Some Empirical Results Concerning Causal Learning and Representation

This chapter explores some empirical results bearing on the descriptive and normative adequacy of different accounts of causal learning and representation. It begins by contrasting associative accounts with accounts that attribute additional structure to causal representation, arguing in favor of the latter. Empirical results supporting the claim that adult humans often reason about causal relationships using interventionist counterfactuals are presented. Contrasts between human and nonhuman primate causal cognition are also discussed, as well as some experiments concerning causal cognition in young children. A proposal about what is involved in having adult human causal representations is presented and some issues about how these might develop over time are explored.

The Relationship of Hadith Style to the Social Society of the Nusantara: A Study on Qami 'Al-Tughyan by Nawawi Al-Bantani

One of the nusantara scholars with famous work inscriptions is Nawawi al-Bantani. These works are recorded in a multidisciplinary scope, one of which is Qami 'al-Tughyan. The significance of this research lies in the influence of environmental factors of Nawawi in the nusantara which have an influence on the style of writing, especially in the field of hadith. This study aims to reveal the facts of causality with the orientation of the literature analysis surrounding Nawawi's notes in compiling the Qami' al-Tughyan. The author will take an inductive qualitative approach by conducting a literature review through related literatures, derived from the object variables in the first ten sections (syu'bah) of the book Qami 'al-Tughyan. Then, the data will be explored in order to produce comprehensive and optimal research results. This research proves that the work recording model used by Nawawi is a causal representation of the situation in the nusantara, especially with regard to the practice of imperialism towards the indigenous people.

A Stroll through the Loop-Tree Duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.

Lotty – The loop-tree duality automation

Elaborating on the novel formulation of the loop-tree duality, we introduce the Mathematica package Lotty that automates the latter at multi-loop level. By studying the features of Lotty and recalling former studies, we discuss that the representation of any multi-loop amplitude can be brought in a form, at integrand level, that only displays physical information, which we refer to as the causal representation of multi-loop Feynman integrands. In order to elucidate the role of Lotty in this automation, we recall results obtained for the calculation of the dual representation of integrands up-to four loops. Likewise, within Lotty framework, we provide support to the all-loop causal representation recently conjectured by the same author. The numerical stability of the integrands generated by Lotty is studied in two-loop planar and non-planar topologies, where a numerical integration is performed and compared with known results.

Loop-tree duality from vertices and edges

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This representation is found to manifest compact expressions for multi-loop topologies that have the same number of vertices. Interestingly, integrands considered in former studies, with up-to six vertices and L internal lines, display the same structure of up-to four-loop ones. The former is an insight that there should be a correspondence between vertices and the collection of internal lines, edges, that characterise a multi-loop topology. By virtue of this relation, in this paper, we embrace an approach to properly classify multi-loop topologies according to vertices and edges. Differently from former studies, we consider the most general topologies, by connecting vertices and edges in all possible ways. Likewise, we provide a procedure to generate causal representation of multi-loop topologies by considering the structure of causal propagators. Explicit causal representations of loop topologies with up-to nine vertices are provided.

Causal representation of multi-loop Feynman integrands within the loop-tree duality

The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.

Information Thermodynamics for Time Series of Signal-Response Models

The entropy production in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. Such a connection was formalized for bipartite (or multipartite) systems with an integral fluctuation theorem in [Phys. Rev. Lett. 111, 180603 (2013)]. Here we introduce the information thermodynamics for time series, that are non-bipartite in general, and we show that the link between irreversibility and information can only result from an incomplete causal representation. In particular, we consider a backward transfer entropy lower bound to the conditional time series irreversibility that is induced by the absence of feedback in signal-response models. We study such a relation in a linear signal-response model providing analytical solutions, and in a nonlinear biological model of receptor-ligand systems where the time series irreversibility measures the signaling efficiency.

MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

Imprecise Bayesian Networks as Causal Models

This article considers the extent to which Bayesian networks with imprecise probabilities, which are used in statistics and computer science for predictive purposes, can be used to represent causal structure. It is argued that the adequacy conditions for causal representation in the precise context—the Causal Markov Condition and Minimality—do not readily translate into the imprecise context. Crucial to this argument is the fact that the independence relation between random variables can be understood in several different ways when the joint probability distribution over those variables is imprecise, none of which provides a compelling basis for the causal interpretation of imprecise Bayes nets. I conclude that there are serious limits to the use of imprecise Bayesian networks to represent causal structure.