Prediction bounds for higher order total variation regularized least squares

We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of $(k-1)^{\rm th}$ order differences. Our approach is based on combining a general oracle inequality for the $\ell_1$-penalized least squares estimator with "interpolating vectors" to upper-bound the "effective sparsity". This allows one to show that the $\ell_1$-penalty on the $k^{\text{th}}$ order differences leads to an estimator that can adapt to the number of jumps in the $(k-1)^{\text{th}}$ order differences of the underlying signal or an approximation thereof. We show the result for $k \in \{1,2,3,4\}$ and indicate how it could be derived for general $k\in \mathbb{N}$.Comment: 28 page

On the total variation regularized estimator over a class of tree graphs

We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs. As a side result, we get insights into the irrepresentable condition for such tree graphs.Comment: 42 page

Antibody Complementarity-Determining Regions (CDRs): A Bridge between Adaptive and Innate Immunity

Background: It has been documented that, independently from the specificity of the native antibody (Ab) for a given antigen (Ag), complementarity determining regions (CDR)-related peptides may display differential antimicrobial, antiviral and antitumor activities. Methodology/Principal Findings: In this study we demonstrate that a synthetic peptide with sequence identical to VHCDR3 of a mouse monoclonal Ab (mAb) specific for difucosyl human blood group A is easily taken up by macrophages with subsequent stimulation of: i) proinflammatory cytokine production; ii) PI3K-Akt pathway and iii) TLR-4 expression. Significantly, V HCDR3 exerts therapeutic effect against systemic candidiasis without possessing direct candidacidal properties. Conclusions/Significance: These results open a new scenario about the possibility that, beyond the half life of immunoglobulins, Ab fragments may effectively influence the antiinfective cellular immune response in a way reminiscen

TiO2@BSA nano-composites investigated through orthogonal multi-techniques characterization platform.

Abstract Biocompatible coating based on bovine serum albumin (BSA) was applied on two different TiO2 nanoparticles (aeroxide P25 and food grade E171) to investigate properties and stability of resulting TiO2@BSA composites, under the final perspective to create a "Safe-by-Design" coating, able to uniform, level off and mitigate surface chemistry related phenomena, as naturally occurring when nano-phases come in touch with proteins enriched biological fluids. The first step towards validating the proposed approach is a detailed characterization of surface chemistry with the quantification of amount and stability of BSA coating deposited on nanoparticles' surfaces. At this purpose, we implemented an orthogonal multi-techniques characterization platform, providing important information on colloidal behavior, particle size distribution and BSA-coating structure of investigated TiO2 systems. Specifically, the proposed orthogonal approach enabled the quantitative determination of bound and free (not adsorbed) BSA, a key aspect for the design of intentionally BSA coated nano-structures, in nanomedicine and, overall, for the control of nano-surface reactivity. In fact, the BSA-coating strategy developed and the orthogonal characterisation performed can be extended to different designed nanomaterials in order to further investigate the protein-corona formation and promote the implementation of BSA engineered coating as a strategy to harmonize the surface reactivity and minimize the biological impact

Adaptive rates for total variation image denoising

We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised images that are piecewise constant on rectangular sets. We prove that, if the true image is piecewise constant on just a few rectangular sets, the denoised image converges to the true image at a parametric rate, up to a log factor. More generally, we show that the denoised image enjoys oracle properties, that is, it is almost as good as if some aspects of the true image were known. In other words, image denoising with total variation regularization leads to an adaptive reconstruction of the true image. (© 2020 Microtome Publishing)ISSN:1532-4435ISSN:1533-792

Prediction bounds for higher order total variation regularized least squares

We establish adaptive results for trend filtering: least squares estimation with a penalty on the total variation of $(k-1)^{\rm th}$ order differences. Our approach is based on combining a general oracle inequality for the $\ell_1$-penalized least squares estimator with "interpolating vectors" to upper-bound the "effective sparsity". This allows one to show that the $\ell_1$-penalty on the $k^{\text{th}}$ order differences leads to an estimator that can adapt to the number of jumps in the $(k-1)^{\text{th}}$ order differences of the underlying signal or an approximation thereof. We show the result for $k \in \{1,2,3,4\}$ and indicate how it could be derived for general $k\in \mathbb{N}$

On the total variation regularized estimator over a class of tree graphs

We generalize to tree graphs obtained by connecting path graphs an oracle result obtained for the Fused Lasso over the path graph. Moreover we show that it is possible to substitute in the oracle inequality the minimum of the distances between jumps by their harmonic mean. In doing so we prove a lower bound on the compatibility constant for the total variation penalty. Our analysis leverages insights obtained for the path graph with one branch to understand the case of more general tree graphs. As a side result, we get insights into the irrepresentable condition for such tree graphs.ISSN:1935-752