern China

Abstract. Mounting evidence points to elevated regional flood hazards in a changing climate, but existing knowledge about their processes and controls is limited. This is partially attributed to inadequate characterizations of the spatial extent and potential drivers of these floods. Here we develop a machine-learning-based framework (mainly including the Density Based Spatial Clustering Applications with Noise (DBSCAN) clustering algorithm and a conditional random forest model) to examine the processes and controls of regional floods over eastern China. Our empirical analyses are based on a dense network of stream gauging stations with continuous observations of annual maximum flood peaks (i.e. magnitude and timing) during the period 1980–2017. A comprehensive catalogue of 318 regional floods is developed. We reveal a pronounced clustering of regional floods in both space and time over eastern China. This is dictated by cyclonic precipitating systems and/or their interactions with topography. We highlight contrasting behaviours of regional floods in terms of their spatial extents and intensities. These contrasts are determined by fine-scale structures of flood-producing storms and anomalous soil moisture. While land surface properties might play a role in basin-scale flood processes, it is more critical to capture spatial–temporal rainfall variabilities and soil moisture anomalies for reliable large-scale flood hazard modelling and impact assessments. Our analyses contribute to flood science by better characterizing the spatial dimension of flood hazards and can serve as a basis for collaborative flood risk management in a changing climate.

Bowen’s Formula for a Dynamical Solenoid

More than 50 years ago, Rufus Bowen noticed a natural relation between the ergodic theory and the dimension theory of dynamical systems. He proved a formula, known today as the Bowen’s formula, that relates the Hausdorff dimension of a conformal repeller to the zero of a pressure function defined by a single conformal map. In this paper, we extend the result of Bowen to a sequence of conformal maps. We present a dynamical solenoid, i.e., a generalized dynamical system obtained by backward compositions of a sequence of continuous surjections (fn:X→X)n∈N defined on a compact metric space (X,d). Under mild assumptions, we provide a self-contained proof that Bowen’s formula holds for dynamical conformal solenoids. As a corollary, we obtain that the Bowen’s formula holds for a conformal surjection f:X→X of a compact

Aligning the new work environment with OECD Goal 8: a design case of a global automobile brand from Turkey

Purpose This paper aims to investigate the economic sustainability of new work environments by exploring how interior design strategies can contribute to the Organization for Economic Co-operation and Development (OECD)’s Sustainable Development Goal (SDG) 8, which focuses on decent work and economic growth. SDG 8 aims to foster sustained, inclusive and sustainable economic development, as well as full and productive employment. Design/methodology/approach The pilot study was conducted at a global automobile brand’s largest facility in Kocaeli/Turkey, where 102 employees participated in stakeholder meetings divided into 18 groups. Additionally, 46 employees were interviewed through focus groups and one-on-one sessions across nine encounters. The collected data were analyzed using deductive thematic analysis, interpreting codes and themes related to spatial politics, timing politics and hybrid working culture in the new work environment. Findings Identified themes include individually focused tasks, virtual collaboration, agile working, socialization and urban interaction. These themes are then traced through the conceptual design proposal developed by the interior design team and discussed in relation to their alignment with SDG 8.2 (diversify, innovate and upgrade for economic productivity), SDG 8.4 (improve resource efficiency in consumption and production) and SDG 8.8 (protect labor rights and promote safe and secure working environments for all workers). Research limitations/implications These three targets (for inclusivity and innovation, for environmentally sustainable and for employee well-being) were selected for their relevance in shaping the physical work environment. Originality/value The key finding of this paper is the need for a deeper understanding of economic sustainability in interior design and the contribution of SDG 8 targets on the spatial, temporal and cultural dimensions of new work environments. Brands committed to sustainability must adopt new work models and reimagine their work environments to enhance employee satisfaction and performance, through comprehensive user research and design solutions aligned with SDG 8.

The Use of continuous action representations to scale deep reinforcement learning for inventory control

Abstract Deep reinforcement learning (DRL) can solve complex inventory problems with a multi-dimensional state space. However, most approaches use a discrete action representation and do not scale well to problems with multi-dimensional action spaces. We use DRL with a continuous action representation for inventory problems with a large (multi-dimensional) discrete action space. To obtain feasible discrete actions from a continuous action representation, we add a tailored mapping function to the policy network that maps the continuous outputs of the policy network to a feasible integer solution. We demonstrate our approach to multi-product inventory control. We show how a continuous action representation solves larger problem instances and requires much less training time than a discrete action representation. Moreover, we show its performance matches state-of-the-art heuristic replenishment policies. This promising research avenue might pave the way for applying DRL in inventory control at scale and in practice.

DGTNet：dynamic graph attention transformer network for traffic flow forecasting

Abstract Graph-based traffic flow prediction plays a crucial role in urban traffic management and planning. In this paper, we propose a novel Dynamic Graph Attention Transformer Network (DGTnet), which is designed to address the issue of inadequately integrating of temporal and spatial dimensions in traditional models. DGTnet maintains temporal continuity while revealing the complex dynamic relationships between key nodes in the urban traffic system, capturing the periodic changes in the rhythm of city life. Specifically, this study adopts adaptive signal decomposition technology to decompose traffic data into multiple intrinsic mode functions (IMFs), effectively capturing the dynamic changes in traffic flow. This decomposition method is key to the implementation of DGTnet dynamic graph construction, enabling the analysis of traffic flow at different time scales, thereby providing a new perspective for traffic flow prediction research. In the traffic prediction module, we comprehensively consider node, edge, and graph structural information, adopting a multi-head self-attention mechanism to achieve direct cross-modeling in both temporal and spatial dimensions. Finally, we introduce a position-wise feed forward network layer to integrate different types of data and capture nonlinear relationships. The experimental results, based on the public transportation network data sets METR_LA, PEMS_BAY, PEMS03 and PEMS07, demonstrate that DGTNet exhibits notable enhancements in three evaluation indicators, namely the Mean Absolute Percentage Error (MAPE), the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The pertinent code has been made available for public access at https://github.com/chenjing0616/DGTNet.

Gridded Severe Hail Nowcasting Using 3D U-Nets, Lightning Observations, and the Warn-on-Forecast System

Abstract Hailstorms cause billions of dollars in damage across the United States each year. Part of this cost could be reduced by increasing warning lead times. To contribute to this effort, we developed a nowcasting machine learning model that uses a 3D U-Net to produce gridded severe hail nowcasts for up to 40 minutes in advance. The three U-Net dimensions uniquely incorporate one temporal and two spatial dimensions. Our predictors consist of a combination of output from the National Severe Storms Laboratory Warn-on-Forecast System (WoFS) numerical weather prediction ensemble and remote sensing observations from Vaisala’s National Lightning Detection Network (NLDN). Ground truth for prediction was derived from the Maximum Expected Size of Hail calculated from the gridded NEXRAD WSR-88D radar (GridRad) dataset. Our U-Net was evaluated by comparing its test set performance against rigorous hail nowcasting baselines. These baselines included WoFS ensemble HAILCAST and a logistic regression model trained on WoFS 2-5 km updraft helicity. The 3D U-Net outperformed both these baselines for all forecast period timesteps. Its predictions yielded a neighborhooded maximum critical success index (max CSI) of ~0.48 and ~0.30 at forecast minutes 20 and 40, respectively. These max CSIs exceeded the ensemble HAILCAST max CSIs by as much as ~0.35. The NLDN observations were found to increase the U-Net performance by more than a factor of 4 at some timesteps. This system has shown success when nowcasting hail during complex severe weather events, and if used in an operational environment, may prove valuable.

Radiological assessment of Sella Turcica morphology correlates with skeletal classes in an Austrian population: an observational study.

This study aimed to analyze variations in the sella turcica (ST) concerning its size, shape, and bridging, providing first reference values in Austrian individuals. Additionally, it assessed associations between these morphological and demographic parameters and their correlation with patients' skeletal class. 208 lateral cephalometric radiographs (154 female, 54 male; age 8-58 years) from DPU Dental Clinic (Austria) were included. Size, skeletal class, shape, age, and gender of ST were tested for significance in correlation using, (M)ANOVA, and chi-square. Linear dimensions of ST ranged from 11.1 to 12.9mm across readers, with a standard deviation of 2.0-2.2mm. Normal ST (49.76%) and round ST (58.77%) were the most frequent. ST bridging was detected in 6.97%. Skeletal class I appeared most frequently (54.8%). Statistical significance was observed between age, gender, and ST length, with further significant age effects on ST shape. Moreover, age showed significant modification of ST shape, while skeletal parameters appeared unaffected by other ST parameters. These preliminary findings define normal ST dimensions in an Austrian population, offering reference values for clinical interpretation and broadening the available European data. Clear associations between morphological and demographic parameters were detected. Additionally, these findings may contribute to diagnostic and therapeutic strategies in orthodontics and craniofacial pathology. Future studies employing cone beam computed tomography (CBCT) along a larger sample size could enhance the generalizability of these findings.

REGULARITIES OF DEVELOPMENT AND FORMATION OF EMBRYOTOPOGRAPHY OF THE THYROID AND PARATHYROID GLANDS IN HUMAN EMBRYOS OF 7-9 WEEKS OF GESTATION

The article describes the peculiarities of development and formation of variants of external shape and localization of thyroid and parathyroid glands in human embryos of 7-9 weeks of gestation.Aim of the study. The objective of the study was to fi nd the regularities of development and formation of embryotopographic relations between the thyroid and parathyroid glands during 7-9 weeks of the human intrauterine development. Material and methods. The study was carried out using a complex of morphological methods on 42 samples of human embryos without external signs of anatomical deviations or developmental defects. The specimens were taken from the museums of the Department of Human Anatomy of M. H. Turkevytch and the Department of Anatomy, Clinical Anatomy and Operative Surgery of the Bukovinian State Medical University.Results and discussion. In embryos with parietococcygeal length (PCL) of 14,0-17,0 mm intensive organogenesis processes of thyroid gland occur: separation of gland lobes, loss of connection with aortic arch and establishment of close correlations with laryngeal rudiment and vagus nerves. Therefore, the thyroid gland becomes semicircular. In embryos with 18,0-24,0 mm PCL there is a separation of the isthmus from the lateral lobes of the thyroid. Initially it is caused by intensive growth of the cricoid arch. Gradually the gland becomes H-shaped and fragmentation of the caudal part of the thyroglossal duct occurs. When the PCL reaches 29.5-31.0 mm, folliculogenesis begins and the thyroid gland becomes horseshoe- shaped. 9-week embryos show clear individual variations in the external shape of the thyroid gland: semicircular, H-shaped, and horseshoe. Areas of undiff erentiated epithelial tissue are found in the thyroid parenchyma, especially in its center.Conclusions. The conducted study has shown that during the 7-9 weeks of intrauterine development the structural organization of the thyroid and parathyroid rudiments becomes more complicated. Tight embryotopographic relations are established between them. Vascularization intensifi es and the connective tissue capsules of the thyroid and parathyroid glands are formed. At the same time their linear dimensions increase rapidly.

Evaluating the Dynamic Comprehensive Resilience of Urban Road Network: A Case Study of Rainstorm in Xi’an, China

Rainstorms and flooding are among the most common natural disasters, which have a number of impacts on the transport system. This reality highlights the importance of understanding resilience—the ability of a system to resist disruptions and quickly recover to operational status after damage. However, current resilience assessments often overlook transport network functions and lack dynamic spatiotemporal analysis, posing challenges for comprehensive disaster impact evaluations. This study proposes an SR-PR-FR comprehensive resilience evaluation model from three dimensions: structure resilience (SR), performance resilience (PR), and function resilience (FR). Moreover, a simulation model based on Geographic Information System (GIS) and Simulation of Urban MObility (SUMO) is developed to analyze the dynamic spatial–temporal effects of a rainstorm on traffic during Xi’an’s evening rush hour. The results reveal that the southwest part of Xi’an is most prone to being congested and slower to recover, while downtown flooding is the deepest, severely affecting emergency services’ efficiency. In addition, the road network resilience returns to 70% of the normal values only before the morning rush the next day. These research results are presented across both temporal and spatial dimensions, which can help managers propose more targeted recommendations for strengthening urban risk management.

Controlling the orientation of ellipsoidal nanoparticles using fractional vector beams

In the field of nanotechnology, achieving precise manipulation of ellipsoidal nanoparticles presents a significant challenge because it requires controlling five degrees of freedom, including three spatial dimensions (position in 3D space) and two angular dimensions (polar and azimuthal angles). In this work, we investigate both the optical forces and trapping potentials on an ellipsoidal nanoparticle produced by tightly focused fractional vector beams (FVBs). Unlike the integer vector beams (IVBs), which manipulate only three spatial dimensions of ellipsoidal particles, FVB with an initial phase not only provides spatial position control but also enables precise manipulation of spatial orientation. Moreover, by adjusting the topological index and initial phase of the incident FVBs, arbitrary orientations in the 3D space of ellipsoidal nanoparticles can be achieved. Our results may find interesting applications in microfluidics, biomedical engineering, and nanotechnology.

Can one hear the shape of a crystal?

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question “Can one hear the shape of a drum?” concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n≥2). Here, we ask what is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multiparticle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral four-, three- and two-particle bases in one, two, and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identically the same g2(r)'s for all values of r. Based on our analyses, we conjecture that nmin(d)=4, 3, 2 for d=1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n=3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radial pair information. Published by the American Physical Society 2024

Chemically reactive and aging macromolecular mixtures. II. Phase separation and coarsening.

In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities.

Three-Dimensional CKANs: UUV Noncooperative Target State Estimation Approach Based on 3D Convolutional Kolmogorov–Arnold Networks

Accurate and stable estimation of the position and trajectory of noncooperative targets is crucial for the safe navigation and operation of sonar-equipped underwater unmanned vehicles (UUVs). However, the uncertainty associated with sonar observations and the unpredictability of noncooperative target movements often undermine the stability of traditional Bayesian methods. This paper presents an innovative approach for noncooperative target state estimation utilizing 3D Convolutional Kolmogorov–Arnold Networks (3DCKANs). By establishing a non-Markovian model that characterizes state estimation of UUV noncooperative targets under uncertain observations, we leverage historical data to construct 3D Convolutional Kolmogorov–Arnold Networks. This network learns the patterns of sonar observations and target state transitions from a substantial offline dataset, allowing it to approximate the posterior probability distribution derived from past observations effectively. Additionally, a sliding window technique is integrated into the convolutional neural network to enhance the estimator’s fault tolerance with respect to observation data in both temporal and spatial dimensions, particularly when posterior probabilities are unknown. The incorporation of the Kolmogorov–Arnold representation within the convolutional layers enhances the network’s capacity for nonlinear expression and adaptability in processing spatial information. Finally, we present statistical experiments and simulation cases to validate the accuracy and stability of the proposed method.

A Primer on Stochastic Partial Differential Equations with Spatially Correlated Noise

With the growing number of microscale devices from computer memory to microelectromechanical systems, such as lab-on-a-chip biosensors and the increased ability to experimentally measure at the micro- and nanoscale, modeling systems with stochastic processes is a growing need across science. In particular, stochastic partial differential equations (SPDEs) naturally arise from continuum models—for example, a pillar magnet's magnetization or an elastic membrane's mechanical deflection. In this review, I seek to acquaint the reader with SPDEs from the point of view of numerically simulating their finite-difference approximations, without the rigorous mathematical details of assigning probability measures to the random field solutions. I will stress that these simulations with spatially uncorrelated noise may not converge as the grid size goes to zero in the way that one expects from deterministic convergence of numerical schemes in two or more spatial dimensions. I then present some models with spatially correlated noise that maintain sampling of the physically relevant equilibrium distribution. Numerical simulations are presented to demonstrate the dynamics; the code is publicly available on GitHub.