New Approximability Results for the Robust k-Median Problem

We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i \subseteq V}_{i=1}^m$. The objective is to open a set $F \subseteq V$ of $k$ facilities such that the worst case connection cost over all client sets is minimized; in other words, minimize $\max_{i} \sum_{v \in S_i} d(F,v)$. Anthony et al.\ showed an $O(\log m)$ approximation algorithm for any metric and APX-hardness even in the case of uniform metric. In this paper, we show that their algorithm is nearly tight by providing $\Omega(\log m/ \log \log m)$ approximation hardness, unless ${\sf NP} \subseteq \bigcap_{\delta >0} {\sf DTIME}(2^{n^{\delta}})$. This hardness result holds even for uniform and line metrics. To our knowledge, this is one of the rare cases in which a problem on a line metric is hard to approximate to within logarithmic factor. We complement the hardness result by an experimental evaluation of different heuristics that shows that very simple heuristics achieve good approximations for realistic classes of instances.Comment: 19 page

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states

We prove that quantum many-body systems on a one-dimensional lattice locally relax to Gaussian states under non-equilibrium dynamics generated by a bosonic quadratic Hamiltonian. This is true for a large class of initial states - pure or mixed - which have to satisfy merely weak conditions concerning the decay of correlations. The considered setting is a proven instance of a situation where dynamically evolving closed quantum systems locally appear as if they had truly relaxed, to maximum entropy states for fixed second moments. This furthers the understanding of relaxation in suddenly quenched quantum many-body systems. The proof features a non-commutative central limit theorem for non-i.i.d. random variables, showing convergence to Gaussian characteristic functions, giving rise to trace-norm closeness. We briefly relate our findings to ideas of typicality and concentration of measure.Comment: 27 pages, final versio

Isolator-free switchable uni- and bidirectional hybrid mode-locked erbium-doped fiber laser

An Erbium-doped fibre ring laser hybrid mode-locked with single-wall carbon nanotubes (SWNT) and nonlinear polarisation evolution (NPE) without an optical isolator has been investigated for various cavity conditions. Precise control of the state of polarisation (SOP) in the cavity ensures different losses for counter-propagating optical fields. As the result, the laser operates in quasi-unidirectional regime in both clockwise (CW) and counter-clockwise (CCW) directions with the emission strengths difference of the directions of 22 dB. Furthermore, by adjusting the net birefringence in the cavity, the laser can operate in a bidirectional generation. In this case, a laser pumped with 75 mW power at 980 nm generates almost identical 790 and 570 fs soliton pulses with an average power of 1.17 and 1.11 mW. The operation stability and pulse quality of the soliton pulses in both unidirectional regimes are highly competitive with those generated in conventional ring fibre lasers with isolator in the cavity. Demonstrated bidirectional laser operation can find vital applications in gyroscopes or precision rotation sensing technologies

LGALS3 (lectin, galactoside-binding, soluble, 3)

Review on LGALS3 (lectin, galactoside-binding, soluble, 3), with data on DNA, on the protein encoded, and where the gene is implicated

Effects of liraglutide versus placebo on cardiovascular events in patients with type 2 diabetes mellitus and chronic kidney disease

BACKGROUND: LEADER trial (Liraglutide Effect and Action in Diabetes: Evaluation of CV Outcome Results) results demonstrated cardiovascular benefits for patients with type 2 diabetes mellitus at high cardiovascular risk on standard of care randomized to liraglutide versus placebo. The effect of glucagon-like peptide-1 receptor agonist liraglutide on cardiovascular events and all-cause mortality in patients with type 2 diabetes mellitus and chronic kidney disease is unknown. Liraglutide's treatment effects in patients with and without kidney disease were analyzed post hoc. METHODS: Patients were randomized (1:1) to liraglutide or placebo, both in addition to standard of care. These analyses assessed outcomes stratified by baseline estimated glomerular filtration rate (eGFR; <60 versus ≥60 mL/min/1.73 m2) and baseline albuminuria. The primary outcome (composite of cardiovascular death, nonfatal myocardial infarction, or nonfatal stroke) and secondary outcomes, including all-cause mortality and individual components of the primary composite outcome, were analyzed using Cox regression. RESULTS: Overall, 2158 and 7182 patients had baseline eGFR <60 or ≥60 mL/min/1.73 m2, respectively. In patients with eGFR <60 mL/min/1.73 m2, risk reduction for the primary composite cardiovascular outcome with liraglutide was greater (hazard ratio [HR], 0.69; 95% CI, 0.57-0.85) versus those with eGFR ≥60 mL/min/1.73 m2 (HR, 0.94; 95% CI, 0.83-1.07; interaction P=0.01). There was no consistent effect modification with liraglutide across finer eGFR subgroups (interaction P=0.13) and when analyzing eGFR as a continuous variable (interaction P=0.61). Risk reductions in those with eGFR <60 versus ≥60 mL/min/1.73 m2 were as follows: for nonfatal myocardial infarction, HR, 0.74; 95% CI, 0.55-0.99 versus HR, 0.93; 95% CI, 0.77-1.13; for nonfatal stroke, HR, 0.51; 95% CI, 0.33-0.80 versus HR, 1.07; 95% CI, 0.84-1.37; for cardiovascular death, HR, 0.67; 95% CI, 0.50-0.90 versus HR, 0.84; 95% CI, 0.67-1.05; for all-cause mortality, HR, 0.74; 95% CI, 0.60-0.92 versus HR, 0.90; 95% CI, 0.75-1.07. Risk reduction for the primary composite cardiovascular outcome was not different for those with versus without baseline albuminuria (HR, 0.83; 95% CI, 0.71-0.97; and HR, 0.92; 95% CI, 0.79-1.07, respectively; interaction P=0.36). CONCLUSIONS: Liraglutide added to standard of care reduced the risk for major cardiovascular events and all-cause mortality in patients with type 2 diabetes mellitus and chronic kidney disease. These results appear to apply across the chronic kidney disease spectrum enrolled. CLINICAL TRIAL REGISTRATION: URL: https://www.clinicaltrials.gov/ . Unique identifier: NCT01179048

Proteasomal activity-based probes mark protein homeostasis in muscles

Bio-organic Synthesi