Search results for " set"
showing 10 items of 2095 documents
On Sets of Words of Rank Two
2019
Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …
Spatial Structures of the Philippines: Urbanization and Regional Inequalities
2017
This chapter examines the fundamental spatial structures of the Philippines. It defines the role and organization of the different levels of the administrative hierarchy (provinces, regions, cities and municipalities) down to the barangay and sitio/purok levels. This leads to the definition of the “urban” in the Philippines and the rise of urbanization in recent decades, from the original urban settlements of the Spanish era, with their patterns following the same rules as in Latin America (fort, church and plaza), to today’s cities. Forms of housing have evolved over time, from the archetypal bamboo/nipa hut (bahay kubo) and the urban stone and wood house of the elites (bahay na bato), now…
Effective interactions in Ricci-Based Gravity below the non-metricity scale
2020
We show how minimally-coupled matter fields of arbitrary spin, when coupled to Ricci-Based Gravity theories, develop non-trivial effective interactions that can be treated perturbatively only below a characteristic high-energy scale $\Lambda_Q$. Our results generalize to arbitrary matter fields those recently obtained for spin 1/2 fields in \cite{Latorre:2017uve}. We then use this interactions to set bounds on the high-energy scale $\Lambda_Q$ that controls departures of Ricci-Based Gravity theories from General Relativity. Particularly, for Eddington-inspired Born-Infeld gravity we obtain the strong bound $ |\kappa|<3.5 \times 10^{-14} \text{ m}^5 \text{kg}^{-1}\text{s}^{-2} $.
Holographic duals of 6d RG flows
2018
A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements $\mu_\mathrm{L,R}$ in $G$. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for $G=\mathrm{SU}(k)$, where AdS$_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS$_7$ vacua, determined by two nilpotent elements, which are naturally …
Acceleration radiation, transition probabilities, and trans-Planckian physics
2010
An important question in the derivation of the acceleration radiation, which also arises in Hawking's derivation of black hole radiance, is the need to invoke trans-Planckian physics in describing the creation of quanta. We point out that this issue can be further clarified by reconsidering the analysis in terms of particle detectors, transition probabilities and local two-point functions. By writing down separate expressions for the spontaneous-and induced-transition probabilities of a uniformly accelerated detector, we show that the bulk of the effect comes from the natural (non-trans-Planckian) scale of the problem, which largely diminishes the importance of the trans-Planckian sector. T…
The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
2019
We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master integrals. The latter are known to evaluate to non-planar pentagon functions, described by a 31-letter symbol alphabet. We express the final result for the amplitude in terms of uniform weight four symbols, multiplied by a small set of rational factors. The amplitude satisfies the expected factorization properties when one external graviton becomes soft, and when two external gravitons become collinear. We verify that the soft divergences of the amplitude ex…
On the maximal superalgebras of supersymmetric backgrounds
2009
17 pages.-- ISI article identifier:000262585300016.-- ArXiv pre-print avaible at:http://arxiv.org/abs/0809.5034
Towards the theory of M-approximate systems: Fundamentals and examples
2010
The concept of an M-approximate system is introduced. Basic properties of the category of M-approximate systems and in a natural way defined morphisms between them are studied. It is shown that categories related to fuzzy topology as well as categories related to rough sets can be described as special subcategories of the category of M-approximate systems.
Improving point matching on multimodal images using distance and orientation automatic filtering
2016
International audience; Speed Up Robust Features SURF is one of the most popular and efficient methods used for image registration task. In order to achieve a correct registration, a good matching of feature point is required. However in the case of multimodal images, the high and non-linear intensity changes between different modalities led to many outliers (mismatching of detected points) and consequently a fail in the registration. Therefore, in this paper we introduce an efficient method devoted to the detection and removal of such outlier. It's based on an automatic filtering of outliers on both distance and orientation between features points. We tested our proposed method on a set of…
ARROWS AND EARTH SHRINES: TOWARDS A HISTORY OF DAGARA EXPANSION IN SOUTHERN BURKINA FASO
2002
The history of the Black Volta region in what is currently south-west Burkina Faso and north-west Ghana has been marked by the agricultural expansion of Dagara-speaking groups. This article explores how and why these groups were able to expand at the expense of neighbouring segmentary societies such as the Phuo and the Sisala. Violence certainly played a role in their territorial expansion, but so did specific strategies of ritual appropriation of new territories. The Dagara system, with its characteristic fission of existing earth shrines and networks of interlinked shrines, allowed mobility and helped the migrants bring new territories under their ritual control. In addition, patriclans a…