Facile One-Pot Synthesis of White Emitting Gold Nano-cluster solutions composed of Red, Green and Blue Emitters

Gold nanoclusters (AuNC) have emerged as a new class of stable and biocompatible photo-emitters. While red emitting clusters comprising ca. 20-25 Au atoms are readily synthesized by several methods, smaller...

Cluster solutions in networks of weakly coupled oscillators on a 2D square torus

We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.

SEGMENTATION OF TREK AND TRAIL RACE RUNNERS AS TOURISTS

This paper seeks to supplement the theory of sports marketing with additional knowledge on the participants in trek and trail races, provide basis for better understanding of their motives and behavior. The research instrument is a questionnaire consisting of 30 questions where the first part concerns with behavior at races; the second part consists of statements about the motives and the third part of descriptive questions. There were 194 participants who were interviewed by an online survey. The statistical analysis was conducted using factor analysis and cluster analysis. Five different factors / types of motivation and behavior of trek and trail race runners were extracted. Cluster analysis was also conducted and three cluster solutions were retained. Implications for marketing practice, limitations of the research and recommendations for future research were also given.

Multistability of Globally Coupled Duffing Oscillators

We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized clusters, as a consequence of the bistability of individual oscillators. The multiplicity of these solutions, induced by the many possible ways of distributing the oscillators between the two clusters, implies that the ensemble can exhibit multistability. As the strength of coupling grows, however, the two-cluster solutions are replaced by a state of full synchronization. By a combination of analytical and numerical techniques, we study the existence and stability of two-cluster solutions. The role of the distribution of oscillators between the clusters and the relative prevalence of the two stable solutions are disclosed.

SELECTION OF THE NUMBER OF CLUSTERS IN K-MEAN ALGORITHM USING CLUSTER SOLUTION ENTROPY

The article discusses the problem of choosing the number of clusters in popular k-means clustering algorithm. It is noted that an unsuccessful choice of this hyper parameter can lead to the creation of a cluster structure the meaningful interpretation of which in the process of data mining leads to false conclusions and making incorrect management decisions based on them. The aim of the work is to develop a method for automatic selection of the number of clusters for k-means algorithm. The article provides an analytical review of the known methods for determining the number of clusters, their advantages and disadvantages being noted. The proposed approach is based on the elbow method, which uses the entropy of cluster solutions instead of the mean squares of clustering error. A practical example shows that the use of cluster solution entropy makes it possible to choose the number of clusters even in the case when the approach based on clustering error turns out to be untenable.

Spatially localized cluster solutions in inhibitory neural networks

Neurons in the inhibitory network of the striatum display cell assembly firing patterns which recent results suggest may consist of spatially compact neural clusters. Previous computational modeling of striatal neural networks has indicated that non-monotonic, distance-dependent coupling may promote spatially localized cluster firing. Here, we identify conditions for the existence and stability of cluster firing solutions in which clusters consist of spatially adjacent neurons in inhibitory neural networks. We consider simple non-monotonic, distance-dependent connectivity schemes in weakly coupled 1-D networks where cells make strong connections with their kth nearest neighbors on each side. Using the phase model reduction of the network system, we prove the existence of cluster solutions where neurons that are spatially close together are also synchronized in the same cluster, and find stability conditions for these solutions. Our analysis predicts the long-term behavior for networks of neurons, and we confirm our results by numerical simulations of biophysical neuron network models. Additionally, we add weaker coupling between closer neighbors as a perturbation to our network connectivity. We analyze the existence and stability of cluster solutions of the perturbed network and validate our results with numerical simulations. Our results demonstrate that an inhibitory network with non-monotonic, distance-dependent connectivity can exhibit cluster solutions where adjacent cells fire together.

An Ensemble of Locally Reliable Cluster Solutions

Clustering ensemble indicates to an approach in which a number of (usually weak) base clusterings are performed and their consensus clustering is used as the final clustering. Knowing democratic decisions are better than dictatorial decisions, it seems clear and simple that ensemble (here, clustering ensemble) decisions are better than simple model (here, clustering) decisions. But it is not guaranteed that every ensemble is better than a simple model. An ensemble is considered to be a better ensemble if their members are valid or high-quality and if they participate according to their qualities in constructing consensus clustering. In this paper, we propose a clustering ensemble framework that uses a simple clustering algorithm based on kmedoids clustering algorithm. Our simple clustering algorithm guarantees that the discovered clusters are valid. From another point, it is also guaranteed that our clustering ensemble framework uses a mechanism to make use of each discovered cluster according to its quality. To do this mechanism an auxiliary ensemble named reference set is created by running several kmeans clustering algorithms.