(Total) Vector Domination for Graphs with Bounded Branchwidth

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has at least $d(v)$ neighbors in $S$. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the $k$-tuple dominating set problem (this $k$ is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respectto $k$, where $k$ is the size of solution.Comment: 16 page

Influence Diffusion in Social Networks under Time Window Constraints

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network $G=(V,E)$, an integer value $t(v)$ for each node $v\in V$, and a time window size $\lambda$. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node $v$ becomes influenced if the number of its neighbors that have been influenced in the previous $\lambda$ rounds is greater than or equal to $t(v)$. We prove that the problem of finding a minimum cardinality target set that influences the whole network $G$ is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared in: Proceedings of 20th International Colloquium on Structural Information and Communication Complexity (Sirocco 2013), Lectures Notes in Computer Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201

Lentiviral gene therapy corrects platelet phenotype and function in patients with Wiskott-Aldrich syndrome

BACKGROUND: Thrombocytopenia is a serious issue for all patients with classical Wiskott-Aldrich syndrome (WAS) and X-linked thrombocytopenia (XLT) because it causes severe and life-threatening bleeding. Lentiviral gene therapy (GT) for WAS has shown promising results in terms of immune reconstitution. However, despite the reduced severity and frequency of bleeding events, platelet counts remain low in GT-treated patients. OBJECTIVE: We carefully investigated platelet defects in terms of phenotype and function in untreated patients with WAS and assessed the effect of GT treatment on platelet dysfunction. METHODS: We analyzed a cohort of 20 patients with WAS/XLT, 15 of them receiving GT. Platelet phenotype and function were analyzed by using electron microscopy, flow cytometry, and an aggregation assay. Platelet protein composition was assessed before and after GT by means of proteomic profile analysis. RESULTS: We show that platelets from untreated patients with WAS have reduced size, abnormal ultrastructure, and a hyperactivated phenotype at steady state, whereas activation and aggregation responses to agonists are decreased. GT restores platelet size and function early after treatment and reduces the hyperactivated phenotype proportionally to WAS protein expression and length of follow-up. CONCLUSIONS: Our study highlights the coexistence of morphologic and multiple functional defects in platelets lacking WAS protein and demonstrates that GT normalizes the platelet proteomic profile with consequent restoration of platelet ultrastructure and phenotype, which might explain the observed reduction of bleeding episodes after GT. These results are instrumental also from the perspective of a future clinical trial in patients with XLT only presenting with microthrombocytopenia

Two examples of minimal Cheeger sets in the plane

We construct two minimal Cheeger sets in the Euclidean plane, i.e., unique minimizers of the ratio \u201cperimeter over area\u201d among their own measurable subsets. The first one gives a counterexample to the so- called weak regularity property of Cheeger sets, as its perimeter does not coincide with the 1-dimensional Hausdorff measure of its topological boundary. The second one is a kind of porous set, whose boundary is not locally a graph at many of its points, yet it is a weakly regular open set admitting a unique (up to vertical translations) nonparametric solution to the prescribed mean curvature equation, in the extremal case corresponding to the capillarity for perfectly wetting fluids in zero gravity

Clinical, immunological, and molecular features of typical and atypical severe combined immunodeficiency: Report of the italian primary immunodeficiency network

Severe combined immunodeficiencies (SCIDs) are a group of inborn errors of the immune system, usually associated with severe or life-threatening infections. Due to the variability of clinical phenotypes, the diagnostic complexity and the heterogeneity of the genetic basis, they are often difficult to recognize, leading to a significant diagnostic delay (DD). Aim of this study is to define presenting signs and natural history of SCID in a large cohort of patients, prior to hematopoietic stem cell or gene therapies. To this purpose, we conducted a 30-year retro-prospective multicenter study within the Italian Primary Immunodeficiency Network. One hundred eleven patients, diagnosed as typical or atypical SCID according to the European Society for Immune Deficiencies criteria, were included. Patients were subsequently classified based on the genetic alteration, pathogenic mechanism and immunological classification. A positive relationship between the age at onset and the DD was found. SCID patients with later onset were identified only in the last decade of observation. Syndromic SCIDs represented 28% of the cohort. Eight percent of the subjects were diagnosed in Intensive Care Units. Fifty-three percent had an atypical phenotype and most of them exhibited a discordant genotype-immunophenotype. Pre-treatment mortality was higher in atypical and syndromic patients. Our study broadens the knowledge of clinical and laboratory manifestations and genotype/phenotype correlation in patients with SCID and may facilitate the diagnosis of both typical and atypical forms of the disease in countries where newborn screening programs have not yet been implemented

Lentiviral Hematopoietic Stem Cell Gene Therapy in Patients with Wiskott-Aldrich Syndrome.

iskott-Aldrich syndrome (WAS) is an inherited immunodeficiency caused by mutations in the gene encoding WASP, a protein regulating the cytoskeleton. Hematopoietic stem/progenitor cell (HSPC) transplants can be curative, but, when matched donors are unavailable, infusion of autologous HSPCs modified ex vivo by gene therapy is an alternative approach. We used a lentiviral vector encoding functional WASP to genetically correct HSPCs from three WAS patients and reinfused the cells after a reduced-intensity conditioning regimen. All three patients showed stable engraftment of WASP-expressing cells and improvements in platelet counts, immune functions, and clinical scores. Vector integration analyses revealed highly polyclonal and multilineage haematopoiesis resulting from the gene-corrected HSPCs. Lentiviral gene therapy did not induce selection of integrations near oncogenes, and no aberrant clonal expansion was observed after 20 to 32 months. Although extended clinical observation is required to establish long-term safety, lentiviral gene therapy represents a promising treatment for WAS

Hematopoietic Cell Transplantation Cures Adenosine Deaminase 2 Deficiency: Report on 30 Patients

PURPOSE: Deficiency of adenosine deaminase 2 (DADA2) is an inherited inborn error of immunity, characterized by autoinflammation (recurrent fever), vasculopathy (livedo racemosa, polyarteritis nodosa, lacunar ischemic strokes, and intracranial hemorrhages), immunodeficiency, lymphoproliferation, immune cytopenias, and bone marrow failure (BMF). Tumor necrosis factor (TNF-α) blockade is the treatment of choice for the vasculopathy, but often fails to reverse refractory cytopenia. We aimed to study the outcome of hematopoietic cell transplantation (HCT) in patients with DADA2. METHODS: We conducted a retrospective study on the outcome of HCT in patients with DADA2. The primary outcome was overall survival (OS). RESULTS: Thirty DADA2 patients from 12 countries received a total of 38 HCTs. The indications for HCT were BMF, immune cytopenia, malignancy, or immunodeficiency. Median age at HCT was 9 years (range: 2-28 years). The conditioning regimens for the final transplants were myeloablative (n = 20), reduced intensity (n = 8), or non-myeloablative (n = 2). Donors were HLA-matched related (n = 4), HLA-matched unrelated (n = 16), HLA-haploidentical (n = 2), or HLA-mismatched unrelated (n = 8). After a median follow-up of 2 years (range: 0.5-16 years), 2-year OS was 97%, and 2-year GvHD-free relapse-free survival was 73%. The hematological and immunological phenotypes resolved, and there were no new vascular events. Plasma ADA2 enzyme activity normalized in 16/17 patients tested. Six patients required more than one HCT. CONCLUSION: HCT was an effective treatment for DADA2, successfully reversing the refractory cytopenia, as well as the vasculopathy and immunodeficiency. CLINICAL IMPLICATIONS: HCT is a definitive cure for DADA2 with > 95% survival