15,821 research outputs found
Ideals of varieties parameterized by certain symmetric tensors
The ideal of a Segre variety is generated by the 2-minors of a generic hypermatrix of indeterminates. We extend this result to the case of SegreVeronese varieties. The main tool is the concept of âweak generic hypermatrixâ which allows us to treat also the case of projection of Veronese surfaces from a set of generic points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension 2
Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes
We give a partial "quasi-stratification" of the secant varieties of the order
Veronese variety of . It covers the set
of all points lying on the linear span of
curvilinear subschemes of , but two "quasi-strata" may overlap. For
low border rank two different "quasi-strata" are disjoint and we compute the
symmetric rank of their elements. Our tool is the Hilbert schemes of
curvilinear subschemes of Veronese varieties. To get a stratification we attach
to each the minimal label of a quasi-stratum
containing it.Comment: 16 page
Ab Initio Electron-Phonon Interactions Using Atomic Orbital Wavefunctions
The interaction between electrons and lattice vibrations determines key
physical properties of materials, including their electrical and heat
transport, excited electron dynamics, phase transitions, and superconductivity.
We present a new ab initio method that employs atomic orbital (AO)
wavefunctions to compute the electron-phonon (e-ph) interactions in materials
and interpolate the e-ph coupling matrix elements to fine Brillouin zone grids.
We detail the numerical implementation of such AO-based e-ph calculations, and
benchmark them against direct density functional theory calculations and
Wannier function (WF) interpolation. The key advantages of AOs over WFs for
e-ph calculations are outlined. Since AOs are fixed basis functions associated
with the atoms, they circumvent the need to generate a material-specific
localized basis set with a trial-and-error approach, as is needed in WFs.
Therefore, AOs are ideal to compute e-ph interactions in chemically and
structurally complex materials for which WFs are challenging to generate, and
are also promising for high-throughput materials discovery. While our results
focus on AOs, the formalism we present generalizes e-ph calculations to
arbitrary localized basis sets, with WFs recovered as a special case
Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion
We calculate high-temperature graph expansions for the Ising spin glass model
with 4 symmetric random distribution functions for its nearest neighbor
interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility
\chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for
the general d-dimensional hyper-cubic lattice, where the parameter J determines
the width of the distributions. We explain in detail how the expansions are
calculated. The analysis, using the Dlog-Pad\'e approximation and the
techniques known as M1 and M2, leads to estimates for the critical threshold
(J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and
8 for all the distribution functions. In each dimension the values for \gamma
agree, within their uncertainty margins, with a common value for the different
distributions, thus confirming universality.Comment: 13 figure
Two theoretical interpretations of the dissonance between fertility intentions and behaviour
In the paper we outline two possible theoretical interpretations for the inconsistency often observed between fertility intentions and fertility behaviour. We draw on socio-psychological models of human behaviour which emphasise the role of normative-affective factors on decision-making processes. The first interpretation is based on the observation that family and fertility choices are gradually shifting from a zone where behaviour is normative regulated to a zone of normative indifference, where mere rational decision-making based on cost-benefit considerations is at work. The dissonance between fertility choices and declared intentions depends on the fact that the former are based on rational considerations, while the latter are still constrained by a normative familistic philosophy. The second interpretation assumes the existence of an interposing mechanism in the sequence expectations-behaviour. These mechanisms, as anxiety and avoidance dispositions, filter the passage from individual value orientations in the affective sphere to their actual behaviour. We base our argument on two sets of information. First, we use a survey which allows us to construct empirical indicators of psychological dispositions connected to expectations related to family and fertility behaviours (Abacus 1996, Italy). Second, we analyse 54 non-structured interviews conducted in Northern Italy, which give a detailed picture of the hypothesised mechanisms and suggest new directions for research.
Sum rules of codon usage probabilities
In the crystal basis model of the genetic code, it is deduced that the sum of
usage probabilities of the codons with C and A in the third position for the
quartets and/or sextets is independent of the biological species for
vertebrates. A comparison with experimental data shows that the prediction is
satisfied within about 5 %.Comment: 7 page
Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays
Supermassive black hole -- host galaxy relations are key to the computation
of the expected gravitational wave background (GWB) in the pulsar timing array
(PTA) frequency band. It has been recently pointed out that standard relations
adopted in GWB computations are in fact biased-high. We show that when this
selection bias is taken into account, the expected GWB in the PTA band is a
factor of about three smaller than previously estimated. Compared to other
scaling relations recently published in the literature, the median amplitude of
the signal at yr drops from to
. Although this solves any potential tension between
theoretical predictions and recent PTA limits without invoking other dynamical
effects (such as stalling, eccentricity or strong coupling with the galactic
environment), it also makes the GWB detection more challenging.Comment: 6 pages 4 figures, submitted to MNRAS letter
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