Spatial Regularization Research Articles

Пилотные инновационные территориальные кластеры: пространственная дифференциация, закономерности развития и эффективность

The article is devoted to the study of an important component of innovative infrastructure – pilot innovative territorial clusters. The mainstages of their formation wereconsidered,spatial patterns of development,structure and economic efficiency were identified and analyzed. The purpose of the study is to analyze the spatial regularities of pilot innovative territorial clusters functioning to justify the promising directions of the state cluster policy contributing to the effective use of the financial resources of the federal budget by determining priority investment directions and establishing on this basis the recipients of state support in the cluster with the greatest potential in the context of limited financial resources. This is promising primarily for justifying the stimulation of new high-tech industries and enterprises. The study was carried out on the basis of materials from official federal and regional statistics, information and analytical reports of the Association of Clusters, Technoparks and SEZs of Russia, official ratings of regions innovative development, legislative acts of the federal and regional levels. Patterns of functioning and trends in the development of innovative territorial clusters have been identified. The main purpose of the emerging innovative territorial clusters is to saturate the huge domestic market with high-tech goods, services and technologies in order to achieve the country’s technological independence. Promising directions for improving the cluster policy of Russia are formulated.

Landscape effects of urbanisation in a post-socialist city. A case study of Wrocław (Poland)

Progressing urbanisation is contributing to the changes of vertical and horizontal landscape structure. The aim of this paper is to investigate the spatial regularities of changes in the landscape pattern that resulted from the urbanisation processes in Wrocław (Poland) between 1994 and 2020. The research area is an example of a post-socialist city characterized by fluctuating spatial processes, especially after the economic and political transformation of the year 1989. In the empirical part, authors have analysed the changes in the number of buildings and the structure of land cover using methods of spatial analysis in a GIS environment, with a particular focus on landscape metrics. The results show two main trends in landscape changes within the city boundaries, which the authors refer to as expansion and transformation. These processes were related to various driving forces and their intensity depended on analysed sub-periods and distance from the city centre. Expansion and transformation are mainly exhibited by an increase in developed area at the cost of the decline of natural and open areas (especially agricultural lands) and densification in central areas.

Weakly-supervised cloud detection and effective cloud removal for remote sensing images

We propose a one-stop automatic cloud processing scheme for RSI, including weakly supervised cloud detection and effective cloud removal. First, to avoid using massive expensive paired-labeled data, we use the idea of adversarial training to detect clouds, that is, randomly selecting some unpaired cloud and cloudless images to alternatively train a spectral-normalized Markov discriminator to obtain cloud masks. Second, a two-stage downsampling-restoring-upsampling-refining scheme is used to remove detected clouds. In order to further improve the rationality and fineness, we construct a fractional-order anisotropic filter kernel and design a convolution process to impose spatial regularization constraints on the loss construction at each stage, taking to account confidence values and structural priorities. Comprehensive experimental results show that our proposed networks are superior to the SOTA methods in terms of objective indicators and subjective performance. In addition, the performance of our one-stop approach in automatically detecting and eliminating clouds is also very satisfactory.

Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis

Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction–diffusion system exhibiting diffusion–driven (Turing) instability. While both systems, reaction–diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective.

Creating ad hoc graphical representations of number

The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., ‘IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., ‘7’ and ‘VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1–16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment – such as shape, configural cues, or 1-to-1 correspondence – as the basis for innovating more abstract number representations.

Well-posedness and exponential stability of nonlinear Maxwell equations for dispersive materials with interface

In this paper we consider an abstract Cauchy problem for a Maxwell system modeling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning the macroscopic Maxwell equations into a system of nonlinear integro-differential equations. Within the framework of evolutionary equations, we obtain well-posedness in function spaces exponentially weighted in time and of different spatial regularity and formulate various conditions on the material functions, leading to exponential stability on a bounded domain.

Deep Learning‐Based Bluetooth Low‐Energy 5.1 Multianchor Indoor Positioning with Attentional Data Filtering

Indoor positioning system (IPS) technologies have widespread applications in logistics, intelligent manufacturing, healthcare monitoring, etc. The recently released Bluetooth low‐energy (BLE) 5.1 specification enables in‐phase and quadrature‐phase (I/Q) data measurements. It allows angle of arrival estimation and becomes a natural choice for IPS implementation. Conventional BLE 5.1 IPSs use multiple anchors to provide massive redundancy to improve system robustness. It however demands effective approaches to leverage redundancy. Besides, interference due to various environmental factors can introduce severe errors to I/Q data and affect positioning accuracy. Facing these challenges, herein, a novel deep learning‐based multianchor BLE 5.1 IPS is proposed. The system aggregates measurements from multiple anchors and makes them available at regular time steps. Then, a novel attentional filtering network tailored to infer high‐quality I/Q sample data is developed and a spatial regularization loss incorporating spatial location relationships to strengthen the feature embedding discrimination is proposed. Two multianchor BLE 5.1 I/Q sample datasets are developed and released for public download. Numerical experiments are carried out to compare the proposed method with previous BLE 5.1 IPS methods and methods utilizing other radio frequency data. Results indicate that the proposed method consistently achieves submeter accuracy and significantly outperforms the state‐of‐the‐art approaches.

Whole-brain multivariate hemodynamic deconvolution for functional MRI with stability selection

Conventionally, analysis of functional MRI (fMRI) data relies on available information about the experimental paradigm to establish hypothesized models of brain activity. However, this information can be inaccurate, incomplete or unavailable in multiple scenarios such as resting-state, naturalistic paradigms or clinical conditions. In these cases, blind estimates of neuronal-related activity can be obtained with paradigm-free analysis methods such as hemodynamic deconvolution. Yet, current formulations of the hemodynamic deconvolution problem have three important limitations: (1) their efficacy strongly depends on the appropriate selection of regularization parameters, (2) being univariate, they do not take advantage of the information present across the brain, and (3) they do not provide any measure of statistical certainty associated with each detected event. Here we propose a novel approach that addresses all these limitations. Specifically, we introduce multivariate sparse paradigm free mapping (Mv-SPFM), a novel hemodynamic deconvolution algorithm that operates at the whole brain level and adds spatial information via a mixed-norm regularization term over all voxels. Additionally, Mv-SPFM employs a stability selection procedure that removes the need to select regularization parameters and also lets us obtain an estimate of the true probability of having a neuronal-related BOLD event at each voxel and time-point based on the area under the curve (AUC) of the stability paths. Besides, we present a formulation tailored for multi-echo fMRI acquisitions (MvME-SPFM), which allows us to better isolate fluctuations of BOLD origin on the basis of their linear dependence with the echo time (TE) and to assign physiologically interpretable units (i.e., changes in the apparent transverse relaxation ΔR2∗) to the resulting deconvolved events. Remarkably, we demonstrate that Mv-SPFM achieves comparable performance even when using a single-echo formulation. We demonstrate that this algorithm outperforms existing state-of-the-art deconvolution approaches, and shows higher spatial and temporal agreement with the activation maps and BOLD signals obtained with a standard model-based linear regression approach, even at the level of individual neuronal events. Furthermore, we show that by employing stability selection, the performance of the algorithm depends less on the selection of temporal and spatial regularization parameters λ and ρ. Consequently, the proposed algorithm provides more reliable estimates of neuronal-related activity, here in terms of ΔR2∗, for the study of the dynamics of brain activity when no information about the timings of the BOLD events is available. This algorithm will be made publicly available as part of the splora Python package.

Attentive Deep Image Quality Assessment for Omnidirectional Stitching

Omnidirectional images or videos are commonly generated via the stitching of multiple images or videos, and the quality of omnidirectional stitching strongly influences the quality of experience (QoE) of the generated scenes. Although there were many studies research the omnidirectional image quality assessment (IQA), the evaluation of the omnidirectional stitching quality has not been sufficiently explored. In this paper, we focus on the IQA for the omnidirectional stitching of dual fisheye images. We first establish an omnidirectional stitching image quality assessment (OSIQA) database, which includes 300 distorted images and 300 corresponding reference images generated from 12 raw scenes. The database contains a variety of distortion types caused by omnidirectional stitching, including color distortion, geometric distortion, blur distortion, and ghosting distortion, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">etc.</i> A subjective quality assessment study is conducted on the database and human opinion scores are collected for the distorted omnidirectional images. We then devise a deep learning based objective IQA metric termed Attentive Multi-channel IQA Net. In particular, we extend hyper-ResNet by developing a subnetwork for spatial attention and propose a spatial regularization item. Experimental results show that our proposed FR and NR models achieve the best performance compared with the state-of-the-art FR and NR IQA metrics on the OSIQA database. The OSIQA database as well as the proposed Attentive Multi-channel IQA Net will be released to facilitate future research.

Regularity theory for a new class of fractional parabolic stochastic evolution equations

A new class of fractional-order parabolic stochastic evolution equations of the form (∂t+A)γX(t)=W˙Q(t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\partial _t + A)^\\gamma X(t) = {\\dot{W}}^Q(t)$$\\end{document}, t∈[0,T]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t\\in [0,T]$$\\end{document}, γ∈(0,∞)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma \\in (0,\\infty )$$\\end{document}, is introduced, where -A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-A$$\\end{document} generates a C0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0$$\\end{document}-semigroup on a separable Hilbert space H and the spatiotemporal driving noise W˙Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\dot{W}}^Q$$\\end{document} is the formal time derivative of an H-valued cylindrical Q-Wiener process. Mild and weak solutions are defined; these concepts are shown to be equivalent and to lead to well-posed problems. Temporal and spatial regularity of the solution process X are investigated, the former being measured by mean-square or pathwise smoothness and the latter by using domains of fractional powers of A. In addition, the covariance of X and its long-time behavior are analyzed. These abstract results are applied to the cases when A:=Lβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A:= L^\\beta $$\\end{document} and Q:=L~-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q:={\\widetilde{L}}^{-\\alpha }$$\\end{document} are fractional powers of symmetric, strongly elliptic second-order differential operators defined on (i) bounded Euclidean domains or (ii) smooth, compact surfaces. In these cases, the Gaussian solution processes can be seen as generalizations of merely spatial (Whittle–)Matérn fields to space–time.

Playing hide and seek: Contextual regularity learning develops between 3 and 5 years of age

The ability to acquire contextual regularities is fundamental in everyday life because it helps us to navigate the environment, directing our attention where relevant events are more likely to occur. Sensitivity to spatial regularities has been largely reported from infancy. Nevertheless, it is currently unclear when children can use this rapidly acquired contextual knowledge to guide their behavior. Evidence of this ability is indeed mixed in school-aged children and, to date, it has never been explored in younger children and toddlers. The current study investigated the development of contextual regularity learning in children aged 3 to 5 years. To this aim, we designed a new contextual learning paradigm in which young children were presented with recurring configurations of bushes and were asked to guess behind which bush a cartoon monkey was hiding. In a series of two experiments, we manipulated the relevance of color and visuospatial cues for the underlying task goal and tested how this affected young children’s behavior. Our results bridge the gap between the infant and adult literatures, showing that sensitivity to spatial configurations persists from infancy to childhood, but it is only around the fifth year of life that children naturally start to integrate multiple cues to guide their behavior.

Mineral identification based on natural feature-oriented image processing and multi-label image classification

Artificial intelligence (AI) technology has significant potential in Earth sciences, particularly in mineral identification for industrial exploration, geological mapping, and archaeological research. However, traditional methods are time-consuming, expensive, and complex. And existing mineral identification methods based on mineral photos face several critical challenges, including lack of consideration for natural image features captured in real environments, limitations of single-label classification which does not align with multi-mineral occurrences in nature, and growing computational complexity as the number of identifiable mineral labels increases. Therefore, this paper proposes an efficient mineral identification model based on multi-label image classification, focusing on natural environmental features. First, realistic feature datasets are created by simulating mineral photos in real environments. Then, the model uses the query-label (Query2Label) framework, with MaxViT-T (Multi-Axis Vision Transformer-Tiny) as the feature extraction network and the asymmetric loss function. Knowledge distillation is employed to improve identification accuracy while reducing computational complexity. The proposed model achieves an impressive average identification accuracy of 84.74% on a dataset of 495,756 mineral photos, surpassing existing models like ResNet-101, ML-GCN (Multi-Label Graph Convolutional Network), and SRN (Spatial Regularization Net). It maintains a lower parameter count and computational complexity. In the end, ablation experiments demonstrate the effectiveness of each optimization scheme.

Sequential Regularization Method for the Identification of Mold Heat Flux during Continuous Casting Using Inverse Problem Solutions Techniques

A two-dimensional transient inverse heat-conduction problem (2DIHCP) was established to determine the mold heat flux using observed temperatures. The sequential regularization method (SRM) was used with zeroth-, first-, and second-order spatial regularization to solve the 2DIHCP. The accuracy of the 2DIHCP was investigated under two strict test conditions (Case 1: heat flux with time-spatial periodically varying, and Case 2: that with sharp variations). The effects of the number of future time steps, regularization parameters, order of regularization, discrete grids, and time step size on the accuracy of the 2DIHCP were analyzed. The results showed that the minimum relative error (epred) of the predicted Case 1 heat flux is 5.05%, 5.39%, and 5.88% for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 2 heat flux are 6.31%, 6.30%, and 6.36%. Notably, zeroth- and first-order spatial regularization had higher accuracy than second-order spatial regularization, while zeroth-order spatial regularization was comparable to first-order. Additionally, first-order spatial regularization was more accurate in reconstructing heat flux containing sharp spatial variations. The CPU time of the predicted Case 2 heat flux is 1.71, 1.71, and 1.70 s for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 1 heat flux are 6.18, 6.15, and 6.17 s. It is noteworthy that the choice of spatial regularization order does not significantly impact the required computing time. Lastly, the minimum epred of Case 2 heat flux with zeroth-order spatial regularization is 7.96%, 6.42%, and 7.87% for time step sizes of 1/fs, 1/2fs, and 1/5fs, respectively. The accuracy of the inverse analysis displays an initial improvement followed by degradation as the time step size decreases. A recommended time step size is 1/2fs, where fs denotes the temperature-sampling rate.

Formation of Innovative Territorial Clusters in the Regions of Russia

Introduction. The modern development of Russia is based on the priority development of high-tech industries and the corresponding infrastructure as prerequisites for achieving technical and technological leadership in the global economy. The innovative development of the country largely depends on the success of scientific and technological policy at the regional level. The purpose of the study is to analyze the spatial regularities of the functioning of innovative territorial clusters to justify promising directions of state cluster policy. Materials and Methods. The study was carried out on the basis of official statistical information of the Federal State Statistics Service, information and analytical reports of the Association of Clusters, Technoparks and Special Economic Zones of Russia, official ratings of innovative development of regions, legislative acts of the federal and regional levels. Based on geo-information technologies, a series of analytical maps have been created that reflect and visualize various aspects of the functioning of innovative territorial clusters in the context of all regions of the Russian Federation. Results. Spatial patterns of the formation of innovative territorial clusters in the regions of Russia have been identified. It is noted that the implementation of the cluster policy contributes to a more rational use of federal budget funds by determining priority investment areas and establishing on this basis the recipients of state support in the cluster with the greatest potential in the context of limited financial resources. This is especially promising when justifying the stimulation of new high-tech industries and enterprises. The patterns of functioning and development trends of innovative territorial clusters are identified. Promising directions for improving Russia’s cluster policy are formulated. Discussion and Conclusion. The author considers that the main purpose of the emerging innovative territorial clusters is the saturation of the domestic market with high-tech goods, services and technologies to achieve the technological independence of the country. The results of the study can be used by organizations and decision makers to substantiate ways to improve cluster policy in the regions of the country.

Multifractal Characteristics of Uranium Grade Distribution and Spatial Regularities in a Sandstone-Type Uranium Deposit in Xinjiang, China

Based on an analysis of the spatial distribution of uranium grade in 338 boreholes of a uranium deposit in Xinjiang, the enrichment and spatial variation of uranium ore in two stopes of the deposit are discussed using multifractal theory. The distribution characteristics of the uranium ore of the two stopes are studied by multifractal parameters: the scaling exponent of mass τ(q), the scaling exponent α(q) of each sub-set and its corresponding fractal dimension f(α), the fractal dimension D0 and information dimension D1. The differences of uranium distribution in the two stopes can be quantified well by using multifractal spectrum and multifractal parameters such as Δα, Δf and R. After a comprehensive multifractal distribution analysis, 10 m × 10 m is defined as a fence unit, and the window sizes ε=3,6,9⋯,45 are set; the singularity exponents α of the two stopes are calculated by using this element concentration–area method. The results show that the multifractal theory and model can organically combine spatial structure information, scale change information and anisotropy information to obtain low-grade and weak mineral resources information and can effectively distinguish complex and superimposed anomalies. This will provide a basis for the local concentration and spatial variation rules of uranium distribution and the design of the parameters of the leaching uranium mining well site.

Completeness out of incompleteness: Inferences from regularities in imperfect information ensembles.

Handling imperfect information problems is fundamental to perception, learning, and decision-making. Ensemble perception may partially overcome imperfect information by providing global clues. However, if not all cluster elements are readily accessible, the observations required for computing statistics are incomplete. In this case, these elements' internal correlations (i.e., regularity) could serve as clues to elucidate the missing pieces. We thus investigated spatial regularity's role in ensemble perception under imperfect information situations created using partially occluded stimuli. In two experiments, we manipulated circle size (Experiment 1) and line orientation (Experiment 2) to linearly vary with its location; spatial regularity thus supplied clues for inferring information of the invisible parts. Participants estimated the mean of the targeted feature of the entire cluster, including visible and invisible parts. We observed robust biases toward the overall cluster in the estimations, implying the invisible parts were considered during ensemble perception. We proposed this effect could be understood as assessing evidence from visible parts to construct the missing parts. Experiment 3 employed a periodicity regularity to deter participants from using specific strategies, and consistent results were found. We then developed a generative model, the Regularity-Based Model, to simulate the inference process, which better captured the pattern of human outcomes than the comparative model. These findings indicate the visual system could use high-level structural information to infer scenes with incomplete information, thus producing more accurate ensemble representations. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Learning dynamic spatial-temporal regularized correlation filter tracking with response deviation suppression via multi-feature fusion

Visual object tracking (VOT) for intelligent video surveillance has attracted great attention in the current research community, thanks to advances in computer vision and camera technology. Meanwhile, discriminative correlation filter (DCF) trackers garnered significant interest owing to their high accuracy and low computing cost. Many researchers have introduced spatial and temporal regularization into the DCF framework to achieve a more robust appearance model and further improve tracking performance. However, these algorithms typically set fixed spatial and temporal regularization parameters, which limit flexibility and adaptability under cluttered and challenging scenarios. To overcome these problems, in this work, we propose a new dynamic spatial–temporal regularization for the DCF tracking model that emphasizes the filter to concentrate on more reliable regions during the training stage. Furthermore, we present a response deviation-suppressed regularization term for responses to encourage temporal consistency and avoid model degradation by suppressing relative response changes between two consecutive frames. Moreover, we introduce a multi-memory tracking framework to exploit various features and each memory contributes to tracking the target across all frames. Significant experiments on the OTB-2013, OTB-2015, TC-128, UAV-123, UAVDT, and DTB-70 datasets have revealed that the performance thereof outperformed many state-of-the-art trackers based on DCF and deep-based frameworks in terms of tracking accuracy and tracking success rate.

Related Variety and Regional Development: A Critique

Evolutionary approaches in economic geography have contributed substantially to the growing body of knowledge of regional development processes and their underlying mechanisms. One key concept in the literature on evolutionary economic geography is that of related variety. Herein, regional industry structure is represented through the level of related variety of technologies, skills, or outputs. The related variety concept proposes that regional economic development is favored when an economy diversifies into products or technologies that are closely related to the stock of existing activities. In this article, we raise substantive questions regarding the internal logic of the concept of related variety, its spatial expressions, measurement specifics, empirical regularities and biases, and its possible short- and long-term effects on regional development. Based on this investigation, we make suggestions for improvements to future research.

Error Estimation and Optimization of the Direct Simulation Monte Carlo Method Taking into Account Spatial Regularization

The direct simulation Monte Carlo method is widely used for solving rarefied gas dynamics problems. The focus in this paper is on the study of the error introduced by spatial regularization of the interaction between two particles. Two approaches to spatial regularization and three direct simulation Monte Carlo algorithms implementing these approaches are considered. An upper bound on the error of these algorithms in the metric of the space of continuous functions is constructed, and conditionally optimal parameters that guarantee a prescribed error level in probability are obtained. Using the classical Fourier problem as an example, the error introduced by regularization is numerically investigated, and the constructed conditionally optimal parameters are tested.

Selection errors: How do target and distractor features affect attentional capture and learning of spatial distractor regularities?

Selection errors: How do target and distractor features affect attentional capture and learning of spatial distractor regularities?