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Let $G$ be a countable group and $\mu$ a probability measure on $G$. We build a new framework to compute asymptotic quantities associated with the $\mu$-random walk on $G$, using methods from harmonic analysis on groups and Banach space theory, most notably the complex interpolation. It is shown that under mild conditions, the Lyapunov exponent of the $\mu$-random walk with respect to a weight $\omega$ on $G$ can be computed in terms of the asymptotic behavior of the spectral radius of $\mu$ in an ascending class of weighted group algebras, and we prove that for natural choices of $\omega$ and $\mu$, the Lyapunov exponent vanishes. Also, we show that the Avez entropy of the $\mu$-random walk can be realized as the Lyapunov exponent of $\mu$ with respect to a suitable weight. Next, by considering the spectral radius in the algebras of $p$-pseudofunctions on $G$, we introduce a new asymptotic quantity, which we call convolution entropy. We show that for groups with the property of rapid decay, the convolution entropy coincides with the Avez entropy. Subsequently, we apply our results to stationary dynamical systems consisting of an action of a group with the property of rapid decay on a probability space. We prove that whenever the associated Koopman representation is weakly contained in the left-regular representation of the group, then the Avez entropy coincides with the Furstenberg entropy of the stationary space. This gives a characterization of (Zimmer) amenability for actions of rapid decay groups on stationary spaces.

Relightable object acquisition is a key challenge in simplifying digital asset creation. Complete reconstruction of an object typically requires capturing hundreds to thousands of photographs under controlled illumination, with specialized equipment. The recent progress in differentiable rendering improved the quality and accessibility of inverse rendering optimization. Nevertheless, under uncontrolled illumination and unstructured viewpoints, there is no guarantee that the observations contain enough information to reconstruct the appearance properties of the captured object. We thus propose to consider the acquisition process from a signal-processing perspective. Given an object's geometry and a lighting environment, we estimate the properties of the materials on the object's surface in seconds. We do so by leveraging frequency domain analysis, considering the recovery of material properties as a deconvolution, enabling fast error estimation. We then quantify the uncertainty of the estimation, based on the available data, highlighting the areas for which priors or additional samples would be required for improved acquisition quality. We compare our approach to previous work and quantitatively evaluate our results, showing similar quality as previous work in a fraction of the time, and providing key information about the certainty of the results., Comment: Project page: https://brdf-uncertainty.github.io

Structurally anisotropic materials are ubiquitous in several application fields, yet their accurate optical characterization remains challenging due to the lack of general models linking their scattering coefficients to the macroscopic transport observables, and the need to combine multiple measurements to retrieve their direction-dependent values. Here, we present an improved method for the experimental determination of light transport tensor coefficients from the diffusive rates measured along all three directions, based on transient transmittance measurements and a generalized Monte Carlo model. We apply our method to the characterization of light transport properties in two common anisotropic materials - polytetrafluoroethylene (PTFE) tape and paper - highlighting the magnitude of systematic deviations that are typically incurred when neglecting anisotropy.

Purpose. To alleviate the manual contouring burden, deep learning (DL) based automated contouring has been explored. However, due to the poor contrast resolution of preclinical irradiator CBCT, these methods have been limited to high contrast - minimally anatomically complex - structures such as the heart and lungs. Thus, low contrast abdominal CBCT DL-based segmentation has yet to be addressed. In this work we explore a DL-based model in conjunction with iodine-based contrast agent approach to allow precise automatic contouring of mouse abdominal, thorax, and skeletal structures in under a second. Methods. A DL U-net-like architecture was trained to contour mice organs in small animal radiation research platform CBCT scans. 41 mice were contoured by a human expert, using semi-automatic segmentation methods, after injection of iodine contrast agent, establishing a ground truth for the DL model. The model was trained on a dataset of 26 mice, while 2 mice were used for validation, tuning the model during training, and 15 mice used for performance evaluation testing. The model consists of a pre-processor, and a post-processor for volumetric reconstruction of the DL-predicted probability maps. Model performance was evaluated using both qualitative and distance metrics, including the dice similarity score, precision score, Hausdorff Distance (HD), and mean surface distance (MSD). Results. Performance of the DL-based iodine contrast-enhanced model provided high quality predicted contours in under a second, with the median for all organs being reported: dice $>$ 91\%, precision $>$ 95\%, HD50 $<$ 1.0 mm, and MSD $<$ 1.41 mm. Conclusion. The proposed combination of a DL-based and iodine contrast-enhanced model proved as a viable method to vastly improve efficiency of small animal CBCT image-guided RT preclinical trials.

Anisotropic light transport is extremely common among scattering materials, yet a comprehensive picture of how macroscopic diffusion is determined by microscopic tensor scattering coefficients is not fully established yet. In this work, we present a theoretical and experimental study of diffusion in structurally anisotropic media with uniaxially symmetric scattering coefficients. Exact analytical relations are derived in the case of index-matched turbid media, unveiling the general relation between microscopic scattering coefficients and the resulting macroscopic diffusion tensor along different directions. Excellent agreement is found against anisotropic Monte Carlo simulations up to high degrees of anisotropy, in contrast with previously proposed approaches. The obtained solutions are used to analyze experimental measurements of anisotropic light transport in polystyrene foam samples under different degrees of uniaxial compression, providing a practical example of their applicability.

The development of new anti-counterfeiting solutions is a constant challenge and involves several research fields. Much interest is devoted to systems that are impossible to clone, based on the Physical Unclonable Function (PUF) paradigm. In this work, new strategies based on electrospinning and electrospraying of dye-doped polymeric materials are presented for the manufacturing of flexible free-standing films that embed different PUF keys. Films can be used to fabricate anticounterfeiting labels having three encryption levels: i) a map of fluorescent polymer droplets, with non deterministic positions on a dense yarn of polymer nanofibers; ii) a characteristic fluorescence spectrum for each label; iii) a challenge-response pairs (CRPs) identification protocol based on the strong nature of the physical unclonable function. The intrinsic uniqueness introduced by the deposition techniques encodes enough complexity into the optical anti-counterfeiting tag to generate thousands of cryptographic keys. The simple and cheap fabrication process as well as the multilevel authentication makes such colored polymeric unclonable tags a practical solution in the secure protection of merchandise in our daily life.

We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle meshes to other surface representations like point clouds, nonmanifold meshes, and polygonal meshes. To build the prolongation operators, we associate each point of the hierarchy to a triangle constructed from points in the next coarser level. We obtain well-shaped candidate triangles by computing graph Voronoi diagrams centered around the coarse points and determining neighboring Voronoi cells. Our selection of triangles ensures that the connections of each point to points at adjacent coarser and finer levels are balanced in the tangential directions. As a result, we obtain sparse prolongation matrices with three entries per row and fast convergence of the solver., Comment: Ruben Wiersma and Ahmad Nasikun contributed equally. To be published in SIGGRAPH 2023. 16 pages total (8 main, 5 supplement), 14 figures

The application of parity-time (PT) symmetry in optics, especially PT-symmetry breaking, has attracted considerable attention as a novel approach to controlling light propagation. Here, we report optical limiting by two coupled optical cavities with a PT-symmetric spectrum of reflectionless modes. The optical limiting is related to broken PT symmetry due to light-induced changes in one of the cavities. Our experimental implementation is a three-mirror resonator of alternating layers of ZnS and cryolite with a PT-symmetric spectral degeneracy of two reflectionless modes. The optical limiting is demonstrated by measurements of single 532-nm 6-ns laser pulses. At fluences below 10 mJ/cm2, the multilayer exhibits a flat-top passband at 532 nm. At higher fluences, laser heating combined with the thermo-optic effect in ZnS leads to cavity detuning and PT-symmetry breaking of the reflectionless modes. As a result, the entire multilayer structure quickly becomes highly reflective, protecting itself from laser-induced damage. The cavity detuning mechanism can differ at much higher limiting thresholds and include nonlinearity., Comment: 17 pages, 5 figures

Transport processes underpin a multitude of phenomena, ranging from the propagation of atoms on lattices, to the mobility patterns of microorganisms and earthquakes, to name a few. The dynamics of these processes is very rich and key to understanding the complex nature of the underlying physics, but the way in which we classify them is often too simplistic to fully reflect this complexity. Here, we report on the experimental observation of a breakdown of self-similar propagation for light inside a scattering medium - a transport regime exhibiting different scaling rates for each spatial moment of the associated probability distribution. Notably, we show that this phenomenon arises for light waves even in the simple case of isotropic and homogeneous disorder, and can be controlled by tuning the turbidity of the system. These results support the idea that the traditional dichotomy between normal and anomalous diffusion is reductive and that a richer framework should be constructed based on the concept of self-similarity as this class of transport regimes may be far more common that it is currently believed. In addition, this insight can help understand scenarios where transport is dominated by rare propagation events, as in non-linear and active media, or more generally in other fields of research.

The integration of renewable energy sources into power systems is expected to increase significantly in the coming decades. This can result in critical situations related to the strong variability in space and time of weather patterns. During these critical situations the power system experiences a structural shortage of energy across multiple time steps and regions, leading to Energy Not Served (ENS) events. Our research explores the relationship between six weather regimes that describe the large scale atmospheric flow and ENS events in Europe by simulating future power systems. Our results indicate that most regions have a specific weather regime that leads to the highest number of ENS events. However, ENS events can still occur during any weather regime, but with a lower probability. In particular, our findings show that ENS events in western and central European countries often coincide with either the positive Scandinavian Blocking (SB+), characterised by cold air penetrating Europe under calm weather conditions from north-eastern regions, or North Atlantic Oscillation (NAO+) weather regime, characterised by westerly flow and cold air in the southern half of Europe. Additionally, we found that the relative impact of one of these regimes reaches a peak 10 days before ENS events in these countries. In Scandinavian and Baltic countries, on the other hand, our results indicate that the relative prevalence of the negative Atlantic Ridge (AR-) weather regime is higher during and leading up to the ENS event., Comment: Rogier H. Wuijts and Laurens P. Stoop contributed equally to this work

We construct several new classes of bifunctors $(A,B)\mapsto A\otimes_{\alpha} B$, where $A\otimes_\alpha B$ is a cross norm completion of $A\odot B$ for each pair of C*-algebras $A$ and $B$. For the first class of bifunctors considered $(A,B)\mapsto A\otimes_p B$ ($1\leq p\leq\infty$), $A\otimes_p B$ is a Banach algebra cross-norm completion of $A\odot B$ constructed in a fashion similar to $p$-pseudofunctions of a locally compact group. We also consider $\otimes_{p,q}$ for H\"older conjugate $p,q\in [1,\infty]$ -- a Banach $*$-algebra analogue of the tensor product $\otimes_p$. By taking enveloping C*-algebras of $A\otimes_{p,q} B$, we arrive at a third bifunctor $(A,B)\mapsto A\otimes_{\mathrm C^*_{p,q}} B$ where the resulting algebra $A\otimes_{\mathrm C^*_{p,q}} B$ is a C*-algebra. For groups belonging to a large class of non-amenable discrete groups possessing both the rapid decay and Haagerup property, we show that the tensor products $\mathrm C^*_{\mathrm r}(G_1)\otimes_{\mathrm C^*_{p,q}}\mathrm C^*_{\mathrm r}(G_2)$ coincide with a Brown-Guentner type C*-completion of $\mathrm \ell^1(G_1\times G_2)$ and conclude that if $2\leq p'

Disordered photonic structures are promising materials for the realization of physical unclonable functions (PUF), physical objects that can overcome the limitations of conventional digital security methods and that enable cryptographic protocols immune against attacks by future quantum computers. One PUF limitation, so far, has been that their physical configuration is either fixed or can only be permanently modified, and hence allowing only one token per device. We show that it is possible to overcome this limitation by creating a reconfigurable structure made by light-transformable polymers, in which the physical structure of the unclonable function itself can be reversibly reconfigured. We term this novel concept Hyper PUF or HPUF in that it allows a large number of physical unclonable functions to co-exist simultaneously within one and the same device. The physical transformation of the structure is done all-optically in a reversible and spatially controlled fashion. Our novel technology provides a massive enhancement in security generating more complex keys containing a larger amount of information. At the same time, it allows for new applications, for example serving multiple clients on a single encryption device and the practical implementation of quantum secure authentication of data.

Due to their unmatched entropy, complexity, and security level, optical Physical Unclonable Functions (PUFs) currently receive a lot of interest in the literature. Despite the large body of existing works, however, one of their core features has never been quantified in detail, namely their physical unclonability. This paper tackles this fundamental and yet largely unaddressed issue. In simulations and/or experiments, the sensitivity of diffraction-based optical responses is investigated with respect to various small alterations such as variation in the position, size, and number of the scatterers, as well as perturbations in the spatial alignment between the physical unclonable function (PUF) and the measurement apparatus. Our analysis focuses on 2D optical PUFs because of their relevance in integrated applications and the need to reply to security concerns that can be raised when the physical structure of the geometry is accessible. Among the results of this study, the sensitivity analysis shows that a positional perturbation of scatterers on the order of \SI{30}{\nano\meter}, i.e., far below the wavelength of the probing laser light of \SI{632}{\nano\meter} wavelength, is sufficient to invalidate the PUF response and thus detect a forgery attempt. These results support and quantify the high adversarial efforts required to clone optical PUFs, even for 2D layouts., Comment: 8 pages, 7 figures and Supporting Information

We conduct a systematic study of traces on locally compact groups, in particular traces on their universal and reduced C*-algebras. We introduce the trace kernel, and examine its relation to the von Neumann kernel and to small-invariant neighbourhood (SIN) quotients. In doing so, we introduce the class of residually-$SIN$ groups, which contains both $SIN$ and maximally almost periodic groups. We examine in detail the trace kernel for connected groups. We study traces on reduced C*-algebras, giving a simple proof for compactly generated groups that existence of such a trace is equivalent to having an open normal amenable subgroup, and we display non-discrete groups admitting unique trace. We finish by examining amenable traces and the factorization property. We show for property (T) groups that amenable trace kernels coincide with von Neumann kernels. We show for totally disconnected groups that amenable trace separation implies the factorization property. We use amenable traces to give a simple proof that amenability of the group is equivalent to simultaneous nuclearity and possessing a trace of its reduced C*-algebra. As a final application of the results obtained in the paper, we address the embeddability of group C*-algebras into simple AF algebras. As a consequence, if a locally compact group is amenable and tracially separated (trace kernel is trivial), then its reduced C*-algebra is quasi-diagonal.

Deep learning has improved vanishing point detection in images. Yet, deep networks require expensive annotated datasets trained on costly hardware and do not generalize to even slightly different domains, and minor problem variants. Here, we address these issues by injecting deep vanishing point detection networks with prior knowledge. This prior knowledge no longer needs to be learned from data, saving valuable annotation efforts and compute, unlocking realistic few-sample scenarios, and reducing the impact of domain changes. Moreover, the interpretability of the priors allows to adapt deep networks to minor problem variations such as switching between Manhattan and non-Manhattan worlds. We seamlessly incorporate two geometric priors: (i) Hough Transform -- mapping image pixels to straight lines, and (ii) Gaussian sphere -- mapping lines to great circles whose intersections denote vanishing points. Experimentally, we ablate our choices and show comparable accuracy to existing models in the large-data setting. We validate our model's improved data efficiency, robustness to domain changes, adaptability to non-Manhattan settings., Comment: CVPR2022, code available at https://github.com/yanconglin/VanishingPoint_HoughTransform_GaussianSphere

We present a parallel robot mechanism and the constitutive laws that govern the deformation of its constituent soft actuators. Our ultimate goal is the real-time motion-correction of a patient's head deviation from a target pose where the soft actuators control the position of the patient's cranial region on a treatment machine. We describe the mechanism, derive the stress-strain constitutive laws for the individual actuators and the inverse kinematics that prescribes a given deformation, and then present simulation results that validate our mathematical formulation. Our results demonstrate deformations consistent with our radially symmetric displacement formulation under a finite elastic deformation framework.

Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D~data. In this paper, we aim to construct anisotropic convolution layers that work directly on the surface derived from a point cloud. This is challenging because of the lack of a global coordinate system for tangential directions on surfaces. We introduce DeltaConv, a convolution layer that combines geometric operators from vector calculus to enable the construction of anisotropic filters on point clouds. Because these operators are defined on scalar- and vector-fields, we separate the network into a scalar- and a vector-stream, which are connected by the operators. The vector stream enables the network to explicitly represent, evaluate, and process directional information. Our convolutions are robust and simple to implement and match or improve on state-of-the-art approaches on several benchmarks, while also speeding up training and inference., Comment: 8 pages, 5 figures, 7 tables; ACM Transactions on Graphics 41, 4, Article 105 (SIGGRAPH 2022)

We present gas-phase InfraRed Multiple Photon Dissociation (IRMPD) spectroscopy of cationic phenanthrene, pyrene, and perylene over the 100$-$1700 cm$^{-1}$ (6-95 $\mu$m) spectral range. This range covers both local vibrational modes involving C$-$C and C$-$H bonds in the mid-IR, and large-amplitude skeletal modes in the far-IR. The experiments were done using the 7T Fourier-Transform Ion Cyclotron Resonance (FTICR) mass spectrometer integrated in the Free-Electron Laser for Intra-Cavity Experiments (FELICE), and findings were complemented with Density Functional Theory (DFT) calculated harmonic and anharmonic spectra, matching the experimental spectra well. The experimental configuration that enables this sensitive spectroscopy of the strongly-bound, photo-resistant Polycyclic Aromatic Hydrocarbons (PAHs) over a wide range can provide such high photon densities that even combination modes with calculated intensities as low as 0.01 km$\cdot$mol$^{-1}$ near 400 cm$^{-1}$ (25 $\mu$m) can be detected. Experimental frequencies from this work and all currently available IRMPD spectra for PAH cations were compared to theoretical frequencies from the NASA Ames PAH IR Spectroscopic Database to verify predicted trends for far-IR vibrational modes depending on PAH shape and size, and only a relatively small redshift (6$-$11 cm$^{-1}$) was found between experiment and theory. The absence of spectral congestion and the drastic reduction in bandwidth with respect to the mid-IR make the far-IR fingerprints viable candidates for theoretical benchmarking, which can aid in the search for individual large PAHs in the interstellar medium., Comment: to be submitted to the Monthly Notices of the Royal Astronomical Society

We present the experimental InfraRed Multiple Photon Dissociation (IRMPD) spectrum and fragmentation mass spectrum of the irregular, cationic PAH dibenzo[a,l]pyrene (C$_{24}$H$_{14}^+$) in the 6-40 $\mu$m / 250-1650 cm$^{-1}$ range. The use of the the Free-Electron Laser for IntraCavity Experiments (FELICE) enabled us to record its Far-InfraRed (FIR) spectrum for the first time. We aim to understand how irregularity affects the infrared spectrum and fragmentation chemistry of PAHs. Dibenzo[a,l]pyrene is an asymmetric, non-planar molecule, for which all vibrational modes are in principle IR-active. Calculated harmonic Density Function Theory (DFT) and anharmonic Density Functional based Tight Binding Molecular Dynamics (DFTB-MD) spectra show a large wealth of bands, which match the experiment well, but with a few differences. The periphery of the molecule contains several edge geometries, but out of all possible modes in the 11-14 $\mu$m out-of-plane C-H bending region, only one band at 13.5 $\mu$m is prominent. This fact and the richness of the C-C stretching range make irregular PAHs a possible contributor to D-class interstellar spectra. The fragmentation mass spectra reveal facile 2H-loss and no [2C, 2H]-loss, which is attributed to the sterically hindered, non-planar cove region, which could protect irregular PAHs from radiation damage., Comment: Accepted for publication in The Journal of Molecular Spectroscopy

Purpose: Deformable Image Registration (DIR) can benefit from additional guidance using corresponding landmarks in the images. However, the benefits thereof are largely understudied, especially due to the lack of automatic landmark detection methods for three-dimensional (3D) medical images. Approach: We present a Deep Convolutional Neural Network (DCNN), called DCNN-Match, that learns to predict landmark correspondences in 3D images in a self-supervised manner. We trained DCNN-Match on pairs of Computed Tomography (CT) scans containing simulated deformations. We explored five variants of DCNN-Match that use different loss functions and assessed their effect on the spatial density of predicted landmarks and the associated matching errors. We also tested DCNN-Match variants in combination with the open-source registration software Elastix to assess the impact of predicted landmarks in providing additional guidance to DIR. Results: We tested our approach on lower-abdominal CT scans from cervical cancer patients: 121 pairs containing simulated deformations and 11 pairs demonstrating clinical deformations. The results showed significant improvement in DIR performance when landmark correspondences predicted by DCNN-Match were used in the case of simulated (p = $0e^0$) as well as clinical deformations (p = 0.030). We also observed that the spatial density of the automatic landmarks with respect to the underlying deformation affect the extent of improvement in DIR. Finally, DCNN-Match was found to generalize to Magnetic Resonance Imaging (MRI) scans without requiring retraining, indicating easy applicability to other datasets. Conclusions: DCNN-Match learns to predict landmark correspondences in 3D medical images in a self-supervised manner, which can improve DIR performance., Comment: accepted paper in the Journal of Medical Imaging