Distal Esophageal Spasm: An Updated Review.

Distal esophageal spasm is characterized by premature contractions of the distal esophageal smooth muscle leading to non-obstructive dysphagia and non-cardiac chest pain. Diagnosis requires the presence of symptoms along with evidence of at least 20% premature contractions in the setting of a normal lower esophageal sphincter relaxation on high-resolution manometry. New updates to the Chicago Classification have improved the diagnostic accuracy of this method. Functional lumen imaging probe is a growing diagnostic modality that gives a more complete picture of esophageal motility. Pharmacologic treatment remains inadequate. Endoscopic myotomy might be of benefit for non-achalasia esophageal motility disorders. More research is required to better understand the pathophysiology and develop safe and long-lasting management for this disease.

Robust Low-Tubal-Rank Tensor Completion Based on Tensor Factorization and Maximum Correntopy Criterion.

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low tubal rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this article, we propose a new objective function for low-tubal-rank tensor completion, which uses correntropy as the error measure to mitigate the effect of the outliers. To efficiently optimize the proposed objective, we leverage a half-quadratic minimization technique whereby the optimization is transformed to a weighted low-tubal-rank tensor factorization problem. Subsequently, we propose two simple and efficient algorithms to obtain the solution and provide their convergence and complexity analysis. Numerical results using both synthetic and real data demonstrate the robust and superior performance of the proposed algorithms.

Persistent Post-endoscopic Retrograde Cholangiopancreatography Hiccups: An Unusual Presentation of Bile Reflux.

Bile reflux is a pathological retrograde flow of bile into the stomach that may lead to gastric overdistension and gastritis. It generally manifests as abdominal pain, nausea, vomiting, or heartburn. Hiccups have thus far not been described as part of its presentation. Here, we describe a case of excessive post-endoscopic retrograde cholangiopancreatography bile accumulation in the stomach that caused persistent hiccups requiring endoscopic suctioning.

Fooling the Big Picture in Classification Tasks.

Minimally perturbed adversarial examples were shown to drastically reduce the performance of one-stage classifiers while being imperceptible. This paper investigates the susceptibility of hierarchical classifiers, which use fine and coarse level output categories, to adversarial attacks. We formulate a program that encodes minimax constraints to induce misclassification of the coarse class of a hierarchical classifier (e.g., changing the prediction of a 'monkey' to a 'vehicle' instead of some 'animal'). Subsequently, we develop solutions based on convex relaxations of said program. An algorithm is obtained using the alternating direction method of multipliers with competitive performance in comparison with state-of-the-art solvers. We show the ability of our approach to fool the coarse classification through a set of measures such as the relative loss in coarse classification accuracy and imperceptibility factors. In comparison with perturbations generated for one-stage classifiers, we show that fooling a classifier about the 'big picture' requires higher perturbation levels which results in lower imperceptibility. We also examine the impact of different label groupings on the performance of the proposed attacks. Supplementary Information: The online version contains supplementary material available at 10.1007/s00034-022-02226-w.

Sketch-based community detection in evolving networks.

We consider an approach for community detection in time-varying networks. At its core, this approach maintains a small sketch graph to capture the essential community structure found in each snapshot of the full network. We demonstrate how the sketch can be used to explicitly identify six key community events which typically occur during network evolution: growth, shrinkage, merging, splitting, birth, and death. Based on these detection techniques, we formulate a community detection algorithm which can process a network concurrently exhibiting all processes. One advantage afforded by the sketch-based algorithm is the efficient handling of large networks. Whereas detecting events in the full graph may be computationally expensive, the small size of the sketch allows changes to be quickly assessed. A second advantage occurs in networks containing clusters of disproportionate size. The sketch is constructed such that there is equal representation of each cluster, thus reducing the possibility that the small clusters are lost in the estimate. We present a new standardized benchmark based on the stochastic block model which models the addition and deletion of nodes, as well as the birth and death of communities. When coupled with existing benchmarks, this new benchmark provides a comprehensive suite of tests encompassing all six community events. We provide analysis and a set of numerical results demonstrating the advantages of our approach both in runtime and in the handling of small clusters.

A differentiable approach to the maximum independent set problem using dataless neural networks.

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. In this paper, we propose a different approach in that no data is required for training the neural networks that produce the solution. In this sense, what we present is not a machine learning solution, but rather one that is dependent on neural networks and where backpropagation is applied to a loss function defined by the structure of the neural network architecture as opposed to a training dataset. In particular, we reduce the popular combinatorial optimization problem of finding a maximum independent set to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. Additionally, we propose a universal graph reduction procedure to handle large-scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental results on both real and synthetic graphs demonstrate that our proposed method performs on par or outperforms state-of-the-art learning-based methods in terms of the size of the found set without requiring any training data.

Coarse to Fine Two-Stage Approach to Robust Tensor Completion of Visual Data.

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which catalyzed the development of robust algorithms that alleviate the effect of outliers. However, existing robust methods largely presume that the corruption is sparse, which may not hold in practice. In this article, we develop a two-stage robust tensor completion approach to deal with tensor completion of visual data with a large amount of gross corruption. A novel coarse-to-fine framework is proposed which uses a global coarse completion result to guide a local patch refinement process. To efficiently mitigate the effect of a large number of outliers on tensor recovery, we develop a new M-estimator-based robust tensor ring recovery method which can adaptively identify the outliers and alleviate their negative effect in the optimization. The experimental results demonstrate the superior performance of the proposed approach over state-of-the-art robust algorithms for tensor completion.

What is the maximum differential group delay achievable by a space-time wave packet in free space?

The group velocity of 'space-time' wave packets - propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations - can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum - and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced 'pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.

Detection of brain stimuli using Ramanujan periodicity transforms.

OBJECTIVE: The ability to efficiently match the frequency of the brain's response to repetitive visual stimuli in real time is the basis for reliable SSVEP-based brain-computer-interfacing (BCI). APPROACH: The detection of different stimuli is posed as a composite hypothesis test, where SSVEPs are assumed to admit a sparse representation in a Ramanujan periodicity transform (RPT) dictionary. For the binary case, we develop and analyze the performance of an RPT detector based on a derived generalized likelihood ratio test. Our approach is extended to multi-hypothesis multi-electrode settings, where we capture the spatial correlation between the electrodes using pre-stimulus data. We also introduce a new metric for evaluating SSVEP detection schemes based on their achievable efficiency and discrimination rate tradeoff for given system resources. MAIN RESULTS: We obtain exact distributions of the test statistic in terms of confluent hypergeometric functions. Results based on extensive simulations with both synthesized and real data indicate that the RPT detector substantially outperforms spectral-based methods. Its performance also surpasses the calibration-free state-of-the-art canonical correlation analysis (CCA) and filter bank CCA (FBCCA) methods with respect to accuracy and sample complexity in short data lengths regimes crucial for real-time applications. The proposed approach is asymptotically optimal as it closes the gap to a perfect measurement bound as the data length increases. In contrast to existing supervised methods which are highly data-dependent, the RPT detector only uses pre-stimulus data to estimate the per-subject spatial correlation, thereby dispensing with considerable overhead associated with data collection for a large number of subjects and stimuli. SIGNIFICANCE: Our work advances the theory and practice of emerging real-time BCI and affords a new framework for comparing SSVEP detection schemes across a wider spectrum of operating regimes.

Multi-Modal Non-Line-of-Sight Passive Imaging.

We consider the non-line-of-sight (NLOS) imaging of an object using the light reflected off a diffusive wall. The wall scatters incident light such that a lens is no longer useful to form an image. Instead, we exploit the 4D spatial coherence function to reconstruct a 2D projection of the obscured object. The approach is completely passive in the sense that no control over the light illuminating the object is assumed and is compatible with the partially coherent fields ubiquitous in both the indoor and outdoor environments. We formulate a multi-criteria convex optimization problem for reconstruction, which fuses the reflected field's intensity and spatial coherence information at different scales. Our formulation leverages established optics models of light propagation and scattering and exploits the sparsity common to many images in different bases. We also develop an algorithm based on the alternating direction method of multipliers to efficiently solve the convex program proposed. A means for analyzing the null space of the measurement matrices is provided as well as a means for weighting the contribution of individual measurements to the reconstruction. This paper holds promise to advance passive imaging in the challenging NLOS regimes in which the intensity does not necessarily retain distinguishable features and provides a framework for multi-modal information fusion for efficient scene reconstruction.

Interferometry-based modal analysis with finite aperture effects.

We analyze the effects of aperture finiteness on interferograms recorded to unveil the modal content of optical beams in arbitrary bases using generalized interferometry. We develop a scheme for modal reconstruction from interferometric measurements that accounts for the ensuing clipping effects. Clipping-cognizant reconstruction is shown to yield significant performance gains over traditional schemes that overlook such effects that do arise in practice.

On the inverse problem of source reconstruction from coherence measurements.

We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data are the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which uses the authors' recent closed-form approximation formula for the coherence of the propagated field. The developed algorithms require a small data sample for convergence and yield stable inversion by exploiting information in the coherence as opposed to intensity-only measurements. Examples with both simulated and experimental data demonstrate the ability of the proposed approach to simultaneously recover complex sources in different planes transverse to the direction of propagation.

Compressive optical interferometry under structural constraints.

Compressive sensing (CS) combines data acquisition with compression coding to reduce the number of measurements required to reconstruct a sparse signal. In optics, this usually takes the form of projecting the field onto sequences of random spatial patterns that are selected from an appropriate random ensemble. We show here that CS can be exploited in 'native' optics hardware without introducing added components. Specifically, we show that random sub-Nyquist sampling of an interferogram suffices to reconstruct the field modal structure despite the structural constraints of the measurement system set by its limited degrees of freedom. The distribution of the reduced (and structurally constrained) sensing matrices corresponding to random measurements is provably incoherent and isotropic, which helps us carry out CS successfully. We implement compressive interferometry using a generalized Mach-Zehnder interferometer in which the traditional temporal delay is replaced with a linear transformation corresponding to a fractional transform. By randomly sampling the order of the fractional transform, we efficiently reconstruct the modal content of the input beam in the Hermite-Gaussian and Laguerre-Gaussian bases.

Hidden Quantum Processes, Quantum Ion Channels, and 1/ fθ-Type Noise.

In this letter, we perform a complete and in-depth analysis of Lorentzian noises, such as those arising from [Formula: see text] and [Formula: see text] channel kinetics, in order to identify the source of [Formula: see text]-type noise in neurological membranes. We prove that the autocovariance of Lorentzian noise depends solely on the eigenvalues (time constants) of the kinetic matrix but that the Lorentzian weighting coefficients depend entirely on the eigenvectors of this matrix. We then show that there are rotations of the kinetic eigenvectors that send any initial weights to any target weights without altering the time constants. In particular, we show there are target weights for which the resulting Lorenztian noise has an approximately [Formula: see text]-type spectrum. We justify these kinetic rotations by introducing a quantum mechanical formulation of membrane stochastics, called hidden quantum activated-measurement models, and prove that these quantum models are probabilistically indistinguishable from the classical hidden Markov models typically used for ion channel stochastics. The quantum dividend obtained by replacing classical with quantum membranes is that rotations of the Lorentzian weights become simple readjustments of the quantum state without any change to the laboratory-determined kinetic and conductance parameters. Moreover, the quantum formalism allows us to model the activation energy of a membrane, and we show that maximizing entropy under constrained activation energy yields the previous [Formula: see text]-type Lorentzian weights, in which the spectral exponent [Formula: see text] is a Lagrange multiplier for the energy constraint. Thus, we provide a plausible neurophysical mechanism by which channel and membrane kinetics can give rise to [Formula: see text]-type noise (something that has been occasionally denied in the literature), as well as a realistic and experimentally testable explanation for the numerical values of the spectral exponents. We also discuss applications of quantum membranes beyond [Formula: see text]-type -noise, including applications to animal models and possible impact on quantum foundations.

Wide-field interferometric measurement of a nonstationary complex coherence function.

Spatial coherence function (SCF) is a complex function of two spatial coordinates that, in general, carries more information than the bare intensity distribution. A fast and quantitatively accurate measurement of the SCF is extremely important for a range of applications in optical sensing and imaging. Here, we demonstrate an efficient two-step procedure for measuring the full-field complex coherence function. The measurement relies on an optimized design of a wavefront shearing interferometer capable of characterizing spatially inhomogeneous fields over an extended angular domain. The measurement precision is confirmed by the excellent agreement with a numerical estimation based on Fresnel calculations. We demonstrate that the sensitivity and the measurement range afforded by our instrument permits us to reliably describe the differences in the complex coherence functions that are due to subtle modifications in the shape, position, and orientation of radiation sources.

Spatial coherence of fields from generalized sources in the Fresnel regime.

Analytic expressions of the spatial coherence of partially coherent fields propagating in the Fresnel regime in all but the simplest of scenarios are largely lacking, and calculation of the Fresnel transform typically entails tedious numerical integration. Here, we provide a closed-form approximation formula for the case of a generalized source obtained by modulating the field produced by a Gauss-Shell source model with a piecewise constant transmission function, which may be used to model the field's interaction with objects and apertures. The formula characterizes the coherence function in terms of the coherence of the Gauss-Schell beam propagated in free space and a multiplicative term capturing the interaction with the transmission function. This approximation holds in the regime where the intensity width of the beam is much larger than the coherence width under mild assumptions on the modulating transmission function. The formula derived for generalized sources lays the foundation for the study of the inverse problem of scene reconstruction from coherence measurements.

Incoherent lensless imaging via coherency back-propagation.

The two-point complex coherence function constitutes a complete representation for scalar quasi-monochromatic optical fields. Exploiting dynamically reconfigurable slits implemented with a digital micromirror device, we report on measurements of the complex two-point coherence function for partially coherent light scattering from a "scene" composing one or two objects at different transverse and axial positions with respect to the source. Although the intensity shows no discernible shadows in the absence of a lens, numerically back-propagating the measured complex coherence function allows estimating the objects' sizes and locations and, thus, the reconstruction of the scene subject to the effects of occlusion and shadowing.

Coherence measurements of scattered incoherent light for lensless identification of an object's location and size.

In the absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that measuring the complex spatial coherence function can help in the identification of the size and location of a one-dimensional object placed in the path of a partially coherent light source. The complex coherence function is measured in the far field through wavefront sampling, which is performed via dynamically reconfigurable slits implemented on a digital micromirror device (DMD). The impact of an object - parameterized by size and location - that either intercepts or reflects incoherent light is studied. The experimental results show that measuring the spatial coherence function as a function of the separation between two slits located symmetrically around the optical axis can identify the object transverse location and angle subtended from the detection plane (the ratio of the object width to the axial distance from the detector). The measurements are in good agreement with numerical simulations of a forward model based on Fresnel propagators. The rapid refresh rate of DMDs may enable real-time operation of such a lensless coherency imaging scheme.

Basis-neutral Hilbert-space analyzers.

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes - a critical task for spatial-mode multiplexing and quantum communication - basis-specific principles are invoked that are altogether distinct from that of 'delay'. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis - exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a 'delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a 'Hilbert-space analyzer' capable of projecting optical beams onto any modal basis.

A New Statistical Model of Electroencephalogram Noise Spectra for Real-Time Brain-Computer Interfaces.

OBJECTIVE: A characteristic of neurological signal processing is high levels of noise from subcellular ion channels up to whole-brain processes. In this paper, we propose a new model of electroencephalogram (EEG) background periodograms, based on a family of functions which we call generalized van der Ziel-McWhorter (GVZM) power spectral densities (PSDs). To the best of our knowledge, the GVZM PSD function is the only EEG noise model that has relatively few parameters, matches recorded EEG PSD's with high accuracy from 0 to over 30 Hz, and has approximately 1/fθ behavior in the midfrequencies without infinities. METHODS: We validate this model using three approaches. First, we show how GVZM PSDs can arise in a population of ion channels at maximum entropy equilibrium. Second, we present a class of mixed autoregressive models, which simulate brain background noise and whose periodograms are asymptotic to the GVZM PSD. Third, we present two real-time estimation algorithms for steady-state visual evoked potential (SSVEP) frequencies, and analyze their performance statistically. RESULTS: In pairwise comparisons, the GVZM-based algorithms showed statistically significant accuracy improvement over two well-known and widely used SSVEP estimators. CONCLUSION: The GVZM noise model can be a useful and reliable technique for EEG signal processing. SIGNIFICANCE: Understanding EEG noise is essential for EEG-based neurology and applications such as real-time brain-computer interfaces, which must make accurate control decisions from very short data epochs. The GVZM approach represents a successful new paradigm for understanding and managing this neurological noise.