Symmetries of double ratios and an equation for Möbius structures

2021 ◽  
Vol 33 (1) ◽  
pp. 47-56
Author(s):  
S. Buyalo
Keyword(s):  
Symmetric Groups ◽  
Content Type ◽  
Irreducible Components ◽  
Orthogonal Representations

Orthogonal representations η n : S n ↷ R N \eta _n\colon S_n\curvearrowright \mathbb {R}^N of the symmetric groups S n S_n , n ≥ 4 n\ge 4 , with N = n ! / 8 N=n!/8 , emerging from symmetries of double ratios are treated. For n = 5 n=5 , the representation η 5 \eta _5 is decomposed into irreducible components and it is shown that a certain component yields a solution of the equations that describe the Möbius structures in the class of sub-Möbius structures. In this sense, a condition determining the Möbius structures is implicit already in symmetries of double ratios.

scholarly journals Goodwillie Approximations to Higher Categories

2021 ◽  
Vol 272 (1333) ◽  
Author(s):  
Gijs Heuts
Keyword(s):  
Homotopy Theory ◽  
Symmetric Groups ◽  
Homotopy Groups ◽  
Rational Homotopy Theory ◽  
Rational Homotopy ◽  
Content Type ◽  
Simply Connected ◽  
Derivatives Of ◽  
Connected Spaces

We construct a Goodwillie tower of categories which interpolates between the category of pointed spaces and the category of spectra. This tower of categories refines the Goodwillie tower of the identity functor in a precise sense. More generally, we construct such a tower for a large class of ∞ \infty -categories C \mathcal {C} and classify such Goodwillie towers in terms of the derivatives of the identity functor of C \mathcal {C} . As a particular application we show how this provides a model for the homotopy theory of simply-connected spaces in terms of coalgebras in spectra with Tate diagonals. Our classification of Goodwillie towers simplifies considerably in settings where the Tate cohomology of the symmetric groups vanishes. As an example we apply our methods to rational homotopy theory. Another application identifies the homotopy theory of p p -local spaces with homotopy groups in a certain finite range with the homotopy theory of certain algebras over Ching’s spectral version of the Lie operad. This is a close analogue of Quillen’s results on rational homotopy.

scholarly journals Typical representations via fixed point sets in Bruhat–Tits buildings

2021 ◽  
Vol 25 (36) ◽  
pp. 1021-1048
Author(s):  
Peter Latham ◽  
Monica Nevins
Keyword(s):  
Fixed Point ◽  
Maximal Compact Subgroup ◽  
Sufficient Conditions ◽  
Compact Subgroup ◽  
Supercuspidal Representation ◽  
Content Type ◽  
Branching Rules ◽  
Irreducible Components ◽  
Tits Building ◽  
Fixed Point Sets

For a tame supercuspidal representation π \pi of a connected reductive p p -adic group G G , we establish two distinct and complementary sufficient conditions, formulated in terms of the geometry of the Bruhat–Tits building of G G , for the irreducible components of its restriction to a maximal compact subgroup to occur in a representation of G G which is not inertially equivalent to π \pi . The consequence is a set of broadly applicable tools for addressing the branching rules of π \pi and the unicity of [ G , π ] G [G,\pi ]_G -types.

scholarly journals Littlewood complexes for symmetric groups

2021 ◽  
Vol 25 (20) ◽  
pp. 594-605
Author(s):  
Christopher Ryba
Keyword(s):  
Symmetric Groups ◽  
Irreducible Representations ◽  
Content Type

We construct a complex L ∙ λ \mathcal {L}_\bullet ^\lambda resolving the irreducible representations S λ [ n ] \mathcal {S}^{\lambda [n]} of the symmetric groups S n S_n by representations restricted from G L n ( k ) GL_n(k) . This construction lifts to R e p ( S ∞ ) \mathrm {Rep}(S_\infty ) , where it yields injective resolutions of simple objects. It categorifies stable Specht polynomials, and allows us to understand evaluations of these polynomials for all n n .

scholarly journals Limits of Characters of Wreath Products 𝔖n(T) of a Compact Group T With the Symmetric Groups and Characters of 𝔖∞(T), I

2009 ◽  
Vol 193 ◽  
pp. 1-93
Author(s):  
Takeshi Hirai ◽  
Etsuko Hirai ◽  
Akihito Hora
Keyword(s):  
Compact Group ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Continuous Limit ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Irreducible Characters ◽  
Induced Representations ◽  
Irreducible Components ◽  
Necessary And Sufficient

AbstractIn the first half of this paper, all the limits of irreducible characters of Gn = 𝔖n(T) as n → ∞ are calculated. The set of all continuous limit functions on G = 𝔖 ∞(T) is exactly equal to the set of all characters of G determined in [HH6]. We give a necessary and sufficient condition for a series of irreducible characters of Gn to have a continuous limit and also such a condition to have a discontinuous limit. In the second half, we study the limits of characters of certain induced representations of Gn which are usually reducible. The limits turn out to be characters of G, and we analyse which of irreducible components are responsible to these limits.

The More Control, the Better?

2014 ◽  
Vol 26 (2) ◽  
pp. 81-91 ◽  
Author(s):  
Jeeyun Oh ◽  
Mun-Young Chung ◽  
Sangyong Han
Keyword(s):  
Mixed Design ◽  
Negative Effects ◽  
Story Structure ◽  
Content Type ◽  
High User ◽  
User Control ◽  
Rigorous Research ◽  
Control Versus ◽  
The Media ◽  
The Impact

Despite of the popularity of interactive movie trailers, rigorous research on one of the most apparent features of these interfaces – the level of user control – has been scarce. This study explored the effects of user control on users’ immersion and enjoyment of the movie trailers, moderated by the content type. We conducted a 2 (high user control versus low user control) × 2 (drama film trailer versus documentary film trailer) mixed-design factorial experiment. The results showed that the level of user control over movie trailer interfaces decreased users’ immersion when the trailer had an element of traditional story structure, such as a drama film trailer. Participants in the high user control condition answered that they were less fascinated with, absorbed in, focused on, mentally involved with, and emotionally affected by the movie trailer than participants in the low user control condition only with the drama movie trailer. The negative effects of user control on the level of immersion for the drama trailer translated into users’ enjoyment. The impact of user control over interfaces on immersion and enjoyment varies depending on the nature of the media content, which suggests a possible trade-off between the level of user control and entertainment outcomes.

GREEN OPEN ACCESS IN KENYA: A REVIEW OF THE CONTENT, POLICIES AND USAGE OF INSTITUTIONAL REPOSITORIES

Mousaion ◽  
2016 ◽  
Vol 33 (3) ◽  
pp. 25-54
Author(s):  
Wanyenda Leonard Chilimo
Keyword(s):  
Developing Countries ◽  
Open Access ◽  
Descriptive Study ◽  
Google Scholar ◽  
Research Institutions ◽  
Journal Articles ◽  
Content Type ◽  
Institutional Repositories ◽  
Current State ◽  
Theses And Dissertations

 There is scant research-based evidence on the development and adoption of open access (OA) and institutional repositories (IRs) in Africa, and in Kenya in particular. This article reports on a study that attempted to fill that gap and provide feedback on the various OA projects and advocacy work currently underway in universities and research institutions in Kenya and in other developing countries. The article presents the findings of a descriptive study that set out to evaluate the current state of IRs in Kenya. Webometric approaches and interviews with IR managers were used to collect the data for the study. The findings showed that Kenya has made some progress in adopting OA with a total of 12 IRs currently listed in the Directory of Open Access Repositories (OpenDOAR) and five mandatory self-archiving policies listed in the Registry of Open Access Repositories Mandatory Archiving Policies (ROARMAP). Most of the IRs are owned by universities where theses and dissertations constitute the majority of the content type followed by journal articles. The results on the usage and impact of materials deposited in Kenyan IRs indicated that the most viewed publications in the repositories also received citations in Google Scholar, thereby signifying their impact and importance. The results also showed that there was a considerable interest in Swahili language publications among users of the repositories in Kenya.

Motivating Exercise Through Social Media: Is a Picture Always Worth a Thousand Words?

2018 ◽  
Author(s):  
Caitlyn Johnston ◽  
William E. Davis
Keyword(s):  
Social Media ◽  
Individual Differences ◽  
Experimental Design ◽  
Health Behaviors ◽  
Media Content ◽  
Exercise Motivation ◽  
Positive Health ◽  
Content Type ◽  
Within Subjects

In the present study, we examined how the influence of exercise-related social media content on exercise motivation might differ across content type (with images vs. without images) and account type (individual vs. corporate). Using a 2 × 2 within-subjects experimental design, 229 participants viewed a series of 40 actual social media posts across the four conditions (individual posts with images, corporate posts with images, individual posts without images, and corporate posts without images) in a randomized order. Participants rated the extent to which they felt each social media post motivated them to exercise, would motivate others to exercise, and was posted for extrinsic reasons. Participants also completed other measures of individual differences including their own exercise motivation. Posts with images from individuals were more motivating than posts with images from corporations; however, corporate posts without images were more motivating than posts without images from individuals. Participants expected others to be similarly motivated by the stimuli, and perceived corporate posts as having been posted for more extrinsic reasons than individuals’ posts. These findings enhance our understanding of how social media may be used to promote positive health behaviors.

Evaluation of gamma thalamotomy for parkinsonian and other tremors: survival of neurons adjacent to the thalamic lesion after gamma thalamotomy

2000 ◽  
Vol 93 (supplement_3) ◽  
pp. 120-127 ◽  
Author(s):  
Chihiro Ohye ◽  
Tohru Shibazaki ◽  
Junji Ishihara ◽  
Jie Zhang
Keyword(s):  
Tissue Reaction ◽  
Vascular Lesions ◽  
Thalamic Lesion ◽  
Mr Images ◽  
Unsatisfactory Result ◽  
Content Type ◽  
Rhythmic Discharge ◽  
Latent Interval ◽  
Fine Print

Object. The effects of gamma thalamotomy for parkinsonian and other kinds of tremor were evaluated. Methods. Thirty-six thalamotomies were performed in 31 patients by using a 4-mm collimator. The maximum dose was 150 Gy in the initial six cases, which was reduced to 130 Gy thereafter. The longest follow-up period was 6 years. The target was determined on T2-weighted and proton magnetic resonance (MR) images. The point chosen was in the lateral-most part of the thalamic ventralis intermedius nucleus. This is in keeping with open thalamotomy as practiced at the authors' institution. In 15 cases, gamma thalamotomy was the first surgical procedure. In other cases, previous therapeutic or vascular lesions were visible to facilitate targeting. Two types of tissue reaction were onserved on MR imaging: a simple oval shape and a complex irregular shape. Neither of these changes affected the clinical course. In the majority of cases, the tremor subsided after a latent interval of approximately 1 year after irradiation. The earliest response was demonstrated at 3 months. In five cases the tremor remained. In four of these cases, a second radiation session was administered. One of these four patients as well as another patient with an unsatisfactory result underwent open thalamotomy with microrecording. In both cases, depth recording adjacent to the necrotic area revealed normal neuronal activity, including the rhythmic discharge of tremor. Minor coagulation was performed and resulted in immediate and complete arrest of the remaining tremor. Conclusions. Gamma thalamotomy for Parkinson's disease seems to be an alternative useful method in selected cases.

Gamma knife radiosurgery as a single treatment modality for large cerebral arteriovenous malformations

2000 ◽  
Vol 93 (supplement_3) ◽  
pp. 113-119 ◽  
Author(s):  
D. Hung-Chi Pan ◽  
Wan-Yuo Guo ◽  
Wen-Yuh Chung ◽  
Cheng-Ying Shiau ◽  
Yue-Cune Chang ◽  
...  
Keyword(s):  
Gamma Knife ◽  
Arteriovenous Malformations ◽  
Radiation Treatment ◽  
Gamma Knife Radiosurgery ◽  
Consecutive Series ◽  
Content Type ◽  
Obliteration Rate ◽  
Complete Obliteration ◽  
Fine Print

Object. A consecutive series of 240 patients with arteriovenous malformations (AVMs) treated by gamma knife radiosurgery (GKS) between March 1993 and March 1999 was evaluated to assess the efficacy and safety of radiosurgery for cerebral AVMs larger than 10 cm3 in volume. Methods. Seventy-six patients (32%) had AVM nidus volumes of more than 10 cm3. During radiosurgery, targeting and delineation of AVM nidi were based on integrated stereotactic magnetic resonance (MR) imaging and x-ray angiography. The radiation treatment was performed using multiple small isocenters to improve conformity of the treatment volume. The mean dose inside the nidus was kept between 20 Gy and 24 Gy. The margin dose ranged between 15 to 18 Gy placed at the 55 to 60% isodose centers. Follow up ranged from 12 to 73 months. There was complete obliteration in 24 patients with an AVM volume of more than 10 cm3 and in 91 patients with an AVM volume of less than 10 cm3. The latency for complete obliteration in larger-volume AVMs was significantly longer. In Kaplan—Meier analysis, the complete obliteration rate in 40 months was 77% in AVMs with volumes between 10 to 15 cm3, as compared with 25% for AVMs with a volume of more than 15 cm3. In the latter, the obliteration rate had increased to 58% at 50 months. The follow-up MR images revealed that large-volume AVMs had higher incidences of postradiosurgical edema, petechiae, and hemorrhage. The bleeding rate before cure was 9.2% (seven of 76) for AVMs with a volume exceeding 10 cm3, and 1.8% (three of 164) for AVMs with a volume less than 10 cm3. Although focal edema was more frequently found in large AVMs, most of the cases were reversible. Permanent neurological complications were found in 3.9% (three of 76) of the patients with an AVM volume of more than 10 cm3, 3.8% (three of 80) of those with AVM volume of 3 to 10 cm3, and 2.4% (two of 84) of those with an AVM volume less than 3 cm3. These differences in complications rate were not significant. Conclusions. Recent improvement of radiosurgery in conjunction with stereotactic MR targeting and multiplanar dose planning has permitted the treatment of larger AVMs. It is suggested that gamma knife radiosurgery is effective for treating AVMs as large as 30 cm3 in volume with an acceptable risk.

Factors related to complete occlusion of arteriovenous malformations after gamma knife radiosurgery

2000 ◽  
Vol 93 (supplement_3) ◽  
pp. 96-101 ◽  
Author(s):  
Jong Hee Chang ◽  
Jin Woo Chang ◽  
Yong Gou Park ◽  
Sang Sup Chung
Keyword(s):  
Gamma Knife ◽  
Arteriovenous Malformations ◽  
Gamma Knife Radiosurgery ◽  
Maximum Diameter ◽  
Content Type ◽  
Complete Occlusion ◽  
Factors Associated ◽  
Martin Grade ◽  
Fine Print

Object. The authors sought to evaluate the effects of gamma knife radiosurgery (GKS) on cerebral arteriovenous malformations (AVMs) and the factors associated with complete occlusion. Methods. A total of 301 radiosurgical procedures for 277 cerebral AVMs were performed between December 1988 and December 1999. Two hundred seventy-eight lesions in 254 patients who were treated with GKS from May 1992 to December 1999 were analyzed. Several clinical and radiological parameters were evaluated. Conclusions. The total obliteration rate for the cases with an adequate radiological follow up of more than 2 years was 78.9%. In multivariate analysis, maximum diameter, angiographically delineated shape of the AVM nidus, and the number of draining veins significantly influenced the result of radiosurgery. In addition, margin radiation dose, Spetzler—Martin grade, and the flow pattern of the AVM nidus also had some influence on the outcome. In addition to the size, topography, and radiosurgical parameters of AVMs, it would seem to be necessary to consider the angioarchitectural and hemodynamic aspects to select proper candidates for radiosurgery.

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