IA Scholar Query: An exact solution method for quadratic matching: The one-quadratic-term technique and generalisations.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 01 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440New horizons for fundamental physics with LISA
https://scholar.archive.org/work/rykns2xqszhupnwisuewkwmmca
The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of gravitational waves can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas.K G Arun, Enis Belgacem, Robert Benkel, et al, Philippe Jetzerwork_rykns2xqszhupnwisuewkwmmcaThu, 01 Dec 2022 00:00:00 GMTFoundational Semantics of Dynamically Scheduled Attribute Grammar Evaluation
https://scholar.archive.org/work/anqgd2b7unas5payhfzeamv6ou
The similarities and differences between attribute grammar systems are obscured by their implementations. A formalism that captures the essence of such systems would allow for equivalence, correctness, and other analyses to be formally framed and proven. We present Saiga, a core language and small-step operational semantics that precisely captures the fundamental concepts of the evaluation of dynamically scheduled attribute grammars. We also present and discuss evaluation semantics for reference, parameterised, cached, and higher order attribute grammars. Saiga's utility is demonstrated through proofs about the system's operation, equivalence proofs between distinct Saiga attribute grammar programs, and "step count" comparisons between such programs. The language, semantics and proofs have been mechanised in Lean.Scott Buckleywork_anqgd2b7unas5payhfzeamv6ouWed, 23 Nov 2022 00:00:00 GMTSearch for electroweak production of supersymmetric particles in compressed mass spectra with the ATLAS detector at the LHC
https://scholar.archive.org/work/syrsys6kc5cv5ohkityim6kady
Two analyses searching for the production of supersymmetric particles through the electroweak interaction are presented: the chargino search, targeting the pair production of charginos decaying into W bosons and neutralinos, and the displaced track search, looking for charged tracks arising from the decays of higgsinos into pions. These searches target compressed phase spaces, where the mass difference between the next-to-lightest and lightest supersymmetric particle is relatively small. The searches use proton-proton collision data collected at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC. In the chargino search, the targeted mass difference between charginos and neutralinos is close to the mass of the W boson. In such phase space, the chargino pair production is kinematically similar to the WW background, making the chargino signal experimentally challenging to be discriminated from the WW background. Machine learning techniques are adopted to separate the supersymmetric signal from the backgrounds. The results exclude chargino masses up to about 140 GeV for mass splittings down to about 100 GeV, superseding the previous results in particularly interesting regions where the chargino pair production could have hidden behind the looking-alike WW background. In the displaced track search, the mass difference between the produced sparticles and the lightest neutralinos goes down to 0.3 GeV. The experimental signature has a low momentum charged track with an origin displaced from the collision point. The results show that the analysis has the sensitivity to exclude different hypotheses for higgsino masses up to 175 GeV if no excess is observed in data. For lower masses, the larger signal cross-section allows to achieve higher significance for different mass splitting scenarios. All these signal hypotheses have not been probed by any existing analysis of LHC data.Eric Ballabenework_syrsys6kc5cv5ohkityim6kadyTue, 22 Nov 2022 00:00:00 GMTThe fate of discrete torsion on resolved heterotic Z2xZ2 orbifolds using (0,2) GLSMs
https://scholar.archive.org/work/77owfqwvebag3ht6dewngrcv7q
This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them. This question is addressed for resolutions of the non-compact C3/Z2xZ2 and the compact T6/Z2xZ2 orbifolds to keep track of local and global aspects. The GLSMs associated with the non-compact orbifold with or without torsion are to a large extent equivalent: only when expressed in the same superfield basis, a field redefinition anomaly arises among them, which in the orbifold limit reproduces the discrete torsion phases. Previously unknown, novel resolution GLSMs for T6/Z2xZ2 are constructed. The GLSM associated with the torsional compact orbifold suffers from mixed gauge anomalies, which need to be cancelled by appropriate logarithmic superfield dependent FI-terms on the worldsheet, signalling H-flux due to NS5-branes supported at the exceptional cycles.A.E. Faraggi, S. Groot Nibbelink, M. Hurtado Herediawork_77owfqwvebag3ht6dewngrcv7qTue, 22 Nov 2022 00:00:00 GMTRiemannian Score-Based Generative Modelling
https://scholar.archive.org/work/yrst4vzuhzfl7fc4r753yiky7m
Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a "noising" stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a "denoising" process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.Valentin De Bortoli, Emile Mathieu, Michael Hutchinson, James Thornton, Yee Whye Teh, Arnaud Doucetwork_yrst4vzuhzfl7fc4r753yiky7mTue, 22 Nov 2022 00:00:00 GMTA New Residual Distribution Hydrodynamics Solver for Astrophysical Simulations
https://scholar.archive.org/work/fjxz4silgrebdcbvcqkr5hao3e
Many astrophysical systems can only be accurately modelled when the behaviour of their baryonic gas components is well understood. The residual distribution (RD) family of partial differential equation (PDE) solvers produce approximate solutions to the corresponding fluid equations. We present a new implementation of the RD method. The solver efficiently calculates the evolution of the fluid, with up to second order accuracy in both time and space, across an unstructured triangulation, in both 2D and 3D. We implement a novel variable time stepping routine, which applies a drifting mechanism to greatly improve the computational efficiency of the method. We conduct extensive testing of the new implementation, demonstrating its innate ability to resolve complex fluid structures, even at very low resolution. We can resolve complex structures with as few as 3-5 resolution elements, demonstrated by Kelvin-Helmholtz and Sedov blast tests. We also note that we find cold cloud destruction time scales consistent with those predicted by a typical PPE solver, albeit the exact evolution shows small differences. The code includes three residual calculation modes, the LDA, N and blended schemes, tailored for scenarios from smooth flows (LDA), to extreme shocks (N), and both (blended). We compare our RD solver results to state-of-the-art solvers used in other astrophysical codes, demonstrating the competitiveness of the new approach, particularly at low resolution. This is of particular interest in large scale astrophysical simulations, where important structures, such as star forming gas clouds, are often resolved by small numbers of fluid elements.Ben Morton, Sadegh Khochfar, Zhenyu Wuwork_fjxz4silgrebdcbvcqkr5hao3eMon, 21 Nov 2022 00:00:00 GMTDiscretisations and Preconditioners for Magnetohydrodynamics Models
https://scholar.archive.org/work/e3ywh5aywrhypdoh5slgo3t3lm
The magnetohydrodynamics (MHD) equations are generally known to be difficult to solve numerically, due to their highly nonlinear structure and the strong coupling between the electromagnetic and hydrodynamic variables, especially for high Reynolds and coupling numbers. In the first part of this work, we present a scalable augmented Lagrangian preconditioner for a finite element discretisation of the 𝐁-𝐄 formulation of the incompressible viscoresistive MHD equations. For stationary problems, our solver achieves robust performance with respect to the Reynolds and coupling numbers in two dimensions and good results in three dimensions. Our approach relies on specialised parameter-robust multigrid methods for the hydrodynamic and electromagnetic blocks. The scheme ensures exactly divergence-free approximations of both the velocity and the magnetic field up to solver tolerances. In the second part, we focus on incompressible, resistive Hall MHD models and derive structure-preserving finite element methods for these equations. We present a variational formulation of Hall MHD that enforces the magnetic Gauss's law precisely (up to solver tolerances) and prove the well-posedness of a Picard linearisation. For the transient problem, we present time discretisations that preserve the energy and magnetic and hybrid helicity precisely in the ideal limit for two types of boundary conditions. In the third part, we investigate anisothermal MHD models. We start by performing a bifurcation analysis for a magnetic Rayleigh–Bénard problem at a high coupling number S=1,000 by choosing the Rayleigh number in the range between 0 and 100,000 as the bifurcation parameter. We study the effect of the coupling number on the bifurcation diagram and outline how we create initial guesses to obtain complex solution patterns and disconnected branches for high coupling numbers.Fabian Laakmannwork_e3ywh5aywrhypdoh5slgo3t3lmSun, 20 Nov 2022 00:00:00 GMTHigh-Level Modelling and Solving for Online, Real-Time, and Multiagent Combinatorial Optimisation
https://scholar.archive.org/work/irdhjuvvuvfgnist333kkjl2am
This thesis presents a novel framework for declarative modelling and continual solving of dynamic combinatorial problems (e.g., planning the routes of delivery vehicles). This framework is then enhanced with a garbage collection mechanism, ensuring that the evolving problem's internal representation remains small as time progresses. Experiments show that garbage collection vastly improves runtime. This thesis presents another novel framework allowing experimentation with fairness in similar problems, which we show can achieve remarkably fair and resource-efficient solutions. Finally, this thesis presents one novel constraint propagation algorithm for variance and one for the Gini coefficient, which we show improve runtime.ALEXANDER JOHAN PHILIPPE EKwork_irdhjuvvuvfgnist333kkjl2amSun, 20 Nov 2022 00:00:00 GMTA Conservative Cartesian Cut Cell Method for the Solution of the Incompressible Navier-Stokes Equations on Staggered Meshes
https://scholar.archive.org/work/dr64igxapzglpnfgjvdpx75mqm
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by body-fitted meshes. These methods however introduce new challenges, as the formulation of accurate and well-posed discrete operators becomes nontrivial. Here, a conservative cartesian cut cell method is proposed for the solution of the incompressible Navier--Stokes equation on staggered Cartesian grids. Emphasis is set on the structure of the discrete operators, designed to mimic the properties of the continuous ones while retaining a nearest-neighbor stencil. For convective transport, a divergence is proposed and shown to also be skew-symmetric as long as the divergence-free condition is satisfied, ensuring mass, momentum and kinetic energy conservation (the latter in the inviscid limit). For viscous transport, conservative and symmetric operators are proposed for Dirichlet boundary conditions. Symmetry ensures the existence of a sink term (viscous dissipation) in the discrete kinetic energy budget, which is beneficial for stability. The cut-cell discretization possesses the much desired summation-by-parts (SBP) properties. In addition, it is fully conservative, mathematically provably stable and supports arbitrary geometries. The accuracy and robustness of the method are then demonstrated with flows past a circular cylinder and an airfoil.Alejandro Quirós Rodríguez, Tomas Fullana, Vincent Le Chenadec, Taraneh Sayadiwork_dr64igxapzglpnfgjvdpx75mqmSat, 19 Nov 2022 00:00:00 GMTRobotic manipulators for in situ inspections of jet engines
https://scholar.archive.org/work/akn6hclqbnggrcnwxuhvh2oiby
Jet engines need to be inspected periodically and, in some instances, repaired. Currently, some of these maintenance operations require the engine to be removed from the wing and dismantled, which has a significant associated cost. The capability of performing some of these inspections and repairs while the engine is on-wing could lead to important cost savings. However, existing technology for on-wing operations is limited, and does not suffice to satisfy some of the needs. In this work, the problem of performing on-wing operations such as inspection and repair is analysed, and after an extensive literature review, a novel robotic system for the on-wing insertion and deployment of probes or other tools is proposed. The system consists of a fine-positioner, which is a miniature and dexterous robotic manipulator; a gross-positioner, which is a device to insert the fine-positioner to the engine region of interest; an end-effector, such as a probe; a deployment mechanism, which is a passive device to ensure correct contact between probe and component; and a feedback system that provides information about the robot state for control. The research and development work conducted to address the main challenges to create this robotic system is presented in this thesis. The work is focussed on the fine-positioner, as it is the most relevant and complex part of the system. After a literature review of relevant work, and as part of the exploration of potential robot concepts for the system, the kinematic capabilities of concentric tube robots (CTRs) are first investigated. The complete set of stable trajectories that can be traced in follow-the-leader motion is discovered. A case study involving simulations and an experiment is then presented to showcase and verify the work. The research findings indicate that CTRs are not suitable for the fine-positioner. However, they show that CTRs with non-annular cross section can be used for the gross-positioner. In addition, the new trajectories discovered show promise in minimally i [...]Arnau Garriga Casanovas, Ferdinando Rodriguez Y Baena, Engineering And Physical Sciences Research Council, Rolls-Royce Group Plc.work_akn6hclqbnggrcnwxuhvh2oibyFri, 18 Nov 2022 00:00:00 GMTGraviton scattering in self-dual radiative space-times
https://scholar.archive.org/work/tm56nujnf5d5bkmnyekxjfsafy
The construction of amplitudes on curved space-times is a major challenge, particularly when the background has non-constant curvature. We give formulae for all tree-level graviton scattering amplitudes in curved self-dual radiative space-times; these are chiral, source-free, asymptotically flat spaces determined by free characteristic data at null infinity. Such space-times admit an elegant description in terms of twistor theory, which provides the powerful tools required to exploit their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitude directly from the Einstein-Hilbert action of general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes in self-dual radiative space-times exhibit many novel features that are absent in Minkowski space, including tail effects. There remain residual integrals due to the functional degrees of freedom in the background space-time, but our formulae have many fewer such integrals than would be expected from space-time perturbation theory. In highly symmetric special cases, such as self-dual plane waves, the number of residual integrals can be further reduced, resulting in much simpler expressions for the scattering amplitudes.Tim Adamo, Lionel Mason, Atul Sharmawork_tm56nujnf5d5bkmnyekxjfsafyThu, 17 Nov 2022 00:00:00 GMTSchurly you're joking - quantum-classical correspondence in phase space for non-Hermitian systems
https://scholar.archive.org/work/fieqcdj3mrhhxldbbkgljrn6xi
In closed quantum systems described by Hermitian Hamiltonians the Husimi distributions of stationary states are closely related to classical phase space structures. To each state there is assigned a unique area of the Planck cell partitioned phase space. The localisation of the stationary states upon specific regions of phase space can be related to the classical dynamics and energies. In systems described by non-normal operators, and in particular non-Hermitian Hamiltonians, the general non-orthogonality of the stationary states stands in the way of the application of many standard ideas of quantum-classical correspondence. Many of these can be recovered if the Schur vectors are used instead of the eigenvectors. For specific classes of non-Hermitian systems, with simple loss profiles, this correspondence between the Schur vectors and features of the classical phase space are well investigated. For general non-Hermitian systems with more complex gain-loss profiles, however, there is a lack of methods and understanding. In this thesis we will address this problem by associating to each Schur vector an area of phase space described by the classical analogue of the quantum norm, which we describe as classical norm maps. An algorithm will be introduced that constructs from the norm maps a classical density that shows remarkably close correspondence to the Husimi distributions of the Schur vectors. We will demonstrate this correspondence in both regular and chaotic non-Hermitian systems.Joseph Hall, Eva-Maria Graefe, European Research Councilwork_fieqcdj3mrhhxldbbkgljrn6xiThu, 17 Nov 2022 00:00:00 GMTModelling the free energy of solvation: from data-driven to statistical mechanical approaches
https://scholar.archive.org/work/mogwa64tkbf5vovzxufciqff6m
The Gibbs free energy of solvation for a given solute in a solvent, usually considered at infinite dilution, provides a simple thermodynamic description of the solution and is related to numerous solvation properties. In the context of solution chemistry, it provides a route to understanding the effect of solvents on equilibrium constants and reaction rates. In the discovery of new drugs, the effectiveness of a drug depends in part on solubility and permeability, leading to the prediction of Gibbs free energy of solvation values to be used frequently in quantitative drug design. Given the importance of the Gibbs free energy of solvation, many predictive tools were developed, spanning quantum mechanical (QM) methods, empirical methods, and classical methods. Of note, empirical methods are data-driven approaches through statistical learning. In this work, we assembled a database of experimental Gibbs free energies of solvation and a corresponding set of 9 quantum mechanical (QM) solute descriptors and 12 bulk solvent descriptors. We also partitioned the Gibbs free energy of solvation into an electrostatic term and a nonelectrostatic term. The electrostatic term is the difference between the electronic energies of a solute in a vacuum and solvent obtained though using the X3LYP/6-31 G(d,p) electronic structure method and the Polarizable Continuum Model (PCM). We then obtain a separate database of derived nonelectrostatic energies alongside the Gibbs free energy of solvation database which are used to develop models using statistical and regression methodologies such as partial least squares (PLS), quadratic partial least squares (QPLS) and automatic learning of algebraic models for optimisation (ALAMO). We then carry out a systematic comparison of various activity coefficients, data-driven models, an equation of state, and a hybrid QM/activity coefficient model. Notable models include the Dortmund version of UNIFAC model (modUNIFAC (Do)), the statistical associating fluid theory (SAFT- γ Mie), and the conductor-like [...]Nur Redzuan Nur Jazlan, Claire Adjiman, Amparo Galindowork_mogwa64tkbf5vovzxufciqff6mThu, 17 Nov 2022 00:00:00 GMTSecond-order inertial forces and torques on a sphere in a viscous steady linear flow
https://scholar.archive.org/work/j3xzg67yivcs3i32gy2tk5kbza
We compute the full set of second-order inertial corrections to the instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in a general steady linear flow. This is achieved by using matched asymptotic expansions and formulating the problem in a coordinate system co-moving with the background flow. Effects of the fluid-velocity gradients are assumed to be small, but to dominate over those of the velocity difference between the body and fluid, which makes the results essentially relevant to nearly neutrally buoyant particles. The outer solution (which at first order is responsible for the Basset-Boussinesq history force at short time and for shear-induced forces such as the Saffman lift force at long time) is expressed via a flow-dependent tensorial kernel. The second-order inner solution brings a number of different contributions to the force and torque. Some are proportional to the relative translational or angular acceleration between the particle and fluid, while others take the form of products of the rotation/strain rate of the background flow and the relative translational or angular velocity between the particle and fluid. Adding the outer and inner contributions, the known added-mass force or the spin-induced lift force are recovered, and new effects involving the rotation/strain rate of the background flow are revealed. The resulting force and torque equations provide a rational extension of the classical Basset-Boussinesq-Oseen equation incorporating all first- and second-order fluid inertia effects resulting from both unsteadiness and velocity gradients of the carrying flow.Fabien Candelier, Rabah Mehaddi, Bernhard Mehlig, Jacques Magnaudetwork_j3xzg67yivcs3i32gy2tk5kbzaThu, 17 Nov 2022 00:00:00 GMTRandomised subspace methods for non-convex optimization, with applications to nonlinear least-squares
https://scholar.archive.org/work/y4liqlstkzenfnb6eq5tfzvdiu
We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such as Gaussian and sparse sketching, using Johnson-Lindenstrauss embedding properties. We show that, when safeguarded with trust region or quadratic regularization, this random subspace approach satisfies, with high probability, a complexity bound of order 𝒪(ϵ^-2) to drive the (full) gradient below ϵ; matching in the accuracy order, deterministic counterparts of these methods and securing almost sure convergence. Furthermore, no problem dimension dependence appears explicitly in the projection size of the sketching matrix, allowing the choice of low-dimensional subspaces. We particularise this framework to Random Subspace Gauss-Newton (RS-GN) methods for nonlinear least squares problems, that only require the calculation of the Jacobian in the subspace; with similar complexity guarantees. Numerical experiments with RS-GN on CUTEst nonlinear least squares are also presented, with some encouraging results.Coralia Cartis and Jaroslav Fowkes and Zhen Shaowork_y4liqlstkzenfnb6eq5tfzvdiuThu, 17 Nov 2022 00:00:00 GMTNear-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
https://scholar.archive.org/work/5cil662o5bclbky4ypzlw2akiq
Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen a major boost in the last decade, we are still a long way from reaching the maturity of a full-fledged quantum computer. That said, we will be in the Noisy-Intermediate Scale Quantum (NISQ) era for a long time, working on dozens or even thousands of qubits quantum computing systems. An outstanding challenge, then, is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise. To address this challenge, several near-term quantum computing techniques, including variational quantum algorithms, error mitigation, quantum circuit compilation and benchmarking protocols, have been proposed to characterize and mitigate errors, and to implement algorithms with a certain resistance to noise, so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications. Besides, the development of near-term quantum devices is inseparable from the efficient classical simulation, which plays a vital role in quantum algorithm design and verification, error-tolerant verification and other applications. This review will provide a thorough introduction of these near-term quantum computing techniques, report on their progress, and finally discuss the future prospect of these techniques, which we hope will motivate researchers to undertake additional studies in this field.He-Liang Huang, Xiao-Yue Xu, Chu Guo, Guojing Tian, Shi-Jie Wei, Xiaoming Sun, Wan-Su Bao, Gui-Lu Longwork_5cil662o5bclbky4ypzlw2akiqThu, 17 Nov 2022 00:00:00 GMTThe problem of time in quantum cosmology
https://scholar.archive.org/work/c3dkpfjx2jgmfo65ut5gvf6bdi
This thesis contains an analysis of the problem of time in quantum cosmology and its application to a cosmological minisuperspace model. In the first part, we introduce the problem of time and the theoretical foundations. In the second part, we focus on a specific minisuperspace universe, analyse it classically, and quantise it using the canonical quantisation method. The chosen model is a flat FLRW universe with a free massless scalar field and a perfect fluid. We extract the Wheeler–DeWitt equation, and calculate its solutions. There are three dynamical variables that may be used as clock parameters, namely a coordinate t conjugated to the perfect fluid mass, the massless scalar field φ, and v, a positive power of the scale factor. We define three quantum theories, each one based on assuming one of the previous dynamical quantities as the clock. This quantisation method is then compared with the Dirac quantisation. We find that, in each quantisation procedure, covariance is broken, leading to inequivalent quantum theories. In the third part, the properties of each theory are analysed. Unitarity of each theory is implemented by adding a boundary condition on the allowed states. Requiring unitarity is what breaks general covariance in the quantum theory. In the fourth part, we study the numerical properties of the wave functions in the three theories, paying special attention to singularity resolution and other divergences from the classical theory. The t-clock theory is able to resolve the singularity, the φ-clock theory presents some non trivial dynamics that can be associated with a resolution of spatial infinity, and the v-clock theory does not show significant deviations from the classical theory. In the last part, we expand our analysis in order to include another quantisation method: path integral quantisation, and finally, we conclude.Lucía Menéndez-Pidalwork_c3dkpfjx2jgmfo65ut5gvf6bdiWed, 16 Nov 2022 00:00:00 GMTSignature Methods in Machine Learning
https://scholar.archive.org/work/flra4olwvvc5jiu6yv47y62xrq
Signature-based techniques give mathematical insight into the interactions between complex streams of evolving data. These insights can be quite naturally translated into numerical approaches to understanding streamed data, and perhaps because of their mathematical precision, have proved useful in analysing streamed data in situations where the data is irregular, and not stationary, and the dimension of the data and the sample sizes are both moderate. Understanding streamed multi-modal data is exponential: a word in n letters from an alphabet of size d can be any one of d^n messages. Signatures remove the exponential amount of noise that arises from sampling irregularity, but an exponential amount of information still remain. This survey aims to stay in the domain where that exponential scaling can be managed directly. Scalability issues are an important challenge in many problems but would require another survey article and further ideas. This survey describes a range of contexts where the data sets are small enough to remove the possibility of massive machine learning, and the existence of small sets of context free and principled features can be used effectively. The mathematical nature of the tools can make their use intimidating to non-mathematicians. The examples presented in this article are intended to bridge this communication gap and provide tractable working examples drawn from the machine learning context. Notebooks are available online for several of these examples. This survey builds on the earlier paper of Ilya Chevryev and Andrey Kormilitzin which had broadly similar aims at an earlier point in the development of this machinery. This article illustrates how the theoretical insights offered by signatures are simply realised in the analysis of application data in a way that is largely agnostic to the data type.Terry Lyons, Andrew D. McLeodwork_flra4olwvvc5jiu6yv47y62xrqTue, 15 Nov 2022 00:00:00 GMTBlack holes and nilmanifolds: quasinormal modes as the fingerprints of extra dimensions?
https://scholar.archive.org/work/7qqoxyfndbgzdlq6h3cu27r7g4
We investigate whether quasinormal modes (QNMs) can be used in the search for signatures of extra dimensions. To address a gap in the Beyond Standard Model (BSM) literature, we focus here on higher dimensions characterised by negative Ricci curvature. As a first step, we consider a product space comprised of a four-dimensional Schwarzschild black hole space-time and a three-dimensional nilmanifold (twisted torus); we model the black hole perturbations as a scalar test field. We find that the extra-dimensional geometry can be stylised in the QNM effective potential as a squared mass-like term. We then compute the corresponding QNM spectrum using three different numerical methods, and determine constraints on this possible extra-dimensional observable from gravitational-wave considerations.Anna Chrysostomou, Alan Cornell, Aldo Deandrea, Étienne Ligout, Dimitrios Tsimpiswork_7qqoxyfndbgzdlq6h3cu27r7g4Tue, 15 Nov 2022 00:00:00 GMTEnumerative geometry, topological recursion, and the semi-infinite wedge
https://scholar.archive.org/work/7qxj6ud7vjacradco7ttq5cps4
Recent decades have seen an explosion of activity in the symbiotic relationship between mathematics and physics. From this interplay has emerged the notion of topological recursion, a general theory that appears to govern seemingly disparate problems in geometry, algebra, and mathematical physics. This thesis considers four such problems lying at the confluence of these fields. The results include the resolution of outstanding conjectures from the literature as well as the introduction of new mathematical structures whose fascinating properties should inspire future discovery. This research forms part of a rich tapestry of ongoing work that connects diverse areas of mathematics.ELLENA HRISTOVA MOSKOVSKYwork_7qxj6ud7vjacradco7ttq5cps4Tue, 15 Nov 2022 00:00:00 GMT