89 research outputs found
Lotka' s Law, Co-authorship and Interdisciplinary Publishing
No full textThe robustness or breakdown of Lotka's law about the frequency distribution of scientific productivity depends on scientific cooperation, counting methods, interdisciplinary publishing and selection methods for sample collections. We have chosen to analyse the relationship using Mandelbrot's equivalent distribution model because this model is sensitive and uses the original data (scores). Five sets of authors and publications, the two sets used by Lotka, a set from High Energy Physics, a set from Microbiology and a set based on applicants to a research programme promoting young researchers have been used. It is shown that even for a sample of authors in High-Energy Physics with extremely strong co-authorship, Mandelbrot's distribution law is robust when complete-normalized (fractional) counting is used whereas complete counting results in a breakdown. In the field of Microbiology with much weaker cooperation, both counting methods result in a breakdown of Mandelbrot's law. Today a field like Microbiology with the corresponding set of journals, probably has a large content of interdisciplinary publishing and therefore no more fulfills the precondition of Lotka's law, that the total production of the authors (sources) is considered. For a set of applicants for the Emmy Noether Programme of the German Research Foundation. Mandelbrot's law breaks down despite the fact that all publications co-authored by the applicants are taken into account. In agreement with Bayes' theorem of conditional probabilities these results lead to the conjecture that any selection process of authors and/or publications causes a breakdown of Mandelbrot's law and, as a consequence Lotka's law
Why Kendall Tau?
No full textThis article, authored by G.E. Noether of the University of Connecticut, discusses the differences between the Kendall coefficient and the Spearman correlation coefficient as well as assesses its uses and advantages. The author intertwines both text and mathematic formula to help illustrate the concepts in this article. Additionally, the author provides external references for those interested in further study of this topic
Classification of the Horndeski cosmologies via Noether symmetries
No full text© 2018, The Author(s). Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like f(R) gravity, Brans–Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out
Off-shell Noether current and conserved charge in Horndeski theory
No full textAbstractWe derive the off-shell Noether current and potential in the context of Horndeski theory, which is the most general scalar–tensor theory with a Lagrangian containing derivatives up to second order while yielding at most to second-order equations of motion in four dimensions. Then the formulation of conserved charges is proposed on basis of the off-shell Noether potential and the surface term got from the variation of the Lagrangian. As an application, we calculate the conserved charges of black holes in a scalar–tensor theory with non-minimal coupling between derivatives of the scalar field and the Einstein tensor
Classification of the Horndeski cosmologies via Noether symmetries
No full text© 2018, The Author(s). Adopting Noether point symmetries, we classify and integrate dynamical systems coming from Horndeski cosmologies. The method is particularly effective both to select the form of Horndeski models and to derive exact cosmological solutions. Starting from the Lagrangians selected by the Noether symmetries, it is possible to derive several modified theories of gravity like f(R) gravity, Brans–Dicke gravity, string inspired gravity and so on. In any case, exact solutions are found out
Noether symmetry in Horndeski Lagrangian
No full textThe Noether symmetry issue for Horndeski Lagrangian has been studied. We have been proven a series of theorems about
the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been
made on Horndeski Lagrangian. We have been proven that for Horndeski Lagrangian always is possible to find a way to make
symmetrization.The accepted manuscript in pdf format is listed with the files at the bottom of this page. The presentation of the authors' names and (or) special characters in the title of the manuscript may differ slightly between what is listed on this page and what is listed in the pdf file of the accepted manuscript; that in the pdf file of the accepted manuscript is what was submitted by the author
Skeletons of Prym varieties and Brill-Noether theory
No full textWe show that the non-Archimedean skeleton of the Prym variety associated to an unramified double cover of an algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) to the tropical Prym variety of the associated tropical double cover. This confirms a conjecture by Jensen and the first author. We prove a new upper bound on the dimension of the Prym-Brill-Noether locus for generic unramified double covers of curves with fixed even gonality on the base. Our methods also give a new proof of the classical Prym-Brill-Noether Theorem for generic unramified double covers that is originally due to Welters and Bertram
First integrals of holonomic systems without Noether symmetries
No full textA theorem is proved that determines the first integrals of the form I=Kab(t,q)q˙aq˙b+Ka(t,q)q˙a+K(t,q) of autonomous holonomic systems using only the collineations of the kinetic metric that is defined by the kinetic energy or the Lagrangian of the system. It is shown how these first integrals can be associated via the inverse Noether theorem with a gauged weak Noether symmetry, which admits the given first integral as a Noether integral. It is shown also that the associated Noether symmetry is possible to satisfy the conditions for a Hojman or a form-invariance symmetry; therefore, the so-called non-Noetherian first integrals are gauged weak Noether integrals. The application of the theorem requires a certain algorithm due to the complexity of the special conditions involved. We demonstrate this algorithm by a number of solved examples. We choose examples from published works in order to show that our approach produces new first integrals not found before with the standard methods. © 2020 Author(s)
The Noether problem for Hopf algebras
No full textIn previous work, Eli Aljadeff and the first-named author attached an algebra B_H of rational fractions to each Hopf algebra H. The generalized Noether problem is the following: for which finite-dimensional Hopf algebra H is B_H the localization of a polynomial algebra? A positive answer to this question when H is the algebra of functions on a finite group implies a positive answer for the classical Noether problem for the group. We show that the generalized Noether problem has a positive answer for all pointed finite-dimensional Hopf algebras over a field of characteristic zero. We actually give a precise description of B_H for such a Hopf algebra, including a bound on the degrees of the generators.A theory of polynomial identities for comodule algebras over a Hopf algebra H gives rise to a universal comodule algebra whose subalgebra of coinvariants V_H maps injectively into B_H. In the second half of this paper, we show that B_H is a localization of V_H when again H is a pointed finite-dimensional Hopf algebra in characteristic zero. We also report on a result by Uma Iyer showing that the same localization result holds when H is the algebra of functions on a finite group
Ring Signature Confidential Transactions for Monero
No full textThis article introduces a method of hiding transaction amounts in
the strongly decentralized anonymous cryptocurrency Monero. Similar
to Bitcoin, Monero is a cryptocurrency which is distributed through
a proof of work ``mining\u27\u27 process. The original Monero protocol
was based on CryptoNote, which uses ring signatures and one-time keys
to hide the destination and origin of transactions. Recently the technique
of using a commitment scheme to hide the amount of a transaction has
been discussed and implemented by Bitcoin Core Developer Gregory Maxwell.
In this article, a new type of ring signature, A Multi-layered Linkable
Spontaneous Anonymous Group signature is described which allows for hidden
amounts, origins and destinations of transactions with reasonable
efficiency and verifiable, trustless coin generation. The author would like to note that early drafts of this were publicized in the Monero Community and on the bitcoin research irc channel. Blockchain hashed drafts are available in \cite{Snoe}
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