Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Content Classification of Multimedia Documents using Partitions of Low-Level Features

Audio-visual documents obtained from German TV news are classified according to the IPTC topic categorization scheme. To this end usual text classification techniques are adapted to speech, video, and non-speech audio. For each of the three modalities word analogues are generated: sequences of syllables for speech, “video words” based on low level color features (color moments, color correlogram and color wavelet), and “audio words” based on low-level spectral features (spectral envelope and spectral flatness) for non-speech audio. Such audio and video words provide a means to represent the different modalities in a uniform way. The frequencies of the word analogues represent audio-visual documents: the standard bag-of-words approach. Support vector machines are used for supervised classification in a 1 vs. n setting. Classification based on speech outperforms all other single modalities. Combining speech with non-speech audio improves classification. Classification is further improved by supplementing speech and non-speech audio with video words. Optimal F-scores range between 62% and 94% corresponding to 50% - 84% above chance. The optimal combination of modalities depends on the category to be recognized. The construction of audio and video words from low-level features provide a good basis for the integration of speech, non-speech audio and video.

Shades of CORDS in the Kush : the false hope of "unity of effort" in American counterinsurgency /

"Counterinsurgency (COIN) requires an integrated military, political, and economic program best developed by teams that field both civilians and soldiers. These units should operate with some independence but under a coherent command. In Vietnam, after several false starts, the United States developed an effective unified organization, Civil Operations and Revolutionary Development Support (CORDS), to guide the counterinsurgency. CORDS had three components absent from our efforts in Afghanistan today: sufficient personnel (particularly civilian), numerous teams, and a single chain of command that united the separate COIN programs of the disparate American departments at the district, provincial, regional, and national levels. This paper focuses on the third issue and describes the benefits that unity of command at every level would bring to the American war in Afghanistan. The work begins with a brief introduction to counterinsurgency theory, using a population-centric model, and examines how this warfare challenges the United States. It traces the evolution of the Provincial Reconstruction Teams (PRTs) and the country team, describing problems at both levels. Similar efforts in Vietnam are compared, where persistent executive attention finally integrated the government's counterinsurgency campaign under the unified command of the CORDS program. The next section attributes the American tendency towards a segregated response to cultural differences between the primary departments, executive neglect, and societal concepts of war. The paper argues that, in its approach to COIN, the United States has forsaken the military concept of unity of command in favor of 'unity of effort' expressed in multiagency literature. The final sections describe how unified authority would improve our efforts in Afghanistan and propose a model for the future."--P. iii.

Memoir on the theory of the partitions of numbers /

Mode of access: Internet.

The story of Unity.

"An abridgement of [the author's] The household of faith."

The 1959 steel strike, a triumph of unity and democracy.

Cover title.

Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Central elements of the elliptic Zn monodromy matrix algebra at roots of unity

The central elements of the algebra of monodromy matrices associated with the Z(n) R-matrix are studied. When the crossing parameter w takes a special rational value w = n/N, where N and n are positive coprime integers, the center is substantially larger than that in the generic case for which the quantum determinant provides the center. In the trigonometric limit, the situation corresponds to the quantum group at roots of unity. This is a higher rank generalization of the recent results by Belavin and Jimbo. (c) 2004 Elsevier B.V. All rights reserved.

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.

Unity stronger than divisions. Ukraine's internal diversity. OSW Point of View Number 40, March 2014

Ukraine is deeply divided internally, although as a result of the changes that have taken place since its independence, the country’s internal divisions now have less and less to do with territorial divides, and the split into historical ‘sub-Ukraines’ has become less pronounced, especially for the younger generation. Ukraine is not a country of two competing regional identities, one in the west, the other in the east. The western identity, in which the unity of Ukraine is a key value, coexists with the multiple and diverse local patriotisms of the different regions in the east and the south of the country. The present protest movement has consolidated the country’s sense of unity. Its opponents have also been championing the indivisibility of Ukraine, even while they demanded a thorough decentralisation of the country, which was often mistaken for separatism. Russia has been stirring up separatist tendencies in Ukraine, but with little success. Crimea is an exception here, because in most respects it has remained unaffected by the dynamics of the social processes transforming mainland Ukraine – separatist tendencies are indeed deeply rooted in the peninsula.

The unity of Western civilization;

"The following essays are the substance of a course of lectures delivered at a summer school at the Woodbrooke settlement, near Birmingham, in August, 1915"--Pref.

From apartheid to unity: white capital and black power in the racial integration of South African football, 1976-1992

This article analyses the complex process that deracialised and democratised South African football between the early 1970s and 1990s. Based mainly on archival documents, it argues that growing isolation from world sport, exemplified by South Africa's expulsion from the Olympic movement in 1970 and FIFA in 1976, and the reinvigoration of the liberation struggle with the Soweto youth uprising triggered a process of gradual desegregation in the South African professional game. While Pretoria viewed such changes as a potential bulwark against rising black militancy, white football and big business had their own reasons for eventually supporting racial integration, as seen in the founding of the National Soccer League. As negotiations for a new democratic South Africa began in earnest between the African National Congress (ANC) and the National Party (NP) in the latter half of the 1980s, transformations in football and politics paralleled and informed each other. Previously antagonistic football associations began a series of 'unity talks' between 1985 and 1986 that eventually culminated in the formation of a single, non-racial South African Football Association in December 1991, just a few days before the Convention for a Democratic South Africa (CODESA) opened the process of writing a new post-apartheid constitution. Finally, three decades of isolation came to an end as FIFA welcomed South Africa back into world football in 1992 - a powerful example of the seemingly boundless potential of a liberated and united South Africa ahead of the first democratic elections in 1994.