scholarly journals Combinatorial duality and intersection product: A direct approach

2005 ◽  
Vol 57 (2) ◽  
pp. 273-292 ◽  
Author(s):  
Gottfried Barthel ◽  
Jean-Paul Brasselet ◽  
Karl-Heinz Fieseler ◽  
Ludger Kaup
Author(s):  
B. Roy Frieden

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.


2016 ◽  
Vol 77 (S 02) ◽  
Author(s):  
Kazimierz Niemczyk ◽  
Robert Bartoszewicz ◽  
Krzysztof Morawski ◽  
Izabela Popieluch
Keyword(s):  

Author(s):  
Louis Kaplow

Throughout the world, the rule against price fixing is competition law's most important and least controversial prohibition. Yet there is far less consensus than meets the eye on what constitutes price fixing, and prevalent understandings conflict with the teachings of oligopoly theory that supposedly underlie modern competition policy. This book offers a fresh, in-depth exploration of competition law's horizontal agreement requirement, presents a systematic analysis of how best to address the problem of coordinated oligopolistic price elevation, and compares the resulting direct approach to the orthodox prohibition. The book elaborates the relevant benefits and costs of potential solutions, investigates how coordinated price elevation is best detected in light of the error costs associated with different types of proof, and examines appropriate sanctions. Existing literature devotes remarkably little attention to these key subjects and instead concerns itself with limiting penalties to certain sorts of interfirm communications. Challenging conventional wisdom, the book shows how this circumscribed view is less well grounded in the statutes, principles, and precedents of competition law than is a more direct, functional proscription. More important, by comparison to the communications-based prohibition, the book explains how the direct approach targets situations that involve both greater social harm and less risk of chilling desirable behavior—and is also easier to apply.


Author(s):  
Lie Fu ◽  
Robert Laterveer ◽  
Charles Vial

AbstractGiven a smooth projective variety, a Chow–Künneth decomposition is called multiplicative if it is compatible with the intersection product. Following works of Beauville and Voisin, Shen and Vial conjectured that hyper-Kähler varieties admit a multiplicative Chow–Künneth decomposition. In this paper, based on the mysterious link between Fano varieties with cohomology of K3 type and hyper-Kähler varieties, we ask whether Fano varieties with cohomology of K3 type also admit a multiplicative Chow–Künneth decomposition, and provide evidence by establishing their existence for cubic fourfolds and Küchle fourfolds of type c7. The main input in the cubic hypersurface case is the Franchetta property for the square of the Fano variety of lines; this was established in our earlier work in the fourfold case and is generalized here to arbitrary dimension. On the other end of the spectrum, we also give evidence that varieties with ample canonical class and with cohomology of K3 type might admit a multiplicative Chow–Künneth decomposition, by establishing this for two families of Todorov surfaces.


Author(s):  
R. Rajakulasingam ◽  
J. Kho ◽  
G. Almeer ◽  
C. Azzopardi ◽  
S. L. James ◽  
...  

Abstract Objective We describe a novel and safe CT biopsy technique that we have termed the “Birmingham intervention tent technique (BITT).” This technique is ideal for biopsying osseous lesions where a direct approach is not possible due to difficult positioning. Methods The BITT uses a plastic surgical forceps clamp attached at an angle to the biopsy needle, creating a tent shape. The finger rings of the forceps is stabilized on the table. Results In our institution, we have already used the BITT successfully in over 10 cases. Conclusion The BITT is an inexpensive and reproducible technique.


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