Linear Arguments Research Articles

Spiral movement: Writingwithfascism and urban violence

How to move against the rise of the far-right and seemingly unstoppable autocratic leaders in many Western liberal democracies? Antifascism’s interest in the built environment is often limited to the collection of address data of right-wing extremists with the aim of locating its enemies. In this piece, I write with fascism and violence through vignettes of urban situatedness. I adopt an eclectic approach, engaging with diverse theories of violence and establishing loose connections between classical sociology and fascist urbanisation, liberalism in practice and historical fascism, and material aesthetics and right-wing spaces. In so doing, I highlight endemic forms of state and capitalist violence and their spatial manifestations of ghettoisation, beautification and overcoding. Acknowledging the limits of factual knowledge and liberal appeals to the truth in breaking through fascist worldviews of domination, the architecture of the text uses a circular infrastructure that connects various parties: ‘they’ (Twitter users), ‘I’ (author), ‘you’ (Walter Benjamin), and numerous ‘we’ who are thrown together in urban environments. Rather than developing a linear argument that tries to persuade fascists, I explore writing as a collective political practice that refutes totalising accounts. With the aim of opening meaning-makings through returning to and reworking numerous views, I respond to a spiral of violence with a movement that is organised around a shared commitment to an anti-oppressive, non-hierarchical world; a movement that is out of someone’s control and that spirals towards collective liberation.

Inverse parabolic problem with the Heaviside function arising in finance

The inverse problem arising in finance is both mathematically and practically interesting problem. First, we attempt to solve the inverse problem arising in binary option model. Using standard linearization and contraction arguments, we prove the stability and uniqueness of the solution of the inverse problem which originates from the diffusion equation with the initial condition given by the Heaviside function. Second, we numerically identify the local volatilities from given artificial prices of the binary option. In accordance with theory we propose the effective identification around the at-the-money level.

Bounded multiplicity for eigenvalues of a circular vibrating clamped plate

We prove that no eigenvalue of the clamped disk can have multiplicity greater than six. Our method of proof is based on a new recursion formula, linear algebra arguments and a transcendency theorem due to Siegel and Shidlovskii.

Analytical results for directional and quadratic selection gradients for log-linear models of fitness functions.

Log‐linear models are widely used for assessing determinants of fitness in empirical studies, for example, in determining how reproductive output depends on trait values or environmental conditions. Similarly, theoretical works of fitness and natural selection employ log‐linear models, often with a negative quadratic term, generating Gaussian fitness functions. However, in the specific application of regression‐based analysis of natural selection, such models are rarely employed. Rather, OLS regression is the predominant means of assessing the form of natural selection. OLS regressions allow specific evolutionary quantitative parameters, selection gradients, to be estimated, and benefit from the fact that the associated statistical models are easily applied. We examine whether selection gradients can be directly expressed in terms of the coefficients of models using exponential fitness functions with linear or quadratic arguments. Such models can be easily fitted with generalized linear models (GLMs). The expressions we obtain coincide with those for Gaussian functions, but relax the major constraint that the (log) fitness function is concave (downwardly curved). Additionally these results lead to univariate and multivariate analyses of both linear and quadratic selection that potentially incorporate pragmatic and interpretable models of fitness functions, where the parameters can be related analytically to selection gradients, and that can be operationalized using widely available statistical tools.

Writing through the Body

Writing through the Body Eileen DiPofi (bio) A Review of The Small Book of Hip Checks: On Queer Gender, Race, and Writing by Erica Rand. Durham, NC: Duke University Press, 2021. Pp. 152. $89.95 cloth, $23.95 paper. In her latest monograph, Erica Rand brings the intimate writing style and focus on the embodied experiences of race, gender, sexuality, class, and ability that characterized her previous book, Red Nails, Black Skates (2012), expanding her scope beyond the skating rink and in provocative new directions.1 The Small Book of Hip Checks argues for the hips as an overdetermined corporeal site where multiple histories, cultural norms, social processes, and identifications collide. Rand asserts that "as racialized and classed markers of gender and sexuality, hips bear weight and meaning, fate and contradiction" (1). With careful attention to the ways in which hips are socially constructed as texts, Rand resists essentializing discourses that assume the body always precedes its gendering. Opening outward from the hips, she explores the body as a nexus of expression and regulation. The Small Book of Hip Checks analyzes cultural sites at which individual bodies come into contact with the systemic forces of race, gender, sexuality, and nation, largely focusing on popular and material culture (including sports, films, memoirs, and sex toys) but also with attention to how practices of activism, public mourning, and individual resistance negotiate embodiment. In part a work of cultural analysis, and in part autotheory, Rand explores her own subjectivity within these structures of power. [End Page 225] However, what is most innovative about The Small Book of Hip Checks is Rand's attention to the embodied experience of writing itself. By structuring her book through short chapters that prioritize juxtaposition over flow, bringing seemingly disparate objects into conversation, Rand prizes an "embrace of redirection, revisitation, and interruption" (15) rather than a traditional linear argument. This approach demonstrates the unexpected insights to be gained through approaching writing as a queer practice. Queer and feminist thinkers have long sought to foster unexpected intimacies between texts, sparking insights that might be otherwise imperceptible within normative academic frameworks. For example, Carolyn Dinshaw posits a methodology of "touching" that puts different historical moments in contact to produce "connections between incommensurate entities."2 As Ann Cvetkovich observes, such a methodology enables erotic and affective intimacies to emerge between historical and contemporary bodies.3 In a similar vein, Gayatri Gopinath employs a tactic of "queer curation," which "stages 'collisions and encounters' between aesthetic practices that may seem discontinuous," revealing insights and inspiring affective responses that might otherwise go unnoticed.4 In The Small Book of Hip Checks, Rand resolutely marks her place in this tradition, placing texts in conversation that might normally be separated to see what insights their proximity might inspire. Importantly, Rand does not reduce the bodies she studies to objects, but rather places her own body in conversation within them, reflecting on how her own gender, sexuality, and race have signified through her hips, and how, as her body has changed, this signification has, too. As such, the book balances an analysis of the intersecting processes of gendering and racialization on differently classed and sexualized bodies alongside Rand's meta-analysis of her own body as writer and social subject. Rand grounds her study through three interpretations of hip check: as "point of inspection," as "flirtation device," and as "sports move" (2). Respectively, these three distillations encompass Rand's concerns with the policing of bodies, embodied forms of resistance, and queer approaches to writing, commingling throughout the text to produce intimacies between writer, readers, and objects of study. Rand's first interpretation of hip check, as "point of inspection," evidences her commitment to analyses of how bodies are disciplined along the lines of race, gender, size, and sexuality. Rand provides a plethora of short readings demonstrating how hips are sites of judgment regarding a body's conformity to normative ideals, with hips—and, by extension, other [End Page 226] body parts—deemed too wide, indicating feminine, racialized, and classed excess that demands regulation. Rand's case studies demonstrate her attention to how gender policing is amplified and differentially applied "for people read as gender-nonconforming and/or...

Parameter estimation in branching processes with almost sure extinction

We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when the current population size is z≥1. As is standard in branching process theory, an asymptotic analysis of the estimators requires us to condition on non-extinction up to a finite generation n and let n→∞; however, because the processes become extinct with probability one, we are able to demonstrate that our estimators do not satisfy the classical consistency property (C-consistency). This leads us to define the concept of Q-consistency, and we prove that our estimators are Q-consistent and asymptotically normal. To investigate the circumstances in which a C-consistent estimator is preferable to a Q-consistent estimator, we then provide two C-consistent estimators for subcritical Galton–Watson branching processes. Our results rely on a combination of linear operator theory, coupling arguments, and martingale methods.

In lockdown with my inner saboteur: A collaborative collage on self‐compassion

AbstractDear reader, we are writing this piece as a collaborative collage based on our experience of our ongoing PhD journey in a “top” business school, on self‐compassion and the inner saboteur, all saturated by the unpredictable developments of the COVID‐19 pandemic. Contrary to the linear argumentation of academic writing, collage writing works by opening up “new possibilities for understanding” what is written (Herrmann, 2020, p. 298). This introduction is where we manage your expectations, by letting you know that what follows below does not replicate the structure or the form of a conventionally organized paper.

Mathematical analysis of an age-structured HIV model with intracellular delay

<p style='text-indent:20px;'>In this paper, we study an age-structured HIV model with intracellular delay, logistic growth and antiretrowviral therapy. We first rewrite the model as an abstract non-densely defined Cauchy problem and obtain the existence of the unique positive steady state. Then through the linearization arguments we investigate the asymptotic behavior of steady states by determining the distribution of eigenvalues. We obtain successfully the globally asymptotic stability for the null equilibrium and (locally) asymptotic stability for the positive equilibrium respectively. Moreover, we also prove that Hopf bifurcations occur around the positive equilibrium under some conditions. In addition, we address the persistence of the semi-flow by showing the existence of a global attractor. Finally, some numerical examples are provided to illustrate the main results.</p>

Solutions of General Fractional-Order Differential Equations by Using the Spectral Tau Method

Here, in this article, we investigate the solution of a general family of fractional-order differential equations by using the spectral Tau method in the sense of Liouville–Caputo type fractional derivatives with a linear functional argument. We use the Chebyshev polynomials of the second kind to develop a recurrence relation subjected to a certain initial condition. The behavior of the approximate series solutions are tabulated and plotted at different values of the fractional orders ν and α. The method provides an efficient convergent series solution form with easily computable coefficients. The obtained results show that the method is remarkably effective and convenient in finding solutions of fractional-order differential equations.

Speculative Experimentation in (Methodological) Pluriverse

This article is slightly modified from the Invited Egon Guba Memorial Lecture I gave at the American Educational Research Association (AERA) annual meeting in 2021. Drs. Aaron Kuntz and Juha Suoranta served as my discussants and their individual responses and comments are linked to this article. I think of this article having many potential provocations and imagined audiences while I intentionally did not carry forward linear and logical argumentation structure. Instead, I thought about qualitative pasts, many presences of today’s qualitative inquiries and I aimed to vision potentially more diverse and inviting qualitative futures. I wrote within and through interrelated plural flows of relationality, including speculative, experimentative, and methodological flows. Furthermore, speculative experimentation inspired me as one methodological possibility as it offers opportunities for creative imagination, critical hesitation, reflective questioning, and thinking with unthinkable futures.

A virtual island journey: place and place writing in lockdown

The Covid lockdowns of 2020 and 2021 led many people to reassess their relationship to places. This article attempts, during this time of restricted movement, to imaginatively deep-map an island in the mouth of the Shannon in west Clare where my grandmother was born and raised. My deep-mapping of the island is by necessity virtual, assembled piecemeal from memories, daydreams, family recollections, historical fragments and that powerful, semi-enchanted sense of co-presence that can be found online. Unable to make a physical journey, I rely on the accretive and associative techniques of contemporary place writing. The article uses montage, juxtaposition, thick description, dense detail, imaginative reconstruction and the essayistic blending of undisciplined bits of knowledge, all of which do some of the work of conventional linear argument. As in place writing, the micro-study of a small, special place becomes a way of thinking more widely about our relationship to the earth in a time of environmental and public health emergency. The article is both my own experiment in place writing and an argument for the fresh perspectives that place writing can bring to cultural geography.

Thermo-mechanical Transport in Rotor Chains

We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic dynamics, we perform extensive numerical computations based on a finite difference method for the system of partial differential equations describing the macroscopic steady state. We first present a formal derivation of these stationary equations based on a linear response argument and local equilibrium assumptions. We then study various properties of the solutions to these equations. This allows to characterize the regime of parameters leading to uphill energy diffusion -- a situation in which the energy flows in the direction of the gradient of temperature -- and to identify regions of parameters corresponding to a negative energy conductivity (i.e. a positive linear response of the energy current to a gradient of temperature). The macroscopic equations we derive are consistent with some previous results obtained by numerical simulation of the microscopic physical system, which confirms their validity.

Eigenfunctions of the Fourier transform with specified zeros

AbstractEigenfunctions of the Fourier transform with prescribed zeros played a major role in the proof that theE8and the Leech lattice give the best sphere packings in respective dimensions 8 and 24 by Cohn, Kumar, Miller, Radchenko and Viazovska. The functions used for a linear programming argument were constructed as Laplace transforms of certain modular and quasimodular forms. Similar constructions were used by Cohn and Gonçalves to find a function satisfying an optimal uncertainty principle in dimension 12. This paper gives a unified view on these constructions and develops the machinery to find the underlying forms in all dimensions divisible by 4. Furthermore, the positivity of the Fourier coefficients of the quasimodular forms occurring in this context is discussed.

Information Storage in the Stochastic Ising Model

Most information storage devices write data by modifying the local state of matter, in the hope that sub-atomic local interactions stabilize the state for sufficiently long time, thereby allowing later recovery. Motivated to explore how temporal evolution of physical states in magnetic storage media affects their capacity, this work initiates the study of information retention in locally-interacting particle systems. The system dynamics follow the stochastic Ising model (SIM) over a 2-dimensional $\sqrt {{n}}\times \sqrt {{n}}$ grid. The initial spin configuration $ {X}_{0}$ serves as the user-controlled input. The output configuration ${X}_{{t}}$ is produced by running $t$ steps of Glauber dynamics. Our main goal is to evaluate the information capacity ${I}_{{n}}({t}):=\max _{{p}_{{X}_{0}}}{I}({X}_{0};{X}_{{t}})$ when time $t$ scales with the system’s size $n$ . While the positive (but low) temperature regime is our main interest, we start by exploring the simpler zero-temperature dynamics. We first show that at zero temperature, order of $\sqrt {{n}}$ bits can be stored in the system indefinitely by coding over stable, striped configurations. While $\sqrt {{n}}$ is order optimal for infinite time, backing off to ${t} , higher orders of ${I}_{{n}}({t})$ are achievable. First, via linear coding arguments imply we show that ${I}_{{n}}({t}) = \Theta ({n})$ for ${t}={O}({n})$ . To go beyond the linear scale, we develop a droplet-based achievability scheme that reliably stores $\Omega \left ({{n}/\log {n}}\right)$ for ${t}={O}({n}\log {n})$ time ( $\log {n}$ can be replaced with any ${o}({n})$ function). Moving to the positive but low temperature regime, two main results are provided. First, we show that an initial configuration drawn from the Gibbs measure cannot retain more than a single bit for ${t}\geq \exp ({C}\beta {n}^{1/4+\epsilon })$ time. On the other hand, when scaling time with the inverse temperature $\beta $ , the stripe-based coding scheme (that stores for infinite time at zero temperature) is shown to retain its bits for ${e}^{{c}\beta }$ .

Indigenous Wisdom, Capital, Technology and Education.

This article contrasts specific aspects of indigenous world views and wisdom on the one hand with specific themes in capitalism, colonisation, corporate interests, technology and education, on the other and argues that there is a fundamental clash of values between them. There is no assumption of a homogenous indigenous wisdom and no claim is made about novel insight into capitalism, colonisation, corporate interests and technology and education. The contribution is in tracing lines of thought in all of them and, by juxtaposing them in the context of a contemporary upsurge in digital/online/blended learning with particular attention to the global techno-corporation, to expose a fundamental clash of values that deserves more thorough scrutiny than it is getting. The paper does not present a linear argument, but rather a woven tapestry of themes. The conclusion is that education would be better served by the insights of indigenous wisdom and a more critical and tempered view of capitalism and technology.

Exposing the “Voice” of Self-Comprehension to the “Noise” of Materiality

In this brief article, the author reflects on the academic requirements of doctoral studies in art and indicates that it is split between what he calls the “voice” of self-comprehension and the “noise” of materiality. To overcome this inherent dichotomy, the suggestion is being made to use critically artistic arguments which are complex assemblages of semantics and non-semantics rather than logical, linear, and summarisable formal arguments. The role of noise in artistic arguments—and by extension in artistic research—is exposed as destabilising but necessary. Towards the end of the article, the reader/viewer is invited to revisit photographically, a diagrammatic story titled “Spaces and Surfaces” which introduces and exposes research through diagrams and image atlases rather than through conventional written text alone. The author believes that the artistic contribution may reflect on the raised issues.

Spreading properties of a three-component reaction-diffusion model for the population of farmers and hunter-gatherers

In this paper, we investigate the spreading properties of solutions of farmer and hunter-gatherer model which is a three-component reaction-diffusion system. Ecologically, the model describes the geographical spreading of an initially localized population of farmers into a region occupied by hunter-gatherers. This model was proposed by Aoki, Shida and Shigesada in 1996. By numerical simulations and some formal linearization arguments, they concluded that there are four different types of spreading behaviors depending on the parameter values. Despite such intriguing observations, no mathematically rigorous studies have been made to justify their claims. The main difficulty comes from the fact that the comparison principle does not hold for the entire system. In this paper, we give theoretical justification to all of the four types of spreading behaviors observed by Aoki et al. Furthermore, we show that a logarithmic phase drift of the front position occurs as in the scalar KPP equation. We also investigate the case where the motility of the hunter-gatherers is larger than that of the farmers, which is not discussed in the paper of Aoki et al.

A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

Abstract In this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

Bryan’s Maximum Entropy Method—Diagnosis of a Flawed Argument and Its Remedy

The Maximum Entropy Method (MEM) is a popular data analysis technique based on Bayesian inference, which has found various applications in the research literature. While the MEM itself is well-grounded in statistics, I argue that its state-of-the-art implementation, suggested originally by Bryan, artificially restricts its solution space. This restriction leads to a systematic error often unaccounted for in contemporary MEM studies. The goal of this paper is to carefully revisit Bryan’s train of thought, point out its flaw in applying linear algebra arguments to an inherently nonlinear problem, and suggest possible ways to overcome it.

Numerical solution for generalized nonlinear fractional integro-differential equations with linear functional arguments using Chebyshev series

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential equations. Spectral collocation method is extended to study this problem as a matrix discretization scheme, where the fractional derivatives are characterized in the Caputo sense. The collocation method transforms the given equation and conditions to an algebraic nonlinear system of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. The introduced operational matrix of derivatives includes arbitrary order derivatives and the operational matrix of ordinary derivative as a special case. To the best of authors’ knowledge, there is no other work discussing this point. Numerical test examples are given, and the achieved results show that the recommended method is very effective and convenient.