scholarly journals An explicit formula for ndinv, a new statistic for two-shuffle parking functions

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Angela Hicks ◽  
Yeonkyung Kim
Keyword(s):  
Explicit Formula ◽  
Parking Functions ◽  
Recursive Definition ◽  
Classical Definition ◽  
Inversion Number ◽  
International Audience ◽  
New Interpretation ◽  
The One ◽  
Definition Of ◽  
New Statistics

International audience In a recent paper, Duane, Garsia, and Zabrocki introduced a new statistic, "ndinv'', on a family of parking functions. The definition was guided by a recursion satisfied by the polynomial $\langle\Delta_{h_m}C_p1C_p2...C_{pk}1,e_n\rangle$, for $\Delta_{h_m}$ a Macdonald eigenoperator, $C_{p_i}$ a modified Hall-Littlewood operator and $(p_1,p_2,\dots ,p_k)$ a composition of n. Using their new statistics, they are able to give a new interpretation for the polynomial $\langle\nabla e_n, h_j h_n-j\rangle$ as a q,t numerator of parking functions by area and ndinv. We recall that in the shuffle conjecture, parking functions are q,t enumerated by area and diagonal inversion number (dinv). Since their definition is recursive, they pose the problem of obtaining a non recursive definition. We solved this problem by giving an explicit formula for ndinv similar to the classical definition of dinv. In this paper, we describe the work we did to construct this formula and to prove that the resulting ndinv is the same as the one recursively defined by Duane, Garsia, and Zabrocki. Dans un travail récent Duane, Garsia et Zabrocki ont introduit une nouvelle statistique, "ndinv'' pour une famille de Fonctions Parking. Ce "ndinv" découle d'une récurrence satisfaite par le polynôme $\langle\Delta_{h_m}C_p1C_p2...C_{pk}1,e_n\rangle$, oú $\Delta_{h_m}$ est un opérateur linéaire avec fonctions propres les polynômes de Macdonald, les $C_{p_i}$ sont des opérateurs de Hall-Littlewood modifiés et $(p_1,p_2,\dots ,p_n)$ est un vecteur à composantes entières positives. Par moyen de cette statistique, ils ont réussi à donner une nouvelle interprétation combinatoire au polynôme $\langle\nabla e_n, h_j h_n-j\rangle$ on remplaçant "dinv'" par "ndinv". Rappelons nous que la conjecture "Shuffle"' exprime ce même polynôme comme somme pondérée de Fonctions Parking avec poids t à la "aire'" est q au "dinv". Puisque il donnent une définition récursive du "ndinv" il posent le problème de l'obtenir d'une façon directe. On rèsout se problème en donnant une formule explicite qui permet de calculer directement le "ndinv" à la manière de la formule classique du "dinv". Dans cet article on décrit le travail qu'on a fait pour construire cette formule et on démontre que nôtre formule donne le même "ndinv" récursivement construit par Duane, Garsia et Zabrocki.

scholarly journals Non-commutative Frobenius characteristic of generalized parking functions : Application to enumeration

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Jean-Baptiste Priez ◽  
Aladin Virmaux
Keyword(s):  
Symmetric Functions ◽  
Parking Functions ◽  
Recursive Definition ◽  
Parking Function ◽  
International Audience ◽  
Function Module ◽  
Definition Of ◽  
Nous Utilisons

International audience We give a recursive definition of generalized parking functions that allows them to be viewed as a species. From there we compute a non-commutative characteristic of the generalized parking function module and deduce some enumeration formulas of structures and isomorphism types. We give as well an interpretation in several bases of non commutative symmetric functions. Finally, we investigate an inclusion-exclusion formula given by Kung and Yan. Nous donnons une définition récursive des fonctions de parking généralisées nous permettant de munir ces dernières d’une structure d’espèce. Nous utilisons ce point de vu pour donner une caractéristique de Frobenius non-commutative du module des fonctions de parking généralisées que nous appliquons afin de donner de nombreuses formules d’énumération de structures et de type d’isomorphismes, ainsi qu’une interprétation dans plusieurs bases des fonctions symétriques non commutatives. Enfin, nousétudions une formule d’inclusion-exclusion provenant de Kung et Yan.

scholarly journals Crystal energy via charge

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Cristian Lenart ◽  
Anne Schilling
Keyword(s):  
Energy Function ◽  
Tensor Products ◽  
Macdonald Polynomials ◽  
Recursive Definition ◽  
R Matrix ◽  
Single Column ◽  
Nous Montrons ◽  
International Audience ◽  
Definition Of

International audience The Ram–Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types ${A}$ and ${C}$ it can be defined on tensor products of Kashiwara–Nakashima single column crystals. In this paper we show that the charge is equal to the (negative of the) energy function on affine crystals. The algorithm for computing charge is much simpler than the recursive definition of energy in terms of the combinatorial ${R}$-matrix. La formule de Ram et Yip pour les polynômes de Macdonald (à t = 0) fournit une statistique que nous appelons la charge. Dans les types ${A}$ et ${C}$, elle peut être définie sur les produits tensoriels des cristaux pour les colonnes de Kashiwara–Nakashima. Dans ce papier, nous montrons que la charge est égale à (l'opposé de) la fonction d'énergie sur cristaux affines. L'algorithme pour calculer la charge est bien plus simple que la définition récursive de l'énergie en fonction de la ${R}$-matrice combinatoire.

scholarly journals On the original formulation and on the resonance over time of Grassmann’s Law: remarks on a still open issue

2019 ◽  
Vol 61 (1) ◽  
pp. 107-130
Author(s):  
Marianna Pozza
Keyword(s):  
Historical Linguistic ◽  
Present Article ◽  
The Other ◽  
Original Formulation ◽  
Open Issue ◽  
New Interpretation ◽  
The One ◽  
Definition Of ◽  
Over Time

Abstract The present article aims to reconsider in detail the original formulation of Grassmann’s law (GL), proposed by Grassmann (1863), since the main handbooks of Indo-European linguistics often repeat an extremely concise and sometimes incomplete formulation of the phenomenon without going into the details of Grassmann’s original reasoning, from which the definition of the phonetic “law” took its shape. In fact, we intend to highlight, on the one hand, the route whereby the scholar arrived at the decisive formulation of the principle which took its name from him, on the other the research ideas already present in the article of 1863 and only partially taken into account by subsequent studies. In addition to offering an overview, as complete as possible, of the resonance and influence of GL among linguists (both within a general and a historical linguistic perspective), over the years, the intent is to show the fruitfulness of ideas that still today could be used for new studies on the topic and to offer a possible, new interpretation of this phonetic change.

Topological and metric entropy for group and semigroup actions

2019 ◽  
Vol 7 (1) ◽  
pp. 38-47
Author(s):  
Luchezar Stoyanov
Keyword(s):  
Invariant Measure ◽  
Topological Entropy ◽  
Metric Entropy ◽  
Semigroup Action ◽  
Semigroup Actions ◽  
Advantages And Disadvantages ◽  
Classical Definition ◽  
Giordano Bruno ◽  
The One ◽  
Definition Of

AbstractIt is well-known that the classical definition of topological entropy for group and semigroup actions is frequently zero in some rather interesting situations, e.g. smooth actions of ℤk+ (k >1) on manifolds. Different definitions have been considered by several authors. In the present article we describe the one proposed in 1995 by K.H.Hofmann and the author which produces topological entropy not trivially zero for such smooth actions. We discuss this particular approach, and also some of the main properties of the topological entropy defined in this way, its advantages and disadvantages compared with the classical definition. We also discuss some recent results, obtained jointly with Andrzej Biś, Dikran Dikranjan and Anna Giordano Bruno, of a similar definition of metric entropy, i.e. entropy with respect to an invariant measure for a group or a semigroup action, and some of its properties.

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.

Democracy and Political Culture

2019 ◽  
Author(s):  
Ross McKibbin
Keyword(s):  
Political Culture ◽  
Case Studies ◽  
Social System ◽  
Political System ◽  
Democratic Politics ◽  
Social Structures ◽  
The Political ◽  
The Subject ◽  
The One ◽  
Definition Of

This book is an examination of Britain as a democratic society; what it means to describe it as such; and how we can attempt such an examination. The book does this via a number of ‘case-studies’ which approach the subject in different ways: J.M. Keynes and his analysis of British social structures; the political career of Harold Nicolson and his understanding of democratic politics; the novels of A.J. Cronin, especially The Citadel, and what they tell us about the definition of democracy in the interwar years. The book also investigates the evolution of the British party political system until the present day and attempts to suggest why it has become so apparently unstable. There are also two chapters on sport as representative of the British social system as a whole as well as the ways in which the British influenced the sporting systems of other countries. The book has a marked comparative theme, including one chapter which compares British and Australian political cultures and which shows British democracy in a somewhat different light from the one usually shone on it. The concluding chapter brings together the overall argument.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

scholarly journals AB0677 REVISING THE DEFINITION OF REACTIVE ARTHRITIS AND DIFFERENTIATION FROM UNDIFFERENTIATED SPONDYLOARTHRITIS

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar
Keyword(s):  
Causative Agent ◽  
Reactive Arthritis ◽  
Case Reports ◽  
Experimental Studies ◽  
Classification Criteria ◽  
General Definition ◽  
Parasitic Infections ◽  
Undifferentiated Spondyloarthritis ◽  
Classical Definition ◽  
Definition Of

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared

scholarly journals Beyond Classical Definition: The Non-definition of Gamification

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Mario S. Staller ◽  
Swen Koerner
Keyword(s):  
Empirical Investigation ◽  
Working Life ◽  
Pedagogical Practice ◽  
Police Recruits ◽  
Design Elements ◽  
The Subject ◽  
Anchor Points ◽  
The One ◽  
Definition Of ◽  
Game Elements

AbstractGamification is regularly defined as the use of game elements in non-gaming contexts. However, discussions in the context of the pedagogical value of gamification suggest controversies on various levels. While on the one hand, the potential is seen in the design of joyful learning environments, critics point out the pedagogical dangers or the problems related to optimizing working life. It becomes apparent that the assumptions guiding action on the subject matter of gamification in educational contexts differ, which leads to different derivations for pedagogical practice—but also allows for different perspectives on initially controversial positions. Being aware of these assumptions is the claim of a reflexive pedagogy. With regard to the pedagogical use of gamifying elements and their empirical investigation, there are three main anchor points to consider from a reflexive stance: (a) the high context-specificity of the teaching undertaken and (b) the (non-)visibility of the design elements and (c) the (non-)acceptance of the gamified elements by the students. We start by providing a discussion of the definitional discourse on what is understood as gamification leading to our argument for a non-definition of gamification. We describe the potential of this non-definition of gamification and exemplify its use in a gamified concept of teaching police recruits professional reflexivity. The concept features the narrative of a potential crime that has been undertaken and that students decide for themselves if they want to engage with it.

scholarly journals The contribution of resident physicians to hospital productivity

2021 ◽  
Author(s):  
Maria J. Perez-Villadóniga ◽  
Ana Rodriguez-Alvarez ◽  
David Roibas
Keyword(s):  
Production Functions ◽  
Weighted Sum ◽  
Main Hypothesis ◽  
Resident Physicians ◽  
Suitable Parameter ◽  
Functional Forms ◽  
The One ◽  
Definition Of ◽  
Hospital Productivity ◽  
Natural Hypothesis

AbstractResident physicians play a double role in hospital activity. They participate in medical practices and thus, on the one hand, they should be considered as an input. Also, they are medical staff in training and, on the other hand, must be considered as an output. The net effect on hospital activities should therefore be empirically determined. Additionally, when considering their role as active physicians, a natural hypothesis is that resident physicians are not more productive than senior ones. This is a property that standard logarithmic production functions (including Cobb–Douglas and Translog functional forms) cannot verify for the whole technology set. Our main contribution is the development of a Translog modification, which implies the definition of the input “doctors” as a weighted sum of senior and resident physicians, where the weights are estimated from the empirical application. This modification of the standard Translog is able, under suitable parameter restrictions, to verify our main hypothesis across the whole technology set while determining if the net effect of resident physicians in hospitals’ production should be associated to an output or to an input. We estimate the resulting output distance function frontier with a sample of Spanish hospitals. Our findings show that the overall contribution of resident physicians to hospitals’ production allows considering them as an input in most cases. In particular, their average productivity is around 37% of that corresponding to senior physicians.

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