General Mass Research Articles

On factorization hierarchy of equations for banana Feynman integrals

We present a review of the relations between various equations for maximal cut banana Feynman diagrams, i.e. integrals with propagators substituted with δ-functions. We consider both equal and generic masses. There are three types of equation to consider: those in coordinate space, their Fourier transform and Picard-Fuchs equations originating from the parametric representation. First we review the properties of the corresponding differential operators themselves, mainly their factorization properties at the equal mass locus and their form at special values of the dimension. Then we study the relation between the Fourier transform of the coordinate space equations and the Picard-Fuchs equations and show that they are related by factorization as well. The equations in question are the counterparts of the Virasoro constraints in the much-better studied theory of eigenvalue matrix models and are the first step towards building a full-fledged theory of Feynman integrals, which will reveal their hidden integrable structure.

Lenacapavir to prevent HIV infection: current prices versus estimated costs of production.

Despite improvements in treatment and oral pre-exposure prophylaxis (PrEP) access, 1.3 million people acquired HIV in 2022. Six-monthly lenacapavir PrEP could benefit tens of millions of people at high risk of infection. However, prices are currently up to $44 819 per person per year (pppy). We projected minimum lenacapavir pricing based on generic mass production and a Cost-Plus (Cost+) model. Current active pharmaceutical ingredient (API) and key starting materials (KSMs) costs were obtained from export databases. The routes of synthesis (ROS) were analysed to project a cost of goods (COGs). Formulation, vials and profit margin costs were included using standardized algorithms and Cost+ pricing. We estimated prices with scale-up to supply 1 million then 10 million treatment-years, comparing this with national list prices. The lenacapavir API is currently exported from India for $64 480/kg on 1 kg scale. Based on the ROS and KSMs, API COGs of $25 000/kg and $10 000/kg are achievable for a committed demand of 1 million (2 million tonnes/annum of API) and 10 million treatment-years, respectively. Including formulation steps, injectable lenacapavir could be mass produced for approximately $94 pppy for 1 million and $41 for 10 million treatment-years, if voluntary licences are in place and competition between generic suppliers substantially improves. Greater scale-up with improvements in manufacturers' ROS could reduce prices further. Currently lenacapavir costs $25 395-44 819 pppy. Lenacapavir could be mass produced for <$100 pppy at launch. Voluntary licensing and multiple suppliers are required to achieve these low prices. This mechanism is already in place for other antiretrovirals. To date, Gilead has not agreed lenacapavir voluntary licences with the Medicines Patent Pool.

Spinning binary dynamics in cubic effective field theories of gravity

We study the binary dynamics of two Kerr black holes with arbitrary spin vectors in the presence of parity-even and parity-odd cubic deformations of gravity. We first derive the tree-level Compton amplitudes for a Kerr black hole in cubic gravity, which we then use to compute the two-to-two amplitudes of the massive bodies to leading order in the deformation and the post-Minkowskian expansion. The required one-loop computations are performed using the leading singularity approach as well as the heavy-mass effective field theory (HEFT) approach. These amplitudes are then used to compute the leading-order momentum and spin kick in cubic gravity in the KMOC formalism. Our results are valid for generic masses and spin vectors, and include all the independent parity-even and parity-odd cubic deformations of Einstein-Hilbert gravity. We also present spin-expanded expressions for the momentum and spin kicks, and the all-order in spin deflection angle in the case of aligned spins.

Static sphere observers and geodesics in Schwarzschild-de Sitter spacetime

We analyze null- and spacelike radial geodesics in Schwarzschild-de Sitter spacetime connecting two conjugate static sphere observers, i.e. free-falling observers at a fixed radius in between the two horizons. We explicitly determine the changes in the causal structure with respect to these natural observers as a result of the inward bending of the black hole singularity, as well as the outward bending of asymptotic infinity. Notably, the inward and outward bending changes as a function of the black hole mass, first increasing towards a maximum and then decreasing to vanish in the extreme Nariai limit. For a generic mass of the black hole this implies the existence of finite size (temporal) windows for the presence of symmetric radial geodesics between the static sphere observers probing the interior region of the black hole, as well as the exterior de Sitter region. We determine the size of the interior (black hole) and exterior (de Sitter) temporal windows in 4, 5 and 6 spacetime dimensions, finding that they are equal in D = 5, and compute the proper lengths of the symmetric radial geodesics. We comment on the implications for information exchange and the potential role of the symmetric radial geodesics in a geodesic approximation of static sphere correlators in Schwarzschild-de Sitter spacetime.

Epitope mapping of SARS-CoV-2 RBDs by hydroxyl radical protein footprinting reveals the importance of including negative antibody controls

Understanding protein-protein interactions is crucial for drug design and investigating biological processes. Various techniques, such as CryoEM, X-ray spectroscopy, linear epitope mapping, and mass spectrometry-based methods, can be employed to map binding regions on proteins. Commonly used mass spectrometry-based techniques are cross-linking and hydrogen‑deuterium exchange (HDX). Another approach, hydroxyl radical protein footprinting (HRPF), identifies binding residues on proteins but faces challenges due to high initial costs and complex setups.This study introduces a generally applicable method using Fenton chemistry for epitope mapping in a standard mass spectrometry laboratory. It emphasizes the importance of controls, particularly the inclusion of a negative antibody control, not widely utilized in HRPF epitope mapping. Quantification by TMT labelling is introduced to reduce false positives, enabling direct comparison between sample conditions and biological triplicates. Additionally, six technical replicates were incorporated to enhance the depth of analysis.Observations on the receptor-binding domain (RBD) of SARS-CoV-2 Spike Protein, Alpha and Delta variants, revealed both binding and opening regions. Significantly changed peptides upon mixing with a negative control antibody suggested structural alterations or nonspecific binding induced by the antibody alone. Integration of negative control antibody experiments and high overlap between biological triplicates led to the exclusion of 40% of significantly changed regions. The final identified binding region correlated with existing literature on neutralizing antibodies against RBD.The presented method offers a straightforward implementation for HRPF analysis in a generic mass spectrometry-based laboratory. Enhanced data reliability was achieved through increased technical and biological replicates alongside negative antibody controls.

Analytical exploration of generic undamped mass–spring chains: A comprehensive study

Analysis of structural vibrations presents challenges due to the coupling between different degrees of freedom, often preventing the derivation of analytical expressions for quantities such as poles, vibration amplitude, etc. While numerical methods are commonly employed to tackle such challenges, their purely numerical nature prevents achieving a comprehensive understanding of the system behaviour. This paper builds on a novel recursive transfer function formulation recently proposed by the authors to analytically characterise the dynamics of generic undamped mass-chain systems. This approach provides fundamental properties and analytical insights that cannot be obtained through current numerical approaches, representing a significant breakthrough in the understanding of vibrations and offering valuable insights for analysing complex vibrating systems. These results presented in this paper allow for a rapid assessment of the minimum phase nature of the vibration system through straightforward stability assessment, and present analytical expressions for sums and multiplications of natural frequencies squared by induction and Vieta’s formulas. Furthermore, it derives conditions for existence of repeated roots using direct analytical derivation of the characteristics equations, including purely imaginary roots and repeated roots at the origin, showing that repeated roots can only occur when some forms of spatial symmetries exist, and confirms bounds for the arithmetic mean of natural frequencies by using inequalities between geometric, arithmetic and quadratic means. Additionally, analytical conditions are established for systems with different degrees of freedom to share the same roots, providing a theoretical foundation for eigenvalue assignment in the time domain or pole placement in the frequency domain. This foundation enables the determination of desired natural frequencies from scratch using transparent analytical conditions, without relying on complex algorithms typically required by current inverse methodologies involving passive structural modifications or active controllers. Moreover, this paper also explores the relationship between independent and coupled vibrations, providing insights for comparing natural frequencies. Overall, this paper contributes to a deeper understanding of structural vibrations through analytical exploration and offers practical guidance for eigenvalue assignment and natural frequency analysis.

Uptake of the core outcome set on polycystic ovary syndrome before and after its publication.

Does the core outcome set (COS) on polycystic ovary syndrome (PCOS) impact the selection of research outcomes? Following the publication of the COS on PCOS, an increasing number of trials are reporting both the generic domain and body mass index; however, the uptake of this COS has not been as extensive as expected. The COS on PCOS included 33 core outcomes in the following seven domains: the generic (3), metabolic (8), reproductive (7), pregnancy (10), psychological (3), oncological (1), and long-term (1). This was done to improve consistency in outcome selection and definition. However, thus far, no studies have investigated the effectiveness of this COS in the above-mentioned tasks. A methodological study based on the trial registries, including 395 eligible clinical trials registered between 1 January 2018 and 21 September 2022. A total of 1258 registered clinical studies on PCOS were retrieved from the World Health Organization International Clinical Trials Registry Platform. Of those, 395 were selected according to the inclusion and exclusion criteria, and divided into two groups based on the publication date of the COS on PCOS (4 February 2020): pre-publication and post-publication. The practical uptake of this COS was explored after data collation, assessment, comparison of the uptake of core outcomes or domains before and after the publication of this COS, and correlation analysis between the domains. There were 26 out of 33 core outcomes and five out of seven domains reported in the 395 trials. The highest uptake was observed for the reproductive domain and the reproductive hormonal profile (63.0% and 38.7%, respectively). After the publication of the COS on PCOS, the uptake of the generic domain and body mass index increased from 24.1% to 35.8% (P = 0.011) and 17.8% to 26.5% (P = 0.039), respectively. The total number of reported core outcomes in the generic domain met statistical significance (P = 0.012). Moreover, multivariable analyses still supported the above finding in the generic domain. Correlation analysis showed that most of the domains were positively correlated with each other. However, the pregnancy domain was negatively correlated with the metabolic domain. Reasons responsible for the unsatisfactory uptake may be the absence of specific definitions of core outcomes, as well as the lack of awareness among researchers regarding this COS. Due to the lack of standardized definition of outcomes, it was difficult to avoid some subjectivity in the process of consistency assessment. Two years after its publication, there was no substantial improvement in the uptake of the COS on PCOS. This suggests that this COS may require further revision, refinement, and promotion to improve the comparability of PCOS studies. This work was funded by Beijing Municipal Health Science and Technology Achievements and Appropriate Technology Promotion Project (BHTPP2022069), and the special fund of Beijing Key Clinical Specialty Construction Project.The authors do not have conflicts of interest to declare. N/A.

Constraints on sequential discontinuities from the geometry of on-shell spaces

We present several classes of constraints on the discontinuities of Feynman integrals that go beyond the Steinmann relations. These constraints follow from a geometric formulation of the Landau equations that was advocated by Pham, in which the singularities of Feynman integrals correspond to critical points of maps between on-shell spaces. To establish our results, we review elements of Picard-Lefschetz theory, which connect the homotopy properties of the space of complexified external momenta to the homology of the combined space of on-shell internal and external momenta. An important concept that emerges from this analysis is the question of whether or not a pair of Landau singularities is compatible — namely, whether or not the Landau equations for the two singularities can be satisfied simultaneously. Under conditions we describe, sequential discontinuities with respect to non-compatible Landau singularities must vanish. Although we only rigorously prove results for Feynman integrals with generic masses in this paper, we expect the geometric and algebraic insights that we gain will also assist in the analysis of more general Feynman integrals.

Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation

We explore the mathematical relationship between holographic Wilsonian renormalization group (HWRG) and stochastic quantization (SQ) of scalar field theory with its generic mass, self-interaction and [Formula: see text]-multiple-trace deformation on the [Formula: see text]-dimensional conformal boundary defined in AdS[Formula: see text] space–time. We understand that once we define our Euclidean action, [Formula: see text] as [Formula: see text], then the stochastic process will reconstruct the HWRG data via solving Langevin equation and computing stochastic correlation functions. The [Formula: see text] is given by [Formula: see text], where [Formula: see text] is the boundary counter term and [Formula: see text] is the boundary deformation which gives a boundary condition. In our study, we choose the boundary condition adding (marginal)[Formula: see text]-multiple-trace deformation to the holographic dual field theory. In this theory, we establish maps between fictitious time, [Formula: see text] evolution of stochastic [Formula: see text]-point, ([Formula: see text])-point correlation functions and the (AdS)radial, [Formula: see text] evolution of [Formula: see text]-multiple-trace and ([Formula: see text])-multiple-trace deformations, respectively, once we take identifications of [Formula: see text] and between some of the constants appearing in both sides.

Inelastic exponentiation and classical gravitational scattering at one loop

We calculate the inelastic 2 → 3 one-loop amplitude for the scattering of two point-like, spinless objects with generic masses involving the additional emission of a single graviton. We focus on the near-forward, or classical, limit. Our results include the leading and subleading orders in the soft-region expansion, which captures all non-analytic contributions in the transferred momentum and in the graviton’s frequency. This allows us to check the first constraint arising from the inelastic exponentiation put forward in refs. [1–3], and to calculate the 2 → 3 one-loop matrix element of the N-operator, linked to the S-matrix by S = eiN, showing that it is real, classical and free of infrared divergences. We discuss how our results feature in the calculation of the O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(G3) corrections to the asymptotic waveform.

Algorithms for minimal Picard–Fuchs operators of Feynman integrals

In even space-time dimensions the multi-loop Feynman integrals are integrals of rational function in projective space. By using an algorithm that extends the Griffiths--Dwork reduction for the case of projective hypersurfaces with singularities, we derive Fuchsian linear differential equations, the Picard--Fuchs equations, with respect to kinematic parameters for a large class of massive multi-loop Feynman integrals. With this approach we obtain the differential operator for Feynman integrals to high multiplicities and high loop orders. Using recent factorisation algorithms we give the minimal order differential operator in most of the cases studied in this paper. Amongst our results are that the order of Picard--Fuchs operator for the generic massive two-point $n-1$-loop sunset integral in two-dimensions is $2^{n}-\binom{n+1}{\left\lfloor \frac{n+1}{2}\right\rfloor }$ supporting the conjecture that the sunset Feynman integrals are relative periods of Calabi--Yau of dimensions $n-2$. We have checked this explicitly till six loops. As well, we obtain a particular Picard--Fuchs operator of order 11 for the massive five-point tardigrade non-planar two-loop integral in four dimensions for generic mass and kinematic configurations, suggesting that it arises from $K3$ surface with Picard number 11. We determine as well Picard--Fuchs operators of two-loop graphs with various multiplicities in four dimensions, finding Fuchsian differential operators with either Liouvillian or elliptic solutions.

Evaluation of three-loop self-energy master integrals with four or five propagators

I obtain identities satisfied by the three-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These identities are then recast in terms of the corresponding renormalized master integrals, enabling straightforward numerical evaluation of them by the differential equations approach. Some benchmark examples are provided. The method used to obtain the derivative identities relies only on the general form implied by integration by parts relations, without actually following the usual integration by parts reduction procedure. As a byproduct, I find a simple formula giving the expansion of the master integrals to arbitrary order in the external momentum invariant, in terms of known derivatives of the corresponding vacuum integrals.

On the Euclidean action of de Sitter black holes and constrained instantons

We compute the on-shell Euclidean action of Schwarzschild-de Sitter black holes, and take their contributions in the gravitational path integral into account using the formalism of constrained instantons. Although Euclidean de Sitter black hole geometries have conical singularities for generic masses, their on-shell action is finite and is shown to be independent of the Euclidean time periodicity and equal to minus the sum of the black hole and cosmological horizon entropy. We apply this result to compute the probability for a nonrotating, neutral arbitrary mass black hole to nucleate spontaneously in empty de Sitter space, which separates into a constant and a “non-perturbative” contribution, the latter corresponding to the proper saddle-point instanton in the Nariai limit. We also speculate on some further applications of our results, most notably as potential non-perturbative corrections to correlators in the de Sitter vacuum.

Parametrized post-Einsteinian framework for precessing binaries

In general relativity, isolated black holes obey the no hair theorems, which fix the multipolar structure of their exterior spacetime. However, in modified gravity, or when the compact objects are not black holes, the exterior spacetime may have a different multipolar structure. When two black holes are in a binary, this multipolar structure determines the morphology of the dynamics of orbital and spin precession. In turn, the precession dynamics imprint onto the gravitational waves emitted by an inspiraling compact binary through specific amplitude and phase modulations. The detection and characterization of these amplitude and phase modulations can therefore lead to improved constraints on fundamental physics with gravitational waves. Recently, analytic precessing waveforms were calculated in two scenarios: (i) dynamical Chern-Simons gravity, where the no-hair theorems are violated, and (ii) deformed compact objects with generic mass quadrupole moments. In this work, we use these two examples to propose an extension of the parameterized post-Einsteinian~(ppE) framework to include precession effects. The new framework contains $2n$ ppE parameters $(\mathscr{b}^{\rm ppE}_{(m',n)}, b^{\rm ppE}_{(m',n)})$ for the waveform phase, and $2n$ ppE parameters $(\mathscr{a}^{\rm ppE}_{(m',n)}, a^{\rm ppE}_{(m',n)})$ for the waveform amplitudes. The number of ppE corrections $n$ corresponds to the minimum number of harmonics necessary to achieve a given likelihood threshold when comparing the truncated ppE waveform with the exact one, and $(m',n)$ corresponds to the harmonic numbers of the harmonics containing ppE parameters. We show explicitly how these ppE parameters map to the specific example waveforms discussed above. The proposed ppE framework can serve as a basis for future tests of general relativity with gravitational waves from precessing binaries.

Pattern formation on dynamic membranes.

Pattern formation defines cell identities and plays a crucial role in arguably all membrane functionality such are cell division, motility, communication, adhesion, etc. Cell often evolves by changing their shape, which translates to membrane dynamics, hence leading to pattern formation on dynamic surfaces. While pattern formation on static shapes has been intensively studied both theoretically and experimentally, the understanding of patterning on moving shapes remains largely elusive. We study force distribution on dynamic but initially spherical or cylindrical shapes by our surface dynamics equations. For simplicity, we consider small deformation of incompressible sphere and cylinder and show that shape dynamics induce nonuniform force distributions, therefore clarifying spontaneous polarisation, symmetry breaking, and rich static and moving pattern formations. Based on surface dynamics equations we derive a generic Young-Laplace equation which indicates that practically any static and dynamic patterns are possible in incompressible systems and if so, the question is what is the underlying mechanism that controls cell identity? The answer to the problem is again a surface dynamics equation that guarantees mass conservation. In other words, dynamic surfaces induce dynamic surface mass density that is governed by a generic mass balance equation and the last one controls the identity. While mass balance itself is regulated by an active or passive influx of material particles on the surface. The last statement for cell membrane means that membrane mass balance is in full correlation with cell-governed reaction, synthesis, and diffusion. The same statement can be reached for the charge balance equation which is also part of surface dynamics equations.

Estimating Space-Dependent Coefficients for 1D Transport Using Gaussian Processes as State Estimator in the Frequency Domain

This letter presents a method to estimate the space-dependent transport coefficients (diffusion, convection, reaction, and source/sink) for a generic scalar transport model, e.g., heat or mass. As the problem is solved in the frequency domain, the complex valued state as a function of the spatial variable is estimated using Gaussian process regression. The resulting probability density function of the state, together with a semi-discretization of the model, and a linear parameterization of the coefficients are used to determine the maximum likelihood solution for these space-dependent coefficients. The proposed method is illustrated by simulations.

NLO deflections for spinning particles and Kerr black holes

We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.

Generic AI models for mass transfer coefficient prediction in amine-based CO2 absorber, Part I: BPNN model

Accurate and reliable prediction of mass transfer coefficient is critical to evaluate the mass transfer performance of amine-based carbon capture process. This work aims to establish a generic mass transfer model applicable to CO2 absorption into amine solutions in absorber columns. A series of back-propagation neural network (BPNN) models were established based on the experimental data of 23 amine-based systems. The BPNN models trained for a specific CO2 absorption process matched well with the experimental data with all the AAREs of below 4%. Meanwhile, models with better applicability were proposed and established by introducing extra parameters related to amine properties or column characteristics to better describe and predict the mass transfer behavior in different amine-based systems. Particularly, the generic mass transfer coefficient model was developed with the consideration of all influencing factors including operating conditions, amine properties, and packing characteristics, to achieve the accurate prediction of mass transfer coefficient of CO2 absorption into amine solutions in packed columns. The developed generic model could serve as a fast and efficient tool for preliminary selection and evaluation of potential amines by presenting the mass transfer performance in CO2 absorber.

Amplitude bases in generic EFTs

We present for the first time an efficient algorithm to find a basis of kinematically independent structures built of (massless and massive) spinor helicity variables in four dimensions. This method provides a classification of independent contact terms for the scattering amplitudes with generic masses, spins, and multiplicity in any effective field theory (EFT). These contact terms are in one-to-one correspondence with a complete set of irrelevant operators in the EFT. As basic applications of our method, we classify the D2nF4 contact terms in SU(N) Yang-Mills theory for n ≤ 8, dimension-six operators involving five W±, Z and γ vector bosons, and spin-tidal effective interactions for spin-1 massive particles in gravitational theories.

Finite time blow-up in the higher dimensional parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system

In this work, we mainly study nonnegative classical solutions to a Neumann initial-boundary value problem for the following parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system{ut=Δu−χ∇⋅(u∇v)−ξ∇⋅(u∇w),x∈Ω,t>0,0=Δv−v+u,x∈Ω,t>0,wt=−vw,x∈Ω,t>0 in a bounded and smooth domain Ω⊂Rn(n≥1) with χ,ξ≥0, nonnegative initial data (u0,w0) and homogeneous Neumann boundary conditions.In this setup, we first show pure haptotaxis (χ=0) cannot induce any blow-up and pattern for any n≥1, showing haptotaxis is overbalanced by diffusion on boundedness and longtime behavior. Then, in the radial setting with Ω=BR⊂Rn(n≥3), it is well-known that small mass of ‖u0‖L1(Ω) can lead to blow-up in the corresponding Keller-Segel chemotaxis-only model obtained by setting w≡0, known as generic mass blow-up phenomenon [23]. Herein, in the presence of the temporal nonlocality brought by haptotaxis, we show, in an explicit realm of the form χ‖u0‖L1(Ω)>A(n,R)ξ‖w0‖L∞(Ω), that the aforementioned generic mass finite time blow-up phenomenon preserves. This seems to be the first rigorous blow-up result in relevant chemotaxis-haptotaxis models. The blow-up result also suggests that haptotatic cross-diffusion may not be negligible compared to chemotactic aggregation in ≥3D, in contrast to the recently detected 2D negligibility of haptotaxis in a minimal chemotaxis-haptotaxis model [16].