Random tensor models—the multi-orientable (MO) model

2021 ◽  
pp. 209-233
Author(s):  
Adrian Tanasa
Keyword(s):  
Feynman Graph ◽  
General Term ◽  
Intermediate Step ◽  
Tensor Model ◽  
Invariant Model ◽  
Tensor Models ◽  
Feynman Graphs ◽  
The One ◽  
Definition Of

In its first section, this chapter presents the definition of the multi-orientable tensor model. The 1/N expansion and the large N limit of this model are exposed in the second section of the chapter. In the third section, a thorough enumerative combinatorial analysis of the general term of the 1/N expansion is presented. The implementation of the double scaling mechanism is then exhibited in the fourth section. This chapter presents the multi-orientable (MO) tensor model and it follows the review article. This rank three model, having O(N) U(N) O(N) symetry, can be seen as an intermediate step between the U(N) invariant model presented in the previous chapter, and the O(N) invariant model presented in the following chapter. The class of Feynman graph generated by perturbative expansion of MO model is strictly larger than the class of Feynman graphs of the U(N) invariant model and strictly smaller than the one of the O(N) invariant model.

scholarly journals Asymptotic Expansion of the Multi-Orientable Random Tensor Model

10.37236/4629 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Eric Fusy ◽  
Adrian Tanasa
Keyword(s):  
Asymptotic Expansion ◽  
Matrix Models ◽  
Three Dimensional ◽  
Natural Generalization ◽  
General Term ◽  
Tensor Model ◽  
Half Integer ◽  
Tensor Models ◽  
Random Tensor

Three-dimensional random tensor models are a natural generalization of the celebrated matrix models. The associated tensor graphs, or 3D maps, can be classified with respect to a particular integer or half-integer, the degree of the respective graph. In this paper we analyze the general term of the asymptotic expanion in $N$, the size of the tensor, of a particular random tensor model, the multi-orientable tensor model. We perform their enumeration and we establish which are the dominant configurations of a given degree.

The Sachdev–Ye–Kitaev (SYK) holographic model

2021 ◽  
pp. 260-290
Author(s):  
Adrian Tanasa
Keyword(s):  
Gaussian Distribution ◽  
Mechanical Model ◽  
Quantum Mechanical ◽  
Tensor Model ◽  
Holographic Model ◽  
Leading Order ◽  
Tensor Models ◽  
Feynman Graphs ◽  
Non Gaussian ◽  
Random Tensor

In this chapter, we first review the Sachdev–Ye–Kitaev (SYK) model, which is a quantum mechanical model of N fermions. The model is a quenched model, which means that the coupling constant is a random tensor with Gaussian distribution. The SYK model is dominated in the large N limit by melonic graphs, in the same way the tensor models presented in the previous three chapters are dominated by melonic graphs. We then present a purely graph theoretical proof of the melonic dominance of the SYK model. It is this property which led E. Witten to relate the SYK model to the coloured tensor model. In the rest of the chapter we deal with the so-called coloured SYK model, which is a particular case of the generalisation of the SYK model introduced by D. Gross and V. Rosenhaus. We first analyse in detail the leading order and next-to-leading order vacuum, two- and four-point Feynman graphs of this model. We then exhibit a thorough asymptotic combinatorial analysis of the Feynman graphs at an arbitrary order in the large N expansion. We end the chapter by an analysis of the effect of non-Gaussian distribution for the coupling of the model.

scholarly journals Double scaling limit for the O(N)3-invariant tensor model

2022 ◽  
Author(s):  
Valentin Bonzom ◽  
Victor Nador ◽  
Adrian Tanasa
Keyword(s):  
Scaling Limit ◽  
Tensor Model ◽  
Invariant Tensor ◽  
Generating Series ◽  
Tensor Models ◽  
Feynman Graphs ◽  
Diagrammatic Analysis ◽  
Finite Sum ◽  
Double Scaling Limit ◽  
The Continuum

Abstract We study the double scaling limit of the O(N)3-invariant tensor model, initially introduced in Carrozza and Tanasa, Lett. Math. Phys. (2016). This model has an interacting part containing two types of quartic invariants, the tetrahedric and the pillow one. For the 2-point function, we rewrite the sum over Feynman graphs at each order in the 1/N expansion as a finite sum, where the summand is a function of the generating series of melons and chains (a.k.a. ladders). The graphs which are the most singular in the continuum limit are characterized at each order in the 1/N expansion. This leads to a double scaling limit which picks up contributions from all orders in the 1/N expansion. In contrast with matrix models, but similarly to previous double scaling limits in tensor models, this double scaling limit is summable. The tools used in order to prove our results are combinatorial, namely a thorough diagrammatic analysis of the Feynman graphs, as well as an analytic analysis of the singularities of the relevant generating series.

Random tensor models—the O(N)3-invariant model

2021 ◽  
pp. 234-259
Author(s):  
Adrian Tanasa
Keyword(s):  
Critical Exponents ◽  
Perturbative Expansion ◽  
Critical Regime ◽  
Leading Order ◽  
Invariant Model ◽  
Analytic Combinatorics ◽  
Tensor Models ◽  
Feynman Graphs ◽  
Random Tensor

We define in this chapter a class of tensor models endowed with O(N)3-invariance, N being again the size of the tensor. This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model and the U(N)3-invariant models treated in the previous two chapters. We first exhibit the existence of a large N expansion for such a model with general interactions (non-necessary quartic). We then focus on the quartic model and we identify the leading order and next-to-leading Feynman graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the so-called critical exponents. This is achieved through the use of various analytic combinatorics techniques.

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 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.

Ex Meritis Praevisis: Predestination, Grace, and Free Will in intra-Jesuit Controversies (1587-1613)

2020 ◽  
Vol 7 (1) ◽  
pp. 111-150
Author(s):  
Eleonora Rai
Keyword(s):  
Free Will ◽  
Society Of Jesus ◽  
Modern Age ◽  
Sovereign Authority ◽  
Theological Debate ◽  
The One ◽  
Definition Of ◽  
The Relationship ◽  
God’S Foreknowledge ◽  
Catholic Theological

AbstractThis article retraces the intra-Jesuit theological debates on the theology of salvation, including the relationship between the elements of predestination, God’s foreknowledge, Grace, and free will, in the delicate passage between the sixteenth and the seventeenth centuries, and within the debates on Augustine’s theological legacy. Specifically, it explores the Flemish Jesuit Leonard Lessius’ theology and the discussions raised by it within the Society of Jesus, in order to show how soteriology has been central in the process of self-definition of the Jesuit identity in the Early Modern Age. This is particularly clear from the internal debates developed between Lessius, on the one hand, and General Claudio Acquaviva and curial theologian Roberto Bellarmino, on the other hand. Not only does the article investigate little known aspects of intra-Catholic theological debate in the post Tridentine period, but it also shows how deep pastoral and moral concerns strongly contributed to the rise of Lessius’ open-minded theology of salvation, which seemed to deprive God’s sovereign authority in favour of humankind’s free will, and human agency in the process of salvation.

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