Inexact accelerated high-order proximal-point methods

In this paper, we present a new framework of bi-level unconstrained minimization for development of accelerated methods in Convex Programming. These methods use approximations of the high-order proximal points, which are solutions of some auxiliary parametric optimization problems. For computing these points, we can use different methods, and, in particular, the lower-order schemes. This opens a possibility for the latter methods to overpass traditional limits of the Complexity Theory. As an example, we obtain a new second-order method with the convergence rate $$O\left( k^{-4}\right) $$ O k - 4 , where k is the iteration counter. This rate is better than the maximal possible rate of convergence for this type of methods, as applied to functions with Lipschitz continuous Hessian. We also present new methods with the exact auxiliary search procedure, which have the rate of convergence $$O\left( k^{-(3p+1)/ 2}\right) $$ O k - ( 3 p + 1 ) / 2 , where $$p \ge 1$$ p ≥ 1 is the order of the proximal operator. The auxiliary problem at each iteration of these schemes is convex.

Inexact Distributed Reconstruction via Alternating Direction Method

Total variation (TV)-based CT image reconstruction has been shown to be experimentally capable of producing accurate reconstructions from sparse-view data. In this study, an inexact distributed reconstruction algorithm based on TV minimization has been developed. The algorithm is relatively simple as it uses the inexact alternating direction method, which involves linearization and proximal points techniques. The outstanding acceleration factor is achieved as the algorithm distributes the data and computation to individual nodes. Experimental results demonstrate that the proposed method can accelerate the alternating direction total variation minimization (ADTVM) algorithm with very little accuracy loss.

Reevaluation of Factors Affecting Bunch Drop in Date Palm

Severe damage has been observed in Israeli date palm (Phoenix dactylifera L.) plantations of the Medjool cultivar as a result of drying and dropping of fruit bunches. Both fractures and rot occurred during peduncle (fruit stalk) development at proximal points located deep within the crown. The phenomenon has been previously described as “cross–cut” or “V-cut.” The present study aimed to characterize the phenomenon and identify the main causal factors. Annual surveys have revealed high levels of fruit bunch drop in all ‘Medjool’ cultivation areas in Israel. Arenipses sabella and other insects were only occasionally detected in the damaged fruit stalks. Similar damage levels observed in insecticide-treated and untreated plots suggested that insects were not directly responsible for this phenomenon. Tissue decay was detected in many of the freshly fallen fruit stalks. The pathogenic fungus, Fusarium proliferatum, was detected in most of the necrotic fruit stalks. Fusarium proliferatum isolates from infected fruit stalks generated necrotic lesions in fruit stalk tissue in vitro. However, fungicide treatments on trees in the orchards were ineffective in reducing bunch drop. On the other hand, restraining the growth rate of the fruit stalk, by reducing irrigation levels (to 20%) during the period of fruit stalk development and growth, significantly reduced bunch drop levels in most of the examined plots. These data suggest that bunch drop in ‘Medjool’ date palm is caused mainly by physiological disorders related to fruit stalk development and growth.

Rotational Speed Control by Optical PWM Operation for Single Cells

To rotating single cells, we harness light pressure generated by light absorption as a rotating torque, illuminating the two proximal points from different directions using two beams. Rotational speed is controlled by optical pulse width modulation (PWM) that controls the amount of light received per unit of time by controlling the time of illumination. To change the illumination time, the pencil of rays is scanned by a galvanometric mirror.