Deep Learning Solution of the Eigenvalue Problem for Differential Operators

Solving the eigenvalue problem for differential operators is a common problem in many scientific fields. Classical numerical methods rely on intricate domain discretization and yield nonanalytic or nonsmooth approximations. We introduce a novel neural network-based solver for the eigenvalue problem of differential self-adjoint operators, where the eigenpairs are learned in an unsupervised end-to-end fashion. We propose several training procedures for solving increasingly challenging tasks toward the general eigenvalue problem. The proposed solver is capable of finding the M smallest eigenpairs for a general differential operator. We demonstrate the method on the Laplacian operator, which is of particular interest in image processing, computer vision, and shape analysis among many other applications. In addition, we solve the Legendre differential equation. Our proposed method simultaneously solves several eigenpairs and can be easily used on free-form domains. We exemplify it on L-shape and circular cut domains. A significant contribution of this work is an analysis of the numerical error of this method. In particular an upper bound for the (unknown) solution error is given in terms of the (measured) truncation error of the partial differential equation and the network structure.

Interactions of hydrophilic quantum dots with defect-free and defect containing supported lipid membranes

Quantum dots (QDs) are semiconductor nanoparticles with unique optical and electronic properties, whose interest as potential nano-theranostic platforms for imaging and sensing is increasing. The design and use of QDs requires the understanding of cell-nanoparticle interactions at a microscopic and nanoscale level. Model systems such as supported lipid bilayers (SLBs) are useful, less complex platforms mimicking physico-chemical properties of cell membranes. In this work, we investigated the effect of topographical homogeneity of SLBs bearing different surface charge in the adsorption of hydrophilic QDs. Using quartz-crystal microbalance, a label-free surface sensitive technique, we show significant differences in the interactions of QDs onto homogeneous and inhomogeneous SLBs formed following different strategies. Within short time scales, QDs adsorb onto topographically homogeneous, defect-free SLBs is driven by electrostatic interactions, leading to no layer disruption. After prolonged QD exposure, the nanomechanical stability of the SLB decreases suggesting nanoparticle insertion. In the case of inhomogeneous, defect containing layers, QDs target preferentially membrane defects, driven by a subtle interplay of electrostatic and entropic effects, inducing local vesicle rupture and QD insertion at membrane edges.

Downregulation of dystrophin expression in pupae of the whitefly Bemisia tabaci inhibits the emergence of adults

The whitefly Bemisia tabaci is a major pest to agriculture. Adults are able to fly for long distances and to colonize staple crops, herbs and ornamentals, and to vector viruses belonging to several important taxonomic groups. During their early development, whiteflies mature from eggs through several nymphal stages (instars I to IV) until adults emerge from pupae. We aim at reducing whitefly populations by inhibiting the emergence of adults from nymphs. Here we targeted dystrophin, a conserved protein essential for the development of the muscle system in humans, other animals and insects. We have exploited the fact that whitefly nymphs developing on tomato leaves feed from the plant phloem via their stylets. Thus, we delivered dystrophin-silencing double-stranded RNA to nymphs developing on leaves of tomato plantlets with their roots bathing in the silencing solution. Downregulation of dystrophin expression occurred mainly in pupae. Dystrophin silencing induced also the downregulation of the dystrophin-associated protein genes actin and tropomyosin, and disrupted F-actin. Most significantly, the treatment inhibited the emergence of adults from pupae, suggesting that targeting dystrophin may help to restrain whitefly populations. This study demonstrates for the first time the important role of dystrophin in the development of a major insect pest to agriculture.

Modeling of the diffusion MR signal in calibrated model systems and nerves

Diffusion NMR is a powerful tool for gleaning microstructural information on opaque systems. In this work, the signal decay in single-pulsed-field gradient diffusion NMR experiments performed on a series of phantoms of increasing complexity, where the ground truth is known a priori, was modeled and used to identify microstructural features of these complex phantoms. We were able to demonstrate that, without assuming the number of components or compartments, the modeling can identify the number of restricted components, detect their sizes with an accuracy of a fraction of a micrometer, determine their relative populations, and identify and characterize free diffusion when present in addition to the components exhibiting restricted diffusion. After the accuracy of the modeling had been demonstrated, this same approach was used to study fixed nerves under different experimental conditions. It seems that this approach is able to characterize both the averaged axon diameter and the relative population of the different diffusing components in the neuronal tissues examined.

The CONNECT project: Combining macro- and micro-structure

In recent years, diffusion MRI has become an extremely important tool for studying the morphology of living brain tissue, as it provides unique insights into both its macrostructure and microstructure. Recent applications of diffusion MRI aimed to characterize the structural connectome using tractography to infer connectivity between brain regions. In parallel to the development of tractography, additional diffusion MRI based frameworks (CHARMED, AxCaliber, ActiveAx) were developed enabling the extraction of a multitude of micro-structural parameters (axon diameter distribution, mean axonal diameter and axonal density). This unique insight into both tissue microstructure and connectivity has enormous potential value in understanding the structure and organization of the brain as well as providing unique insights to abnormalities that underpin disease states. The CONNECT (Consortium Of Neuroimagers for the Non-invasive Exploration of brain Connectivity and Tracts) project aimed to combine tractography and micro-structural measures of the living human brain in order to obtain a better estimate of the connectome, while also striving to extend validation of these measurements. This paper summarizes the project and describes the perspective of using micro-structural measures to study the connectome.

Airway CD8(+) T cells induced by pulmonary DNA immunization mediate protective anti-viral immunity

Vaccination strategies for protection against a number of respiratory pathogens must induce T-cell populations in both the pulmonary airways and peripheral lymphoid organs. In this study, we show that pulmonary immunization using plasmid DNA formulated with the polymer polyethyleneimine (PEI-DNA) induced antigen-specific CD8(+) T cells in the airways that persisted long after antigen local clearance. The persistence of the cells was not mediated by local lymphocyte proliferation or persistent antigen presentation within the lung or airways. These vaccine-induced CD8(+) T cells effectively mediated protective immunity against respiratory challenges with vaccinia virus and influenza virus. Moreover, this protection was not dependent upon the recruitment of T cells from peripheral sites. These findings demonstrate that pulmonary immunization with PEI-DNA is an efficient approach for inducing robust pulmonary CD8(+) T-cell populations that are effective at protecting against respiratory pathogens.

Deblurring of color images corrupted by impulsive noise

We consider the problem of restoring a multichannel image corrupted by blur and impulsive noise (e.g., salt-and-pepper noise). Using the variational framework, we consider the L1 fidelity term and several possible regularizers. In particular, we use generalizations of the Mumford-Shah (MS) functional to color images and gamma-convergence approximations to unify deblurring and denoising. Experimental comparisons show that the MS stabilizer yields better results with respect to Beltrami and total variation regularizers. Color edge detection is a beneficial by-product of our methods.

Semi-blind image restoration via Mumford-Shah regularization

Image restoration and segmentation are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates semi-blind image deconvolution (parametric blur-kernel), and Mumford-Shah segmentation. The functional is formulated using the T-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified treatment of the semi-blind restoration and segmentation problems, the important special case of known blur is also considered and promising results are obtained.

Commercial Fibrin Sealants Are Not Equivalent in a Rabbit Liver-Resection Model Which Quantitatively Evaluates Hemostasis and Formation of Adhesions

A rabbit partial liver resection model was used to determine the hemostatic effectiveness of a new fibrin sealant. Persistent bleeding, with a mean bleeding time of 372 s and blood loss of 18 ml, from a resected lobe of the liver was achieved after rabbits in the untreated control group had been infused continuously with unfractionated heparin over 20 min with 0.2 IU/ml at a rate of 1 ml/min. Spraying the resected surface with the new fibrin sealant, Quixil, reduced bleeding to < 1 ml and the post-resection bleeding times was 25 s. Bleeding time, blood loss and the volume of sealant used in the rabbit model were inversely correlated with the thrombin concentration in the sealant. In direct comparisons with Tissucol and Beriplast, Quixil was associated with the shortest bleeding times, the lowest volume of sealant used and the lowest score of abdominal adhesions.

Functional correlates with left-right asymmetry of visual evoked potentials in stroke patients: modeling and experimental results

OBJECTIVE

To determine the correlation between a clinical measure of function in patients after first stroke and left-right scalp amplitude of visual evoked potentials using a theoretical model of the head.

DESIGN

A random sample of first-stroke patients underwent routine function measurement and investigation of left-right scalp potential asymmetry. Results of the encephalographic tests were compared with those of a healthy subject. To examine the effect of the conductivity in the damaged area on the potential asymmetry, numerical calculations were performed on a model, with four concentric circular compartments representing the brain, cerebrospinal fluid layer, skull, and scalp. The damaged region was modeled as a circular section.

SETTING

Neurologic rehabilitation ward of a major rehabilitation hospital and university-affiliated biomedical engineering laboratory.

PATIENTS

Four men aged 58 to 71 years, 3 with brain thrombosis and 1 with hemorrhagic stroke. The patients were admitted for rehabilitation an average of 3 weeks after the stroke and stayed for an average of 137 days. Damage was confined to the right brain in all cases; three of the patients had neglect syndrome and/or sensory disturbances. A healthy subject without stroke was also examined.

MEASURES

Function was measured with the Functional Independence Measure (FIM) at 48 to 72 hours from admission and during the last week before discharge. Functional gain was calculated by subtracting the FIM admission score from the discharge score. Left-right scalp visual evoked potential amplitude was studied with flash stimuli according to the 10-20 international system and a theoretical model of the head based on two-dimensional computed tomography images; the volume conductor equation was solved numerically using the finite volume method. Left-right potential asymmetry and the damaged-region-to-brain-area ratio were calculated and correlated with the FIM values by linear regression analysis. Negative asymmetry indicates that the activity in the right damaged hemisphere is lower than in the undamaged one.

RESULTS

A negative correlation was noted between the FIM score on admission and the left-right scalp potential amplitude asymmetry, and between the FIM gain and the damaged-region-to-brain-area ratio obtained from the computed tomography image. Asymmetry was negative in the thrombotic patients and positive in the hemorrhagic one. The healthy subject showed nonsignificant asymmetry.

CONCLUSION

A relationship might exist between the left-right asymmetry of the scalp visual evoked potential and both the damaged-region-to-brain-area ratio and the functional outcome of rehabilitation in poststroke patients. The modeling study shows that the left-right asymmetry is most likely the result of changes in the conductivity at the damaged area, which, in turn, are probably associated with patient functional status and evolution. Further validation in larger groups of patients and normal subjects is needed before these parameters can serve as useful indices for clinical purposes.

Left-right asymmetry of visual evoked potentials in brain-damaged patients: a mathematical model and experimental results

The left-right asymmetry in the potential amplitude on the scalp was studied in poststroke patients by using flash visual evoked potential (VEP) and a numerical two-dimensional model of the head. The left-right asymmetry of the VEP was measured in three patients after thrombosis, in one after hemorrhage, and in one healthy subject. The numerical model used computed tomography images to define the different compartments of the head. The volume conductor equation for the potential distribution created by a dipole source in the occipital region was solved numerically with use of a finite volume method. Left-right asymmetry was calculated with several values of conductivity of the damaged region. The experimental results revealed a negative asymmetry in the three patients after thrombosis (i.e., the potential amplitude over the ischemic hemisphere was smaller than that over the intact hemisphere), whereas, in the patient after hemorrhage, a positive asymmetry was found. Nonsignificant left-right asymmetry was found in the healthy subject. The numerical model revealed that the electrical conductivity of the damaged tissue has a major effect on the left-right asymmetry. Negative asymmetry, such as that found for patients after thrombosis, was obtained when the conductivity of the damaged region was greater than that of the brain, whereas positive asymmetry (hemorrhage patient) was obtained when that conductivity was smaller than that of the brain. This finding indicates that the left-right asymmetry in the scalp VEP of patients after brain damage may be a result of changes in the conductivity of the volume conductor (the ischemic region) between the source and the electrodes.