scholarly journals Enumerative Problems Inspired by Mayer's Theory of Cluster Integrals

10.37236/1785 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Pierre Leroux
Keyword(s):  
Functional Equations ◽  
Essential Role ◽  
Block Size ◽  
Virial Expansion ◽  
Connected Components ◽  
Complete Graphs ◽  
Size Distributions ◽  
Structural Relationships ◽  
Class B

The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing rigorously the virial expansion for imperfect gases. We first review these functional equations, putting the emphasis on the structural relationships between the various classes of graphs. We then investigate the problem of enumerating some classes of connected graphs all of whose 2-connected components (blocks) are contained in a given class $B$. Included are the species of Husimi graphs ($B =$ "complete graphs"), cacti ($B =$ "unoriented cycles"), and oriented cacti ($B =$ "oriented cycles"). For each of these, we address the question of their labelled and unlabelled enumeration, according (or not) to their block-size distributions. Finally we discuss the molecular expansion of these species. It consists of a descriptive classification of the unlabelled structures in terms of elementary species, from which all their symmetries can be deduced.

A 3-tier classification of cerebral arteriovenous malformations

2011 ◽  
Vol 114 (3) ◽  
pp. 842-849 ◽  
Author(s):  
Robert F. Spetzler ◽  
Francisco A. Ponce
Keyword(s):  
Surgical Outcomes ◽  
Arteriovenous Malformations ◽  
Neurological Deficits ◽  
Cerebral Arteriovenous Malformations ◽  
Pooled Data ◽  
Class A ◽  
Tier System ◽  
Class B ◽  
Class C

Object The authors propose a 3-tier classification for cerebral arteriovenous malformations (AVMs). The classification is based on the original 5-tier Spetzler-Martin grading system, and reflects the treatment paradigm for these lesions. The implications of this modification in the literature are explored. Methods Class A combines Grades I and II AVMs, Class B are Grade III AVMs, and Class C combines Grades IV and V AVMs. Recommended management is surgery for Class A AVMs, multimodality treatment for Class B, and observation for Class C, with exceptions to the latter including recurrent hemorrhages and progressive neurological deficits. To evaluate whether combining grades is warranted from the perspective of surgical outcomes, the 3-tier system was applied to 1476 patients from 7 surgical series in which results were stratified according to Spetzler-Martin grades. Results Pairwise comparisons of individual Spetzler-Martin grades in the series analyzed showed the fewest significant differences (p < 0.05) in outcomes between Grades I and II AVMs and between Grades IV and V AVMs. In the pooled data analysis, significant differences in outcomes were found between all grades except IV and V (p = 0.38), and the lowest relative risks were found between Grades I and II (1.066) and between Grades IV and V (1.095). Using the pooled data, the predictive accuracies for surgical outcomes of the 5-tier and 3-tier systems were equivalent (receiver operating characteristic curve area 0.711 and 0.713, respectively). Conclusions Combining Grades I and II AVMs and combining Grades IV and V AVMs is justified in part because the differences in surgical results between these respective pairs are small. The proposed 3-tier classification of AVMs offers simplification of the Spetzler-Martin system, provides a guide to treatment, and is predictive of outcome. The revised classification not only simplifies treatment recommendations; by placing patients into 3 as opposed to 5 groups, statistical power is markedly increased for series comparisons.

Assessment of harvest blocks generated from operational polygons and forest-cover polygons in tactical and strategic planning

2001 ◽  
Vol 31 (4) ◽  
pp. 682-693 ◽  
Author(s):  
John Nelson
Keyword(s):  
Strategic Planning ◽  
Landscape Structure ◽  
Forest Cover ◽  
Block Size ◽  
Cost Effective ◽  
Size Distributions ◽  
Strategic Plans ◽  
Important Barrier ◽  
Interior Forest ◽  
Block Size Distribution

Manually designing harvest units for strategic planning is expensive. This paper compares blocking methods based on forest-cover polygons and manually designed harvest units. Routines are used to split and aggregate polygons into three block size distributions: (i) uniform 40-ha blocks; (ii) uniform 120-ha blocks; and (iii) by area, one-third 20 ha, one-third 60 ha, and one-third 150 ha. Three harvest rules that influence adjacency and the cutting of polygons within a block are applied to each block size distribution to compare forecasts generated by forest-cover and operational blocks. Generally, volume flows from the two methods deviate by less than 5%, and the highest deviations usually occur during the first 20 years. Projected landscape structure, as measured by interior forest area, is also similar under the two blocking methods. The results indicate that forest-cover data provide a reasonable alternative to manual blocking in tactical and strategic plans. This is significant because it removes an important barrier to timely and cost-effective planning, especially for large geographic problems where manual blocking is not an option.

Nets of quadrics and deformations of Σ3〈3〉 singularities

1989 ◽  
Vol 105 (1) ◽  
pp. 109-115
Author(s):  
S. A. Edwards ◽  
C. T. C. Wall
Keyword(s):  
Parameter Space ◽  
General Type ◽  
Single Parameter ◽  
Connected Components ◽  
Quadratic Maps ◽  
Nets Of Quadrics

The 2-jet of a Σ3 map-germ f:(3, 0) → (3, 0) determines a net of quadratic maps from 3 to 3; for nets of general type this jet is sufficient for equivalence. The classification of such nets involves a single parameter c. It is shown in [7], also in [3], that the versai unfolding of f is topologically trivial over the parameter space. However, there are 4 connected components of this space of nets. The main object of this paper is to show that the corresponding unfolded maps are of different topological types.

scholarly journals Climate Adaptation Plans in the Context of Coastal Settlements: The Case of Portugal

2020 ◽  
Vol 12 (20) ◽  
pp. 8559
Author(s):  
Francesca Dal Cin ◽  
Martin Fleischmann ◽  
Ombretta Romice ◽  
João Pedro Costa
Keyword(s):  
Urban Areas ◽  
Essential Role ◽  
Climate Adaptation ◽  
Coastal Planning ◽  
Sea Levels ◽  
Response Plan ◽  
Rising Sea Levels ◽  
The Impact ◽  
The Relationship

The impact of sea-level rise on coastal towns is expected to be a major challenge, with millions of people exposed. The climate-induced risk assessment of coastal areas subject to flooding plays an essential role in planning effective measures for adaptation plans. However, in European legislation, as well as in the regional plans adopted by the member states, there is no clear reference to urban settlement, as this concept is variable and difficult to categorise from the policy perspective. This lack of knowledge makes it complicated to implement efficient adaptation plans. This research examines the presence of the issue in Portugal’s coastal settlements, the European coastal area most vulnerable to rising sea levels, using the case of seashore streets as the most exposed waterfront public urban areas. Using the morphometric classification of the urban fabric, we analyse the relationship between urban typology and legislative macro-areas aimed at providing integrated adaptation plans. The study suggests that there is only a minimal relationship between the proposed classification and the geographical zones currently identified in coastal planning policies. Such incongruence suggests the need for change, as the policy should be able to provide a response plan tailored to the specificities of urban areas.

scholarly journals CLASSIFICATION OF SYMMETRY GROUPS FOR PLANAR -BODY CHOREOGRAPHIES

2013 ◽  
Vol 1 ◽  
Author(s):  
JAMES MONTALDI ◽  
KATRINA STECKLES
Keyword(s):  
Braid Group ◽  
Connected Components ◽  
Symmetry Groups ◽  
Exceptional Groups ◽  
Strong Force ◽  
Symmetry Properties ◽  
Foundational Work ◽  
Force Potential ◽  
Planar Body

AbstractSince the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the $n$-body problem: periodic motions where the $n$ bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part, we classify all possible symmetry groups of planar $n$-body collision-free choreographies. These symmetry groups fall into two infinite families and, if $n$ is odd, three exceptional groups. In the second part, we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in $n$-body systems governed by a strong force potential.

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