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The expressive power of deep neural networks is manifested by their remarkable ability to approximate multivariate functions in a way that appears to overcome the curse of dimensionality. This ability is exemplified by their success in solving high-dimensional problems where traditional numerical solvers fail due to their limitations in accurately representing high-dimensional structures. To provide a theoretical framework for explaining this phenomenon, we analyze the approximation of Hölder functions defined on a d -dimensional smooth manifold M embedded in R D , with d ≪ D , using deep neural networks. We prove that the uniform convergence estimates of the approximation and generalization errors by deep neural networks with ReLU activation functions do not depend on the ambient dimension D of the function but only on its lower manifold dimension d , in a precise sense. Our result improves existing results from the literature where approximation and generalization errors were shown to depend weakly on D. • Deep ReLU neural networks exhibit remarkable approximation properties for multivariate functions. • We prove that the approximation error of manifold-embedded data depends only on the manifold dimension. • Argument relies on preservation of pairwise ambient distances on the manifold. • Our result improves existing results where the approximation error depends weakly on the ambient dimension. • Our result implies an improved estimate of the generalization error. [ABSTRACT FROM AUTHOR]

Background Automated detection and segmentation of somas in fluorescent images of neurons is a major goal in quantitative studies of neuronal networks, including applications of high-content-screenings where it is required to quantify multiple morphological properties of neurons. Despite recent advances in image processing targeted to neurobiological applications, existing algorithms of soma detection are often unreliable, especially when processing fluorescence image stacks of neuronal cultures. New method In this paper, we introduce an innovative algorithm for the detection and extraction of somas in fluorescent images of networks of cultured neurons where somas and other structures exist in the same fluorescent channel. Our method relies on a new geometrical descriptor called Directional Ratio and a collection of multiscale orientable filters to quantify the level of local isotropy in an image. To optimize the application of this approach, we introduce a new construction of multiscale anisotropic filters that is implemented by separable convolution. Results Extensive numerical experiments using 2D and 3D confocal images show that our automated algorithm reliably detects somas, accurately segments them, and separates contiguous ones. Comparison with existing methods We include a detailed comparison with state-of-the-art existing methods to demonstrate that our algorithm is extremely competitive in terms of accuracy, reliability and computational efficiency. Conclusions Our algorithm will facilitate the development of automated platforms for high content neuron image processing. A Matlab code is released open-source and freely available to the scientific community. [ABSTRACT FROM AUTHOR]

The major limitation in current facial recognition systems is that they do not perform very well in uncontrolled environments, that is, when faces present variations in pose, illumination, facial expressions and environment. This is a serious obstacle in applications such as law enforcement and surveillance systems. To address this limitation, in this paper we introduce an improved approach to ensure robust face recognition, that relies on two innovative ideas. First, we apply a new multiscale directional framework, called Shearlet Network (SN), to extract facial features. The advantage of this approach comes from the highly sparse representation properties of the shearlet framework that is especially designed to robustly extract the fundamental geometric content of an image. Second, we apply a refinement of the Multi-Task Sparse Learning (MTSL) framework to exploit the relationships among multiple shared tasks generated by changing the regularization parameter during the recognition stage. We provide extensive numerical tests to show that our Sparse Multi-Regularized Shearlet Network (SMRSN) algorithm performs very competitively when compared against different state-of-the-art methods on different experimental protocols, including face recognition in uncontrolled conditions and single-sample-per-person. [ABSTRACT FROM AUTHOR]

Abstract: PRISMA (PRecursore IperSpettrale della Missione Applicativa) hyperspectral instrument is an advanced hyperspectral sensor including a panchromatic camera at medium resolution. The instrument is the focus of the new Earth observation mission that a consortium of Italian companies has started developing under contract of Italian Space Agency. Key features of the instrument are the very high requirement for signal-to-noise and the high quality of data that have to be provided. To meet these demanding figures the optical system has been based on a high transmittance optical system, including a single mirror telescope and two prism spectrometers based on an innovative concept to minimize number of optical elements, while high performance detectors have been chosen for the photon detection. To provide the required data quality for the entire mission lifetime an accurate calibration unit (radiometric and spectral) will be included in the instrument optomechanical assembly. The thermo-mechanical design of the instrument is based on innovative concepts, considering that the use of prism spectrometers implies a tight control of temperature variations to guarantee the stability of all instrument features once in orbit. The presented paper describes the concepts and design principle of the optomechanical assembly of the instrument, at the present status of development. [Copyright &y& Elsevier]

[Display omitted] Measuring single cell responses to the universe of chemicals (drugs, natural products, environmental toxicants etc.) is of paramount importance to human health as phenotypic variability in sensing stimuli is a hallmark of biology that is considered during high throughput screening. One of the ways to approach this problem is via high throughput, microscopy-based assays coupled with multi-dimensional single cell analysis methods. Here, we will summarize some of the efforts in this vast and growing field, focusing on phenotypic screens (e.g., Cell Painting), single cell analytics and quality control, with particular attention to environmental toxicology and drug screening. We will discuss advantages and limitations of high throughput assays with various end points and levels of complexity. [ABSTRACT FROM AUTHOR]

Background Phosphorylation plays an essential role in regulating voltage-gated sodium (Na v ) channels and excitability. Yet, a surprisingly limited number of kinases have been identified as regulators of Na v channels. We posited that glycogen synthase kinase 3 (GSK3), a critical kinase found associated with numerous brain disorders, might directly regulate neuronal Na v channels. Methods We used patch-clamp electrophysiology to record sodium currents from Na v 1.2 channels stably expressed in HEK-293 cells. mRNA and protein levels were quantified with RT-PCR, Western blot, or confocal microscopy, and in vitro phosphorylation and mass spectrometry to identify phosphorylated residues. Results We found that exposure of cells to GSK3 inhibitor XIII significantly potentiates the peak current density of Na v 1.2, a phenotype reproduced by silencing GSK3 with siRNA. Contrarily, overexpression of GSK3β suppressed Na v 1.2-encoded currents. Neither mRNA nor total protein expression was changed upon GSK3 inhibition. Cell surface labeling of CD4-chimeric constructs expressing intracellular domains of the Na v 1.2 channel indicates that cell surface expression of CD4-Na v 1.2 C-tail was up-regulated upon pharmacological inhibition of GSK3, resulting in an increase of surface puncta at the plasma membrane. Finally, using in vitro phosphorylation in combination with high resolution mass spectrometry, we further demonstrate that GSK3β phosphorylates T 1966 at the C-terminal tail of Na v 1.2. Conclusion These findings provide evidence for a new mechanism by which GSK3 modulates Na v channel function via its C-terminal tail. General significance These findings provide fundamental knowledge in understanding signaling dysfunction common in several neuropsychiatric disorders. [ABSTRACT FROM AUTHOR]