Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Accurate Determination of Conformational Transitions in Oligomeric Membrane Proteins

The structural dynamics governing collective motions in oligomeric membrane proteins play key roles in vital biomolecular processes at cellular membranes. In this study, we present a structural refinement approach that combines solid-state NMR experiments and molecular simulations to accurately describe concerted conformational transitions identifying the overall structural, dynamical, and topological states of oligomeric membrane proteins. The accuracy of the structural ensembles generated with this method is shown to reach the statistical error limit, and is further demonstrated by correctly reproducing orthogonal NMR data. We demonstrate the accuracy of this approach by characterising the pentameric state of phospholamban, a key player in the regulation of calcium uptake in the sarcoplasmic reticulum, and by probing its dynamical activation upon phosphorylation. Our results underline the importance of using an ensemble approach to characterise the conformational transitions that are often responsible for the biological function of oligomeric membrane protein states

Modulation of galactic protons in the heliosphere during the unusual solar minimum of 2006 to 2009

The last solar minimum activity period, and the consequent minimum modulation conditions for cosmic rays, was unusual. The highest levels of galactic protons were recorded at Earth in late 2009 in contrast to expectations. Proton spectra observed for 2006 to 2009 from the PAMELA cosmic ray detector on-board the Resurs-DK1 satellite are presented together with the solutions of a comprehensive numerical model for the solar modulation of cosmic rays. The model is used to determine what mechanisms were mainly responsible for the modulation of protons during this period, and why the observed spectrum for 2009 was the highest ever recorded. From mid-2006 until December 2009 we find that the spectra became significantly softer because increasingly more low energy protons had reached Earth. To simulate this effect, the rigidity dependence of the diffusion coefficients had to decrease significantly below ~3 GeV. The modulation minimum period of 2009 can thus be described as relatively more "diffusion dominated" than previous solar minima. However, we illustrate that drifts still had played a significant role but that the observable modulation effects were not as well correlated with the waviness of the heliospheric current sheet as before. Protons still experienced global gradient and curvature drifts as the heliospheric magnetic field had decreased significantly until the end of 2009, in contrast to the moderate decreases observed during previous minimum periods. We conclude that all modulation processes contributed to the observed increases in the proton spectra for this period, exhibiting an intriguing interplay of these major mechanisms

Short and highly efficient synthetic promoters for melanoma-specific gene expression.

Here, we report the construction and functional analysis of synthetic promoters designed for gene therapy applications requiring strong and specific gene expression in melanoma cell lines. We have analysed the transcriptional activity of different combinations of two transcriptional regulatory modules, a melanocyte-specific element from the human tyrosinase promoter and a cell-cycle-specific element from the human alpha-fetoprotein promoter. Transient expression assays in different cell lines show that several of these composite synthetic promoters can drive a strong and selective expression of a reporter gene in melanoma cell, providing us with a new powerful tool for gene therapy of melanomas

Cartoon-texture evolution for two-region image segmentation

Two-region image segmentation is the process of dividing an image into two regions of interest, i.e., the foreground and the background. To this aim, Chan et al. (SIAM J Appl Math 66(5):1632–1648, 2006) designed a model well suited for smooth images. One drawback of this model is that it may produce a bad segmentation when the image contains oscillatory components. Based on a cartoon-texture decomposition of the image to be segmented, we propose a new model that is able to produce an accurate segmentation of images also containing noise or oscillatory information like texture. The novel model leads to a non-smooth constrained optimization problem which we solve by means of the ADMM method. The convergence of the numerical scheme is also proved. Several experiments on smooth, noisy, and textural images show the effectiveness of the proposed model

Quantum limit of photothermal cooling

We study the problem of cooling a mechanical oscillator using the photothermal (bolometric) force. Contrary to previous attempts to model this system, we take into account the noise effects due to the granular nature of photon absorption. This allows us to tackle the cooling problem down to the noise dominated regime and to find reasonable estimates for the lowest achievable phonon occupation in the cantilever

Guidelines for e-Startup Promotion Strategy

Startup businesses have always played an important role in the global economy, but recently their importance has grown significantly. For this reason, governments around the world have amended regulation and created incentives to encourage their development. However, statistics show that startups have an extremely high mortality rate, often due to a lack of strategic planning, wrong marketing investments or inefficient resource allocation. The purpose of this paper is to propose a decision-driven tool which will enable the creation of a successful promotional strategy. The proposed strategy is a three-stage process allowing startups to gradually eliminate non-optimal advertising formats. The first stage focuses on the analysis of the e-market where the startup operates. The second stage is dedicated to the economic environment that the new company will face relative to its available resources. Its aim is to reject overly expensive advertising formats by linking costs to availability of funds. The third and last stage is a cost effectiveness analysis, allowing the entrepreneur to identify the best advertising formats and using an impact-factor as a proxy of effectiveness. The proposed methodology has been applied to the case of an Italian early-stage startup for validatio

On the continuum limit of epidemiological models on graphs: convergence and approximation results

We focus on an epidemiological model (the archetypical SIR system) defined on graphs and study the asymptotic behavior of the solutions as the number of vertices in the graph diverges. By relying on the theory of so called graphons we provide a characterization of the limit and establish convergence results. We also provide approximation results for both deterministic and random discretizations.Comment: 30 pages, 1 figur