Vertex Sparsifiers: New Results from Old Techniques

Given a capacitated graph $G = (V,E)$ and a set of terminals $K \subseteq V$, how should we produce a graph $H$ only on the terminals $K$ so that every (multicommodity) flow between the terminals in $G$ could be supported in $H$ with low congestion, and vice versa? (Such a graph $H$ is called a flow-sparsifier for $G$.) What if we want $H$ to be a "simple" graph? What if we allow $H$ to be a convex combination of simple graphs? Improving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC 2010], we give efficient algorithms for constructing: (a) a flow-sparsifier $H$ that maintains congestion up to a factor of $O(\log k/\log \log k)$, where $k = |K|$, (b) a convex combination of trees over the terminals $K$ that maintains congestion up to a factor of $O(\log k)$, and (c) for a planar graph $G$, a convex combination of planar graphs that maintains congestion up to a constant factor. This requires us to give a new algorithm for the 0-extension problem, the first one in which the preimages of each terminal are connected in $G$. Moreover, this result extends to minor-closed families of graphs. Our improved bounds immediately imply improved approximation guarantees for several terminal-based cut and ordering problems.Comment: An extended abstract appears in the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX), 2010. Final version to appear in SIAM J. Computin

Measuring the refractive index of bovine corneal stromal cells using quantitative phase imaging

The cornea is the primary refractive lens in the eye and transmits >90% of incident visible light. It has been suggested that the development of postoperative corneal haze could be due to an increase in light scattering from activated corneal stromal cells. Quiescent keratocytes are thought to produce crystallins that match the refractive index of their cytoplasm to the surrounding extracellular material, reducing the amount of light scattering. To test this, we measured the refractive index (RI) of bovine corneal stromal cells, using quantitative phase imaging of live cells in vitro, together with confocal microscopy. The RI of quiescent keratocytes (RI = 1.381 ± 0.004) matched the surrounding matrix, thus supporting the hypothesis that keratocyte cytoplasm does not scatter light in the normal cornea. We also observed that the RI drops after keratocyte activation (RI = 1.365 ± 0.003), leading to a mismatch with the surrounding intercellular matrix. Theoretical scattering models showed that this mismatch would reduce light transmission in the cornea. We conclude that corneal transparency depends on the matching of refractive indices between quiescent keratocytes and the surrounding tissue, and that after surgery or wounding, the resulting RI mismatch between the activated cells and their surrounds significantly contributes to light scattering

The effect of vitamin C deficiency and chronic ultraviolet-B exposure on corneal ultrastructure: a preliminary investigation

Purpose: In the visually debilitating condition of climatic droplet keratopathy, corneal transparency is progressively lost. Although the precise cause of the disease and the mechanism by which it progresses are not known, a lifetime exposure to high solar radiation and a vitamin C–deficient diet may be involved in its development. This study examines the effect of dietary ascorbate levels and ultraviolet (UV)-B exposure on corneal stromal structure. Methods: Eight guinea pigs were divided into four treatment groups (A, B, C, and D). For 15 weeks, Groups A and C were fed an ascorbate-rich diet (2 mg/100 g bodyweight/day), while Groups B and D received an ascorbate-deficient diet (0.07 mg/100 g bodyweight/day). For the last 12 weeks of the study, Groups C and D also experienced chronic UVB exposure (0.12 J/cm2 for 40 min/day). Following euthanasia, the corneas were enucleated and their stromal ultrastructure examined using X-ray scattering and electron microscopy. Results: UVB exposure resulted in an increased corneal thickness (p<0.001), but this was not accompanied by a widespread expansion of the collagen fibrillar array, and in the case of ascorbate-deficient animals, stromal thickening was associated with the compaction of collagen fibrils (p<0.01). Neither UVB exposure nor ascorbic acid deficiency caused any change in the average diameter or D-periodicity of the stromal collagen fibrils. Conclusions: UVB-induced changes in the corneal ultrastructure were most pronounced in animals fed an ascorbic acid–deficient diet. This suggests that ascorbic acid may play a vital role in protecting the corneal stroma from the harmful effects of UVB

Deregulated expression of hnRNP A/B proteins in human non-small cell lung cancer: parallel assessment of protein and mRNA levels in paired tumour/non-tumour tissues

<p>Abstract</p> <p>Background</p> <p>Heterogeneous nuclear ribonucleoproteins (hnRNPs) of the A/B type (hnRNP A1, A2/B1, A3) are highly related multifunctional proteins participating in alternative splicing by antagonising other splicing factors, notably ASF/SF2. The altered expression pattern of hnRNP A2/B1 and/or splicing variant B1 alone in human lung cancer and their potential to serve as molecular markers for early diagnosis remain issues of intense investigation. The main objective of the present study was to use paired tumour/non-tumour biopsies from patients with non-small cell lung cancer (NSCLC) to investigate the expression profiles of hnRNP A1, A2/B1 and A3 in conjunction with ASF/SF2.</p> <p>Methods</p> <p>We combined western blotting of tissue homogenates with immunohistochemical examination of fixed tissue sections and quantification of mRNA expression levels in tumour versus adjacent normal-looking areas of the lung in the same patient.</p> <p>Results</p> <p>Our study, in addition to clear evidence of mostly uncoupled deregulation of hnRNPs A/B, has revealed hnRNP A1 to be the most deregulated protein with a high frequency of over-expression (76%), followed by A3 (52%) and A2/B1 (43%). Moreover, direct comparison of protein/mRNA levels showed a lack of correlation in the case of hnRNP A1 (as well as of ASF/SF2), but not of A2/B1, suggesting that different mechanisms underlie their deregulation.</p> <p>Conclusion</p> <p>Our results provide strong evidence for the up-regulation of hnRNP A/B in NSCLC, and they support the existence of distinct mechanisms responsible for their deregulated expression.</p

The effect of vitamin C deficiency and chronic ultraviolet-B exposure on corneal ultrastructure: a preliminary investigation

Purpose: In the visually debilitating condition of climatic droplet keratopathy, corneal transparency is progressively lost. Although the precise cause of the disease and the mechanism by which it progresses are not known, a lifetime exposure to high solar radiation and a vitamin C–deficient diet may be involved in its development. This study examines the effect of dietary ascorbate levels and ultraviolet (UV)-B exposure on corneal stromal structure. Methods: Eight guinea pigs were divided into four treatment groups (A, B, C, and D). For 15 weeks, Groups A and C were fed an ascorbate-rich diet (2 mg/100 g bodyweight/day), while Groups B and D received an ascorbate-deficient diet (0.07 mg/100 g bodyweight/day). For the last 12 weeks of the study, Groups C and D also experienced chronic UVB exposure (0.12 J/cm2 for 40 min/day). Following euthanasia, the corneas were enucleated and their stromal ultrastructure examined using X-ray scattering and electron microscopy. Results: UVB exposure resulted in an increased corneal thickness (p<0.001), but this was not accompanied by a widespread expansion of the collagen fibrillar array, and in the case of ascorbate-deficient animals, stromal thickening was associated with the compaction of collagen fibrils (p<0.01). Neither UVB exposure nor ascorbic acid deficiency caused any change in the average diameter or D-periodicity of the stromal collagen fibrils. Conclusions: UVB-induced changes in the corneal ultrastructure were most pronounced in animals fed an ascorbic acid–deficient diet. This suggests that ascorbic acid may play a vital role in protecting the corneal stroma from the harmful effects of UVB

Efficacy of Er:YAG laser on periodontitis as an adjunctive non‐surgical treatment: A split‐mouth randomized controlled study

Aim To evaluate the adjunctive efficacy of Er:YAG laser use with mechanical scaling and root planing (SRP ) for non‐surgical treatment of periodontitis. Materials and Methods In a randomized, single‐blinded, controlled trial, 27 patients were recruited. Using a split‐mouth design, two quadrants were randomly allocated into either a test group or a control group. The test quadrants received Er:YAG laser (ERL ; 100 mJ /pulse; 15 Hz to hard tissue and 50 mJ /pulse; 30 Hz to soft tissue) plus SRP treatment, while the control quadrants received SRP only. We evaluated periodontal indexes, including probing depth (PD ), clinical attachment level (CAL ), bleeding index (BI ), and plaque index (PLI ) at baseline, 3 months, and 6 months. Results The PD and CAL means in the ERL + SRP group were significantly lower than those in the SRP group at 3‐month follow‐up (PD : 2.98 ± 0.38 mm vs. 3.09 ± 0.35 mm; CAL : 4.51 ± 0.69 mm vs. 4.72 ± 0.67 mm) and 6‐month follow‐up (PD : 2.91 ± 0.31 mm vs. 3.02 ± 0.30 mm; CAL : 4.52 ± 0.65 mm vs. 4.72 ± 0.66 mm; p = 0.03 for both PD and CAL ). There were no significant differences in BI and PLI between two groups. Conclusions The Er:YAG laser treatment combined with conventional SRP significantly improved PD and CAL compared to SRP therapy alone; however, these differences were very small and, as a result, the adjunctive effect of Er:YAG laser is likely to be minimal clinically important

Effect of smoking on subgingival microflora of patients with periodontitis in Japan

<p>Abstract</p> <p>Background</p> <p>Smoking is a risk factor for periodontitis. To clarify the contribution of smoking to periodontitis, it is essential to assess the relationship between smoking and the subgingival microflora. The aim of this study was to gain an insight into the influence of smoking on the microflora of Japanese patients with periodontitis.</p> <p>Methods</p> <p>Sixty-seven Japanese patients with chronic periodontitis (19 to 83 years old, 23 women and 44 men) were enrolled in the present study. They consisted of 30 smokers and 37 non-smokers. Periodontal parameters including probing pocket depth (PPD) and bleeding on probing (BOP) and oral hygiene status were recorded. Detection of <it>Aggregatibacter actinomycetemcomitans, Porphyromonas gingivalis, Prevotella intermedia, Tannerella forsythia, Fusobacterium nucleatum/periodonticum, Treponema denticola </it>and <it>Campylobacter rectus </it>in subgingival plaque samples was performed by polymerase chain reaction. Association between the detection of periodontopathic bacteria and smoking status was analyzed by multiple logistic regression analysis and chi-square test.</p> <p>Results</p> <p>A statistically significant association was found between having a PPD ≥ 4 mm and detection of <it>T. denticola, P. intermedia, T. forsythia</it>, or <it>C. rectus</it>, with odds ratios ranging from 2.17 to 3.54. A significant association was noted between BOP and the detection of <it>C. rectus </it>or <it>P. intermedia</it>, and smoking, with odds ratios ranging from 1.99 to 5.62. Prevalence of <it>C. rectus </it>was higher in smokers than non-smokers, whereas that of <it>A. actinomycetemcomitans </it>was lower in smokers.</p> <p>Conclusions</p> <p>Within limits, the analysis of the subgingival microbial flora in smokers and non-smokers with chronic periodontitis suggests a relevant association between smoking and colonization by the specific periodontal pathogens including <it>C. rectus</it>.</p

Quantification of collagen organization in the peripheral human cornea at micron-scale resolution

The collagen microstructure of the peripheral cornea is important in stabilizing corneal curvature and refractive status. However, the manner in which the predominantly orthogonal collagen fibrils of the central cornea integrate with the circumferential limbal collagen is unknown. We used microfocus wide-angle x-ray scattering to quantify the relative proportion and orientation of collagen fibrils over the human corneolimbal interface at intervals of 50 μm. Orthogonal fibrils changed direction 1–1.5 mm before the limbus to integrate with the circumferential limbal fibrils. Outside the central 6 mm, additional preferentially aligned collagen was found to reinforce the cornea and limbus. The manner of integration and degree of reinforcement varied significantly depending on the direction along which the limbus was approached. We also employed small-angle x-ray scattering to measure the average collagen fibril diameter from central cornea to limbus at 0.5 mm intervals. Fibril diameter was constant across the central 6 mm. More peripherally, fibril diameter increased, indicative of a merging of corneal and scleral collagen. The point of increase varied with direction, consistent with a scheme in which the oblique corneal periphery is reinforced by chords of scleral collagen. The results have implications for the cornea's biomechanical response to ocular surgeries involving peripheral incision

Riboflavin/UVA Collagen Cross-Linking-Induced Changes in Normal and Keratoconus Corneal Stroma

Purpose To determine the effect of Ultraviolet-A collagen cross-linking with hypo-osmolar and iso-osmolar riboflavin solutions on stromal collagen ultrastructure in normal and keratoconus ex vivo human corneas. Methods Using small-angle X-ray scattering, measurements of collagen D-periodicity, fibril diameter and interfibrillar spacing were made at 1 mm intervals across six normal post-mortem corneas (two above physiological hydration (swollen) and four below (unswollen)) and two post-transplant keratoconus corneal buttons (one swollen; one unswollen), before and after hypo-osmolar cross-linking. The same parameters were measured in three other unswollen normal corneas before and after iso-osmolar cross-linking and in three pairs of swollen normal corneas, in which only the left was cross-linked (with iso-osmolar riboflavin). Results Hypo-osmolar cross-linking resulted in an increase in corneal hydration in all corneas. In the keratoconus corneas and unswollen normal corneas, this was accompanied by an increase in collagen interfibrillar spacing (p<0.001); an increase in fibril diameter was also seen in two out of four unswollen normal corneas and one unswollen keratoconus cornea (p<0.001). Iso-osmolar cross-linking resulted in a decrease in tissue hydration in the swollen normal corneas only. Although there was no consistent treatment-induced change in hydration in the unswollen normal samples, iso-osmolar cross-linking of these corneas did result in a compaction of collagen fibrils and a reduced fibril diameter (p<0.001); these changes were not seen in the swollen normal corneas. Collagen D-periodicity was not affected by either treatment. Conclusion The observed structural changes following Ultraviolet-A cross-linking with hypo-osmolar or iso-osmolar riboflavin solutions are more likely a consequence of treatment-induced changes in tissue hydration rather than cross-linking