Effects of impurities on radiation damage of silicon solar cells

Impurities effects on radiation damage of silicon solar cell

Power Law of Customers' Expenditures in Convenience Stores

In a convenience store chain, a tail of the cumulative density function of the expenditure of a person during a single shopping trip follows a power law with an exponent of -2.5. The exponent is independent of the location of the store, the shopper's age, the day of week, and the time of day.Comment: 9 pages, 5 figures. Accepted for publication in Journal of the Physical Society of Japan Vol.77No.

Degree distributions of growing networks

The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each immediately attach to a pre-existing node, and (ii) creation of new links between pre-existing nodes. This process naturally generates correlated in- and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained

Percolation in Directed Scale-Free Networks

Many complex networks in nature have directed links, a property that affects the network's navigability and large-scale topology. Here we study the percolation properties of such directed scale-free networks with correlated in- and out-degree distributions. We derive a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. In the first regime we regain the known directed percolation mean field exponents. In contrast, the second and third regimes are characterized by anomalous exponents, which we calculate analytically. In the third regime the network is resilient to random dilution, i.e., the percolation threshold is p_c->1.Comment: Latex, 5 pages, 2 fig

Mining the Automotive Industry: A Network Analysis of Corporate Positioning and Technological Trends

The digital transformation is driving revolutionary innovations and new market entrants threaten established sectors of the economy such as the automotive industry. Following the need for monitoring shifting industries, we present a network-centred analysis of car manufacturer web pages. Solely exploiting publicly-available information, we construct large networks from web pages and hyperlinks. The network properties disclose the internal corporate positioning of the three largest automotive manufacturers, Toyota, Volkswagen and Hyundai with respect to innovative trends and their international outlook. We tag web pages concerned with topics like e-mobility and environment or autonomous driving, and investigate their relevance in the network. Sentiment analysis on individual web pages uncovers a relationship between page linking and use of positive language, particularly with respect to innovative trends. Web pages of the same country domain form clusters of different size in the network that reveal strong correlations with sales market orientation. Our approach maintains the web content's hierarchical structure imposed by the web page networks. It, thus, presents a method to reveal hierarchical structures of unstructured text content obtained from web scraping. It is highly transparent, reproducible and data driven, and could be used to gain complementary insights into innovative strategies of firms and competitive landscapes, which would not be detectable by the analysis of web content alone.Comment: Preprint version to be published in Springer Nature (presented at CompleNet 2020

Universal Behavior of Load Distribution in Scale-free Networks

We study a problem of data packet transport in scale-free networks whose degree distribution follows a power-law with the exponent $\gamma$. We define load at each vertex as the accumulated total number of data packets passing through that vertex when every pair of vertices send and receive a data packet along the shortest path connecting the pair. It is found that the load distribution follows a power-law with the exponent $\delta \approx 2.2(1)$, insensitive to different values of $\gamma$ in the range, $2 < \gamma \le 3$, and different mean degrees, which is valid for both undirected and directed cases. Thus, we conjecture that the load exponent is a universal quantity to characterize scale-free networks.Comment: 5 pages, 5 figures, revised versio

Truncation of power law behavior in "scale-free" network models due to information filtering

We formulate a general model for the growth of scale-free networks under filtering information conditions--that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, i.e., that it decays as a power law with an exponential truncation controlled not only by the system size but also by a feature not previously considered, the subset of the network ``accessible'' to the node. We test our model with empirical data for the World Wide Web and find agreement.Comment: LaTeX2e and RevTeX4, 4 pages, 4 figures. Accepted for publication in Physical Review Letter

Complexity transitions in global algorithms for sparse linear systems over finite fields

We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to changes in performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary to the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.Comment: 23 pages, 8 figure

Connectivity of Growing Random Networks

A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of pre-existing links k to that site. For homogeneous connection kernels, A_k ~ k^gamma, different behaviors arise for gamma1, and gamma=1. For gamma<1, the number of sites with k links, N_k, varies as stretched exponential. For gamma>1, a single site connects to nearly all other sites. In the borderline case A_k ~ k, the power law N_k ~k^{-nu} is found, where the exponent nu can be tuned to any value in the range 2<nu<infinity.Comment: 4 pages, 2 figures, 2 column revtex format final version to appear in PRL; contains additional result

A Geometric Fractal Growth Model for Scale Free Networks

We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of that vertex with proportionality constant m-1 (m>1). We consider the two cases: first, each offspring is connected to its parent vertex only, forming a tree structure, and secondly, it is connected to both its parent and grandparent vertices, forming a loop structure. We find that both models exhibit power-law behaviors in their degree distributions with the exponent $\gamma=1+\ln (2m-1)/\ln m$. Thus, by tuning m, the degree exponent can be adjusted in the range, $2 <\gamma < 3$. We also solve analytically a mean shortest-path distance d between two vertices for the tree structure, showing the small-world behavior, that is, $d\sim \ln N/\ln {\bar k}$, where N is system size, and $\bar k$ is the mean degree. Finally, we consider the case that the number of offsprings is the same for all vertices, and find that the degree distribution exhibits an exponential-decay behavior