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Deep learning has proven to be a suitable alternative to least-squares (LSQ) fitting for parameter estimation in various quantitative MRI (QMRI) models. However, current deep learning implementations are not robust to changes in MR acquisition protocols. In practice, QMRI acquisition protocols differ substantially between different studies and clinical settings. The lack of generalizability and adoptability of current deep learning approaches for QMRI parameter estimation impedes the implementation of these algorithms in clinical trials and clinical practice. Neural Controlled Differential Equations (NCDEs) allow for the sampling of incomplete and irregularly sampled data with variable length, making them ideal for use in QMRI parameter estimation. In this study, we show that NCDEs can function as a generic tool for the accurate prediction of QMRI parameters, regardless of QMRI sequence length, configuration of independent variables and QMRI forward model (variable flip angle T1-mapping, intravoxel incoherent motion MRI, dynamic contrast-enhanced MRI). NCDEs achieved lower mean squared error than LSQ fitting in low-SNR simulations and in vivo in challenging anatomical regions like the abdomen and leg, but this improvement was no longer evident at high SNR. NCDEs reduce estimation error interquartile range without increasing bias, particularly under conditions of high uncertainty. These findings suggest that NCDEs offer a robust approach for reliable QMRI parameter estimation, especially in scenarios with high uncertainty or low image quality. We believe that with NCDEs, we have solved one of the main challenges for using deep learning for QMRI parameter estimation in a broader clinical and research setting., Comment: 29 pages, 10 figures, 7 supplementary figures, pre-print

Lubrication flows between two solid surfaces can be found in a variety of biological and engineering settings. In many of these systems, the lubricant exhibits viscoelastic properties, which modify the associated lubrication forces. Here, we experimentally study viscoelastic lubrication by considering the motion of a submerged cylinder sliding down an incline. We demonstrate that cylinders move faster when released in a viscoelastic Boger liquid compared to a Newtonian liquid with similar viscosity. Cylinders exhibit pure sliding motion in viscoelastic liquids, in contrast to the stick-slip motion observed in Newtonian liquids. We rationalize our results by using the second-order fluid model, which predicts a lift force on the cylinder arising from the normal-stress differences provided by the dissolved polymers. The interplay between viscoelastic lift, viscous friction, and gravity leads to a prediction for the sliding speed, which is consistent with our experimental results for weakly viscoelastic flows. Finally, we identify a remarkable difference between the lubrication of cylindrical and spherical contacts, as the latter does not exhibit any lift for weak viscoelasticity.

Upper bounds are obtained for the $p$-capacity of compact sets in $\R^d$, with $d \ge 2$ and $1

We prove that in the algebraic metacomplexity framework, the decomposition of metapolynomials into their isotypic components can be implemented efficiently, namely with only a quasipolynomial blowup in the circuit size. This means that many existing algebraic complexity lower bound proofs can be efficiently converted into isotypic lower bound proofs via highest weight metapolynomials, a notion studied in geometric complexity theory. In the context of algebraic natural proofs, our result means that without loss of generality algebraic natural proofs can be assumed to be isotypic. Our proof is built on the Poincar\'e--Birkhoff--Witt theorem for Lie algebras and on Gelfand--Tsetlin theory, for which we give the necessary comprehensive background., Comment: 29 pages. Comments are welcome!

Integrated microwave photonic (MWP) front-ends are capable of ultra-broadband signal reception and processing. However, state-of-the-art demonstrations are limited to performing only one specific functionality at any given time, which fails to meet the demands of advanced radio frequency applications in real-world electromagnetic environments. In this paper, we present a major departure from the current trend, which is a novel integrated MWP front-end capable of simultaneous cascaded functions with enhanced performances. Our integrated MWP front-end can delay or phase-shift signals within the selected frequency band while simultaneously suppressing noise signals in other frequency bands, resembling the function of a conventional RF front-end chain. Moreover, we implement an on-chip linearization technique to improve the spurious-free dynamic range of the system. Our work represents a paradigm shift in designing RF photonic front-ends and advancing their practical applications.

Central charge is a fundamental quantity in conformal field theories (CFT), and plays a crucial role in determining universality classes of critical points in two-dimensional systems. Despite its significance, the measurement of central charge has remained elusive thus far. In this work, we present the first experimental determination of the central charge using a universal quantum processor. Using a classically optimized variational quantum circuit and employing advanced error mitigation techniques, we successfully prepare ground states of various $1+1D$ quantum spin chain models at their critical point. Leveraging the heavy-hex structure of IBM quantum processors, we are able to implement periodic boundary conditions and mitigate boundary effects. We then extract the central charge from the scaling behavior of the sub-leading term of R{\'{e}}nyi generalizations of classical Shannon entropy, computed for local Pauli measurements in the conformal bases ($\sigma^{z}$ and $\sigma^x$). The experimental results are consistent with the known central charge values for the transverse field Ising (TFI) chain ($c=0.5$) and the XXZ chain ($c=1$), achieving relative errors as low as 5 percent., Comment: 7 + 13 pages, 4 + 11 figures

Qualitative properties such as convexity and monotonicity of the heat content in Riemannian manifolds and in Euclidean space in particular are obtained., Comment: 14 pages

In the classical Drossel-Schwabl forest fire process, vertices of a lattice become occupied at rate $1$, and they are hit by lightning at some tiny rate $\zeta > 0$, which causes entire connected components to burn. In this paper, we study a variant where fires are coming from the boundary of the forest instead. In particular we prove that, for the case without recoveries where the forest is an $N \times N$ box in the triangular lattice, the probability that the center of the box gets burnt tends to $0$ as $N \rightarrow \infty$ (but substantially slower than the one-arm probability of critical Bernoulli percolation). And, for the case where the forest is the upper-half plane, we show (still for the version without recoveries) that no infinite occupied cluster emerges. We also discuss analogs of some of these results for the corresponding models with recoveries, and explain how our results and proofs give valuable insight on a process considered earlier by Graf., Comment: 23 pages, 6 figures

Realizing controlled operations is fundamental to the design and execution of quantum algorithms. In quantum simulation and learning of quantum many-body systems, an important subroutine consists of implementing a controlled Hamiltonian time-evolution. Given only black-box access to the uncontrolled evolution $e^{-iHt}$, controlizing it, i.e., implementing $\mathrm{ctrl}(e^{-iHt}) = |0\langle\rangle 0|\otimes I + |1\langle\rangle 1 |\otimes e^{-iHt}$ is non-trivial. Controlization has been recently used in quantum algorithms for transforming unknown Hamiltonian dynamics [OKTM24] leveraging a scheme introduced in Refs. [NSM15, DNSM21]. The main idea behind the scheme is to intersperse the uncontrolled evolution with suitable operations such that the overall dynamics approximates the desired controlled evolution. Although efficient, this scheme uses operations randomly sampled from an exponentially large set. In the present work, we show that more efficient controlization schemes can be constructed with the help of orthogonal arrays for unknown 2-local Hamiltonians. This construction can also be generalized to $k$-local Hamiltonians. Moreover, our controlization schemes based on orthogonal arrays can take advantage of the interaction graph's structure and be made more efficient., Comment: Updated references

Pre-fault tolerant quantum computers have already demonstrated the ability to estimate observable values accurately, at a scale beyond brute-force classical computation. This has been enabled by error mitigation techniques that often rely on a representative model on the device noise. However, learning and maintaining these models is complicated by fluctuations in the noise over unpredictable time scales, for instance, arising from resonant interactions between superconducting qubits and defect two-level systems (TLS). Such interactions affect the stability and uniformity of device performance as a whole, but also affect the noise model accuracy, leading to incorrect observable estimation. Here, we experimentally demonstrate that tuning of the qubit-TLS interactions helps reduce noise instabilities and consequently enables more reliable error-mitigation performance. These experiments provide a controlled platform for studying the performance of error mitigation in the presence of quasi-static noise. We anticipate that the capabilities introduced here will be crucial for the exploration of quantum applications on solid-state processors at non-trivial scales., Comment: 8 pages, 4 figures (13 pages, 8 figures for supplementary material), reference numbering has been fixed at v2

We present simultaneous Chandra X-ray Observatory and Hubble Space Telescope observations of three certain (X5, X7, W37) and two likely (X4, W17) quiescent neutron-star low-mass X-ray binaries (qLMXBs) in the globular cluster 47 Tuc. We study these systems in the X-ray, optical and near-ultraviolet (NUV) using the simultaneous data and additional non-contemporaneous HST data. We have discovered a blue and variable NUV counterpart to W17. We have not securely identified the eclipsing qLMXB W37 in the optical or NUV. Deeper high-resolution imaging is needed to further investigate the faint NUV excess near the centre of the W37 error circle. We suggest that a previously identified optical astrometric match to X7 is likely the true counterpart. The Halpha emission and the location of the counterpart in the colour-magnitude diagram, indicate that the secondary is probably a non-degenerate, H-rich star. This is consistent with previous results from fitting X7's X-ray spectrum. In X4, the simultaneous X-ray and optical behaviour supports the earlier suggestion that the X-ray variability is driven by changes in accretion rate. The X-ray eclipses in X5 coincide with minima in the optical/NUV light curves. Comparison of the 47 Tuc qLMXBs with the cataclysmic variables (CVs) in the cluster confirms that overall the qLMXBs have larger X-ray-to-optical flux ratios. Based on their optical/NUV colors, we conclude that the accretion disks in the qLMXBs are less prominent than in CVs. This makes the ratio of X-ray flux to excess blue optical flux a powerful discriminator between CVs and qLMXBs., Comment: accepted by MNRAS

If a locally cartesian closed category carries a weak factorisation system, then the left maps are stable under pullback along right maps if and only if the right maps are closed under pushforward along right maps. We refer to this statement as the Frobenius equivalence and in this paper we state and prove an analogical statement for algebraic weak factorisation systems. These algebraic weak factorisation systems are an explicit variant of the more traditional weak factorisation systems in that the factorisation and the lifts are part of the structure of an algebraic weak factorisation system and are not merely required to exist. Our work has been motivated by the categorical semantics of type theory, where the Frobenius equivalence provides a useful tool for constructing dependent function types. We illustrate our ideas using split fibrations of groupoids, which are the backbone of the groupoid model of Hofmann and Streicher.

Safety-critical infrastructures, such as bridges, are periodically inspected to check for existing damage, such as fatigue cracks and corrosion, and to guarantee the safe use of the infrastructure. Visual inspection is the most frequent type of general inspection, despite the fact that its detection capability is rather limited, especially for fatigue cracks. Machine learning algorithms can be used for augmenting the capability of classical visual inspection of bridge structures, however, the implementation of such an algorithm requires a massive annotated training dataset, which is time-consuming to produce. This paper proposes a semi-automatic crack segmentation tool that eases the manual segmentation of cracks on images needed to create a training dataset for a machine learning algorithm. Also, it can be used to measure the geometry of the crack. This tool makes use of an image processing algorithm, which was initially developed for the analysis of vascular systems on retinal images. The algorithm relies on a multi-orientation wavelet transform, which is applied to the image to construct the so-called "orientation scores", i.e. a modified version of the image. Afterwards, the filtered orientation scores are used to formulate an optimal path problem that identifies the crack. The globally optimal path between manually selected crack endpoints is computed, using a state-of-the-art geometric tracking method. The pixel-wise segmentation is done afterwards using the obtained crack path. The proposed method outperforms fully automatic methods and shows potential to be an adequate alternative to the manual data annotation.

The study of 3D magnetic nanostructures has uncovered a range of rich phenomena including the stabilization and control of topological spin textures using nanoscale curvature, dynamic effects allowing controlled spin-wave emission, and novel ground states enabled by collective 3D frustrated interactions. From a technological perspective, 3D nanostructures offer routes to ultrahigh density data storage, massive interconnectivity within neuromorphic devices, as well as applications within health technologies, such as mechanical induction of stem cell differentiation. However, the fabrication of 3D nanomagnetic systems with feature sizes down to 10 nm poses a significant challenge. In this work we present a means of fabricating sub-100 nm 3D ferromagnetic nanowires, with both cross-sectional and longitudinal curvature, using two-photon lithography at a wavelength of 405 nm, combined with conventional deposition. Physical characterization illustrates that nanostructures with lateral features as low as 70 nm can be rapidly and reproducibly fabricated. A range of novel domain walls, with anti-vortex textures, coupled transverse textures, and hybrid vortex/anti-vortex textures are found to be enabled by the cross-sectional curvature of the system, as demonstrated by finite-element micromagnetic simulations. Magnetic force microscopy experiments in an externally applied magnetic field are used to image the injection and pinning of domain walls in the 3D magnetic nanowire. At specific field values, domain walls are observed to hop from trap to trap, providing a direct means to probe the local energy landscape. A simple model is presented demonstrating that thickness gradients and local roughness dictate the variation of pinning probability across the wire.

For an open set $\Om \subset \R^2$ let $\lambda(\Om)$ denote the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Om)$. Let $w_\Om$ be the torsion function for $\Om$, and let $\|.\|_p$ denote the $L^p$ norm. It is shown that there exist {$\eta_1>0,\eta_2>0$} such that { (i) $\|w_{\Om}\|_{\infty} \lambda(\Om)\ge 1+\eta_1$ for any non-empty, open, simply connected set $\Om\subset \R^2$ with $\lb(\Om) >0$, (ii) $\|w_{\Om}\|_1\lambda(\Om)\le {(1-\eta_2)}|\Om|$ for any non-empty, open, simply connected set $\Om\subset\R^2$ with finite measure $|\Om|$., Comment: 19 pages, 2 figures

We will show make two contributions to the theory of effective Kan fibrations, which are a more explicit version of the notion of a Kan fibration, a notion which plays a fundamental role in simplicial homotopy theory. We will show that simplicial Malcev algebras are effective Kan complexes and that the effective Kan fibrations can be seen as the right class in an algebraic weak factorisation system. In addition, we will introduce two strengthenings of the notion of an effective Kan fibration, the symmetric effective and degenerate-preferring Kan fibrations, and show that the previous results holds for these strengthenings as well., Comment: Minor corrections

We have analyzed Chandra and Suzaku observations of the globular cluster Terzan 6, made when the recurrent transient GRS 1747-312 was in quiescence. Our analysis reveals the presence of a second eclipsing, bursting neutron-star low-mass X-ray binary in the central regions of the cluster, in addition to GRS 1747-312. The new source, which we name Terzan 6 X2, is located only ~0.7 arcsec away from GRS 1747-312 in the 2021 Chandra images. The detection of a 5.14 ks-long eclipse in the light curve of X2 at a time not predicted by the ephemeris of GRS 1747-312 confirms that it is an unrelated source. Using the Suzaku light curve from 2009, which in addition to a type-I X-ray burst also showed an eclipse-like feature, we constrain the orbital period to be longer than 16.27 h. The 0.5-10 keV luminosities of X2 vary in the range of ~0.24-5.9x10^34 erg/s on time scales of months to years. We have identified a plausible optical counterpart of X2 in HST F606W and F814W images. This star varied by 2.7 mag in V_606 between epochs separated by years. In the cluster color-magnitude diagram, the variable counterpart lies in the blue-straggler region when it was optically bright, about 1.1-1.7 mag above the main-sequence turn-off. From the orbital period-density relation of Roche-lobe filling stars we find the mass-donor radius to be >0.8 Rsun., Comment: Accepted by ApJ; the orbital period and X-ray ephemeris of Terzan X2 have been added as note in the proof

Error-mitigation techniques such as probabilistic error cancellation and zero-noise extrapolation benefit from accurate noise models. The sparse Pauli-Lindblad noise model is one of the most successful models for those applications. In existing implementations, the model decomposes into a series of simple Pauli channels with one- and two-local terms that follow the qubit topology. While the model has been shown to accurately capture the noise in contemporary superconducting quantum processors for error mitigation, it is important to consider higher-weight terms and effects beyond nearest-neighbor interactions. For such extended models to remain practical, however, we need to ensure that they can be learned efficiently. In this work we present new techniques that accomplish exactly this. We introduce twirling based on Pauli rotations, which enables us to automatically generate single-qubit learning correction sequences and reduce the number of unique fidelities that need to be learned. In addition, we propose a basis-selection strategy that leverages graph coloring and uniform covering arrays to minimize the number of learning bases. Taken together, these techniques ensure that the learning of the extended noise models remains efficient, despite their increased complexity.

We introduce a new version of arithmetic in all finite types which extends the usual versions with primitive notions of extensionality and extensional equality. This new hybrid version allows us to formulate a strong form of extensionality, which we call converse extensionality. Inspired by Brouwer's notion of apartness, we show that converse extensionality can be eliminated in a way which improves on results from our previous work. We also explain how standard proof-theoretic interpretations, like realizability and functional interpretations, can be extended to such hybrid systems, and how that might be relevant to proof-mining.

Probabilistic error cancellation (PEC) is a technique that generates error-mitigated estimates of expectation values from ensembles of quantum circuits. In this work we extend the application of PEC from unitary-only circuits to dynamic circuits with measurement-based operations, such as mid-circuit measurements and classically-controlled (feedforward) Clifford operations. Our approach extends the sparse Pauli-Lindblad noise model to measurement-based operations while accounting for non-local measurement crosstalk in superconducting processors. Our mitigation and monitoring experiments provide a holistic view for the performance of the protocols developed in this work. These capabilities will be a crucial tool in the exploration of near-term dynamic circuit applications., Comment: Minor updates to v1

Upper bounds are obtained for the Newtonian capacity of compact sets in $\R^d,\,d\ge 3$ in terms of the perimeter of the $r$-parallel neighbourhood of $K$. For compact, convex sets in $\R^d,\,d\ge 3$ with a $C^2$ boundary the Newtonian capacity is bounded from above by $(d-2)M(K)$, where $M(K)>0$ is the integral of the mean curvature over the boundary of $K$ with equality if $K$ is a ball. For compact, convex sets in $\R^d,\,d\ge 3$ with non-empty interior the Newtonian capacity is bounded from above by $\frac{(d-2)P(K)^2}{d|K|}$ with equality if $K$ is a ball. Here $P(K)$ is the perimeter of $K$ and $|K|$ is its measure. A quantitative refinement of the latter inequality in terms of the Fraenkel asymmetry is also obtained. An upper bound is obtained for expected Newtonian capacity of the Wiener sausage in $\R^d,\,d\ge 5$ with radius $\varepsilon$ and time length $t$., Comment: 15 pages

Supermassive black holes in active galactic nuclei (AGN) are known to launch relativistic jets, which are observed across the entire electromagnetic spectrum and are thought to be efficient particle accelerators. Their primary radiation mechanism for radio emission is polarized synchrotron emission produced by a population of non-thermal electrons. In this Letter, we present a global general relativistic magnetohydrodynamical (GRMHD) simulation of a magnetically arrested disk (MAD). After the simulation reaches the MAD state, we show that waves are continuously launched from the vicinity of the black hole and propagate along the interface between the jet and the wind. At this interface, a steep gradient in velocity is present between the mildly relativistic wind and the highly relativistic jet. The interface is, therefore, a shear layer, and due to the shear, the waves generate roll-ups that alter the magnetic field configuration and the shear layer geometry. We then perform polarized radiation transfer calculations of our GRMHD simulation and find signatures of the waves in both total intensity and linear polarization, effectively lowering the fully resolved polarization fraction. The tell-tale polarization signatures of the waves could be observable by future Very Long Baseline Interferometric observations, e.g., by the next-generation Event Horizon Telescope., Comment: 20 pages, 17 figures, accepted for publication in ApJL

We investigate how much type theory is able to prove about the natural numbers. A classical result in this area shows that dependent type theory without any universes is conservative over Heyting Arithmetic (HA). We build on this result by showing that type theories with one level of universes are conservative over Higher-order Heyting Arithmetic (HAH). Although this clearly depends on the specific type theory, we show that the interpretation of logic also plays a major role. For proof-irrelevant interpretations, we will see that strong versions of type theory prove exactly the same higher-order arithmetical formulas as HAH. Conversely, proof-relevant interpretations prove strictly more second-order arithmetical formulas than HAH, however they still prove exactly the same first-order arithmetical formulas. Along the way, we investigate the different interpretations of logic in type theory, and to what extent dependent type theories can be seen as extensions of higher-order logic. We apply our results by proving De Jongh's theorem for type theory., Comment: 23 pages

The research on the properties of spin waves (SWs) in three-dimensional nanosystems is an innovative idea in the field of magnonics. Mastering and understanding the nature of magnetization dynamics and binding of SWs at surfaces, edges, and in-volume parts of three-dimensional magnetic systems enables the discovery of new phenomena and suggests new possibilities for their use in magnonic and spintronic devices. In this work, we use numerical methods to study the effect of geometry and external magnetic field manipulations on the localization and dynamics of SWs in crescent-shaped (CS) waveguides. It is shown that changing the magnetic field direction in these waveguides breaks the symmetry and affects the localization of eigenmodes with respect to the static demagnetizing field. This in turn has a direct effect on their frequency. Furthermore, CS structures were found to be characterized by significant saturation at certain field orientations, resulting in a cylindrical magnetization distribution. Thus, we present chirality-based nonreciprocal dispersion relations for high-frequency SWs, which can be controlled by the field direction (shape symmetry) and its amplitude (saturation).

In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those realizability toposes which are obtained from partial combinatory algebras. Since there are many examples of arrow algebras and arrow algebras have a number of closure properties, including a notion of subalgebra given by a nucleus, arrow algebras provide a flexible tool for constructing toposes; we illustrate this by providing some general tools for creating toposes for Kreisel's modified realizability., Comment: Revised version after comments by referee and Umberto Tarantino

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function's (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular as part of many learning algorithms, notably for neural networks. This paper uses Prolog to systematically derive gradient-based forward- and reverse-mode AD variants from a simple executable specification: evaluation of the symbolic derivative. Along the way we demonstrate that several Prolog features (DCGs, co-routines) contribute to the succinct formulation of the algorithm. We also discuss two applications in probabilistic programming that are enabled by our Prolog algorithms. The first is parameter learning for the Sum-Product Loop Language and the second consists of both parameter learning and variational inference for probabilistic logic programming., Comment: accepted for publication in the issues of Theory and Practice of Logic Programming dedicated to ICLP 2023

Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience. However, not all effects can be classified as algebraic; some need a more sophisticated handling. In particular, effects that have or create a delimited scope need special care, as their continuation consists of two parts-in and out of the scope-and their modular composition introduces additional complexity. These effects are called scoped and have gained attention by their growing applicability and adoption in popular libraries. While calculi have been designed with algebraic effects & handlers built in to facilitate their use, a calculus that supports scoped effects & handlers in a similar manner does not yet exist. This work fills this gap: we present $\lambda_{\mathit{sc}}$, a calculus with native support for both algebraic and scoped effects & handlers. It addresses the need for polymorphic handlers and explicit clauses for forwarding unknown scoped operations to other handlers. Our calculus is based on Eff, an existing calculus for algebraic effects, extended with Koka-style row polymorphism, and consists of a formal grammar, operational semantics, a (type-safe) type-and-effect system and type inference. We demonstrate $\lambda_{\mathit{sc}}$ on a range of examples.

Purpose: Medical imaging has become increasingly important in diagnosing and treating oncological patients, particularly in radiotherapy. Recent advances in synthetic computed tomography (sCT) generation have increased interest in public challenges to provide data and evaluation metrics for comparing different approaches openly. This paper describes a dataset of brain and pelvis computed tomography (CT) images with rigidly registered CBCT and MRI images to facilitate the development and evaluation of sCT generation for radiotherapy planning. Acquisition and validation methods: The dataset consists of CT, CBCT, and MRI of 540 brains and 540 pelvic radiotherapy patients from three Dutch university medical centers. Subjects' ages ranged from 3 to 93 years, with a mean age of 60. Various scanner models and acquisition settings were used across patients from the three data-providing centers. Details are available in CSV files provided with the datasets. Data format and usage notes: The data is available on Zenodo (https://doi.org/10.5281/zenodo.7260705) under the SynthRAD2023 collection. The images for each subject are available in nifti format. Potential applications: This dataset will enable the evaluation and development of image synthesis algorithms for radiotherapy purposes on a realistic multi-center dataset with varying acquisition protocols. Synthetic CT generation has numerous applications in radiation therapy, including diagnosis, treatment planning, treatment monitoring, and surgical planning., Comment: 15 pages, 4 figures, 9 tables, pre-print submitted to Medical Physics - dataset. The training dataset is available on Zenodo at https://doi.org/10.5281/zenodo.7260705 from April, 1st 2023

Background: Synthetic computed tomography (sCT) has been proposed and increasingly clinically adopted to enable magnetic resonance imaging (MRI)-based radiotherapy. Deep learning (DL) has recently demonstrated the ability to generate accurate sCT from fixed MRI acquisitions. However, MRI protocols may change over time or differ between centres resulting in low-quality sCT due to poor model generalisation. Purpose: investigating domain randomisation (DR) to increase the generalisation of a DL model for brain sCT generation. Methods: CT and corresponding T1-weighted MRI with/without contrast, T2-weighted, and FLAIR MRI from 95 patients undergoing RT were collected, considering FLAIR the unseen sequence where to investigate generalisation. A ``Baseline'' generative adversarial network was trained with/without the FLAIR sequence to test how a model performs without DR. Image similarity and accuracy of sCT-based dose plans were assessed against CT to select the best-performing DR approach against the Baseline. Results: The Baseline model had the poorest performance on FLAIR, with mean absolute error (MAE)=106$\pm$20.7 HU (mean$\pm\sigma$). Performance on FLAIR significantly improved for the DR model with MAE=99.0$\pm$14.9 HU, but still inferior to the performance of the Baseline+FLAIR model (MAE=72.6$\pm$10.1 HU). Similarly, an improvement in $\gamma$-pass rate was obtained for DR vs Baseline. Conclusions: DR improved image similarity and dose accuracy on the unseen sequence compared to training only on acquired MRI. DR makes the model more robust, reducing the need for re-training when applying a model on sequences unseen and unavailable for retraining., Comment: Preprint submitted to Physica Medica on 2023-02-16 for review. Also published in Zenodo at https://doi.org/10.5281/zenodo.7742642

Algebraic effects & handlers are a modular approach for modeling side-effects in functional programming. Their syntax is defined in terms of a signature of effectful operations, encoded as a functor, that are plugged into the free monad; their denotational semantics is defined by fold-style handlers that only interpret their part of the syntax and forward the rest. However, not all effects are algebraic: some need to access an internal computation. For example, scoped effects distinguish between a computation in scope and out of scope; parallel effects parallellize over a computation, latent effects defer a computation. Separate definitions have been proposed for these higher-order effects and their corresponding handlers, often leading to expedient and complex monad definitions. In this work we propose a generic framework for higher-order effects, generalizing algebraic effects & handlers: a generic free monad with higher-order effect signatures and a corresponding interpreter. Specializing this higher-order syntax leads to various definitions of previously defined (scoped, parallel, latent) and novel (writer, bracketing) effects. Furthermore, we formally show our framework theoretically correct, also putting different effect instances on formal footing; a significant contribution for parallel, latent, writer and bracketing effects.

Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several small- to medium-sized protein simulations, reproducing the CG equilibrium distribution, and preserving dynamics of all-atom simulations such as protein folding events.

Automatic differentiation (AD) has been a topic of interest for researchers in many disciplines, with increased popularity since its application to machine learning and neural networks. Although many researchers appreciate and know how to apply AD, it remains a challenge to truly understand the underlying processes. From an algebraic point of view, however, AD appears surprisingly natural: it originates from the differentiation laws. In this work we use Algebra of Programming techniques to reason about different AD variants, leveraging Haskell to illustrate our observations. Our findings stem from three fundamental algebraic abstractions: (1) the notion of module over a semiring, (2) Nagata's construction of the 'idealization of a module', and (3) Kronecker's delta function, that together allow us to write a single-line abstract definition of AD. From this single-line definition, and by instantiating our algebraic structures in various ways, we derive different AD variants, that have the same extensional behaviour, but different intensional properties, mainly in terms of (asymptotic) computational complexity. We show the different variants equivalent by means of Kronecker isomorphisms, a further elaboration of our Haskell infrastructure which guarantees correctness by construction. With this framework in place, this paper seeks to make AD variants more comprehensible, taking an algebraic perspective on the matter.

Flexible systems are linear systems of inclusions in which the elements of the coefficient matrix are external numbers in the sense of nonstandard analysis. External numbers represent real numbers with small, individual error terms. Using Gaussian elimination, a flexible system can be put into a row-echelon form with increasing error terms at the right-hand side. Then parameters are assigned to the error terms and the resulting system is solved by common methods of linear algebra. The solution set may have indeterminacy not only in terms of linear spaces, but also of modules. We determine maximal robustness for flexible systems., Comment: 37 pages

Generating samples from the output distribution of a quantum circuit is a ubiquitous task used as a building block of many quantum algorithms. Here we show how to accomplish this task on a noisy quantum processor lacking full-blown error correction for a special class of quantum circuits dominated by Clifford gates. Our approach is based on Coherent Pauli Checks (CPCs) that detect errors in a Clifford circuit by verifying commutation rules between random Pauli-type check operators and the considered circuit. Our main contributions are as follows. First, we derive a simple formula for the probability that a Clifford circuit protected by CPCs contains a logical error. In the limit of a large number of checks, the logical error probability is shown to approach the value ${\approx}7\epsilon n/5$, where $n$ is the number of qubits and $\epsilon$ is the depolarizing error rate. Our formula agrees nearly perfectly with the numerical simulation results. Second, we show that CPCs are well-suited for quantum processors with a limited qubit connectivity. For example, the difference between all-to-all and linear qubit connectivity is only a 3X increase in the number of CNOT gates required to implement CPCs. Third, we describe simplified one-sided CPCs which are well-suited for mitigating measurement errors in the single-shot settings. Finally, we report an experimental demonstration of CPCs with up to 10 logical qubits and more than 100 logical CNOT gates. Our experimental results show that CPCs provide a marked improvement in the logical error probability for the considered task of sampling the output distribution of quantum circuits., Comment: 30 pages, 20 figures

Background: Respiratory-resolved four-dimensional magnetic resonance imaging (4D-MRI) provides essential motion information for accurate radiation treatments of mobile tumors. However, obtaining high-quality 4D-MRI suffers from long acquisition and reconstruction times. Purpose: To develop a deep learning architecture to quickly acquire and reconstruct high-quality 4D-MRI, enabling accurate motion quantification for MRI-guided radiotherapy. Methods: A small convolutional neural network called MODEST is proposed to reconstruct 4D-MRI by performing a spatial and temporal decomposition, omitting the need for 4D convolutions to use all the spatio-temporal information present in 4D-MRI. This network is trained on undersampled 4D-MRI after respiratory binning to reconstruct high-quality 4D-MRI obtained by compressed sensing reconstruction. The network is trained, validated, and tested on 4D-MRI of 28 lung cancer patients acquired with a T1-weighted golden-angle radial stack-of-stars sequence. The 4D-MRI of 18, 5, and 5 patients were used for training, validation, and testing. Network performances are evaluated on image quality measured by the structural similarity index (SSIM) and motion consistency by comparing the position of the lung-liver interface on undersampled 4D-MRI before and after respiratory binning. The network is compared to conventional architectures such as a U-Net, which has 30 times more trainable parameters. Results: MODEST can reconstruct high-quality 4D-MRI with higher image quality than a U-Net, despite a thirty-fold reduction in trainable parameters. High-quality 4D-MRI can be obtained using MODEST in approximately 2.5 minutes, including acquisition, processing, and reconstruction. Conclusion: High-quality accelerated 4D-MRI can be obtained using MODEST, which is particularly interesting for MRI-guided radiotherapy., Comment: Code available at https://gitlab.com/computational-imaging-lab/modest

Artificial spin-ices consist of lithographic arrays of single-domain magnetic nanowires organised into frustrated lattices. These geometries are usually two-dimensional, allowing a direct exploration of physics associated with frustration, topology and emergence. Recently, three-dimensional geometries have been realised, in which transport of emergent monopoles can be directly visualised upon the surface. Here we carry out an exploration of the three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed within a diamond-bond lattice geometry. We find a rich phase diagram, consisting of a double-charged monopole crystal, a single-charged monopole crystal and conventional spin-ice with pinch points associated with a Coulomb phase. In our experimental demagnetised systems, broken symmetry forces formation of ferromagnetic stripes upon the surface, a configuration that forbids the formation of the lower energy double-charged monopole crystal. Instead, we observe crystallites of single magnetic charge, superimposed upon an ice background. The crystallites are found to form due to the intricate distribution of magnetic charge around a three-dimensional nanostructured vertex, which locally favours monopole formation. Our work suggests that engineered surface energetics can be used to tune the ground state of experimental three-dimensional ASI systems.

Dynamic induction control is a wind farm flow control strategy that utilises wind turbine thrust variations to accelerate breakdown of the aerodynamic wake and improve downstream turbine performance. However, when floating wind turbines are considered, additional dynamics and challenges appear that make optimal control difficult. In this work, we propose an adjoint optimisation framework for non-linear economic model-predictive control, which utilises a novel coupling of an existing aerodynamic wake model to floating platform hydrodynamics. Analysis of the frequency response for the coupled model shows that it is possible to achieve wind turbine thrust variations without inducing large motion of the rotor. Using economic model-predictive control, we find dynamic induction results that lead to an improvement of 7% over static induction control, where the dynamic controller stimulates wake breakdown with only small variations in rotor displacement. This novel model formulation provides a starting point for the adaptation of dynamic wind farm flow control strategies for floating wind turbines., Comment: 6 pages, 8 figures, accepted for publication for IFAC World Congress 2023

The OSSS inequality [O'Donnell, Saks, Schramm and Servedio, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05), Pittsburgh (2005)] gives an upper bound for the variance of a function f of independent 0-1 valued random variables, in terms of the influences of these random variables and the computational complexity of a (randomised) algorithm for determining the value of f. Duminil-Copin, Raoufi and Tassion [Annals of Mathematics 189, 75-99 (2019)] obtained a generalization to monotonic measures and used it to prove new results for Potts models and random-cluster models. Their generalization of the OSSS inequality raises the question if there are still other measures for which a version of that inequality holds. We derive a version of the OSSS inequality for a family of measures that are far from monotonic, namely the k-out-of-n measures (these measures correspond with drawing k elements from a set of size n uniformly). We illustrate the inequality by studying the event that there is an occupied horizontal crossing of an R times R box on the triangular lattice in the site percolation model where exactly half of the vertices in the box are occupied., Comment: 25 pages. Compared with the previous version: Improvement of factor log n in the main theorem (Theorem 1.1). Proof of that theorem has been substantially changed. Additional author (Henk Don)

We study forest fire processes in two dimensions. On a given planar lattice, vertices independently switch from vacant to occupied at rate $1$ (initially they are all vacant), and any connected component "is burnt" (its vertices become instantaneously vacant) as soon as its cardinality crosses a (typically large) threshold $N$, the parameter of the model. Our analysis provides a detailed description, as $N \to \infty$, of the process near and beyond the critical time $t_c$ (at which an infinite cluster would arise in the absence of fires). In particular we prove a somewhat counterintuitive result: there exists $\delta > 0$ such that with high probability, the origin does not burn before time $t_c + \delta$. This provides a negative answer to Open Problem 4.1 of van den Berg and Brouwer [Comm. Math. Phys., 2006]. Informally speaking, the result can be explained in terms of the emergence of fire lanes, whose total density is negligible (as $N \to \infty$), but which nevertheless are sufficiently robust with respect to recoveries. We expect that such a behavior also holds for the classical Drossel-Schwabl model. A large part of this paper is devoted to analyzing recoveries during the interval $[t_c, t_c + \delta]$. These recoveries do have a "microscopic" effect, but it turns out that their combined influence on macroscopic scales (and in fact on relevant "mesoscopic" scales) vanishes as $N \to \infty$. In order to prove this, we use key ideas of Kiss, Manolescu and Sidoravicius [Ann. Probab., 2015], introducing a suitable induction argument to extend and strengthen their results. We then use it to prove that a deconcentration result in our earlier joint work with Kiss on volume-frozen percolation also holds for the forest fire process. As we explain, significant additional difficulties arise here, since recoveries destroy the nice spatial Markov property of frozen percolation., Comment: 53 pages, 7 figures

The ability to computationally generate novel yet physically foldable protein structures could lead to new biological discoveries and new treatments targeting yet incurable diseases. Despite recent advances in protein structure prediction, directly generating diverse, novel protein structures from neural networks remains difficult. In this work, we present a new diffusion-based generative model that designs protein backbone structures via a procedure that mirrors the native folding process. We describe protein backbone structure as a series of consecutive angles capturing the relative orientation of the constituent amino acid residues, and generate new structures by denoising from a random, unfolded state towards a stable folded structure. Not only does this mirror how proteins biologically twist into energetically favorable conformations, the inherent shift and rotational invariance of this representation crucially alleviates the need for complex equivariant networks. We train a denoising diffusion probabilistic model with a simple transformer backbone and demonstrate that our resulting model unconditionally generates highly realistic protein structures with complexity and structural patterns akin to those of naturally-occurring proteins. As a useful resource, we release the first open-source codebase and trained models for protein structure diffusion.

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time. Due to the computationally expensive nature of their standard solution methods, neural PDE surrogates have become an active research topic to accelerate these simulations. However, current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated. Viewing the time evolution of such correlated fields through the lens of multivector fields allows us to overcome these limitations. Multivector fields consist of scalar, vector, as well as higher-order components, such as bivectors and trivectors. Their algebraic properties, such as multiplication, addition and other arithmetic operations can be described by Clifford algebras. To our knowledge, this paper presents the first usage of such multivector representations together with Clifford convolutions and Clifford Fourier transforms in the context of deep learning. The resulting Clifford neural layers are universally applicable and will find direct use in the areas of fluid dynamics, weather forecasting, and the modeling of physical systems in general. We empirically evaluate the benefit of Clifford neural layers by replacing convolution and Fourier operations in common neural PDE surrogates by their Clifford counterparts on 2D Navier-Stokes and weather modeling tasks, as well as 3D Maxwell equations. For similar parameter count, Clifford neural layers consistently improve generalization capabilities of the tested neural PDE surrogates. Source code for our PyTorch implementation is available at https://microsoft.github.io/cliffordlayers/., Comment: Accepted at ICLR-2023

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum, respectively) with respect to this new data-driven connection and corresponding Riemannian manifold. Then we use these shortest curves for geodesic tracking of complex vasculature in multi-orientation image representations defined on $\mathbb{M}_{2}$. The data-driven Cartan connection characterizes the Hamiltonian flow of all geodesics. It also allows for improved adaptation to curvature and misalignment of the (lifted) vessel structure that we track via globally optimal geodesics. We compute these geodesics numerically via steepest descent on distance maps on $\mathbb{M}_2$ that we compute by a new modified anisotropic fast-marching method. Our experiments range from tracking single blood vessels with fixed endpoints to tracking complete vascular trees in retinal images. Single vessel tracking is performed in a single run in the multi-orientation image representation, where we project the resulting geodesics back onto the underlying image. The complete vascular tree tracking requires only two runs and avoids prior segmentation, placement of extra anchor points, and dynamic switching between geodesic models. Altogether we provide a geodesic tracking method using a single, flexible, transparent, data-driven geodesic model providing globally optimal curves which correctly follow highly complex vascular structures in retinal images. All experiments in this article can be reproduced via documented Mathematica notebooks available at GitHub (https://github.com/NickyvdBerg/DataDrivenTracking).

We present an algorithm that, given a representation of a road network in lane-level detail, computes a route that minimizes the expected cost to reach a given destination. In doing so, our algorithm allows us to solve for the complex trade-offs encountered when trying to decide not just which roads to follow, but also when to change between the lanes making up these roads, in order to -- for example -- reduce the likelihood of missing a left exit while not unnecessarily driving in the leftmost lane. This routing problem can naturally be formulated as a Markov Decision Process (MDP), in which lane change actions have stochastic outcomes. However, MDPs are known to be time-consuming to solve in general. In this paper, we show that -- under reasonable assumptions -- we can use a Dijkstra-like approach to solve this stochastic problem, and benefit from its efficient $O(n \log n)$ running time. This enables an autonomous vehicle to exhibit lane-selection behavior as it efficiently plans an optimal route to its destination., Comment: Appeared at the 15th International Workshop on the Algorithmic Foundations of Robotics (WAFR) 2022

We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $\kappa$-localise in $L^2$., Comment: 24 pages, 5 figures. To appear in EMS Surveys

Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely in conjunction with algebraic operations. Although proposals for scoped operations exist, they are either ad-hoc and unprincipled, or too inconvenient for practical programming. This paper provides the best of both worlds: a theoretically-founded model of scoped effects that is convenient for implementation and reasoning. Our new model is based on an adjunction between a locally finitely presentable category and a category of functorial algebras. Using comparison functors between adjunctions, we show that our new model, an existing indexed model, and a third approach that simulates scoped operations in terms of algebraic ones have equal expressivity for handling scoped operations. We consider our new model to be the sweet spot between ease of implementation and structuredness. Additionally, our approach automatically induces fusion laws of handlers of scoped effects, which are useful for reasoning and optimisation., Comment: Extended version of the paper Structured Handling of Scoped Effects in ESOP 2022

Noise in pre-fault-tolerant quantum computers can result in biased estimates of physical observables. Accurate bias-free estimates can be obtained using probabilistic error cancellation (PEC), which is an error-mitigation technique that effectively inverts well-characterized noise channels. Learning correlated noise channels in large quantum circuits, however, has been a major challenge and has severely hampered experimental realizations. Our work presents a practical protocol for learning and inverting a sparse noise model that is able to capture correlated noise and scales to large quantum devices. These advances allow us to demonstrate PEC on a superconducting quantum processor with crosstalk errors, thereby providing an important milestone in opening the way to quantum computing with noise-free observables at larger circuit volumes.

The removal of microbubbles from substrates is crucial for the efficiency of many catalytic and electrochemical gas evolution reactions in liquids. The current work investigates the coalescence and detachment of bubbles generated from catalytic decomposition of hydrogen peroxide. Self-propelled detachment, induced by the coalescence of two bubbles, is observed at sizes much smaller than those determined by buoyancy. Upon coalescence, the released surface energy is partly dissipated by the bubble oscillations, working against viscous drag. The remaining energy is converted to the kinetic energy of the out-of-plane jumping motion of the merged bubble. The critical ratio of the parent bubble sizes for the jumping to occur is theoretically derived from an energy balance argument and found to be in agreement with the experimental results. The present results provide both physical insight for the bubble interactions and practical strategies for applications in chemical engineering and renewable energy technologies like electrolysis.

Explainable artificial intelligence (xAI) is seen as a solution to making AI systems less of a black box. It is essential to ensure transparency, fairness, and accountability, which are especially paramount in the financial sector. The aim of this study was a preliminary investigation of the perspectives of supervisory authorities and regulated entities regarding the application of xAI in the fi-nancial sector. Three use cases (consumer credit, credit risk, and anti-money laundering) were examined using semi-structured interviews at three banks and two supervisory authorities in the Netherlands. We found that for the investigated use cases a disparity exists between supervisory authorities and banks regarding the desired scope of explainability of AI systems. We argue that the financial sector could benefit from clear differentiation between technical AI (model) ex-plainability requirements and explainability requirements of the broader AI system in relation to applicable laws and regulations., Comment: BNAIC/BeneLearn 2021 conference paper