45,815 research outputs found
Topological atomic displacements, Kirchhoff and Wiener indices of molecules
We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic displacements due to small vibrations/oscillations of atoms from their equilibrium positions. In addition, we show that the topological atomic displacements correlate with the temperature factors (B-factors) of atoms obtained by X-ray crystallography for both organic molecules and biological macromolecules
GTI-space : the space of generalized topological indices
A new extension of the generalized topological indices (GTI) approach is carried out torepresent 'simple' and 'composite' topological indices (TIs) in an unified way. Thisapproach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randićconnectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index andreverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given
Global and local properties of AdS(2) higher spin gravity
Two-dimensional BF theory with infinitely many higher spin fields is
proposed. It is interpreted as the AdS(2) higher spin gravity model describing
a consistent interaction between local fields in AdS(2) space including
gravitational field, higher spin partially-massless fields, and dilaton fields.
We carry out analysis of the frame-like and the metric-like formulation of the
theory. Infinite-dimensional higher spin global algebras and their
finite-dimensional truncations are realized in terms of o(2,1) - sp(2) Howe
dual auxiliary variables.Comment: 51 pages; v2: comments and refs added, typos removed, JHEP versio
Persistent Topology of Syntax
We study the persistent homology of the data set of syntactic parameters of
the world languages. We show that, while homology generators behave erratically
over the whole data set, non-trivial persistent homology appears when one
restricts to specific language families. Different families exhibit different
persistent homology. We focus on the cases of the Indo-European and the
Niger-Congo families, for which we compare persistent homology over different
cluster filtering values. We investigate the possible significance, in
historical linguistic terms, of the presence of persistent generators of the
first homology. In particular, we show that the persistent first homology
generator we find in the Indo-European family is not due (as one might guess)
to the Anglo-Norman bridge in the Indo-European phylogenetic network, but is
related to the position of Ancient Greek and the Hellenic branch within the
network.Comment: 15 pages, 25 jpg figure
Nongeometric Flux Compactifications
We investigate a simple class of type II string compactifications which
incorporate nongeometric "fluxes" in addition to "geometric flux" and the usual
H-field and R-R fluxes. These compactifications are nongeometric analogues of
the twisted torus. We develop T-duality rules for NS-NS geometric and
nongeometric fluxes, which we use to construct a superpotential for the
dimensionally reduced four-dimensional theory. The resulting structure is
invariant under T-duality, so that the distribution of vacua in the IIA and IIB
theories is identical when nongeometric fluxes are included. This gives a
concrete framework in which to investigate the possibility that generic string
compactifications may be nongeometric in any duality frame. The framework
developed in this paper also provides some concrete hints for how mirror
symmetry can be generalized to compactifications with arbitrary H-flux, whose
mirrors are generically nongeometric.Comment: 26 pages, JHEP3. v3: references, minor corrections, and
clarifications added. v4: sign correcte
Graph analysis of functional brain networks: practical issues in translational neuroscience
The brain can be regarded as a network: a connected system where nodes, or
units, represent different specialized regions and links, or connections,
represent communication pathways. From a functional perspective communication
is coded by temporal dependence between the activities of different brain
areas. In the last decade, the abstract representation of the brain as a graph
has allowed to visualize functional brain networks and describe their
non-trivial topological properties in a compact and objective way. Nowadays,
the use of graph analysis in translational neuroscience has become essential to
quantify brain dysfunctions in terms of aberrant reconfiguration of functional
brain networks. Despite its evident impact, graph analysis of functional brain
networks is not a simple toolbox that can be blindly applied to brain signals.
On the one hand, it requires a know-how of all the methodological steps of the
processing pipeline that manipulates the input brain signals and extract the
functional network properties. On the other hand, a knowledge of the neural
phenomenon under study is required to perform physiological-relevant analysis.
The aim of this review is to provide practical indications to make sense of
brain network analysis and contrast counterproductive attitudes
Two-Point Functions in ABJM Matrix Model
We introduce non-trivial two-point functions of the super Schur polynomials
in the ABJM matrix model and study their exact values with the Fermi gas
formalism. We find that, although defined non-trivially, these two-point
functions enjoy two simple relations with the one-point functions. One of them
is associated with the Littlewood-Richardson rule, while the other is more
novel. With plenty of data, we also revisit the one-point functions and study
how the diagonal BPS indices are split asymmetrically by the degree difference.Comment: 53 pages, 5 eps figure
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