A polynomial bound for untangling geometric planar graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput. Geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed. We answer this question in the affirmative with \epsilon=1/4. The previous best known bound was \Omega((\log n / \log\log n)^{1/2}). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was O(n\log n)^{2/3}. We answer a question of Spillner and Wolff [arXiv:0709.0170 2007] by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than 3(n^{1/2}-1) vertices fixed. Moreover, we improve the lower bound to (n/2)^{1/2}.Comment: 14 pages, 7 figure

Dynamic ham-sandwich cuts in the plane

We design efficient data structures for dynamically maintaining a ham-sandwich cut of two point sets in the plane subject to insertions and deletions of points in either set. A ham-sandwich cut is a line that simultaneously bisects the cardinality of both point sets. For general point sets, our first data structure supports each operation in O(n1/3+ε) amortized time and O(n4/3+ε) space. Our second data structure performs faster when each point set decomposes into a small number k of subsets in convex position: it supports insertions and deletions in O(logn) time and ham-sandwich queries in O(klog4n) time. In addition, if each point set has convex peeling depth k , then we can maintain the decomposition automatically using O(klogn) time per insertion and deletion. Alternatively, we can view each convex point set as a convex polygon, and we show how to find a ham-sandwich cut that bisects the total areas or total perimeters of these polygons in O(klog4n) time plus the O((kb)polylog(kb)) time required to approximate the root of a polynomial of degree O(k) up to b bits of precision. We also show how to maintain a partition of the plane by two lines into four regions each containing a quarter of the total point count, area, or perimeter in polylogarithmic time.Engineering and Applied Science

Deterministic Sampling and Range Counting in Geometric Data Streams

We present memory-efficient deterministic algorithms for constructing epsilon-nets and epsilon-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.Comment: 12 pages, 1 figur

Contamination of depressional wetlands in the Mpumalanga Lake District of South Africa near a global emission hotspot

The Mpumalanga Lake District (MLD) of South Africa hosts a regionally unique cluster of water bodies of great importance for wetland biodiversity. It is also located close to a global hotspot for coal-fired power station emissions but the local impacts from these sources of pollution are poorly understood. Sediment cores from three contrasting wetlands were ²¹⁰Pb dated and analysed for a range of contaminants linked to fossil fuel combustion, including trace elements, Hg, sulphur and spheroidal carbonaceous fly-ash particles (SCPs). At the two sites with pre-industrial (1900) baseline sediments, Pb, Zn and especially Cr concentrations and fluxes showed significant increases in the impact period (post-1975). Mercury showed the greatest proportional increase in flux (>4-fold) of all trace metals. Mercury and sulphur concentrations and fluxes showed highly significant correlations with emissions over the corresponding periods, while SCPs in sediments also closely tracked emissions. In a global context, levels of sediment contamination are relatively minor compared with other heavily industrialised regions, with only Cr exceeding the sediment Probable Effects Concentration for biological impact post-1975. Despite the relatively large increases in Hg, concentrations do not reach the Threshold Effects Concentration. The unexpectedly low levels of contamination may be due to i) low levels of many trace contaminants in South African coals compared to global averages, ii) prevailing recirculation patterns which transport pollution away from the study area during the wet season, minimising wet deposition, and iii) pollutant remobilisation through desiccation of wetlands or volatilization. The effects of hydrology and sediment accumulation rates lead to differential transport and preservation of organic-associated and more volatile contaminants (e.g. Hg, S) relative to non-volatile trace elements in wetlands of the MLD. The greatest fluxes of Hg and S are recorded in the site with the highest catchment: lake area ratio, lowest salinity and greatest sediment organic matter content

Feasibility of Tomotherapy-Based Image-Guided Radiotherapy to Reduce Aspiration Risk in Patients with Non-Laryngeal and Non-Pharyngeal Head and Neck Cancer

PURPOSE: The study aims to assess the feasibility of Tomotherapy-based image-guided radiotherapy (IGRT) to reduce the aspiration risk in patients with non-laryngeal and non-hypopharyngeal cancer. A retrospective review of 48 patients undergoing radiation for non-laryngeal and non-hypopharyngeal head and neck cancers was conducted. All patients had a modified barium swallow (MBS) prior to treatment, which was repeated one month following radiotherapy. Mean middle and inferior pharyngeal dose was recorded and correlated with the MBS results to determine aspiration risk. RESULTS: Mean pharyngeal dose was 23.2 Gy for the whole group. Two patients (4.2%) developed trace aspiration following radiotherapy which resolved with swallowing therapy. At a median follow-up of 19 months (1-48 months), all patients were able to resume normal oral feeding without aspiration. CONCLUSION AND CLINICAL RELEVANCE: IGRT may reduce the aspiration risk by decreasing the mean pharyngeal dose in the presence of large cervical lymph nodes. Further prospective studies with IGRT should be performed in patients with non-laryngeal and non-hypopharyngeal head and neck cancers to verify this hypothesis

Contamination of depressional wetlands in the Mpumalanga Lake District of South Africa near a global emission hotspot

The Mpumalanga Lake District (MLD) of South Africa hosts a regionally unique cluster of water bodies of great importance for wetland biodiversity. It is also located close to a global hotspot for coal-fired power station emissions but the local impacts from these sources of pollution are poorly understood. Sediment cores from three contrasting wetlands were 210Pb dated and analysed for a range of contaminants linked to fossil fuel combustion, including trace elements, Hg, sulphur and spheroidal carbonaceous fly-ash particles (SCPs). At the two sites with pre-industrial (1900) baseline sediments, Pb, Zn and especially Cr concentrations and fluxes showed significant increases in the impact period (post-1975). Mercury showed the greatest proportional increase in flux (>4-fold) of all trace metals. Mercury and sulphur concentrations and fluxes showed highly significant correlations with emissions over the corresponding periods, while SCPs in sediments also closely tracked emissions. In a global context, levels of sediment contamination are relatively minor compared with other heavily industrialised regions, with only Cr exceeding the sediment Probable Effects Concentration for biological impact post-1975. Despite the relatively large increases in Hg, concentrations do not reach the Threshold Effects Concentration. The unexpectedly low levels of contamination may be due to i) low levels of many trace contaminants in South African coals compared to global averages, ii) prevailing recirculation patterns which transport pollution away from the study area during the wet season, minimising wet deposition, and iii) pollutant remobilisation through desiccation of wetlands or volatilization. The effects of hydrology and sediment accumulation rates lead to differential transport and preservation of organic-associated and more volatile contaminants (e.g. Hg, S) relative to non-volatile trace elements in wetlands of the MLD. The greatest fluxes of Hg and S are recorded in the site with the highest catchment: lake area ratio, lowest salinity and greatest sediment organic matter content

IMECE2004-60386 THERMAL CONTROL OF LASER POWDER DEPOSITION-HEAT TRANSFER CONSIDERATIONS

ABSTRACT Laser based solid free-form fabrication is an emerging metallurgical forming process aimed at rapid production of high quality, near net shape products directly from starting powders. Laser powder deposition shares, with other free-form technologies, the common characteristic that part fabrication occurs directly from a 3-D computer aided design (CAD) model. The microstructure evolution and resulting material properties of the component part (strength, ductility, etc.) fabricated using laser deposition are dependent upon process operating parameters such as melt pool size, laser power, head (manipulator) speed, and powder flow rate. Presently, set points for these parameters are often determined through manual manipulation of the system control and trial and error. This paper discusses the development of a path-planning, feed-forward, process-driven control system algorithm that generates a component part thermal history within given constraints, thereby assuring optimal part quality and minimizing final residual stresses. A thermal model of the deposition process drives the control algorithm. The development of the thermal model is the subject of this paper. The model accounts for temperature-dependent properties and phase change processes. Model validation studies are presented including comparisons with known analytic solutions as well as comparisons with data from experiments conducted in the laser laboratory at SDSM&T. INTRODUCTION Laser based solid free-form fabrication is an emerging metallurgical forming process aimed at rapid production of high quality, near net shape products directly from starting powders The SDSMT Advanced Materials Processing (AMP) center has a continuous wave (CW) 3 kW Nd: YAG laser equipped with two metal powder-feed systems and mounted on a Fanuc 16Mi robot. This equipment allows for direct laser deposition, solid freeform fabrication, and graded alloy research and development programs on titanium, nickel, and other refractory metal alloys. Current research includes projects aimed at improving performance of armored vehicles [2] and aerospace vehicles There is significant experimental evidence indicating a relationship between laser powder deposition operatin

Do salivary bypass tubes lower the incidence of pharyngocutaneous fistula following total laryngectomy? A retrospective analysis of predictive factors using multivariate analysis

Salivary bypass tubes (SBT) are increasingly used to prevent pharyngocutaneous fistula (PCF) following laryngectomy and pharyngolaryngectomy. There is minimal evidence as to their efficacy and literature is limited. The aim of the study was to determine if SBT prevent PCF. The study was a multicentre retrospective case control series (level of evidence 3b). Patients who underwent laryngectomy or pharyngolaryngectomy for cancer or following cancer treatment between 2011 and 2014 were included in the study. The primary outcome was development of a PCF. Other variables recorded were age, sex, prior radiotherapy or chemoradiotherapy, prior tracheostomy, type of procedure, concurrent neck dissection, use of flap reconstruction, use of prophylactic antibiotics, the suture material used for the anastomosis, tumour T stage, histological margins, day one post-operative haemoglobin and whether a salivary bypass tube was used. Univariate and multivariate analysis were performed. A total of 199 patients were included and 24 received salivary bypass tubes. Fistula rates were 8.3% in the SBT group (2/24) and 24.6% in the control group (43/175). This was not statistically significant on univariate (p value 0.115) or multivariate analysis (p value 0.076). In addition, no other co-variables were found to be significant. No group has proven a benefit of salivary bypass tubes on multivariate analysis. The study was limited by a small case group, variations in tube duration and subjects given a tube may have been identified as high risk of fistula. Further prospective studies are warranted prior to recommendation of salivary bypass tubes following laryngectomy

Natural archives of long-range transported contamination at the remote lake Letšeng-la Letsie, Maloti Mountains, Lesotho

Naturally accumulating archives, such as lake sediments and wetland peats, in remote areas may be used to identify the scale and rates of atmospherically deposited pollutant inputs to natural ecosystems. Co-located lake sediment and wetland cores were collected from Letšeng-la Letsie, a remote lake in the Maloti Mountains of southern Lesotho. The cores were radiometrically dated and analysed for a suite of contaminants including trace metals and metalloids (Hg, Pb, Cu, Ni, Zn, As), fly-ash particles, stable nitrogen isotopes, polycyclic aromatic hydrocarbons (PAHs) and persistent organic pollutants such as polychlorinated biphenyls (PCBs), polybrominated flame retardants (PBDEs) and hexachlorobenzene (HCB). While most trace metals showed no recent enrichment, mercury, fly-ash particles, high molecular weight PAHs and total PCBs showed low but increasing levels of contamination since c.1970, likely the result of long-range transport from coal combustion and other industrial sources in the Highveld region of South Africa. However, back-trajectory analysis revealed that atmospheric transport from this region to southern Lesotho is infrequent and the scale of contamination is low. To our knowledge, these data represent the first palaeolimnological records and the first trace contaminant data for Lesotho, and one of the first multi-pollutant historical records for southern Africa. They therefore provide a baseline for future regional assessments in the context of continued coal combustion in South Africa through to the mid-21st century