The expected mean width of a random polytope associated with a ball

2012 ◽  
Vol 53 (2) ◽  
pp. 571-577
Author(s):  
Uwe Bäsel
Keyword(s):  
Random Polytope ◽  
Mean Width

scholarly journals Interaction of Poisson hyperplane processes and convex bodies

2019 ◽  
Vol 56 (4) ◽  
pp. 1020-1032 ◽  
Author(s):  
Rolf Schneider
Keyword(s):  
Convex Body ◽  
Convex Bodies ◽  
Random Polytope ◽  
Mean Width ◽  
The Mean

AbstractGiven a stationary and isotropic Poisson hyperplane process and a convex body K in ${\mathbb R}^d$ , we consider the random polytope defined by the intersection of all closed half-spaces containing K that are bounded by hyperplanes of the process not intersecting K. We investigate how well the expected mean width of this random polytope approximates the mean width of K if the intensity of the hyperplane process tends to infinity.

scholarly journals Ethnic variation in medial orbital wall anatomy and its implications for decompression surgery

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Minhui Amy Chan ◽  
Farah Ibrahim ◽  
Arjunan Kumaran ◽  
Kailing Yong ◽  
Anita Sook Yee Chan ◽  
...  
Keyword(s):  
Relative Position ◽  
Ethmoid Sinus ◽  
Decompression Surgery ◽  
Ethnic Variation ◽  
Sinus Wall ◽  
Orbital Wall ◽  
Mean Width ◽  
Significant Difference ◽  
The Mean ◽  
Medial Orbital Wall

Abstract Background To describe the inter-ethnic variation in medial orbital wall anatomy between Chinese, Malay, Indian and Caucasian subjects. Methods Single-centre, retrospective, Computed Tomography (CT)-based observational study. 20 subjects of each ethnicity, were matched for gender and laterality. We excluded subjects younger than 16 years and those with orbital pathology. OsiriX version 8.5.1 (Pixmeo., Switzerland) and DICOM image viewing software CARESTREAM Vue PACS (Carestream Health Inc., USA) were used to measure the ethmoidal sinus length, width and volume, medial orbital wall and floor angle and the relative position of the posterior ethmoid sinus to the posterior maxillary wall. Statistical analyses were performed using Statistical Package for Social Sciences version 25.0 (IBM, USA). Results There were 12 males (60 %) in each group, with no significant difference in age (p = 0.334–0.994). The mean ethmoid sinus length in Chinese, Malay, Indian and Caucasian subjects, using the Chinese as reference, were 37.2, 36.9, 38.0 and 37.4mm, the mean width was 11.6, 10.5, 11.4 and 10.0mm (p = 0.020) and the mean ethmoid sinus volume were 3362, 3652, 3349 and 3898mm3 respectively. The mean medial orbital wall and floor angle was 135.0, 131.4, 131.0 and 136.8 degrees and the mean relative position of posterior ethmoid sinus to posterior maxillary wall were − 2.0, -0.2, -1.5 and 1.6mm (p = 0.003) respectively. Conclusions No inter-ethnic variation was found in decompressible ethmoid sinus volume. Caucasians had their posterior maxillary sinus wall anterior to their posterior ethmoidal walls unlike the Chinese, Malay and Indians. Awareness of ethnic variation is essential for safe orbital decompression.

scholarly journals Electrochemical treatment of ex vivo human abdominal skin and potential use in scar management: A pilot study

2021 ◽  
Vol 7 ◽  
pp. 205951312098853
Author(s):  
Dana M Hutchison ◽  
Amir A Hakimi ◽  
Avin Wijayaweera ◽  
Soohong Seo ◽  
Ellen M Hong ◽  
...  
Keyword(s):  
Color Change ◽  
Ex Vivo ◽  
Low Cost ◽  
Histological Evaluation ◽  
Ph Change ◽  
Level Of Evidence ◽  
Abdominal Skin ◽  
Electrochemical Therapy ◽  
Mean Width ◽  
Scar Management

Introduction: Scar treatments aim to address pathologic collagen deposition; however, they can be expensive or difficult to control. Electrochemical therapy (ECT) offers a simple alternative treatment. The purpose of this study is to examine the acid-base and histological changes in ex vivo human abdominal skin following ECT. Methods: Forty-two ex vivo human panniculus tissue sections collected from six individuals were tumesced with normal saline. ECT was performed by inserting two platinum needle electrodes connected to a DC power supply into each specimen. Voltage was varied (3–6 V) and applied for 5 minutes. Each specimen was sectioned across both electrode insertion sites and immediately stained with pH sensitive dye. The width of dye color change for each dosimetry pair was calculated. Hematoxylin and eosin staining was used to evaluate samples. Results and Discussion: ECT caused a spatially localised and dose-dependent increased area of acidic and basic pH around the anode and cathode, respectively. A significantly greater mean width of pH change was generated at the cathode compared to the anode in all treatment groups. Histological evaluation displayed broad condensation and hyalinisation of dermal collagen. Conclusion: ECT triggered dermal pH alterations and changed the underlying structural framework of the specimen. This technology may serve as a low-cost, minimally invasive local soft-tissue remodeling technique with potential application in scar management. Level of Evidence: 5 Lay Summary Electrochemical therapy is a novel treatment that causes spatially selective dermal injury in areas of interest. This study measures the effects of electrochemical therapy when applied to abdominal skin. Electrochemical therapy appears to have beneficial effects by causing a highly localised reduction in collagen content or local softening of tissue, which is consistent with other studies on scar therapies, including chemexfoliation, radiofrequency technologies, and lasers. However, electrochemical therapy can be performed at a fraction of the costs of these aforementioned modalities.

scholarly journals Convex Bodies of Minimal Volume, Surface Area and Mean Width with Respect to Thin Shells

2008 ◽  
Vol 60 (1) ◽  
pp. 3-32 ◽  
Author(s):  
Károly Böröczky ◽  
Károly J. Böröczky ◽  
Carsten Schütt ◽  
Gergely Wintsche
Keyword(s):  
Unit Ball ◽  
Surface Area ◽  
Convex Bodies ◽  
Extreme Points ◽  
Thin Shells ◽  
Minimal Volume ◽  
Asymptotic Formulae ◽  
Mean Width

AbstractGiven r > 1, we consider convex bodies in En which contain a fixed unit ball, and whose extreme points are of distance at least r from the centre of the unit ball, and we investigate how well these convex bodies approximate the unit ball in terms of volume, surface area and mean width. As r tends to one, we prove asymptotic formulae for the error of the approximation, and provide good estimates on the involved constants depending on the dimension.

Cervical and High Thoracic Ligamentum Flavum Frequently Fails to Fuse in the Midline

2003 ◽  
Vol 99 (6) ◽  
pp. 1387-1390 ◽  
Author(s):  
Philipp Lirk ◽  
Christian Kolbitsch ◽  
Guenther Putz ◽  
Joshua Colvin ◽  
Hans Peter Colvin ◽  
...  
Keyword(s):  
Ligamentum Flavum ◽  
Epidural Needle ◽  
Complete Fusion ◽  
Thoracic Epidural ◽  
Loss Of Resistance ◽  
Ligamenta Flava ◽  
Mean Width ◽  
Human Cadavers ◽  
The Mean ◽  
High Thoracic Epidural

Background Cervical and high thoracic epidural anesthesia and analgesia have gained increasing importance in the treatment of painful conditions and as components of anesthetics for cardiac and breast surgery. In contrast to the hanging-drop technique, the loss-of-resistance technique is thought to rely on the penetration of the ligamentum flavum. However, the exact morphology of the ligamentum flavum at different vertebral levels remains controversial. Therefore, the aim of this study was to investigate the incidence and morphology of cervical and high thoracic ligamentum flavum mid-line gaps in embalmed cadavers. Methods Vertebral column specimens were obtained from 52 human cadavers. On each dissected level, ligamentum flavum mid-line gaps were recorded and evaluated with respect to shape and size. Results The following variations were encountered: complete fusion in the mid-line, mid-line fusion with a gap in the caudal part, mid-line gap, and mid-line gap with widened caudal end. The incidence of mid-line gaps at the following levels was: C3-C4: 66%, C4-C5: 58%, C5-C6: 74%, C6-C7: 64%, C7-T1: 51%, Th1-Th2: 21%, Th2-Th3: 11%, Th3-Th4: 4%, Th4-Th5: 2%, and Th5-Th6: 2%. The mean width of mid-line gaps was 1.0 +/- 0.3 mm. Conclusions In conclusion, the present study shows that gaps in the ligamenta flava are frequent at cervical and high thoracic levels but become rare at the T3/T4 level and below, such that one cannot always rely on the ligamentum flavum as a perceptible barrier to epidural needle placement at these levels.

scholarly journals Radiographic Measurement of Cochlear in Sudanese Population using High Resolution Computed Tomography (HRCT)

2021 ◽  
Vol 29 (2) ◽  
Author(s):  
Lubna Bushara ◽  
Mohamed Yousef ◽  
Ikhlas Abdelaziz ◽  
Mogahid Zidan ◽  
Dalia Bilal ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Hearing Loss ◽  
High Resolution ◽  
Temporal Bone ◽  
Healthy Subjects ◽  
Cochlear Nerve ◽  
High Resolution Computed Tomography ◽  
Mean Width ◽  
The Mean ◽  
The Right

This study aimed to determine the measurements of the cochlea among healthy subjects and hearing deafness subjects using a High Resolution Computed Tomography (HRCT). A total of 230 temporal bone HRCT cases were retrospectively investigated in the period spanning from 2011 to 2015. Three 64-slice units were used to examine patients with clinical complaints of hearing loss conditions at three Radiology departments in Khartoum, Sudan. For the control group (A) healthy subjects, the mean width of the right and left cochlear were 5.61±0.40 mm and 5.56±0.58 mm, the height were 3.56±0.36 mm and 3.54±0.36 mm, the basal turn width were 1.87±0.19 mm and 1.88 ±0.18 mm, the width of the cochlear nerve canal were 2.02±1.23 and 1.93±0.20, cochlear nerve density was 279.41±159.02 and 306.84±336.9 HU respectively. However, for the experimental group (B), the mean width of the right and left cochlear width were 5.38±0.46 mm and 5.34±0.30 mm, the height were 3.53±0.25 mm and 3.49±0.28mm, the basal turn width were 1.76±0.13 mm, and 1.79±0.13 mm, the width of the cochlear nerve canal were 1.75±0.18mm and 1.73±0.18mm, and cochlear nerve density were 232.84±316.82 and 196.58±230.05 HU, respectively. The study found there was a significant difference in cochlea’s measurement between the two groups with a p-value < 0.05. This study had established baseline measurements for the cochlear for the healthy Sudanese population. Furthermore, it found that HRCT of the temporal bone was the best for investigation of the cochlear and could provide a guide for the clinicians to manage congenital hearing loss.

scholarly journals The Micro-Geometry Evaluation on Steel Sheets after Chemical Surface Treatment

2013 ◽  
Vol 10 (2) ◽  
pp. 22-25
Author(s):  
Dagmar Draganovská ◽  
Miroslav Tomáš ◽  
Peter Ižol
Keyword(s):  
Surface Treatment ◽  
Steel Sheet ◽  
Unit Length ◽  
Mean Deviation ◽  
Maximum Height ◽  
Chemical Surface ◽  
Steel Sheets ◽  
Mean Width ◽  
The Mean ◽  
Metal Materials

Abstract The protection of metal materials by coatings is one of the most important way to protect the surface against corrosion. Galvanisation of metal surfaces by an electric current is one of the most frequent way of surface treatment due to its wide application. The paper is oriented to the evaluation of the surface quality in terms of micro-geometry. The basic surface of the steel sheet S235JRG2 has been evaluted and compared to the degreased one, galvanized one and surface after galvanizing, chromatizing and phosphating. The microgeometry parameters such as the arithmetical mean deviation Ra, the maximum height of profile Rz, the total height of profile Rt as well as the the mean width of the profile elements RSm and the number of peaks per unit length RPc has been compared.

scholarly journals First Report of Botryotinia fuckeliana Causing Soft Rots in Potato in Scotland

Plant Disease ◽  
2000 ◽  
Vol 84 (7) ◽  
pp. 806-806 ◽  
Author(s):  
J. W. Choiseul ◽  
S. F. Carnegie
Keyword(s):  
Room Temperature ◽  
Solanum Tuberosum L ◽  
Gray Mold ◽  
Agricultural Science ◽  
Seed Potatoes ◽  
Low Temperature Storage ◽  
Agar Plug ◽  
Mean Width ◽  
Affected Tissue ◽  
Botryotinia Fuckeliana

Botryotinia fuckeliana (de Bary) Whetzel (syn. Botrytis cinerea Pers.:Fr.) causes gray mold on the foliage of a large range of horticultural and agricultural crops, including potato (Solanum tuberosum L.). This weak pathogen may also produce pit rots on potato tubers (1). In April 1999, two lots of seed potatoes produced in Scotland were found to contain a significant number of tubers with soft rots. The cultivars were Maritiema and Charlotte, with 2.2 and 0.5% of rotted tubers, respectively. The rots on tubers of cv. Maritiema were all soft, wet, and extensive, with a distinct edge, but the proportion of this type of rot was much lower (approximately 30%) on the cv. Charlotte tubers. Gray sporangiophores developed around tuber eyes. When the tubers were cut, the affected tissue was peach to pink-gray in color but darkened on exposure to air, and was soft and water-soaked in appearance with a pale brown or, occasionally, yellow margin. A faint vinegary odor could be detected occasionally. B. fuckeliana was isolated on potato dextrose agar (PDA) from all 15 tubers of cv. Maritiema and from the three (out of 13) tubers of cv. Charlotte that had large, soft rots. Tubers produced at Scottish Agricultural Science Agency's Gogarbank farm near Edinburgh in 1998 were used for confirmatory pathogenicity tests conducted in late April and May 1999. Using a cork borer, a wound 5 mm in diameter and 5 mm deep was made in each tuber and 5-mm-diameter agar plug from either the edge of a colony of B. fuckeliana or of PDA was inserted into the wound. Nine tubers of cvs. Maritiema and Charlotte were inoculated for each treatment and tubers incubated at 5°C in boxes lined with moist filter paper. Rots, similar to those on the commercial seed tubers, developed after 28 days at wound sites inoculated with B. fuckeliana. The fungus was isolated by placing a small piece of rotted tissue from each rot on PDA. B. fuckeliana was recovered from all rots. The mean width of rots was 51 mm for cv. Maritiema compared with 40 mm for cv. Charlotte. Depth of rots was similar for both varieties. Lesions did not develop at wound sites inoculated with PDA agar only. In a second experiment, tubers of cv. Maritiema were inoculated with B. fuckeliana as described above and incubated at 5°C or room temperature (15 to 18°C). There were nine tubers for each temperature. After 21 days, no lesions had developed on tubers incubated at room temperature, but large, soft rots were present on those incubated at 5°C. The lesions produced by B. fuckeliana in these experiments were relatively large compared with the 5-m-deep rots reported previously (1) after 60 days of incubation. The appearance of these rots is similar to that for other diseases, e.g., pink rot and watery wound rot, and infections by this fungus may have been incorrectly diagnosed in the past. Moreover, the development of such rots may be favored by the recent increase in the use of low temperature storage for seed potatoes. Reference: (1) H. W. Platt. Can. J. Plant. Pathol. 16:341, 1994.

Processing of form and motion in area 21a of cat visual cortex

1993 ◽  
Vol 10 (1) ◽  
pp. 93-115 ◽  
Author(s):  
B. Dreher ◽  
A. Michalski ◽  
R. H. T. Ho ◽  
C. W. F. Lee ◽  
W. Burke
Keyword(s):  
Spatial Organization ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Orientation Tuning ◽  
Area 17 ◽  
Horizontal Strip ◽  
Tuning Curves ◽  
Mean Width ◽  
Area 21A ◽  
The Mean

AbstractExtracellular recordings from single neurons have been made from presumed area 21a of the cerebral cortex of the cat, anesthetized with N2O/O2/sodium pentobarbitone mixture. Area 21a contains mainly a representation of a central horizontal strip of contralateral visual field about 5 deg above and below the horizontal meridian.Excitatory discharge fields of area 21a neurons were substantially (or slightly but significantly) larger than those of neurons at corresponding eccentricities in areas 17, 19, or 18, respectively. About 95% of area 21a neurons could be activated through either eye and the input from the ipsilateral eye was commonly dominant. Over 90% and less than 10% of neurons had, respectively, C-type and S-type receptive-field organization. Virtually all neurons were orientation-selective and the mean width at half-height of the orientation tuning curves at 52.9 deg was not significantly different from that of neurons in areas 17 and 18. About 30% of area 21a neurons had preferred orientations within 15 deg of the vertical.The mean direction-selectivity index (32.8%) of area 21a neurons was substantially lower than the indices for neurons in areas 17 or 18. Only a few neurons exhibited moderately strong end-zone inhibition. Area 21a neurons responded poorly to fast-moving stimuli and the mean preferred velocity at about 12.5 deg/s was not significantly different from that for area 17 neurons.Selective pressure block of Y fibers in contralateral optic nerve resulted in a small but significant reduction in the preferred velocities of neurons activated via the Y-blocked eye. By contrast, removal of the Y input did not produce significant changes in the spatial organization of receptive fields (S or C type), the size of the discharge fields, the width of orientation tuning curves, or direction-selectivity indices.Our results are consistent with the idea that area 21a receives its principal excitatory input from area 17 and is involved mainly in form rather than motion analysis.

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