Graph limits and parameter testing

Previous research has revealed the uniqueness-facilitation effect in the multiple object tracking (MOT) task: simple distinct identities and surface features of moving targets could facilitate attentional tracking. By adapting compound stimuli, the present study investigated whether the global or local properties played the main role in the uniqueness-facilitation effect in the MOT task. The uniqueness of local properties, of global properties or of both local and global properties were considered. Observers’ tracking performance in alternative conditions were compared with that in the homogeneous condition wherein all stimuli have identical local and global properties. Results from two experiments suggest that the global properties played the key role in facilitating tracking. The distinctiveness of local properties can also facilitate tracking with global properties being homogeneous. However, when the stimuli’s global properties are distinct from each other—whether the local properties being unique or not—observers’ tracking performance can achieve the same level as that in the unitary-uniqueness condition wherein the moving objects were distinct unitary letters. These results revealed a global superiority effect in the MOT task. Finally, the facilitation effects of the global and local properties might depend on the stimulus sparsity. When the compound stimuli had fewer local elements, the uniqueness facilitation effect on tracking decreased.

Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a region do not invalidate properties stated about the remainder of the heap. This concept is key to enabling modular reasoning and also extends to concurrency. While heaps are naturally related to mathematical graphs, many ubiquitous graph properties are non-local in character, such as reachability between nodes, path lengths, acyclicity and other structural invariants, as well as data invariants which combine with these notions. Reasoning modularly about such graph properties remains notoriously difficult, since a local modification can have side-effects on a global property that cannot be easily confined to a small region. In this paper, we address the question: What separation algebra can be used to avoid proof arguments reverting back to tedious global reasoning in such cases? To this end, we consider a general class of global graph properties expressed as fixpoints of algebraic equations over graphs. We present mathematical foundations for reasoning about this class of properties, imposing minimal requirements on the underlying theory that allow us to define a suitable separation algebra. Building on this theory we develop a general proof technique for modular reasoning about global graph properties over program heaps, in a way which can be integrated with existing separation logics. To demonstrate our approach, we present local proofs for two challenging examples: a priority inheritance protocol and the non-blocking concurrent Harris list.

Minimal reducible bounds for induced-hereditary properties

In this paper we study the relationships between local and global properties in networks of dynamical systems by focusing on two global properties, synchronization and peak-to-peak dynamics, and on two local properties, coherence of the components of the network and coupling strength. The analysis is restricted to networks of low-dimensional chaotic oscillators, i.e. oscillators which have peak-to-peak dynamics when they work in isolation. The results are obtained through simulation, first by considering pairs of coupled Lorenz, Rössler and Chua systems, and then by studying the behavior of spatially extended tritrophic food chains described by the Rosenzweig–MacArthur model. The conclusion is that synchronization and peak-to-peak dynamics are different aspects of the same collective behavior, which is easily obtained by enhancing local coupling and coherence. The importance of these findings is briefly discussed within the context of ecological modeling.

This study compared adults (Homo sapiens), young children (Homo sapiens), and adult tamarins (Saguinus oedipus) while they discriminated global and local properties of stimuli. Subjects were trained to discriminate a circle made of circle elements from a square made of square elements and were tested with circles made of squares and squares made of circles. Adult humans showed a global bias in testing that was unaffected by the density of the elements in the stimuli. Children showed a global bias with dense displays but discriminated by both local and global properties with sparse displays. Adult tamarins' biases matched those of the children. The striking similarity between the perceptual processing of adult monkeys and humans diagnosed with autism and the difference between this and normatively developing human perception is discussed.

Cellular systems are organized as a complex web of interactions among numerous macromolecules. Among the others, proteins are important since they play important role in virtually every biological process that occurs in the cell. Cellular systems are constantly challenged by fluctuations in the surrounding environment. In response, repertoire of the protein contents in the cell constantly alters, accordingly the interactions among them. Mathematically, these protein–protein interactions (PPIs) can be conceptualized in the form of graph or network for ease in analysis. A node in the graph represents protein and its link with other node is represented by edge. The local and global topological properties of the network reveal organization principles of underlying interactions among total proteins of an organism. The local properties specify importance of a particular protein in the network whereas global properties reflect their organization operational in the cell. Over the years, several graph theoretic and clustering techniques proposed for analysis of complex physical world have been applied to understand dynamic organization of the cellular networks. These methods promise to become more informative as the high quality PPI networks increase by orders of magnitude. This chapter provides an overview on various topological properties of networks and their significance in understanding biological systems.

Abnormal cortical folding is commonly linked to disease and has the potential to be used as an early biomarker. Current methods of assessing the cortex usually require two-dimensional (2D) manual measurements or are designed for MRI scans. We propose the first automated method to measure both local and global properties of the 3D developing cortical plate from ultrasound volumes. We analyse the lesser studied second trimester, as it has the potential to be used as a biomarker for early detection of cortical malformations. Transabdominal fetal brain ultrasound volumes collected as part of INTERGROWTH-21st were used throughout this work. The cortical plate was manually annotated on a set of ultrasound atlases between 18–22 weeks of gestation and propagated back onto 307 individual volumes. A deep neural network was trained to segment the cortex using 75% of the scans and tested on the remaining 25%. Each segmented cortex was further analysed, measuring global properties such as surface area and volume, and local properties such as curvature, thickness, and depth from skull. Our deep learning network accurately segmented each cortical plate in under 2 seconds, with a Dice accuracy of 80 ± 2%. The surface area and volume of the cortical were found to span 39.1-111.7cm2 and 4.4-17.2cm3, respectively, which follows the growth curves previously measured from fetal MRI studies in the third trimester. The segmented cortical surfaces and local measurements can be seen in figure 1, showing the Sylvian fissure depth increase from 4 to 9 mm. Our method accurately assesses the developing cortex in 3D using deep learning. This method has the potential to become routine to assess development and compare growth and gyrification between different fetal cohorts. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

ObjectiveThis study aimed to examine the alterations in gray matter networks related to tau retention in Alzheimer's disease (AD) patients and cognitively normal (CN) older individuals.MethodsEighteen amyloid-positive AD patients and 30 age- and sex-matched amyloid-negative CN controls were enrolled. All underwent 3D T1-weighted MRI, amyloid positron-emission tomography imaging (PET) with 11C-Pittsburgh Compound B (PiB), and tau PET with 18F-THK5351. The structural networks extracted from the T1-weighted MRI data based on cortical similarities within single subjects were analyzed. Based on graph theoretical approach, global and local network properties across the whole brain were computed. Group comparisons of global and local network properties were evaluated between the groups. Then, we correlated the global and local network measures with total cerebral 18F-THK5351 retention.ResultsAD patients moved toward more randomized global network compared to controls and regional differences were observed in the default mode network (DMN) area. No significant correlations existed between global network properties and tau retention. On a local level, AD and controls showed opposite relationships between network properties and tau retention mainly in the DMN areas; CN controls showed positive correlations, whereas AD showed negative correlations.ConclusionWe found opposite relationships between local network properties and tau retention between amyloid-positive AD patients and amyloid-negative controls. Our findings suggest that the presence of amyloid and induced exacerbated tau retention alter the relationship of local network properties and tau retention.

This paper reports a study that has established the possibility of improving the effectiveness of the method of figurative transformations in order to minimize symmetrical Boolean functions in the main and polynomial bases. Prospective reserves in the analytical method were identified, such as simplification of polynomial function conjuncterms using the created equivalent transformations based on the method of inserting the same conjuncterms followed by the operation of super-gluing the variables. The method of figurative transformations was extended to the process of minimizing the symmetrical Boolean functions with the help of algebra in terms of rules for simplifying the functions of the main and polynomial bases and developed equivalent transformations of conjuncterms. It was established that the simplification of symmetric Boolean functions by the method of figurative transformations is based on a flowchart with repetition, which is the actual truth table of the assigned function. This is a sufficient resource to minimize symmetrical Boolean functions that makes it possible to do without auxiliary objects, such as Karnaugh maps, cubes, etc. The perfect normal form of symmetrical functions can be represented by binary matrices that would represent the terms of symmetrical Boolean functions and the OR or XOR operation for them. The experimental study has confirmed that the method of figurative transformations that employs the 2-(n, b)-design, and 2-(n, x/b)-design combinatorial systems improves the efficiency of minimizing symmetrical Boolean functions. Compared to analogs, this makes it possible to enhance the productivity of minimizing symmetrical Boolean functions by 100‒200 %. There are grounds to assert the possibility of improving the effectiveness of minimizing symmetrical Boolean functions in the main and polynomial bases by the method of figurative transformations. This is ensured, in particular, by using the developed equivalent transformations of polynomial function conjuncterms based on the method of inserting similar conjuncterms followed by the operation of super-gluing the variables.

A jump to the bell number for hereditary graph properties

Love, Rouder, and Wisniewski (1999) and Ripoll and Marty (2005) showed that subjects could process global properties very quickly in a same/different task on abstract visual scenes for which the conspicuity of local and global properties had been controlled. In this new experiment, two important new factors were manipulated: saliency of the global pattern and location of local similarity. The results showed that the saliency of the global form as well as the location of local similarity determines the strength of global and local effects. Global effects continue to manifest themselves even when the extraction of the global form is difficult. Finally, the whole pattern of results suggests that local and global processing proceeds simultaneously and involves two attentional systems whose spatial characteristics are very different.

Recent studies suggest that the autoantibodies against adrenergic/muscarinic receptors might be one of the causes and potential markers of myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS). The purpose of this study was to investigate the structural network changes related to autoantibody titers against adrenergic/muscarinic receptors in ME/CFS by performing a single-subject gray matter similarity-based structural network analysis. We prospectively examined 89 consecutive right-handed ME/CFS patients who underwent both brain MRI including 3D T1-wighted images and a blood analysis of autoantibodies titers against β1 adrenergic receptor (β1 AdR-Ab), β2 AdR-Ab, M3 acetylcholine receptor (M3 AchR-Ab), and M4 AchR-Ab. Single-subject gray matter similarity-based structural networks were extracted from segmented gray matter images for each patient. We calculated local network properties (betweenness centrality, clustering coefficient, and characteristic path length) and global network properties (normalized path length λ, normalized clustering coefficient γ, and small-world network value δ). We investigated the correlations between the autoantibody titers and regional gray matter/white matter volumes, the local network properties, and the global network properties. Betweenness centrality showed a significant positive correlation with β1-AdR-Ab in the right dorsolateral prefrontal cortex. The characteristic path length showed a significant negative correlation with β2-AdR-Ab in the right precentral gyrus. There were no significant correlations between the antibody titers and the regional gray matter/white matter volumes, and the global network properties. Our findings suggest that β1 AdR-Ab and β2 AdR-Ab are potential markers of ME/CFS.

The concept of nanoscopic-to-macroscopic homogenization of a sculptured thin film (STF) into a unidirectionally nonhomogeneous continuum is presented. The global constitutive properties of linear STFs are connected to the so-called local or reference constitutive properties by rotation dyadics. The local properties are obtained using the Bruggeman formalism for dielectric as well as bianisotropic STFs. Limitations of the presented approach are discussed, and some avenues for further theoretical research are suggested.

Introducing new technologies into infrastructure (wind turbines, electric vehicles, low-carbon materials and so on) often demands materials that are ‘critical’; their supply is likely to be disrupted owing to limited reserves, geopolitical instability, environmental issues and/or increasing demand. Non-critical materials may become critical if introduced into infrastructure, owing to its gigatonne scale. This potentially poses significant risk to the development of low-carbon infrastructure. Analysis of this risk has previously overlooked the relationship between the ‘local properties’ that determine the selection of a technology and the overall vulnerability of the system, a global property. Treating materials or components as elements having fixed properties overlooks optima within the local–global variable space that could be exploited to minimise vulnerability while maximising performance. In this study, a framework for such analysis is presented along with a preliminary measure of relative materials criticality by way of a case study (a wind turbine generator). Although introduction of critical materials (in this case, rare earth metals) enhances technical performance by up to an order of magnitude, the associated increase in criticality may be two or three orders of magnitude. Analysis at the materials and component levels produces different results; design decisions should be based on analysis at several levels.

On uniform convergence of linear operators on the probabilistic normed space