Notion Of Separation Research Articles

Twisted conjugacy and separability

Abstract A group 𝐺 is twisted conjugacy separable if, for every automorphism 𝜑, distinct 𝜑-twisted conjugacy classes can be separated in a finite quotient. Likewise, 𝐺 is completely twisted conjugacy separable if, for any group 𝐻 and any two homomorphisms φ , ψ \varphi,\psi from 𝐻 to 𝐺, distinct ( φ , ψ ) (\varphi,\psi) -twisted conjugacy classes can be separated in a finite quotient. We study how these properties behave with respect to taking subgroups, quotients and finite extensions, and compare them to other notions of separability in groups. Finally, we show that, for polycyclic-by-nilpotent-by-finite groups, being completely twisted conjugacy separable is equivalent to all quotients being residually finite.

Decolonisation, biopolitics and neoliberalism: An Australian study into the problems of legal decision-making

This paper examines the importance of decolonisation to counter the ongoing harms of state-sanctioned child removal policies that disproportionately affect First Nations families and communities in Victoria, Australia. Ongoing legacies of structural disadvantage, including drug abuse, mental ill-health, limited and conditional income support, and housing insecurity, are governed through a selective biopolitical vision that has informed child protection policies since colonisation. Family separation is assumed to protect both vulnerable children and the general community. We argue this logic reinforces structural inequalities that place unreasonable burdens on First Nations mothers to engage in ‘desirable’ and responsible parenting. We present current statistics on the over-representation of First Nations children in the Victorian child protection system, then describe how Western notions of biopolitics view family separation as central to protecting children. This approach now invokes neoliberal modes of governing through risk management, rather than supporting vulnerable families. We then briefly describe Victoria’s child protection system, and critically examine key factual and procedural issues emerging from the application of the ‘best interests’ principle in four case studies documenting legal appeals instigated by First Nations families. We conclude by proposing decolonisation as a counterpoint to a governmental rationality that endorses the protection of children through state-sanctioned family separation.

The Separation of Powers and Judicial Independence in South Africa: A Theoretical Critique

Section 165(2) of the South African Constitution of 1996 proclaims the independence of the courts. This principle is predicated on the philosophical notion of separation of powers prominently adopted in democratic countries like South Africa (SA). Separation of powers and the behavioural demands on judgeship have produced a general conception that the judiciary is independent; even of politics. This is not the case, politics and judiciary are inseparable since they both seek to achieve the same political objectives. This article adopts Critical Legal Theory (CLT) with historical and philosophical analysis to theoretically repudiate the generalisation. This is a qualitative study and has identified a gap in SA constitutional scholarship regarding interrogating the concept of judicial independence. Resolving this issue the article contends that politics are innate to the judiciary. This reasoning stems from the interrogation of the classical development of the “separation of powers”, and the principle of judicial independence. As a complex phenomenon, judicial independence here is not being explored institutionally and administratively. Rather, it is probed from its conceptual premises. Through court judgments, court activism, and South Africa’s history of constitutional development, the article determines that the judiciary and the law in SA are innate in politics. The intent is to disabuse scholarship from accepting the generalisation of the principle of judicial independence. This is not an anti-constitution critique, but a belief/notion that if adjudicators are not strangled with “judicial independence” general narrative, the courts will expedite the constitutions’ transformative objectives.

Single-exponential FPT algorithms for enumerating secluded [formula omitted]-free subgraphs and deleting to scattered graph classes

The celebrated notion of important separators bounds the number of small (S,T)-separators in a graph which are ‘farthest from S’ in a technical sense. In this paper, we introduce a generalization of this powerful algorithmic primitive, tailored to undirected graphs, that is phrased in terms of k-secluded vertex sets: sets with an open neighborhood of size at most k. In this terminology, the bound on important separators says that there are at most 4k maximal k-secluded connected vertex sets C containing S but disjoint from T. We generalize this statement significantly: even when we demand that G[C] avoids a finite set F of forbidden induced subgraphs, the number of such maximal subgraphs is 2O(k) and they can be enumerated efficiently. This enumeration algorithm allows us to give improved parameterized algorithms for Connectedk-SecludedF-Free Subgraph and for deleting into scattered graph classes.

Homeomorphisms of the real line with singularities.

Given a real number a ≠ 0, we consider the set of homeomorphisms f: R\{0}→ R \{a} where{(x, y):x=0}is a vertical asymtote, {(x, y):y=a} is a horizontal asymtote and f is strictly increasing in each connected component (−∞,0) and (0,+∞). In this context, similar to circle homeomorphisms, all possible dynamics are shown. It is established the relationship between existence of periodic orbits and the limit sets. Also, whenever f−n(0) ≠a for all n ∈ N, then the non-existence of periodic orbits leads to a non-trivial limit set, which is either the whole line R or perfect and nowhere dense. It is shown a notion of separation of points that leads to transitivity

Christian Citizens in a Democratic State: Is a True Separation of Church and State Really Possible?

In many North American Protestant circles, especially those with Baptist or Free Church roots, the notion of the total separation of church and state is presented as the ideal to be attained in all church and state relations. We are told that the state should have no legislative power to ordain anything in relation to church doctrine or practice, and that the church should be entirely excluded from all political, secular, or state actions. In this paper, we are going to suggest that such an approach to church–state relations (even though some might think that it flows from or is necessary for democracy) is, in fact, impossible in a true democracy. We will first consider the nature of the church and the state, and present three principles that Maritain suggests are first principles in this debate. We will then look at the classical notion of the “Citizen”. We will conclude by arguing that based upon the nature of a citizen, of the church, and of the state, a strict separation of church and state is, in fact, impossible.

On the role of logical separability in knowledge compilation

Knowledge compilation is an alternative solution to address demanding reasoning tasks with high complexity via converting knowledge bases into a suitable target language. The notion of logical separability, proposed by Levesque, offers a general explanation for the tractability of clausal entailment for two remarkable languages: decomposable negation normal form and prime implicates. It is interesting to explore what role logical separability plays in problem tractability. In this paper, we apply the notion of logical separability to a number of reasoning problems within the context of propositional logic: satisfiability checking (CO), clausal entailment checking (CE), model counting (CT), model enumeration (ME) and forgetting (FO), as well as their dual tasks, contributing to several recursive procedures. We provide the corresponding logical separability based properties: CO-logical separability, CE-logical separability, CT-logical separability, ME-logical separability and their duals. Based on these properties, we then identify four novel normal forms: CO-LSNNF, CE-LSNNF, CT-LSNNF and ME-LSNNF, as well as their dual languages. We show that each of them is the necessary and sufficient condition under which the corresponding procedure is correct. We finally integrate the above normal forms into the knowledge compilation map.

Graphical Principal Component Analysis of Multivariate Functional Time Series

In this article, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a unified framework for functional graphical models and dynamic principal component analysis, and further extend it to optimally reconstruct signals from contaminated functional data using graphical-level information. We investigate asymptotic properties of the resulting estimators and illustrate the effectiveness of our proposed approach through extensive simulations. We apply our method to hourly air pollution data that were collected from a monitoring network in China. Supplementary materials for this article are available online.

Inference versus assumption in light of the Finnish evidential-modal adverbs näköjään and varmaan

Abstract Inference is usually defined as a speaker’s personal but indirect evidence that is based on something that the speaker can directly witness (such as the result of an event), while assumption is based on something such as the speaker’s general knowledge of the world. This paper is concerned with inference and assumption in light of the semantics of the Finnish inferential and assumptive adverbs näköjään (inference) and varmaan (assumption). These are examined by administering a questionnaire study. The discussed scenarios differ according to three factors: the presence or lack of visual or sensory evidence, the temporal relations between the evidence and the claim that is made, and the strength of the evidence. The results of the study clearly establish that inference and assumption are separate notions (coded by different adverbs) and that the (non-) observability of the evidence noted above explains only a part of the attested cases; in general, the use of the adverbs is determined by how reliable the speaker considers the evidence to be. As a consequence, this paper proposes new definitions based on the speakers’ selection of the appropriate inferential/assumptive adverb based on how strongly they are willing to vouch for the truth value of their statement.

Turning Back Time to Keep Writing

Abstract This paper addresses the “regressive” temporality of melancholic memory that developed cross-culturally within the modern, predominantly progress-oriented time-consciousness. Outlining the theoretical—Freudian and post-Freudian—perspective on melancholia, this essay continues with a case study of a text that embodies a particularly “regressive” response to a personal loss, Bruno Schulz's short story “Sanatorium pod klepsydrą” [Sanatorium under the sign of the hourglass, 1937]. My reading of this short story will be structured around the narrator's “trick” of turning back time, motivated by his willingness to keep the memory of his lost loved one, his father, alive. For Freud, such a “trick” indicates the failure to mourn, which results in the pathologic condition of melancholia. I will argue, however, that the narrator deliberately refuses to “work through” his grief because it is precisely through this circular and infinite regression that he explores his creative abilities and shapes his fluid modernist self. My analysis is particularly focused on the dynamic boundaries between the “real” and imaginary spaces that the narrator constructs, balancing and at the same time de-stabilizing the notions of separation and encounter, distance and immersion, determinacy and freedom. As I will show, through this process the narrator finds himself in between two realities, in a point of suspension, which becomes the only possible position or, rather, condition for modernist, hyper-reflexive writing.

A Unified Analysis of Penalty-Based Collision Energies

We analyze a wide class of penalty energies used for contact response through the lens of a reduced frame. Applying our analysis to both spring-based and barrier-based energies, we show that we can obtain closed-form, analytic eigensystems that can be used to guarantee positive semidefiniteness in implicit solvers. Our approach is both faster than direct numerical methods, and more robust than approximate methods such as Gauss-Newton. Over the course of our analysis, we investigate physical interpretations for two separate notions of length. Finally, we showcase the stability of our analysis on challenging strand, cloth, and volume scenarios with large timesteps on the order of 1/40 s.

Towards a Shared Practice of Encampment: An Historical Investigation of UNRWA and the UNHCR to 1967

Abstract This article reconsiders refugee studies’ longstanding commitment to the notion of a near-total separation between the UNHCR and UNRWA through an historical investigation of both organizations’ early approaches to refugee encampment. Without disputing the importance of the historical and institutional divisions between the two, it seeks to point out that with respect to the practice of encampment, the two agencies gradually drew nearer to each other during their first two decades of operation, as the UNHCR extended its reach into the decolonizing world and UNRWA expanded its operations across the Middle East. The parallels became particularly clear in 1967, when the ‘Protocol on the Status of Refugees’ formalized the UNHCR’s encampment-focused expansion into the decolonizing world at roughly the same time that the second Arab-Israeli war created the conditions for UNRWA to enshrine encampment as a more or less permanent institutional strategy.

Development of a Domestic Water Medium Rice De-Stoning Machine

It has become critical to build a de-stoning machine that can be used in our homes whenever we need it. As a result, the goal of this research was to develop and build a wet-method household rice destoning equipment. The design was built utilizing locally accessible materials and was based on the notion of material separation using water as a medium of separation. A reservoir, hopper, de-stoning chamber, washing chamber, impeller, water filter, and brush drum make up the machine. The produced machine was powered by a 1 horsepower variable electric motor that communicated the rotating motion of the driving pulley to the driven pulley, which was supported by bearings, through a V-belt. The machine was built and tested, and it was discovered that 2kg/10minutes and 20.04kg/hour of processed rice were destoned at a de-stoning speed of 400rpm, which is the optimal speed for maximum speed separation. The destoning machine's effectiveness in terms of stone removal is approximately approaching 100 percent free of impurities, making it ideal for residential usage. This discovery elucidates the potential to deal with the challenges of stone removal from locally produced rice using hand and manual method, which are inefficient, time and energy wastage, it acts as a rice processing industry innovation.

Separation profile, isoperimetry, growth and compression

We give lower and upper bounds for the separation profile (introduced by Benjamini, Schramm & Timár) for various graphs using isoperimetric profile, volume growth and Hilbertian compression. For graphs which have polynomial isoperimetry and growth, we show that the separation profile is bounded between n a and n b for some a,b∈(0,1). For many amenable groups, we prove a lower bound of n/log(n) a for some a>1, and for groups admitting “good” embeddings into an ℓ p space we prove an upper bound of n/log(n) b for some b∈(0,1). We show that solvable groups of exponential growth cannot have a separation profile bounded above by a sublinear power function. We also introduce a notion of local separation, with applications for percolation clusters of ℤ d and graphs which have polynomial isoperimetry and growth.

A classification of peak-pit maximal Condorcet domains

In this paper, we introduce a weaker notion of separability for set-systems and demonstrate that the class of maximal weakly separated systems precisely corresponds to the class of peak-pit maximal Condorcet domains. Additionally, we present a generalisation of arrangements of pseudolines and establish that the sets of chamber sets from them coincide with maximal weakly separated systems, enabling the construction of all peak-pit maximal Condorcet domains. Furthermore, we reveal that peak-pit maximal Condorcet domains coincide with connected maximal Condorcet domains.

Multiway Spherical Clustering Via Degree-Corrected Tensor Block Models

We consider the problem of multiway clustering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recommendation system, neuroimaging, community detection, and hypergraph partitions in social networks. The allowance of degree heterogeneity provides great flexibility in clustering models, but the extra complexity poses significant challenges in both statistics and computation. Here, we develop a degree-corrected tensor block model with estimation accuracy guarantees. We present the phase transition of clustering performance based on the notion of angle separability, and we characterize three signal-to-noise regimes corresponding to different statistical-computational behaviors. In particular, we demonstrate that an intrinsic statistical-to-computational gap emerges only for tensors of order three or greater. Further, we develop an efficient polynomial-time algorithm that provably achieves exact clustering under mild signal conditions. The efficacy of our procedure is demonstrated through two data applications, one on human brain connectome project, and another on Peru Legislation network dataset.

Japanese Philosophers on Plato's Ideas

AbstractAlthough Plato studies occupy an important place in academia, the empiricist stance in considering reality, the modern epistemology of the self-identical ego, the devaluation of the image and imagination, and the restrictions on philosophy within academic research sometimes cause us to lose sight of the essence of Plato's texts and thought when analysing them. Discussing Plato from a Japanese perspective, this paper will introduce three Japanese thinkers, Sakabe Megumi, Izutsu Toshihiko, and Ino-ue Tadashi, who have critically examined modern Western philosophy from their own philosophical backgrounds and provided valuable suggestions. Taking into account the arguments of these Japanese thinkers, this paper emphasizes the notions of separation, purification, and transcendence as core concepts of Plato's philosophy.

An integrative view of human hippocampal function: Differences with other species and capacity considerations.

We describe an integrative model that encodes associations between related concepts in the human hippocampal formation, constituting the skeleton of episodic memories. The model, based on partially overlapping assemblies of "concept cells," contrast markedly with the well-established notion of pattern separation, which relies on conjunctive, context dependent single neuron responses, instead of the invariant, context independent responses found in the human hippocampus. We argue that the model of partially overlapping assemblies is better suited to cope with memory capacity limitations, that the finding of different types of neurons and functions in this area is due to a flexible and temporary use of the extraordinary machinery of the hippocampus to deal with the task at hand, and that only information that is relevant and frequently revisited will consolidate into long-term hippocampal representations, using partially overlapping assemblies. Finally, we propose that concept cells are uniquely human and that they may constitute the neuronal underpinnings of cognitive abilities that are much further developed in humans compared to other species.

Grab it and change it, it’s yours: Affect, attitude and politics in 1970s Northern Irish punk music

This paper argues for incorporation of attitude into geographical work on affect. We do so through an engagement with affect in musical experiences and adopting as our focus punk music in Northern Ireland during the 1970s. Through a combination of lyrical analysis and in-depth interviews with some of those involved in the punk scene in Northern Ireland at that time, we find that affective responses to musical experiences can be translated into attitude, shifting from intentional expression, e.g., through clothing or demeanour, to habituation and pre-reflective persistence at the level of the everyday, extending the duration of affect and interweaving the cognitive and pre-reflective. Further, through our emphasis on the temporalities of affect, our focus on punk music in Northern Ireland at the height of the Troubles identifies the attitudinal prefiguration of an anarchist utopia. However, due to the habituation of attitude, this political aspect becomes invisible to and unacknowledged by those exhibiting and instantiating it. This paper extends the affective moment into durable attitudinal dispositions, unsettles rigid notions of separation between the cognitive and pre-reflective, questions the radical openness of affect in the face of the regulatory power of attitude, provides theoretical insights into punk as instantiating an attitudinal form of utopia, and contributes to growing engagement with the political potential of affect.

Ethnography and Volumography: Drawings of Theory on the Blackboard

The author presents drawings made on the blackboard in front of his students at the university. This article aims to show the heuristic value of drawing in view of a human-oriented anthropology, i.e. focused on a human being, as detached as possible from other humans, situations or contexts. The drawings aim to illustrate the differences between ethnography and what he calls volumography, which focuses on the human being as a VoB. Throughout the article, the author discusses the notions of separation, perspective, and relation. In asking who is really describing this or that person in the spectrum of sciences, the author proposes that this task falls to existential anthropology.