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

Ginseng for erectile dysfunction

BACKGROUND: Dietary supplements with ginseng, or ginseng alone, are widely used for a broad range of conditions, including erectile dysfunction. Ginseng is particularly popular in Asian countries. Individual studies assessing its effects are mostly small, of uneven methodological quality and have unclear results. OBJECTIVES: To assess the effects of ginseng on erectile dysfunction. SEARCH METHODS: We conducted systematic searches on multiple electronic databases, including CENTRAL, MEDLINE, Embase, CINAHL, AMED, and loco-regional databases of east Asia, from their inceptions to 30 January 2021 without restrictions on language and publication status. Handsearches included conference proceedings. SELECTION CRITERIA: We included randomized or quasi-randomized controlled trials that evaluated the use of any type of ginseng as a treatment for erectile dysfunction compared to placebo or conventional treatment. DATA COLLECTION AND ANALYSIS: Two authors independently classified studies and three authors independently extracted data and assessed risk of bias in the included studies. We rated the certainty of evidence according to the GRADE approach. MAIN RESULTS: We included nine studies with 587 men with mild to moderate erectile dysfunction, aged from 20 to 70 years old. The studies all compared ginseng to placebo. We found only short-term follow-up data (up to 12 weeks).  Primary outcomes Ginseng appears to have a trivial effect on erectile dysfunction when compared to placebo based on the Erectile Function Domain of the International Index of Erectile Function (IIEF)-15 instrument (scale: 1 to 30, higher scores imply better function; mean difference [MD] 3.52, 95% confidence interval [CI] 1.79 to 5.25; I² = 0%; 3 studies; low certainty evidence) assuming a minimal clinically important difference (MCID) of 4.  Ginseng probably also has a trivial effect on erectile function when compared to placebo based on the IIEF-5 instrument (scale: 1 to 25, higher scores imply better function; MD 2.39, 95% CI 0.89 to 3.88; I² = 0%; 3 studies; moderate certainty evidence) assuming a MCID of 5. Ginseng may have little to no effect on adverse events compared to placebo (risk ratio [RR] 1.45, 95% CI 0.69 to 3.03; I² = 0%; 7 studies; low certainty evidence). Based on 86 adverse events per 1000 men in the placebo group, this would correspond to 39 more adverse events per 1000 (95% CI 27 fewer to 174 more). Secondary outcomes Ginseng may improve men's self-reported ability to have intercourse (RR 2.55, 95% CI 1.76 to 3.69; I² = 23%; 6 studies; low certainty evidence). Based on 207 per 1000 men self-reporting the ability to have intercourse in the placebo group, this would correspond to 321 more men (95% CI 158 more to 558 more) per 1000 self-reporting the ability to have intercourse. Ginseng may have a trivial effect on men's satisfaction with intercourse based on the Intercourse Satisfaction Domain of the IIEF-15 (scale: 0 to 15, higher scores imply greater satisfaction; MD 1.19, 95% CI 0.41 to 1.97; I²=0%; 3 studies; low certainty evidence) based on a MCID of 25% improvement from baseline. It may also have a trivial effect on men's satisfaction with intercourse based on item 5 of the IIEF-5 (scale: 0 to 5, higher scores imply more satisfaction; MD 0.60, 95% CI 0.02 to 1.18; 1 study; low certainty evidence) based on a MCID of 25% improvement from baseline. No study reported quality of life as an outcome. We found no trial evidence to inform comparisons to other treatments for erectile dysfunction, such as phosphodiesterase-5 inhibitors. We were unable to conduct any predefined subgroup analyses. AUTHORS' CONCLUSIONS: Based on mostly low certainty evidence, ginseng may only have trivial effects on erectile function or satisfaction with intercourse compared to placebo when assessed using validated instruments. Ginseng may improve men's self-reported ability to have intercourse. It may have little to no effect on adverse events. We found no trial evidence comparing ginseng to other agents with a more established role in treating erectile dysfunction, such as phosphodiesterase-5 inhibitors

A network-based dynamical ranking system for competitive sports

From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based ranking systems are derived from static networks, i.e., aggregation of the results of games over time. However, the score of a player (or team) fluctuates over time. Defeating a renowned player in the peak performance is intuitively more rewarding than defeating the same player in other periods. To account for this factor, we propose a dynamic variant of such a network-based ranking system and apply it to professional men's tennis data. We derive a set of linear online update equations for the score of each player. The proposed ranking system predicts the outcome of the future games with a higher accuracy than the static counterparts.Comment: 6 figure

Reading Single DNA with DNA Polymerase Followed by Atomic Force Microscopy

The importance of DNA sequencing in the life sciences and personalized medicine is continually increasing. Single-molecule sequencing methods have been developed to analyze DNA directly without the need for amplification. Here, we present a new approach to sequencing single DNA molecules using atomic force microscopy (AFM). In our approach, four surface conjugated nucleotides were examined sequentially with a DNA polymerase immobilized AFM tip. By observing the specific rupture events upon examination of a matching nucleotide, we could determine the template base bound in the polymerase's active site. The subsequent incorporation of the complementary base in solution enabled the next base to be read. Additionally, we observed that the DNA polymerase could incorporate the surface-conjugated dGTP when the applied force was controlled by employing the force-clamp mode.X1114Ysciescopu

AROS Is a Significant Biomarker for Tumor Aggressiveness in Non-cirrhotic Hepatocellular Carcinoma

Despite a low risk of liver failure and preserved liver function, non-cirrhotic hepatocellular carcinoma (HCC) has a poor prognosis. In the current study, we evaluated an active regulator of SIRT1 (AROS) as a prognostic biomarker in non-cirrhotic HCC. mRNA levels of AROS were measured in tumor and non-tumor tissues obtained from 283 non-cirrhotic HCC patients. AROS expression was exclusively up-regulated in recurrent tissues from the non-cirrhotic HCC patients (P = 0.015) and also in tumor tissues irrespective of tumor stage (P < 0.001) or BCLC stage (P < 0.001). High mRNA levels of AROS were statistically significantly associated with tumor stage (P < 0.001), BCLC stage (P = 0.007), alpha fetoprotein (AFP) level (P = 0.013), microvascular invasion (P = 0.001), tumor size (P = 0.036), and portal vein invasion (P = 0.005). Kaplan-Meir curve analysis demonstrated that HCC patients with higher AROS levels had shorter disease-free survival (DFS) in both the short-term (P < 0.001) and long-term (P = 0.005) compared to those with low AROS. Cox regression analysis demonstrated that AROS is a significant predictor for DFS along with large tumor size, tumor multiplicity, vascular invasion, and poor tumor differentiation, which are the known prognostic factors. In conclusion, AROS is a significant biomarker for tumor aggressiveness in non-cirrhotic hepatocellular carcinoma.1122Ysciescopu

Robust Bounds on Choosing from Large Tournaments

Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out any alternative in large random tournaments. Nevertheless, all analytical results thus far have assumed a rigid probabilistic model, in which either a tournament is chosen uniformly at random, or there is a linear order of alternatives and the orientation of all edges in the tournament is chosen with the same probabilities according to the linear order. In this work, we consider a significantly more general model where the orientation of different edges can be chosen with different probabilities. We show that a number of common tournament solutions, including the top cycle and the uncovered set, are still unlikely to rule out any alternative under this model. This corresponds to natural graph-theoretic conditions such as irreducibility of the tournament. In addition, we provide tight asymptotic bounds on the boundary of the probability range for which the tournament solutions select all alternatives with high probability.Comment: Appears in the 14th Conference on Web and Internet Economics (WINE), 201

Electron-Spin Excitation Coupling in an Electron Doped Copper Oxide Superconductor

High-temperature (high-Tc) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds. The evolution of the AF phase with doping and its spatial coexistence with superconductivity are governed by the nature of charge and spin correlations and provide clues to the mechanism of high-Tc superconductivity. Here we use a combined neutron scattering and scanning tunneling spectroscopy (STS) to study the Tc evolution of electron-doped superconducting Pr0.88LaCe0.12CuO4-delta obtained through the oxygen annealing process. We find that spin excitations detected by neutron scattering have two distinct modes that evolve with Tc in a remarkably similar fashion to the electron tunneling modes in STS. These results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometer length scales, and the dominant electron-boson coupling at low energies originates from the electron-spin excitations.Comment: 30 pages, 12 figures, supplementary information include

On the Tractability of (k, i)-Coloring

In an undirected graph, a proper ( k, i )-coloring is an assign- ment of a set of k colors to each vertex such that any two adjacent vertices have at most i common colors. The ( k, i )-coloring problem is to compute the minimum number of colors required for a proper ( k, i )- coloring. This is a generalization of the classic graph colo ring problem. Majumdar et. al. [CALDAM 2017] studied this problem and show ed that the decision version of the ( k, i )-coloring problem is fixed parameter tractable (FPT) with tree-width as the parameter. They aske d if there exists an FPT algorithm with the size of the feedback vertex s et (FVS) as the parameter without using tree-width machinery. We ans wer this in positive by giving a parameterized algorithm with the size o f the FVS as the parameter. We also give a faster and simpler exact algo rithm for ( k, k − 1)-coloring, and make progress on the NP-completeness of sp ecific cases of ( k, i )-colorin

Universality of pseudogap and emergent order in lightly doped Mott insulators

It is widely believed that high-temperature superconductivity in the cuprates emerges from doped Mott insulators. The physics of the parent state seems deceivingly simple: The hopping of the electrons from site to site is prohibited because their on-site Coulomb repulsion U is larger than the kinetic energy gain t. When doping these materials by inserting a small percentage of extra carriers, the electrons become mobile but the strong correlations from the Mott state are thought to survive; inhomogeneous electronic order, a mysterious pseudogap and, eventually, superconductivity appear. How the insertion of dopant atoms drives this evolution is not known, nor whether these phenomena are mere distractions specific to hole-doped cuprates or represent the genuine physics of doped Mott insulators. Here, we visualize the evolution of the electronic states of (Sr1-xLax)2IrO4, which is an effective spin-1/2 Mott insulator like the cuprates, but is chemically radically different. Using spectroscopic-imaging STM, we find that for doping concentration of x=5%, an inhomogeneous, phase separated state emerges, with the nucleation of pseudogap puddles around clusters of dopant atoms. Within these puddles, we observe the same glassy electronic order that is so iconic for the underdoped cuprates. Further, we illuminate the genesis of this state using the unique possibility to localize dopant atoms on topographs in these samples. At low doping, we find evidence for much deeper trapping of carriers compared to the cuprates. This leads to fully gapped spectra with the chemical potential at mid-gap, which abruptly collapse at a threshold of around 4%. Our results clarify the melting of the Mott state, and establish phase separation and electronic order as generic features of doped Mott insulators.Comment: This version contains the supplementary information and small updates on figures and tex

Empowerment: An Idea Whose Time Has Come in Diabetes Education

We have learned much in the past 10 years about how to help patients to acquire diabetes-related knowledge and skills and how to use strategies to help patients change behaviors. However, the application ofknowledge and techniques should be guided by a relevant, coherent, educational philosophy. Empowerment offers a practical conceptual framework for diabetes patient education. Empowering patients provides them with the knowledge, skills, and responsibility to effect change and has the potential to promote overall health and maximize the use of available resources. It is an idea whose time has come for diabetes education.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68779/2/10.1177_014572179101700108.pd