A Proximal Approach for a Class of Matrix Optimization Problems

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a general framework where the regularization term is split in two parts, one being a spectral function while the other is arbitrary. A Douglas-Rachford approach is proposed to address such problems and a list of proximity operators is provided allowing us to consider various choices for the fit-to-data functional and for the regularization term. Numerical experiments show the validity of this approach for solving convex optimization problems encountered in the context of sparse covariance matrix estimation. Based on our theoretical results, an algorithm is also proposed for noisy graphical lasso where a precision matrix has to be estimated in the presence of noise. The nonconvexity of the resulting objective function is dealt with a majorization-minimization approach, i.e. by building a sequence of convex surrogates and solving the inner optimization subproblems via the aforementioned Douglas-Rachford procedure. We establish conditions for the convergence of this iterative scheme and we illustrate its good numerical performance with respect to state-of-the-art approaches

Predicting toxicity through computers: a changing world

The computational approaches used to predict toxicity are evolving rapidly, a process hastened on by the emergence of new ways of describing chemical information. Although this trend offers many opportunities, new regulations, such as the European Community's 'Registration, Evaluation, Authorisation and Restriction of Chemicals' (REACH), demand that models be ever more robust

Regularization Techniques for Inverse Problem in DOT Applications

Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near-infra-red light to investigate the optical coefficients distribution in biological tissues. The surface of the tissue is illuminated by light sources, then the outgoing light is measured by detectors placed at various locations on the surface itself. In order to reconstruct the optical coefficients, a mathematical model of light propagation is employed: such model leads to the minimization of the discrepancy between the detected data and the corresponding theoretical field. Due to severe ill-conditioning, regularization techniques are required: common procedures consider mainly \u2113 1-norm (LASSO) and \u2113 2-norm (Tikhonov) regularization. In the present work we investigate two original approaches in this context: The elastic-net regularization, previously used in machine learning problems, and the Bregman procedure. Numerical experiments are performed on synthetic 2D geometries and data, to evaluate the performance of these approaches. The results show that these techniques are indeed suitable choices for practical applications, where DOT is used as a cheap, first-level and almost real-Time screening technique for breast cancer detection

Magnetic signatures of domain walls in s+is and s+id superconductors: Observability and what that can tell us about the superconducting order parameter

One of the defining features of spontaneously broken time-reversal symmetry (BTRS) is the existence of domain walls, the detection of which would be strong evidence for such systems. There is keen interest in BTRS currently, in part, due to recent muon spin rotation experiments, which have pointed towards Ba1−xKxFe2As2 exhibiting a remarkable case of s-wave superconductivity with spontaneously broken time-reversal symmetry. A key question, however, is how to differentiate between the different theoretical models which describe such a state. Two particularly popular choices of model are s+is and s+id superconducting states. In this paper, we obtain solutions for domain walls in s+is and s+id systems, including the effects of lattice anisotropies. We show that, in general, both models exhibit spontaneous magnetic fields that extend along the entire length of the domain wall. We demonstrate the qualitative difference between the magnetic signatures of s+is and s+id domain walls and propose a procedure to extract the superconducting pairing symmetry from the magnetic-field response of domain walls

Synapsin I controls synaptic maturation of long-range projections in the lateral amygdala in a targeted selective fashion

The amygdala, and more precisely its lateral nucleus, is thought to attribute emotional valence to external stimuli by generating long-term plasticity changes at long-range projections to principal cells. Aversive experience has also been shown to modify pre- and post-synaptic markers in the amygdala, suggesting their possible role in the structural organization of adult amygdala networks. Here, we focused on how the maturation of cortical and thalamic long-range projections occurs on principal neurons and interneurons in the lateral amygdala (LA). We performed dual electrophysiological recordings of identified cells in juvenile and adult GAD67-GFP mice after independent stimulation of cortical and thalamic afferent systems. The results demonstrate that synaptic strengthening occurs during development at synapses projecting to LA principal neurons, but not interneurons. As synaptic strengthening underlies fear conditioning which depends, in turn, on presence and increasing expression of synapsin I, we tested if synapsin I contributes to synaptic strengthening during development. Interestingly, the physiological synaptic strengthening of cortical and thalamic synapses projecting to LA principal neurons was virtually abolished in synapsin I knockout mice, but not differences were observed in the excitatory projections to interneurons. Immunohistochemistry analysis showed that the presence of synapsin I is restricted to excitatory contacts projecting to principal neurons in LA of adult mice. These results indicate that synapsin I is a key regulator of the maturation of synaptic connectivity in this brain region and that is expression is dependent on postsynaptic identity

QSAR Model for Cytotoxicity of Silica Nanoparticles on Human Embryonic Kidney Cells1

Abstract A predictive model for cytotoxicity of 20 and 50 nm silica nanoparticles has been built using so-called optimal descriptors as mathematical functions of size, concentration and exposure time. These parameters have been encoded into 31 combinations 'concentration-exposure-size'. The calculation has been carried out by means of the CORAL software ( http://www.insilico.eu/coral/ ) using three random splits of the obtained systems into training and test sets. The statistical quality of the best model for cell viability (%) of cultured human embryonic kidney cells (HEK293) exposed to different concentrations of silica nanoparticles measured by MTT assay is satisfactory

Mild Inactivation of RE-1 Silencing Transcription Factor (REST) Reduces Susceptibility to Kainic Acid-Induced Seizures

RE-1 Silencing Transcription factor (REST) controls several steps in neural development by modulating the expression of a wide range of neural genes. Alterations in REST expression have been associated with the onset of epilepsy; however, whether such alterations are deleterious or represent a protective homeostatic response remains elusive. To study the impact of REST modulation on seizure propensity, we developed a tool for its negative modulation in vivo. The tool is composed of the paired-amphipathic helix 1 (PAH1) domain, a competitive inhibitor of REST activation by mSin3, fused to the light-oxygen-voltage sensing 2 (LOV2) domain of Avena sativa phototropin 1, a molecular switch to alternatively hide or expose the PAH1 inhibitor. We employed the C450A and I539E light-independent AsLOV2 variants to mimic the closed (inactive) and open (active) states of LOV2-PAH1, respectively. Recombinant AAV1/2 viral particles (rAAVs) allowed LOV2-PAH1 expression in HEK293T cells and primary neurons, and efficiently transduced hippocampal neurons in vivo. mRNA expression analysis revealed an increased expression of several neuronal genes in the hippocampi of mice expressing the open probe. AAV-transduced mice received a single dose of kainic acid (KA), a treatment known to induce a transient increase of REST levels in the hippocampus. Remarkably, mice expressing the active variant displayed a reduced number of KA-induced seizures, which were less severe compared to mice carrying the inactive probe. These data support the validity of our tool to modulate REST activity in vivo and the potential impact of REST modulation on epileptogenesis

Engineering REST-Specific Synthetic PUF Proteins to Control Neuronal Gene Expression: A Combined Experimental and Computational Study

Regulation of gene transcription is an essential mechanism for differentiation and adaptation of organisms. A key actor in this regulation process is the repressor element 1 (RE1)-silencing transcription factor (REST), a transcriptional repressor that controls more than 2000 putative target genes, most of which are neuron-specific. With the purpose of modulating REST expression, we exploited synthetic, ad hoc designed, RNA binding proteins (RBPs) able to specifically target and dock to REST mRNA. Among the various families of RBPs, we focused on the Pumilio and FBF (PUF) proteins, present in all eukaryotic organisms and controlling a variety of cellular functions. Here, a combined experimental and computational approach was used to design and test 8- and 16-repeat PUF proteins specific for REST mRNA. We explored the conformational properties and atomic features of the PUF-RNA recognition code by Molecular Dynamics simulations. Biochemical assays revealed that the 8- and 16-repeat PUF-based variants specifically bind the endogenous REST mRNA without affecting its translational regulation. The data also indicate a key role of stacking residues in determining the binding specificity. The newly characterized REST-specific PUF-based constructs act as excellent RNA-binding modules and represent a versatile and functional platform to specifically target REST mRNA and modulate its endogenous expression

QSPR modeling for enthalpies of formation of organometallic compounds by means of SMILES-based optimal descriptors

Organometallic compounds are an important class of chemicals, because many of them have vital biochemical features. There are studies on the quantitative structure-property/activity relationships (QSPR/QSAR) for organic substances [1-5], but only a few articles have deal with QSPR for organometallic compounds Simplified molecular input line entry system (SMILES) [9-13] has been used as an alternative for molecular graphs in the QSPR/QSAR analyses SMILES-based optimal descriptors were calculated a

Relaxation properties in classical diamagnetism

It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out