On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

The Kodaira dimension of the moduli of K3 surfaces

The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46,50,54,58,60.Comment: 47 page

High Pressure Thermoelasticity of Body-centered Cubic Tantalum

We have investigated the thermoelasticity of body-centered cubic (bcc) tantalum from first principles by using the linearized augmented plane wave (LAPW) and mixed--basis pseudopotential methods for pressures up to 400 GPa and temperatures up to 10000 K. Electronic excitation contributions to the free energy were included from the band structures, and phonon contributions were included using the particle-in-a-cell (PIC) model. The computed elastic constants agree well with available ultrasonic and diamond anvil cell data at low pressures, and shock data at high pressures. The shear modulus $c_{44}$ and the anisotropy change behavior with increasing pressure around 150 GPa because of an electronic topological transition. We find that the main contribution of temperature to the elastic constants is from the thermal expansivity. The PIC model in conjunction with fast self-consistent techniques is shown to be a tractable approach to studying thermoelasticity.Comment: To be appear in Physical Review

A multi-species synthesis of physiological mechanisms in drought-induced tree mortality

Widespread tree mortality associated with drought 92 has been observed on all forested continents, and global change is expected to exacerbate vegetation vulnerability. Forest mortality has implications for future biosphere-atmosphere interactions of carbon, water, and energy balance, and is poorly represented in dynamic vegetation models. Reducing uncertainty requires improved mortality projections founded on robust physiological processes. However, the proposed mechanisms of drought-induced mortality, including hydraulic failure and carbon starvation, are unresolved. A growing number of empirical studies have investigated these mechanisms, but data have not been consistently analyzed across species and biomes using a standardized physiological framework. Here we show that xylem hydraulic failure was ubiquitous across multiple tree taxa at drought induced mortality. All species assessed had 60% or higher loss of xylem hydraulic conductivity, consistent with proposed theoretical and modelled survival thresholds. We found diverse responses in non-structural carbohydrate reserves at mortality, indicating that evidence supporting carbon starvation was not universal. Reduced non-structural carbohydrates were more common for gymnosperms than angiosperms, associated with xylem hydraulic vulnerability, and may have a role in reducing hydraulic function. Our finding that hydraulic failure at drought-induced mortality was persistent across species indicates that substantial improvement in vegetation modelling can be achieved using thresholds in hydraulic function

A multi-species synthesis of physiological mechanisms in drought-induced tree mortality

Widespread tree mortality associated with drought 92 has been observed on all forested continents, and global change is expected to exacerbate vegetation vulnerability. Forest mortality has implications for future biosphere-atmosphere interactions of carbon, water, and energy balance, and is poorly represented in dynamic vegetation models. Reducing uncertainty requires improved mortality projections founded on robust physiological processes. However, the proposed mechanisms of drought-induced mortality, including hydraulic failure and carbon starvation, are unresolved. A growing number of empirical studies have investigated these mechanisms, but data have not been consistently analyzed across species and biomes using a standardized physiological framework. Here we show that xylem hydraulic failure was ubiquitous across multiple tree taxa at drought induced mortality. All species assessed had 60% or higher loss of xylem hydraulic conductivity, consistent with proposed theoretical and modelled survival thresholds. We found diverse responses in non-structural carbohydrate reserves at mortality, indicating that evidence supporting carbon starvation was not universal. Reduced non-structural carbohydrates were more common for gymnosperms than angiosperms, associated with xylem hydraulic vulnerability, and may have a role in reducing hydraulic function. Our finding that hydraulic failure at drought-induced mortality was persistent across species indicates that substantial improvement in vegetation modelling can be achieved using thresholds in hydraulic function

Search for single vector-like B quark production and decay via B → bH(b¯b) in pp collisions at √s = 13 TeV with the ATLAS detector

A search is presented for single production of a vector-like B quark decaying into a Standard Model b-quark and a Standard Model Higgs boson, which decays into a b¯b pair. The search is carried out in 139 fb−1 of √s = 13 TeV proton-proton collision data collected by the ATLAS detector at the LHC between 2015 and 2018. No significant deviation from the Standard Model background prediction is observed, and mass-dependent exclusion limits at the 95% confidence level are set on the resonance production cross-section in several theoretical scenarios determined by the couplings cW, cZ and cH between the B quark and the Standard Model W, Z and Higgs bosons, respectively. For a vector-like B occurring as an isospin singlet, the search excludes values of cW greater than 0.45 for a B resonance mass (mB) between 1.0 and 1.2 TeV. For 1.2 TeV < mB < 2.0 TeV, cW values larger than 0.50–0.65 are excluded. If the B occurs as part of a (B, Y) doublet, the smallest excluded cZ coupling values range between 0.3 and 0.5 across the investigated resonance mass range 1.0 TeV < mB < 2.0 TeV

Searches for exclusive Higgs boson decays into D⁎γ and Z boson decays into D0γ and Ks0γ in pp collisions at √s = 13 TeV with the ATLAS detector

Searches for exclusive decays of the Higgs boson into D⁎γ and of the Z boson into D0γ and Ks0γ can probe flavour-violating Higgs boson and Z boson couplings to light quarks. Searches for these decays are performed with a pp collision data sample corresponding to an integrated luminosity of 136.3 fb−1 collected at s=13TeV between 2016–2018 with the ATLAS detector at the CERN Large Hadron Collider. In the D⁎γ and D0γ channels, the observed (expected) 95% confidence-level upper limits on the respective branching fractions are B(H→D⁎γ)&lt;1.0(1.2)×10−3, B(Z→D0γ)&lt;4.0(3.4)×10−6, while the corresponding results in the Ks0γ channel are B(Z→Ks0γ)&lt;3.1(3.0)×10−6

Combination of searches for heavy spin-1 resonances using 139 fb−1 of proton-proton collision data at √s = 13 TeV with the ATLAS detector

A combination of searches for new heavy spin-1 resonances decaying into diferent pairings of W, Z, or Higgs bosons, as well as directly into leptons or quarks, is presented. The data sample used corresponds to 139 fb−1 of proton-proton collisions at √s = 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq, bb, tt¯, and tb) or third-generation leptons (τν and τ τ ) are included in this kind of combination for the frst time. A simplifed model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confdence level and are compared with predictions for the benchmark model. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The complementarity of the various analyses increases the sensitivity to new physics, and the resulting constraints are stronger than those from any individual analysis considered. The data exclude a heavy vector-boson triplet with mass below 5.8 TeV in a weakly coupled scenario, below 4.4 TeV in a strongly coupled scenario, and up to 1.5 TeV in the case of production via vector-boson fusion

Search for resonances decaying into photon pairs in 139 fb−1 of pp collisions at √s = 13 TeV with the ATLAS detector

Searches for new resonances in the diphoton final state, with spin 0 as predicted by theories with an extended Higgs sector and with spin 2 using a warped extra-dimension benchmark model, are presented using 139 fb−1 of √s = 13 TeV pp collision data collected by the ATLAS experiment at the LHC. No significant deviation from the Standard Model is observed and upper limits are placed on the production cross-section times branching ratio to two photons as a function of the resonance mass

Measurement of vector boson production cross sections and their ratios using pp collisions at √s = 13.6 TeV with the ATLAS detector

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