Approximating Minimum Cost Connectivity Orientation and Augmentation

We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph $G$ that admits an orientation covering a nonnegative crossing $G$-supermodular demand function, as defined by Frank. An important example is $(k,\ell)$-edge-connectivity, a common generalization of global and rooted edge-connectivity. Our algorithm is based on a non-standard application of the iterative rounding method. We observe that the standard linear program with cut constraints is not amenable and use an alternative linear program with partition and co-partition constraints instead. The proof requires a new type of uncrossing technique on partitions and co-partitions. We also consider the problem setting when the cost of an edge can be different for the two possible orientations. The problem becomes substantially more difficult already for the simpler requirement of $k$-edge-connectivity. Khanna, Naor, and Shepherd showed that the integrality gap of the natural linear program is at most $4$ when $k=1$ and conjectured that it is constant for all fixed $k$. We disprove this conjecture by showing an $\Omega(|V|)$ integrality gap even when $k=2$

How good is the orthopaedic literature?

Randomized trials constitute approximately 3% of the orthopaedic literature Concerns regarding quality of the orthopaedic literature stem from a widespread notion that the overall quality of the surgical literature is in need of improvement. Limitations in surgical research arises primarily from two pervasive issues: 1) A reliance on low levels of evidence to advance surgical knowledge, and 2) Poor reporting quality among the high level surgical evidence that is available. The scarcity of randomized trials may be largely attributable to several unique challenges which make them difficult to conduct. We present characteristics of the orthopaedic literature and address the challenges of conducting randomized trials in surgery

Vortices in Superfluid Fermi Gases through the BEC to BCS Crossover

We have analyzed a single vortex at T=0 in a 3D superfluid atomic Fermi gas across a Feshbach resonance. On the BCS side, the order parameter varies on two scales: $k_{F}^{-1}$ and the coherence length $\xi$, while only variation on the scale of $\xi$ is seen away from the BCS limit. The circulating current has a peak value $j_{max}$ which is a non-monotonic function of $1/k_F a_s$ implying a maximum critical velocity $\sim v_F$ at unitarity. The number of fermionic bound states in the core decreases as we move from the BCS to BEC regime. Remarkably, a bound state branch persists even on the BEC side reflecting the composite nature of bosonic molecules.Comment: 4 Pages, 4 Figure

A bioinformatics approach to microRNA-sequencing analysis

The rapid expansion of Next Generation Sequencing (NGS) data availability has made exploration of appropriate bioinformatics analysis pipelines a timely issue. Since there are multiple tools and combinations thereof to analyze any dataset, there can be uncertainty in how to best perform an analysis in a robust and reproducible manner. This is especially true for newer omics applications, such as miRNomics, or microRNA-sequencing (miRNA-sequencing). As compared to transcriptomics, there have been far fewer miRNA-sequencing studies performed to date, and those that are reported seldom provide detailed description of the bioinformatics analysis, including aspects such as Unique Molecular Identifiers (UMIs). In this article, we attempt to fill the gap and help researchers understand their miRNA-sequencing data and its analysis. This article will specifically discuss a customizable miRNA bioinformatics pipeline that was developed using miRNA-sequencing datasets generated from human osteoarthritis plasma samples. We describe quality assessment of raw sequencing data files, reference-based alignment, counts generation for miRNA expression levels, and novel miRNA discovery. This report is expected to improve clarity and reproducibility of the bioinformatics portion of miRNA-sequencing analysis, applicable across any sample type, to promote sharing of detailed protocols in the NGS field