T-Path Formula and Atomic Bases for Cluster Algebras of Type D

Atomic Bases and $T$-path Formula for Cluster Algebras of Type $D$

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2524 ◽

2015 ◽

Vol DMTCS Proceedings, 27th... (Proceedings) ◽

Author(s):

Emily Gunawan ◽

Gregg Musiker

Keyword(s):

Cluster Algebra ◽

Cluster Algebras ◽

Combinatorial Proof ◽

Expansion Formula ◽

Type D ◽

International Audience ◽

T Path ◽

Nous Utilisons

International audience We extend a $T$-path expansion formula for arcs on an unpunctured surface to the case of arcs on a once-punctured polygon and use this formula to give a combinatorial proof that cluster monomials form the atomic basis of a cluster algebra of type $D$. Nous généralisons une formule de développement en $T$-chemins pour les arcs sur une surface non-perforée aux arcs sur un polygone à une perforation. Nous utilisons cette formule pour donner une preuve combinatoire du fait que les monômes amassées constituent la base atomique d’une algèbre amassée de type $D$.

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Cluster Algebras of Type D: Pseudotriangulations Approach

The Electronic Journal of Combinatorics ◽

10.37236/5282 ◽

2015 ◽

Vol 22 (4) ◽

Cited By ~ 2

Author(s):

Cesar Ceballos ◽

Vincent Pilaud

Keyword(s):

Perfect Matchings ◽

Cluster Algebras ◽

Combinatorial Interpretation ◽

Small Disk ◽

Cluster Complexes ◽

Type D ◽

Initial Cluster ◽

Centrally Symmetric ◽

Combinatorial Model ◽

Exchange Relations

We present a combinatorial model for cluster algebras of type $D_n$ in terms of centrally symmetric pseudotriangulations of a regular $2n$ gon with a small disk in the centre. This model provides convenient and uniform interpretations for clusters, cluster variables and their exchange relations, as well as for quivers and their mutations. We also present a new combinatorial interpretation of cluster variables in terms of perfect matchings of a graph after deleting two of its vertices. This interpretation differs from known interpretations in the literature. Its main feature, in contrast with other interpretations, is that for a fixed initial cluster seed, one or two graphs serve for the computation of all cluster variables. Finally, we discuss applications of our model to polytopal realizations of type $D$ associahedra and connections to subword complexes and $c$-cluster complexes.

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On positive geometries of quartic interactions: one loop integrands from polytopes

Journal of High Energy Physics ◽

10.1007/jhep07(2021)136 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Mrunmay Jagadale ◽

Alok Laddha

Keyword(s):

Large Class ◽

Scattering Amplitude ◽

Cluster Algebras ◽

Seminal Work ◽

New Class ◽

Type D ◽

Kinematic Space ◽

The One

Abstract Building on the seminal work of Arkani-Hamed, He, Salvatori and Thomas (AHST) [1] we explore the positive geometry encoding one loop scattering amplitude for quartic scalar interactions. We define a new class of combinatorial polytopes that we call pseudo-accordiohedra whose poset structures are associated to singularities of the one loop integrand associated to scalar quartic interactions. Pseudo-accordiohedra parametrize a family of projective forms on the abstract kinematic space defined by AHST and restriction of these forms to the type-D associahedra can be associated to one-loop integrands for quartic interactions. The restriction (of the projective form) can also be thought of as a canonical top form on certain geometric realisations of pseudo-accordiohedra. Our work explores a large class of geometric realisations of the type-D associahedra which include all the AHST realisations. These realisations are based on the pseudo-triangulation model for type-D cluster algebras discovered by Ceballos and Pilaud [2].

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The Type D Construct

European Journal of Psychological Assessment ◽

10.1027/1015-5759/a000189 ◽

2014 ◽

Vol 30 (4) ◽

pp. 283-288 ◽

Cited By ~ 3

Author(s):

Gesine Grande ◽

Matthias Romppel ◽

Matthias Michal ◽

Elmar Brähler

Keyword(s):

Social Functioning ◽

Negative Affectivity ◽

Population Based ◽

Type D Personality ◽

Social Orientation ◽

German Population ◽

Social Competencies ◽

Social And Emotional ◽

Type D ◽

Worse Prognosis

The interaction of negative affectivity (NA) and social inhibition (SI), known as the Type D personality, is associated with a worse prognosis in cardiac patients. Until now, causal models have been speculative, and this is partly due to a lack of clarity related to the validity of SI, its role in emotion regulation, and the postulated independence of social and emotional functioning. To examine the construct validity of the Type D personality, we analyzed associations of NA and SI with different measures of affectivity, social anxiety, and social competencies in a German population-based representative sample (n = 2,495). Both NA and SI were associated with all other measures of social functioning and negative affect (all rs > .30) and showed considerable cross-loadings (NA: a 1 = .39, a 2 = .63; SI: a1 = .73 and a2 = .34) in a two-factor solution with the factors labeled as Social Functioning and Negative Affectivity. The SI subscale did not properly differentiate between social fears and social competencies, which emerged as rather different aspects of social functioning. Further studies should examine the effect of broader dimensions of social orientation and competencies and their interaction with NA on cardiac prognosis.

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Illness Perception and Its Changes During Six Months After Cardiac Rehabilitation

European Journal of Health Psychology ◽

10.1027/2512-8442/a000034 ◽

2019 ◽

Vol 26 (3) ◽

pp. 90-100

Author(s):

Justė Lukoševičiūtė ◽

Kastytis Šmigelskas

Keyword(s):

New York ◽

Social Factors ◽

Nyha Class ◽

Illness Perception ◽

Heart Association ◽

Class Iii ◽

Cognitive Representations ◽

Coronary Syndrome ◽

Type D ◽

New York Heart Association

Abstract. Illness perception is a concept that reflects patients' emotional and cognitive representations of disease. This study assessed the illness perception change during 6 months in 195 patients (33% women and 67% men) with acute coronary syndrome, taking into account the biological, psychological, and social factors. At baseline, more threatening illness perception was observed in women, persons aged 65 years or more, with poorer functional capacity (New York Heart Association [NYHA] class III or IV) and comorbidities ( p < .05). Type D personality was the only independent factor related to more threatening illness perception (βs = 0.207, p = .006). At follow-up it was found that only self-reported cardiovascular impairment plays the role in illness perception change (βs = 0.544, p < .001): patients without impairment reported decreasing threats of illness, while the ones with it had a similar perception of threat like at baseline. Other biological, psychological, and social factors were partly associated with illness perception after an acute cardiac event but not with perception change after 6 months.

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