搜索结果：Journal of tropical medicine

We explore the tropical analog of spinors by representing tropical geometries as foliated Riemann surfaces endowed with degenerate complex structures. We investigate tropical limits of the Laplace-Beltrami operator and explicitly construct its square root, which defines a tropical Dirac operator. We find that the tropical Clifford algebra is classified as a degenerate Clifford algebra with nilpotent generators. The nilpotent generator allows us to work with a new kind of representation that allows for Grassmann odd numbers, effectively supersymmetrizing the tropical spin bundle. We show through Dirac-Bergmann's quantization procedure, that the corresponding tropicalized quantum field theories enjoy a purely fermionic topological symmetry which can be expected to give a new class of path integral localization that we call tropical localization similar to the alternative localization method recently constructed by Choi and Takhtajan. We also discuss how the tropical Dirac operator, when twisted by gauge fields, obeys a tropical version of the Lichnerowicz identity, thereby demonstrating how some elements of Yang-Mills curvature should arise in the tropical limit.

Rankings of scholarly journals based on citation data are often met with skepticism by the scientific community. Part of the skepticism is due to disparity between the common perception of journals' prestige and their ranking based on citation counts. A more serious concern is the inappropriate use of journal rankings to evaluate the scientific influence of authors. This paper focuses on analysis of the table of cross-citations among a selection of Statistics journals. Data are collected from the Web of Science database published by Thomson Reuters. Our results suggest that modelling the exchange of citations between journals is useful to highlight the most prestigious journals, but also that journal citation data are characterized by considerable heterogeneity, which needs to be properly summarized. Inferential conclusions require care in order to avoid potential over-interpretation of insignificant differences between journal ratings. Comparison with published ratings of institutions from the UK's Research Assessment Exercise shows strong correlation at aggregate level between assessed research quality and journal citation `export scores' within the discipline of Statistics.

Interdisciplinary research is critical for innovation and addressing complex societal issues. We characterise the interdisciplinary knowledge structure of PubMed research articles in medicine as correlation networks of medical concepts and compare the interdisciplinarity of articles between high-ranking (impactful) and less high-ranking (less impactful) medical journals. We found that impactful medical journals tend to publish research that are less interdisciplinary than less impactful journals. Observing that they bridge distant knowledge clusters in the networks, we find that cancer-related research can be seen as one of the main drivers of interdisciplinarity in medical science. Using signed difference networks, we also investigate the clustering of deviations between high and low impact journal correlation networks. We generally find a mild tendency for strong link differences to be adjacent. Furthermore, we find topic clusters of deviations that shift over time. In contrast, topic clusters in the original networks are static over time and can be seen as the core knowledge structure in medicine. Overall, journals and policymakers should encourage initiatives to accommodate int

We study anisotropic scaling limits of topological field theories using tropical geometry. The resulting topological field theories are characterized by foliated geometries and are invariant under foliation-preserving gauge transformations. We demonstrate the tropicalization for the 2D BF theory and generalize the prescription to topological Yang-Mills and Chern-Simons theories. We call the tropical limit of the BF theory, the \textit{TBF} theory, which is an anisotropic generalization of the BF theory with an additional adjoint-valued field $T$ that enforces a projectability condition onto the leaves of the foliation. The TBF theory localizes onto the moduli space of tropicalized flat connections $\mathcal{M}(Σ_g,G)$ on a foliated Riemann surface $Σ_g$ of genus $g$. The tropical connections exhibit anisotropic behavior; their holonomy is sensitive only to the leaves of the foliation. We analyze this moduli space two distinct ways, Firstly, they are classified by leaf-wise holonomy whose dimension can be explicitly calculated for the case of tropical projective space $\mathbb{TP}^1$ by the moduli space isomorphism $\mathcal{M}\left(\mathbb{TP} ^1, G\right) \cong \operatorname{Hom}(

We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and study tropical notions of volume associated to both divisors and tropical modules. We prove optimal asymptotic results for each case. In addition, we show that the tropical volume is compatible with the tropicalization of curves.

Using the Scopus dataset (1996-2007) a grand matrix of aggregated journal-journal citations was constructed. This matrix can be compared in terms of the network structures with the matrix contained in the Journal Citation Reports (JCR) of the Institute of Scientific Information (ISI). Since the Scopus database contains a larger number of journals and covers also the humanities, one would expect richer maps. However, the matrix is in this case sparser than in the case of the ISI data. This is due to (i) the larger number of journals covered by Scopus and (ii) the historical record of citations older than ten years contained in the ISI database. When the data is highly structured, as in the case of large journals, the maps are comparable, although one may have to vary a threshold (because of the differences in densities). In the case of interdisciplinary journals and journals in the social sciences and humanities, the new database does not add a lot to what is possible with the ISI databases.

A number of journal classification systems have been developed in bibliometrics since the launch of the Citation Indices by the Institute of Scientific Information (ISI) in the 1960s. These systems are used to normalize citation counts with respect to field-specific citation patterns. The best known system is the so-called "Web-of-Science Subject Categories" (WCs). In other systems papers are classified by algorithmic solutions. Using the Journal Citation Reports 2014 of the Science Citation Index and the Social Science Citation Index (n of journals = 11,149), we examine options for developing a new system based on journal classifications into subject categories using aggregated journal-journal citation data. Combining routines in VOSviewer and Pajek, a tree-like classification is developed. At each level one can generate a map of science for all the journals subsumed under a category. Nine major fields are distinguished at the top level. Further decomposition of the social sciences is pursued for the sake of example with a focus on journals in information science (LIS) and science studies (STS). The new classification system improves on alternative options by avoiding the problem

We study the geometry of tropical extensions of hyperfields, including the ordinary, signed and complex tropical hyperfields. We introduce the framework of 'enriched valuations' as hyperfield homomorphisms to tropical extensions, and show that a notable family of them are relatively algebraically closed. Our main results are hyperfield analogues of Kapranov's theorem and the Fundamental theorem of tropical geometry. Utilising these theorems, we introduce fine tropical varieties and prove a structure theorem for them in terms of their initial ideals.

We address the problem of existence of refined (i.e., depending on a formal parameter) tropical enumerative invariants, and we present two new examples of a refined count of rational marked tropical curves. One of the new invariants counts plane rational tropical curves with an unmarked vertex of arbitrary valency. It was motivated by the tropical enumeration of plane cuspidal tropical curves given by Y. Ganor and the author, which naturally led to consideration of plane tropical curves with an unmarked four-valent vertex. Another refined invariant counts rational tropical curves of a given degree in the Euclidean space of arbitrary dimension matching specific constraints, which make the spacial refined invariant similar to known planar invariants.

We introduce a notion of tropical vector bundle on a tropical toric variety which is a tropical analogue of a torus equivariant vector bundle on a toric variety. Alternatively it can be called a toric matroid bundle. We define equivariant $K$-theory and characteristic classes of these bundles. As a particular case, we show that any matroid comes with tautological tropical toric vector bundles over the permutahedral toric variety and the corresponding equivariant $K$-classes and Chern classes recover the tautological classes of matroids constructed in the recent work of Berger-Eur-Spink-Tseng. In analogy with toric vector bundles, we define sheaf of sections and Euler characteristic as well as positivity notions such as global generation, ampleness and nefness for tropical toric vector bundles. Moreover, we prove a vanishing of higher cohomologies result. Finally, we study the splitting of our tropical toric vector bundles and, in particular, an analogue of Grothendieck's theorem on splitting of vector bundles on projective line.

Using "Analyze Results" at the Web of Science, one can directly generate overlays onto global journal maps of science. The maps are based on the 10,000+ journals contained in the Journal Citation Reports (JCR) of the Science and Social Science Citation Indices (2011). The disciplinary diversity of the retrieval is measured in terms of Rao-Stirling's "quadratic entropy." Since this indicator of interdisciplinarity is normalized between zero and one, the interdisciplinarity can be compared among document sets and across years, cited or citing. The colors used for the overlays are based on Blondel et al.'s (2008) community-finding algorithms operating on the relations journals included in JCRs. The results can be exported from VOSViewer with different options such as proportional labels, heat maps, or cluster density maps. The maps can also be web-started and/or animated (e.g., using PowerPoint). The "citing" dimension of the aggregated journal-journal citation matrix was found to provide a more comprehensive description than the matrix based on the cited archive. The relations between local and global maps and their different functions in studying the sciences in terms of journal lit

Hassett's moduli spaces of weighted stable curves form an important class of alternate modular compactifications of the moduli space of smooth curves with marked points. In this article we define a tropical analogue of these moduli spaces and show that the naive set-theoretic tropicalization map can be identified with a natural deformation retraction onto the non-Archimedean skeleton. This result generalizes work of Abramovich, Caporaso, and Payne treating the Deligne-Knudsen-Mumford compactification of the moduli space of smooth curves with marked points. We also study tropical analogues of the tautological maps, investigate the dependence of the tropical moduli spaces on the weight data, and consider the example of Losev-Manin spaces.

In this paper we propose a general functorial definition of the operation of \emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $Γ$ a finitely generated subsemigroup of a lattice, $γ: Γ\rightarrow R/ R^*$ a morphism of semigroups, and $\V(R)$ the topological space of valuations on $R$ taking values in $\R \cup \infty$. Then we may \emph{tropicalize} with respect to $γ$ any subset $\W$ of the space of valuations $\V(R)$. By definition, we get a subset of a rational polyhedral cone canonically associated to $Γ$, enriched with strata at infinity. In particular, when $R$ is a local ring, $γ$ is a \emph{local} morphism of semigroups, and $\W$ is the space of valuations which are either positive or non-negative on $R$, we call these processes \emph{local tropicalizations}. They depend only on the ambient toroidal structure, which in turn allows to define tropicalizations of subvarieties of toroidal embeddings. We prove that with suitable hypothesis, these local tropicalizations are the supports of finite rational polyhedral fans enriched with strata at infinity and we compare the global and local tropicalizations of a subvariety of a toric variety.

Publication patterns of 79 forest scientists awarded major international forestry prizes during 1990-2010 were compared with the journal classification and ranking promoted as part of the 'Excellence in Research for Australia' (ERA) by the Australian Research Council. The data revealed that these scientists exhibited an elite publication performance during the decade before and two decades following their first major award. An analysis of their 1703 articles in 431 journals revealed substantial differences between the journal choices of these elite scientists and the ERA classification and ranking of journals. Implications from these findings are that additional cross-classifications should be added for many journals, and there should be an adjustment to the ranking of several journals relevant to the ERA Field of Research classified as 0705 Forestry Sciences.

We show that points in the intersection of the tropicalizations of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations intersect in the expected dimension. We also prove a similar result for intersections inside an ambient subvariety of the torus, when the tropicalizations meet inside a facet of multiplicity 1. The proofs require not only the geometry of compactified tropicalizations of subvarieties of toric varieties, but also new results about the geometry of finite type schemes over non-noetherian valuation rings of rank 1. In particular, we prove subadditivity of codimension and a principle of continuity for intersections in smooth schemes over such rings, generalizing well-known theorems over regular local rings. An appendix on the topology of finite type morphisms may also be of independent interest.

Dyads of journals related by citations can agglomerate into specialties through the mechanism of triadic closure. Using the Journal Citation Reports 2011, 2012, and 2013, we analyze triad formation as indicators of integration (specialty growth) and disintegration (restructuring). The strongest integration is found among the large journals that report on studies in different scientific specialties, such as PLoS ONE, Nature Communications, Nature, and Science. This tendency towards large-scale integration has not yet stabilized. Using the Islands algorithm, we also distinguish 51 local maxima of integration. We zoom into the cited articles that carry the integration for: (i) a new development within high-energy physics and (ii) an emerging interface between the journals Applied Mathematical Modeling and the International Journal of Advanced Manufacturing Technology. In the first case, integration is brought about by a specific communication reaching across specialty boundaries, whereas in the second, the dyad of journals indicates an emerging interface between specialties. These results suggest that integration picks up substantive developments at the specialty level. An advantage o

We introduce a novel methodology for mapping academic institutions based on their journal publication profiles. We believe that journals in which researchers from academic institutions publish their works can be considered as useful identifiers for representing the relationships between these institutions and establishing comparisons. However, when academic journals are used for research output representation, distinctions must be introduced between them, based on their value as institution descriptors. This leads us to the use of journal weights attached to the institution identifiers. Since a journal in which researchers from a large proportion of institutions published their papers may be a bad indicator of similarity between two academic institutions, it seems reasonable to weight it in accordance with how frequently researchers from different institutions published their papers in this journal. Cluster analysis can then be applied to group the academic institutions, and dendrograms can be provided to illustrate groups of institutions following agglomerative hierarchical clustering. In order to test this methodology, we use a sample of Spanish universities as a case study. We f

We introduce the notion of tropical area of a tropical curve defined in an open subset of $\mathbb R^n$. We prove that the number of vertices of a tropical curve is bounded by the area of the curve. The approach is totally elementary yet tricky. Our proof employs ideas from intersection theory in algebraic geometry. The result can be interpreted as the fact that the moduli space of tropical curves with bounded area is of finite type.

Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated terms, find a natural formulation in tropical analysis and can be used for model reduction.