Optimal General Matchings

Given a graph $G=(V,E)$ and for each vertex $v \in V$ a subset $B(v)$ of the set $\{0,1,\ldots, d_G(v)\}$, where $d_G(v)$ denotes the degree of vertex $v$ in the graph $G$, a $B$-factor of $G$ is any set $F \subseteq E$ such that $d_F(v) \in B(v)$ for each vertex $v$, where $d_F(v)$ denotes the number of edges of $F$ incident to $v$. The general factor problem asks the existence of a $B$-factor in a given graph. A set $B(v)$ is said to have a {\em gap of length} $p$ if there exists a natural number $k \in B(v)$ such that $k+1, \ldots, k+p \notin B(v)$ and $k+p+1 \in B(v)$. Without any restrictions the general factor problem is NP-complete. However, if no set $B(v)$ contains a gap of length greater than $1$, then the problem can be solved in polynomial time and Cornuejols \cite{Cor} presented an algorithm for finding a $B$-factor, if it exists. In this paper we consider a weighted version of the general factor problem, in which each edge has a nonnegative weight and we are interested in finding a $B$-factor of maximum (or minimum) weight. In particular, this version comprises the minimum/maximum cardinality variant of the general factor problem, where we want to find a $B$-factor having a minimum/maximum number of edges. We present an algorithm for the maximum/minimum weight $B$-factor for the case when no set $B(v)$ contains a gap of length greater than $1$. This also yields the first polynomial time algorithm for the maximum/minimum cardinality $B$-factor for this case

A note on linear Sperner families

In an earlier work we described Gr\"obner bases of the ideal of polynomials over a field, which vanish on the set of characteristic vectors $\mathbf{v} \in \{0,1\}^n$ of the complete $d$ unifom set family over the ground set $[n]$. In particular, it turns out that the standard monomials of the above ideal are {\em ballot monomials}. We give here a partial extension of the latter fact. We prove that the lexicographic standard monomials for linear Sperner systems are also ballot monomials. A set family is a linear Sperner system if the characteristic vectors satisfy a linear equation $a_1v_1+\cdots +a_nv_n=k$, where $0<a_q\leq a_2\leq \cdots \leq a_n$ and $k$ are integers. As an application, we confirm a conjecture of Frankl for linear Sperner systems.Comment: 12 page

Tightening slip knots in raw and degummed silk to increase toughness without losing strength

NMP is supported by the European Research Council (ERC StG Ideas 2011 BIHSNAM n. 279985 on “Bio-Inspired hierarchical super-nanomaterials”, ERC PoC 2013-1 REPLICA2 n. 619448 on “Large-area replication of biological anti-adhesive nanosurfaces”, ERC PoC 2013-2 KNOTOUGH n. 632277 on “Super-tough knotted fibres”), by the European Commission under the Graphene Flagship (WP10 “Nanocomposites”, n. 604391) and by the Provincia Autonoma di Trento (“Graphene Nanocomposites”, n. S116/2012-242637 and reg.delib. n. 2266)

The global distribution of the Duffy blood group

Blood group variants are characteristic of population groups, and can show conspicuous geographic patterns. Interest in the global prevalence of the Duffy blood group variants is multidisciplinary, but of particular importance to malariologists due to the resistance generally conferred by the Duffy-negative phenotype against Plasmodium vivax infection. Here we collate an extensive geo-database of surveys, forming the evidence-base for a multi-locus Bayesian geostatistical model to generate global frequency maps of the common Duffy alleles to refine the global cartography of the common Duffy variants. We show that the most prevalent allele globally was FY*A, while across sub-Saharan Africa the predominant allele was the silent FY*BES variant, commonly reaching fixation across stretches of the continent. The maps presented not only represent the first spatially and genetically comprehensive description of variation at this locus, but also constitute an advance towards understanding the transmission patterns of the neglected P. vivax malaria parasite

The European Hematology Association Roadmap for European Hematology Research: a consensus document

The European Hematology Association (EHA) Roadmap for European Hematology Research highlights major achievements in diagnosis and treatment of blood disorders and identifies the greatest unmet clinical and scientific needs in those areas to enable better funded, more focused European hematology research. Initiated by the EHA, around 300 experts contributed to the consensus document, which will help European policy makers, research funders, research organizations, researchers, and patient groups make better informed decisions on hematology research. It also aims to raise public awareness of the burden of blood disorders on European society, which purely in economic terms is estimated at €23 billion per year, a level of cost that is not matched in current European hematology research funding. In recent decades, hematology research has improved our fundamental understanding of the biology of blood disorders, and has improved diagnostics and treatments, sometimes in revolutionary ways. This progress highlights the potential of focused basic research programs such as this EHA Roadmap. The EHA Roadmap identifies nine ‘sections’ in hematology: normal hematopoiesis, malignant lymphoid and myeloid diseases, anemias and related diseases, platelet disorders, blood coagulation and hemostatic disorders, transfusion medicine, infections in hematology, and hematopoietic stem cell transplantation. These sections span 60 smaller groups of diseases or disorders. The EHA Roadmap identifies priorities and needs across the field of hematology, including those to develop targeted therapies based on genomic profiling and chemical biology, to eradicate minimal residual malignant disease, and to develop cellular immunotherapies, combination treatments, gene therapies, hematopoietic stem cell treatments, and treatments that are better tolerated by elderly patients