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Do Successful Researchers Reach the Self-Organized Critical Point?
No full textThe index of success of the researchers is now mostly measured using the Hirsch index (h). Our recent precise demonstration, that statistically (Formula presented.), where (Formula presented.) and (Formula presented.) denote, respectively, the total number of publications and total citations for the researcher, suggests that average number of citations per paper ((Formula presented.)), and hence h, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations (Formula presented.), rather by the inequalities among citations from publications to publications. Specifically, we show that for highly successful authors, the yearly variations in the Gini index (g, giving the average inequality of citations for the publications) and the Kolkata index (k, giving the fraction of total citations received by the top (Formula presented.) fraction of publications; (Formula presented.) corresponds to Pareto’s 80/20 law) approach each other to (Formula presented.), signaling a precursor for the arrival of (or departure from) the self-organized critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the g and k for the highly successful among them (mostly Nobel laureates, highest rank Stanford cite-scorers, and a few others) reach and hover just above (and then) below that (Formula presented.) mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of k and g fit a linear relationship, (Formula presented.), with (Formula presented.), as suggested by an approximate Landau-type expansion of the Lorenz function, and this also indicates (Formula presented.) for the (extrapolated) SOC precursor mark
Dynamical behaviors of a constant prey refuge ratio-dependent prey-predator model with Allee and fear effects
No full textIn this paper, we consider a nonlinear ratio-dependent prey-predator model with constant prey refuge in the prey population. Both Allee and fear phenomena are incorporated explicitly in the growth rate of the prey population. The qualitative behaviors of the proposed model are investigated around the equilibrium points in detail. Hopf bifurcation including its direction and stability for the model is also studied. We observe that fear of predation risk can have both stabilizing and destabilizing effects and induces bubbling phenomenon in the system. It is also observed that for a fixed strength of fear, an increase in the Allee parameter makes the system unstable, whereas an increase in prey refuge drives the system toward stability. However, higher values of both the Allee and prey refuge parameters have negative impacts and the populations go to extinction. Further, we explore the variation of densities of the populations in different bi-parameter spaces, where the coexistence equilibrium point remains stable. Numerical simulations are carried out to explore the dynamical behaviors of the system with the help of MATLAB software
Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning
No full textError syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching-(MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML-based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-Threshold for various noise models. We show that the proposed ML-based decoding method achieves ∼ 5 × higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search-based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors and thus a further improvement of ∼ 14% in the threshold over the basic ML decoder. Last, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search
Endogeneity-corrected stochastic frontier with market imperfections
No full textWhile the product and labour market imperfections reveal efficiency losses, they may influence technology adoption and its change, raising the endogeneity issue of productivity and efficiency estimates. Using a two-step approach, this work offers the endogeneity-corrected stochastic frontier for such a contemporaneous relation and accounts for efficiency and productivity losses due to market imperfections. A modified frontier function, defined as the residue per capital unit, has been drawn from the Cobb–Douglas function to estimate the terms containing the product and labour market imperfections along with other factors capturing the levels of technology, scale and technical efficiency. First, a standard frontier panel model estimates technology and technical efficiency terms with a proxy function in polynomials of market imperfection terms used for the contemporaneous relation, and then a GMM approach applies to the residue to estimate the parameters containing market imperfections. The estimated results using the three-digit industries across 17 major Indian states for 2008–2016 reveal a strong presence of product and labour market imperfections and associated efficiency losses. The efficiency in the product market has been lower and has further deteriorated in most industries, but not in the labour market
Equilibria in abstract economies with a continuum of agents with discontinuous and non-ordered preferences
No full textThis paper focus on the problem of the existence of an equilibrium in abstract economies and exchange economies. Spanning over the literature we have managed to extend and generalize some previous results. In particular, we generalize the main theorem of Yannelis (1987) on the existence of an equilibrium in an abstract economy with a continuum of agents, by allowing for discontinuous preferences. As a corollary of this result, we extend the finite agent Cournot–Nash equilibrium existence theorems with discontinuous preferences (e.g., Reny, 1999; Bareli and Meneghel, 2013; He and Yannelis, 2016; among others), to a continuum of agents. We also obtain an existence theorem for an abstract economy which allows for a convexifying effect on aggregation and nonconvex strategy and constraint sets. Furthermore, our new main theorem is used to prove the existence of a Walrasian equilibrium with a continuum of agents with discontinuous, non-ordered, interdependent and price-dependent preferences and thus extending the results of Aumman (1966) and Schmeidler (1969)
Exploring multistability and bifurcations in a three-species Smith growth model incorporating refuge, harvesting, and time delays
No full textThis study delves into a tritrophic ecological model encompassing three distinct species, elucidating predator–prey dynamics through the lens of Smith growth pattern. The model integrates several pivotal ecological elements, including an additive Allee effect dictating prey growth, a ratio-dependent functional response characterizing predator–prey interactions, the provision of refuge for intermediate predators, and the incorporation of a Michaelis–Menten-type harvesting mechanism of the top predators. Moreover, we incorporate gestation and harvesting delays as novel factors to scrutinize their impact on the overall dynamics of the food web system. Through an extensive analysis of the delayed and non-delayed models, our investigation rigorously explores the equilibrium points, stability attributes, and bifurcations structures. In the absence of time delay, our findings underscore the profound influence wielded by factors such as refuge availability, Allee effect, harvesting, and the availability of environmental resources in dictating the survival prospects of the involved species. Furthermore, our exploratory analysis uncovers a rich tapestry of intricate dynamics, encompassing chaotic behavior, periodic oscillations and, multistability. These revelations underscore the profound complexity inherent in the ecosystem, particularly accentuated by the temporal delays involved in gestation and harvesting processes. The nuanced interplay between these temporal delays and ecological parameters contributes to the emergence of diverse and complex dynamics, elucidating the intricate nature of the ecological systems
Free Licensing in a Differentiated Duopoly
No full textWe construct a differentiated duopoly model to study whether free licensing can be profitable without network externalities and demand shift effect. The efficient firm possesses a superior input-saving technology and sells inputs to the backward firm. However, the optimal input price can be constrained or unconstrained in equilibrium depending on the constellation of parameters. We have shown that free licensing can be profitable if the innovation size is small and the transferee’s input production cost is sufficiently large. But free licensing is never profitable if products are homogeneous. An increase in market size also reduces the possibility of free licensing. We have also derived an implication of free licensing in the context of pollution problem
Global synchronization in generalized multilayer higher-order networks
No full textNetworks incorporating higher-order interactions are increasingly recognized for their ability to introduce novel dynamics into various processes, including synchronization. Previous studies on synchronization within multilayer networks have often been limited to specific models, such as the Kuramoto model, or have focused solely on higher-order interactions within individual layers. Here, we present a comprehensive framework for investigating synchronization, particularly global synchronization, in multilayer networks with higher-order interactions. Our framework considers interactions beyond pairwise connections, both within and across layers. We demonstrate the existence of a stable global synchronous state, with a condition resembling the master stability function, contingent on the choice of coupling functions. Our theoretical findings are supported by simulations using Hindmarsh-Rose neuronal and Rössler oscillators. These simulations illustrate how synchronization is facilitated by higher-order interactions, both within and across layers, highlighting the advantages over scenarios involving interactions within single layers
Implementation in undominated strategies with applications to auction design, public good provision and matching
No full textThis paper considers implementation in undominated strategies by finite mechanisms, where multiple outcomes may be implemented at a single state of the world. We establish a sufficient condition for implementation applicable in a general environment with private values. We apply it to three well-known environments and obtain strikingly permissive results. In the single-object auction, the second-price auction with a reserve price can be outperformed in terms of revenue. In the public good provision problem, the Vickrey–Clarke–Groves mechanism can be outperformed from the viewpoint of a designer who wishes to minimise deficit subject to efficiency. In the two-sided matching environment where preferences on one side of the market are private information, the social choice correspondence that outputs all stable matchings at every preference profile, is implementable
Kernel-based estimation of spectral risk measures
No full textSpectral risk measures (SRMs) belong to the family of coherent risk measures. A natural estimator for the class of SRMs takes the form of L-statistics. Various authors have studied and derived the asymptotic properties of the empirical estimator of SRMs; we propose a kernel-based estimator. We investigate the large-sample properties of general L-statistics based on independent and identically distributed observations and dependent observations and apply them to our estimator. We prove that it is strongly consistent and asymptotically normal. Using Monte Carlo simulation, we compare the finite-sample performance of our proposed kernel estimator with that of several existing estimators for different SRMs and observe that our proposed kernel estimator outperforms all the other estimators. Based on our simulation study, we estimate the exponential SRM for heavily traded futures (that is, the Nikkei 225, Deutscher Aktienindex, Financial Times Stock Exchange 100 and Hang Seng futures). We also discuss the use of SRMs in setting the initial-margin requirements of clearinghouses. Finally, we perform an SRM backtesting exercise