Search

A major challenge for the realisation of useful universal quantum computers is achieving high fidelity two-qubit entangling gate operations. However, calibration errors can affect the quantum gate operations and limit their fidelity. To reduce such errors it is desirable to have an analytical understanding and quantitative predictions of the effects that miscalibrations of gate parameters have on the gate performance. In this work, we study a systematic perturbative expansion in miscalibrated parameters of the Molmer-Sorensen entangling gate, which is widely used in trapped ion quantum processors. Our analytical treatment particularly focuses on systematic center line detuning miscalibrations. Via a unitary Magnus expansion, we compute the gate evolution operator which allows us to obtain relevant key properties such as relative phases, electronic populations, quantum state purity and fidelities. These quantities, subsequently, are used to assess the performance of the gate using the fidelity of entangled states as performance metric. We verify the predictions from our model by benchmarking them against measurements in a trapped-ion quantum processor. The method and the results presented here can help design and calibrate high-fidelity gate operations of large-scale quantum computers., Comment: 17 pages, 13 figures

The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multi-dimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used Molmer-Sorensen entangling gate operation in a trapped ion quantum information processor. The protocol exploits Bayesian parameter estimation methods which includes a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a median gate infidelity of $1.3(1)\cdot10^{-3}$, requiring only $1200\pm500$ experimental cycles, while completing the entire gate calibration procedure in less than one minute. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models., Comment: 20 pages, 11 figures; Fixed typo in abstract

Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a family of functors $\mathcal{D}_p$, $1\leq p \leq\infty$, that assign, to each metric pair $(X,A)$, a pointed metric space $\mathcal{D}_p(X,A)$. Moreover, we show that $\mathcal{D}_{\infty}$ is sequentially continuous with respect to the Gromov-Hausdorff convergence of metric pairs, and we prove that $\mathcal{D}_p$ preserves several useful metric properties, such as completeness and separability, for $p \in [1,\infty)$, and geodesicity and non-negative curvature in the sense of Alexandrov, for $p=2$. For the latter case, we describe the metric of the space of directions at the empty diagram. We also show that the Fr\'echet mean set of a Borel probability measure on $\mathcal{D}_p(X,A)$, $1\leq p \leq\infty$, with finite second moment and compact support is non-empty. As an application of our geometric framework, we prove that the space of Euclidean persistence diagrams, $\mathcal{D}_{p}(\mathbb{R}^{2n},\Delta_n)$, $1\leq n$ and $1\leq p<\infty$, has infinite covering, Hausdorff, asymptotic, Assouad, and Assouad-Nagata dimensions., Comment: Final version. To appear in the Journal of Applied and Computational Topology. 39 pages

In this paper, we study certain inequalities and a related result for weighted Sobolev spaces on H\"older-$\alpha$ domains, where the weights are powers of the distance to the boundary. We obtain results regarding the divergence equation's solvability, and the improved Poincar\'e, the fractional Poincar\'e, and the Korn inequalities. The proofs are based on a local-to-global argument that involves a kind of atomic decomposition of functions and the validity of a weighted discrete Hardy-type inequality on trees. The novelty of our approach lies in the use of this weighted discrete Hardy inequality and a sufficient condition that allows us to study the weights of our interest. As a consequence, the assumptions on the weight exponents that appear in our results are weaker than those in the literature., Comment: 34 pages, and 3 figures

Kurdyka-{\L}ojasiewicz (K{\L}) functions are real-valued functions characterized by a differential inequality involving the norm of their gradient. This class of functions is quite rich, containing objects as diverse as subanalytic, transnormal or Morse functions. We prove that the zero locus of a Kurdyka-{\L}ojasiewicz function admits a mapping cylinder neighborhood. This implies, in particular, that wildly embedded topological 2-manifolds in 3-dimensional Euclidean space, such as Alexander horned spheres, do not arise as the zero loci of K{\L} functions., Comment: 27 pages, to appear in Annales de l`Institut Fourier

Detailed analysis of seizure semiology, the symptoms and signs which occur during a seizure, is critical for management of epilepsy patients. Inter-rater reliability using qualitative visual analysis is often poor for semiological features. Therefore, automatic and quantitative analysis of video-recorded seizures is needed for objective assessment. We present GESTURES, a novel architecture combining convolutional neural networks (CNNs) and recurrent neural networks (RNNs) to learn deep representations of arbitrarily long videos of epileptic seizures. We use a spatiotemporal CNN (STCNN) pre-trained on large human action recognition (HAR) datasets to extract features from short snippets (approx. 0.5 s) sampled from seizure videos. We then train an RNN to learn seizure-level representations from the sequence of features. We curated a dataset of seizure videos from 68 patients and evaluated GESTURES on its ability to classify seizures into focal onset seizures (FOSs) (N = 106) vs. focal to bilateral tonic-clonic seizures (TCSs) (N = 77), obtaining an accuracy of 98.9% using bidirectional long short-term memory (BLSTM) units. We demonstrate that an STCNN trained on a HAR dataset can be used in combination with an RNN to accurately represent arbitrarily long videos of seizures. GESTURES can provide accurate seizure classification by modeling sequences of semiologies., Comment: Accepted at the 24th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI 2021)

In this paper, we provide a notion of $\infty$-bicategories fibred in $\infty$-bicategories which we call 2-Cartesian fibrations. Our definition is formulated using the language of marked biscaled simplicial sets: Those are scaled simplicial sets equipped with an additional collection of triangles containing the scaled 2-simplices, which we call lean triangles, in addition to a collection of edges containing all degenerate 1-simplices. We prove the existence of a left proper combinatorial simplicial model category whose fibrant objects are precisely the 2-Cartesian fibrations over a chosen scaled simplicial set $S$. Over the terminal scaled simplicial set, this provides a new model structure modeling $\infty$-bicategories, which we show is Quillen equivalent to Lurie's scaled simplicial set model. We conclude by providing a characterization of 2-Cartesian fibrations over an $\infty$-bicategory. This characterization then allows us to identify those 2-Cartesian fibrations arising as the coherent nerve of a fibration of $\operatorname{Set}^+_{\Delta}$-enriched categories, thus showing that our definition recovers the preexisting notions of fibred 2-categories., Comment: Comments welcome!

Accurate segmentation of brain resection cavities (RCs) aids in postoperative analysis and determining follow-up treatment. Convolutional neural networks (CNNs) are the state-of-the-art image segmentation technique, but require large annotated datasets for training. Annotation of 3D medical images is time-consuming, requires highly-trained raters, and may suffer from high inter-rater variability. Self-supervised learning strategies can leverage unlabeled data for training. We developed an algorithm to simulate resections from preoperative magnetic resonance images (MRIs). We performed self-supervised training of a 3D CNN for RC segmentation using our simulation method. We curated EPISURG, a dataset comprising 430 postoperative and 268 preoperative MRIs from 430 refractory epilepsy patients who underwent resective neurosurgery. We fine-tuned our model on three small annotated datasets from different institutions and on the annotated images in EPISURG, comprising 20, 33, 19 and 133 subjects. The model trained on data with simulated resections obtained median (interquartile range) Dice score coefficients (DSCs) of 81.7 (16.4), 82.4 (36.4), 74.9 (24.2) and 80.5 (18.7) for each of the four datasets. After fine-tuning, DSCs were 89.2 (13.3), 84.1 (19.8), 80.2 (20.1) and 85.2 (10.8). For comparison, inter-rater agreement between human annotators from our previous study was 84.0 (9.9). We present a self-supervised learning strategy for 3D CNNs using simulated RCs to accurately segment real RCs on postoperative MRI. Our method generalizes well to data from different institutions, pathologies and modalities. Source code, segmentation models and the EPISURG dataset are available at https://github.com/fepegar/ressegijcars ., Comment: To be published in the International Journal of Computer Assisted Radiology and Surgery (IJCARS) - Special issue MICCAI 2020

The performance of object detection methods based on LiDAR information is heavily impacted by the availability of training data, usually limited to certain laser devices. As a result, the use of synthetic data is becoming popular when training neural network models, as both sensor specifications and driving scenarios can be generated ad-hoc. However, bridging the gap between virtual and real environments is still an open challenge, as current simulators cannot completely mimic real LiDAR operation. To tackle this issue, domain adaptation strategies are usually applied, obtaining remarkable results on vehicle detection when applied to range view (RV) and bird's eye view (BEV) projections while failing for smaller road agents. In this paper, we present a BEV domain adaptation method based on CycleGAN that uses prior semantic classification in order to preserve the information of small objects of interest during the domain adaptation process. The quality of the generated BEVs has been evaluated using a state-of-the-art 3D object detection framework at KITTI 3D Object Detection Benchmark. The obtained results show the advantages of the proposed method over the existing alternatives., Comment: Submitted to IEEE International Conference on Intelligent Transportation Systems (ITSC2021)

In pulsed Doppler radars, the classic Chinese remainder theorem (CCRT) is a common method to resolve Doppler ambiguities caused by fast-moving targets. Another issue concerning high-velocity targets is related to the loss in the signal-to-noise ratio (SNR) after performing range compression. In particular, this loss can be partially mitigated by the use of subpulse processing (SP). Modern radars combine these techniques in order to reliably unfold the target velocity. However, the presence of background noise may compromise the Doppler estimates. Hence, a rigorous statistical analysis is imperative. In this work, we provide a comprehensive analysis on Doppler estimation. In particular, we derive novel closed-form expressions for the probability of detection (PD) and probability of false alarm (PFA). To this end, we consider the newly introduce SP along with the CCRT. A comparison analysis between SP and the classic pulse processing (PP) technique is also carried out. Numerical results and Monte-Carlo simulations corroborate the validity of our expressions and show that the SP-plus-CCRT technique helps to greatly reduce the PFA compared to previous studies, thereby improving radar detection., Comment: 11 pages, 17 figures

This paper addresses the standard generalized likelihood ratio test (GLRT) detection problem of weak signals in background noise. In so doing, we consider a nonfluctuating target embedded in complex white Gaussian noise (CWGN), in which the amplitude of the target echo and the noise power are assumed to be unknown. Important works have analyzed the performance for the referred scenario and proposed GLRT-based detectors. Such detectors are projected at an early stage (i.e., prior to the formation of a post-beamforming scalar waveform), thereby imposing high demands on hardware, processing, and data storage. From a hardware perspective, most radar systems fail to meet these strong requirements. In fact, due to hardware and computational constraints, most radars use a combination of analog and digital beamformers (sums) before any estimation or further pre-processing. The rationale behind this study is to derive a GLRT detector that meets the hardware and system requirements. In this work, we design and analyze a more practical and easy-to-implement GLRT detector, which is projected after the analog beamforming. The performance of the proposed detector is analyzed and the probabilities of detection (PD) and false alarm (PFA) are derived in closed form. Moreover, we show that in the low signal-to-noise ratio (SNR) regime, the post-beamforming GLRT detector performs better than both the classic pre-beamforming GLRT detector and the square-law detector. This finding suggests that if the signals are weak, instead of processing the signals separately, we first must to reinforce the overall signal and then assembling the system's detection statistic. At last, the SNR losses are quantified, in which the superiority of the post-beamforming GLRT detector was evidenced as the number of antennas and samples increase., Comment: 13 pages, 12 figures, 1 table

Most sensor setups for onboard autonomous perception are composed of LiDARs and vision systems, as they provide complementary information that improves the reliability of the different algorithms necessary to obtain a robust scene understanding. However, the effective use of information from different sources requires an accurate calibration between the sensors involved, which usually implies a tedious and burdensome process. We present a method to calibrate the extrinsic parameters of any pair of sensors involving LiDARs, monocular or stereo cameras, of the same or different modalities. The procedure is composed of two stages: first, reference points belonging to a custom calibration target are extracted from the data provided by the sensors to be calibrated, and second, the optimal rigid transformation is found through the registration of both point sets. The proposed approach can handle devices with very different resolutions and poses, as usually found in vehicle setups. In order to assess the performance of the proposed method, a novel evaluation suite built on top of a popular simulation framework is introduced. Experiments on the synthetic environment show that our calibration algorithm significantly outperforms existing methods, whereas real data tests corroborate the results obtained in the evaluation suite. Open-source code is available at https://github.com/beltransen/velo2cam_calibration, Comment: Published on IEEE Transactions on Intelligent Transportation Systems

Using graphs to model irregular information domains is an effective approach to deal with some of the intricacies of contemporary (network) data. A key aspect is how the data, represented as graph signals, depend on the topology of the graph. Widely-used approaches assume that the observed signals can be viewed as outputs of graph filters (i.e., polynomials of a matrix representation of the graph) whose inputs have a particular structure. Diffused graph signals, which correspond to an originally sparse (node-localized) signal percolated through the graph via filtering, fall into this class. In that context, this paper deals with the problem of jointly identifying graph filters and separating their (sparse) input signals from a mixture of diffused graph signals, thus generalizing to the graph signal processing framework the classical blind demixing (blind source separation) of temporal and spatial signals. We first consider the scenario where the supporting graphs are different across the signals, providing a theorem for demixing feasibility along with probabilistic bounds on successful recovery. Additionally, an analysis of the degenerate problem of demixing with a single graph is also presented. Numerical experiments with synthetic and real-world graphs empirically illustrating the main theoretical findings close the paper., Comment: 13 pages, 3 figures, journal article submitted to TSP

In this paper, we derive a highly accurate approximation for the probability of detection (PD) of a non-coherent detector operating with Weibull fluctuation targets. To do so, we assume a pulse-to-pulse decorrelation during the coherent processing interval (CPI). Specifically, the proposed approximation is given in terms of: i) a closed-form expression derived in terms of the Fox's H-function, for which we also provide a portable and efficient MATHEMATICA routine; and ii) a fast converging series obtained through a comprehensive calculus of residues. Both solutions are fast and provide very accurate results. In particular, our series representation, besides being a more tractable solution, also exhibits impressive savings in computational load and computation time compared to previous studies. Numerical results and Monte-Carlo simulations corroborated the validity of our expressions., Comment: 10 pages, 12 figures. To appear in IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature., Comment: Final version. To appear in the Bulletin of the London Mathematical Society

Given an $\infty$-bicategory $\mathbb{D}$ with underlying $\infty$-category $\mathcal{D}$, we construct a Cartesian fibration $\operatorname{Tw}(\mathbb{D})\to \mathcal{D} \times \mathcal{D}^{\operatorname{op}}$, which we call the enhanced twisted arrow $\infty$-category, classifying the restricted mapping category functor $\operatorname{Map}_{\mathbb{D}}:\mathcal{D}^{\operatorname{op}}\times \mathcal{D} \to \mathbb{D}^{\operatorname{op}} \times \mathbb{D} \to \operatorname{Cat}_{\infty}$. With the aid of this new construction, we provide a description of the $\infty$-category of natural transformations $\operatorname{Nat}(F,G)$ as an end for any functors $F$ and $G$ from an $\infty$-category to an $\infty$-bicategory. As an application of our results, we demonstrate that the definition of weighted colimits presented in arXiv:1501.02161 satisfies the expected 2-dimensional universal property., Comment: 35 pages

Under mild topological restrictions, this article establishes that a smooth, closed, simply connected manifold of dimension at most seven which can be decomposed as the union of two disk bundles must be rationally elliptic. In dimension five, such manifolds are classified up to diffeomorphism, while the same is true in dimension six when either the second Betti number vanishes or the third Betti number is non-trivial., Comment: 38 pages, final version. To appear in the Indiana University Journal of Mathematics

In this paper, a multi-modal 360$^{\circ}$ framework for 3D object detection and tracking for autonomous vehicles is presented. The process is divided into four main stages. First, images are fed into a CNN network to obtain instance segmentation of the surrounding road participants. Second, LiDAR-to-image association is performed for the estimated mask proposals. Then, the isolated points of every object are processed by a PointNet ensemble to compute their corresponding 3D bounding boxes and poses. Lastly, a tracking stage based on Unscented Kalman Filter is used to track the agents along time. The solution, based on a novel sensor fusion configuration, provides accurate and reliable road environment detection. A wide variety of tests of the system, deployed in an autonomous vehicle, have successfully assessed the suitability of the proposed perception stack in a real autonomous driving application., Comment: Accepted for publication in IEEE ITSC 2020

Resective surgery may be curative for drug-resistant focal epilepsy, but only 40% to 70% of patients achieve seizure freedom after surgery. Retrospective quantitative analysis could elucidate patterns in resected structures and patient outcomes to improve resective surgery. However, the resection cavity must first be segmented on the postoperative MR image. Convolutional neural networks (CNNs) are the state-of-the-art image segmentation technique, but require large amounts of annotated data for training. Annotation of medical images is a time-consuming process requiring highly-trained raters, and often suffering from high inter-rater variability. Self-supervised learning can be used to generate training instances from unlabeled data. We developed an algorithm to simulate resections on preoperative MR images. We curated a new dataset, EPISURG, comprising 431 postoperative and 269 preoperative MR images from 431 patients who underwent resective surgery. In addition to EPISURG, we used three public datasets comprising 1813 preoperative MR images for training. We trained a 3D CNN on artificially resected images created on the fly during training, using images from 1) EPISURG, 2) public datasets and 3) both. To evaluate trained models, we calculate Dice score (DSC) between model segmentations and 200 manual annotations performed by three human raters. The model trained on data with manual annotations obtained a median (interquartile range) DSC of 65.3 (30.6). The DSC of our best-performing model, trained with no manual annotations, is 81.7 (14.2). For comparison, inter-rater agreement between human annotators was 84.0 (9.9). We demonstrate a training method for CNNs using simulated resection cavities that can accurately segment real resection cavities, without manual annotations., Comment: 13 pages, 6 figures, accepted at the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) 2020

Engineering of thermoelectric materials requires an understanding of thermal conduction by lattice and electronic degrees of freedom. Filled skutterudites denote a large family of materials suitable for thermoelectric applications where reduced lattice thermal conduction attributed to localized low-frequency vibrations (rattling) of filler cations inside large cages of the structure. In this work, a multi-wavelength method of exploiting X-ray dynamical diffraction in single crystals of CeFe$_4$P$_{12}$ is presented and applied to resolve the atomic amplitudes of vibrations. The results suggest that the vibrational dynamics of the whole filler-cage system is the actual active mechanism behind the optimization of thermoelectric properties., Comment: 14 pages, 4 figures

Given a marked $\infty$-category $\mathcal{D}^{\dagger}$ (i.e. an $\infty$-category equipped with a specified collection of morphisms) and a functor $F: \mathcal{D} \to \mathbb{B}$ with values in an $\infty$-bicategory, we define $\operatorname{colim}^{\dagger} F$, the marked colimit of $F$. We provide a definition of weighted colimits in $\infty$-bicategories when the indexing diagram is an $\infty$-category and show that they can be computed in terms of marked colimits. In the maximally marked case $\mathcal{D}^{\sharp}$, our construction retrieves the $\infty$-categorical colimit of $F$ in the underlying $\infty$-category $\mathcal{B} \subseteq \mathbb{B}$. In the specific case when $\mathbb{B}=\mathfrak{Cat}_{\infty}$, the $\infty$-bicategory of $\infty$-categories and $\mathcal{D}^{\flat}$ is minimally marked, we recover the definition of lax colimit of Gepner-Haugseng-Nikolaus. We show that a suitable $\infty$-localization of the associated coCartesian fibration $\operatorname{Un}_{\mathcal{D}}(F)$ computes $\operatorname{colim}^{\dagger} F$. Our main theorem is a characterization of those functors of marked $\infty$-categories $f:\mathcal{C}^{\dagger} \to \mathcal{D}^{\dagger}$ which are marked cofinal. More precisely, we provide sufficient and necessary criteria for the restriction of diagrams along $f$ to preserve marked colimits., Comment: 17 pages. Minor revisions. Submitted for publication. Comments welcome