scholarly journals Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Guy R. Jehu
Keyword(s):  
Scattering Amplitudes ◽  
The Other ◽  
High Multiplicity ◽  
Feynman Integrals ◽  
Lower Point ◽  
Compact Representations ◽  
Multiplicity One ◽  
Close Relationship ◽  
Complete Set

Abstract We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external momenta. These formulae apply for integrals with at least two more external legs than the dimension of the external momenta, and are presented in terms of two possible bases: one composed of a subset of descendant integrals with one fewer external legs, the other composed of the complete set of minimally-descendant integrals with just one more leg than the dimension of external momenta. In 3+1 dimensions, particularly compact representations of kinematic invariants can be computed, which easily lend themselves to spinor-helicity or trace representations. The reduction formulae have a close relationship with D-dimensional unitarity cuts, and thus provide a path towards computing full (all-ϵ) expressions for scattering amplitudes at arbitrary multiplicity.

Albrecht Durer and the 16TH Century Melancholy

2020 ◽  
Vol 2 ◽  
pp. 37-49
Author(s):  
Marcel Henrique Rodrigues
Keyword(s):  
Religious Culture ◽  
The Other ◽  
16Th Century ◽  
Other Hand ◽  
Close Relationship ◽  
The One ◽  
Deep Sense

Little has been discussed in academia about the close relationship between the Renaissance of the 16th century and melancholy humor, and esoteric elements arising mainly from Florentine Neoplatonism. The link between melancholy and esotericism becomes very clear when we analyze the gravure “Melencolia I” by Albrecht Dürer (1471-1528), composed of a significant number of symbols that refer to an esoteric religious culture that then emerged. Renaissance melancholy gained several nuances. On the one hand, it was considered a sin, a despicable mood characteristic of witches; on the other hand, a deep sense of inspiration typical of men of “genius”. This ambivalence also occurred in the firmament, as the melancholic people were guided by the dark planet Saturn, according to astrological belief. We also have the cultural scenario of the 16th century, especially in Dürer's Germany, which contributed to strengthening the melancholy issues.

Epodes

1972 ◽  
Vol 6 ◽  
pp. 6-14
Keyword(s):  
Social Status ◽  
Lyric Poetry ◽  
The Other ◽  
Similar Attitude ◽  
Other Hand ◽  
Close Relationship

Horace was writing hisEpodes1at the same time as he was writingSatires. The nameEpodesis derived from the metrical term ό ἐπῳδός (і.е. στίχος) which signifies the second and shorter line of a couplet, but Horace himself referred to them asiambi(soEpod. 14. 7,Epist. i. 19. 23). The collection is titledLiber Epodonin the MSS. and the title was used by grammarians of the fourth and fifth centuries. Butiambigives a better idea of their basic inspiration. Horace says of them(Epist. i. 19. 21-5):So he claims(a)originality,(b)Archilochus as a model,(c)that he was the first Roman to use Archilochus as a model, and(d)that he discarded the vicious personal invective of Archilochus. The judgement disregards Catullus, who had writteniambibefore Horace, but whose similarity to Archilochus did not extend far beyond metre and invective. There is a consistency in Horace’s poetic career: he began by recreating the poetry of Archilochus in hisEpodes, and his later—and greatest— work was the recreation in hisOdesof the lyric poetry of poets like Sappho, Alcaeus, and Pindar. There is a similarly close relationship between theSatiresand theEpistles;and, furthermore, all of his writing uses an autobiographical technique. There is another sort of consistency too, for basicallyEpodesandSatiresexpress a similar attitude of mind: anger, contempt, and amusement are the fundamental emotions (though he often transcends these emotions in both works), and a plausible case can be made out for regarding this as a sign of a young man of low social status, unsure of himself and his talent, and already finding ways of expressing a personality that were not too self-revealing. TheOdesandEpistles, on the other hand, express a more meditative, more philosophical, more humane attitude, yet ultimately no more self-revealing.

Dreams of Truck Drivers: A Test of the Continuity Hypothesis of Dreaming

2005 ◽  
Vol 25 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Michael Schredl ◽  
Arthur Funkhouser ◽  
Nicole Arn
Keyword(s):  
Empirical Studies ◽  
Truck Drivers ◽  
The Other ◽  
Continuity Hypothesis ◽  
Future Studies ◽  
Daytime Activity ◽  
Close Relationship ◽  
The One ◽  
Dream Emotions ◽  
The Relationship

Empirical studies largely support the continuity hypothesis of dreaming. The present study investigated the frequency and emotional tone of dreams of truck drivers. On the one hand, the findings of the present study partly support the continuity regarding the time spent with driving/being in the truck and driving dreams and, on the other hand, a close relationship was found between daytime mood (feelings of stress, job satisfaction) and dream emotions, i.e., different dream characteristics were affected by different aspects of daytime activity. The results, thus, indicate that it is necessary to define very clearly how this continuity is to be conceptualized. The approach of formulating a mathematical model (cf. [1]) should be adopted in future studies in order to specify the factors and their magnitude in the relationship between waking and dreaming.

scholarly journals Metabolism of the nucleic acids of rumen bacteria by preruminant and ruminant lambs

1981 ◽  
Vol 45 (3) ◽  
pp. 517-527 ◽  
Author(s):  
M. A. Razzaque ◽  
J. H. Topps ◽  
R. N. B. Kay ◽  
J. M. Brockway
Keyword(s):  
Nucleic Acids ◽  
Bacterial Culture ◽  
Total Activity ◽  
Total Radioactivity ◽  
The Other ◽  
Nucleic Acid Content ◽  
Rumen Bacteria ◽  
Total Nucleic Acid ◽  
Purine Base ◽  
Close Relationship

1. A rumen bacterial culture containing specifically labelled nucleic acids was prepared using [8-14C]adenine.2. The labelled preparation was given in a liquid diet to two preruminant lambs and via a rumen tube to two ruminant lambs. The radioactivity excreted in exhaled gases, faeces and urine and that incorporated into tissues was determined.3 The preruminant lambs absorbed 58.3% of the total radioactivity measured after 24 h and the ruminant lambs 66.6% of the total activity measured after 48 h.4. Of the total radioactivity absorbed the preruminant lambs exhaled 38%, excreted 34% in urine and retained 29% in tissues. The corresponding values for the ruminant lambs were 12,41 and 47% respectively.5. There was a close relationship between total nucleic acid content and radioactivity per g of tissues of both preruminant and ruminant lambs.6. Of the radioactivity in the urine, the ruminant and one preruminant lamb excreted most in the fraction containing allantoin, while the other lamb excreted most activity in the uric acid fraction.7. The salvaging of the breakdown products of bacterial nucleic acids to make tissue nucleic acids appears to be an important synthesis in preruminant and ruminant lambs and of the likely precursors the purine base may be more important than the nucleoside.

Resolving the Lourinia armata (Claus, 1866) complex with remarks on the monophyletic status of Louriniidae, Monard 1927 (Copepoda: Harpacticoida)

Zootaxa ◽  
2021 ◽  
Vol 5051 (1) ◽  
pp. 346-386
Author(s):  
SÜPHAN KARAYTUĞ ◽  
SERDAR SAK ◽  
ALP ALPER ◽  
SERDAR SÖNMEZ
Keyword(s):  
Comparative Evaluation ◽  
Species Complex ◽  
Detailed Examination ◽  
The Other ◽  
Phylogenetic Position ◽  
Nicobar Island ◽  
Other Hand ◽  
The Family ◽  
Close Relationship ◽  
Almost All

An attempt was made to test if Lourinia armata (Claus, 1866)—as it is currently diagnosed—represents a species complex. Detailed examination and comparisons of several specimens collected from different localities suggest that L. armata indeed represents a complex of four closely related morphospecies that can be differentiated from one another by only detailed observations. One of the four species is identified as Lourinia aff. armata and the other three species are described as new to science and named as Lourinia wellsi sp. nov., L. gocmeni sp. nov., and L. aldabraensis sp. nov. Detailed review of previous species records indicates that the genus Lourinia Wilson, 1924 is distributed worldwide. Ceyloniella nicobarica Sewell, 1940, originally described from Nicobar Island and previously considered a junior subjective synonym of L. armata is reinstated as Lourinia nicobarica (Sewell, 1940) comb. nov. on the basis of the unique paddle-shaped caudal ramus seta V. It is postulated that almost all of these records are unreliable in terms of representing true Lourinia aff. armata described herein. On the other hand, the comparative evaluation of the illustrations and descriptions in the published literature indicates the presence of several new species waiting to be discovered in the genus Lourinia.                 It has been determined that, according to updated modern keys, the recent inclusion of the monotypic genus Archeolourinia Corgosinho & Schizas, 2013 in the Louriniidae is not justified since Archeolourinia shermani Corgosinho & Schizas, 2013 does not belong to this family but should be assigned to the Canthocamptidae. On the other hand, it has been argued that the exact phylogenetic position of the Louriniidae still remains problematic since none of the diagnostic characters supports the monophyly of the family within the Oligoarthra. It has also been argued that the close relationship between Louriniidae and Canthocamptidae is supported since both families share the homologous sexual dimorphism (apophysis) on P3 endopod. The most important characteristic that can possibly be used to define Louriniidae is the reduction of maxilliped.  

scholarly journals Universe and Inner Self in Early Indian and Early Greek Thought

2016 ◽  
Keyword(s):  
Economic Development ◽  
The Other ◽  
European Origin ◽  
Greek Thought ◽  
Indian Thought ◽  
Inner Self ◽  
Cosmic Order ◽  
Socio Economic Development ◽  
Close Relationship ◽  
The Universe

This book focuses from various perspectives on the striking similarities (as well as the concomitant differences) between early Greek and early Indian thought. In both cultures there occurred at about the same time the birth of 'philosophy', the idea of the universe as an intelligible order in which personal deity is (at most) marginal and the inner self is at the centre of attention. The similarities include a pentadic structure of narrative and cosmology, a basic conception of cosmic order or harmony, a close relationship between universe and inner self, techniques of soteriological inwardness and self-immortalisation, the selflessness of theory, envisaging the inner self as a chariot, the interiorisation of ritual, and ethicised reincarnation. Explanations for the similarites are a shared Indo-European origin, parallel socio-economic development, and influence in one direction or the other.

scholarly journals Dal nostro inviato in Unione Sovietica

2018 ◽  
Author(s):  
Alberto Zava
Keyword(s):  
Soviet Union ◽  
Travel Literature ◽  
The Other ◽  
The Soviet Union ◽  
Close Relationship ◽  
The Many ◽  
Newspaper Articles

Writings by three Italian journalist-authors provide an evocative picture of the Soviet Union during the ’50s and ’60s, interpreted through different personal styles, analytical systems and reporting techniques. In close relationship with the many-sided reality of the Soviet landscape, the meeting with the ‘other’ (geographically, culturally and in personal terms) allows Enrico Emanuelli, Carlo Levi and Guido Piovene to realise individual volumes of reportage (Emanuelli and Levi) or newspaper articles (Piovene) poised between travel literature and the informative-journalistic dimension.

scholarly journals Timed ATL: Forget Memory, Just Count

2019 ◽  
Vol 66 ◽  
pp. 197-223
Author(s):  
Michal Jozef Knapik ◽  
Etienne Andre ◽  
Laure Petrucci ◽  
Wojciech Jamroga ◽  
Wojciech Penczek
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Discrete Time ◽  
The Other ◽  
Simple Pattern ◽  
Perfect Recall ◽  
Other Hand ◽  
Compact Representations ◽  
Time Extension ◽  
Number Of Visits

In this paper we investigate the Timed Alternating-Time Temporal Logic (TATL), a discrete-time extension of ATL. In particular, we propose, systematize, and further study semantic variants of TATL, based on different notions of a strategy. The notions are derived from different assumptions about the agents’ memory and observational capabilities, and range from timed perfect recall to untimed memoryless plans. We also introduce a new semantics based on counting the number of visits to locations during the play. We show that all the semantics, except for the untimed memoryless one, are equivalent when punctuality constraints are not allowed in the formulae. In fact, abilities in all those notions of a strategy collapse to the “counting” semantics with only two actions allowed per location. On the other hand, this simple pattern does not extend to the full TATL. As a consequence, we establish a hierarchy of TATL semantics, based on the expressivity of the underlying strategies, and we show when some of the semantics coincide. In particular, we prove that more compact representations are possible for a reasonable subset of TATL specifications, which should improve the efficiency of model checking and strategy synthesis.

scholarly journals The diagrammatic coaction beyond one loop

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Samuel Abreu ◽  
Ruth Britto ◽  
Claude Duhr ◽  
Einan Gardi ◽  
James Matthew
Keyword(s):  
Differential Equations ◽  
Hypergeometric Functions ◽  
Differential Forms ◽  
Feynman Graph ◽  
Loop Order ◽  
Feynman Integrals ◽  
Mathematical Properties ◽  
Multiple Polylogarithms ◽  
Complete Set ◽  
General Tool

Abstract The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions. The coaction on the functions is constructed by pairing a basis of differential forms, corresponding to master integrals, with a basis of integration contours, corresponding to independent cut integrals. At one loop, a general diagrammatic coaction was established using dimensional regularisation, which may be realised in terms of a global coaction on hypergeometric functions, or equivalently, order by order in the ϵ expansion, via a local coaction on multiple polylogarithms. The present paper takes the first steps in generalising the diagrammatic coaction beyond one loop. We first establish general properties that govern the diagrammatic coaction at any loop order. We then focus on examples of two-loop topologies for which all integrals expand into polylogarithms. In each case we determine bases of master integrals and cuts in terms of hypergeometric functions, and then use the global coaction to establish the diagrammatic coaction of all master integrals in the topology. The diagrammatic coaction encodes the complete set of discontinuities of Feynman integrals, as well as the differential equations they satisfy, providing a general tool to understand their physical and mathematical properties.

scholarly journals Multi-Bloch vector representation of the qutrit

2011 ◽  
Vol 11 (5&6) ◽  
pp. 361-373
Author(s):  
Pawel Kurzynski
Keyword(s):  
Quantum State ◽  
Quantum Systems ◽  
Quantum States ◽  
The Other ◽  
Two Dimensional ◽  
Bloch Vector ◽  
Vector Representation ◽  
Alternative Approach ◽  
Complete Set

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state. However, not every Bloch vector corresponds to a quantum state. It seems that only for two-dimensional quantum systems it is easy to distinguish proper Bloch vectors from improper ones, i.e. the ones corresponding to quantum states from the other ones. I propose an alternative approach to the problem in which more than one vector is used. In particular, I show that a state of the qutrit can be described by the three qubit-like Bloch vectors.

Sign in / Sign up

Export Citation Format

Share Document