Second-order Connectivity Research Articles

Visual Micro-Pattern Propagation.

Statistic observations demonstrate that visual feature patterns or structure patterns recur high-frequently within/across homo/heterogeneous images. Motivated by the interdependencies of visual patterns, we propose visual micro-pattern propagation (VMPP) to facilitate universal visual pattern learning. Especially, we present a graph framework to unify the conventional micro-pattern propagations in spatial, temporal, cross-modal and cross-task domains. A general formulation of pattern propagation named cross-graph model is presented under this framework, and accordingly a factorized version is derived for more efficient computation as well as better understanding. To correlate homo/heterogeneous patterns, in cross-graph we introduce two types of pattern relations from feature-level and structure-level. The structure pattern relation defines second-order visual connections for heterogeneous patterns by measuring first-order visual relations of homogeneous feature patterns. In virtue of the constructed first-/second-order connections, we design feature pattern diffusion and structure pattern diffusion to prop up various pattern propagation cases. To fulfill different pattern diffusions involved, further, we deeply study two fundamental visual problems, multi-task pixel-level prediction and online dual-modal object tracking, and accordingly propose two end-to-end pattern propagation networks by encapsulating and integrating some necessary diffusion modules therein. We conduct extensive experiments by dissecting every diffusion component as well as comparing numerous advanced methods. The experiments validate the effectiveness of our proposed various pattern diffusion ways and meantime report the state-of-the-art results on the two representative visual problems.

Who Matters Most? Migrant Networks, Tie Strength, and First Rural–Urban Migration to Dakar

Social networks' influence on migration has long been explored largely through the lenses of cumulative causation and social capital theory. This article aims to reconceptualize elements of these theories for the case of rural-urban migration and test their utility in explaining first-migration timing. We use a uniquely extensive social network survey linked to prospectively collected migration data in rural Senegal. We decompose migrant networks into return migrants, current migrants, and nonmigrant residents of the destination to capture heterogeneity in migration-relevant social capital. As expected, the number of nonmigrant alters living in the capital, Dakar, has an outsized association with the migration hazard, the number of current migrants from the village living in Dakar has a smaller association, and the number of return migrants has little association. Drawing on social capital theory, we test the influence of (1) subjectively assessed tie strength between the ego and their network alters and (2) structurally weak ties measured through second-order ("friend of a friend") connections. Weak and strong subjective ties to current migrants and nonmigrant Dakar residents are positively associated with the first-migration hazard. Structurally weak ties to current migrants are too, but only for individuals with no direct ties to current migrants.

The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics' Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.

Study on quantitative structure-biodegradability relationships of amine collectors by GFA-ANN method

In this study, the biodegradability of 17 amine collectors, categorized by fatty amine, quaternary ammonium compounds and oxygen-containing amine collectors, are tested with the Closed Bottle Test for 90 days, and the results indicate most amine collectors are not readily biodegradable. The oxygen-containing amine collectors have the best biodegradability due to the introduced oxygen-containing functional groups, subsequently fatty amine collectors with branched chains, while the tested quaternary ammonium compounds all have poor biodegradation ability. Besides, we search for and calculate 35 molecular descriptors to develop the quantitative structure biodegradability relationship (QSBR) of amine collectors. With the Genetic Function Approximation (GFA) algorithm, two sets of important molecular descriptors related to biodegradability (q) of amine collectors are selected from 35 molecular descriptors. Based on internal and external validations, the robust and reliable non-linear QSBR model with the squared correlation coefficient above 0.99 is determined via Artificial Neural Network (ANN) method, where the descriptors are respectively CL, N, ELUMO, δv2, indicating the biodegradable ability of amine collectors is correlated with the alkyl chain lengths (CL), the number of nitrogen atom-containing compounds (N), energy of the lowest unoccupied molecular orbital (ELUMO) and valence second-order connectivity index (δv2).

Brain Resilience: The Effect of White Matter Disease on Brain Networks in Cognitively Normal Older Adults

Brain pathologies are increasingly understood to confer mobility risk, but the malleability of functional brain networks may be a mechanism for mobility reserve. In particular, white matter hyperintensities (WMH) are strongly associated with mobility and alter functional network connectivity. To assess the potential role of brain networks as a mechanism of mobility reserve, 116 participants with MRI from the Brain Networks and Mobility Function (B-NET) were categorized into 4 groups based on median splits of SPPB scores and WMH burden: Expected Healthy (EH: low WMH, SPPB>10, N=45), Expected Impaired (EI: high WMH, SPPB10, N=24), Unexpected Impaired (EI: low WMH, SPPB<10, N=10) and Unexpected Unhealthy (UH: low WMH, SPPB<10, N=37). Functional brain networks were calculated using graph theory methods and white matter hyperintensities were quantified with the Lesion Segmentation Toolbox (LST) in SPM12. Somatomotor cortex community structure (SMC-CS) was similar between UH and EH with both having higher consistency than EI and UI. However, UH displayed a unique increase in second-order connections between the motor cortex and the anterior cingulate. It is possible that this increase in connections is a signal of higher reserve or resilience in UH participants and may indicate a mechanism of compensation in regards to mobility function and advanced WMH burden. These data suggest functional brain networks may be a mechanism for mobility resilience in older adults at mobility risk due to WMH burden.

EFFECTS OF FUNCTIONAL BRAIN NETWORKS AND WHITE MATTER DISEASE ON MOBILITY OF OLDER ADULTS IN AN EXERCISE INTERVENTION

Declining mobility is associated with increased accumulation of white matter hyperintensities (WMH). However, a high WMH burden is not always accompanied by impaired mobility. Our previous work demonstrates that some variance in mobility may be explained by brain network connectivity. Here, we extended this work by measuring WMHs and brain networks in older adults participating in a lifestyle intervention. The Short Physical Performance Battery (SPPB) and resting state functional magnetic resonance imaging (fMRI) were collected before and after a 5-month caloric restriction plus aerobic exercise intervention in 57 obese, sedentary adults aged 65-78. Participants were categorized based on median splits of baseline SPPB scores and WMH burden: Expected Healthy (EH: low WMH, SPPB≥11, n=16), Expected Impaired (EI: high WMH, SPPB≤10, n=17), Unexpected Healthy (UH: high WMH, SPPB≥11, n=12), and Unexpected Impaired (UI: low WMH, SPPB≤10, n=12). Graph theory-based methods were used to characterize brain networks and compare the four groups. At baseline, the somatomotor cortex community structure (SMC-CS) was less consistent in EI (p=0.05) and UI (p=0.23) compared to EH. The EI (mean=1.25, p=0.003) and UI (mean=1.57, p=0.001) significantly improved their SPPB scores following the intervention. Although both groups had equivalent SPPB scores, SMC-CS was less consistent in the UH than EH (p=0.16). However, UH displayed a significant (p=0.004) increase in second-order connections to the precuneus compared to EH. These data suggest that studying brain networks could improve the understanding of the development of mobility disability and the CNS contributions to mobility independent of white matter disease.

Fractal algorithm for 3D‐printed continuous porous scaffold design

In practice, 3D modelling software, such as UG and Pro/E, are commonly adopted to design porous scaffolds within given contours. However, this manual method is quite time-consuming and complicated with poor adaptability. In this study, a novel facial algorithm is proposed for smart scaffold design. By forming a dendritic fractal network, the second-order uniformity and complete connectivity of pores are guaranteed while considering the axial symmetry of certain orthopaedic implants, and the algorithm is adapted for concave and hollow contour shapes. Through experiments, the stability of the algorithm and the characteristics of the two vital performance indicators, i.e. porosity P and surface area ratio R, are studied. The results show that P and R of the generated model are insensitive to the shape of the input model, which proves the stability of authors’ method, and the maximum available porosity reaches 78%, higher than the maximum effective porosity found in the literature.

Нормали на многообразии и порождающие их отображения

The first- and second-order canonical forms are considered on a smooth m-manifold. The approach connected with coordinate expressions of basic and fiber forms, and first- and second-order tangent vectors on a manifold is implemented. It is shown that the basic first- and secondorder tangent vectors are first- and second-order Pfaffian (generalized) differentiation operators of functions set on a manifold. Normals on a manifold are considered. Differentials of the basic first-order (second-order) tangent vectors are linear maps from the first-order tangent space to the second-order (third-order) tangent space. Differentials of the basic first-order tangent vectors (basic vectors of the first-order normal) set a map which takes a first-order tangent vector into the second-order normal for the first-order tangent space of (into the third-order normal for second-order tangent space). The map given by differentials of the basic first-order tangent vectors takes all tangent vectors to the vectors of the second-order normal. Such splitting the osculating space in the direct sum of the first-order tangent space and second-order normal defines the simplest (canonical) affine connection which horizontal subspace is the indicated normal. This connection is flat and symmetric. The second-order normal is the horizontal subspace for this connection. Derivatives of some basic vectors in the direction of other basic vectors are equal to values of differentials of the first vectors on the second vectors, and the order of differentials is equal to the order of vectors along which differentiation is made. The maps set by differentials of basic vectors of r-order normal for (r – 1)-order tangent space take the basic first-order tangent vectors to the basic vectors of (r + 1)-order normal for r-order tangent space. Horizontal vectors for the simplest second-order connection are constructed. Second-order curvature and torsion tensors vanish in this connection. For horizontal vectors of the simplest second-order connection there is the decomposition by means of the basic vectors of the secondand third-order normals.

Correlation analysis of the π-electronic energy and the second-order general connectivity index for benzenoid chains

Benzenoid chains are natural graph representations of chain hydrocarbons. For a given benzenoid chain [Formula: see text], we find an expression of its second-order general connectivity index, denoted by [Formula: see text], in terms of inlet features of [Formula: see text]. It is also shown that the second-order general connectivity index [Formula: see text] correlates well with the [Formula: see text]-electronic energy of [Formula: see text] for [Formula: see text], especially for [Formula: see text].

Sharp Bounds for the Second-Order General Connectivity Index of Hexagonal Chains

Given H, a hexagonal chain, we determine an expression of its second-order general connectivity index, denoted by χ2α(H), in terms of inlet features of H. Moreover, by applying the method in integer programming theory, we completely determine the extremal chains with the minimal or maximal χ2α(H) over the set of hexagonal chains.

Beet Root Juice: An Ergogenic Aid for Exercise and the Aging Brain.

Exercise has positive neuroplastic effects on the aging brain. It has also been shown that ingestion of beet root juice (BRJ) increases blood flow to the brain and enhances exercise performance. Here, we examined whether there are synergistic effects of BRJ and exercise on neuroplasticity in the aging brain. Peak metabolic equivalent (MET) capacity and resting-state magnetic resonance imaging functional brain network organization are reported on 26 older (mean age = 65.4 years) participants randomly assigned to 6 weeks of exercise + BRJ or exercise + placebo. Somatomotor community structure consistency was significantly enhanced in the exercise + BRJ group following the intervention (MBRJ = -2.27, SE = 0.145, MPlacebo = -2.89, SE = 0.156, p = .007). Differences in second-order connections between the somatomotor cortex and insular cortex were also significant; the exercise + BRJ group (M = 3.28, SE = 0.167) had a significantly lower number of connections than exercise + placebo (M = 3.91, SE = 0.18, p = .017) following the intervention. Evaluation of peak MET capacity revealed a trend for the exercise + BRJ group to have higher MET capacity following the intervention. Older adults who exercised and consumed BRJ demonstrated greater consistency within the motor community and fewer secondary connections with the insular cortex compared with those who exercised without BRJ. The exercise + BRJ group had brain networks that more closely resembled those of younger adults, showing the potential enhanced neuroplasticity conferred by combining exercise and BRJ consumption.

Aspects of randomness in neural graph structures.

In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the presence of serious uncertainties, such as major undersampling of the experimental data. In the specific case of neural systems, however, a few moderately robust experimental reconstructions have been reported, and these have long served as fundamental prototypes for studying connectivity patterns in the nervous system. In this paper, we provide a comparative analysis of these "historical" graphs, both in their directed (original) and symmetrized (a common preprocessing step) forms, and provide a set of measures that can be consistently applied across graphs (directed or undirected, with or without self-loops). We focus on simple structural characterizations of network connectivity and find that in many measures, the networks studied are captured by simple random graph models. In a few key measures, however, we observe a marked departure from the random graph prediction. Our results suggest that the mechanism of graph formation in the networks studied is not well captured by existing abstract graph models in their first- and second-order connectivity.

Graph Theory Analysis of Functional Brain Networks and Mobility Disability in Older Adults

The brain's structural integrity is associated with mobility function in older adults. Changes in function may be evident earlier than changes in structure and may be more directly related to mobility. Therefore, we assessed whether functional brain networks varied with mobility function in older adults. Short Physical Performance Battery (SPPB) and resting state functional magnetic resonance imaging were collected on 24 young (mean age = 26.4±5.1) and 48 older (mean age = 72.04±5.1) participants. Older participants were divided into three groups by SPPB score: Low SPPB (score = 7-9), Mid SPPB (score = 10), High SPPB (score = 11-12).Graph theory-based methods were used to characterize and compare brain network organization. Connectivity in the somatomotor cortex distinguished between groups based on SPPB score. The community structure of the somatomotor cortex was significantly less consistent in the Low SPPB group (mean = 0.097±0.05) compared with Young (mean = 0.163±0.09, p = .03) SPPB group. Striking differences were evident in second-order connections between somatomotor cortex and superior temporal gyrus and insula that reached statistical significance. The Low SPPB group (mean = 140.87±109.30) had a significantly higher number of connections than Young (mean = 45.05±33.79, p = .0003) or High (mean = 49.61±35.31, p = .002) SPPB group. Older adults with poorer mobility function exhibited reduced consistency of somatomotor community structure and a greater number of secondary connections with vestibular and multisensory regions of the brain. Further study is needed to fully interpret these effects, but analysis of functional brain networks adds new insights to the contribution of the brain to mobility.

Factors associated with high-frequency illicit methadone use among rural Appalachian drug users

Background: In recent years there has been a sharp increase in the use of illicit methadone as well as methadone-related overdose deaths. Objective: The purpose of this study was to describe factors associated with low- and high-frequency methadone use in a cohort of rural Appalachian drug users. Methods: Interviews assessing sociodemographics, illicit drug use and drug treatment, psychiatric disorders, health and sociometric drug network characteristics were conducted with 503 rural drug users between 2008 and 2010. A two-level mixed effects regression model was utilized to differentiate low- (one use per month or less in the past six months) versus high-frequency (daily or weekly use in the past six months) illicit methadone users. Results: The lifetime prevalence of illicit methadone use in this population was 94.7% (n = 476) and slightly less than half (46.3%) were high-frequency users. In the mixed effects regression model, initiating illicit methadone use at a younger age was associated with high-frequency illicit methadone use. Taking a prescribed medication for a physical problem, undergoing additional weeks of outpatient drug free treatment, daily OxyContin® use in the past month, and having fewer ties and second-order connections in the drug network reduced the odds of high-frequency illicit methadone use. Conclusions: Rates of illicit methadone use and high-frequency illicit methadone use among this sample of rural drug users were considerably higher than those previously reported in the literature. Health practitioners in rural areas should routinely screen for illicit opioid use, including methadone.

Simultaneously emerging Braitenberg codes and compositionality

Although many researchers have suggested that compositional concepts should be sensorimotor grounded, the method to accomplish this remains unclear. This article introduces a second-order neural network with parametric biases (sNNPB) that learns compositional structures based on sensorimotor time series data. The data was produced by a simulated robot that executed distinct object interactions (move-to and orient-toward). We show that various sNNPB setups can learn to compositionally imitate object interactions beyond the interactions that were specifically trained, which was not possible with previous neural network (NN) architectures, including recurrent neural networks (RNNs). We also show that these imitation capabilities are accomplished by developing a self-organized, geometrically arranged compositional concept structure in the PB values and task-oriented, Braitenberg-like sensory encodings in hidden sensory layers. Because second-order connections were necessary to accomplish the task, we hypothesize that such connections may be essential to drive the learning of both sensorimotor-grounded compositional structures and Braitenberg-like, behavior-oriented ‘‘pro-presentations.’’ From a cognitive perspective, we show how sensorimotor time series of interactions may be processed to generate the signals necessary to develop semantically compositional structures.

Higher order Hessian structures on manifolds

In this paper we define nth order Hessian structures on manifolds and study them. In particular, whenn = 3, we make a detailed study and establish a one-to-one correspondence betweenthird-order Hessian structures and acertain class of connections on the second-order tangent bundle of a manifold. Further, we show that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also we define second-order geodesics of special second-order connection which gives a geometric characterization of symmetric third-order Hessian structures.

Environmentally-benign transition metal catalyst design using optimization techniques

Transition metal catalysts play a crucial role in many industrial applications, including the manufacture of lubricants, smoke suppressants, corrosion inhibitors and pigments. The development of novel catalysts is commonly performed using a trial-and-error approach which is costly and time-consuming. The application of computer-aided molecular design (CAMD) to this problem has the potential to greatly decrease the time and effort required to improve current catalytic materials in terms of their efficacy and biological effects. This work applies an optimization approach to redesign environmentally-benign homogeneous catalysts, specifically those which contain transition metal centers, to improve certain physical properties. Two main tasks must be achieved in order to perform the molecular design of a novel catalyst: biological and chemical properties must be estimated directly from the molecular structure, and the resulting optimization problem must be solved in a reasonable time. In this work, connectivity indices are used for the first time to predict the physical properties of a homogeneous catalyst. The existence of multiple oxidation states for transition metals requires a reformulation of the original equations for these indices. Once connectivity index descriptors have been defined for transition metal catalysts, structure–property correlations are then developed based on regression analysis using literature data for various properties of interest, including toxicity and electronegativity. These structure–property correlations are then used within an optimization framework to design novel homogeneous catalyst structures for use in a given application. The use of connectivity indices which define the topology of the molecule within the formulation guarantees that a complete molecular structure is obtained when the global optimum is found. In this work, second-order connectivity indices are used to obtain more information about steric features of the catalyst molecules, and non-linear correlations are employed to improve the accuracy of the property prediction equations. The structure–property correlations are then combined with linear structural feasibility constraints to form a mixed-integer non-linear program (MINLP), which when solved to optimality results in a catalyst molecule which most closely matches given property targets. To solve the resulting optimization problem, two methods are applied: Tabu search (a stochastic method), and outer approximation, a deterministic approach. For the outer approximation solution, a data structure is used which permits all equations except for the property prediction expressions to be written in linear forms. The computational efficiency of Tabu search is not strongly dependent on the existence of non-linear constraints, so for solution using this method, a non-linear form for the second-order connectivity index was chosen, which decreases the number of binary variables required. The solution methods are compared using three examples involving the design of environmentally-benign homogeneous catalysts containing molybdenum centers. Results show the efficacy of the formulation, and provide evidence that the Tabu search algorithm is more suitable for this type of molecular design algorithm than the commercially available deterministic approach.

Physicochemical Interpretation of Molecular Connectivity Indices

Molecular connectivity indices are identified as components of the molecular accessibility. The first- and second-order connectivity indices represent molecular accessibility areas and volumes, respectively, whereas higher order indices represent magnitudes in higher dimensional spaces. In identifying accessibility perimeters, we recognized the atom degrees as a measure of the accessibility perimeter of the corresponding atom. The Randic and connectivity indices are identified as the two components of the molecular accessibility area. The accessibility perimeter is computed here from the van der Waals and covalent radii of the atoms and the overlapping angle between the van der Waals circumferences of bonded atoms. The description of the accessibility area in terms of the first-order Randic and connectivity indices accounts for the success of these descriptors in correlating different physicochemical and biological properties because they are a measure of the extension of intermolecular interactions. A th...

Differentiable Connections with Poincar{e} Groups of Local Transformations. {III}

In the canonical smooth fiber bundles Π:∝n+1↑∝n, we study generalized differentiable connections constructed by the author in papers [4] and [5]. Special emphasis is laid on the investigation of the behavior of these connections under local transformations of the classical Poincar{e} groups ℙ(1,n) and extended Poincar{e} groups \(\tilde {\mathbb {P}}(1,n)\) canonically acting in the given connections. We found all first-order nonholonomic affine, Γ1, Γ2, and Γ1,2-connections with the groups ℙ(1,n) and \(\tilde {\mathbb {P}}(1,n)\) of local transformations and also constructed classes of the corresponding invariant second-order connections.

Goal Directed Adaptive Behavior in Second-Order Neural Networks: The MAXSON family of architectures

The paper presents a neural network architecture (MAXSON) based on second-order connections that can learn a multiple goal approach/avoid task using reinforcement from the environment. It also enables an agent to learn vicariously, from the successes and failures of other agents. The paper shows that MAXSON can learn certain spatial navigation tasks much faster than traditional Q-learning, as well as learn goal directed behavior, increasing the agent's chances of long-term sur vival. The paper shows that an extension of MAXSON (V-MAXSON) enables agents to learn vicariously, and this improves the overall survivability of the agent population.