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In this work we dig into the process of scientific discovery by looking at a yet unexploited source of information: Polymath projects. Polymath projects are an original attempt to collectively solve mathematical problems in an online collaborative environment. To investigate the Polymath experiment, we analyze all the posts related to the projects that arrived to a peer reviewed publication with a particular attention to the organization of labor and the innovations originating from the author contributions. We observe that a significant presence of sporadic contributor boosts the productivity of the most active users and that productivity, in terms of number of posts, grows super-linearly with the number of contributors. When it comes to innovation in large scale collaborations, there is no exact rule determining, a priori, who the main innovators will be. Sometimes, serendipitous interactions by sporadic contributors can have a large impact on the discovery process and a single post by an occasional participant can steer the work into a new direction.
A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpreted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firms technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.
We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general formula for such distribution of productivity is obtained, using the detail-balance condition necessary for equilibrium in the Ehrenfest-Brillouin model. We also carry out an empirical analysis on the average number of workers in given productivity sectors on the basis of an exhaustive dataset in Japan. The theoretical formula succeeds in explaining the two distinctive observational facts in a unified way, that is, a Boltzmann distribution with negative temperature on low-to-medium productivity side and a decreasing part in a power-law form on high productivity side.
We perform an in-depth analysis on the inequality in 863 Wikimedia projects. We take the complete editing history of 267,304,095 Wikimedia items until 2016, which not only covers every language edition of Wikipedia, but also embraces the comple
The peer-to-peer (P2P) economy has been growing with the advent of the Internet, with well known brands such as Uber or Airbnb being examples thereof. In the insurance sector the approach is still in its infancy, but some companies have started to explore P2P-based collaborative insurance products (eg. Lemonade in the U.S. or Inspeer in France). The actuarial literature only recently started to consider those risk sharing mechanisms, as in Denuit and Robert (2021) or Feng et al. (2021). In this paper, describe and analyse such a P2P product, with some reciprocal risk sharing contracts. Here, we consider the case where policyholders still have an insurance contract, but the first self-insurance layer, below the deductible, can be shared with friends. We study the impact of the shape of the network (through the distribution of degrees) on the risk reduction. We consider also some optimal setting of the reciprocal commitments, and discuss the introduction of contracts with friends of friends to mitigate some possible drawbacks of having people without enough connections to exchange risks.
Swarm Intelligence is a metaheuristic optimization approach that has become very predominant over the last few decades. These algorithms are inspired by animals physical behaviors and their evolutionary perceptions. The simplicity of these algorithms allows researchers to simulate different natural phenomena to solve various real-world problems. This paper suggests a novel algorithm called Donkey and Smuggler Optimization Algorithm (DSO). The DSO is inspired by the searching behavior of donkeys. The algorithm imitates transportation behavior such as searching and selecting routes for movement by donkeys in the actual world. Two modes are established for implementing the search behavior and route-selection in this algorithm. These are the Smuggler and Donkeys. In the Smuggler mode, all the possible paths are discovered and the shortest path is then found. In the Donkeys mode, several donkey behaviors are utilized such as Run, Face & Suicide, and Face & Support. Real world data and applications are used to test the algorithm. The experimental results consisted of two parts, firstly, we used the standard benchmark test functions to evaluate the performance of the algorithm in respect to the most popular and the state of the art algorithms. Secondly, the DSO is adapted and implemented on three real-world applications namely; traveling salesman problem, packet routing, and ambulance routing. The experimental results of DSO on these real-world problems are very promising. The results exhibit that the suggested DSO is appropriate to tackle other unfamiliar search spaces and complex problems.