scholarly journals Distinguishing the Chambers of the Moment Polytope

2004 ◽  
Vol 2 (1) ◽  
pp. 109-131
Author(s):  
R. F. Goldin ◽  
T. S. Holm ◽  
L. C. Jeffrey
Keyword(s):  
Moment Polytope ◽  
The Moment

scholarly journals Brick Manifolds and Toric Varieties of Brick Polytopes

10.37236/5038 ◽  
2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Laura Escobar
Keyword(s):  
Toric Variety ◽  
Toric Varieties ◽  
Moment Map ◽  
Twisted Product ◽  
General Fiber ◽  
Moment Polytope ◽  
The Moment ◽  
Subword Complex ◽  
Do So

Bott-Samelson varieties are a twisted product of $\mathbb{C}\mathbb{P}^1$'s with a map into $G/B$. These varieties are mostly studied in the case in which the map into $G/B$ is birational to the image; however in this paper we study a fiber of this map when it is not birational. We prove that in some cases the general fiber, which we christen a brick manifold, is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to translate this problem into one in terms of the "subword complexes" of Knutson and Miller. Pilaud and Stump realized certain subword complexes as the dual of the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is the generalized associahedron realized by Hohlweg, Lange and Thomas. These stories connect in a nice way: we show that the moment polytope of the brick manifold is the brick polytope. In particular, we give a nice description of the toric variety of the associahedron. We give each brick manifold a stratification dual to the subword complex. In addition, we relate brick manifolds to Brion's resolutions of Richardon varieties.

scholarly journals On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold

2012 ◽  
Vol 148 (6) ◽  
pp. 1985-2003 ◽  
Author(s):  
Chi Li
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Limit Behavior ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Continuity Method ◽  
Type Singularity ◽  
Moment Polytope ◽  
The Moment ◽  
Monge Ampere

AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the moment polytope.

scholarly journals Bott-Samelson Varieties, Subword Complexes and Brick Polytopes

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Laura Escobar
Keyword(s):  
Toric Variety ◽  
Simplicial Complexes ◽  
Flag Variety ◽  
Moment Map ◽  
Coxeter System ◽  
International Audience ◽  
Moment Polytope ◽  
The Moment ◽  
Subword Complex ◽  
Do So

International audience Bott-Samelson varieties factor the flag variety $G/B$ into a product of $\mathbb{C}\mathbb{P}^1$'s with a map into $G/B$. These varieties are mostly studied in the case in which the map into $G/B$ is birational; however in this paper we study fibers of this map when it is not birational. We will see that in some cases this fiber is a toric variety. In order to do so we use the moment map of a Bott-Samelson variety to translate this problem into a purely combinatorial one in terms of a subword complex. These simplicial complexes, defined by Knutson and Miller, encode a lot of information about reduced words in a Coxeter system. Pilaud and Stump realized certain subword complexes as the dual to the boundary of a polytope which generalizes the brick polytope defined by Pilaud and Santos. For a nice family of words, the brick polytope is the generalized associahedron realized by Hohlweg and Lange. These stories connect in a nice way: the moment polytope of a fiber of the Bott-Samelson map is the Brick polytope. In particular, we give a nice description of the toric variety of the associahedron.

scholarly journals An approach of the minimal model program for horospherical varieties via moment polytopes

2015 ◽  
Vol 2015 (708) ◽  
Author(s):  
Boris Pasquier
Keyword(s):  
Minimal Model ◽  
Toric Varieties ◽  
Cartier Divisor ◽  
Model Program ◽  
Minimal Model Program ◽  
Spherical Varieties ◽  
The Family ◽  
Moment Polytope ◽  
The Moment ◽  
Moment Polytopes

AbstractWe describe the minimal model program in the family of ℚ-Gorenstein projective horospherical varieties, by studying a family of polytopes defined from the moment polytope of a Cartier divisor of the variety we begin with. In particular, we generalize the results on MMP for toric varieties due to M. Reid, and we complete the results on MMP for spherical varieties due to M. Brion in the case of horospherical varieties.

scholarly journals The moment polytope of the abelian polygon space

2021 ◽  
pp. 107834
Author(s):  
Navnath Daundkar ◽  
Priyavrat Deshpande
Keyword(s):  
Moment Polytope ◽  
The Moment

The High Resolution Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 316-317
Author(s):  
A. V. Crewe
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
High Vacuum ◽  
Scanning Transmission Electron Microscope ◽  
Ultra High Vacuum ◽  
Resolving Power ◽  
Imaging Characteristics ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
The Moment

The high resolution STEM is now a fact of life. I think that we have, in the last few years, demonstrated that this instrument is capable of the same resolving power as a CEM but is sufficiently different in its imaging characteristics to offer some real advantages.It seems possible to prove in a quite general way that only a field emission source can give adequate intensity for the highest resolution^ and at the moment this means operating at ultra high vacuum levels. Our experience, however, is that neither the source nor the vacuum are difficult to manage and indeed are simpler than many other systems and substantially trouble-free.

Pinocytotic-Like Forms of Mitochondria From Rat Anterior Pituitary

1968 ◽  
Vol 26 ◽  
pp. 146-147
Author(s):  
Burton B. Silver
Keyword(s):  
Electron Micrographs ◽  
Conformational Changes ◽  
Anterior Pituitary ◽  
Dynamic State ◽  
Surrounding Cell ◽  
The Matrix ◽  
The Moment ◽  
Cell Medium ◽  
Sectioned Tissue ◽  
State Of Activity

Sectioned tissue rarely indicates evidence of what is probably a highly dynamic state of activity in mitochondria which have been reported to undergo a variety of movements such as streaming, divisions and coalescence. Recently, mitochondria from the rat anterior pituitary have been fixed in a variety of configurations which suggest that conformational changes were occurring at the moment of fixation. Pinocytotic-like vacuoles which may be taking in or expelling materials from the surrounding cell medium, appear to be forming in some of the mitochondria. In some cases, pores extend into the matrix of the mitochondria. In other forms, the remains of what seems to be pinched off vacuoles are evident in the mitochondrial interior. Dense materials, resembling secretory droplets, appear at the junction of the pores and the cytoplasm. The droplets are similar to the secretory materials commonly identified in electron micrographs of the anterior pituitary.

Advances in Stem Instrumentation for Biology

1990 ◽  
Vol 48 (1) ◽  
pp. 362-363
Author(s):  
J. S. Wall
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Carbon Films ◽  
Specimen Preparation ◽  
Material Deposition ◽  
Active User ◽  
Percent Improvement ◽  
Scanning Transmission ◽  
The Moment ◽  
Film Substrate ◽  
High Level

The forte of the Scanning transmission Electron Microscope (STEM) is high resolution imaging with high contrast on thin specimens, as demonstrated by visualization of single heavy atoms. of equal importance for biology is the efficient utilization of all available signals, permitting low dose imaging of unstained single molecules such as DNA.Our work at Brookhaven has concentrated on: 1) design and construction of instruments optimized for a narrow range of biological applications and 2) use of such instruments in a very active user/collaborator program. Therefore our program is highly interactive with a strong emphasis on producing results which are interpretable with a high level of confidence.The major challenge we face at the moment is specimen preparation. The resolution of the STEM is better than 2.5 A, but measurements of resolution vs. dose level off at a resolution of 20 A at a dose of 10 el/A2 on a well-behaved biological specimen such as TMV (tobacco mosaic virus). To track down this problem we are examining all aspects of specimen preparation: purification of biological material, deposition on the thin film substrate, washing, fast freezing and freeze drying. As we attempt to improve our equipment/technique, we use image analysis of TMV internal controls included in all STEM samples as a monitor sensitive enough to detect even a few percent improvement. For delicate specimens, carbon films can be very harsh-leading to disruption of the sample. Therefore we are developing conducting polymer films as alternative substrates, as described elsewhere in these Proceedings. For specimen preparation studies, we have identified (from our user/collaborator program ) a variety of “canary” specimens, each uniquely sensitive to one particular aspect of sample preparation, so we can attempt to separate the variables involved.

Traumatic Brain Injury: A Trauma Surgeon's Perspective

2012 ◽  
Vol 22 (3) ◽  
pp. 82-89
Author(s):  
Oscar D. Guillamondegui
Keyword(s):  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Multidisciplinary Approach ◽  
Trauma Team ◽  
The United States ◽  
Long Term Outcomes ◽  
Term Care ◽  
Injured Brain ◽  
The Moment

Traumatic brain injury (TBI) is a serious epidemic in the United States. It affects patients of all ages, race, and socioeconomic status (SES). The current care of these patients typically manifests after sequelae have been identified after discharge from the hospital, long after the inciting event. The purpose of this article is to introduce the concept of identification and management of the TBI patient from the moment of injury through long-term care as a multidisciplinary approach. By promoting an awareness of the issues that develop around the acutely injured brain and linking them to long-term outcomes, the trauma team can initiate care early to alter the effect on the patient, family, and community. Hopefully, by describing the care afforded at a trauma center and by a multidisciplinary team, we can bring a better understanding to the armamentarium of methods utilized to treat the difficult population of TBI patients.

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