Notion Of Complexity Research Articles

Imagination theory: Anthropological perspectives

The term imagination and its derivatives often serve as points of departures, yet a concise understanding of imagination in anthropology is lacking. In this paper, we argue for a contextualized anthropological approach to imagination; a complex notion which has been used to describe the human capacity to mentally (re)create that what is not materially present; the creative process of imagining; and the individual and social products of such a process. We address terminological particularities, conceptual differences, and related concepts in addition to discussing the importance of methods and the poetic imagination. In doing so, we consolidate and elaborate on previous analytical and conceptual works to provide a more explicit middle-range theory of imagination from an anthropological perspective. While we propose understanding imagination as a guiding action in situations of uncertainty or ignorance and emphasize focusing on everyday processes and practices, our discussions provide a framework to discuss and compare empirically grounded findings regarding imagination.

Permutation group entropy: A new route to complexity for real-valued processes.

This is a review of group entropy and its application to permutation complexity. Specifically, we revisit a new approach to the notion of complexity in the time series analysis based on both permutation entropy and group entropy. As a result, the permutation entropy rate can be extended from deterministic dynamics to random processes. More generally, our approach provides a unified framework to discuss chaotic and random behaviors.

Mathematical Connections and the Mathematics Teacher’s Specialised Knowledge

This study seeks to explore the relationship between recent findings on mathematical connections and the Mathematics Teacher’s Specialised knowledge model. From a qualitative approach, we seek to explore the specialised knowledge mobilised during the establishment of mathematical connections in different contexts. The study takes into consideration the results from previous studies that were conducted with both prospective and in service teachers. The results suggest the need to include the notion of complexity in the mathematical connections defined by the Mathematics Teacher’s Specialised knowledge model. Similarly, they suggest that it is possible to find some ambiguities in the use of the model, so it would be enriching to consider the current classification of mathematical connections in order to improve the model as an analytical tool. Finally, the results suggest the need to include mathematical connections as part of the pedagogical content knowledge domain, since the knowledge of this domain could be mobilised during the establishment of mathematical connections.

Bounds on quantum evolution complexity via lattice cryptography

We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal’ operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to \sim 10^4∼104.

Statistical complexity and the road to equilibrium in many-body chaotic quantum systems.

In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., the road to equilibrium. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally, by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.

What I Think about When I Think about Teaching Ethics: A Philosophical Exploration in Pedagogy

What I Think about When I Think about Teaching Ethics: A Philosophical Exploration in Pedagogy

The Ancient Greek Roots of Human Rights

The Ancient Greek Roots of Human Rights

History Beyond The Frame: Exploring The Art In Spiegelman’s Maus

The attempt to reflect on the horrific past through the medium of comics sets the tone of the narrative put forth by Art Spiegelman. An episode in World history that is otherwise extremely difficult to talk about is portrayed in a manner that enables the readers to delve deeper into the realm of the Holocaust. The complex notions of power politics and dehumanization are reflected in Maus (Spiegelman Vol.1-2) with an aim to discover the long-lost memory of atrocities meted out to the Jewish community.

How much consciousness is there in complexity?

The notion of complexity currently receives significant attention in neuroscience, mainly through the popularity of the Integrated Information Theory (IIT). It has proven successful in research centred on discriminating states of consciousness, while little theoretical and experimental effort was directed toward studying the content. In this paper, we argue that exploring the relationship between complexity and conscious content is necessary to understand the importance of information-theoretic measures for consciousness research properly. We outline how content could be experimentally operationalised and how rudimental testable hypotheses can be formulated without requiring IIT formalisms. This approach would not only allow for a better understanding of aspects of consciousness captured by complexity but could also facilitate comparison efforts for theories of consciousness.

Structural models of the paremiological units with the modality component in Spanish, English, and Tatar language

This present study is focused on the comparative analysis of the grammatical and structural characteristics of paremiological units (PUs) with a modality element in Spanish, English, as well as the Tatar language. PUs with that element is absorbing for analyzing the linguistics worldview of Spanish, English, and Tatar language. This study’s relevance is defined by the reality that PUs are among the most contradictory and complex notions in linguistics. The subject of the study is related to linguistics to recognize the structure and features of PUs of Spanish, English, and also Tatar language. To fulfil the study’s aims, a descriptive-analytical method is utilized. This study revolves around the structural - lexical and structural - grammatical characteristics of the PUs expression of the compared tongues. The particular and general sorts utilizing the modality component of the linguistic worldview are determined, and their classification as well. The study outcomes provided are highly interesting to scientists examining the notions of PUs in Spanish, English, and Tatar language. The results have the capacity to be employed in the analysis and study of research and cultural issues and language learning procedure.

Social Deprivation, Healthcare Access and Diabetic Foot Ulcer: A Narrative Review.

The diabetic foot ulcer (DFU) is a common and serious complication of diabetes. There is also a strong relationship between the environment of the person living with a DFU and the prognosis of the wound. Financial insecurity seems to have a major impact, but this effect can be moderated by social protection systems. Socioeconomic and socio-educational deprivations seem to have a more complex relationship with DFU risk and prognosis. The area of residence is a common scale of analysis for DFU as it highlights the effect of access to care. Yet it is important to understand other levels of analysis because some may lead to over-interpretation of the dynamics between social deprivation and DFU. Social deprivation and DFU are both complex and multifactorial notions. Thus, the strength and characteristics of the correlation between the risk and prognosis of DFU and social deprivation greatly depend not only on the way social deprivation is calculated, but also on the way questions about the social deprivation−DFU relationship are framed. This review examines this complex relationship between DFU and social deprivation at the individual level by considering the social context in which the person lives and his or her access to healthcare.

Comparing the collective behavior of banking industry in emerging markets versus mature ones by random matrix approach

One of the essential features of capital markets as an adaptive complex network is their collective behavior. In this paper, we have analyzed the collective behavior of banking sectors of four stock markets, which are composed of emerging and mature ones. By plotting the dendrograms and heat maps of the correlation matrices, it is found that the mature markets are more similar to each other. By applying the method of Random matrix theory(RMT), one of the important complexity notions, and its tools: participation ratio(PR) and relative participation ratio(RPR), it is obvious that mature markets have a lower degree of collective behavior than the emerging ones. By perturbing the correlation matrix of these markets, it is found that the mature markets are more vulnerable. It means that emerging markets that have lower cross-correlations are less vulnerable to perturbations. The findings of this paper are useful for policymakers of these countries to concentrate on the market structures and their behaviors.

Spectral form factor of a quantum spin glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

Circuit Complexity in Topological Quantum Field Theory

AbstractQuantum circuit complexity has played a central role in recent advances in holography and many‐body physics. Within quantum field theory, it has typically been studied in a Lorentzian (real‐time) framework. In a departure from standard treatments, we aim to quantify the complexity of the Euclidean path integral. In this setting, there is no clear separation between space and time, and the notion of unitary evolution on a fixed Hilbert space no longer applies. As a proof of concept, we argue that the pants decomposition provides a natural notion of circuit complexity within the category of 2‐dimensional bordisms and use it to formulate the circuit complexity of states and operators in 2‐dimensional topological quantum field theory. We comment on analogies between our formalism and others in quantum mechanics, such as tensor networks and second quantization.

Hermann Kantorowicz’ Concept of Legal Science and the Social Role of Legal Scholarship Today

Hermann Kantorowicz was a great legal scholar, who taught not only in Germany, but also in the United States, at Oxford and at Cambridge. His work bridges the intellectual divide between the common and civil laws not just because of his cosmopolitan biography, but also because of the exceptional breadth of his academic interests. In Germany, Kantorowicz has always been known best as a leading figure of the free law movement ( Freirechtsbewegung). This paper focuses instead on Kantorowicz’ idea of legal science. There are at least two reasons why Kantorowicz’ contributions to the issue are worth re-reading today. On the one hand, he discussed these questions in a manner which engages deeply with philosophical scholarship, relying primarily on concepts developed by Heinrich Rickert, Wilhelm Windelband, and Max Weber. On the other hand, Kantorowicz developed his ideas of legal science wholly independently of nineteenth century (or contemporary) programmes to re-construct the law in the form of a fully rational, internally coherent system. In this respect Kantorowicz’ ideas fit in well with modern, more fluid and complex notions of law and multi-layered legal systems.

Simple and fast algorithm for binary integer and online linear programming

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and is free of matrix inversion. It can be viewed as both an approximate algorithm for solving binary integer LPs and a fast algorithm for solving online LP problems. The algorithm is inspired by an equivalent form of the dual problem of the relaxed LP and it essentially performs (one-pass) projected stochastic subgradient descent in the dual space. We analyze the algorithm in two different models, stochastic input and random permutation, with minimal technical assumptions on the input data. The algorithm achieves \(O\left( m \sqrt{n}\right) \) expected regret under the stochastic input model and \(O\left( (m+\log n)\sqrt{n}\right) \) expected regret under the random permutation model, and it achieves \(O(m \sqrt{n})\) expected constraint violation under both models, where n is the number of decision variables and m is the number of constraints. The algorithm enjoys the same performance guarantee when generalized to a multi-dimensional LP setting which covers a wider range of applications. In addition, we employ the notion of the permutational Rademacher complexity and derive regret bounds for two earlier online LP algorithms for comparison. Both algorithms improve the regret bound by a factor of \(\sqrt{m}\) by paying more computational cost. Furthermore, we demonstrate how to convert the possibly infeasible solution to a feasible one through a randomized procedure. Numerical experiments illustrate the general applicability and effectiveness of the algorithms.

Climate change, a challenging topic in the French curriculum (in 7th grade)

As part of a renewed focus on current environmental concerns, the new geography programs set out for middle schools introduced new subjects on global change in 2015, subsequently replaced by a focus on climate change in 2020. The case study approach to teaching, imposed by official directives, makes it difficult for middle school students to understand these complex notions. This research attempts to analyze how students appropriate these notions and to verify whether they are capable of reasoning in a systemic way, i.e. of adopting the required approach for understanding such complexity. This article explores an epistemological analysis of global change and climate change, a didactic study of school textbooks and an examination of teachers’ discourse and students’ work in order to address this question.

Deterministic functions on amenable semigroups and a generalization of the Kamae-Weiss theorem on normality preservation

A classical Kamae-Weiss theorem states that an increasing sequence (ni)i∈ℕ of positive lower density is normality preserving, i.e., has the property that for any normal binary sequence (bn)n∈ℕ, the sequence $${({n_i})_{i \in \mathbb{N}}}$$ is normal, if and only if (ni)i∈ℕ is a deterministic sequence. Given a countable cancellative amenable semigroup G, and a Følner sequence $${\cal F} = {({F_n})_{n \in}}$$ in G, we introduce the notions of normality preservation, determinism and subexponential complexity for subsets of G with respect to $${\cal F}$$ and show that for sets of positive lower $${\cal F}$$ -density these three notions are equivalent. The proof utilizes the apparatus of the theory of tilings of amenable groups and the notion of tile-entropy We also prove that under a natural assumption on $${\cal F}$$ positive lower $${\cal F}$$ -density follows from normality preservation. Finally, we provide numerous examples of normality preserving sets in various semigroups.

Quantitative sheaf theory

We introduce a notion of complexity of a complex of ℓ \ell -adic sheaves on a quasi-projective variety and prove that the six operations are “continuous”, in the sense that the complexity of the output sheaves is bounded solely in terms of the complexity of the input sheaves. A key feature of complexity is that it provides bounds for the sum of Betti numbers that, in many interesting cases, can be made uniform in the characteristic of the base field. As an illustration, we discuss a few simple applications to horizontal equidistribution results for exponential sums over finite fields.

A refinement of Cauchy–Schwarz complexity

We introduce a notion of complexity for systems of linear forms called sequential Cauchy–Schwarz complexity, which is parametrized by two positive integers k,ℓ and refines the notion of Cauchy–Schwarz complexity introduced by Green and Tao. We prove that if a system of linear forms has sequential Cauchy–Schwarz complexity at most (k,ℓ) then any average of 1-bounded functions over this system is controlled by the 21−ℓ-th power of the Gowers Uk+1-norms of the functions. For ℓ=1 this agrees with Cauchy–Schwarz complexity, but for ℓ>1 there are systems that have sequential Cauchy–Schwarz complexity at most (k,ℓ) whereas their Cauchy–Schwarz complexity is greater than k. Our main application illustrates this with systems over a prime field Fp, denoted by Φk,M, which can be viewed as M-dimensional arithmetic progressions of length k. For each M≥2 we prove that Φk,M has sequential Cauchy–Schwarz complexity at most (k−2,|Φk,M|) (where |Φk,M| is the number of forms in the system), whereas the Cauchy–Schwarz complexity of Φk,M can be greater than k−2. Thus we obtain polynomial true-complexity bounds for Φk,M with exponent 2−|Φk,M|. A recent general theorem of Manners, proved independently with different methods, implies a similar application but with different polynomial true-complexity bounds, as explained in the paper. In separate work, we use our application to give a new proof of the inverse theorem for Gowers norms on Fpn, and related results on ergodic actions of Fpω.