Contrast-enhanced ultrasonography in hepatosplenic sarcoidosis

We report a case of a 38-year-old woman with atypical pain in the left lower hemi-abdomen. On abdominal B-mode ultrasonography the liver was normal; the spleen showed multiple subcentimetric hypoechoic nodules. A multidetector CT-examination revealed multiple small low-attenuation nodules in the liver and the spleen, suggestive for metastatic disease. Contrast-enhanced ultrasound (CEUS) revealed two hypoechoic nodules in the liver that were visible in the portal phase and disappeared in the late phase. The focal splenic lesions were visible as irregular hypo-enhancing nodules. An MRI examination, including T1, T2 and contrast-enhanced images, could not confirm the exact nature of the lesions. A core biopsy of a splenic nodule yielded non-caseating epithelioid cell granulomas. Different complementary examinations were normal and hepatosplenic sarcoidosis was diagnosed. The pain in the left lower hemi-abdomen was ascribed to irritable bowel syndrome

Variational Estimates for Discrete Schr\"odinger Operators with Potentials of Indefinite Sign

Let $H$ be a one-dimensional discrete Schr\"odinger operator. We prove that if \sigma_{\ess} (H)\subset [-2,2], then $H-H_0$ is compact and \sigma_{\ess}(H)=[-2,2]. We also prove that if $H_0 + \frac14 V^2$ has at least one bound state, then the same is true for $H_0 +V$. Further, if $H_0 + \frac14 V^2$ has infinitely many bound states, then so does $H_0 +V$. Consequences include the fact that for decaying potential $V$ with $\liminf_{|n|\to\infty} |nV(n)| > 1$, $H_0 +V$ has infinitely many bound states; the signs of $V$ are irrelevant. Higher-dimensional analogues are also discussed.Comment: 17 page

Fast inference in nonlinear dynamical systems using gradient matching

Parameter inference in mechanistic models of coupled differential equations is a topical problem. We propose a new method based on kernel ridge regression and gradient matching, and an objective function that simultaneously encourages goodness of fit and penalises inconsistencies with the differential equations. Fast minimisation is achieved by exploiting partial convexity inherent in this function, and setting up an iterative algorithm in the vein of the EM algorithm. An evaluation of the proposed method on various benchmark data suggests that it compares favourably with state-of-the-art alternatives

Inference in Nonlinear Differential Equations

Parameter inference in mechanistic models of coupled differential equations is a challenging problem. We propose a new method using kernel ridge regression in Reproducing Kernel Hilbert Spaces (RKHS). A three-step gradient matching algorithm is developed and applied to a realistic biochemical model

Parameter Inference in Differential Equation Models of Biopathways using Time Warped Gradient Matching

Parameter inference in mechanistic models of biopathways based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the fact that each parameter adaptation involves a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. However, gradient matching critically hinges on the smoothing scheme for function interpolation, with spurious wiggles in the interpolant having a dramatic effect on the subsequent inference. The present article demonstrates that a time warping approach aiming to homogenize intrinsic functional length scales can lead to a signifi- cant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from a dynamical system with periodic limit cycle and a biopathway

Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion

The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, and non-intrusive nature makes the method appealing in various areas of application. We present a complete analysis of the ensemble Kalman inversion with perturbed observations for a fixed ensemble size when applied to linear inverse problems. The well-posedness and convergence results are based on the continuous time scaling limits of the method. The resulting coupled system of stochastic differential equations allows to derive estimates on the long-time behaviour and provides insights into the convergence properties of the ensemble Kalman inversion. We view the method as a derivative free optimization method for the least-squares misfit functional, which opens up the perspective to use the method in various areas of applications such as imaging, groundwater flow problems, biological problems as well as in the context of the training of neural networks

Broadside Dual-channel Orthogonal-Polarization Radiation using a Double-Asymmetric Periodic Leaky-Wave Antenna

The paper demonstrates that double unit-cell asymmetry in periodic leaky-wave antennas (P-LWAs), i.e. asymmetry with respect to both the longitudinal and transversal axes of the structure -- or longitudinal asymmetry (LA) and transversal asymmetry (TA) -- allows for the simultaneous broadside radiation of two orthogonal modes excited at the two ports of the antenna. This means that the antenna may simultaneously support two orthogonal channels, which represents an interesting polarization diversity characteristics for wireless communications. The double asymmetric (DA) unit cell combines a circularly polarized LA unit cell and a coupled mode TA unit cell, where the former provides equal radiation in the series and shunt modes while the latter separates these two modes in terms of their excitation ports. It is also shown that the degree of TA in the DA unit cell controls the cross-polarization discrimination level. The DA P-LWA concept is illustrated by two examples, a series-fed line-connected patch (SF-LCP) P-LWA and a series-fed capacitively-coupled patch (SF-CCP) P-LWA, via full-wave simulation and also experiment for the SF-LCP P-LWA case

Approximate parameter inference in systems biology using gradient matching: a comparative evaluation

Background: A challenging problem in current systems biology is that of parameter inference in biological pathways expressed as coupled ordinary differential equations (ODEs). Conventional methods that repeatedly numerically solve the ODEs have large associated computational costs. Aimed at reducing this cost, new concepts using gradient matching have been proposed, which bypass the need for numerical integration. This paper presents a recently established adaptive gradient matching approach, using Gaussian processes, combined with a parallel tempering scheme, and conducts a comparative evaluation with current state of the art methods used for parameter inference in ODEs. Among these contemporary methods is a technique based on reproducing kernel Hilbert spaces (RKHS). This has previously shown promising results for parameter estimation, but under lax experimental settings. We look at a range of scenarios to test the robustness of this method. We also change the approach of inferring the penalty parameter from AIC to cross validation to improve the stability of the method. Methodology: Methodology for the recently proposed adaptive gradient matching method using Gaussian processes, upon which we build our new method, is provided. Details of a competing method using reproducing kernel Hilbert spaces are also described here. Results: We conduct a comparative analysis for the methods described in this paper, using two benchmark ODE systems. The analyses are repeated under different experimental settings, to observe the sensitivity of the techniques. Conclusions: Our study reveals that for known noise variance, our proposed method based on Gaussian processes and parallel tempering achieves overall the best performance. When the noise variance is unknown, the RKHS method proves to be more robust

Statistical inference in mechanistic models: time warping for improved gradient matching

Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios