scholarly journals Non-Shannon inequalities in the entropy vector approach to causal structures

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 57 ◽  
Author(s):  
Mirjam Weilenmann ◽  
Roger Colbeck
Keyword(s):  
Causal Structure ◽  
Conditional Entropy ◽  
Classical Case ◽  
Conditional Mutual Information ◽  
Entropic Inequalities ◽  
Starting Point ◽  
Outer Approximations ◽  
Open Question ◽  
Causal Structures ◽  
Vector Approach

A causal structure is a relationship between observed variables that in general restricts the possible correlations between them. This relationship can be mediated by unobserved systems, modelled by random variables in the classical case or joint quantum systems in the quantum case. One way to differentiate between the correlations realisable by two different causal structures is to use entropy vectors, i.e., vectors whose components correspond to the entropies of each subset of the observed variables. To date, the starting point for deriving entropic constraints within causal structures are the so-called Shannon inequalities (positivity of entropy, conditional entropy and conditional mutual information). In the present work we investigate what happens when non-Shannon entropic inequalities are included as well. We show that in general these lead to tighter outer approximations of the set of realisable entropy vectors and hence enable a sharper distinction of different causal structures. Since non-Shannon inequalities can only be applied amongst classical variables, it might be expected that their use enables an entropic distinction between classical and quantum causal structures. However, this remains an open question. We also introduce techniques for deriving inner approximations to the allowed sets of entropy vectors for a given causal structure. These are useful for proving tightness of outer approximations or for finding interesting regions of entropy space. We illustrate these techniques in several scenarios, including the triangle causal structure.

scholarly journals Complex Causal Structures of Neighbourhood Change: Evidence From a Functionalist Model and Yelp Data

2021 ◽  
Author(s):  
Daniel Silver ◽  
Thiago H Silva
Keyword(s):  
Large Scale ◽  
Causal Structure ◽  
Functional Model ◽  
Large Scale Data ◽  
Proposed Model ◽  
Neighbourhood Change ◽  
Key Aspects ◽  
Open Question ◽  
Causal Structures ◽  
Scale Data

Why some neighbourhoods change over time but others retain their identity remains an open question. Several attempts have been made to answer this question, with a family of models emerging as a result. However, empirically evaluating neighbourhood evolution models is a challenging task, because most require information that is difficult to obtain in traditional sources. For this reason, researchers have turned to new datasets, such as census microdata, Twitter, and Yelp. In this study, we articulate a functional model of neighbourhood change and continuity, adapted from a classical functionalist model proposed by Stinchcombe in 1968. We argue this model provides a relatively simple way to capture key aspects of the complex causal structure of neighbourhood change that are implicit in much neighbourhood change research but rarely formulated explicitly. We demonstrate how to assess the proposed model empirically using large-scale data from Yelp.com. Our results indicate that our approach can potentially help to understand the nature of neighbourhood change and be useful in different applications.

scholarly journals Cyclic quantum causal models

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Jonathan Barrett ◽  
Robin Lorenz ◽  
Ognyan Oreshkov
Keyword(s):  
Causal Reasoning ◽  
Causal Structure ◽  
Bell Inequalities ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Causal Models ◽  
Causal Order ◽  
Quantum Processes ◽  
Causal Explanations ◽  
Causal Structures

AbstractCausal reasoning is essential to science, yet quantum theory challenges it. Quantum correlations violating Bell inequalities defy satisfactory causal explanations within the framework of classical causal models. What is more, a theory encompassing quantum systems and gravity is expected to allow causally nonseparable processes featuring operations in indefinite causal order, defying that events be causally ordered at all. The first challenge has been addressed through the recent development of intrinsically quantum causal models, allowing causal explanations of quantum processes – provided they admit a definite causal order, i.e. have an acyclic causal structure. This work addresses causally nonseparable processes and offers a causal perspective on them through extending quantum causal models to cyclic causal structures. Among other applications of the approach, it is shown that all unitarily extendible bipartite processes are causally separable and that for unitary processes, causal nonseparability and cyclicity of their causal structure are equivalent.

scholarly journals The Inflation Technique Completely Solves the Causal Compatibility Problem

2020 ◽  
Vol 8 (1) ◽  
pp. 70-91 ◽  
Author(s):  
Miguel Navascués ◽  
Elie Wolfe
Keyword(s):  
Linear Programming ◽  
Latent Variables ◽  
Causal Explanation ◽  
Causal Structure ◽  
Categorical Variables ◽  
False Negatives ◽  
The Given ◽  
Causal Structures ◽  
Compatibility Question ◽  
Structure Graph

AbstractThe causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suffer from false negatives, i.e. they admit incompatible distributions as apparently compatible with the given graph. In 10.1515/jci-2017-0020, one of us introduced the inflation technique for formulating useful relaxations of the causal compatibility problem in terms of linear programming. In this work, we develop a formal hierarchy of such causal compatibility relaxations. We prove that inflation is asymptotically tight, i.e., that the hierarchy converges to a zero-error test for causal compatibility. In this sense, the inflation technique fulfills a longstanding desideratum in the field of causal inference. We quantify the rate of convergence by showing that any distribution which passes the nth-order inflation test must be $\begin{array}{} \displaystyle {O}{\left(n^{{{-}{1}}/{2}}\right)} \end{array}$-close in Euclidean norm to some distribution genuinely compatible with the given causal structure. Furthermore, we show that for many causal structures, the (unrelaxed) causal compatibility problem is faithfully formulated already by either the first or second order inflation test.

Hardy spaces on ZN

2002 ◽  
Vol 132 (1) ◽  
pp. 25-43 ◽  
Author(s):  
Santiago Boza ◽  
María J. Carro
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Atomic Decomposition ◽  
Classical Case ◽  
Positive Answer ◽  
Riesz Transforms ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Definition Of ◽  
Open Question

The work of Coifman and Weiss concerning Hardy spaces on spaces of homogeneous type gives, as a particular case, a definition of Hp(ZN) in terms of an atomic decomposition.Other characterizations of these spaces have been studied by other authors, but it was an open question to see if they can be defined, as it happens in the classical case, in terms of a maximal function or via the discrete Riesz transforms.In this paper, we give a positive answer to this question.

The 3 C's of the Circular Economy for Food. A conceptual framework for circular design in the food system

2021 ◽  
Author(s):  
Franco Fassio
Keyword(s):  
Sustainable Development ◽  
Conceptual Framework ◽  
Circular Economy ◽  
Food System ◽  
Raw Material ◽  
Starting Point ◽  
Development Goals ◽  
Definition Of ◽  
Open Question ◽  
Circular Design

Food, the basic connecting unit of all the UN's Sustainable Development Goals, plays a crucial role in the ecological transition towards a circular economic paradigm. This paper takes scientific considerations as a starting point in order to contribute to the definition of a theoretical-operational framework in which to grow the Circular Economy for Food. This is a still-open question in a sector of the circular economy that is emerging as vital to sustainable development. The 3 C's of Capital, Cyclicality and Co-evolution offer a systemic, holistic vision of the food system's role. Within this conceptual framework, the designers can find the main boundaries of the system, within which to express their creativity. The aim must be to avoid damaging relationships with the best supplier of raw material known to humanity (Nature), respecting planetary boundaries and at the same time offering a fair space to civil society.

scholarly journals Is coding a relevant metaphor for the brain?

2018 ◽  
Vol 42 ◽  
Author(s):  
Romain Brette
Keyword(s):  
Brain Function ◽  
Neural Coding ◽  
Causal Structure ◽  
Linear Chain ◽  
Neural Codes ◽  
Experimental Parameters ◽  
Representational Power ◽  
Causal Structures ◽  
Perceptual Systems ◽  
The Brain

Abstract “Neural coding” is a popular metaphor in neuroscience, where objective properties of the world are communicated to the brain in the form of spikes. Here I argue that this metaphor is often inappropriate and misleading. First, when neurons are said to encode experimental parameters, the neural code depends on experimental details that are not carried by the coding variable (e.g., the spike count). Thus, the representational power of neural codes is much more limited than generally implied. Second, neural codes carry information only by reference to things with known meaning. In contrast, perceptual systems must build information from relations between sensory signals and actions, forming an internal model. Neural codes are inadequate for this purpose because they are unstructured and therefore unable to represent relations. Third, coding variables are observables tied to the temporality of experiments, whereas spikes are timed actions that mediate coupling in a distributed dynamical system. The coding metaphor tries to fit the dynamic, circular, and distributed causal structure of the brain into a linear chain of transformations between observables, but the two causal structures are incongruent. I conclude that the neural coding metaphor cannot provide a valid basis for theories of brain function, because it is incompatible with both the causal structure of the brain and the representational requirements of cognition.

scholarly journals Experimental Implications of Negative Quantum Conditional Entropy—H2 Mobility in Nanoporous Materials

2020 ◽  
Vol 10 (22) ◽  
pp. 8266
Author(s):  
C. Aris Chatzidimitriou-Dreismann
Keyword(s):  
Information Theory ◽  
Translational Motion ◽  
Conditional Entropy ◽  
Classical Case ◽  
Quantum Thermodynamics ◽  
Incoherent Neutron Scattering ◽  
Quantum Conditional Entropy ◽  
Del Rio ◽  
Incoherent Neutron ◽  
Fictitious Particle

During the last few decades, considerable advances in quantum information theory have shown deep existing connections between quantum correlation effects (like entanglement and quantum discord) and thermodynamics. Here the concept of conditional entropy plays a considerable role. In contrast to the classical case, quantum conditional entropy can take negative values. This counter-intuitive feature, already well understood in the context of information theory, was recently shown theoretically to also have a physical meaning in quantum thermodynamics [del Rio et al. Nature 2011, 474, 61]. Extending this existing work, here we provide evidence of the significance of negative conditional entropy in a concrete experimental context: Incoherent Neutron Scattering (INS) from protons of H2 in nano-scale environments; e.g., in INS from H2 in C-nanotubes, the data of the H2 translational motion along the nanotube axis seems to show that the neutron apparently scatters from a fictitious particle with mass of 0.64 atomic mass units (a.m.u.)—instead of the value of 2 a.m.u. as conventionally expected. An independent second experiment confirms this finding. However, taking into account the possible negativity of conditional entropy, we explain that this effect has a natural interpretation in terms of quantum thermodynamics. Moreover, it is intrinsically related to the number of qubits capturing the interaction of the two quantum systems H2 and C-nanotube. The considered effect may have technological applications (e.g., in H-storage materials and fuel cells).

scholarly journals Is there another people? Populism, radical democracy and immanent critique

2020 ◽  
pp. 019145372091045
Author(s):  
Victor Kempf
Keyword(s):  
Radical Democracy ◽  
Political Community ◽  
Right Wing ◽  
Constructivist Approach ◽  
Left Wing ◽  
The People ◽  
Starting Point ◽  
Immanent Critique ◽  
Right Wing Populism ◽  
Open Question

This article explores the possibility of a notion of left-wing populism that is conceptually opposed to the identitarian logic of embodiment that characterises right-populist interpellations of ‘the people’. In the first part, I will demonstrate, that in Laclau’s constructivist approach, any populist embodiment of the people actually has a partial, subaltern and performative origin. On this basis, it becomes possible to distinguish between a radical-democratic version of the people that is self-reflexively aware of this origin and a regressive and reified one that ideologically betrays and negates its own subaltern tradition of democratic struggle by proclaiming to embody a positive, pre-established substance of ‘rooted’, ‘well-born’ community. In the second part of the article, I will focus on this self-negation as a starting point for an immanent critique of right-wing populism. Such an immanent critique is promising, because it could overcome the shortcomings of decisionism and moralism that limit the contemporary critique of right-wing populism. However, it remains still an open question how to defend and define a negativist truth of political community and subjectivation that is necessary for developing such a left-Hegelian critique of regressive and reified notions of ‘the people’.

scholarly journals The Impact of the Oil Sector on Commodity Prices: Correlation or Causation?

2010 ◽  
Vol 42 (3) ◽  
pp. 477-485 ◽  
Author(s):  
Sayed H. Saghaian
Keyword(s):  
Time Series ◽  
Graph Theory ◽  
Causal Structure ◽  
Commodity Prices ◽  
Oil Prices ◽  
Causal Link ◽  
Energy Markets ◽  
Oil Sector ◽  
The Impact ◽  
Causal Structures

The interconnections of agriculture and energy markets have increased through the rise in the new biofuel agribusinesses and the oil-ethanol-corn linkages. The question is whether these linkages have a causal structure by which oil prices affect commodity prices and through these links, instability is transferred from energy markets to already volatile agricultural markets. In this article, we present empirical results using contemporary time-series analysis and Granger causality supplemented by a directed graph theory modeling approach to identify the links and plausible contemporaneous causal structures among energy and commodity variables. The results show that although there is a strong correlation among oil and commodity prices, the evidence for a causal link from oil to commodity prices is mixed.

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