Hardness of Graph Pricing through Generalized Max-Dicut

The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games Conjecture (UGC). We show that it is NP-hard to approximate within a factor better than 1/4 under the UGC, so that the simple combinatorial algorithm might be the best possible. We also prove that for any $\epsilon > 0$, there exists $\delta > 0$ such that the integrality gap of $n^{\delta}$-rounds of the Sherali-Adams hierarchy of linear programming for Graph Pricing is at most 1/2 + $\epsilon$. This work is based on the effort to view the Graph Pricing problem as a Constraint Satisfaction Problem (CSP) simpler than the standard and complicated formulation. We propose the problem called Generalized Max-Dicut($T$), which has a domain size $T + 1$ for every $T \geq 1$. Generalized Max-Dicut(1) is well-known Max-Dicut. There is an approximation-preserving reduction from Generalized Max-Dicut on directed acyclic graphs (DAGs) to Graph Pricing, and both our results are achieved through this reduction. Besides its connection to Graph Pricing, the hardness of Generalized Max-Dicut is interesting in its own right since in most arity two CSPs studied in the literature, SDP-based algorithms perform better than LP-based or combinatorial algorithms --- for this arity two CSP, a simple combinatorial algorithm does the best.Comment: 28 page

A Robust AFPTAS for Online Bin Packing with Polynomial Migration

In this paper we develop general LP and ILP techniques to find an approximate solution with improved objective value close to an existing solution. The task of improving an approximate solution is closely related to a classical theorem of Cook et al. in the sensitivity analysis for LPs and ILPs. This result is often applied in designing robust algorithms for online problems. We apply our new techniques to the online bin packing problem, where it is allowed to reassign a certain number of items, measured by the migration factor. The migration factor is defined by the total size of reassigned items divided by the size of the arriving item. We obtain a robust asymptotic fully polynomial time approximation scheme (AFPTAS) for the online bin packing problem with migration factor bounded by a polynomial in $\frac{1}{\epsilon}$. This answers an open question stated by Epstein and Levin in the affirmative. As a byproduct we prove an approximate variant of the sensitivity theorem by Cook at el. for linear programs

Quantum State During and after O(4)O(4)-Symmetric Bubble Nucleation with Gravitaional Effects

We extend our previous analysis of the quantum state during and after $O(4)$-symmetric bubble nucleation to the case including gravitational effects. We find that there exists a simple relationship between the case with and without gravitational effects. In a special case of a conformally coupled scalar field which is massless except on the bubble wall, the state is found to be conformally equivalent to the case without gravity.Comment: 31 pages plain Tex file, uuencoded postscript figure file is available from [email protected] upon request, KUNS126

PHF2 regulates homology-directed DNA repair by controlling the resection of DNA double strand breaks

Post-translational histone modifications and chromatin remodelling play a critical role controlling the integrity of the genome. Here, we identify histone lysine demethylase PHF2 as a novel regulator of the DNA damage response by regulating DNA damage-induced focus formation of 53BP1 and BRCA1, critical factors in the pathway choice for DNA double strand break repair. PHF2 knockdown leads to impaired BRCA1 focus formation and delays the resolution of 53BP1 foci. Moreover, irradiation-induced RPA phosphorylation and focus formation, as well as localization of CtIP, required for DNA end resection, to sites of DNA lesions are affected by depletion of PHF2. These results are indicative of a defective resection of double strand breaks and thereby an impaired homologous recombination upon PHF2 depletion. In accordance with these data, Rad51 focus formation and homology-directed double strand break repair is inhibited in cells depleted for PHF2. Importantly, we demonstrate that PHF2 knockdown decreases CtIP and BRCA1 protein and mRNA levels, an effect that is dependent on the demethylase activity of PHF2. Furthermore, PHF2-depleted cells display genome instability and are mildly sensitive to the inhibition of PARP. Together these results demonstrate that PHF2 promotes DNA repair by homologous recombination by controlling CtIP-dependent resection of double strand breaks.España Ministerio de Ciencia e Innovacion SAF2016-80626-REspaña, Fundación Canaria Instituto de Investigación Sanitaria de Canarias (FIISC) [PIFUN16/18

The association between social determinants of health and self-reported diabetic retinopathy: An exploratory analysis

One-third of Americans with diabetes will develop diabetic retinopathy (DR), the leading cause of blindness in working-age Americans. Social determinants of health (SDOHs) are conditions in a person’s environment that may impact health. The objective of this study was to determine whether there is an association between SDOHs and DR in patients with type II diabetes. This cross-section study used data from the 2018 Behavioral Risk Factor Surveillance System (BRFSS). This study included people with self-reported diabetes in the US in 2018 (n = 60,703). Exposure variables included homeownership, marital status, income, health care coverage, completed level of educa-tion, and urban vs. rural environment. The outcome variable was DR. Logistic regression analysis were applied to calculate odds ratios (ORs) and 95% confidence intervals (CIs). Alaskan Native/Na-tive American (OR 2.11; 95% CI: 1.14–3.90), out of work (OR 2.82; 95% CI: 1.62–4.92), unable to work (OR 2.14; 95% CI: 1.57–2.91), did not graduate high school (OR 1.91; 95% CI: 1.30–2.79), only gradu-ated high school (OR 1.43; 95% CI 1.08–1.97), or only attended college or technical school without graduating (OR 1.42; 95% CI: 1.09–1.86) were SDOHs associated with DR in patients with diabetes. Health care providers should identify these possible SDOHs affecting their diabetic patients

The Length of an SLE - Monte Carlo Studies

The scaling limits of a variety of critical two-dimensional lattice models are equal to the Schramm-Loewner evolution (SLE) for a suitable value of the parameter kappa. These lattice models have a natural parametrization of their random curves given by the length of the curve. This parametrization (with suitable scaling) should provide a natural parametrization for the curves in the scaling limit. We conjecture that this parametrization is also given by a type of fractal variation along the curve, and present Monte Carlo simulations to support this conjecture. Then we show by simulations that if this fractal variation is used to parametrize the SLE, then the parametrized curves have the same distribution as the curves in the scaling limit of the lattice models with their natural parametrization.Comment: 18 pages, 10 figures. Version 2 replaced the use of "nu" for the "growth exponent" by 1/d_H, where d_H is the Hausdorff dimension. Various minor errors were also correcte

Simplified risk stratification criteria for identification of patients with MRSA bacteremia at low risk of infective endocarditis: implications for avoiding routine transesophageal echocardiography in MRSA bacteremia

The aim of this study was to identify patients with methicillin-resistant Staphylococcus aureus (MRSA) bacteremia with low risk of infective endocarditis (IE) who might not require routine trans-esophageal echocardiography (TEE). We retrospectively evaluated 398 patients presenting with MRSA bacteremia for the presence of the following clinical criteria: intravenous drug abuse (IVDA), long-term catheter, prolonged bacteremia, intra-cardiac device, prosthetic valve, hemodialysis dependency, vertebral/nonvertebral osteomyelitis, cardio-structural abnormality. IE was diagnosed using the modified Duke criteria. Of 398 patients with MRSA bacteremia, 26.4 % of cases were community-acquired, 56.3 % were health-care-associated, and 17.3 % were hospital-acquired. Of the group, 44 patients had definite IE, 119 had possible IE, and 235 had a rejected diagnosis. Out of 398 patients, 231 were evaluated with transthoracic echocardiography (TTE) or TEE. All 44 patients with definite IE fulfilled at least one criterion (sensitivity 100 %). Finally, a receiver operator characteristic (ROC) curve was obtained to evaluate the total risk score of our proposed criteria as a predictor of the presence of IE, and this was compared to the ROC curve of a previously proposed criteria. The area under the ROC curve for our criteria was 0.710, while the area under the ROC curve for the criteria previously proposed was 0.537 (p < 0.001). The p-value for comparing those 2 areas was less than 0.001, indicating statistical significance. Patients with MRSA bacteremia without any of our proposed clinical criteria have very low risk of developing IE and may not require routine TEE

Vector Bin Packing with Multiple-Choice

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types, each with its own cost and $D$-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about $\ln D$ times the optimum. For the running time to be polynomial we require $D=O(1)$ and $T=O(\log n)$. This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin