Species interactions and diversity: A unified framework using Hill numbers

Biodiversity describes the variety of organisms on planet earth. Ecologists have long hoped for a synthesis between analyses of biodiversity and analyses of biotic interactions among species, such as predation, competition, and mutualism. However, it is often unclear how to connect details of these interactions with complex modern analyses of biodiversity. To resolve this gap, we propose a unification of models of biotic interactions and measurements of diversity. We show that analyses of biodiversity obscure details about biotic interactions. For example, identical changes in biodiversity can arise from predation, competition or mutualism. Our approach indicates that traditional models of community assembly miss key facets of diversity change. Instead, we suggest that analyses of diversity change should focus on partitions, which measure mechanisms that directly shape changes in diversity, notably species level selection and immigration, rather than traditional analyses of biotic interactions

Accurate determination of blackbody radiation shifts in a strontium molecular lattice clock

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr2 molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10−16 level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr2 and provides a framework for evaluating BBR shifts in other homonuclear molecules

Species interactions and diversity: A unified framework using Hill numbers

Biodiversity describes the variety of organisms on planet earth. Ecologists have long hoped for a synthesis between analyses of biodiversity and analyses of biotic interactions among species, such as predation, competition and mutualism. However, it is often unclear how to connect details of these interactions with complex modern analyses of biodiversity. To resolve this gap, we propose a unification of models of biotic interactions and measurements of diversity. We show that analyses of biodiversity obscure details about biotic interactions. For example, identical changes in biodiversity can arise from predation, competition or mutualism. Our approach indicates that traditional models of community assembly miss key facets of diversity change. Instead, we suggest that analyses of diversity change should focus on partitions, which measure mechanisms that directly shape changes in diversity, notably species level selection and immigration, rather than traditional analyses of biotic interactions

Precise Determination of Blackbody Radiation Shifts in a Strontium Molecular Lattice Clock

Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr$_2$ molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the $10^{-16}$ level. This constitutes an important step towards mHz-level molecular spectroscopy in Sr$_2$, and provides a framework for evaluating BBR shifts in other homonuclear molecules.Comment: 6 pages, 4 figures, updated reference

Gluon-propagator functional form in the Landau gauge in SU(3) lattice QCD: Yukawa-type gluon propagator and anomalous gluon spectral function

We study the gluon propagator $D_{\mu\nu}^{ab}(x)$ in the Landau gauge in SU(3) lattice QCD at $\beta$ = 5.7, 5.8, and 6.0 at the quenched level. The effective gluon mass is estimated as $400 \sim 600$MeV for $r \equiv (x_\alpha x_\alpha)^{1/2} = 0.5 \sim 1.0$ fm. Through the functional-form analysis of $D_{\mu\nu}^{ab}(x)$ obtained in lattice QCD, we find that the Landau-gauge gluon propagator $D_{\mu\mu}^{aa}(r)$ is well described by the Yukawa-type function $e^{-mr}/r$ with $m \simeq 600$MeV for $r = 0.1 \sim 1.0$ fm in the four-dimensional Euclidean space-time. In the momentum space, the gluon propagator $\tilde D_{\mu\mu}^{aa}(p^2)$ with $(p^2)^{1/2}= 0.5 \sim 3$ GeV is found to be well approximated with a new-type propagator of $(p^2+m^2)^{-3/2}$, which corresponds to the four-dimensional Yukawa-type propagator. Associated with the Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $\rho(\omega)$ of the gluon field. The mass parameter $m$ turns out to be the effective gluon mass in the infrared region of $\sim$ 1fm. As a remarkable fact, the obtained gluon spectral function $\rho(\omega)$ is almost negative-definite for $\omega >m$, except for a positive $\delta$-functional peak at $\omega=m$.Comment: 20 pages, 15 figure

A terahertz vibrational molecular clock with systematic uncertainty at the 10−1410^{-14} level

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times10^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions.Comment: 17 pages, 8 figure

Lattice QCD analysis for Faddeev-Popov eigenmodes in terms of gluonic momentum components in the Coulomb gauge

We analyze the relation between Faddeev-Popov eigenmodes and gluon-momentum components in the Coulomb gauge using SU(3) lattice QCD. In the Coulomb gauge, the color-Coulomb energy is largely enhanced by near-zero Faddeev-Popov eigenmodes, which would lead to the confining potential. By the ultraviolet-momentum gluon cut, the color-Coulomb energy and the Faddeev-Popov spectrum are almost unchanged. In contrast to the ultraviolet insensitivity, the color-Coulomb energy and the Faddeev-Popov eigenmodes drastically change by infrared-momentum gluon cut. Without infrared gluons, the color-Coulomb energy tends to become non-confining, and near-zero Faddeev-Popov eigenmodes vanish. We also investigate the full FP eigenmodes, and find that infrared gluons widely influence both high and low Faddeev-Popov eigenmodes.Comment: 8 pages, 5 figure

Lagrangian Floer superpotentials and crepant resolutions for toric orbifolds

We investigate the relationship between the Lagrangian Floer superpotentials for a toric orbifold and its toric crepant resolutions. More specifically, we study an open string version of the crepant resolution conjecture (CRC) which states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold $\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after analytic continuation of quantum parameters and a change of variables. Relating this conjecture with the closed CRC, we find that the change of variable formula which appears in closed CRC can be explained by relations between open (orbifold) Gromov-Witten invariants. We also discover a geometric explanation (in terms of virtual counting of stable orbi-discs) for the specialization of quantum parameters to roots of unity which appears in Y. Ruan's original CRC ["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math. Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open and closed orbifold Gromov-Witten invariants. Along the way, we also prove an open mirror theorem for these toric orbifolds.Comment: 48 pages, 1 figure; v2: references added and updated, final version, to appear in CM

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio

Unified ethical principles and an animal research ‘Helsinki’ declaration as foundations for international collaboration

Ethical frameworks are the foundation for any research with humans or nonhuman animals. Human research is guided by overarching international ethical principles, such as those defined in the Helsinki Declaration by the World Medical Association. However, for nonhuman animal research, because there are several sets of ethical principles and national frameworks, it is commonly thought that there is substantial variability in animal research approaches internationally and a lack of an animal research ‘Helsinki Declaration’, or the basis for one. We first overview several prominent sets of ethical principles, including the 3Rs, 3Ss, 3Vs, 4Fs and 6Ps. Then using the 3Rs principles, originally proposed by Russell & Burch, we critically assess them, asking if they can be Replaced, Reduced or Refined. We find that the 3Rs principles have survived several replacement challenges, and the different sets of principles (3Ss, 3Vs, 4Fs and 6Ps) are complementary, a natural refinement of the 3Rs and are ripe for integration into a unified set of principles, as proposed here. We also overview international frameworks and documents, many of which incorporate the 3Rs, including the Basel Declaration on animal research. Finally, we propose that the available animal research guidance documents across countries can be consolidated, to provide a similar structure as seen in the Helsinki Declaration, potentially as part of an amended Basel Declaration on animal research. In summary, we observe substantially greater agreement on and the possibility for unification of the sets of ethical principles and documents that can guide animal research internationally