Branch Cuts Research Articles

Context dependence in a tropical forest: Repeated disturbance reduces soil nitrate response but increases phosphate

AbstractHurricanes and other extreme events are increasing in many regions, yet their long‐term impacts on ecosystem function are uncertain. In forested ecosystems, soil solution chemistry provides an important tool to assess the impacts of disturbance on nutrient cycling and dissolved organic carbon dynamics. Here, we address the dependence of soil solution chemistry on disturbance regime using a novel combination of both experimental and observational results collected over a period of 16 years in montane tropical sites in the Luquillo Experimental Forest of Puerto Rico. Soil solution was sampled following various combinations of canopy trimming and detrital manipulation (2004), repeated manipulation (2014), drought (2015), and Hurricane Maria (2017). Soil solution was sensitive to disturbance but resilient, with return to baseline after 12–18 months. Any disturbance regime that involved loss of canopy and detrital inputs to the forest floor resulted in increased nitrate concentrations, but the response declined with repeated disturbance. Lysimeters in plots that had received no experimental manipulation had 1.5 times higher response to Hurricane Maria than those previously manipulated. The response to disturbance thus showed clear context dependence, with disturbance history affecting disturbance response. Among the nutrients and major ions, only nitrate showed a response to experimental manipulations, drought, and Hurricane Maria. In contrast to nitrate, soil solution potassium was unaltered by initial experimental manipulation but increased dramatically following drought and Hurricane Maria. Phosphorus only increased following Hurricane Maria and only in plots that had twice received experimental trimming and deposition of cut branches on the forest floor. Stoichiometry of dissolved organic matter also changed in these plots, with decreased carbon to nitrogen ratios. The potassium response suggests that damage to roots from tropical cyclones and drought is an important driver of the biogeochemical response to tropical storms. Dampening of soil nitrogen losses and increases in phosphorus losses following successive disturbance events indicates that increased frequency of tropical storms and droughts will result in fundamental alteration of soil biogeochemical cycles, with uncertain effects on forest structure.

Partonic behavior of string scattering amplitudes from holographic QCD models

We study the emergence of partonic behavior in scattering processes at large Mandelstam’s variable s from string amplitudes in holographic backgrounds. We generalize the approach of Polchinski and Strassler [1] in two ways. (i) We analyze several holographic confining backgrounds, in particular the hard wall model, the soft wall model and Witten’s model. (ii) In addition to deriving the asymptotic behavior of the amplitudes at fixed angle and in the Regge limit, we also expand the amplitudes around their poles, integrate over the holographic direction and then re-sum the expansion. Due to dependence of the string tension on the holographic coordinate, the resulting singularities take the form of branch points rather than poles and the amplitudes display branch cuts and acquire a finite imaginary part. This may signal the failure of the PS prescription to reproduce the correct analytic structure at low energies. We also observe that the peaks are more pronounced in the region of small s but fade away for large s. In the fixed angle approximation we find in the hard and soft wall models that mathcal{A} ∼ s2−∆/2 whereas in Witten’s model mathcal{A} ∼ s3−∆/2 and mathcal{A} ∼ s7/3−2∆/3 for the 11D and 10D formulations, respectively. In the Regge regime mathcal{A} ∼ s2t−2+α (log s/t)−1+α where α is the power found in the fixed angle regime. Using the pole expansion the result for each model is Re [ mathcal{A} ] ∼ s−1, Im [ mathcal{A} ] ∼ sα. We compute the corresponding amplitudes for mesons using open strings and find qualitatively similar results as for closed strings.

Quantum carpets in a leaky box: Poincaré's recurrences in the continuous spectrum

The freedom to define branch cuts of the complex function is used to derive an integral representation of the quantum carpet, thus producing a generalization of the Poincar\'e recurrence theorem in the case of the continuous spectrum. This approach provides a different way to renormalize resonant states to be both space and time convergent. The coherence of quantum carpets was related to the properties of the Wigner function in the canonical time-frequency phase space. It has been shown that the distortion of the Wigner function shape is directly responsible for the lack of the ability of the dynamics to produce revivals equally as sharp as the initial wave packet.

Form factors and spectral densities from Lightcone Conformal Truncation

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators \U0001d4aa in ϕ4 theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator \U0001d4aa between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of \U0001d4aa between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator \U0001d4aa is the trace Θ of the stress tensor.

Analytic AC conductivities from holography

We find exact, analytic solutions of the holographic AC conductivity at arbitrary frequency $\omega$ and temperature $T$, in contrast to previous works where the AC conductivity was analytically obtained usually at small $\omega$ and $T$. These solutions enable us to study the analyticity properties of the current-current correlator $G(\omega)$ in detail. The first system we study is the AdS$_5$ planar black hole with momentum dissipation, whose extremal limit has an AdS$_2$ factor. Then we study AdS$_4$ and AdS$_5$ Einstein-dilaton systems whose special cases are maximal gauged supergravities. The solutions show how the poles move and how branch cuts emerge as the temperature varies. As a byproduct, we obtain an R-current correlator in $\mathcal{N}=4$ super-Yang-Mills theory on a sphere at finite temperature in the large $N$ and strong coupling limit.

Residue Classification-Based Robust Phase Unwrapping in High-Noise Region

Synthetic aperture radar interferometry can obtain information on the surface of the earth. In fact, the accuracy of phase unwrapping directly affects the accuracy of the digital elevation model, but the problem that has been puzzling people is the low accuracy of unwrapping in high-noise regions. To solve this problem, we propose a new approach based on an improved branch-cut method, which classifies the branch cut. First, connect the short branch cuts and then use the network-flow method to connect the long branch cuts. By categorized branch cuts, each type of branch cut processes part of the residues and divides the region with high residue density into two regions with low residue density for unwrapped, which solves the problem of low phase unwrapping accuracy in high-noise regions. The experimental results of simulation and measured data show that RCBC method shows high unwrapping accuracy in high-noise regions, very short total length of connected branch cuts, and strong robustness.

Pest categorisation of Malacosoma disstria.

The European Commission requested the EFSA Panel on Plant Health to conduct a pest categorisation of Malacosoma disstria Hübner (Lepidoptera: Lasiocampidae), commonly known as the forest tent caterpillar, for the territory of the EU. M. disstria is a North American polyphagous leaf‐eating pest primarily feeding on deciduous trees belonging to the genera Acer, Malus, Populus, Prunus, Quercus and Tilia. It is a univoltine species. Eggs are laid on twigs and branches. Larvae emerge in the spring to feed on buds and fresh leaves. Host plants can be completely defoliated although they often refoliate and recover within a few weeks. Nevertheless, three consecutive years of heavy defoliation or repeated periods of defoliation combined with drought can cause extensive tree mortality. As such, M. disstria is regarded as one of the most serious hardwood forestry insect pests in North America. Population upsurges leading to outbreaks are cyclical, generally nine to 13 years apart and can last 2–3 years. Outbreaks have been reported in eastern North America since the late 18th century. Outbreaks in western Canada have spanned up to 200,000 km2. Plants for planting, cut branches and isolated bark provide pathways for entry. Host availability and climate suitability suggest that large parts of the EU would be suitable for establishment. The pest could spread naturally by flight within the EU. Eggs on plants for planting could also facilitate spread. The introduction of M. disstria into the EU could lead to serious outbreaks causing significant damage to forest, orchard and amenity trees and shrubs. Phytosanitary measures are available to inhibit the entry and spread of this species. M. disstria satisfies the criteria that are within the remit of EFSA to assess for it to be regarded as a potential Union quarantine pest.

Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions

The quadrature error associated with a regular quadrature rule for evaluation of a layer potential increases rapidly when the evaluation point approaches the surface and the integral becomes nearly singular. Error estimates are needed to determine when the accuracy is insufficient and a more costly special quadrature method should be utilized.The final result of this paper are such quadrature error estimates for the composite Gauss-Legendre rule and the global trapezoidal rule, when applied to evaluate layer potentials defined over smooth curved surfaces in R3. The estimates have no unknown coefficients and can be efficiently evaluated given the discretization of the surface, invoking a local one-dimensional root-finding procedure. They are derived starting with integrals over curves, using complex analysis involving contour integrals, residue calculus and branch cuts. By complexifying the parameter plane, the theory can be used to derive estimates also for curves in R3. These results are then used in the derivation of the estimates for integrals over surfaces. In this procedure, we also obtain error estimates for layer potentials evaluated over curves in R2. Such estimates combined with a local root-finding procedure for their evaluation were earlier derived for the composite Gauss-Legendre rule for layer potentials written in complex form [4]. This is here extended to provide quadrature error estimates for both complex and real formulations of layer potentials, both for the Gauss-Legendre and the trapezoidal rule.Numerical examples are given to illustrate the performance of the quadrature error estimates. The estimates for integration over curves are in many cases remarkably precise, and the estimates for curved surfaces in R3 are also sufficiently precise, with sufficiently low computational cost, to be practically useful.

Universal large-order asymptotic behavior of the strong-coupling and high-temperature series expansions

For theories that exhibit second-order phase transition, we conjecture that the large-order asymptotic behavior of the strong-coupling (high-temperature) series expansion takes the form ${\ensuremath{\sigma}}^{n}{n}^{b}$ where $b$ is a universal parameter. The associated critical exponent is then given by $b+1$. The series itself can be approximated by the hypergeometric approximants ${_{p}F}_{p\ensuremath{-}1}$ which can mimic the same large-order behavior of the given series. Near the tip of the branch cut, the hypergeometric function ${_{p}F}_{p\ensuremath{-}1}$ has a power-law behavior from which the critical exponent and critical coupling can be extracted. We test the conjecture in this work for the perturbation series of the ground state energy of the Yang-Lee model as a strong-coupling form of the $\mathcal{P}\mathcal{T}$-symmetric $i{\ensuremath{\phi}}^{3}$ theory and the high-temperature expansion within the Ising model. From the known $b$ parameter for the Yang-Lee model, we obtain the exact critical exponents, which reflects the universality of $b$. Very accurate prediction for $b$ has been obtained from the many orders available for the high-temperature series expansion of the Ising model, which in turn predicts accurate critical exponents. Apart from critical exponents, the hypergeometric approximants for the Yang-Lee model show almost exact predictions for the ground state energy from low orders of perturbation series as input.

Late-day measurement of excised branches results in uncertainty in the estimation of two stomatal parameters derived from response curves in Populus deltoides Bartr.×Populus nigra L.

Many terrestrial biosphere models depend on an understanding of the relationship between stomatal conductance and photosynthesis. However, unlike the measurement of photosynthetic parameters, such as the maximum carboxylation capacity, where standard methods (e.g., CO2 response or ACi curves) are widely accepted, a consensus method for empirically measuring parameters representing stomatal response has not yet emerged. Most models of stomatal response to environment represent stomatal conductance as being bounded by a lower intercept parameter (g0), and linearly scaled based on a multivariate term described by the stomatal slope parameter (g1). Here we employ the widely used Unified Stomatal Optimization model, to test whether g1 and g0 parameters are impacted by the choice of measurement method, either on an intact branch or a cut branch segment stored in water. We measured paired stomatal response curves on intact and excised branches of a hybrid poplar clone (Populus deltoides Bartr.×Populus nigra L. OP367), measured twice over a diurnal period. We found that predawn branch excision did not significantly affect measured g0 and g1 when measured within 4 h of excision. Measurement in the afternoon resulted in significantly higher values of g1 and lower values of g0, with values changing by 55% and 56%, respectively. Excision combined with afternoon measurement resulted in a marked effect on parameter estimates, with g1 increasing 89% from morning to afternoon and a 25% lower g1 for cut branches than those measured in situ. We also show that in hybrid poplar the differences in parameter estimates obtained from plants measured under different conditions can directly impact models of canopy function, reducing modeled transpiration by 18% over a simulated 12.5-h period. Although these results are only for a single isohydric woody species, our findings suggest that stomatal optimality parameters may not remain constant throughout the day.

Pest categorisation of Thecodiplosis japonensis.

The EFSA Panel on Plant Health performed a pest categorisation of Thecodiplosis japonensis (Diptera: Cecidomyiidae) for the EU territory. This species is not included in the EU Commission Implementing Regulation 2019/2072. T. japonensis Uchida & Inouye is a well‐defined species, native to a large part of Japan, which was introduced to the Republic of Korea and eastern China: Fujian and Shandong. It attacks Pinus densiflora, P. thunbergii and P. luchuensis in Japan; P. densiflora and P. thunbergii in Korea; and P. massoniana in China, and has been observed to attack other two‐needle pine species, including species present in the EU. The pest is univoltine and the adults emerge between May and August. The adults live only for 1 day. Each female oviposits in batches on developing needles. The neonate larvae crawl to the base of the needle fascicle and create a gall in which they feed gregariously by sap sucking. The third‐instar larvae leave the galls in November, overwinter in a cocoon in the soil and pupate at the end of the winter. Degree day models have been developed to predict adult emergence. Survival of overwintering stages is poor below 15°C and above 30°C. The pest can be detected by its symptoms (stunted or dead needles, galls at the base of infected needle fascicles), and identified using morphological characters or the mitochondrial COI gene. T. japonensis is one of the major forest pests in the Republic of Korea, where 1.7 million trees were cut to control it in 2014–2015. It flies uneasily (a few hundred metres) but can be transported in galls on Pinus plants for planting, including artificially dwarfed plants, or with cut branches. Climate matching and host tree distribution suggest that T. japonensis would be able to establish and have an impact in the EU territory. T. japonensis satisfies all the criteria that are within the remit of EFSA to assess for it to be regarded as a potential Union quarantine pest.

Natural selection rules: new positivity bounds for massive spinning particles

We derive new effective field theory (EFT) positivity bounds on the elastic 2 → 2 scattering amplitudes of massive spinning particles from the standard UV properties of unitarity, causality, locality and Lorentz invariance. By bounding the t derivatives of the amplitude (which can be represented as angular momentum matrix elements) in terms of the total ingoing helicity, we derive stronger unitarity bounds on the s- and u-channel branch cuts which determine the dispersion relation. In contrast to previous positivity bounds, which relate the t-derivative to the forward-limit EFT amplitude with no t derivatives, our bounds establish that the t-derivative alone must be strictly positive for sufficiently large helicities. Consequently, they can provide stronger constraints beyond the forward limit which can be used to constrain dimension-6 interactions with a milder assumption about the high-energy growth of the UV amplitude.

Error bounds for the asymptotic expansions of the Hermite polynomials

In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel–Rotach scale. Three cases, depending on whether the scaled variable lies in the outer or oscillatory interval, or it is the turning point, are considered separately. We introduce the ‘branch cut’ technique to express the error terms as integrals on the contour taken as the one-sided limit of curves approaching the branch cut. This new technique enables us to derive simple error bounds in terms of elementary functions. We also provide recursive procedures for the computation of the coefficients appearing in the asymptotic expansions.

Cutting and gluing with running couplings in N=2 QCD

We consider the order parameter $u=\left<{\rm Tr}\phi^2\right>$ as function of the running coupling constant $\tau \in \mathbb{H}$ of asymptotically free $\mathcal{N}=2$ QCD with gauge group $SU(2)$ and $N_f\leq 3$ massive hypermultiplets. If the domain for $\tau$ is restricted to an appropriate fundamental domain $\mathcal{F}_{N_f}$, the function $u$ is one-to-one. We demonstrate that these domains consist of six or less images of an ${\rm SL}(2,\mathbb{Z})$ keyhole fundamental domain, with appropriate identifications of the boundaries. For special choices of the masses, $u$ does not give rise to branch points and cuts, such that $u$ is a modular function for a congruence subgroup $\Gamma$ of ${\rm SL}(2,\mathbb{Z})$ and the fundamental domain is $\Gamma\backslash\mathbb{H}$. For generic masses, however, branch points and cuts are present, and subsets of $\mathcal{F}_{N_f}$ are being cut and glued upon varying the mass. We study this mechanism for various phenomena, such as decoupling of hypermultiplets, merging of local singularities, as well as merging of non-local singularities which give rise to superconformal Argyres-Douglas theories.

Experimental realization of non-Abelian permutations in a three-state non-Hermitian system.

Eigenstates of a non-Hermitian system exist on complex Riemannian manifolds, with multiple sheets connecting at branch cuts and exceptional points (EPs). These eigenstates can evolve across different sheets-a process that naturally corresponds to state permutation. Here, we report the first experimental realization of non-Abelian permutations in a three-state non-Hermitian system. Our approach relies on the stroboscopic encircling of two different exceptional arcs (EAs), which are smooth trajectories of order-2 EPs appearing from the coalescence of two adjacent states. The non-Abelian characteristics are confirmed by encircling the EAs in opposite sequences. A total of five non-trivial permutations are experimentally realized, which together comprise a non-Abelian group. Our approach provides a reliable way of investigating non-Abelian state permutations and the related exotic winding effects in non-Hermitian systems.

A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Pentagon functions for one-mass planar scattering amplitudes

We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent transcendental functions, which we call one-mass pentagon functions. We construct them by using the properties of iterated integrals with logarithmic kernels. The pentagon functions are manifestly free of unphysical branch cuts, do not require analytic continuation, and can be readily evaluated over the whole physical phase space of the massive-particle production channel. We develop an efficient algorithm for their numerical evaluation and present a public implementation suitable for direct phenomenological applications.

Elucidating the ρ-meson’s role as intermediate resonance in the time-like electromagnetic pion form factor

Motivated by the planned measurements of the time-like electromagnetic proton form factors an exploratory study of the time-like electromagnetic pion form factor is presented in a formalism which describes mesons as Poincaré-invariant bound states. In the respective quark interaction kernel, beyond the gluon-intermediated interactions for valence-type quarks, non-valence effects are included by allowing the pions to couple back in a self-consistent manner to the quarks. Consequently, the opening of the dominant ρ decay channel, ρ → ππ, and the presence of a multi-particle branch cut, setting in when the two-pion threshold is crossed, are included consistently, first in the correspondingly calculated quark-photon vertex, and then consequently in the time-like electromagnetic pion form factor. The obtained results are in agreement with the available experimental data and provide further evidence for the effcacy of a vector-meson dominance model. Effects of going beyond the here employed isospin-symmetric limit are discussed. Last but not least, an outlook is provided on how to include in Poincaré-covariant Faddeev approaches the effects of intermediate resonances in the calculation of baryon properties.

The Effect of Temperature and Relative Humidity Inside The Shade Netting on The Growth of Pepper Fruiting Branch Cuttings

Pepper (Piper nigrum L.) has many benefits, especially in its seeds, commonly used as a food flavoring. Pepper effectively increases appetite, increases the digestive glands' activity, and accelerates fatty substances' digestion. In general, pepper production per unit area in Indonesia is low. The average is below 1 ton of dry pepper per hectare. This low productivity is mainly due to inadequate cultivation techniques, such as improper fertilization and inadequate care. The development of pepper cultivation is still running slowly due to the many obstacles faced by farmers. This productivity could be increased if farmers could apply good and correct cultivation techniques. Generally, pepper cultivation in Indonesia uses standards. This technique is expensive and requires intensive maintenance. The pepper seeds commonly planted by farmers come from running shoots. The experimental design used was the split-plot design with shade netting as the first factor and the administration of husk charcoal as the second factor. Other factors observed were climatic factors, including temperature and relative humidity, bird bud burst time, sprouting time, and root-shoot ratio. The results indicated that the shade netting and husk charcoal treatment on the planting medium significantly affected bird bud burst time, sprouting time, and root-shoot ratio. This study aimed to investigate the effect of climate on the growth of pepper cuttings. The results indicated that the best bird bud burst time occurred in treatment n0 (100%), a0 (1:1) 34.67 days, and not significantly different from n0 (100%) a2 (0: 1) 35.00 days. The best sprouting time occurred in treatment n0 (100%) a2 (0: 1) 32.00 days, not significantly different from n0 (100%) a0 (1: 1) 32.50 days. The root-shoot ratio was significantly different in treatment n0 (100%) a1 (1; 0) 5.28 g.

Quantum Spectral Curve for AdS3/CFT2: a proposal

We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.