A Weighted Statistical Network Modeling Approach to Product Competition Analysis

Statistical network models have been used to study the competition among different products and how product attributes influence customer decisions. However, in existing research using network-based approaches, product competition has been viewed as binary (i.e., whether a relationship exists or not), while in reality, the competition strength may vary among products. In this paper, we model the strength of the product competition by employing a statistical network model, with an emphasis on how product attributes affect which products are considered together and which products are ultimately purchased by customers. We first demonstrate how customers’ considerations and choices can be aggregated as weighted networks. Then, we propose a weighted network modeling approach by extending the valued exponential random graph model to investigate the effects of product features and network structures on product competition relations. The approach that consists of model construction, interpretation, and validation is presented in a step-by-step procedure. Our findings suggest that the weighted network model outperforms commonly used binary network baselines in predicting product competition as well as market share. Also, traditionally when using binary network models to study product competitions and depending on the cutoff values chosen to binarize a network, the resulting estimated customer preferences can be inconsistent. Such inconsistency in interpreting customer preferences is a downside of binary network models but can be well addressed by the proposed weighted network model. Lastly, this paper is the first attempt to study customers’ purchase preferences (i.e., aggregated choice decisions) and car competition (i.e., customers’ co-consideration decisions) together using weighted directed networks.

The emergence of a collective sensory response threshold in ant colonies

The sensory response threshold is a fundamental biophysical property of biological systems that underlies many physiological and computational functions, and its systematic study has played a pivotal role in uncovering the principles of neural computation. Here, we show that ant colonies, which perform computational tasks at the group level, have emergent collective sensory response thresholds. Colonies respond collectively to step changes in temperature and evacuate the nest during severe perturbations. This response is characterized by a group-size dependent threshold, and the underlying dynamics are dominated by social feedback between the ants. Using a binary network model, we demonstrate that a balance between short-range excitatory and long-range inhibitory interactions can explain the emergence of the collective response threshold and its size dependency. Our findings illustrate how simple social dynamics allow insect colonies to integrate information about the external environment and their internal state to produce adaptive collective responses.

Search Efficient Binary Network Embedding

Traditional network embedding primarily focuses on learning a continuous vector representation for each node, preserving network structure and/or node content information, such that off-the-shelf machine learning algorithms can be easily applied to the vector-format node representations for network analysis. However, the learned continuous vector representations are inefficient for large-scale similarity search, which often involves finding nearest neighbors measured by distance or similarity in a continuous vector space. In this article, we propose a search efficient binary network embedding algorithm called BinaryNE to learn a binary code for each node, by simultaneously modeling node context relations and node attribute relations through a three-layer neural network. BinaryNE learns binary node representations using a stochastic gradient descent-based online learning algorithm. The learned binary encoding not only reduces memory usage to represent each node, but also allows fast bit-wise comparisons to support faster node similarity search than using Euclidean or other distance measures. Extensive experiments and comparisons demonstrate that BinaryNE not only delivers more than 25 times faster search speed, but also provides comparable or better search quality than traditional continuous vector based network embedding methods. The binary codes learned by BinaryNE also render competitive performance on node classification and node clustering tasks. The source code of the BinaryNE algorithm is available at https://github.com/daokunzhang/BinaryNE.

Mental Fatigue Has Great Impact on the Fractal Dimension of Brain Functional Network

Mental fatigue has serious negative impacts on the brain cognitive functions and has been widely explored by the means of brain functional networks with the neuroimaging technique of electroencephalogram (EEG). Recently, several researchers reported that brain functional network constructed from EEG signals has fractal feature, raising an important question: what are the effects of mental fatigue on the fractal dimension of brain functional network? In the present study, the EEG data of alpha1 rhythm (8-10 Hz) at task state obtained by a mental fatigue model were chosen to construct brain functional networks. A modified greedy colouring algorithm was proposed for fractal dimension calculation in both binary and weighted brain functional networks. The results indicate that brain functional networks still maintain fractal structures even when the brain is at fatigue state; fractal dimension presented an increasing trend along with the deepening of mental fatigue fractal dimension of the weighted network was more sensitive to mental fatigue than that of binary network. Our current results suggested that mental fatigue has great regular impacts on the fractal dimension in both binary and weighted brain functional networks.

A Large-Scale High-Density Weighted Structural Connectome of the Macaque Brain Acquired by Predicting Missing Links

As a substrate for function, large-scale brain structural networks are crucial for fundamental and systems-level understanding of primate brains. However, it is challenging to acquire a complete primate whole-brain structural connectome using track tracing techniques. Here, we acquired a weighted brain structural network across 91 cortical regions of a whole macaque brain hemisphere with a connectivity density of 59% by predicting missing links from the CoCoMac-based binary network with a low density of 26.3%. The prediction model combines three factors, including spatial proximity, topological similarity, and cytoarchitectural similarity—to predict missing links and assign connection weights. The model was tested on a recently obtained high connectivity density yet partial-coverage experimental weighted network connecting 91 sources to 29 target regions; the model showed a prediction sensitivity of 74.1% in the predicted network. This predicted macaque hemisphere-wide weighted network has module segregation closely matching functional domains. Interestingly, the areas that act as integrators linking the segregated modules are mainly distributed in the frontoparietal network and correspond to the regions with large wiring costs in the predicted weighted network. This predicted weighted network provides a high-density structural dataset for further exploration of relationships between structure, function, and metabolism in the primate brain.