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Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work we completely gauge fix that Lorentz gauge symmetry by using a so-called triangular gauge. Having solved the Gauss constraints already classically opens access to new Hilbert space representations which are free of the complications that otherwise arise due to a non Abelian gauge symmetry. In that sense, a connection formulation as being pursued in Loop Quantum Gravity is no longer the only practicable option and other less dimension dependent representations e.g. based on triads and even metrics suggest themselves. These formulations make it easier to identify states representing non-degenerate quantum geometries and thus to investigate the hypersurface deformation algebra which implicitly assumes non-degeneracy.

Schr\"odinger operators often display singularities at the origin, the Coulomb problem in atomic physics or the various matter coupling terms in the Friedmann-Robertson-Walker problem being prominent examples. For various applications it would be desirable to have at one's disposal an explicit basis spanning a dense and invariant domain for such types of Schr\"odinger operators, for instance stationary perturbation theory or the Raleigh-Ritz method. Here we make the observation, that not only a such basis can indeed be provided but that in addition relevant matrix elements and inner products can be computed analytically in closed form, thus providing the required data e.g. for an analytical Gram-Schmid orthonormalisation., Comment: 9 pages

We propose algebraic protocols that enable the definition of protocol templates and session types analogous to the definition of domain-specific types with algebraic datatypes. Parameterized algebraic protocols subsume all regular as well as most context-free and nested session types and, at the same time, replace the expensive superlinear algorithms for type checking by a nominal check that runs in linear time. Algebraic protocols in combination with polymorphism increase expressiveness and modularity by facilitating new ways of parameterizing and composing session types.

This chapter focuses on the status of the implementation of the dynamics in the canonical version of Loop Quantum Gravity (LQG). Concretely this means to provide a mathematical meaning of the quantum Einstein equations, sometimes called Wheeler-DeWitt equations, to give a physical interpretation and Hilbert space structure to its solutions and to construct a representation of the algebra of observables including a physical Hamiltonian. This is a structural overview intentionally skipping technical details., Comment: 52 pages. This is a preprint of a chapter to appear in the "Handbook of Quantum Gravity", edited by Cosimo Bambi, Leonardo Modesto and Ilya Shapiro, 2023, Springer, reproduced with permission of Springer

All formalizations of session types rely on linear types for soundness as session-typed communication channels must change their type at every operation. Embedded language implementations of session types follow suit. They either rely on clever typing constructions to guarantee linearity statically, or on run-time checks that approximate linearity. We present a new language embedded implementation of session types, which is inspired by the inversion of control design principle. With our approach, all application programs are intrinsically session typed and unable to break linearity by construction. Linearity remains a proof obligation for a tiny encapsulated library that can be discharged once and for all when the library is built. We demonstrate that our proposed design extends to a wide range of features of session type systems: branching, recursion, multichannel and higher-order session, as well as context-free sessions. The multichannel extension provides an embedded implementation of session types which guarantees deadlock freedom by construction. The development reported in this paper is fully backed by type-checked Agda code., Comment: 27 pages; in submission

Session types provide a principled approach to typed communication protocols that guarantee type safety and protocol fidelity. Formalizations of session-typed communication are typically based on process calculi, concurrent lambda calculi, or linear logic. An alternative model based on context-sensitive typing and typestate has not received much attention due to its apparent restrictions. However, this model is attractive because it does not force programmers into particular patterns like continuation-passing style or channel-passing style, but rather enables them to treat communication channels like mutable variables. Polymorphic typestate is the key that enables a full treatment of session-typed communication. Previous work in this direction was hampered by its setting in a simply-typed lambda calculus. We show that higher-order polymorphism and existential types enable us to lift the restrictions imposed by the previous work, thus bringing the expressivity of the typestate-based approach on par with the competition. On this basis, we define PolyVGR, the system of polymorphic typestate for session types, establish its basic metatheory, type preservation and progress, and present a prototype implementation., Comment: 29 pages. Short version appears in PPDP 2023

Friction at water-carbon interfaces remains a major puzzle with theories and simulations unable to explain experimental trends in nanoscale waterflow. A recent theoretical framework -- quantum friction (QF)-- proposes to resolve these experimental observations by considering nonadiabatic coupling between dielectric fluctuations in water and graphitic surfaces. Here, using a classical model that enables fine-tuning of the solid's dielectric spectrum, we provide evidence from simulations in general support of QF. In particular, as features in the solid's dielectric spectrum begin to overlap with water's librational and Debye modes, we find an increase in friction in line with that proposed by QF. At the microscopic level, we find that this contribution to friction manifests more distinctly in the dynamics of the solid's charge density than that of water. Our findings suggest that experimental signatures of QF may be more pronounced in the solid's response rather than liquid water's.

The U(1)$^3$ model for 3+1 Euclidian signature general relativity is an interacting, generally covariant field theory with two physical polarisations that shares many features of Lorentzian general relativity. In particular, it displays a non-trivial realisation of the hypersurface deformation algebroid with non-trivial, i.e. phase space dependent structure functions rather than structure constants. In this paper we show that the model admits {\it an exact quantisation}. The quantisation rests on the observation that for this model and in the chosen representation of the canonical commutation relations the density unity hypersurface algebra {\it can be exponentiated on non-degenerate states}. These are states that represent a non-degenerate quantum metric and from a classical perspective are the relevant states on which the hypersurface algebra is representable. The representation of the algebra is exact, with no ambiguities involved and anomaly free. The quantum constraints can be exactly solved using {\it groupoid averaging} and the solutions admit a Hilbert space structure that agrees with the quantisation of a recently found reduced phase space formulation. Using the also recently found covariant action for that model, we start a path integral or spin foam formulation which, due to the Abelian character of the gauge group, is much simpler than for Lorentzian signature general relativity and provides an ideal testing ground for general spin foam models., Comment: 36p, no figures

A basic assumption in classical GR is that the metric field is nowhere degenerate in spacetime. In particular the induced metric on Cauchy surfaces must be nowhere degenerate. It is only under this assumption that one can derive the hypersurace deformation algebra between the initial value constraints which is absolutely transparent from the fact that the {\it inverse} of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface defomation algebra in quantum gravity has to address the issue of non-degenracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been layed to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been propposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions., Comment: 27p, no figures

In constructive quantum field theory (CQFT) it is customary to first regularise the theory at finite UV and IR cut-off. Then one first removes the UV cutoff using renormalisation techniques applied to families of CQFT's labelled by finite UV resolutions and then takes the thermodynamic limit. Alternatively, one may try to work directly without IR cut-off. More recently, wavelets have been proposed to define the renormalisation flow of CQFT's which is natural as they come accompanied with a multi-resolution analysis (MRA). However, wavelets so far have been mostly studied in the non-compact case. Practically useful wavelets that display compact support and some degree of smoothness can be constructed on the real line using Fourier space techniques but explicit formulae as functions of position are rarely available. Compactly supported wavelets can be periodised by summing over period translates keeping orthogonality properties but still yield to rather complicated expressions which generically lose their smoothness and position locality properties. It transpires that a direct approach to wavelets in the compact case is desirable. In this contribution we show that the Dirichlet-Shannon kernels serve as a natural scaling function to define generalised orthonormal wavelet bases on tori or copies of real lines respectively. These generalised wavelets are smooth, are simple explicitly computable functions, display quasi-local properties close to the Haar wavelet and have compact momentum supprt. Accordingly they have a built-in cut-off both in position and momentum, making them very useful for renormalisation applications., Comment: 20p, no figures

The Hamiltonian renormalisation programme motivated by constructive QFT and Osterwalder-Schrader reconstruction which was recently launched for bosonic field theories is extended to fermions. As fermion quantisation is not in terms of measures, the scheme has to be mildly modified accordingly. We exemplify the scheme for free fermions both for compact and non-compact spatial topologies respectively (i.e. with and without IR cut-off) and demonstrate that the convenient Dirichlet or Shannon coarse graining kernels recently advertised in a companion paper lead to a manifestly doubler free flow., Comment: 15p, no figures

Hamiltonian Renormalisation, as defined within this series of works, was derived from covariant Wilson renormalisation via Osterwalder-Schrader reconstruction. As such it directly applies to QFT with a true (physical) Hamiltonian bounded from below. The validity of the scheme was positively tested for free QFT in any dimension with or without Abelian gauge symmetries of Yang-Mills type. The aim of this Hamiltonian renormalisation scheme is to remove quantisation ambiguities of Hamiltonians in interacting QFT that remain even after UV and IR regulators are removed as it happens in highly non-linear QFT such as quantum gravity. While not derived for that case, the renormalisation flow formulae can without change also be applied to QFT without a single true Hamiltonian but rather an infinite number of Hamiltonian constraints. Then a central question is how the constraint algebra reacts to the renormalisation flow. This question should ultimately be addressed in quantum gravity. Before one considers this interacting, constrained QFT it is well motivated to consider a free, constrained QFT where the fixed point is explicitly known. In this paper we therefore address the case of parametrised field theory for which the quantum constraint algebra coincides simultaneously with the hypersurface deformation algebra of quantum gravity (or any other generally covariant theory) and the Virasoro algebra of free, closed, bosonic string theory or other CFT to which the results of this paper apply verbatim. The central result of our investigation is that finite resolution (discretised) constraint algebras {\it must not close} and that anomaly freeness of the continuum algebra is encoded in the convergence behaviour of the renormalisation flow., Comment: 39p, no figures

Java's type system mostly relies on type checking augmented with local type inference to improve programmer convenience. We study global type inference for Featherweight Generic Java (FGJ), a functional Java core language. Given generic class headers and field specifications, our inference algorithm infers all method types if classes do not make use of polymorphic recursion. The algorithm is constraint-based and improves on prior work in several respects. Despite the restricted setting, global type inference for FGJ is NP-complete., Comment: 33 pages, abridged version appears in ECOOP 2022

In order to determine the role of non-thermal transport of hot carriers which is decisive for the dissipation of energy in condensed matter we performed time-resolved broadband femtosecond transient reflectivity measurements on $7-197 \mathrm{nm}$ thick Bi(111) films epitaxially grown on Si(111). We monitored the behavior of the Fourier amplitude and the central frequency of the coherent $A_\mathrm{1g}$ phonon mode as function of the incident fluence, film thickness, and probe wavelength in the range of $580 -700 \mathrm{nm}$. The frequency redshift that follows photoexcitation was used as a robust quantity to determine the effective distribution of excited carriers that governs the displacive excitation mechanism of coherent $A_\mathrm{1g}$ phonons in Bi. For Bi films up to $50 \mathrm{nm}$ thickness a homogeneous excitation due to the ultrafast transport of hot charge carriers is observed, limited by a carrier penetration depth of $60 \mathrm{nm}$ independent of the totally deposited laser energy., Comment: 7 pages, 2 figures

A two-stage lightweight online dereverberation algorithm for hearing devices is presented in this paper. The approach combines a multi-channel multi-frame linear filter with a single-channel single-frame post-filter. Both components rely on power spectral density (PSD) estimates provided by deep neural networks (DNNs). By deriving new metrics analyzing the dereverberation performance in various time ranges, we confirm that directly optimizing for a criterion at the output of the multi-channel linear filtering stage results in a more efficient dereverberation as compared to placing the criterion at the output of the DNN to optimize the PSD estimation. More concretely, we show that training this stage end-to-end helps further remove the reverberation in the range accessible to the filter, thus increasing the \textit{early-to-moderate} reverberation ratio. We argue and demonstrate that it can then be well combined with a post-filtering stage to efficiently suppress the residual late reverberation, thereby increasing the \textit{early-to-final} reverberation ratio. This proposed two stage procedure is shown to be both very effective in terms of dereverberation performance and computational demands, as compared to e.g. recent state-of-the-art DNN approaches. Furthermore, the proposed two-stage system can be adapted to the needs of different types of hearing-device users by controlling the amount of reduction of early reflections., Comment: Accepted for publication in EURASIP Journal on Audio, Speech and Music Processing

In this paper, a neural network-augmented algorithm for noise-robust online dereverberation with a Kalman filtering variant of the weighted prediction error (WPE) method is proposed. The filter stochastic variations are predicted by a deep neural network (DNN) trained end-to-end using the filter residual error and signal characteristics. The presented framework allows for robust dereverberation on a single-channel noisy reverberant dataset similar to WHAMR!. The Kalman filtering WPE introduces distortions in the enhanced signal when predicting the filter variations from the residual error only, if the target speech power spectral density is not perfectly known and the observation is noisy. The proposed approach avoids these distortions by correcting the filter variations estimation in a data-driven way, increasing the robustness of the method to noisy scenarios. Furthermore, it yields a strong dereverberation and denoising performance compared to a DNN-supported recursive least squares variant of WPE, especially for highly noisy inputs., Comment: accepted to INTERSPEECH 2022

This work focuses on online dereverberation for hearing devices using the weighted prediction error (WPE) algorithm. WPE filtering requires an estimate of the target speech power spectral density (PSD). Recently deep neural networks (DNNs) have been used for this task. However, these approaches optimize the PSD estimate which only indirectly affects the WPE output, thus potentially resulting in limited dereverberation. In this paper, we propose an end-to-end approach specialized for online processing, that directly optimizes the dereverberated output signal. In addition, we propose to adapt it to the needs of different types of hearing-device users by modifying the optimization target as well as the WPE algorithm characteristics used in training. We show that the proposed end-to-end approach outperforms the traditional and conventional DNN-supported WPEs on a noise-free version of the WHAMR! dataset., Comment: \copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

Experimental measurements have reported ultra-fast and radius-dependent water transport in carbon nanotubes which are absent in boron nitride nanotubes. Despite considerable effort, the origin of this contrasting (and fascinating) behaviour is not understood. Here, with the aid of machine learning-based molecular dynamics simulations that deliver first-principles accuracy, we investigate water transport in single-wall carbon and boron nitride nanotubes. Our simulations reveal a large, radius-dependent hydrodynamic slippage on both materials with water experiencing indeed a $\approx 5$ times lower friction on carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms across the two materials reveals that the fast water transport on carbon is governed by facile oxygen motion, whereas the higher friction on boron nitride arises from specific hydrogen-nitrogen interactions. This work not only delivers a clear reference of unprecedented accuracy for water flow in single-wall nanotubes, but also provides detailed mechanistic insight into its radius and material dependence for future technological application.

A rigorous implementation of the Wheeler-Dewitt equations was derived in the context of Loop Quantum Gravity (LQG) and was coined Quantum Spin Dynamics (QSD). The Hamiltonian constraint of QSD was criticised as being too local and to prevent "propagation" in canonical LQG. That criticism was based on an algorithm developed for QSD for generating solutions to the Wheeler-DeWitt equations. The fine details of that algorithm could not be worked out because the QSD Hamiltonian constraint makes crucial use of the volume operator which cannot be diagonalised analytically. In this paper, we consider the U(1)$^3$ model for Euclidean vacuum LQG which consists in replacing the structure group SU(2) by U(1)$^3$ and otherwise keeps all properties of the SU(2) theory intact. This enables analytical calculations and the fine details of the algorithm {\it can} be worked out. By considering one of the simplest possible non-trivial class of solutions based on very small graphs, we show that 1. an infinite number of solutions {\it exist} which are 2. generically {\it not normalisable} with respect to the inner product on the space of spatially diffeomorphism invariant distributions and 3. generically display {\it propagation}. Due to the closeness of the U(1)$^3$ model to Euclidean LQG, it is extremely likely that all three properties hold also in the SU(2) case and even more so in physical Lorentzian LQG. These arguments can in principle be made water tight using modern numerical (e.g. ML or QC) methods combined with the techniques developed in this paper which we reserve for future work., Comment: 33p, 2 figures

We present the first results from the SuperWASP Variable Stars (SVS) citizen science project. The photometry archive of the Wide Angle Search for Planets has previously been searched for periodic variations and the results of this search formed the basis of the SVS project on the Zooniverse. The SVS project asks volunteers to visually inspect light curve plots and categorize each one according to a broad classification scheme. Results from the first two years of SVS have now been published online as the SuperWASP Variable Star Photometry Archive (VeSPA). The archive can be browsed online, downloaded in full, or queried, filtered, and sorted to export a refined set of results. An interactive light curve viewer also allows any light curve to be folded at a user-defined period. Analysis of citizen science results and development of VeSPA features are both ongoing. Updated results will be published every six months.