Linear Arguments Research Articles

‘I Don’t Talk to the Police Except Never’: Anna Mendelssohn, Tom Raworth, and Anti-Confessional Life Writing

This article begins with a comparative reading of work by Tom Raworth and Anna Mendelssohn. It demonstrates how both poets construct a surface of language that troubles the relationship between reader and poet through perpetual ‘turns’ which accumulate forms of coherence not reducible to linear arguments or narratives, and also asks the reader to constantly register what forces they apply in order to render meaning in, and through, this surface. In this way, both Raworth and Mendelssohn occupy a defensive position in relation to the reader, and cultivate poetry which ‘hovers on the edge of meaning’. Building on this account of a mode of evasiveness which both poets share, grounded in existing Raworth scholarship, the article goes on to focus specifically on Mendelssohn’s work. Although both poets take up and problematise life writing, Mendelssohn’s is distinct in its relationship to confession, figuring the reader as always potentially an agent of juridical and carceral state power. The article argues that it is this tendency in Mendelssohn’s work which warrants its description as ‘anti-confessional life writing.’

Rohrs' Example Revisited: On the Robustness of Adaptive Iterative Learning Control

AbstractAdaptive feedback based methods in iterative learning control (ILC) have garnered much interest from researchers for some time now. Much as in adaptive feedback control, most of these methods use Lyapunov functions and positive real transfer functions to prove convergence and boundedness of system signals updated through iterative estimations. While Rohrs et al. have motivated further research on the design of robust adaptive feedback controllers by demonstrating in the early 1980's that the algorithms of the time were not robust in the presence of unmodeled dynamics, the topic of robustness has not been studied much in the adaptive iterative learning control (AILC) literature. Inspired by Rohrs' counterexample, we use a model reference AILC scheme to show the lack of robustness to unmodeled dynamics in AILC. We rigorously define the concept of stability in ILC via space concepts, and demonstrate the existence of unstable learning operators. We put forth linear systems arguments to explain how conditions leading to instability can occur, and support heuristic arguments with simulation examples. Our findings indicate that the shortcomings of AILC in terms of robustness are no different than those of adaptive feedback, with the robustness issue more severe in certain cases, and further research is necessary to design robust AILC schemes.

Pathwise superhedging for time-dependent barrier options on càdlàg paths—Finite or infinite tradeable European, One-Touch, lookback or forward starting options

We establish pathwise duality using simple predictable trading strategies for the robust hedging problem associated with a barrier option whose payoff depends on the terminal level and the infimum of a càdlàg strictly positive stock price process, given tradeable European options at all strikes at a single maturity. The result allows for a significant dimension reduction in the computation of the superhedging cost, via an alternate lower-dimensional formulation of the primal problem as a convex optimization problem, which is qualitatively similar to the duality which was formally sketched using linear programming arguments in Duembgen and Rogers [10] for the case where we only consider continuous sample paths. The proof exploits a simplification of a classical result by Rogers (1993) which characterizes the attainable joint laws for the supremum and the drawdown of a uniformly integrable martingale (not necessarily continuous), combined with classical convex duality results from Rockefellar (1974) using paired spaces with compatible locally convex topologies and the Hahn–Banach theorem. We later adapt this result to include additional tradeable One-Touch options using the Kertz and Rösler (1990) condition. We also compute the superhedging cost when in the more realistic situation where there is only finite tradeable European options; for this case we obtain the full duality in the sense of quantile hedging as in Soner (2015), where the superhedge works with probability 1−ε where ε can be arbitrarily small), and we obtain an upper bound for the true pathwise superhedging cost. In Section 5, we extend our analysis to include time-dependent barrier options using martingale coupling arguments, where we now have tradeable European options at both maturities at all strikes and tradeable forward starting options at all strikes. This set up is designed to approximate the more realistic situation where we have a finite number of tradeable Europeans at both maturities plus a finite number of tradeable forward starting options.11The author would like to thank Professors Charles Akemann and Teemu Pennanen for useful discussions.

A linear algebraic derivation of Lorentz transformation from wave equations

It is shown that arbitrary dimensional Lorentz transformation can be obtained from invariance of wave equations using mathematically rigorous, linear algebraic arguments.

New closed-form expressions for SNR estimates of Nakagami fading channels by the method of moments

Method of moments has been a parameter estimation technique appropriate to calculate signal-to-noise ratio (SNR) estimates in fading channel models in which an optimal technique like maximum likelihood estimation is not mathematically tractable. In this article, the ratio of the second moment squared to the fourth moment of the received signal envelope is considered to calculate an exact expression for the SNR estimate in Nakagami-m fading channel for M-QAM and $$\theta $$ -MQAM modulations as well as expressions to evaluate the variance and the mean of the estimate. The paper presents two useful contributions for SNR estimation theory on Nakagami fading. Besides the exact algebraic expression for the estimate for a generalized QAM modulation scheme, its performance is evaluated through a statistical linearization argument.

Ocean eddies and climate predictability.

A suite of coupled climate model simulations and experiments are used to examine how resolved mesoscale ocean features affect aspects of climate variability, air-sea interactions, and predictability. In combination with control simulations, experiments with the interactive ensemble coupling strategy are used to further amplify the role of the oceanic mesoscale field and the associated air-sea feedbacks and predictability. The basic intent of the interactive ensemble coupling strategy is to reduce the atmospheric noise at the air-sea interface, allowing an assessment of how noise affects the variability, and in this case, it is also used to diagnose predictability from the perspective of signal-to-noise ratios. The climate variability is assessed from the perspective of sea surface temperature (SST) variance ratios, and it is shown that, unsurprisingly, mesoscale variability significantly increases SST variance. Perhaps surprising is the fact that the presence of mesoscale ocean features even further enhances the SST variance in the interactive ensemble simulation beyond what would be expected from simple linear arguments. Changes in the air-sea coupling between simulations are assessed using pointwise convective rainfall-SST and convective rainfall-SST tendency correlations and again emphasize how the oceanic mesoscale alters the local association between convective rainfall and SST. Understanding the possible relationships between the SST-forced signal and the weather noise is critically important in climate predictability. We use the interactive ensemble simulations to diagnose this relationship, and we find that the presence of mesoscale ocean features significantly enhances this link particularly in ocean eddy rich regions. Finally, we use signal-to-noise ratios to show that the ocean mesoscale activity increases model estimated predictability in terms of convective precipitation and atmospheric upper tropospheric circulation.

Notes on G2: The Lie algebra and the Lie group

These notes have been prepared for the Workshop on “(Non)-existence of complex structures on S6”, celebrated in Marburg in March, 2017. The material is not intended to be original. It contains a survey about the smallest of the exceptional Lie groups: G2, its definition and different characterizations as well as its relationship to the spheres S6 and S7. With the exception of the summary of the Killing–Cartan classification, this survey is self-contained, and all the proofs are provided. Although these proofs are well-known, they are scattered, some of them are difficult to find, and others require stronger background, while we will usually stick to linear algebra arguments. The approach is algebraical, working at the Lie algebra level most often. We analyze the complex Lie algebra (and group) of type G2 as well as the two real Lie algebras of type G2, the split and the compact one. The octonion algebra will play its role, but it is not the starting point. Also, both the 3-forms approach and the spinorial approach are viewed and connected. Special emphasis is put on relating all the viewpoints by providing precise models.

Algebraic splitting methods for the steady incompressible Navier–Stokes equations at moderate Reynolds numbers

The unsteady incompressible Navier–Stokes equations in primitive variables are often numerically solved by segregating the computation of velocity and pressure, according to either functional analysis arguments following the pioneering work of A.J. Chorin and R. Temam (STD, Split-Then-Discretize paradigm) or linear algebra arguments based on the inexact block factorization of the discretized problem (DTS, Discretize-Then-Split paradigm). The presence of the time derivative allows for the calibration of an appropriate approximation of the pseudo-differential operator of the pressure problem and excellent results in terms of both accuracy and efficiency have been obtained as witnessed by the abundant literature. The extension of the same segregated approach to the steady Navier–Stokes equations is unclear, unless a pseudo-time advancing formulation is undertaken. In this paper we present a methodology for a segregated computation of the primitive variables in a genuinely steady formulation, so to avoid iterations to get to the steady limit. The approach is largely inspired by the algebraic factorization of the unsteady problem (DTS approach), yet we detail specific settings required by the absence of the velocity time-derivative. The basic idea relies on the introduction of some parameters in a modified Picard linearization. We discuss stability bounds and the convergence of the segregated method to the unsplit solution. Several numerical results on different test cases confirm the efficiency of the procedure.

Prony’s Method Under an Almost Sharp Multivariate Ingham Inequality

The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation distance of the parameters and the order of moments. Towards a similar statement in the multivariate case, we present an Ingham inequality which improves the previously best known dimension-dependent constant from square-root growth to a logarithmic one. Secondly, we refine an argument that an Ingham inequality implies identifiability in multivariate Prony methods to the case of commonly used max-degree by a short linear algebra argument, closely related to a flat extension principle and the stagnation of a generalized Hilbert function.

Review: Sacred Scents in Early Christianity and Islam, by Mary Thurlkill

Mary Thurlkill, Sacred Scents in Early Christianity and Islam . Lanham/Boulder/New York/London: Lexington Books, 2016. Pp. xix + 191, ISBN: 9780739174524. $85.00. The historiography of late antiquity has awakened to the senses. Recent studies have elucidated the power of sight, smell, taste, hearing, and touch for delineating religious experience and social boundaries throughout the late antique world. Susan Harvey's Scenting Salvation: Ancient Christianity and the Olfactory Imagination (University of California Press, 2006) deserves special note here, alongside studies by Beatrice Caseau, Georgia Frank, Deborah Green, Rachel Neis, and many others. Mary Thurlkill's intervention in this growing bibliography compares the role of “sacred scent” in the religions of late antiquity and the Islamic world. The book's scope is highly ambitious, ranging from the role of incense in Roman sacrifice to the spice-infused purity rituals prescribed by medieval Islamic jurists. As the author herself emphasizes, comparisons on this scale are challenging, perhaps inherently “messy” (163). Readers who seek a sharp, linear argument may find themselves frustrated by the book's sometimes-meandering style. Its comparative framework, however, yields some valuable insights. “Sensory Worlds,” the first of the book's three parts, considers the role of scent in defining domestic and civic spaces (ch. 1), culinary practices (ch. 2), and health and disease (ch. 3). Each chapter includes Roman, Christian, Jewish, and Islamic material that shows both the material underpinnings of the scent economy—especially Indian Ocean commerce in spices—and the various social settings where scents were deployed. In the Roman world, these settings included baths, banquets, theaters, funerals, temples, and even the Senate, though Cicero chastised Senators who dishonored their togas …

Scaling Relations for Adsorption Energies on Doped Molybdenum Phosphide Surfaces

Molybdenum phosphide (MoP), a well-documented catalyst for applications ranging from hydrotreating reactions to electrochemical hydrogen evolution, has yet to be mapped from a more fundamental perspective, particularly in the context of transition-metal scaling relations. In this work, we use periodic density functional theory to extend linear scaling arguments to doped MoP surfaces and understand the behavior of the phosphorus active site. The derived linear relationships for hydrogenated C, N, and O species on a variety of doped surfaces suggest that phosphorus experiences a shift in preferred bond order depending on the degree of hydrogen substitution on the adsorbate molecule. This shift in phosphorus hybridization, dependent on the bond order of the adsorbate to the surface, can result in selective bond weakening or strengthening of chemically similar species. We discuss how this behavior deviates from transition-metal, sulfide, carbide, and nitride scaling relations, and we discuss potential applica...

Civic Jazz

Civic Jazz

No-arbitrage bounds for the forward smile given marginals

We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek [Financ. Stochastics, 2015, 19, 189–214] and by Hobson and Neuberger [Math. Financ., 2012, 22, 31–56]. We recast this dual approach as a finite-dimensional linear program, and reconcile numerically, in the Black–Scholes and in the Heston model, the two approaches.

Relating domination, exponential domination, and porous exponential domination

The domination number γ(G) of a graph G, its exponential domination number γe(G), and its porous exponential domination number γe∗(G) satisfy γe∗(G)≤γe(G)≤γ(G). We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality. Relaxing the natural integer linear program whose optimum value is γe∗(G), we are led to the definition of the fractional porous exponential domination number γe,f∗(G) of a graph G. For a subcubic tree T of order n, we show γe,f∗(T)=n+26 and γe(T)≤2γe,f∗(T). We characterize the two classes of subcubic trees T with γe(T)=γe,f∗(T) and γ(T)=γe(T), respectively. Using linear programming arguments, we establish several lower bounds on the fractional porous exponential domination number in more general settings.

Our Stolen Grandmother: The Entanglement of Slavery and Colonization in Anna Lee Walters's <em>Ghost Singer</em>

Our Stolen GrandmotherThe Entanglement of Slavery and Colonization in Anna Lee Walters's Ghost Singer Reid Gómez What do we know, really? What can we know, finally? But more importantly, how do we begin to articulate these stories, their stories, this (un)knowing? These conversations take very seriously the question of the absence, or some would even say, the impediments, in the work of mourning the millions of dead in the aftermath of slavery. How do you tell a story that must be told and yet cannot be told? A number of scholars, including Saidiya Hartman, suggest that we begin by "not telling." Patricia J. Saunders, "Fugitive Dreams of iaspora: Conversations with Saidiya Hartman" That life is complicated is a fact of great analytical importance. Patricia J. Williams, Alchemy of Race and Rights: Diary of a Law Professor [End Page 70] REVISITING THE SCENE OF SUBJECTION WITHOUT REPLICATINGTHE GRAMMAR OF VIOLENCE This article has been presented as a paper at a conference, and it has been read by six peer reviewers and two editors. Every version has failed to meet readers' desires for recognizable signposts and context and a cogent argument. My work cannot get past readings tuned to error analysis. Some have suggested that I give up and go back to writing fiction, and others suggest that I find a writing mentor to assist with my obvious and grievous errors in clarity, grace, and style. Clearly, writing is very hard for me—readers say that one thing my writing says eloquently and clearly is that I struggle. I have faced the critical and creative divide for over twenty years now and have recently strained to write everyone else's paper. That paper—the one demanded from me—is impossible to write. Michelle Wright begins the Physics of Blackness: Beyond the Middle Passage Epistemology with a discussion about the immediate cogency provided by linear progress narratives.1 There are rules for how we present knowledge and how we can narrate ourselves and our findings. We are meant to subordinate our research, summarize and evaluate the research of others, and not violate the rules of standard American English. I will return to Wright's work throughout this piece, but I begin here to name the way a desire for linear progressive arguments shapes what is thought of as convincing, believable, relevant, and pertinent—coarsely, what is said to be good writing. I start here in partial explanation for my recent and painful struggle with the writing process. Many will say it is my skill set that limits my work at this moment, and others know it is also the content. I work on slavery and language. Wright asks us to work in an epiphenomenal now that requires us to locate ourselves in space, on land, before beginning our analytical project. I have learned most about writing in two areas of life: through my work on slavery and in my work with sixth graders. At this moment, I point out the several failures inherent in linear progress narrative techniques, failures Wright describes as the assumption of fixed origins, the establishment of cause and effect, and the linkage of linear time within a single body.2 I will return to these as they relate to my subject—the novel Ghost Singer and slavery among the Navajo—in a moment, but I point to them now to indicate the challenge I continue to face in my attempt to write this piece in a way that does not replicate the violence it describes. Reading William Leap's work on American Indian English and remembering my own teaching of Ghost Singer to sixth graders, I have found some useful frames to introduce this writing to readers. Leap cautions readers to remember that the content in such nonstandard English compositions, like my own, "require[s] familiarity with the whole [End Page 71] text, and not just individual segments." Information is "inter-related and inter-dependent."3 This describes what I experience in terms of a failure to provide context: the context I provide goes unrecognized. These same writers, whom I am proud to align myself with, hold their text together by "coordinated imagery not rhetorical...

Coercivity of weighted Kohn Laplacians: The case of model monomial weights in ℂ²

The weighted Kohn Laplacian ◻ φ \Box _\varphi is a natural second order elliptic operator associated to a weight φ : C n → R \varphi :\mathbb {C}^n\rightarrow \mathbb {R} and acting on ( 0 , 1 ) (0,1) -forms, which plays a key role in several questions of complex analysis. We consider here the case of model monomial weights in C 2 \mathbb {C}^2 , i.e., \[ φ ( z , w ) := ∑ ( α , β ) ∈ Γ | z α w β | 2 , \varphi (z,w):=\sum _{(\alpha ,\beta )\in \Gamma }|z^\alpha w^\beta |^2, \] where Γ ⊆ N 2 \Gamma \subseteq \mathbb {N}^2 is finite. Our goal is to prove coercivity estimates of the form \[ ( ∗ ) ◻ φ ≥ μ 2 , (*)\hspace {10pc} \Box _\varphi \geq \mu ^2,\hspace {10pc} \] where μ : C n → R \mu :\mathbb {C}^n\rightarrow \mathbb {R} acts by pointwise multiplication on ( 0 , 1 ) (0,1) -forms, and the inequality is in the sense of self-adjoint operators. We proved in 2015 how to derive from ( ∗ ) (*) new pointwise bounds for the weighted Bergman kernel associated to φ \varphi . Here we introduce a technique to establish ( ∗ ) (*) with \[ μ ( z , w ) = c ( 1 + | z | a + | w | b ) ( a , b ≥ 0 ) , \mu (z,w)=c(1+|z|^a+|w|^b) \qquad (a,b\geq 0), \] where a , b ≥ 0 a,b\geq 0 depend on (and are easily computable from) Γ \Gamma . As a corollary we also prove that, for a wide class of model monomial weights, the spectrum of ◻ φ \Box _\varphi is discrete if and only if the weight is not decoupled, i.e., Γ \Gamma contains at least a point ( α , β ) (\alpha ,\beta ) with α ≠ 0 ≠ β \alpha \neq 0\neq \beta . Our methods comprise a new holomorphic uncertainty principle and linear optimization arguments.

The puzzle of partial migration: Adaptive dynamics and evolutionary game theory perspectives

We consider the phenomenon of partial migration which is exhibited by populations in which some individuals migrate between habitats during their lifetime, but others do not. First, using an adaptive dynamics approach, we show that partial migration can be explained on the basis of negative density dependence in the per capita fertilities alone, provided that this density dependence is attenuated for increasing abundances of the subtypes that make up the population. We present an exact formula for the optimal proportion of migrants which is expressed in terms of the vital rates of migrant and non-migrant subtypes only. We show that this allocation strategy is both an evolutionary stable strategy (ESS) as well as a convergence stable strategy (CSS). To establish the former, we generalize the classical notion of an ESS because it is based on invasion exponents obtained from linearization arguments, which fail to capture the stabilizing effects of the nonlinear density dependence. These results clarify precisely when the notion of a “weak ESS”, as proposed in Lundberg (2013) for a related model, is a genuine ESS. Secondly, we use an evolutionary game theory approach, and confirm, once again, that partial migration can be attributed to negative density dependence alone. In this context, the result holds even when density dependence is not attenuated. In this case, the optimal allocation strategy towards migrants is the same as the ESS stemming from the analysis based on the adaptive dynamics.The key feature of the population models considered here is that they are monotone dynamical systems, which enables a rather comprehensive mathematical analysis.

Linearly convergent away-step conditional gradient for non-strongly convex functions

We consider the problem of minimizing the sum of a linear function and a composition of a strongly convex function with a linear transformation over a compact polyhedral set. Jaggi and Lacoste-Julien (An affine invariant linear convergence analysis for Frank-Wolfe algorithms. NIPS 2013 Workshop on Greedy Algorithms, Frank-Wolfe and Friends, 2014) show that the conditional gradient method with away steps -- employed on the aforementioned problem without the additional linear term -- has a linear rate of convergence, depending on the so-called pyramidal width of the feasible set. We revisit this result and provide a variant of the algorithm and an analysis based on simple linear programming duality arguments, as well as corresponding error bounds. This new analysis (a) enables the incorporation of the additional linear term, and (b) depends on a new constant, that is explicitly expressed in terms of the problem's parameters and the geometry of the feasible set. This constant replaces the pyramidal width, which is difficult to evaluate.

Nonlinear spontaneous symmetry breaking in active polar films

The behaviour of an active polar suspension in a fluid film is analysed in the vanishing Reynolds number limit. We perform a detailed study of the transitions to spontaneously flowing steady states and their associated density variations. Beyond the onset of instability, we find a new transverse symmetry breaking of the flow generated in the film. This spontaneous symmetry breaking is observed despite symmetric boundary conditions (with respect to orientation) on either side of the film. We study this new phenomenon by means of numerical simulations and nonlinear theory, showing that it can be ascribed to the nonlinear coupling, characteristic of polar active systems, of the density gradients with the flow velocity and the orientation field. As such a theoretical analysis based on linear stability arguments typically used to identify phase boundaries is unable to describe it. An extension of the theory to allow for higher-density regimes is also proposed.

Numerical simulation of quadratic BSDEs

This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme. Then we provide a control on the time-discretization error of order $\frac{1}{2}-\varepsilon$ for all $\varepsilon>0$. In the last part, we give a fully implementable algorithm for quadratic BSDEs based on quantization and illustrate our convergence results with numerical examples.