Pole Expansion Research Articles

Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation

The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-conditioned inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two recently developed analytic continuation methods, namely stochastic pole expansion and Nevanlinna analytic continuation, for extracting spectral functions from mock lattice QCD data. We examine a range of Euclidean correlation functions generated by representative models, including the Breit-Wigner model, the Gaussian mixture model, the resonance-continuum model, and the bottomonium model. Then, we apply the two methods to reconstruct spectral functions from charmonium correlation functions computed using lattice QCD simulations at a finite temperature. Our findings demonstrate that the stochastic pole expansion method, when combined with the constrained sampling algorithm and the self-adaptive sampling algorithm, successfully recovers the essential features of the spectral functions and exhibits excellent resilience to noise of input data. In contrast, the Nevanlinna analytic continuation method suffers from numerical instability, often resulting in the emergence of spurious peaks and significant oscillations in the high-energy regions of the spectral functions, even with the application of the Hardy basis function optimization algorithm. Published by the American Physical Society 2024

Stochastic pole expansion method for analytic continuation of the Green's function

Stochastic pole expansion method for analytic continuation of the Green's function

Outcome analysis and assessment of the lower pole expansion following breast augmentation with ergonomic implants: Optimizing results with patient selection based on 5-year data

Silicone implants have gone through adaptations to improve esthetic outcomes. With the progress of technology, including gel rheology, different properties have been introduced. Ergonomic style implants (ESI) feature enhanced rheological properties and provide a shaped contour with a round base. This study investigated outcomes for ESI in breast augmentation concerning lower pole stretching (LPS) and implant stability and describes an algorithm to assist in decision-making. A total of 148 patients (296 breasts) underwent breast augmentation with ESI; this procedure was indicated in patients with good skin quality and <6cm between the nipple-areola complex and the inframammary fold. The mean patient age was 29.6 years (range: 19-39), and 93 patients (62.8%) underwent primary breast augmentation with demi/full projection (average volume of 245 cc [175-375 cc]). Axillary incision and subfascial pocket were indicated in 115 (77.7%) and 72 (48%) cases, respectively. Average LPS values were 32.2% (24.91mm) and 10.86% (9.42mm) at up to 10 days and 10 days to 12 months postprocedure, respectively. Patients were followed for a mean of 29.9±26.4 months (range: 6-66). Complication rates per breast and per patient were 5% and 10%, respectively, and included subcutaneous banding in the axilla (1.6%), implant displacement (1.2%), and wound dehiscence (0.8%). No cases of infection, seroma, or rippling complications were observed. The present decision-making algorithm summarizes the process involved in breast augmentation using ESI and is intended to help standardize decisions. With correct planning, long-lasting outcomes can be achieved due to favorable interactions between ESI and the patient's tissues.

Higgs inflation at the pole

We propose a novel possibility for Higgs inflation where the perturbative unitarity below the Planck scale is ensured by construction and the successful predictions for inflation are accommodated. The conformal gravity coupling for the Higgs field leads to the proximity of the effective Planck mass to zero in the Jordan frame during inflation, corresponding to a pole in the Higgs kinetic term in the Einstein frame. Requiring the Higgs potential to vanish at the conformal pole in the effective theory in the Jordan frame, we make a robust prediction of the successful Higgs inflation. For a successful Higgs inflation at the pole, we take the running quartic coupling for the Higgs field to be small enough at the inflation scale, being consistent with the low-energy data, but we need a nontrivial extension of the SM with extra scalar or gauge fields in order to keep the running Higgs quartic coupling small during inflation. Performing the perturbative analysis of reheating with the known couplings of the SM particles to the Higgs boson, we show that a concrete realization of the Higgs pole inflation can be pinned down by the reheating processes with a general equation of state for the Higgs inflaton. We illustrate some extensions of the simple Higgs pole inflation to the general pole expansions, the running Higgs quartic coupling in the Standard Model and its extension with a singlet scalar field, a supergravity embedding of the Higgs pole inflation.

Predicting the expansion of the lower pole of the breast following smooth breast implant augmentation: A novel shear wave elastography study

This study aimed to educate and demonstrate how the use of shear wave elastography (SWE) can be used to determine the elasticity of patient tissues preoperatively, which can then be used to predict the level of lower pole expansion postoperatively, following breast augmentation surgery. This study evaluated 60 breasts in 30 patients that were divided in 3 equal groups (n=20) according to their predefined elastography criteria measured via SWE (loose, moderate, and tight tissue elasticity). All measurements were taken under maximum stretch between the inferior border of the nipple alveolar complex (NAC) and inframammary fold (IMF) using a measuring tape in millimetres (mm). The follow-up appointments for routine assessments and measurements were done at 3, 6, 12, 18, and 24 months. The study engaged 38 patients over 4 years, but only 10 patients in each group attended all the appointments. Statistical analysis showed the elastic skin types (loose, moderate, and tight) had significantly different rates of lower pole expansion, and the rate of expansion increased significantly after 6 months postoperatively, whereas prior to 6 months, the rates were comparable (p<0.05). The results showed that increasingly elastic skin types have a greater rate of lower pole expansion. This is important for the operating surgeon to be aware of as looser skin types will be more prone to lower pole expansion, and thus, a higher surgical IMF suture may be advised to manage patient expectations. This study can be used as a guideline for surgeons, which will allow for a more predictable surgical planning system that will ultimately lead to fewer revisions and risks for patients worldwide.

Determining the response of optical systems in both time and harmonic domains with the singularity expansion method

Physical systems are characterized by their transfer operators in the harmonic domain. These operators are usually locally approximated as rational functions or pole expansions. We generalize this result and introduce the Multiple-Order Singularity Expansion Method (MOSEM) which offers an exact description of linear systems in terms of their singularities and Laurent series coefficients or zeros. The interest of this approach is first illustrated by the simple but fundamental case of a dispersive Fabry-Perot cavity, where it provides an analytical expression of the reflected field in both the time and harmonic domains. In a second step, we show that this method must be applied for defining the complex expression of the dielectric permittivity that describes the physical response of a system (the material) to an excitation field. This rigorous expression of the permittivity is shown to provide highly accurate results for a broad range of materials.

Immediate surgical mesh-free implant-based breast reconstruction with fascial flap in breast cancer patients after mastectomy.

Surgical meshes are often used in retro-pectoral implant-based breast reconstruction (IBBR) to improve lower pole expansion. However, using of surgical meshes is associated with increased complications and costs. To solve this problem, we have adopted a modified fascia-based IBBR technique using fasciae of pectoral major, serratus anterior, and external oblique muscles to form a sling covering the lower pole of prosthesis since 2014. Data of 788 retro-pectoral IBBR cases, including 250 fascia-based IBBR cases (fascial group) and 538 traditional IBBR cases (control group), treated between 2014 and 2019 were retrospectively analyzed. The surgical outcomes of the fascial and control group were compared. The primary endpoint was the rate of post-operative complications requiring interventions. The secondary endpoint was the rate of explantation. The exploratory endpoint was the time from surgery to complication and explantation. The fascial group had significantly lower rates of developing major post-operative complications (1.2 vs. 6.1%, p = 0.002) and losing prostheses (1.2 vs. 4.3%, p = 0.025), as compared with the control group. The median time from surgery to complication and explantation were 61 (range, 35-115) days and 92 (range, 77-134) days for the fascial group and 35 (range, 6-239) days and 63 (range, 23-483) days for the control group, respectively. Fascia-based IBBR technique had low rates of major post-operative complications and explantation. Fascia-based IBBR technique could be considered as an alternative reconstruction method in properly selected patients.

Analytic Map of Three-Channel S Matrix: Generalized Uniformization and Mittag-Leffler Expansion.

We explore the analytic structure of the three-channel S matrix by generalizing uniformization and making a single-valued map for the three-channel S matrix. First, by means of the inverse Jacobi's elliptic function we construct a transformation from eight Riemann sheets of the center-of-mass energy complex plane onto a torus, on which the three-channel S matrix is represented single-valued. Second, we show that the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering amplitude includes not only topologically trivial but also nontrivial contributions and is given by the Weierstrass zeta function. Finally, taking a simple nonrelativistic effective field theory with contact interaction for the S=-2, I=0, J^{P}=0^{+}, ΛΛ-NΞ-ΣΣ coupled-channel scattering, we demonstrate that as a function of the uniformization variable the scattering amplitude is, in fact, given by the Mittag-Leffler expansion and is dominated by contributions from neighboring poles.

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.

Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation

We consider the half-wave maps (HWM) equation which is a continuum limit of the classical version of the Haldane–Shastry spin chain. In particular, we explore a many-body dynamical system arising from the HWM equation under the pole ansatz. The system is shown to be completely integrable by demonstrating that it exhibits a Lax pair and relevant conservation lows. Subsequently, the analytical multisoliton solutions of the HWM equation are constructed by means of the pole expansion method. The properties of the one- and two-soliton solutions are then investigated in detail as well as their pole dynamics. Last, an asymptotic analysis of the N-soliton solution reveals that no phase shifts appear after the collision of solitons. This intriguing feature is worth noting since it is the first example observed in the head-on collision of rational solitons. A number of problems remain open for the HWM equation, some of which are discussed in concluding remarks.

Scattering matrix pole expansions for complex wave numbers inR-matrix theory

In this follow-up article to [Shadow poles in the alternative parametrization of R-matrix theory, Ducru (2020)], we establish new results on scattering matrix pole expansions for complex wavenumbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory, and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wavenumbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift $\boldsymbol{S}$ and penetration $\boldsymbol{P}$ functions: the legacy Lane \& Thomas "force closure" approach, versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. In this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and unveil new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii $a_c$. We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix -- cancelling spurious poles and guaranteeing generalized unitarity -- while still being able to close channels below thresholds.

Shadow poles in the alternative parametrization of R -matrix theory

Nuclear data libraries (ENDF, JEFF, JENDL, CENDL, etc.) document our phenomenological knowledge of nuclear cross sections as interpreted by R-matrix theory. The R-matrix scattering model can parameterize the energy dependence of the scattering matrix in different ways. This article establishes new results on three such sets of parameters: the Wigner-Eisenbud, the Brune, and the Siegert-Humblet parameters. We show how the latter two arise from invariance to the arbitrary boundary condition, and how they can trade-off more complex parameters for a simpler energy dependence parameterization: the scattering matrix pole expansion of Humblet and Rosenfeld. We establish that the scattering matrix's invariance to channel radius sets a partial differential equation on the widths of the Kapur-Peierls operator, which enables us to derive an explicit transformation of the Siegert-Humblet radioactive residue widths under a change of channel radius. Considering the continuation of the scattering matrix to complex wavenumbers, several new results are established. We unveil there exist more Brune parameters than previously thought, depending on the way the scattering matrix is continued to complex energies. This points to a broader conundrum in the field: how to analytically continue the scattering matrix while closing sub-threshold channels. We argue that, contrary to the Lane and Thomas legacy of force-closing sub-threshold channels which introduces spurious poles, analytic continuation is the physically correct way of defining the scattering matrix for complex wave numbers. To back this claim we establish thee results: analytic continuation cancels spurious poles, enforces the generalized unitarity conditions of Eden and Taylor, and closes massive particle channels below threshold by both quantum tunneling and from the definition of the cross section as the ratio of probability currents.

Quantitative Analysis of Nipple to Inframammary Fold Distance Variation in Tuberous Breast Augmentation: Is there a Progressive Lower Pole Expansion?

In patients with short nipple to inframammary fold (N-IMF) distance, as in tuberous breast, the cohesivity and gel distribution of shaped implants work as a controlled tissue expander, progressively adapting the tissues to the implant's shape. This phenomenon translates into a gradual increase of the N-IMF distance over time, but the true extent to which this occurs has not been quantified to date. This study aims to quantify the postoperative variation of the N-IMF distance in tuberous breast treated with shaped cohesive silicone breast implants. We did a retrospective review of a prospective maintained database of all consecutive patients with bilateral Groulleau I and II tuberous breasts who underwent primary breast augmentation between April 2017 and May 2018 at our institution. To quantify the lower mammary pole's morphological changes, we evaluated the N-IMF distance under maximal stretch as an endpoint. We recorded this value at time 0 (preoperative), immediate post-op (equivalent to the distance planned preoperatively) and at month 1, month 6 and 1-year post-op. Then we calculated the average N-IMF distance variation of our sample of patients with a 99% interval of confidence for each breast obtained. Comparisons were performed using the Sign test and the Mann-Whitney U test. The average implant weight was 353g (range 290-450; SD ±46.147). Of the 54 breasts analyzed, the immediate post-op N-IMF distance was on average 2.43 cm longer than the preop IMF with a 99% confidence interval between 2.01 and 2.86 and SD of ±1.22. The mean difference between the preop N-IMF distance and after 1, 6 and 12 months was respectively 2.78cm (SD,1.56) (99% CI, 2.24-3.34), 3.08 cm (SD, 1.57) (99% CI, 2.53-3.64), and 3.36 (1.55) (99% CI, 2.82-3.91) Comparing immediate postoperative nipple to inframammary fold distance (N-IMF) to the 1, 6 and 12 months N-IMF values, an average of 4.23% (CI 1.3-7.16), 7.74% (CI 4.25-11.23) and 10.84% (CI 7.21-14.49) of skin length, was gained respectively. According to implants' weight, subgroup analysis showed that implants > 400g were associated with significantly higher N-IMF distance increase (p <0.05) compared to implants < 400g. Our findings suggest that a significant progressive postoperative increase in N-IMF distance should be expected in all cases of tuberous breast augmentation with anatomical implants over a 1 year period. This aspect may have an important implication on the IMF incision and the new fold position preoperative planning. LEVEL OF EVIDENCE IV.

Numerical solution of large scale Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree–Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons N is relatively small compared to the matrix size Nb. We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most 𝒪(Nb2) for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with Nb up to 2.88 × 106, and the wall clock time is less than 100 s using 17 280 CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

Explantation in Tissue Expander and Direct-to-Implant Reconstruction with Acellular Dermal Matrix: How to Avoid Early Reconstructive Failures.

In the United States, approximately 57,000 tissue expander/implant-based breast reconstructions are performed each year. Complete submuscular tissue expander coverage affords the best protection against implant exposure but can restrict lower pole expansion. The benefits of using acellular dermal matrix are enticing, but questions remain as to whether or not its presence increases reconstructive failures. The purpose of this study was to investigate predictors of explantation in those patients with acellular dermal matrix reconstructions and to discuss salvage techniques. An approved retrospective review was conducted of 137 patients undergoing 234 individual breast reconstructions over 4 years performed by a single plastic surgeon (J.D.) at a single institution. Patients who underwent implant-based reconstruction with either immediate placement of a tissue expander that was subsequently exchanged for a permanent implant at a second operation or immediate placement of a permanent implant when indicated were included. One hundred thirty-seven patients who underwent 234 implant-based breast reconstructions using acellular dermal matrix met criteria. There was an overall 23 percent complication rate, including any cellulitis, seroma, skin necrosis, and hematoma formation. Significant preoperative risk factors for any postoperative complication included body mass index greater than 25 kg/m2 and a history of radiation therapy before acellular dermal matrix placement. Radiation therapy was found to be a significant risk factor for postoperative skin necrosis. Of explantations, many fluid cultures grew Gram-negative bacteria. Skin necrosis is a serious risk factor for explantation in implant-based reconstruction with acellular dermal matrix. The reconstructive surgeon should consider early excision of any skin necrosis as soon as it is identified. Risk, III.

Muscle-Splitting Transaxillary Revision Breast Augmentation-A Single Surgeon's Experience.

Well discussed in a previous article published by the senior author, primary transaxillary breast augmentation drawbacks include the need to correct complications arising from reuse of the axillary incision which the literature is sparse on. We here discuss a technique in patients who underwent a secondary transaxillary breast augmentation procedure. This study aims to present a technique for transaxillary revision breast augmentation with conversion to a muscle-splitting plane which has the advantage of good upper and medial pole coverage and adequate lower pole expansion. We performed a retrospective chart review of 41 women with previous silicone gel implants placed through a transaxillary incision who presented with rippling or a desire for larger implants (January 2016-July 2020). Inclusion criteria were age 18 years or older and having undergone breast augmentation surgery. Exclusion criteria were active smoking and body mass index (BMI) greater than 30 kg/m2. At one year postoperatively patients were asked a "yes or no" question regarding satisfaction with the overall result and with the scar quality. A total of 41 patients were included in this study; no patients were excluded. The patients' age ranged from 32 to 47 years, the average being 38 years old. All participants were female. Mean BMI was 21.9 kg/m2 and all patients had a pinch test <2cm. Indications for surgery included rippling (all patients) and a desire for larger implant size (n = 5). Size of new implants ranged from 325cc to 430cc; all were of a larger size than those used in the primary surgery. Operative time was on average 53 min. [4483 min.]. Mean follow-up was 13 months, ranging from 12 to 15 months. There was no additional cost related to operative time. Regarding patient satisfaction, 100% replied they were pleased with the overall results and scar quality. There were no major complications. The transaxillary approach for muscle splitting breast augmentation revision surgery offers a safe and reproducible technique. Despite having a mean follow-up of only 13 months, we demonstrate a low rate of complication as well as high degree of patient satisfaction with no extra cost when compared to other techniques. This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

Debye Parameters of Humidity-Varying Soils for Induction Logging Techniques

This paper focuses on the tabulation of calculated Debye coefficients for a wide range of soils for source waves ranging from 300 MHz to 2 GHz. Debye coefficients of different soils will produce accurate FDTD dispersive simulations for wireline logging purposes. The FDTD dispersion analysis is based on an Auxiliary Differential Equation (ADE) method which depends on the Debye coefficients. A complex set of soil data is acquired and used in a twostep numerical solver to calculate the Debye coefficients. For a wide range of soils, Debye coefficients were developed for one, two, and three pole expansions. Most fits for one pole fits were highly inaccurate, so the coefficients generated were disregarded. Coefficients for two and three term expansions were accurate and were generated and tabulated here.

On the pole expansion of electromagnetic fields.

In several publications, it has been shown how to calculate the near- or far-field properties for a given source or incident field using the resonant states, also known as quasi-normal modes. As previously noted, this pole expansion is not unique, and there exist many equivalent formulations with dispersive expansion coefficients. Here, we approach the pole expansion of the electromagnetic fields using the Mittag-Leffler theorem and obtain another set of formulations with constant weight factors for each pole. We compare the performance and applicability of these formulations using analytical and numerical examples. It turns out that the accuracy of all approaches is rather comparable with a slightly better global convergence of the approach based on a formulation with dispersive expansion coefficients. However, other expansions can be superior locally and are typically faster. Our work will help with selecting appropriate formulations for an efficient description of the electromagnetic response in terms of the resonant states.

Five-Body Integral Equations and Solution of the $$\varvec{\eta -4N}$$ Problem

The Alt–Grassberger–Sandhas equations for the five-body problem are solved for the case of the driving two-body potentials limited to s-waves. The separable pole expansion method is employed to convert the equations into the effective quasi-two-body form. Numerical results are presented for five identical bosons as well as for the system containing an $$\eta $$-meson and four nucleons. Accuracy of the separable expansion is investigated. It is shown that both in $$(1+4)$$ and $$(2+3)$$ fragmentation, the corresponding eigenvalues decrease rather rapidly, what, combined with the alternation of their signs, leads to rather good convergence of the results. For the $$\eta -4N$$ system the crucial influence of the subthreshold behavior of the $$\eta N$$ amplitude on the $$\eta $$-nuclear low-energy interaction is discussed.

Modal analysis of anapoles

The resonant interaction between light dielectric scatterers can yield to a resonant light scattering process and to a strong enhancement of the near field intensities at a deep sub-wavelength scale. While Fano resonances can be observed in the scattering spectrum of Mie scatterers, the spectrum of the internal field enhancement is composed of a set of peaks that feature Lorentzian shapes. The question is to know how to optimize the internal field enhancement and how to predict the maximum of the internal field enhancement with respect to the far field response. Here, we derive a pole expansion of the scattering operator to perform a modal analysis of the external and internal field spectra. This pole expansion provides a suitable mathematical description of the Fano resonances observed in the scattering spectrum and of the Lorentzian peaks observed in the internal field spectrum. This modal analysis is also used to predict the maxima of the internal field, i.e. the frequency that yields the strongest field intensity inside the dielectric scatterer.