Information transfer of an Ising model on a brain network

We implement the Ising model on a structural connectivity matrix describing the brain at a coarse scale. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the number of incoming links

Network industries in the new economy

In this paper we discuss two propositions: the supply and demand of knowledge, and network externalities. We outline the characteristics that distinguish knowledge- intensive industries from the general run of manufacturing and service businesses. Knowledge intensity and knowledge specialisation has developed as markets and globalisation have grown, leading to progressive incentives to outsource and for industries to deconstruct. The outcome has been more intensive competition. The paper looks at what is potentially the most powerful economic mechanism: positive feedback, alternatively known as demand-side increasing returns, network effects, or network externalities. We present alternative demand curves that incorporate positive feedback and discuss their potential economic and strategic consequences. We argue that knowledge supply and demand, and the dynamics of network externalities create new situations for our traditional industrial economy such that new types of economies of scale are emerging and "winner takes all" strategies are having more influence. This is the first of a pair of papers. A second paper will take the argument further and look at the nature of firms' strategies in the new world, arguing that technology standards, technical platforms, consumer networks, and supply chain strategies are making a significant contribution to relevant strategies within the new economy

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Granger causality for circular variables

In this letter we discuss use of Granger causality to the analyze systems of coupled circular variables, by modifying a recently proposed method for multivariate analysis of causality. We show the application of the proposed approach on several Kuramoto systems, in particular one living on networks built by preferential attachment and a model for the transition from deeply to lightly anaesthetized states. Granger causalities describe the flow of information among variables.Comment: 4 pages, 5 figure

Submodular Inference of Diffusion Networks from Multiple Trees

Diffusion and propagation of information, influence and diseases take place over increasingly larger networks. We observe when a node copies information, makes a decision or becomes infected but networks are often hidden or unobserved. Since networks are highly dynamic, changing and growing rapidly, we only observe a relatively small set of cascades before a network changes significantly. Scalable network inference based on a small cascade set is then necessary for understanding the rapidly evolving dynamics that govern diffusion. In this article, we develop a scalable approximation algorithm with provable near-optimal performance based on submodular maximization which achieves a high accuracy in such scenario, solving an open problem first introduced by Gomez-Rodriguez et al (2010). Experiments on synthetic and real diffusion data show that our algorithm in practice achieves an optimal trade-off between accuracy and running time.Comment: To appear in the 29th International Conference on Machine Learning (ICML), 2012. Website: http://www.stanford.edu/~manuelgr/network-inference-multitree

Information transfer and criticality in the Ising model on the human connectome

We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows

Information Flow in Networks and the Law of Diminishing Marginal Returns: Evidence from Modeling and Human Electroencephalographic Recordings

We analyze simple dynamical network models which describe the limited capacity of nodes to process the input information. For a proper range of their parameters, the information flow pattern in these models is characterized by exponential distribution of the incoming information and a fat-tailed distribution of the outgoing information, as a signature of the law of diminishing marginal returns. We apply this analysis to effective connectivity networks from human EEG signals, obtained by Granger Causality, which has recently been given an interpretation in the framework of information theory. From the distributions of the incoming versus the outgoing values of the information flow it is evident that the incoming information is exponentially distributed whilst the outgoing information shows a fat tail. This suggests that overall brain effective connectivity networks may also be considered in the light of the law of diminishing marginal returns. Interestingly, this pattern is reproduced locally but with a clear modulation: a topographic analysis has also been made considering the distribution of incoming and outgoing values at each electrode, suggesting a functional role for this phenomenon

Information Technology Investments And Aggregate Productivity

Earlier studies have shown positive and large impacts of information technology (IT) investments on aggregate products in the nascent stage. However, this causal inference may not be applicable in the adult regime with a diminishing marginal productivity. We conduct a 52 cross-country analysis on a 15 year data of IT capital stocks, rather than flows as used in the literature. Controlling for country and time effects, the empirical implications of our study are as follows: First, the IT investment intensity positively affects aggregate productivity controlling for labor, assets, and financial markets. Second, the relative contribution has decreased as the law of diminishing returns predicts. Lastly, software and services have gained more capital allocation on relative terms in exchange for less on hardware. This finding contrasts with the existing argument that the hardware-software mix is time-constant due to substitution

What drives productivity growth?

Economists have long debated the best way to explain the sources of productivity growth. Neoclassical theory and "new growth" theory both regard investment—broadly defined to include purchases of tangible assets, human capital expenditures, and research and development efforts—as a critical source of productivity growth, but they differ in fundamental ways. Most notably, the neoclassical framework focuses on diminishing and internal returns to aggregate capital, while new growth models emphasize constant returns to capital that may yield external benefits. This article finds that despite their differences, both theories help explain productivity growth. The methodological tools of the neoclassical economists allow one to measure the rate of technical change, and the models of the new growth theorists provide an internal explanation for technical progress.Economic development ; Productivity ; Capital ; Technology

Models of efficiency of functioning in trading enterprises under conditions of economic growth

The article examines the models of efficient functioning of trading enterprises in the conditions of economic development during 2016-2019. It is proved that the criterion for measuring efficiency is the evaluation of static and dynamic efficiency of trade activities, which allows changes in the used assets (resources) to be taken into account, an enterprise’s safety margin to be increased and it testifies to the merger (integration) of diminishing returns and economic fluctuations in modern economic macro and microsystems. The results of measuring the efficiency of trading enterprises’ activity show that in order to evaluate the efficiency of the functioning of trading enterprises qualitatively and completely, it is necessary to consider all possible factors. Given the existence of Clark’s law, the authors substantiate an approach to evaluating the performance based on simple one-factor multiple models, which proves that future studies of finding ways to improve the efficiency, which are mainly aimed at extensive resource changes, will be erroneous, unjustified, and most likely, they will reduce the effectiveness of the resource under study. By specifying and parameterising the function of an enterprise’s trade activity in the conditions of economic development, it is possible to evaluate not only the static efficiency of trade activity, but also the impact of the law of diminishing marginal product on the results of the enterprise’s operation. This approach allows us to determine the optimal boundaries of doing business and the most effective marginal size of resource changes to achieve high cost indicators and economic synergy. The article defines clear boundaries between the minimum marginal product ratio (increase in net income relative to the growth in the number of employees) and the maximum average product (productivity) of trading enterprises