scholarly journals Amplituhedron-like geometries

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gabriele Dian ◽  
Paul Heslop
Keyword(s):  
Canonical Form ◽  
Star Product ◽  
Natural Extension ◽  
Tree Level ◽  
Winding Number ◽  
Alternative Definition ◽  
Standard Definition ◽  
Definition Of ◽  
Intrinsic Definition ◽  
Simple Definition

Abstract We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

WHAT IS THE DIFFERENCE BETWEEN (MODERATE) EGALITARIANISM AND PRIORITARIANISM?

2003 ◽  
Vol 19 (1) ◽  
pp. 89-109 ◽  
Author(s):  
KARSTEN KLINT JENSEN
Keyword(s):  
Alternative Definition ◽  
Common View ◽  
Standard Definition ◽  
Common Definition ◽  
The Common ◽  
The Difference ◽  
Definition Of ◽  
Inequality Ordering ◽  
Priority View ◽  
Levelling Down Objection

It is common to define egalitarianism in terms of an inequality ordering, which is supposed to have some weight in overall evaluations of outcomes. Egalitarianism, thus defined, implies that levelling down makes the outcome better in respect of reducing inequality; however, the levelling down objection claims there can be nothing good about levelling down. The priority view, on the other hand, does not have this implication. This paper challenges the common view. The standard definition of egalitarianism implicitly assumes a context. Once this context is made clear, it is easily seen that egalitarianism could be defined alternatively in terms of valuing a benefit to a person inversely to how well off he is relative to others. The levelling down objection does not follow from this definition. Moreover, the common definition does not separate egalitarian orderings from prioritarian ones. It is useful to do this by requiring that on egalitarianism, additively separable orderings should be excluded. But this requirement is stated as a condition on the alternative definition of egalitarianism, from which the levelling down objection does not follow.

scholarly journals A NOTE ON THE IMPLEMENTATION OF POINCARÉ SYMMETRY IN NONCOMMUTATIVE FIELD THEORY

2010 ◽  
Vol 25 (31) ◽  
pp. 5747-5764
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Field Theory ◽  
Star Product ◽  
Space Time ◽  
Noncommutative Field Theory ◽  
Standard Definition ◽  
Time Symmetry ◽  
Poincaré Symmetry ◽  
Definition Of ◽  
Variational Symmetry

We argue that Poincaré symmetry can be implemented in noncommutative field theory (NCFT) if we allow the parameter of noncommutative deformation θμν to change as a two-tensor under the corresponding space–time symmetry. The implementation is consistent with the definition of θμν in terms of space–time coordinates and with the Moyal star product. Inspired by the standard definition of a variational symmetry we found a universal way to correct the implementation of the Poincaré symmetry by a term proportional to the variation of θμν in such a way that the new transformation define a symmetry of the theory. Finally we present as an example the case of NCYM theory and comment about the obstructions to implement generalized space–time symmetries in NCFT-like conformal or diffeomorphism transformations.

scholarly journals The Effect of an Alternative Definition of “Percent Highly Annoyed” on the Exposure–Response Relationship: Comparison of Noise Annoyance Responses Measured by ICBEN 5-Point Verbal and 11-Point Numerical Scales

2021 ◽  
Vol 18 (12) ◽  
pp. 6258
Author(s):  
Makoto Morinaga ◽  
Thu Lan Nguyen ◽  
Shigenori Yokoshima ◽  
Koji Shimoyama ◽  
Takashi Morihara ◽  
...  
Keyword(s):  
Sound Pressure ◽  
Response Relationship ◽  
Alternative Definition ◽  
Exposure Response ◽  
Noise Annoyance ◽  
Numerical Scale ◽  
Verbal Scale ◽  
Sound Pressure Levels ◽  
Acoustic Surveys ◽  
Definition Of

Since the development of the 5-point verbal and 11-point numerical scales for measuring noise annoyance by the ICBEN Team 6, these scales have been widely used in socio-acoustic surveys worldwide, and annoyance responses have been easily compared internationally. However, both the top two categories of the 5–point verbal scale and the top three ones of the 11-point numerical scale are correspond to high annoyance, so it is difficult to precisely compare annoyance responses. Therefore, we calculated differences in day–evening–night-weighted sound pressure levels (Lden) by comparing values corresponding to 10% highly annoyed (HA) on Lden_%HA curves obtained from measurements in 40 datasets regarding surveys conducted in Japan and Vietnam. The results showed that the Lden value corresponding to 10% HA using the 5-point verbal scale was approximately 5 dB lower than that of the 11-point numerical scale. Thus, some correction is required to compare annoyance responses measured by the 5-point verbal and the 11-point numerical scales. The results of this study were also compared with those of a survey in Switzerland.

A simple definition of ‘intentionally’

Cognition ◽  
2021 ◽  
Vol 214 ◽  
pp. 104806
Author(s):  
Tadeg Quillien ◽  
Tamsin C. German
Keyword(s):  
Definition Of ◽  
Simple Definition

A practical metric for melanopic metrology

2019 ◽  
Vol 51 (8) ◽  
pp. 1178-1191 ◽  
Author(s):  
SM Berman ◽  
RD Clear
Keyword(s):  
Ganglion Cell ◽  
Retinal Ganglion Cell ◽  
Vision Research ◽  
Spectral Response ◽  
Retinal Ganglion ◽  
Standard Definition ◽  
Standard Unit ◽  
Vision Science ◽  
The Past ◽  
Definition Of

Over the past decade, there has been a growing interest in lighting research on the effects of the recently discovered melanopsin receptor (also referred to as the intrinsically photosensitive retinal ganglion cell) and its impacts on health and vision. Presently, there is not a generally accepted metrology for dealing with the spectral response of the melanopsin receptor as applied to both lighting and vision research. A proposition to handle this issue from a vision science perspective has been presented in 2014 in the journal Trends in Neurosciences and from a more lighting perspective in 2017 in Lighting Research and Technology. These propositions are complex, and do not retain the CIE standard definition of a lumen. In this paper, we propose an approach based on effective watts and melanopic/photopic ratios that is both simpler and more closely aligned with CIE standard unit definitions. In addition, we include some practical examples of how such ratios are accessible now, and can be used for both lighting and vision research as well as applications.

An alternative definition of sustainable development using stability and chaos theories

2006 ◽  
Vol 14 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Amir Abbas Rassafi ◽  
Hossain Poorzahedy ◽  
Manouchehr Vaziri
Keyword(s):  
Sustainable Development ◽  
Alternative Definition ◽  
Definition Of

The Humdrum Use of Ultimate Authority: Defining and Analysing Chapter VII Resolutions

2009 ◽  
Vol 78 (3) ◽  
pp. 309-342 ◽  
Author(s):  
Patrik Johansson
Keyword(s):  
Cold War ◽  
United Nations ◽  
Security Council ◽  
Security Council Resolution ◽  
Post Cold War ◽  
Standard Definition ◽  
The Status ◽  
Definition Of ◽  
The Cold War ◽  
Business As Usual

AbstractUnder Chapter VII of the Charter of the United Nations, the Security Council has the unique authority to make decisions that are binding on member states. However, the lack of a standard definition of what makes a Security Council resolution "a Chapter VII resolution" has caused disagreement regarding the status of several resolutions. This is unfortunate as the international community should never have to doubt whether a Security Council resolution is in fact adopted under Chapter VII or not. It is also unnecessary. This article addresses this problem by proposing a definition of Chapter VII resolutions, based on two criteria referred to as "Article 39 determinations" and "Chapter VII decisions". On the basis of the proposed definition, the article describes and analyses a dramatic increase in the use of Chapter VII during the post-Cold War era. It concludes that as Chapter VII has come to constitute the majority of Security Council resolutions in recent years, the resort to Chapter VII no longer signifies exceptional determination and resolve, which it did during the Cold War; instead Chapter VII today implies business as usual. An appendix lists all Chapter VII resolutions from 1946–2008.

THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION

2012 ◽  
Vol 15 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JIM GATHERAL ◽  
TAI-HO WANG
Keyword(s):  
Heat Kernel ◽  
Implied Volatility ◽  
Order Term ◽  
Time Integration ◽  
Natural Extension ◽  
Approximation Formula ◽  
Local Volatility ◽  
Improved Performance ◽  
Volatility Function ◽  
Definition Of

In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.

Categorical concepts for parameterized partial specifications

1995 ◽  
Vol 5 (2) ◽  
pp. 153-188 ◽  
Author(s):  
Ingo Claßen ◽  
Martin GroßE-Rhode ◽  
Uwe Wolter
Keyword(s):  
Structural Theory ◽  
Specification Languages ◽  
Alternative Definition ◽  
Categorical Approach ◽  
Categorical Constructions ◽  
Definition Of ◽  
Act One

Categorical constructions inherent to a theory of algebras with strict partial operations are presented and exploited to provide a categorical deduction calculus for conditional existence equations and an alternative definition of such algebras based on the notion of syntactic categories. A compact presentation of the structural theory of parameterized (partial) specifications is given using the categorical approach. This theory is shown to be suitable for providing initial semantics as well as the compositionality results necessary for the definition of specification languages like ACT ONE and ACT TWO

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