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This study leverages convolutional neural networks to enhance the temporal resolution of 3D angiography in intracranial aneurysms focusing on the reconstruction of volumetric contrast data from sparse and limited projections. Three patient-specific IA geometries were segmented and converted into stereolithography files to facilitate computational fluid dynamics simulations. These simulations first modeled blood flow under steady conditions with varying inlet velocities: 0.25 m/s, 0.35 m/s, and 0.45 m/s. Subsequently, 3D angiograms were simulated by labeling inlet particles to represent contrast bolus injections over durations of 0.5s, 1.0s, 1.5s, and 2.0s. The angiographic simulations were then used within a simulated cone beam C arm CT system to generate in-silico rotational DSAs, capturing projections every 10 ms over a 220-degree arc at 27 frames per second. From these simulations, both fully sampled (108 projections) and truncated projection datasets were generated the latter using a maximum of 49 projections. High fidelity volumetric images were reconstructed using a Parker weighted Feldkamp Davis Kress algorithm. A modified U Net CNN was subsequently trained on these datasets to reconstruct 3D angiographic volumes from the truncated projections. The network incorporated multiple convolutional layers with ReLU activations and Max pooling, complemented by upsampling and concatenation to preserve spatial detail. Model performance was evaluated using mean squared error (MSE). Evaluating our U net model across the test set yielded a MSE of 0.0001, indicating good agreement with ground truth reconstructions and demonstrating acceptable capabilities in capturing relevant transient angiographic features. This study confirms the feasibility of using CNNs for reconstructing 3D angiographic images from truncated projections.

This study aims to mitigate these biases and enhance QA analysis by applying a path-length correction (PLC) correction, followed by singular value decomposition (SVD)-based deconvolution, to angiograms obtained through both in-silico and in-vitro methods. We utilized DSA data from in-silico and in-vitro patient-specific intracranial aneurysm models. To remove projection bias, PLC for various views were developed by co-registering the pre-existing 3D vascular geometry mask with the DSA projections, followed by ray tracing to determine paths across 3D vessel structures. These maps were used to normalize the logarithmic angiographic images, correcting for projection-induced foreshortening across different angles. Subsequently, we focused on eliminating injection bias by analyzing the corrected angiograms under varied projection views, injection rates, and flow conditions. Regions of interest at the aneurysm dome and inlet were placed to extract Time Density Curves for the lesion and the arterial input function, respectively. Using three standard SVD methodologies, we extracted the aneurysm Impulse Response function (IRF) and its associated parameters Peak Height (PHIRF), Area Under the Curve (AUCIRF), and Mean Transit Time (MTT). Our methodology employing PLC and SVD-based deconvolution ensures reliable quantitative angiographic measurements across varying conditions, supporting consistent assessments of disease severity and treatment efficacy. This approach significantly enhances intrapatient and intraprocedural reliability in neurovascular diagnostics., Comment: 11 pages, 6figures

In Angiographic Parametric Imaging (API), accurate estimation of parameters from Time Density Curves (TDC) is crucial. However, these estimations are often marred by errors arising from factors such as patient motion, procedural preferences, image noise, and injection variability. While fitting methods like gamma-variate fitting offer a solution to recover incomplete or corrupted TDC data, they might also introduce unforeseen biases. This study investigates the trade-offs and benefits of employing gamma-variate fitting on virtual angiograms to enhance the precision of API biomarkers. Utilizing Computational Fluid Dynamics (CFD) in patient specific 3D geometries, we generated a series of high-definition virtual angiograms at distinct inlet velocities: 0.25m/s, 0.35m/s, and 0.45m/s. These velocities were investigated across injection durations ranging from 0.5s to 2.0s. From these angiograms, TDCs for aneurysms and their corresponding inlets were constructed. To emulate typical clinical challenges, we introduced noise, simulated patient motion, and generated temporally incomplete data sets. These modified TDCs underwent gamma-variate fitting. We quantified both the original and fitted TDC curves using standard angiography metrics such as Cross-Correlation (Cor), Time to Peak (TTP), Mean Transit Time (MTT), Peak Height (PH), Area Under the Curve (AUC), and Maximum Gradient (Max-Gr) for a comprehensive comparison. TDCs enhanced by gamma-variate fitting exhibited a robust correlation with vascular flow dynamics. Our results affirm that gamma-variate fitting can adeptly restore TDCs from fragmentary sequences, elevating the precision of derived API parameters.

During intracranial aneurysm (IA) treatment with Diverters (FDs), the device/parent artery diameters ratio may influence the ability of the device to induce aneurysm healing response. Oversized FDs are safer to deploy but may not induce enough hemodynamic resistance to ensure aneurysm occlusion. Methods based on Computational Fluid Dynamics (CFD) could allow optimal device selection but are time-consuming and inadequate for intra-operative guidance. To address this limitation, we propose to investigate a method for optimal FD selection using Angiographic Parametric Imaging (API) and machine learning (ML). We selected 128 pre-treatment angiographic sequences of IAs which demonstrated full occlusion at six months follow-up. For each IA, we extracted five API parameters from the aneurysm dome and normalized them to the feeding artery corresponding parameters. We dichotomized the dataset based on the FD/ proximal artery diameter ratio as undersized, if the ratio<1 or if multiple FDs were used and oversized otherwise. Single API parameter and ML analysis were used to determine whether API parameters could be used to determine the need for FD under-sizing (i.e., increased flow resistance). Classification accuracy was assessed using area under the receiver operator characteristic (AUROC). In total we identified 51 and 77 cases for the undersized and oversized cohorts respectively. Single API parameter analysis yielded an inadequate AUROC ~0.5 while machine learning using all five API parameters yielded and AUROC of 0.72.

Intraoperative 2D quantitative angiography (QA) for intracranial aneurysms (IAs) has accuracy challenges due to the variability of hand injections. Despite the success of singular value decomposition (SVD) algorithms in reducing biases in computed tomography perfusion (CTP), their application in 2D QA has not been extensively explored. This study seeks to bridge this gap by investigating the potential of SVD-based deconvolution methods in 2D QA, particularly in addressing the variability of injection durations. The study included three internal carotid aneurysm (ICA) cases. Virtual angiograms were generated using Computational Fluid Dynamics (CFD) for three physiologically relevant inlet velocities to simulate contrast media injection durations. Time-density curves (TDCs) were produced for both the inlet and aneurysm dome. Various SVD variants, including standard SVD (sSVD) with and without classical Tikhonov regularization, block-circulant SVD (bSVD), and oscillation index SVD (oSVD), were applied to virtual angiograms. The method was applied on virtual angiograms to recover the aneurysmal dome impulse response function (IRF) and extract flow related parameters such as Peak Height PHIRF, Area Under the Curve AUCIRF, and Mean transit time MTT. Furthermore, we found that SVD can effectively reduce QA parameter variability across various injection durations, enhancing the potential of QA analysis parameters in neurovascular disease diagnosis and treatment. Implementing SVD-based deconvolution techniques in QA analysis can enhance the precision and reliability of neurovascular diagnostics by effectively reducing the impact of injection duration on hemodynamic parameters.

The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying parameters. In this article, we investigate these concepts for the case where the parameters lie on a homogeneous space. Unlike the existing Fisher-Rao theory for general Riemannian manifolds, our focus is to leverage the group-theoretic structure of homogeneous spaces, which is often much easier to work with than their Riemannian structure. The FIM is characterized by identifying the homogeneous space with a coset space, the group-theoretic CRB and its corollaries are presented, and its relationship to the Riemannian CRB is clarified. The application of our theory is illustrated using two examples from engineering: (i) estimation of the pose of a robot and (ii) sensor network localization. In particular, these examples demonstrate that homogeneous spaces provide a natural framework for studying statistical models that are invariant with respect to a group of symmetries., Comment: Supplementary document is available

It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these measures are possible. In particular, (1) We employ the cheatsheet framework to obtain an unbounded parallel quantum query advantage over its randomized analogue for a total function, falsifying a conjecture of Jeffery et al. 2017 (arXiv:1309.6116). (2) We strengthen (1) by constructing a total function which exhibits an unbounded parallel quantum query advantage despite having no sequential advantage, suggesting that genuine quantum advantage could occur entirely due to parallelism. (3) We construct a total function that exhibits a polynomial separation between 2-round quantum and randomized query complexities, contrasting a result of Montanaro in 2010 (arXiv:1001.0018) that there is at most a constant separation for 1-round (nonadaptive) algorithms. (4) We develop a new technique for deriving parallel quantum lower bounds from sequential upper bounds. We employ this technique to give lower bounds for Boolean symmetric functions and read-once formulas, ruling out large parallel query advantages for them. We also provide separations between randomized and deterministic parallel query complexities analogous to items (1)-(3).

Charged Black holes in $AdS_5 \times S^5$ suffer from superradiant instabilities over a range of energies. Hairy black hole solutions (constructed within gauged supergravity) have previously been proposed as endpoints to this instability. We demonstrate that these hairy black holes are themselves unstable to the emission of large dual giant gravitons. We propose that the endpoint to this instability is given by Dual Dressed Black Holes (DDBH)s; configurations consisting of one, two, or three very large dual giant gravitons surrounding a core $AdS$ black hole with one, two, or three $SO(6)$ chemical potentials equal to unity. The dual giants each live at $AdS$ radial coordinates of order $\sqrt{N}$ and each carry charge of order $N^2$. The large separation makes DDBHs a very weakly interacting mix of their components and allows for a simple computation of their thermodynamics. We conjecture that DDBHs dominate the phase diagram of ${\cal N}=4$ Yang-Mills over a range of energies around the BPS plane, and provide an explicit construction of this phase diagram, briefly discussing the interplay with supersymmetry. We develop the quantum description of dual giants around black hole backgrounds and explicitly verify that DDBHs are stable to potential tunneling instabilities, precisely when the chemical potentials of the core black holes equal unity. We also construct the 10-dimensional DDBH supergravity solutions., Comment: 114 pages, 12 figures

Cloth state estimation is an important problem in robotics. It is essential for the robot to know the accurate state to manipulate cloth and execute tasks such as robotic dressing, stitching, and covering/uncovering human beings. However, estimating cloth state accurately remains challenging due to its high flexibility and self-occlusion. This paper proposes a diffusion model-based pipeline that formulates the cloth state estimation as an image generation problem by representing the cloth state as an RGB image that describes the point-wise translation (translation map) between a pre-defined flattened mesh and the deformed mesh in a canonical space. Then we train a conditional diffusion-based image generation model to predict the translation map based on an observation. Experiments are conducted in both simulation and the real world to validate the performance of our method. Results indicate that our method outperforms two recent methods in both accuracy and speed.

We consider the path integral of a quantum field theory in Minkowski spacetime with fixed boundary values (for the elementary fields) on asymptotic boundaries. We define and study the corresponding boundary correlation functions obtained by taking derivatives of this path integral with respect to the boundary values. The S-matrix of the QFT can be extracted directly from these boundary correlation functions after smearing. We interpret this relation in terms of coherent state quantization and derive the constraints on the path-integral as a function of boundary values that follow from the unitarity of the S-matrix. We then study the locality structure of boundary correlation functions. In the massive case, we find that the boundary correlation functions for generic locations of boundary points are dominated by a saddle point which has the interpretation of particles scattering in a small elevator in the bulk, where the location of the elevator is determined dynamically, and the S-matrix can be recovered after stripping off some dynamically determined but non-local ``renormalization'' factors. In the massless case, we find that while the boundary correlation functions are generically analytic as a function on the whole manifold of locations of boundary points, they have special singularities on a sub-manifold, points on which correspond to light-like scattering in the bulk. We completely characterize this singular scattering sub-manifold, and find that the corresponding residues of the boundary correlations at these singularities are precisely given by S-matrices. This analysis parallels the analysis of bulk-point singularities in AdS/CFT and generalizes it to the case of multi-bulk point singularities.

The conventional solutions for fault-detection, identification, and reconstruction (FDIR) require centralized decision-making mechanisms which are typically combinatorial in their nature, necessitating the design of an efficient distributed FDIR mechanism that is suitable for multi-agent applications. To this end, we develop a general framework for efficiently reconstructing a sparse vector being observed over a sensor network via nonlinear measurements. The proposed framework is used to design a distributed multi-agent FDIR algorithm based on a combination of the sequential convex programming (SCP) and the alternating direction method of multipliers (ADMM) optimization approaches. The proposed distributed FDIR algorithm can process a variety of inter-agent measurements (including distances, bearings, relative velocities, and subtended angles between agents) to identify the faulty agents and recover their true states. The effectiveness of the proposed distributed multi-agent FDIR approach is demonstrated by considering a numerical example in which the inter-agent distances are used to identify the faulty agents in a multi-agent configuration, as well as reconstruct their error vectors.

Wireless Sensor Network (WSN) localization refers to the problem of determining the position of each of the agents in a WSN using noisy measurement information. In many cases, such as in distance and bearing-based localization, the measurement model is a nonlinear function of the agents' positions, leading to pairwise interconnections between the agents. As the optimal solution for the WSN localization problem is known to be computationally expensive in these cases, an efficient approximation is desired. In this paper, we show that the inherent sparsity in this problem can be exploited to greatly reduce the computational effort of using an Extended Kalman Filter (EKF) for large-scale WSN localization. In the proposed method, which we call the Low-Bandwidth Extended Kalman Filter (LB-EKF), the measurement information matrix is converted into a banded matrix by relabeling (permuting the order of) the vertices of the graph. Using a combination of theoretical analysis and numerical simulations, it is shown that typical WSN configurations (which can be modeled as random geometric graphs) can be localized in a scalable manner using the proposed LB-EKF approach.

The Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been studied extensively in the literature. However, the challenges involved in implementing the GM-PHD filter efficiently in a distributed (multi-sensor) setting have received little attention. The existing solutions for distributed PHD filtering either have a high computational and communication cost, making them infeasible for resource-constrained applications, or are unable to guarantee the asymptotic convergence of the distributed PHD algorithm to an optimal solution. In this paper, we develop a distributed GM-PHD filtering recursion that uses a probabilistic communication rule to limit the communication bandwidth of the algorithm, while ensuring asymptotic optimality of the algorithm. We derive the convergence properties of this recursion, which uses weighted average consensus of Gaussian mixtures (GMs) to lower (and asymptotically minimize) the Cauchy-Schwarz divergence between the sensors' local estimates. In addition, the proposed method is able to avoid the issue of false positives, which has previously been noted to impact the filtering performance of distributed multi-target tracking. Through numerical simulations, it is demonstrated that our proposed method is an effective solution for distributed multi-target tracking in resource-constrained sensor networks.

A practical challenge which arises in the operation of sensor networks is the presence of sensor faults, biases, or adversarial attacks, which can lead to significant errors incurring in the localization of the agents, thereby undermining the security and performance of the network. We consider the problem of identifying and correcting the localization errors using inter-agent measurements, such as the distances or bearings from one agent to another, which can serve as a redundant source of information about the sensor network's configuration. The problem is solved by searching for a block sparse solution to an underdetermined system of equations, where the sparsity is introduced via the fact that the number of localization errors is typically much lesser than the total number of agents. Unlike the existing works, our proposed method does not require the knowledge of the identities of the anchors, i.e., the agents that do not have localization errors. We characterize the necessary and sufficient conditions on the sensor network configuration under which a given number of localization errors can be uniquely identified and corrected using the proposed method. The applicability of our results is demonstrated numerically by processing inter-agent distance measurements using a sequential convex programming (SCP) algorithm to identify the localization errors in a sensor network.

Most of the computational evidence for the Bose$\small-$Fermi duality of fundamental fields coupled to $U(N)$ Chern$\small-$Simons theories originates in large-$N$ calculations performed in the light-cone gauge. This gauge is ill-suited to computations in curved spacetimes, like the evaluation of the partition function on $\Sigma_g\times S^1$ for arbitrary genus $g$. In this paper, we use another gauge, the 'temporal' gauge, to set up the computation of this partition function. In the large-$N$ limit, and the special case $\Sigma_g=\mathbb{R}^2$, we take the computation through to the end by setting up and solving the gap equations, generalizing tricks explored in arXiv:1410.0558 to finite temperature. Our final results are in perfect agreement with earlier light-cone gauge results, providing a consistency check of both the formalism developed in this paper as well as previously performed light-cone gauge computations. In a follow-up paper, we will report on using our formalism to explicitly compute the partition function on $S^2 \times S^1$ for a finite-sized sphere., Comment: 77 pages

Kerr-AdS$_{d+1}$ black holes for $d\geq 3$ suffer from classical superradiant instabilities over a range of masses above extremality. We conjecture that these instabilities settle down into Grey Galaxies (GGs) - a new class of coarse-grained solutions to Einstein's equations which we construct in $d=3$. Grey Galaxies are made up of a black hole with critical angular velocity $\omega=1$ in the `centre' of $AdS$, surrounded by a large flat disk of thermal bulk gas that revolves around the centre of $AdS$ at the speed of light. The gas carries a finite fraction of the total energy, as its parametrically low energy density and large radius are inversely related. GGs exist at masses that extend all the way down to the unitarity bound. Their thermodynamics is that of a weakly interacting mix of Kerr-AdS black holes and the bulk gas. Their boundary stress tensor is the sum of a smooth `black hole' contribution and a peaked gas contribution that is delta function localized around the equator of the boundary sphere in the large $N$ limit. We also construct another class of solutions with the same charges; `Revolving Black Holes (RBHs)'. RBHs are macroscopically charged $SO(d,2)$ descendants of AdS-Kerr solutions, and consist of $\omega=1$ black holes revolving around the centre of $AdS$ at a fixed radial location but in a quantum wave function in the angular directions. RBH solutions are marginally entropically subdominant to GG solutions and do not constitute the endpoint of the superradiant instability. Nonetheless, we argue that supersymmetric versions of these solutions have interesting implications for the spectrum of supersymmetric states in, e.g. ${\cal N}=4$ Yang-Mills theory., Comment: 110 pages, 7 figures, 41 pages Appendix