scholarly journals Electrical network and Lie theory

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Yi Su
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Group ◽  
Electrical Network ◽  
Type B ◽  
Electrical Networks ◽  
Combinatorial Properties ◽  
Type D ◽  
International Audience ◽  
Type C

International audience Curtis-Ingerman-Morrow studied the space of circular planar electrical networks, and classified all possible response matrices for such networks. Lam and Pylyavskyy found a Lie group $EL_{2n}$ whose positive part $(EL_{2n})_{\geq 0}$ naturally acts on the circular planar electrical network via some combinatorial description, where the action is inspired by the star-triangle transformation of the electrical networks. The Lie algebra $el_{2n}$ is semisimple and isomorphic to the symplectic algebra. In the end of their paper, they suggest a generalization of electrical Lie algebras to all finite Dynkin types. We give the structure of the type $B$ electrical Lie algebra $e_{b_{2n}}$. The nonnegative part $(E_{B_{2n}})_{\geq 0}$ of the corresponding Lie group conjecturally acts on a class of "mirror symmetric circular planar electrical networks". This class of networks has interesting combinatorial properties. Finally, we mention some partial results for type $C$ and $D$ electrical Lie algebras, where an analogous story needs to be developed. Curtis, Ingerman et Morrow ont étudié l’espace des réseaux électriques circulaires plans et ont classifié toutes les matrices de réponses possibles pour ces réseaux. Lam et Pylyavskyy ont trouvé un groupe de Lie $EL_{2n}$ dont la partie positive $(EL_{2n})_{\geq 0}$ agit naturellement sur le réseau électrique circulaire plan par une description combinatoire, où l’action est inspirée par la transformation étoile vers triangle des réseaux électriques. L’algèbre de Lie $el_{2n}$ est semi-simple et isomorphe à l’algèbre symplectique. A la fin de leur article, ils proposent une généralisation des algèbres de Lie électriques pour tous les types de Dynkin finis. Nous donnons la structure de l’algèbre de Lie électrique $e_{b_{2n}}$ du type $B$. La partie positive $(E_{B_{2n}})_{\geq 0}$ du groupe de Lie correspondant agit conjecturalement sur une famille de ”miroirs réseaux électriques circulaires symétriques plans”. Cette famille de réseaux a des propriétés combinatoires intéressantes. Nous donnons enfin quelques résultats partiels de l’algèbre de Lie électrique du type $C$ et du type $D$, où une étude analogue doit être développée.

scholarly journals COMMUTATORS OF SKEW-SYMMETRIC MATRICES

2005 ◽  
Vol 15 (03) ◽  
pp. 793-801 ◽  
Author(s):  
ANTHONY M. BLOCH ◽  
ARIEH ISERLES
Keyword(s):  
Optimal Control ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Group ◽  
Geometric Integration ◽  
Symmetric Matrices ◽  
Frobenius Norm

In this paper we develop a theory for analysing the "radius" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra 𝔰𝔬(n) of skew symmetric matrices where we prove [Formula: see text], X, Y ∈ 𝔰𝔬(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control.

scholarly journals The effectiveness of TiO2 additions to mortar to maintain initial conditions in terms of its reflectance to solar radiation

2017 ◽  
Vol 17 (3) ◽  
pp. 39-56 ◽  
Author(s):  
Sérgio Roberto Andrade Dantas ◽  
Fulvio Vittorino ◽  
Kai Loh
Keyword(s):  
Solar Radiation ◽  
Ultraviolet Radiation ◽  
Initial Conditions ◽  
Type A ◽  
Just Noticeable Difference ◽  
Type B ◽  
Climate Conditions ◽  
Type D ◽  
Type C ◽  
Over Time

Abstract Contact of facades with degradation agents and direct incidence of ultraviolet radiation on external coatings make them more opaque over time, affecting their colour and reflectance characteristics. This study evaluated the effect of adding different TiO2 contents to mortars applied in concrete substrates in order to verify the reflectance maintenance on surfaces after exposure over time. Mortar with different concentrations of TiO2 (1%, 5%, 10%) were produced in relation to the total dry premix, added as a powder and compared to unpainted mortar without TiO2 (type "A") and painted mortar without TiO2 (type "B"), both used as a reference for colour and reflectance. Exposed over 16 months to climate conditions in São Paulo, regarding the maintenance of reflectance and solar radiation, the results showed that type "B" (0%TiO2) painted mortar presented the best performance. Type "C" (1%TiO2) and type "D" (5%TiO2) unpainted mortar remained more stable. Type "A" (0%TiO2) and type "E" (10%TiO2) unpainted mortar showed greater differences according to the Just Noticeable Difference (JND) range caused by dirt pick up.

Feasibility, safety, and changes in systolic blood pressure associated with endovascular revascularization of symptomatic and chronically occluded cervical internal carotid artery using a newly suggested radiographic classification of chronically occluded cervical internal carotid artery: pilot study

2019 ◽  
Vol 130 (5) ◽  
pp. 1468-1477 ◽  
Author(s):  
David Hasan ◽  
Mario Zanaty ◽  
Robert M. Starke ◽  
Elias Atallah ◽  
Nohra Chalouhi ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Carotid Artery ◽  
Internal Carotid Artery ◽  
Internal Carotid ◽  
Type B ◽  
Type D ◽  
Type C ◽  
Radiographic Classification

OBJECTIVEThe overall risk of ischemic stroke from a chronically occluded internal carotid artery (COICA) is around 5%–7% per year despite receiving the best available medical therapy. Here, authors propose a radiographic classification of COICA that can be used as a guide to determine the technical success and safety of endovascular recanalization for symptomatic COICA and to assess the changes in systemic blood pressure following successful revascularization.METHODSThe radiographic images of 100 consecutive subjects with COICA were analyzed. A new classification of COICA was proposed based on the morphology, location of occlusion, and presence or absence of reconstitution of the distal ICA. The classification was used to predict successful revascularization in 32 symptomatic COICAs in 31 patients, five of whom were female (5/31 [16.13%]). Patients were included in the study if they had a COICA with ischemic symptoms refractory to medical therapy. Carotid artery occlusion was defined as 100% cross-sectional occlusion of the vessel lumen as documented on CTA or MRA and confirmed by digital subtraction angiography.RESULTSFour types (A–D) of radiographic COICA were identified. Types A and B were more amenable to safe revascularization than types C and D. Recanalization was successful at a rate of 68.75% (22/32 COICAs; type A: 8/8; type B: 8/8; type C: 4/8; type D: 2/8). The perioperative complication rate was 18.75% (6/32; type A: 0/8 [0%]; type B: 1/8 [12.50%]; type C: 3/8 [37.50%], type D: 2/8 [25.00%]). None of these complications led to permanent morbidity or death. Twenty (64.52%) of 31 subjects had improvement in their symptoms at the 2–6 months’ follow-up. A statistically significant decrease in systolic blood pressure (SBP) was noted in 17/21 (80.95%) patients who had successful revascularization, which persisted on follow-up (p = 0.0001). The remaining 10 subjects in whom revascularization failed had no significant changes in SBP (p = 0.73).CONCLUSIONSThe pilot study suggested that our proposed classification of COICA may be useful as an adjunctive guide to determine the technical feasibility and safety of revascularization for symptomatic COICA using endovascular techniques. Additionally, successful revascularization may lead to a significant decrease in SBP postprocedure. A Phase 2b trial in larger cohorts to assess the efficacy of endovascular revascularization using our COICA classification is warranted.

scholarly journals Postsurgical residual lung complications following left upper trisegmentectomy

2019 ◽  
Author(s):  
Yutaro Koike ◽  
Aritoshi Hattori ◽  
Takeshi Matsunaga ◽  
Kazuya Takamochi ◽  
Shiaki Oh ◽  
...  
Keyword(s):  
Surgical Intervention ◽  
Type A ◽  
X Rays ◽  
Limited Information ◽  
Type B ◽  
Type D ◽  
Thoracic Computed Tomography ◽  
Isolated Segment ◽  
Type C ◽  
Lung Torsion

AbstractOBJECTIVESSegmentectomy has become an increasingly popular surgical procedure for small-sized lung lesions. Left upper trisegmentectomy (LUTS) is one of the most common segmentectomies performed because of its relative ease and simplicity; however, limited information is currently available on the specific postoperative complications associated with this procedure.METHODSAmong 2060 surgically resected cases in our institute between 2009 and 2016, 129 (6.2%) underwent LUTS. Postoperative chest X-rays and/or thoracic computed tomography (CT) scans were retrospectively assessed for all cases to assess postsurgical residual lung complications following LUTS. We categorized cases into 4 groups: type A (atelectasis of the lingular segment), type B (lung torsion of the lingular segment), type C (necrosis of the ‘isolated segment’) and type D (haematoma along stapling lines).RESULTSPostsurgical lung complications following LUTS were observed in 17 (13.1%) patients (type A: n = 7, type B: n = 1, type C: n = 4 and type D: n = 5). Three patients (2.3%) required surgical intervention because of type B (n = 1) and type C (n = 2), namely, decreased permeability and remaining ground glass opacities in the residual lung, showing an exacerbated systemic inflammatory response. In contrast, type A and D cases were successfully observed by chest CT without any surgical intervention, and patients recovered within a few months of surgery.CONCLUSIONSWe identified several postoperative residual lung complications following LUTS. Lung torsion or necrosis of the residual segment may require intensive care, including reoperation. Potentially serious complications always need to be ruled out after LUTS when radiological consolidation is detected postoperatively.

A New Classification of Cochleovestibular Malformations and Implications for Predicting Speech Perception Ability after Cochlear Implantation

2015 ◽  
Vol 20 (2) ◽  
pp. 90-101 ◽  
Author(s):  
Sung-Wook Jeong ◽  
Lee-Suk Kim
Keyword(s):  
Speech Perception ◽  
Cochlear Implantation ◽  
Test Scores ◽  
Type A ◽  
Cochlear Nerve ◽  
Type B ◽  
New Classification ◽  
Type D ◽  
Type C

Objectives: The aims of this study were to introduce a new classification of cochleovestibular malformation (CVM) and to investigate how well this classification can predict speech perception ability after cochlear implantation in children with CVM. Methods: Fifty-nine children with CVM who had used a cochlear implant for more than 3 years were included. CVM was classified into 4 subtypes based on the morphology of the cochlea and the modiolus on temporal bone computed tomography (TBCT): normal cochlea and normal modiolus (type A, n = 16), malformed cochlea and partial modiolus (type B, n = 31), malformed cochlea and no modiolus (type C, n = 6), and no cochlea and no modiolus (type D, n = 6). Speech perception test scores were compared between the subtypes of CVM using analysis of covariance with post hoc Bonferroni test. Univariate and multivariate regression analyses were used to identify the significant predictors of the speech perception test scores. Results: The speech perception test scores after implantation were significantly better in children with CVM type A or type B than in children with CVM type C or type D. The test scores did not differ significantly between the implanted children with CVM type A or type B and those without CVM. In univariate regression analysis, the type of CVM was a significant predictor of the speech perception test scores in implanted children with CVM. Multivariate regression analysis revealed that the age at cochlear implantation, cochlear nerve size and preimplantation speech perception test scores were significant predictors of the postimplantation speech perception test scores. The chance of cochlear nerve deficiency increased progressively from CVM type A to type D. Conclusion: The new classification of CVM based on the morphology of the cochlea and the modiolus is simple and easy to use, and correlated well with postimplantation speech perception ability and cochlear nerve status. This simple classification of CVM using TBCT with cochlear nerve assessment by magnetic resonance imaging is helpful in the preoperative evaluation of children with CVM.

scholarly journals Microsurgical Management of Hypoglossal Schwannomas Over 3 Decades: A Modified Grading Scale to Guide Surgical Approach

2011 ◽  
Vol 69 (suppl_2) ◽  
pp. ons121-ons140 ◽  
Author(s):  
Yoichi Nonaka ◽  
Peter M. Grossi ◽  
Ketan R. Bulsara ◽  
Raymond M. Taniguchi ◽  
Allan H. Friedman ◽  
...  
Keyword(s):  
Sural Nerve ◽  
Hypoglossal Nerve ◽  
Type A ◽  
Nerve Graft ◽  
Type B ◽  
Nerve Reconstruction ◽  
Type D ◽  
Grading Scale ◽  
Type C ◽  
Sural Nerve Graft

Abstract BACKGROUND Schwannomas originating from the hypoglossal nerve are extremely rare. Microsurgical resection with the goal for cure has traditionally been associated with a high risk of postoperative deficits. OBJECTIVE To summarize our clinical experience using tailored cranial base approaches for these formidable lesions. METHODS The clinical records of 13 patients were retrospectively reviewed. In addition, all reported patients in the literature were reviewed. The extreme lateral infrajugular transcondylar-transtubercular exposure approach was used in all of our patients. Based on our experience and literature analysis, we propose the following modified grading scale to facilitate surgical planning: type A, intradural tumors; type B, dumbbell-shaped tumors; type C, extracranial tumors; and type D, peripheral tumors. RESULTS All 13 patients underwent total, near-total, or subtotal tumor resection. Eight patients were men, 5 were women (mean age, 41.7 years). Sural nerve graft reconstruction for the hypoglossal nerve was performed in 4 patients. Three of the 4 patients in whom nerve reconstruction was performed regained satisfactory movement of their tongue. In the review of the literature, the mean patient age was 45.8 years. Patients presented with tongue atrophy (91.6%), headache (60.9%), and dysphagia (31.8%). The tumors were categorized as type A in 31.7% of these patients, type B in 38.6%, type C in 6.2%, and type D in 23.4%. CONCLUSION The extreme lateral infrajugular transcondylar-transtubercular exposure approach, which is a modification of the extreme lateral suboccipital approach, provides sufficient exposure for most intracranial dumbbell-shaped hypoglossal schwannomas. Hypoglossal nerve reconstruction using a sural nerve graft improves tongue atrophy and movement for patients with resected nerves.

COMPUTING THE LAW OF A FAMILY OF SOLVABLE LIE ALGEBRAS

2009 ◽  
Vol 19 (03) ◽  
pp. 337-345 ◽  
Author(s):  
JUAN C. BENJUMEA ◽  
JUAN NÚÑEZ ◽  
ÁNGEL F. TENORIO
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Group ◽  
Triangular Matrices ◽  
Upper Triangular Matrices ◽  
Computational Data ◽  
Solvable Lie Algebras ◽  
Final Output ◽  
The Matrix ◽  
The Law

This paper shows an algorithm which computes the law of the Lie algebra associated with the complex Lie group of n × n upper-triangular matrices with exponential elements in their main diagonal. For its implementation two procedures are used, respectively, to define a basis of the Lie algebra and the nonzero brackets in its law with respect to that basis. These brackets constitute the final output of the algorithm, whose unique input is the matrix order n. Besides, its complexity is proved to be polynomial and some complementary computational data relative to its implementation are also shown.

scholarly journals Pigmentary demarcation lines: a clinical profile of 50 subjects and report of new pattern of pigmentation observed

2018 ◽  
Vol 4 (3) ◽  
pp. 323
Author(s):  
Anju Antony ◽  
Pramod Kumar
Keyword(s):  
Family History ◽  
Type A ◽  
Common Type ◽  
Type B ◽  
Demarcation Line ◽  
Abrupt Transition ◽  
Type D ◽  
History Of ◽  
Type C ◽  
The Common

<p class="abstract"><strong>Background:</strong> Pigmentary demarcation lines (PDL) correspond to a border of abrupt transition between the more deeply pigmented skin of the outer surfaces and the lighter inner surfaces. On the basis of their location they have been classified into eight types, type A to type H. The present study is an attempt to obtain a better understanding of the clinical types of pigmentary demarcation lines in Indians, and to report any previously undescribed patterns of pigmentation.</p><p class="abstract"><strong>Methods:</strong> Patients attending the Outpatient Department for various complaints were examined for the presence of pigmentary demarcation lines, and those with pigmentary demarcation lines were analysed further.<strong></strong></p><p class="abstract"><strong>Results:</strong> 50 subjects of Fitzpatrick skin types 4 and 5, with pigmentary demarcation lines were examined in detail. The various types of pigmentary demarcation lines seen were Type A (38%), Type B (14%), Type C (24%), Type F (22%), Type G (4%), Type H (4%). All types were more common in females with the exception of Type C, which was observed only in males. Type D and Type E PDL were not observed in any of the subjects screened.</p><p class="abstract"><strong>Conclusions:</strong> The most common type of PDL observed in our study was Type A PDL, followed by Type C PDL. The youngest subject was 2 years old, the oldest was aged 75.The majority were seen in adults; Type A and Type C PDL were the common types seen in children. A family history of PDL was present in 5 (10%) and all were females. A hitherto undescribed pigmentary demarcation line is also described along with this study.</p>

scholarly journals The impact of intravertebral cleft on cement leakage in percutaneous vertebroplasty for osteoporotic vertebral compression fractures: a case-control study

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Benqiang Tang ◽  
Songjie Xu ◽  
Xueming Chen ◽  
Libin Cui ◽  
Yanhui Wang ◽  
...  
Keyword(s):  
Case Control Study ◽  
Percutaneous Vertebroplasty ◽  
Cement Leakage ◽  
Vertebral Compression Fractures ◽  
Type B ◽  
Type D ◽  
Vein Type ◽  
Type C ◽  
The Impact ◽  
Control Study

Abstract Background The impact of intravertebral cleft (IVC) on cement leakage in percutaneous vertebroplasty (PVP) for osteoporotic vertebral compression fractures (OVCFs) has been discussed. However, the results were conflicting, as the study population and cement leakage classification were heterogeneous. The aim of the study was to evaluate the impact of IVC on the incidence of leakage through vein, leakage through cortex as well as general leakage in PVP for OVCFs. Methods All patients with OVCFs who underwent PVP between January 2016 and June 2019 at our institution were retrospectively reviewed. Patients were eligible for this case-control study if they were diagnosed as single level fracture in spine. After inclusive and exclusive criteria were met, a total of 139 patients with IVC were enrolled as the study group. Non-IVC controls were matched in a 1:1 ratio in age (within 3 years), sex and fracture severity with patients in study group. Cement leakage were classified into four types [type B (through basivertebral vein), type S (through segmental vein), type-C (through a cortical defect), and type D (intradiscal leakage)], furtherly into two types [venous type (type-B or/and type S) and cortical type (type-C or/and type-D)]. A general leakage rate and a specific leakage rate per each type were compared between both groups. Results Each group included 139 patients. Groups were homogenous for age, sex, fracture severity, fracture location, fracture type, cement volume, puncture approach and property of cement. Compared with control group, IVC group had a significantly lower rate of type-B (20.9% vs. 31.7%, P = 0.041), type-S (24.5% vs. 52.5%, P = 0.000), and venous type leakage (37.4% vs. 67.6%, P = 0.000), a significantly higher rate of type-C (25.9% vs. 12.2%, P = 0.004), type-D (16.5% vs. 6.5%, P = 0.009), and cortical type leakage (40.3% vs. 16.5%, P = 0.000), no significant difference on the rate of general leakage (67.6% vs. 76.3%, P = 0.109). Conclusion IVC decreased the risk of cement leakage through vein and increased the risk of cement leakage through cortex. However, it had no significant effect on the occurrence of general leakage.

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