scholarly journals The Tutte polynomial of symmetric hyperplane arrangements

2020 ◽  
Vol 29 (03) ◽  
pp. 2050004
Author(s):  
Hery Randriamaro
Keyword(s):  
Hyperplane Arrangement ◽  
Dual Graph ◽  
Tutte Polynomial ◽  
Hyperplane Arrangements ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Tutte Polynomials ◽  
One Year ◽  
The One ◽  
Definition Of

The Tutte polynomial is originally a bivariate polynomial which enumerates the colorings of a graph and of its dual graph. Ardila extended in 2007 the definition of the Tutte polynomial on the real hyperplane arrangements. He particularly computed the Tutte polynomials of the hyperplane arrangements associated to the classical Weyl groups. Those associated to the exceptional Weyl groups were computed by De Concini and Procesi one year later. This paper has two objectives: On the one side, we extend the Tutte polynomial computing to the complex hyperplane arrangements. On the other side, we introduce a wider class of hyperplane arrangements which is that of the symmetric hyperplane arrangements. Computing the Tutte polynomial of a symmetric hyperplane arrangement permits us to deduce the Tutte polynomials of some hyperplane arrangements, particularly of those associated to the imprimitive reflection groups.

The Tutte polynomial of ideal arrangements

2020 ◽  
Vol 12 (02) ◽  
pp. 2050017
Author(s):  
Hery Randriamaro
Keyword(s):  
Finite Field ◽  
Hyperplane Arrangement ◽  
Dual Graph ◽  
Tutte Polynomial ◽  
Root Systems ◽  
Field Method ◽  
Hyperplane Arrangements ◽  
Acyclic Orientations ◽  
The Matrix ◽  
Tutte Polynomials

The Tutte polynomial was originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning subgraphs, and of acyclic orientations. In 2007, Ardila extended the notion of Tutte polynomial to hyperplane arrangements, and computed the Tutte polynomials of the classical root systems for certain prime powers of the first variable at the same time. In this paper, we compute the Tutte polynomial of ideal arrangements. These arrangements were introduced in 2006 by Sommers and Tymoczko, and are defined for ideals of root systems. For the ideals of classical root systems, we bring a slight improvement of the finite field method by showing that it can applied on any finite field whose cardinality is not a minor of the matrix associated to the studied hyperplane arrangement. Computing the minor set associated to an ideal of classical root systems particularly permits us to deduce the Tutte polynomials of the classical root systems. For the ideals of the exceptional root systems of type [Formula: see text], [Formula: see text], and [Formula: see text], we use the formula of Crapo.

scholarly journals Face monoid actions and tropical hyperplane arrangements

2017 ◽  
Vol 27 (08) ◽  
pp. 1001-1025
Author(s):  
Marianne Johnson ◽  
Mark Kambites
Keyword(s):  
Hyperplane Arrangement ◽  
Hyperplane Arrangements ◽  
Oriented Matroid ◽  
Definition Of ◽  
The Way

We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin in their definition of a tropical oriented matroid, induces an action of the hyperplane face monoid of the classical braid arrangement on the arrangement, and hence on a number of interesting related structures. Along the way, we introduce a new characterization of the types (in the sense of Develin and Sturmfels) of points with respect to a tropical hyperplane arrangement, in terms of partial bijections which attain permanents of submatrices of a matrix which naturally encodes the arrangement.

scholarly journals Zonotopes, toric arrangements, and generalized Tutte polynomials

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Luca Moci
Keyword(s):  
Characteristic Polynomial ◽  
Hilbert Series ◽  
Hyperplane Arrangement ◽  
Tutte Polynomial ◽  
Integral Points ◽  
Poincaré Polynomial ◽  
Tutte Polynomials ◽  
International Audience ◽  
Toric Arrangement ◽  
Positive Coefficients

International audience We introduce a multiplicity Tutte polynomial $M(x,y)$, which generalizes the ordinary one and has applications to zonotopes and toric arrangements. We prove that $M(x,y)$ satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial $M(x,y)$, likewise the corresponding polynomials for a hyperplane arrangement are specializations of the ordinary Tutte polynomial. Furthermore, $M(1,y)$ is the Hilbert series of the related discrete Dahmen-Micchelli space, while $M(x,1)$ computes the volume and the number of integral points of the associated zonotope. On introduit un polynôme de Tutte avec multiplicité $M(x, y)$, qui généralise le polynôme de Tutte ordinaire et a des applications aux zonotopes et aux arrangements toriques. Nous prouvons que $M(x, y)$ satisfait une récurrence de "deletion-restriction'' et a des coefficients positifs. Le polynôme caractéristique et le polynôme de Poincaré d'un arrangement torique sont des spécialisations du polynôme associé $M(x, y)$, de même que les polynômes correspondants pour un arrangement d'hyperplans sont des spécialisations du polynôme de Tutte ordinaire. En outre, $M(1, y)$ est la série de Hilbert de l'espace discret de Dahmen-Micchelli associé, et $M(x, 1)$ calcule le volume et le nombre de points entiers du zonotope associé.

scholarly journals Migraine and other headaches in transient ischemic attacks

2019 ◽  
Vol 11 (3S) ◽  
pp. 38-45
Author(s):  
E. R. Lebedeva ◽  
N. M. Gurary ◽  
J. Olesen
Keyword(s):  
Tension Headache ◽  
Cerebrovascular Diseases ◽  
Neurological Dysfunction ◽  
Control Group ◽  
Common Symptom ◽  
Transient Ischemic Attacks ◽  
New Type ◽  
One Year ◽  
The One ◽  
Definition Of

Headache is a common symptom in acute cerebrovascular diseases; however, no studies have evaluated the prevalence of specific headache types in patients with transient ischemic attacks (ТIАs).Objective: to analyze all headaches within the last year and the last week before and during ТIАs.Patients and methods. TIA patients included in the study (female 55% (n=120); mean age, 56.1 years) according to the existing definition of TIAs had a transient neurological dysfunction episode caused by focal brain damage or retinal ischemia for up to 24 hours without forming a new acute heart attack on diffusion-weighted MRI (n=112) or CT (n=8). All the patients were examined by one neurologist within one day after their admission. Patients (female 64% (n=192); mean age, 58.7 years) who had been admitted with a diagnosis of lumbago, lumbar spine osteochondrosis, or gastrointestinal ulcer were examined as a control group. A clinical semistructured face-to-face interview with the patients of both groups was carried out to analyze headache.Results and discussion. The prevalence of migraine without aura during one year before TIA was substantially higher in patients with TIA than in control ones: 20.8 and 7.8%, respectively (p=0.002). Twenty-two (18.3%) patients had sentinel or warning headache within the last week before a TIA that manifested as an increase in and greater frequency of previous headache, as lack of effect of painkillers, and as the emergence of a new type of headaches, which were previously absent. During TIAs, 16 (13.3%) patients developed a new type of headache. Twelve of these 16 patients had migraine-like headache; three patients had headache resembling tension headache; one patient had a thunderclap headache. None of the control patients was found to have a new type of headache. TIAs were significantly more common in the vertebrobasilar basin than in the carotid artery one in patients with headache during the last week before and during TIA.Conclusion. The one year prevalence of migraine was significantly higher in ТIА patients than in control patients, and so was the prevalence of headache within the last week before and during TIA. Migraine-like headache prevailed among the new types of headaches in the development of TIA. A previous headache with a change in characteristics and a new type of headache can be predictors for TIA. 

scholarly journals The arithmetic Tutte polynomials of the classical root systems

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Federico Ardila ◽  
Federico Castillo ◽  
Michael Henley
Keyword(s):  
Hyperplane Arrangement ◽  
Tutte Polynomial ◽  
Root Systems ◽  
Field Method ◽  
Topological Invariants ◽  
Signed Graphs ◽  
Tutte Polynomials ◽  
International Audience

International audience Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its <i>arithmetic</i> Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems $A_n, B_n, C_n$, and $D_n$ with respect to their integer, root, and weight lattices. We do it in two ways: by introducing a \emphfinite field method for arithmetic Tutte polynomials, and by enumerating signed graphs with respect to six parameters.

scholarly journals Critical Points and Resonance of Hyperplane Arrangements

2011 ◽  
Vol 63 (5) ◽  
pp. 1038-1057 ◽  
Author(s):  
D. Cohen ◽  
G. Denham ◽  
M. Falk ◽  
A. Varchenko
Keyword(s):  
Critical Points ◽  
Hyperplane Arrangement ◽  
Hyperplane Arrangements ◽  
Critical Set ◽  
Master Function ◽  
The One ◽  
The Relationship

Abstract If is a master function corresponding to a hyperplane arrangement 𝒜 and a collection of weights ⋋, we investigate the relationship between the critical set of , the variety defined by the vanishing of the one-form ⩊⋋ = d log , and the resonance of ⋋. For arrangements satisfying certain conditions, we show that if ⋋ is resonant in dimension p, then the critical set of has codimension at most p. These include all free arrangements and all rank 3 arrangements.

scholarly journals Natural risk warning: comparison of two methodologies

2006 ◽  
Vol 2 ◽  
pp. 335-338
Author(s):  
A. Cavallo ◽  
F. Giannoni
Keyword(s):  
Back Analysis ◽  
Extreme Rainfall ◽  
Rainfall Thresholds ◽  
Natural Risk ◽  
Flood Warning ◽  
Risk Warning ◽  
Risk Forecasting ◽  
One Year ◽  
The One ◽  
Definition Of

Abstract. The Italian network of "Centri Funzionali" is now reaching operational status both in hydro-meteorological risk forecasting and support to the decision making of administrations that issue natural risk warning. Each centre operates for its district of influence. In order to have a nationwide common standard the National Civil Protection Department proposed a quantitative warning methodology based on the definition of rainfall thresholds correlated to historical damages. In the first phase the thresholds have been defined using two studies that cover all Italy: the VAPI (statistics of extreme rainfall and discharges, see reference) and the AVI (database of historical flood and landslide events and reported damages, see reference). This work presents one year back analysis that compares the new methodology and the one that has been usied since 2000 by the Liguria Region Meteorological Centre with regard to flood warning, pinpointing the performance differences in terms of false and missed alerts.

Resources: Internet Resources for the Independent Medical Evaluator – 2007

2007 ◽  
Vol 12 (4) ◽  
pp. 4-7
Author(s):  
Christopher R. Brigham ◽  
Jenny Walker
Keyword(s):  
Head Trauma ◽  
Clonic Seizure ◽  
Acute Subdural Hematoma ◽  
Orbital Fracture ◽  
Orbital Wall ◽  
First Occurrence ◽  
One Year ◽  
The One ◽  
Neurological Injuries ◽  
Medial Orbital Wall

Abstract Rating patients with head trauma and multiple neurological injuries can be challenging. The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides), Fifth Edition, Section 13.2, Criteria for Rating Impairment Due to Central Nervous System Disorders, outlines the process to rate impairment due to head trauma. This article summarizes the case of a 57-year-old male security guard who presents with headache, decreased sensation on the left cheek, loss of sense of smell, and problems with memory, among other symptoms. One year ago the patient was assaulted while on the job: his Glasgow Coma Score was 14; he had left periorbital ecchymosis and a 2.5 cm laceration over the left eyelid; a small right temporoparietal acute subdural hematoma; left inferior and medial orbital wall fractures; and, four hours after admission to the hospital, he experienced a generalized tonic-clonic seizure. This patient's impairment must include the following components: single seizure, orbital fracture, infraorbital neuropathy, anosmia, headache, and memory complaints. The article shows how the ratable impairments are combined using the Combining Impairment Ratings section. Because this patient has not experienced any seizures since the first occurrence, according to the AMA Guides he is not experiencing the “episodic neurological impairments” required for disability. Complex cases such as the one presented here highlight the need to use the criteria and estimates that are located in several sections of the AMA Guides.

Catheter-directed foam sclerotherapy treatment of saphenous vein incompetence

VASA ◽  
2012 ◽  
Vol 41 (2) ◽  
pp. 120-124 ◽  
Author(s):  
Asciutto ◽  
Lindblad
Keyword(s):  
Saphenous Vein ◽  
Short Term ◽  
Foam Sclerotherapy ◽  
Results Of Treatment ◽  
Ulcer Healing Rate ◽  
Complete Obliteration ◽  
Ceap Classification ◽  
One Year ◽  
The One

Background: The aim of this study is to report the short-term results of catheter-directed foam sclerotherapy (CDFS) in the treatment of axial saphenous vein incompetence. Patients and methods: Data of all patients undergoing CDFS for symptomatic primary incompetence of the great or small saphenous vein were prospectively collected. Treatment results in terms of occlusion rate and patients’ grade of satisfaction were analysed. All successfully treated patients underwent clinical and duplex follow-up examinations one year postoperatively. Results: Between September 2006 and September 2010, 357 limbs (337 patients) were treated with CDFS at our institution. Based on the CEAP classification, 64 were allocated to clinical class C3 , 128 to class C4, 102 to class C5 and 63 to class C6. Of the 188 patients who completed the one year follow up examination, 67 % had a complete and 14 % a near complete obliteration of the treated vessel. An ulcer-healing rate of 54 % was detected. 92 % of the patients were satisfied with the results of treatment. We registered six cases of thrombophlebitis and two cases of venous thromboembolism, all requiring treatment. Conclusions: The short-term results of CDFS in patients with axial vein incompetence are acceptable in terms of occlusion and complications rates.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

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