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 study on Poynting effect in brain white matter: A hyperelastic 3D micromechanical model

A novel 3D micromechanical Finite Element Model (FEM) has been developed to depict the Poynting effect in bi-phasic Representative volume element (RVE) with axons embedded in surrounding extra-cellular matrix (ECM) for simulating the brain white matter response under simple and pure shear. In the proposed 3D FEM, nonlinear Ogden hyper-elastic material model describes axons and ECM materials. The modeled bi-phasic RVEs have axons tied to surrounding matrix. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear scenario were simulated. Root mean square deviation (RMSD) were computed for stress and deformation response plots to depict role of axon-ECM orientations & loading condition on the Poynting effect. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane emphasized role of fiber-matrix interactions. At high strains, the stress-strain% plots also indicated modest strain stiffening effects and bending stresses in purely sheared axons

Milnor and Tjurina numbers for an isolated complete intersection singularity

This paper aims to prove that given a isolated complete intersection singularity, the Milnor number will be bounded by a bound depending only on Tjurina number and dimension of the singularity. The proof uses A$\mathfrak{m}$AC (introduced in arXiv:2204.05594) and as with such methods, the bound is purely existential

p493F12 kinase: A novel MAP kinase expressed in a subset of neurons in the human nervous system

AbstractMonoclonal antibody 31712 identifies a cytoplasmic antigen of 49 kDa in human hippocampus and neocortex. The distribution of 31712 immunoreactive neurons closely matches that of Alzheimer's disease (AD) targeted neurons in these areas. In some hippocampal neurons of AD patients, this antigen colocalizes with ALZ-50, indicating the presence of AD pathology in these neurons. Molecular characterization of the 3F12 cDNA revealed it to be a member of the MAP kinase family, showing 43% amino acid sequence identity to human extracellular related kinase 2 (p42mapk). We have confirmed that p493F12 kinase autophosphorylates both threonine and tyrosine residues, as expected for a MAP kinase. The p49 mRNA is expressed exclusively in the nervous system. In the brain, the distribution of these neurons closely corresponds to 31712 antigenbearing neurons. The p493F12 gene maps to the human chromosome 21q21 region, a region that may be important in the pathogenesis of AD and Down's syndrome

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

Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions

Barrier function-based inequality constraints are a means to enforce safety specifications for control systems. When used in conjunction with a convex optimization program, they provide a computationally efficient method to enforce safety for the general class of control-affine systems. One of the main assumptions when taking this approach is the a priori knowledge of the barrier function itself, i.e., knowledge of the safe set. In the context of navigation through unknown environments where the locally safe set evolves with time, such knowledge does not exist. This manuscript focuses on the synthesis of a zeroing barrier function characterizing the safe set based on safe and unsafe sample measurements, e.g., from perception data in navigation applications. Prior work formulated a supervised machine learning algorithm whose solution guaranteed the construction of a zeroing barrier function with specific level-set properties. However, it did not explore the geometry of the neural network design used for the synthesis process. This manuscript describes the specific geometry of the neural network used for zeroing barrier function synthesis, and shows how the network provides the necessary representation for splitting the state space into safe and unsafe regions.Comment: Accepted into American Control Conference (ACC) 202