Maximal induced matchings in triangle-free graphs

An induced matching in a graph is a set of edges whose endpoints induce a $1$-regular subgraph. It is known that any $n$-vertex graph has at most $10^{n/5} \approx 1.5849^n$ maximal induced matchings, and this bound is best possible. We prove that any $n$-vertex triangle-free graph has at most $3^{n/3} \approx 1.4423^n$ maximal induced matchings, and this bound is attained by any disjoint union of copies of the complete bipartite graph $K_{3,3}$. Our result implies that all maximal induced matchings in an $n$-vertex triangle-free graph can be listed in time $O(1.4423^n)$, yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.Comment: 17 page

Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach

In this paper, we study the $k$-forest problem in the model of resource augmentation. In the $k$-forest problem, given an edge-weighted graph $G(V,E)$, a parameter $k$, and a set of $m$ demand pairs $\subseteq V \times V$, the objective is to construct a minimum-cost subgraph that connects at least $k$ demands. The problem is hard to approximate---the best-known approximation ratio is $O(\min\{\sqrt{n}, \sqrt{k}\})$. Furthermore, $k$-forest is as hard to approximate as the notoriously-hard densest $k$-subgraph problem. While the $k$-forest problem is hard to approximate in the worst-case, we show that with the use of resource augmentation, we can efficiently approximate it up to a constant factor. First, we restate the problem in terms of the number of demands that are {\em not} connected. In particular, the objective of the $k$-forest problem can be viewed as to remove at most $m-k$ demands and find a minimum-cost subgraph that connects the remaining demands. We use this perspective of the problem to explain the performance of our algorithm (in terms of the augmentation) in a more intuitive way. Specifically, we present a polynomial-time algorithm for the $k$-forest problem that, for every $\epsilon>0$, removes at most $m-k$ demands and has cost no more than $O(1/\epsilon^{2})$ times the cost of an optimal algorithm that removes at most $(1-\epsilon)(m-k)$ demands

Online unit clustering in higher dimensions

We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of $n$ points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters (subsets) of diameter at most one; while Unit Covering asks to cover all points by the minimum number of balls of unit radius. In this paper, we work in $\mathbb{R}^d$ using the $L_\infty$ norm. We show that the competitive ratio of any online algorithm (deterministic or randomized) for Unit Clustering must depend on the dimension $d$. We also give a randomized online algorithm with competitive ratio $O(d^2)$ for Unit Clustering}of integer points (i.e., points in $\mathbb{Z}^d$, $d\in \mathbb{N}$, under $L_{\infty}$ norm). We show that the competitive ratio of any deterministic online algorithm for Unit Covering is at least $2^d$. This ratio is the best possible, as it can be attained by a simple deterministic algorithm that assigns points to a predefined set of unit cubes. We complement these results with some additional lower bounds for related problems in higher dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

A Quantum Scattering Interferometer

The collision of two ultra-cold atoms results in a quantum-mechanical superposition of two outcomes: each atom continues without scattering and each atom scatters as a spherically outgoing wave with an s-wave phase shift. The magnitude of the s-wave phase shift depends very sensitively on the interaction between the atoms. Quantum scattering and the underlying phase shifts are vitally important in many areas of contemporary atomic physics, including Bose-Einstein condensates, degenerate Fermi gases, frequency shifts in atomic clocks, and magnetically-tuned Feshbach resonances. Precise measurements of quantum scattering phase shifts have not been possible until now because, in scattering experiments, the number of scattered atoms depends on the s-wave phase shifts as well as the atomic density, which cannot be measured precisely. Here we demonstrate a fundamentally new type of scattering experiment that interferometrically detects the quantum scattering phase shifts of individual atoms. By performing an atomic clock measurement using only the scattered part of each atom, we directly and precisely measure the difference of the s-wave phase shifts for the two clock states in a density independent manner. Our method will give the most direct and precise measurements of ultracold atom-atom interactions and will place stringent limits on the time variations of fundamental constants.Comment: Corrected formatting and typo

Asymmetry to symmetry transition of Fano line-shape: Analytical derivation

An analytical derivation of Fano line-shape asymmetry ratio has been presented here for a general case. It is shown that Fano line-shape becomes less asymmetric as \q is increased and finally becomes completely symmetric in the limiting condition of q equal to infinity. Asymmetry ratios of Fano line-shapes have been calculated and are found to be in good consonance with the reported expressions for asymmetry ratio as a function of Fano parameter. Application of this derivation is also mentioned for explanation of asymmetry to symmetry transition of Fano line-shape in quantum confined silicon nanostructures.Comment: 3 figures, Latex files, Theoretica

Tribological properties of room temperature fluorinated graphite heat-treated under fluorine atmosphere

This work is concerned with the study of the tribologic properties of room temperature fluorinated graphite heat-treated under fluorine atmosphere. The fluorinated compounds all present good intrinsic friction properties (friction coefficient in the range 0.05–0.09). The tribologic performances are optimized if the materials present remaining graphitic domains (influenced by the presence of intercalated fluorinated species) whereas the perfluorinated compounds, where the fluorocarbon layers are corrugated (armchair configuration of the saturated carbon rings) present higher friction coefficients. Raman analyses reveal that the friction process induces severe changes in the materials structure especially the partial re-building of graphitic domains in the case of perfluorinated compounds which explains the improvement of μ during the friction tests for these last materials

Airflow Dynamics of Human Jets: Sneezing and Breathing - Potential Sources of Infectious Aerosols

10.1371/journal.pone.0059970PLoS ONE84

Identification and optimization of small molecule antagonists of vasoactive intestinal peptide receptor-1 (VIPR1)

Identification, synthesis and structure-activity relationship of small-molecule VIPR1 antagonists encompassing two chemical series are described

Biopsy confirmation of metastatic sites in breast cancer patients:clinical impact and future perspectives

Determination of hormone receptor (estrogen receptor and progesterone receptor) and human epidermal growth factor receptor 2 status in the primary tumor is clinically relevant to define breast cancer subtypes, clinical outcome,and the choice of therapy. Retrospective and prospective studies suggest that there is substantial discordance in receptor status between primary and recurrent breast cancer. Despite this evidence and current recommendations,the acquisition of tissue from metastatic deposits is not routine practice. As a consequence, therapeutic decisions for treatment in the metastatic setting are based on the features of the primary tumor. Reasons for this attitude include the invasiveness of the procedure and the unreliable outcome of biopsy, in particular for biopsies of lesions at complex visceral sites. Improvements in interventional radiology techniques mean that most metastatic sites are now accessible by minimally invasive methods, including surgery. In our opinion, since biopsies are diagnostic and changes in biological features between the primary and secondary tumors can occur, the routine biopsy of metastatic disease needs to be performed. In this review, we discuss the rationale for biopsy of suspected breast cancer metastases, review issues and caveats surrounding discordance of biomarker status between primary and metastatic tumors, and provide insights for deciding when to perform biopsy of suspected metastases and which one (s) to biopsy. We also speculate on the future translational implications for biopsy of suspected metastatic lesions in the context of clinical trials and the establishment of bio-banks of biopsy material taken from metastatic sites. We believe that such bio-banks will be important for exploring mechanisms of metastasis. In the future,advances in targeted therapy will depend on the availability of metastatic tissue

Structure of the hDmc1-ssDNA filament reveals the principles of its architecture

In eukaryotes, meiotic recombination is a major source of genetic diversity, but its defects in humans lead to abnormalities such as Down's, Klinefelter's and other syndromes. Human Dmc1 (hDmc1), a RecA/Rad51 homologue, is a recombinase that plays a crucial role in faithful chromosome segregation during meiosis. The initial step of homologous recombination occurs when hDmc1 forms a filament on single-stranded (ss) DNA. However the structure of this presynaptic complex filament for hDmc1 remains unknown. To compare hDmc1-ssDNA complexes to those known for the RecA/Rad51 family we have obtained electron microscopy (EM) structures of hDmc1-ssDNA nucleoprotein filaments using single particle approach. The EM maps were analysed by docking crystal structures of Dmc1, Rad51, RadA, RecA and DNA. To fully characterise hDmc1-DNA complexes we have analysed their organisation in the presence of Ca2+, Mg2+, ATP, AMP-PNP, ssDNA and dsDNA. The 3D EM structures of the hDmc1-ssDNA filaments allowed us to elucidate the principles of their internal architecture. Similar to the RecA/Rad51 family, hDmc1 forms helical filaments on ssDNA in two states: extended (active) and compressed (inactive). However, in contrast to the RecA/Rad51 family, and the recently reported structure of hDmc1-double stranded (ds) DNA nucleoprotein filaments, the extended (active) state of the hDmc1 filament formed on ssDNA has nine protomers per helical turn, instead of the conventional six, resulting in one protomer covering two nucleotides instead of three. The control reconstruction of the hDmc1-dsDNA filament revealed 6.4 protein subunits per helical turn indicating that the filament organisation varies depending on the DNA templates. Our structural analysis has also revealed that the N-terminal domain of hDmc1 accomplishes its important role in complex formation through domain swapping between adjacent protomers, thus providing a mechanistic basis for coordinated action of hDmc1 protomers during meiotic recombination