On the Approximability of Digraph Ordering

Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute a labeling $\ell : V \to [k]$ maximizing the number of forward edges, i.e. edges (u,v) such that $\ell$(u) < $\ell$(v). For different values of k, this reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work studies the approximability of Max-k-Ordering and its generalizations, motivated by their applications to job scheduling with soft precedence constraints. We give an LP rounding based 2-approximation algorithm for Max-k-Ordering for any k={2,..., n}, improving on the known 2k/(k-1)-approximation obtained via random assignment. The tightness of this rounding is shown by proving that for any k={2,..., n} and constant $\varepsilon > 0$, Max-k-Ordering has an LP integrality gap of 2 - $\varepsilon$ for $n^{\Omega\left(1/\log\log k\right)}$ rounds of the Sherali-Adams hierarchy. A further generalization of Max-k-Ordering is the restricted maximum acyclic subgraph problem or RMAS, where each vertex v has a finite set of allowable labels $S_v \subseteq \mathbb{Z}^+$. We prove an LP rounding based $4\sqrt{2}/(\sqrt{2}+1) \approx 2.344$ approximation for it, improving on the $2\sqrt{2} \approx 2.828$ approximation recently given by Grandoni et al. (Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact, our approximation algorithm also works for a general version where the objective counts the edges which go forward by at least a positive offset specific to each edge. The minimization formulation of digraph ordering is DAG edge deletion or DED(k), which requires deleting the minimum number of edges from an n-vertex directed acyclic graph (DAG) to remove all paths of length k. We show that both, the LP relaxation and a local ratio approach for DED(k) yield k-approximation for any $k\in [n]$.Comment: 21 pages, Conference version to appear in ESA 201

T1T_1- and T2T_2-spin relaxation time limitations of phosphorous donor electrons near crystalline silicon to silicon dioxide interface defects

A study of donor electron spins and spin--dependent electronic transitions involving phosphorous ($^{31}$P) atoms in proximity of the (111) oriented crystalline silicon (c-Si) to silicon dioxide (SiO$_{2}$) interface is presented for [$^{31}$P] = 10$^{15}$ $\mathrm{cm}^{-3}$ and [$^{31}$P] = 10$^{16}$ $\mathrm{cm}^{-3}$ at about liquid $^4$He temperatures ($T = 5$ $\mathrm{K} - 15$ $\mathrm{K}$). Using pulsed electrically detected magnetic resonance (pEDMR), spin--dependent transitions between the \Phos donor state and two distinguishable interface states are observed, namely (i) \Pb centers which can be identified by their characteristic anisotropy and (ii) a more isotropic center which is attributed to E$^\prime$ defects of the \sio bulk close to the interface. Correlation measurements of the dynamics of spin--dependent recombination confirm that previously proposed transitions between \Phos and the interface defects take place. The influence of these electronic near--interface transitions on the \Phos donor spin coherence time $T_2$ as well as the donor spin--lattice relaxation time $T_1$ is then investigated by comparison of spin Hahn--echo decay measurements obtained from conventional bulk sensitive pulsed electron paramagnetic resonance and surface sensitive pEDMR, as well as surface sensitive electrically detected inversion recovery experiments. The measurements reveal that both $T_2$ and $T_1$ of \Phos donor electrons spins in proximity of energetically lower interface states at $T\leq 13$ K are reduced by several orders of magnitude

Control Banding and Nanotechnology Synergist

The average Industrial Hygienist (IH) loves a challenge, right? Okay, well here is one with more than a few twists. We start by going through the basics of a risk assessment. You have some chemical agents, a few workers, and the makings of your basic exposure characterization. However, you have no occupational exposure limit (OEL), essentially no toxicological basis, and no epidemiology. Now the real handicap is that you cannot use sampling pumps, cassettes, tubes, or any of the media in your toolbox, and the whole concept of mass-to-dose is out the window, even at high exposure levels. Of course, by the title, you knew we were talking about nanomaterials (NM). However, we wonder how many IHs know that this topic takes everything you know about your profession and turns it upside down. It takes the very foundations that you worked so hard in college and in the field to master and pulls it out from underneath you. It even takes the gold standard of our profession, the quantitative science of exposure assessment, and makes it look pretty darn rusty. Now with NM there is the potential to get some aspect of quantitative measurements, but the instruments are generally very expensive and getting an appropriate workplace personal exposure measurement can be very difficult if not impossible. The potential for workers getting exposures, however, is very real, as evidenced by a recent publication reporting worker exposures to polyacrylate nanoparticles in a Chinese factory (Song et al. 2009). With something this complex and challenging, how does a concept as simple as Control Banding (CB) save the day? Although many IHs have heard of CB, most of their knowledge comes from its application in the COSHH Essentials toolkit. While there is conflicting published research on COSHH Essentials and its value for risk assessments, almost all of the experts agree that it can be useful when no OELs are available (Zalk and Nelson 2008). It is this aspect of CB, its utility with uncertainty, that attracted international NM experts to recommend this qualitative risk assessment approach for NM. However, since their CB recommendation was only in theory, we took on the challenge of developing a working toolkit, the CB Nanotool (see Zalk et al. 2009 and Paik et al. 2008), as a means to perform a risk assessment and protect researchers at the Lawrence Livermore National Laboratory. While it's been acknowledged that engineered NM have potentially endless benefits for society, it became clear to us that the very properties that make nanotechnology so useful to industry could also make them dangerous to humans and the environment. Among the uncertainties and unknowns with NM are: the contribution of their physical structure to their toxicity, significant differences in their deposition and clearance in the lungs when compared to their parent material (PM), a lack of agreement on the appropriate indices for exposure to NM, and very little background information on exposure scenarios or populations at risk. Part of this lack of background information can be traced to the lack of risk assessments historically performed in the industry, with a recent survey indicating that 65% of companies working with NM are not doing any kind of NM-specific risk assessment as they focus on traditional PM methods for IH (Helland et al. 2009). The good news is that the amount of peer-reviewed publications that address environmental, health and safety aspects of NM has been increasing over the last few years; however, the percentage of these that address practical methods to reduce exposure and protect workers is orders of magnitude lower. Our intent in developing the CB Nanotool was to create a simplified approach that would protect workers while unraveling the mysteries of NM for experts and non-experts alike. Since such a large part of the toxicological effects of both the physical and chemical properties of NM were unknown, not to mention changing logarithmically as new NM research continues growing, we needed to account for this lack of information as part of the CB Nanotool's risk assessment. We chose a standardized 4 X 4 risk matrix (see figure 1) as our starting point, working with the severity parameters on one axis and the probability parameters on the other. The development of the severity axis was certainly the hardest part of our effort. This required the dissection of NM and its physicochemical properties which are often unknown, adding information on the PM which is far more available, and somehow scoring these input factors in a manner that appropriately weighted each factor. We decided to give unknown input factors a score of 75% of the points for each category, because otherwise the instinct of considering it as extremely dangerous would kick in and the highest level of control would almost always be the outcome

A Grid Computing Based Power System Monitoring Tool Using Gridgain

With the advancement of civilization, Power Sector is undergoing drastic upheavals. With the ever increasing demand and dependence on electric power, protection of power system against failures remains a major challenge, particularly against cascading failures that lead to blackouts. There is a great demand for power systems protection that is scattered all around the globe. Effective monitoring of the power system parameters is a prerequisite in providing effective control and protection schemas. This paper advocates the use of grid computing in power system monitoring which discusses the suitability of grid computing to address the requirements of distinguished power system protection. Albeit, the Supervisory Control And Data Acquisition (SCADA) system is presently implied for monitoring power systems; yet it has its limitations. This paper proposes to use Grid Computing as an aid to the existing SCADA based power system monitoring & control framework and demonstrates is applicability by means of a grid based real-time power system monitoring system. The afore mentioned system has been deployed in desktop computers with GridGain 2.0 as middleware has been employed to set up the grid environment, all relevant details of the design framework has been shown

Poor survival outcomes in HER2 positive breast cancer patients with low grade, node negative tumours

We present a retrospective analysis on a cohort of low-grade, node-negative patients showing that human epidermal growth factor receptor 2 (HER2) status significantly affects the survival in this otherwise very good prognostic group. Our results provide support for the use of adjuvant trastuzumab in patients who are typically classified as having very good prognosis, not routinely offered standard chemotherapy, and who as such do not fit current UK prescribing guidelines for trastuzumab

A long-term optical and X-ray ephemeris of the polar EK Ursae Majoris

We searched for long-term period changes in the polar EK UMa using new optical data and archival X-ray/EUV data. An optical ephemeris was derived from data taken remotely with the MONET/N telescope and compared with the X-ray ephemeris based on Einstein, Rosat, and EUVE data. A three-parameter fit to the combined data sets yields the epoch, the period, and the phase offset between the optical minima and the X-ray absorption dips. An added quadratic term is insignificant and sets a limit to the period change. The derived linear ephemeris is valid over 30 years and the common optical and X-ray period is P=0.0795440225(24) days. There is no evidence of long-term O-C variations or a period change over the past 17 years Delta P = -0.14+-0.50 ms. We suggest that the observed period is the orbital period and that the system is tightly synchronized. The limit on Delta P and the phase constancy of the bright part of the light curve indicate that O-C variations of the type seen in the polars DP Leo and HU Aqr or the pre-CV NN Ser do not seem to occur in EK UMa. The X-ray dips lag the optical minima by 9.5+-0.7 deg in azimuth, providing some insight into the accretion geometry.Comment: 4 pages, 2 Postscript figures, accepted for publication in Astronomy & Astrophysic

Summary of Surface Swipe Sampling for Beryllium on Lead Bricks and Shielding

Approximately 25,000 lbs of lead bricks at Site 300 were assessed by the Site 300 Industrial Hygienis tand Health Physicist for potential contamination of beryllium and radiation for reuse. These lead bricks and shielding had been used as shielding material during explosives tests that included beryllium and depleted uranium. Based on surface swipe sampling that was performed between July 26 and October 11, 2010, specifically for beryllium, the use of a spray encapsulant was found to be an effective means to limit removable surface contamination to levels below the DOE release limit for beryllium, which is 0.2 mcg/100 cm{sup 2}. All the surface swipe sampling data for beryllium and a timeline of when the samples were collected (and a brief description) are presented in this report. On December 15, 2010, the lead bricks and shielding were surveyed with an ion chamber and indicated dose rates less than 0.05 mrem per hour on contact. This represents a dose rate consistent with natural background. An additional suevey was performed on February 8, 2011, using a GM survey instrument to estimate total activity on the lead bricks and shielding, confirming safe levels of radioactivity. The vendor is licensed to possess and work with radioactive material