Incremental subgradient method for nonsmooth convex optimization with fixed point constraints

This paper proposes an incremental subgradient method for solving the problem of minimizing the sum of nondifferentiable, convex objective functions over the intersection of fixed point sets of nonexpansive mappings in a real Hilbert space. The proposed algorithm can work in nonsmooth optimization over constraint sets onto which projections cannot be always implemented, whereas the conventional incremental subgradient method can be applied only when a constraint set is simple in the sense that the projection onto it can be easily implemented. We first study its convergence for a constant step size. The analysis indicates that there is a possibility that the algorithm with a small constant step size approximates a solution to the problem. Next, we study its convergence for a diminishing step size and show that there exists a subsequence of the sequence generated by the algorithm which weakly converges to a solution to the problem. Moreover, we show the whole sequence generated by the algorithm with a diminishing step size strongly converges to the solution to the problem under certain assumptions. We also give examples of real applied problems which satisfy the assumptions in the convergence theorems and numerical examples to support the convergence analyses.     

Fast local image inpainting based on the Allen–Cahn model

In this paper, we propose a fast local image inpainting algorithm based on the Allen–Cahn model. The proposed algorithm is applied only on the inpainting domain and has two features. The first feature is that the pixel values in the inpainting domain are obtained by curvature-driven diffusions and utilizing the image information from the outside of the inpainting region. The second feature is that the pixel values outside of the inpainting region are the same as those in the original input image since we do not compute the outside of the inpainting region. Thus the proposed method is computationally efficient. We split the governing equation into one linear equation and one nonlinear equation by using an operator splitting technique. The linear equation is discretized by using a fully implicit scheme and the nonlinear equation is solved analytically. We prove the unconditional stability of the proposed scheme. To demonstrate the robustness and accuracy of the proposed method, various numerical results on real and synthetic images are presented.     

Relationship between crystallinity and device characteristics of In‐Sn‐Zn oxide

We have reported that the transistors having the c‐axis‐aligned crystalline (CAAC) In‐Ga‐Zn oxide (IGZO) show good performance. Recently, In‐Sn‐Zn Oxide (ITZO) has attracted much attention because of its high electron mobility, as well as IGZO. However, it has been reported that ITZO field effect transistors (FET) tend to have positive Vth (normally‐on characteristics) and poor reliability compared with IGZO‐FETs. We have reported that high‐performance and high‐reliability OS‐FETs can be fabricated by using CAAC‐IGZO, which has high crystallinity and has no clear grain boundaries, as an active layer. Therefore, we have fabricated CAAC‐ITZO thin films to improve performance of ITZO‐FETs by using CAAC‐ITZO as an active layer. In addition, FETs employing CAAC‐ITZO have better characteristics and reliability than FETs using nano‐crystal ITZO. Furthermore, constant photocurrent method (CPM) measurement was carried out in order to estimate density of deep‐level defect states caused by oxygen vacancies in oxide semiconductors. The results show that CAAC‐ITZO has lower density of deep‐level defect states than nano‐crystal ITZO. We attribute the improvement in reliability of ITZO‐FETs to a decrease in deep‐level defect states of an ITZO active layer, as is the case with IGZO.     

Continuum electrostatic approach for evaluating positions and interactions of proteins in a bilayer membrane

Orientations of proteins in the membranes are crucial to their function and stability. Unfortunately the exact positions of these proteins in the lipid bilayer are mostly undetermined. Here, the spatial orientation of membrane proteins within the lipid membrane was evaluated using a Poisson–Boltzmann solvent continuum approach to calculate the electrostatic free energy of the protein solvation at various orientations in an implicit bilayer. The solvation energy was obtained by computing the difference in electrostatic energies of the protein in water and in lipid/water environments, treating each as an implicit solvent model. The optimal position of transmembrane proteins (TMP) in a lipid bilayer is identified by the minimum in the “downhill” pathway of the solvation energy landscape. The energy landscape pattern was considerably conserved in various TMP classes. Evaluation of the position of 1060 membrane proteins from the orientations of proteins in membranes (OPM) database revealed that most of the polytopic and β-barrel proteins were in good agreement with those of the OPM database. The study provides a useful scheme for estimating the membrane solvation energy made by lipid-exposed amino acids in membrane proteins. In addition, our results tested with the bacterial potassium channel model demonstrated the potential usefulness of the approach in assessing the quality of membrane protein models. The present approach should be applicable for constructing transmembrane proteins–lipid configuration suitable for membrane protein simulations and will have utility for the structural modeling of membrane proteins.     

Molecular interaction networks in the analyses of sequence variation and proteomics data

Protein–protein interaction networks are typically generated in standard cell lines or model organisms as it is prohibitively difficult to record large interaction datasets from specific tissues or disease models at a reasonable pace. Although the interaction data are of high confidence, they thus do not reflect in vivo relationships as such. A wealth of physiologically relevant protein information, obtained under different conditions and from different systems, is available including information on genetic variation, protein levels, and PTMs. However, these data are difficult to assess comprehensively because the relationships between the entities remain elusive from the measurements. Here, we exemplarily highlight recent studies that gained deeper insight from genetic variation, protein, and PTM measurements using interaction information pointing toward the importance and potential of interaction networks for the interpretation of sequencing and proteomics data.     

Adaptive detection of range-spread targets without secondary data in multichannel autoregressive process

Adaptive detection of range-spread targets without secondary data is addressed in a multichannel autoregressive Gaussian disturbance with unknown space–time covariance matrix, by utilizing the Rao test. The proposed Rao test without secondary data is theoretically proved to be asymptotically (large-sample in the number of temporal observations) constant false alarm rate with respect to unknown space–time covariance matrix, thanks to an asymptotic equivalence between the Rao test and the generalized likelihood ratio test. Moreover, the performance loss due to no secondary data can be remedied by appropriately increasing the temporal dimension. The performance assessment conducted by Monte Carlo simulation, also in comparison with the existing detector without secondary data, confirms the effectiveness of the proposed detectors.     

An impulse control approach to dike height optimization

This paper determines the optimal timing of dike heightenings as well as the corresponding optimal dike heightenings to protect against floods. To derive the optimal policy, we design an algorithm based on the Impulse Control Maximum Principle. In this way, this paper presents one of the first real-life applications of the Impulse Control Maximum Principle developed by Blaquière. We show that the proposed impulse control (IC) approach performs better than dynamic programming with respect to computational time. This is caused by the fact that IC does not need discretization in time.