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

The pressure-amorphized state in zirconium tungstate: a precursor to decomposition

In contrast to widely accepted view that pressure-induced amorphization arises due to kinetic hindrance of equilibrium phase transitions, here we provide evidence that the metastable pressure-amorphized state in zirconium tungstate is a precursor to decomposition of the compound into a mixture of simple oxides. This is from the volume collapse ΔV across amorphization, which is obtained for the first time by measuring linear dimensions of irreversibly amorphized samples during their recovery to the original cubic phase upon isochronal annealing up to 1000 K. The anomalously large ΔV of 25.7 ± 1.2% being the same as that expected for the decomposition indicates that this amorphous state is probably a precursor to kinetically hindered decomposition. A P–T diagram of the compound is also proposed

Zero delay synchronization of chaos in coupled map lattices

We show that two coupled map lattices that are mutually coupled to one another with a delay can display zero delay synchronization if they are driven by a third coupled map lattice. We analytically estimate the parametric regimes that lead to synchronization and show that the presence of mutual delays enhances synchronization to some extent. The zero delay or isochronal synchronization is reasonably robust against mismatches in the internal parameters of the coupled map lattices and we analytically estimate the synchronization error bounds.Comment: 9 pages, 9 figures ; To appear in Phys. Rev.

Fortification of milk with phytosterol and its effect on sensory and physicochemical properties

peer-reviewedPhytosterols are a group of lipophilic steroid alcohols found in plants, which have been shown to lower cholesterol when supplemented in the diet. A commercial phytosterol preparation was added to milk in the form of an oil-in-water emulsion. For the preparation of an emulsion, diacetyl tartaric acid ester of mono- and diglycerides was used as an emulsifier and butteroil was used as a source of fat. Three emulsion formulations, i.e. A (8% phytosterols), B (10% phytosterols) and C (12% phytosterols), were prepared in which the levels of emulsifier (6.5%) and butteroil (10%) were kept constant, and each emulsion was added to milk at a rate of 5% (w/w). Based on sensory evaluation, B-emulsion formulation was selected for fortification of milk. The phytosterol content of the fortified milk determined by reverse-phase high-performance liquid chromatography was 410.8 mg/100 g. No significant loss in the initial content of phytosterol was observed after 1 week of storage. Sensory and physicochemical analyses indicated that significant differences were not observed between control and fortified milk samples up to 7 days of refrigerated storage. The present study suggests that it is feasible to add phytosterol as a functional ingredient in milk in the form of water-soluble emulsion to enhance health benefits of consumers. Two servings of such fortified milk per day provide almost the entire recommended daily requirement of phytosterol

Diagnostic accuracy of HE4 and risk of ovarian malignancy algorithm in prediction of ovarian cancer in patients with pelvic mass: a regional cancer centre experience

Background: The current study was performed with an objective to evaluate the diagnostic accuracy of HE4 (human epididymis protein) and ROMA in prediction of ovarian cancer in patients with pelvic mass and to compare HE4 and ROMA with CA-125, and RMI (risk of malignancy index) for ovarian cancer prediction in women with pelvic mass.Methods: This was a diagnostic study enrolling 200 patients with pelvic mass who had been scheduled for Primary surgery. Serum HE4 and CA 125 levels were measured. HE4, CA 125 and ROMA, RMI were evaluated for sensitivity, specificity, positive predictive value and negative predictive value. The receiver operating characteristic (ROC) plots were graphed and area under the curve (AUC) values was calculated to investigate the accuracy of each marker for predicting ovarian malignancy.Results: Overall, ROMA showed the highest accuracy as it correctly classified 139/200 (69.5%) patients compared with 133/200 (66.5%) in HE4 and 109/200 (54.5%) in CA 125 and RMI. There were more patients with benign tumors being correctly identified by HE4 (89/119, 74.7%) and ROMA (74/119, 62.1%), than CA 125 which identified 39/119 (32.7%) patients. In our study in premenopausal women ROMA and HE4 have comparable sensitivity (80%and 75%) but higher specificity (64% and 65%) and NPV (86% and 83%) as compared to CA125 which has sensitivity of (83%) but very low specificity (46%) in differentiating benign from malignant masses. In postmenopausal women, HE4 had highest specificity (88%) and, CA125 has highest sensitivity (86%) in detecting ovarian malignancy.Conclusions: HE4 and ROMA showed a high specificity, but were less sensitivity than CA-125 and RMI in premenopausal women. However, ROMA is of comparable sensitivity and HE4 has highest specificity as compared to CA125 in postmenopausal women

Fractal Formation Of A Y-Ba-Cu-O Thin-Film On Srtio3

Fractal formation has been observed after thermal annealing of the rf-sputtered Y-Ba-Cu-O thin film on SrTiO3 substrate. Through energy-dispersive x-ray analysis, it was found that the composition of the fractal was YBa2Cu3Ox and the surrounding film composition was Y2Ba2Cu3Ox. The fractal dimensions D ranging from 1.26 to 1.65 were obtained using the standard sandbox method with different thresholds

Targeting mulitple dyslipidemias with fixed combinations – focus on extended release niacin and simvastatin

Dyslipidemia is a major risk factor in the initiation and progression of cardiovascular diseases such as atherosclerosis. Several pharmacological agents have been developed over the past 50 years which target various lipid components such as low density lipoprotein (LDL) cholesterol, triglyceride, and high density lipoprotein (HDL) cholesterol. Similar to other risk factors such as hypertension and diabetes mellitus, the management of dyslipidemia can be complicated and may require combination therapy for effective treatment. This review discusses the biochemical mechanisms of action and clinical uses for simvastatin (the most widely available and commercially prescribed statin) and niacin, and the combination of these agents in the management and treatment of dyslipidemia