A
bstract
As a simple lattice model that exhibits a phase transition, the Ising model plays a fundamental role in statistical and condensed matter physics. The Ising transition is realized by ...physical systems, such as the liquid-vapor transition. Its continuum limit also furnishes a basic example of interacting quantum field theories and universality classes. Motivated by a recent hybrid bootstrap study of the quantum quartic oscillator, we revisit the conformal bootstrap approach to the 3D Ising model at criticality, without resorting to positivity constraints. We use at most 10 nonperturbative crossing constraints at low derivatives from the Taylor expansion around a crossing symmetric point. The high-lying contributions are approximated by simple analytic formulae deduced from the lightcone singularity structure. Surprisingly, the low-lying properties are determined to good accuracy by this computationally very cheap approach. For instance, the results for the two relevant scaling dimensions (∆
σ
, ∆
ϵ
) ≈ (0
.
518153, 1
.
41278) are close to the most precise rigorous bounds obtained at a much higher computational cost.
A
bstract
We present new closed-form expressions for 4-point scalar conformal blocks in the s- and t-channel lightcone expansions. Our formulae apply to intermediate operators of arbitrary spin in ...general dimensions. For physical spin ℓ, they are composed of at most (ℓ + 1) Gaussian hypergeometric functions at each order.
A
bstract
In the study of conformal field theories, conformal blocks in the lightcone limit are fundamental to the analytic conformal bootstrap method. Here we consider the lightcone limit of 4-point ...functions of generic scalar primaries. Based on the nonperturbative pole structure in spin of Lorentzian inversion, we propose the natural basis functions for cross-channel conformal blocks. In this new basis, we find a closed-form expression for crossed conformal blocks in terms of the Kampé de Fériet function, which applies to intermediate operators of arbitrary spin in general dimensions. We derive the general Lorentzian inversion for the case of identical external scaling dimensions. Our results for the lightcone limit also shed light on the complete analytic structure of conformal blocks in the lightcone expansion.
A
bstract
We present a factorized decomposition of 4-point scalar conformal blocks near the lightcone, which applies to arbitrary intermediate spin and general spacetime dimensions. Then we discuss ...the systematic expansion in large intermediate spin and the resummations of the large-spin tails of Regge trajectories. The basic integrals for the Lorentzian inversion are given by Wilson functions.
A
bstract
We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy ...crossing symmetry. In the new method, we reverse the logic and interpret manifestly crossing-symmetric functions as generating functions of conformal data. Physical CFTs can be obtained by scanning the space of crossing-symmetric functions. By truncating the fusion rules, we are able to concentrate on the low-lying operators and derive some approximate relations for their conformal data. It turns out that the free scalar theory, the 2d minimal model CFTs, the
ϕ
4
Wilson-Fisher CFT, the Lee-Yang CFTs and the Ising CFTs are consistent with the universal relations from the minimal fusion rule
ϕ
1
×
ϕ
1
=
I
+
ϕ
2
+
T
, where
ϕ
1
, ϕ
2
are scalar operators,
I
is the identity operator and
T
is the stress tensor.
The epithelial-mesenchymal transition (EMT) is a developmental process that is important for embryogenesis, wound healing, organ fibrosis, and cancer metastasis. Cancer-associated EMT is not a simple ...process to acquire migration and invasion ability, but a complicated and comprehensive reprogramming, involved in metabolism, epigenetics and differentiation, through which differentiated epithelial cancer cells reverse to an undifferentiated state, not only expressing stem cell markers, but also acquiring stem cell-like functions. Here we review recent ideas and discoveries that illustrate the links among metabolism, epigenetics, and dedifferentiation during EMT, with special emphasis on the primary driving force and ultimate goal of cancer-associated EMT - of the energy and for the energy. Furthermore, we highlight on the specificity of epigenetic modification during EMT, with an aim to explain how the repression of epithelial genes and activation of mesenchymal genes are coordinated simultaneously through EMT. Finally, we provide an outlook on anti-EMT therapeutic approach on epigenetic and metabolic levels, and discuss its potential for clinical application.
Impervious surface is the major component of urban areas, and it has been widely considered as the key for assessing the degree of urban sprawl. While the effectiveness of applying spectral mixture ...analysis (SMA) and spectral indices in mapping urban impervious surface has been proved, most studies have relied either on SMA or spectral indices without considering both. In this study, the SMA and spectral indices were integrated together to map impervious surfaces distributions in both Milwaukee County in the Wisconsin State and Fayette County in the Kentucky State. Specifically, spectral indices were used for identifying major land covers. Two-dimensional feature space plots were generated by calculated spectral indices images for endmember selection and extraction. Linear constrained SMA was finally applied to quantify the fractional impervious surfaces. Research results indicate that the proposed method has achieved a promising accuracy, and better performance was achieved in less developed areas than the developed areas. Moreover, a comparative analysis shows that the proposed method performs better than the conventional method in both the whole study area and the developed areas, and a comparable performance has been achieved in the less developed areas.
We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians ...are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.
Impervious surfaces have been widely considered as the key indicator for evaluating urbanization and environmental quality. As one of the most widely applied methods, spectral mixture analysis (SMA) ...has been commonly used for mapping urban impervious surface fractions. When implementing SMA, the original multispectral remote-sensing reflectance images are served as the foundation and key to successful SMA. However, the limited spectral variances among different land covers from the original reflectance images make it challenging in information extraction and results in unsatisfactory mapping results. To address this issue, a new method has been proposed in this study to improve urban impervious surface mapping through integrating statistical methods and SMA. In particular, two traditional statistical methods, principal component analysis (PCA) and minimum noise fraction rotation (MNF) were applied to highlight the spectral variances among different land covers. Three endmember classes (impervious surface, soil, and vegetation) and corresponding spectra were identified and extracted from the vertices of the 2-D space plots generated by the first three components of each of the statistical analysis methods, PCA and MNF. A new dataset was generated by stacking the first three components of the PCA and MNF (in a total of six components), and a fully constrained linear SMA was implemented to map the fractional impervious surfaces. Results indicate that a promising performance has been achieved by the proposed new method with the systematic error (SE) of −3.45% and mean absolute error (MAE) of 11.52%. Comparative analysis results also show a much better performance achieved by the proposed statistical method-based SMA than the conventional SMA.
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