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We derive the full system of canonical differential equations for all planar two-loop massless six-particle master integrals, and determine analytically the boundary conditions. This fully specifies the solutions, which may be written as Chen iterated integrals. We argue that this is sufficient information for evaluating any scattering amplitude in four dimensions up to the finite part. We support this claim by reducing, for the most complicated integral topologies, integrals with typical Yang-Mills numerators. We use the analytic solutions to the differential equations, together with dihedral symmetry, to provide the full solution space relevant for two-loop six-particle computations. This includes the relevant function alphabet, as well as the independent set of iterated integrals up to weight four. We also provide the answer for all master integrals in terms of iterated integrals that can be readily evaluated numerically. As a proof of concept, we provide a numerical implementation that evaluates the integrals in part of the Euclidean region, and validate this against numerical evaluation of the Feynman integrals. Our result removes the bottleneck of Feynman integral evaluation, paving the way to future analytic evaluations of six-particle scattering amplitudes., Comment: 6 pages, 2 figures, ancillary files available in https://bitbucket.org/yzhphy/2l6p_complete_function_space

Slums, informal settlements, and deprived areas are urban regions characterized by poverty. According to the United Nations, over one billion people reside in these areas, and this number is projected to increase. Additionally, these settlements are integral components of urban systems. We conducted a bibliometrical analysis and scoping study using the Web of Science Database to explore various perspectives on urban poverty, searching for scientific publications on the topic and providing details on the countries where the studies were conducted. Based on 3947 publications, we identify the extent to which domestic research organizations participate in studying urban poverty and which categories of science they investigate, including life sciences \& biomedicine, social sciences, technology, physical sciences, and arts & humanities. Thereby, we find that research on slums is often limited to specific countries, e.g. India, South Africa, Kenya, or Brazil. This focus is not necessarily correlated with the number of people living in slums. The scientific discourse is up to now predominantly shaped by medical and social sciences with few studies addressing technological questions. Finally, our analysis identifies several possible future directions for research on slums., Comment: 36 pages, 19 figures, 15 tables

In this article, we show that it is possible to differentiate between water adsorbed on the outside of a single-walled carbon nanotube and that confined inside. To this aim, we measured the electronic transport of a carbon nanotube based field effect transistor (CNTFET) constructed with an isolated single carbon nanotube subjected to controlled environments. More precisely, this distinction is made possible by observing the evolution of the transfer characteristic as a function of the electric field imposed by the gate voltage. It appears that the presence of water results in a displacement of the electrical neutrality point, corresponding to a charge transfer between the nanotube and its environment. Using this approach, we demonstrate the existence of 3 types of water molecules: (i) chemically adsorbed on the SiO\textsubscript{2} surface of the substrate, i.e., forming silanol groups; (ii) physically adsorbed outside next to the nanotube; and (iii) confined inside the nanotube. The first one can only be eliminated by high temperature treatment under vacuum, the second one desorbs in a moderate vacuum at room temperature, while the confined water can be removed at room temperature at higher vacuum, i.e. $10^{-3}$ mbar. We also observe that both water adsorption outside and water confinement inside the nanotube are spontaneous and rather fast, i.e. less than 1 minute in our experimental conditions, while removing the water adsorbed outside and confined inside takes much longer, i.e. 40-60 minutes, thus indicating that water confinement is thermodynamically favorable. It is also shown that the metallicity of the nanotube has no qualitative influence on its interaction with water. Our results experimentally prove the stronger affinity of water for the inner surface of CNT than for the outer one.

While autoregressive machine-learning-based emulators have been trained to produce stable and accurate rollouts in the climate of the present-day and recent past, none so far have been trained to emulate the sensitivity of climate to substantial changes in CO$_2$ or other greenhouse gases. As an initial step we couple the Ai2 Climate Emulator version 2 to a slab ocean model (hereafter ACE2-SOM) and train it on output from a collection of equilibrium-climate physics-based reference simulations with varying levels of CO$_2$. We test it in equilibrium and non-equilibrium climate scenarios with CO$_2$ concentrations seen and unseen in training. ACE2-SOM performs well in equilibrium-climate inference with both in-sample and out-of-sample CO$_2$ concentrations, accurately reproducing the emergent time-mean spatial patterns of surface temperature and precipitation change with CO$_2$ doubling, tripling, or quadrupling. In addition, the vertical profile of atmospheric warming and change in extreme precipitation rates up to the 99.9999th percentile closely agree with the reference model. Non-equilibrium-climate inference is more challenging. With CO$_2$ increasing gradually at a rate of 2% year$^{-1}$, ACE2-SOM can accurately emulate the global annual mean trends of surface and lower-to-middle atmosphere fields but produces unphysical jumps in stratospheric fields. With an abrupt quadrupling of CO$_2$, ML-controlled fields transition unrealistically quickly to the 4xCO$_2$ regime. In doing so they violate global energy conservation and exhibit unphysical sensitivities of and surface and top of atmosphere radiative fluxes to instantaneous changes in CO$_2$. Future emulator development needed to address these issues should improve its generalizability to diverse climate change scenarios., Comment: 31 pages, 13 figures

Existing machine learning models of weather variability are not formulated to enable assessment of their response to varying external boundary conditions such as sea surface temperature and greenhouse gases. Here we present ACE2 (Ai2 Climate Emulator version 2) and its application to reproducing atmospheric variability over the past 80 years on timescales from days to decades. ACE2 is a 450M-parameter autoregressive machine learning emulator, operating with 6-hour temporal resolution, 1{\deg} horizontal resolution and eight vertical layers. It exactly conserves global dry air mass and moisture and can be stepped forward stably for arbitrarily many steps with a throughput of about 1500 simulated years per wall clock day. ACE2 generates emergent phenomena such as tropical cyclones, the Madden Julian Oscillation, and sudden stratospheric warmings. Furthermore, it accurately reproduces the atmospheric response to El Ni\~no variability and global trends of temperature over the past 80 years. However, its sensitivities to separately changing sea surface temperature and carbon dioxide are not entirely realistic., Comment: 31 pages, 23 figures

We compute analytically the three-loop correlation function of the local operator $\text{tr} \, \phi^3$ inserted into three on-shell states, in maximally supersymmetric Yang-Mills theory. The result is expressed in terms of Chen iterated integrals. We also present our result using generalised polylogarithms, and evaluate them numerically, finding agreement with a previous numerical result in the literature. We observe that the result depends on fewer kinematic singularities compared to individual Feynman integrals. Furthermore, upon choosing a suitable definition of the finite part, we find that the latter satisfies powerful symbol adjacency relations similar to those previously observed for the $\text{tr} \, \phi^2$ case., Comment: 17 pages, 4 figures, 4 tables, 680 integrals

Several recent works have demonstrated the powerful algebraic simplifications that can be achieved for scattering amplitudes through a systematic grading of transcendental quantities. We develop these concepts to construct a minimal basis of functions tailored to a scattering amplitude in a general way. Starting with formal solutions for all master integral topologies, we organise the appearing functions by properties such as their symbol alphabet or letter adjacency. We rotate the basis such that functions with spurious features appear in the least possible number of basis elements. Since their coefficients must vanish for physical quantities, this approach avoids complex cancellations. As a first application, we evaluate all integral topologies relevant to the three-loop $Hggg$ and $Hgq\bar{q}$ amplitudes in the leading-colour approximation and heavy-top limit. We describe the derivation of canonical differential equation systems and present a method for fixing boundary conditions without the need for a full functional representation. Using multiple numerical reductions, we test the maximal transcendentality conjecture for $Hggg$ and identify a new letter which appears in functions of weight 4 and 5. In addition, we provide the first direct analytic computation of a three-point form factor of the operator $\mathrm{Tr}(\phi^2)$ in planar $\mathcal{N}=4$ sYM and find agreement with numerical and bootstrapped results., Comment: 45 pages, 7 figures, 3 tables. Electronic files with results are available under https://zenodo.org/records/13987766; v2 expanded Introduction; v3 small typos, matches journal version

In this paper we discuss the geometric integrand expansion of the five-point Wilson loop with one Lagrangian insertion in maximally supersymmetric Yang-Mills theory. We construct the integrand corresponding to an all-loop class of ladder-type geometries. We then investigate the known two-loop observable from this geometric viewpoint. To do so, we evaluate analytically the new two-loop integrals corresponding to the negative geometry contribution, using the canonical differential equations method. Inspecting the analytic result, we present numerical evidence that in this decomposition, each piece has uniform sign properties, when evaluated in the Amplituhedron region. Finally, we present an alternative bootstrap approach for the ladder-type geometries. We find that certain minimal bootstrap assumptions can be satisfied at two loops, but lead to a contradiction at three loops. This suggests to us that novel alphabet letters are required at this loop order. Indeed studying planar three-loop Feynman integrals, we do identify novel pentagon alphabet letters., Comment: 55 pages+ appendices, 7 figures

The end-to-end connectivity patterns between two points on Earth are highly volatile if mediated via a Low-Earth orbit (LEO) satellite constellation. This is rooted in the enormous speeds at which satellites in LEO must travel relative to the Earth's surface. While changes in end-to-end routes are rare events in stationary and terrestrial applications, they are a dominating factor for connection-oriented services running over LEO constellations and mega-constellations. This paper discusses how TCP-over-constellations is affected by the need for rerouting and how orbital route selection algorithms impact the end-to-end performance of communication. In contrast to the state of the art that primarily optimizes for instantaneous shortest routes (i.e. lowest delay), we propose several algorithms that have route stability and longevity in their focus. We show that this shift in focus comes with vastly improved end-to-end communication performance, and we discuss peculiar effects of the typical TCP-like implementations, taking inspiration from the Starlink constellation in our empirical investigations. The spectrum of algorithms proposed provides a basis for co-designing suitable orbital route selection algorithms and tailored transport control algorithms., Comment: 2024 IEEE International Conference on Communications Workshops (ICC Workshops), Denver, CO, USA, 2024, pp. 1708-1713

Magnetic particle imaging (MPI) is an emerging imaging technique with many applications and a very active field of research. This app provides users with the opportunity to develop some intuition about the inner workings of MPI as it is being researched through NIST's Thermal MagIC project in an interactive and fun way. Users can vary different experimental and post-processing parameters to see how the image quality and particle reconstruction changes for different measurement conditions., Comment: 7 pages, 6 figures

We investigate positivity properties in quantum field theory (QFT). We provide evidence,and in some case proofs, that many building blocks of scattering amplitudes, and in some cases the full amplitudes, satisfy an infinite number of positivity conditions: the functions, as well as all their signed derivatives, are non-negative in a specified kinematic region. Such functions are known as completely monotonic(CM) in the mathematics literature. A powerful way to certify complete monotonicity is via integral representations. We thus show that it applies to planar and non-planar Feynman integrals possessing a Euclidean region,as well as to certain Euler integrals relevant to cosmological correlators and stringy integrals. This implies that in particular that many basic building blocks of perturbation theory, such as master integrals, can be chosen to be completely monotone. We also discuss two pathways for showing complete monotonicity for full amplitudes. One is related to properties of the analytic S-matrix. The other one is a close connection between the CM property and Positive Geometry. Motivated by this, we investigate positivity properties in planar maximally supersymmetric Yang-Mills theory. We present evidence, based on known analytic multi-loop results, that the CM property extends to several physical quantities in this theory. This includes the (suitably normalized) finite remainder function of the six-particle maximally-helicity-violating (MHV) amplitude, four-point scattering amplitudes on the Coulomb branch,four-point correlation functions, as well as the angle-dependent cusp anomalous dimension. Our findings are however not limited to supersymmetric theories. It is shown that the CM property holds for the QCD and QED cusp anomalous dimensions, to three and four loops, respectively. We comment on open questions, and on possible numerical applications of complete monotonicity., Comment: presentation improved, details on Feynman integrals, spectral representations and Choquet theorem added

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS. Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines. The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill. This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies., Comment: NeurIPS 2024; Code is available at https://github.com/Rose-STL-Lab/spherical-dyffusion

The study of collinear behavior for gauge theories in the spacelike region is of great phenomenological and theoretical importance. We analytically calculate the two-loop spacelike splitting amplitude for the full color N=4 Super-Yang-Mills theory. The result is derived by two complementary methods starting from the known amplitude: one is based on a discontinuity analysis, while the other one is based on analytic continuation. Our result explicitly shows terms that violate naive factorization. However we show that factorization is restored at the level of color-summed unpolarized squared amplitudes at next-to-next-to-next-to leading order. We conjecture that the two-loop tripole terms in the generalized splitting amplitudes in QCD are identical to what we obtain in N=4 super Yang-Mills theory., Comment: second version with minor changes

We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, the pentagon-triangle, and the hegaxon-bubble family. This constitutes the first analytic computation of two-loop master integrals with eight scales. We use the method of canonical differential equations. We describe the corresponding integral basis with uniform transcendentality, the relevant function alphabet, and analytic boundary values at a particular point in the Euclidean region up to the fourth order in the regularization parameter $\epsilon$. The results are expressed as one-fold integrals over classical polylogarithms suitable for fast and high-precision evaluation., Comment: 35 pages, 5 figures

The Amplituhedron provides, via geometric means, the all-loop integrand of scattering amplitudes in maximally supersymmetric Yang-Mills theory. Unfortunately, dimensional regularization, used conventionally for integration, breaks the beautiful geometric picture. This motivates us to propose a 'deformed' Amplituhedron. Focusing on the four-particle amplitude, we introduce two deformation parameters, which can be interpreted as particle masses. We provide evidence that the mass pattern corresponds to a specific choice of vacuum expectation values on the Coulomb branch. The deformed amplitude is infrared finite, making the answer well-defined in four dimensions. Leveraging four-dimensional integration techniques based on differential equations, we compute the amplitude up to two loops. In the limit where the deformation parameters are taken to zero, we recover the known Bern-Dixon-Smirnov amplitude. In the limit where only one deformation parameter is taken to zero, we find a connection to the angle-dependent cusp anomalous dimension., Comment: 6 pages, 2 figures

The general structure of infrared divergences in the scattering of massive particles is captured by the soft anomalous dimension matrix. The latter can be computed from a correlation function of multiple Wilson lines. The state-of-the-art two-loop result has a tantalizingly simple structure that is not manifest in the calculations. We argue that the complexity in intermediate steps of the known calculations comes from spurious, regulator-dependent terms. Based on this insight we propose a different infrared regulator that is associated to only one of the Wilson lines. We demonstrate that this streamlines obtaining the two-loop result: computing the required Feynman integrals via the differential equations method, only multiple polylogarithmic functions appear (to all orders in the dimensional regulator), as opposed to elliptic polylogarithms. We show that the new method is promising for higher-loop applications by computing a three-loop diagram of genuine complexity, and provide the answer in terms of multiple polylogarithms. The relatively simple symbol alphabet we obtain may be of interest for bootstrap approaches., Comment: 22 pages, 4 figures

Despite several decades of development, microfluidics lacks a sealing material that can be readily fabricated, leak-tight under high liquid water pressure, stable over a long time, and vacuum compatible. In this paper, we report the performances of a micro-scale processable sealing material for nanofluidic/microfluidics chip fabrication, which enables us to achieve all these requirements. We observed that micrometric walls made of SU-8 photoresist, whose thickness can be as low as 35 $\mu$m, exhibit water pressure leak-tightness from 1.5 bar up to 5.5 bar, no water porosity even after 2 months of aging, and are able to sustain under $10^{-5}$ mbar vacuum. This sealing material is therefore reliable and versatile for building microchips, part of which must be isolated from liquid water under pressure or vacuum. Moreover, the fabrication process we propose does not require the use of aggressive chemicals or high-temperature or high-energy plasma treatment. It thus opens a new perspective to seal microchips where delicate surfaces such as nanomaterials are present.

Existing ML-based atmospheric models are not suitable for climate prediction, which requires long-term stability and physical consistency. We present ACE (AI2 Climate Emulator), a 200M-parameter, autoregressive machine learning emulator of an existing comprehensive 100-km resolution global atmospheric model. The formulation of ACE allows evaluation of physical laws such as the conservation of mass and moisture. The emulator is stable for 100 years, nearly conserves column moisture without explicit constraints and faithfully reproduces the reference model's climate, outperforming a challenging baseline on over 90% of tracked variables. ACE requires nearly 100x less wall clock time and is 100x more energy efficient than the reference model using typically available resources. Without fine-tuning, ACE can stably generalize to a previously unseen historical sea surface temperature dataset., Comment: Accepted at Tackling Climate Change with Machine Learning: workshop at NeurIPS 2023

In recent experiments, unprecedentedly large values for the conductivity of electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing to flow slip and a high pore surface charge density whose origin is still unknown. By accounting for the coupling between the {quantum} CNT and the {classical} electrolyte-filled pore capacitances, we study the case where a gate voltage is applied to the CNT. The computed surface charge and conductivity dependence on reservoir salt concentration and gate voltage are intimately connected to the CNT electronic density of states. This approach provides key insight into why metallic CNTs have larger conductivities than semi-conducting ones.

Although a superconductor has no DC losses, a superconducting system does have significant losses, especially when it comes to power supply. Here, we study two different power supply systems. The first, a conventional one, consists of a transformer and a diode bridge operating at room temperature, plus current leads that allow the current to flow from the room-temperature medium to the cryogenic medium. The second consists of a transformer with a superconducting secondary winding, combined with a diode bridge operating at cryogenic temperature, thus dispensing with the need for current leads. We are experimentally comparing the performance of conventional and superconducting transformers, as well as the performance of a diode bridge at ambient and cryogenic temperatures. Our results indicate that the prototype superconducting transformer developed has lower winding resistance and secondary leakage inductance than the conventional transformer. In addition, we found that only certain diodes are suitable for operation at cryogenic temperatures. Finally, the diode bridge made from adapted diodes shows reduced losses at cryogenic temperature. This experimental work is the first step towards the realization of a complete power supply system for a superconducting device., Comment: in French language, Symposium de Genie Electrique (SGE 2023), Jul 2023, Lille, France

These lecture notes bridge a gap between introductory quantum field theory (QFT) courses and state-of-the-art research in scattering amplitudes. They cover the path from basic definitions of QFT to amplitudes relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction into QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop-integration techniques. These methods help reveal intriguing relations between gauge and gravity amplitudes, and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at CERN's Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics. These course-tested lecture notes include numerous exercises with detailed solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of QFT. Supplementary material, Mathematica notebooks, corrections and further information are provided and maintained at the dedicated website https://scattering-amplitudes.mpp.mpg.de/scattering-amplitudes-in-qft/ ., Comment: 291 pages, 30 figures, 4 tables, 1 appendix

A detailed interpretation of scanning tunneling spectra obtained on unconventional superconductors enables one to gain information on the pairing boson. Decisive for this approach are inelastic tunneling events. Due to the lack of momentum conservation in tunneling from or to the sharp tip, those are enhanced in the geometry of a scanning tunneling microscope compared to planar tunnel junctions. This work extends the method of obtaining the bosonic excitation spectrum by deconvolution from tunneling spectra to nodal $d$-wave superconductors. In particular, scanning tunneling spectra of slightly underdoped $\mathrm{Bi_2Sr_2CaCu_2O_{8+\delta}}$ with a $T_c$ of $82\,\mathrm{K}$ and optimally doped $\mathrm{YBa_2Cu_3O_{6+x}}$ with a $T_c$ of $92\,\mathrm{K}$ reveal a resonance mode in their bosonic excitation spectrum at $\Omega_\mathrm{res} \approx 63\,\mathrm{meV}$ and $\Omega_\mathrm{res} \approx 61\,\mathrm{meV}$ respectively. In both cases, the overall shape of the bosonic excitation spectrum is indicative of predominant spin scattering with a resonant mode at $\Omega_\mathrm{res}<2\Delta$ and overdamped spin fluctuations for energies larger than $2\Delta$. To perform the deconvolution of the experimental data, we implemented an efficient iterative algorithm that significantly enhances the reliability of our analysis.

With much of our lives taking place online, researchers are increasingly turning to information from the World Wide Web to gain insights into geographic patterns and processes. Web scraping as an online data acquisition technique allows us to gather intelligence especially on social and economic actions for which the Web serves as a platform. Specific opportunities relate to near-real-time access to object-level geolocated data, which can be captured in a cost-effective way. The studied geographic phenomena include, but are not limited to, the rental market and associated processes such as gentrification, entrepreneurial ecosystems, or spatial planning processes. Since the information retrieved from the Web is not made available for that purpose, Web scraping faces several unique challenges, several of which relate to location. Ethical and legal issues mainly relate to intellectual property rights, informed consent and (geo-) privacy, and website integrity and contract. These issues also effect the practice of open science. In addition, there are technical and statistical challenges that relate to dependability and incompleteness, data inconsistencies and bias, as well as the limited historical coverage. Geospatial analyses furthermore usually require the automated extraction and subsequent resolution of toponyms or addresses (geoparsing, geocoding). A study on apartment rent in Leipzig, Germany is used to illustrate the use of Web scraping and its challenges. We conclude that geographic researchers should embrace Web scraping as a powerful and affordable digital fieldwork tool while paying special attention to its legal, ethical, and methodological challenges., Comment: 18 pages, 7 figures, 2 tables