Cambridge Univ Research Articles

Spreading in graphs

Several concepts that model processes of spreading (of information, disease, objects, etc.) in graphs or networks have been studied. In many contexts, we assume that some vertices of a graph G are contaminated initially, before the process starts. By the q-forcing rule, a contaminated vertex having at most q uncontaminated neighbors enforces all the neighbors to become contaminated, while by the p-percolation rule, an uncontaminated vertex becomes contaminated if at least p of its neighbors are contaminated. If given a set S of initially contaminated vertices all vertices eventually become contaminated when continuously applying the q-forcing rule (respectively the p-percolation rule), S is called a q-forcing set (respectively, a p-percolating set) in G. In this paper, we consider sets S that are at the same time q-forcing sets and p-percolating sets, and call them (p,q)-spreading sets. Given positive integers p and q, the minimum cardinality of a (p,q)-spreading set in G is a (p,q)-spreading number, σ(p,q)(G), of G. While q-forcing sets have been studied in a dozen of papers, the decision version of the corresponding graph invariant has not been considered earlier, and we fill the gap by proving its NP-completeness. This, in turn, enables us to prove the NP-completeness of the decision version of the (p,q)-spreading number in graphs for an arbitrary choice of p and q. Again, for every p∈N and q∈N∪{∞}, we find a linear-time algorithm for determining the (p,q)-spreading number of a tree, where in the case p≥2 we apply Riedl’s algorithm from [Largest and smallest minimal percolating sets in trees, Electron. J. Combin. 19 (2012) Paper 64] on p-percolation in trees. In addition, we present a lower and an upper bound on the (p,q)-spreading number of a tree and characterize extremal families of trees. In the case of square grids, we combine some results of Bollobás from [The Art of Mathematics: Coffee Time in Memphis. Cambridge Univ. Press, New York, 2006], and the AIM Minimum Rank-Special Graphs Work Group from [Zero forcing sets and the minimum rank of graphs, Linear algebra Appl. 428 2008 1628–1648], and new results on (2,1)-spreading and (4,q)-spreading to obtain σ(p,q)(Pm□Pn) for all (p,q)∈(N∖{3})×(N∪{∞}) and all m,n∈N.

On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions

We consider the inhomogeneous heat equation on the half-space R + d with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the half-space. We also address the case of homogeneous Robin boundary conditions. Our results generalize the case of homogeneous Dirichlet boundary conditions established by Kukavica and Vicol [A direct approach to Gevrey regularity on the half-space. In: Partial differential equations in fluid mechanics. Cambridge: Cambridge Univ. Press; 2018. p. 268–288. (London math. soc. lecture note ser.; vol. 452).].

On matched asymptotic expansion solutions of a bucklewave propagation problem

AbstractIn the present paper, the method of matched asymptotic expansions is used to derive approximate analytical solutions to a model problem related to bucklewave propagation in undersea pipelines. The model problem, introduced by Chater, Hutchinson and Neale (in: Collapse – The Buckling of Structures in Theory and Practice (Thompson, J.M.T., Hunt, G.W., eds.) Cambridge Univ. Press, Cambridge, 1983), consists of a linear elastic beam resting on a nonlinear elastic foundation, with inclusion of axial tension and inertia, related to a propagating buckle. When tension dominates over inertia, it is found that the asymptotic solution describing a propagating buckle has the character of nonoscillatory motion. When tension and inertia forces are of equal magnitude, or when inertia forces dominate over tension, the solutions are found to be oscillatory, but still localized around the bucklewave front. Finally, it is shown that when the propagation speed of the buckle exceeds a critical value, a spatial instability sets in, with exponentially growing amplitude of the beam deflection.

Method for evaluation of the optical uniformity distribution in the white LEDs-based visible light communication applications

The uniformity characteristic of emitted radiation in VLC applications is a factor that can affect the efficiency of a detector and the overall efficiency of the VLC system. In this paper, we theoretically investigate the optical uniformity characteristic of using LEDs in VLC applications in terms of the parameter of the emission angle of LEDs and the spatial distribution of LEDs. The result indicates that the optical uniformity can be controlled at a high level by controlling the emission angle of the LED or distributing the LEDs in the room's space. Full Text: PDF References E.-F. Schubert, J.-K. Kim, "Solid-State Light Sources Getting Smart", Science 308, 1274 (2005). CrossRef N. Narendran, Y. Gu, "Life of LED-based white light sources", J. Display Technol. 1, 167 (2005). CrossRef E. Schubert, Light-Emitting Diodes (Cambridge, Cambridge Univ. Press 2006). CrossRef C.C. Sun, Q.K. Nguyen, T.X. Lee, S.K. Lin, C.S. Wu, T.H. Yang, Y.W. Yu, "Active thermal-fuse for stopping blue light leakage of white light-emitting diodes driven by constant current", Sci. Reports 12, 12433 (2022). CrossRef Z. Ghassemlooy, W. Popoola, S. Rajbhandari. Optical Wireless Communications System and Channel Modelling with MATLAB (Florida, CRC Press, Taylor & Francis Group, 2013). CrossRef A. Burton, H. Le Minh, Z. Ghasemlooy, S. Rajbhandari, "A study of LED lumination uniformity with mobility for visible light communications", IEEE 2012 Int. Workshop on Opt. Wireless Comm. (IWOW), Pisa, Italy, 2012. CrossRef M.S.M. Gismalla, M.F.L. Abdullah, M.I. Niass, B. Das, W.A. Mabrouk. "Effect of optical attocells deployment on the RMSD spread in indoor visible light communication systems", Int. J. Commun Syst. e4349 (2020). CrossRef C. Wang, J. Wang, J. Zhang, J. Wang, H. Du, J. Wang, "Research on uniform illumination distribution of indoor visible light communication", Proc. SPIE 12062, AOPC 2021: Optoelectronics and Nanophotonics (2021). CrossRef M.V. Bhalerao, M. Sumathi, S.S. Sonavane. "Line of sight model for visible light communication using Lambertian radiation pattern of LED", Int. J. Comm. Systems (2016). CrossRef J.F. Zang, Y. Piao. "Research on visible light communication system based on white LEDs", Proc. SPIE 10255, (2016). CrossRef M. Oliveira, F.C.B. Tosta, D.E.F. Guillen, P.P. Monteiro, A.A.P. Poh, "Theoretical and Experimental Analysis of LED Lamp for Visible Light Communications", Wireless Personal Communications 125, 3461(2022). CrossRef J.P. Ding, C. Lin, J.T. Wang, H. Yang, "Effects of Optical Beams on MIMO Visible Light Communication Channel Characteristics", Sensors 22, 216 (2022). CrossRef X. Zhang , N. Zhao, F. Al-Turjman, M.B. Khan, X. Yang. "An Optimization of the Signal-to-Noise Ratio Distribution of an Indoor Visible Light Communication System Based on the Conventional Layout Model", Sustainability 12, 9006 (2020). CrossRef A. Kaewpukdee, P. Uthansakul, "Characteristic of Line-of-Sight in Infrastructure-to-Vehicle Visible Light Communication Using MIMO Technique", Materials Continua 74, 1026 (2023). CrossRef

Generalizations of mock theta functions and radial limits

In the last letter to Hardy, Ramanujan [Collected Papers, Cambridge Univ. Press, 1927; Reprinted, Chelsea, New York, 1962] introduced seventeen functions defined by q q -series convergent for | q | > 1 |q|>1 with a complex variable q q , and called these functions “mock theta functions”. Subsequently, mock theta functions were widely studied in the literature. In the survey of B. Gordon and R. J. McIntosh [A survey of classical mock theta functions, Partitions, q q -series, and modular forms, Dev. Math., vol. 23, Springer, New York, 2012, pp. 95–144], they showed that the odd (resp. even) order mock theta functions are related to the function g 3 ( x , q ) g_3(x,q) (resp. g 2 ( x , q ) g_2(x,q) ). These two functions are usually called “universal mock theta functions”. D. R. Hickerson and E. T. Mortenson [Proc. Lond. Math. Soc. (3) 109 (2014), pp. 382–422] expressed all the classical mock theta functions and the two universal mock theta functions in terms of Appell–Lerch sums. In this paper, based on some q q -series identities, we find four functions, and express them in terms of Appell–Lerch sums. For example, 1 + ( x q − 1 − x − 1 q ) ∑ n = 0 ∞ ( − 1 ; q ) 2 n q n ( x q − 1 , x − 1 q ; q 2 ) n + 1 = 2 m ( x , q 2 , q ) . \begin{equation*} 1+(xq^{-1}-x^{-1}q)\sum _{n=0}^{\infty }\frac {(-1;q)_{2n}q^{n}}{(xq^{-1},x^{-1}q;q^2)_{n+1}}=2m(x,q^2,q). \end{equation*} Then we establish some identities related to these functions and the universal mock theta function g 2 ( x , q ) g_2(x,q) . These relations imply that all the classical mock theta functions can be expressed in terms of these four functions. Furthermore, by means of q q -series identities and some properties of Appell–Lerch sums, we derive four radial limit results related to these functions.

Rank growth of elliptic curves over 𝑁-th root extensions

Fix an elliptic curve E E over a number field F F and an integer n n which is a power of 3 3 . We study the growth of the Mordell–Weil rank of E E after base change to the fields K d = F ( d 2 n ) K_d = F(\!\sqrt [2n]{d}) . If E E admits a 3 3 -isogeny, then we show that the average “new rank” of E E over K d K_d , appropriately defined, is bounded as the height of d d goes to infinity. When n = 3 n = 3 , we moreover show that for many elliptic curves E / Q E/\mathbb {Q} , there are no new points on E E over Q ( d 6 ) \mathbb {Q}(\sqrt [6]d) , for a positive proportion of integers d d . This is a horizontal analogue of a well-known result of Cornut and Vatsal [Nontriviality of Rankin-Selberg L-functions and CM points, L-functions and Galois representations, vol. 320, Cambridge Univ. Press, Cambridge, 2007, pp. 121–186]. As a corollary, we show that Hilbert’s tenth problem has a negative solution over a positive proportion of pure sextic fields Q ( d 6 ) \mathbb {Q}(\sqrt [6]{d}) . The proofs combine our recent work on ranks of abelian varieties in cyclotomic twist families with a technique we call the “correlation trick”, which applies in a more general context where one is trying to show simultaneous vanishing of multiple Selmer groups. We also apply this technique to families of twists of Prym surfaces, which leads to bounds on the number of rational points in sextic twist families of bielliptic genus 3 curves.

Cutoff for rewiring dynamics on perfect matchings

We establish cutoff for a natural random walk (RW) on the set of perfect matchings (PMs), based on “rewiring”. An n-PM is a pairing of 2n objects. The k-PM RW selects k pairs uniformly at random, disassociates the corresponding 2k objects, then chooses a new pairing on these 2k objects uniformly at random. The equilibrium distribution is uniform over all n-PMs. The 2-PM RW was first introduced by Diaconis and Holmes (Proc. Natl. Acad. Sci. USA 95 (1998) 14600–14602; Electron. J. Probab. 7 (2002) no. 6), seen as a RW on phylogenetic trees. They established cutoff in this case. We establish cutoff for the k-PM RW whenever 2≤k≪n. If k≫1, then the mixing time is nklogn to leading order. Diaconis and Holmes (Electron. J. Probab. 7 (2002) no. 6) relate the 2-PM RW to the random transpositions card shuffle. Ceccherini-Silberstein, Scarabotti and Tolli (J. Math. Sci. 141 (2007) 1182–1229; Harmonic Analysis on Finite Groups: Representation Theory, Gelfand Pairs and Markov Chains (2008) Cambridge Univ. Press) establish the same result using representation theory. We are the first to handle k>2. We relate the PM RW to conjugacy-invariant RWs on the permutation group by introducing a “cycle structure” for PMs, then build on work of Berestycki, Schramm, Şengül and Zeitouni (Israel J. Math. 147 (2005) 221–243; Ann. Probab. 39 (2011) 1815–1843; Probab. Theory Related Fields 173 (2019) 1197–1241) on such RWs.

Godless Fictions in the Eighteenth Century: A Literary History of Atheism by James Bryant Reeves

Reviewed by: Godless Fictions in the Eighteenth Century: A Literary History of Atheism by James Bryant Reeves Lisa O'Connell James Bryant Reeves, Godless Fictions in the Eighteenth Century: A Literary History of Atheism (Cambridge: Cambridge Univ. Press, 2020). Pp. 260. $99.99 cloth. That God is dead is a commonplace of modern literary history and, at least until recently, of the secularization and modernization narratives that have shaped our understanding of Enlightenment. Yet, despite the presence of many atheists in eighteenth-century fiction, the "literary history of atheism" has largely gone untold. In Godless Fictions in the Eighteenth Century, James Reeves aims to change that. He offers a fresh, post-secular take on the literary representation of religious non-belief in Britain, arguing that it animated a broad sweep of early fiction, from Tory satire and verse essay to sentimental-moral fiction and pre-Romantic poetry. Reeves's five author-focused chapters make the case that atheism functioned as a richly "generative literary concept" (5–6) and that it did so precisely as a reviled Other for eighteenth-century fictional worlds. The book begins with twinned chapters on Jonathan Swift and Alexander Pope, for whom the rise of atheistic materialism signaled the degeneracy and dullness of the age. Paradoxically, atheism energized each author's most excoriating satires, including The Dunciad and Gulliver's Travels. The analysis continues into less well-traversed literary territory, with chapters on Sarah Fielding and Phebe Gibbes, mid-late-century female writers of didactic novels (David Simple, Lady Louisa Stroud, and Hartly House, Calcutta), whose polite marriage plots, Reeves insists, were no less reliant on godless worlds and characters, set here against author-sanctioned modes of sympathy, sociability, and (female) community tied to Christian belief. Pivoting back to canonical verse, the book's concluding chapter examines a selection of William Cowper's poems and hymns, in which his abiding opposition to atheism grounds an emergent Romantic critique of slavery, imperialism, and oppression. It is fair to say that, for Reeves, atheism's literary history unfolds under the dispensation of an English Anglican nation-state for which unbelief was the antithesis of a godly, ordered society. Accordingly, British authors became "preoccupied with unbelief," he argues, either as a force of imaginative chaos or as a reliable fictional means "to interrogate discourses of selfhood, sociability, tolerance and empire" (5). Only belatedly, under the influence of avowedly atheist writers like Percy Shelley (whose 1810–11 epistolary prank "The Necessity of Atheism" is the subject of the book's coda) as well as the promise of radical political transformation fueled by revolutionary critiques of religion and absolute authority, did the literary treatment of atheism detach from belief and godliness and connect to modern secularization narratives. Even as it unsettles secularization narratives, however, Godless Fictions does not seek to historicize the literary representation of unbelief by framing it within received intellectual histories of atheism or materialism, or even within the politics of the English state which regulated Christian orthodoxy and promoted broader moral reform and outreach efforts. Instead, Reeves's key analytical move is to insist on the primarily affective nature of literary responses to unbelief, noting that "[r]ather than arguing against atheism on rational or epistemological grounds, eighteenth-century literature often rejects it out of pure reflexive disdain" (7). Early in his study, Reeves tells us that, while eighteenth-century commentators and divines [End Page 339] routinely conflated atheism with Christian heterodoxy (Deism, Socinianism, anti-Trinitarianism, etc.), this was not the case in the literary sphere where the atheist emerged as a reviled fictional figure, native to satiric-dystopic speculative worlds and the minor characterology of the novel. Reeves's affect-oriented approach yields two important insights. The first is that British fiction's recurring negative treatment of godless worlds and characters—materialists, dunces, rakes, freethinkers, misanthropes, and the like (all reviled and almost all male)—is subtended by a steady and insistent theism. But this is not a theism tied to religious creed or to Christian-theological argument. It is, rather, as Reeves notes, precognitive, affective, and intensely imaginative, defined by its hostility to unbelief rather than by any positive or prescriptive conception of the divine. A...

The Free Uniform Spanning Forest is disconnected in some virtually free groups, depending on the generator set

We prove the rather counterintuitive result that there exist finite transitive graphs H and integers k such that the Free Uniform Spanning Forest in the direct product of the k-regular tree and H has infinitely many trees almost surely. This shows that the number of trees in the FUSF is not a quasi-isometry invariant. Moreover, we give two different Cayley graphs of the same virtually free group such that the FUSF has infinitely many trees in one, but is connected in the other, answering a question of Lyons and Peres (Probability on Trees and Networks (2016) Cambridge Univ. Press) in the negative. A version of our argument gives an example of a nonunimodular transitive graph where WUSF≠FUSF, but some of the FUSF trees are light with respect to Haar measure. This disproves a conjecture of Tang (Electron. J. Probab. 26 (2021) Paper No. 141).

Specializing Koornwinder polynomials to Macdonald polynomials of type B, C, D and BC

We study the specializations of parameters in Koornwinder polynomials to obtain Macdonald polynomials associated to the subsystems of the affine root system of type \((C_n^\vee ,C_n)\) in the sense of Macdonald (Affine Hecke algebras and orthogonal polynomials, Cambridge tracts in mathematics, Cambridge Univ Press, 2003), and summarize them in what we call the specialization table. As a verification of our argument, we check the specializations to type B, C and D via Ram–Yip type formulas of non-symmetric Koornwinder and Macdonald polynomials.

General Materials

Guide to the Year's WorkGeneral Materials Albert D. Pionke (bio) This year's survey of general materials features chapters from four books. These three edited collections and one monograph position Victorian poets and poetry with respect to the particular writerly legacies of Byron and Keats and the broader scientific and artistic developments in medicine and ballet, respectively. Individual Victorian-era poets discussed, whether concisely or extensively, in these diverse contexts include Matthew Arnold, Elizabeth Barrett and Robert Browning, Oliver Wendell Holmes, Gerard Manley Hopkins, Letitia Elizabeth Landen, Edward Lear, Algernon Charles Swinburne, Alfred Tennyson, Walt Whitman, and Oscar Wilde. Initiated from the weekend symposium "Byron among the Poets," held at All Soul's College, Oxford, in January, 2018, Clare Bucknell and Matthew Ward's edited collection Byron among the English Poets: Literary Tradition and Poetic Legacy (Cambridge: Cambridge Univ. Press, 2021) is "preoccupied both with Byronic allusion and the question of poetic influence more broadly, as it relates to Byron's reworking of his predecessors and to the way Byronic wording, forms and ideas surface and resurface in the work of later writers" (p. 8). Readers of Victorian Poetry may be especially interested in chapters 14 through 17 from the book's third chronologically arranged section, "Afterlives," which "looks ahead to the presence of Byronic forms, motifs, manners and characters in post-Romantic poetry" (p. 12). Thus, in "In-Between Byrons: Byronic Legacies in Women's Poetry of the Late Romantic to Mid-Victorian Era," Sarah Wootton positions Letitia Elizabeth Landon as "a pivotal figure in the dissemination of Byron and Byronic influence from the mid-1820s to the 1840s" (p. 235). Focusing sequentially on "Lorenzo's History" (1824), "Lines Suggested on Visiting Newstead Abbey" (1839), "The Portrait of Lord Byron, at Newstead Abbey" (1840), and "Stanzas. Written Beneath the Portrait of Lord Byron, Painted by Mr West" (1827), Wootton tracks Landon's ambivalent response to Byron's and her own "iconic status . . . while also expressing concerns about the longevity of his verse and use, or misuse, of his poetic skill" (p. 236). Next, Jane Stabler's "Byron and Browning: Something and Nothing" examines "moments [End Page 345] when Robert Browning appears to fall into or in with Byron's cadences, particularly their shared use of the word 'something' and their attention to moments when characters say nothing" (p. 252). Less definite than more straightforwardly verifiable allusions, these "subtler echoings," also referred to as "analogues," are scattered widely across Browning's poetic corpus (pp. 252, 262). Ward's essay, "Arnold's Ambivalence and Byron's Force and Fire," follows. For Ward, "Arnold's writing to and through Byron suggests that he retained a wish for Romantic influence more than he felt an anxiety of influence," especially when faced with the loss of "collective feeling" and "decline of poetry" in his own age (pp. 272, 272, 275). Finally, Richard Cronin rounds out the Victorian portion of "Afterlives" by reexamining Swinburne's ambivalent relationship to Byron. In "A. C. Swinburne and Byron's Bad Ear," Cronin traces Swinburne's shift from "principal restorer" of his predecessor's reputation to "hardened" critic of Byron's "metrical deficiencies" (pp. 287, 289). The irony, Cronin observes, is that even in the 1880s, "when attacking Byron most savagely, Swinburne's tendency is to echo him" (p. 293). Echoes of Victorian poetry also resound in individual chapters from two additional edited collections. Daniel Brown's "Physics and Metaphysics: Poetry and the Unsteady Ascent of Professional Medicine" serves as the fifth chapter of Clark Lawlor and Andrew Mangham's Literature and Medicine: The Nineteenth Century (Cambridge: Cambridge Univ. Press, 2021). Within the period framed by Edward Jenner's smallpox vaccine and Ronald Ross's demonstration of the life cycle of the malarial parasite in mosquitos (1796–1897), Brown reconstructs the increasingly strained relationship between medicine and poetry in the nineteenth century. Through succinct close readings of poems by George Crabb, Samuel Taylor Coleridge, Robert Southey, William Wordsworth, George Gordon, Lord Byron, John Keats, Oliver Wendell Holmes, Alfred Tennyson, Oscar Wilde, Gerard Manley Hopkins, Walt Whitman, Edward Lear, and a host of lesser-known poets and poet-physicians, Brown shows how, "[b]uilding upon the legacies of...

Swinburne

Swinburne Justin A. Sider (bio) At the end of Ezra Pound's querulous review of Edmund Gosse's biography of Algernon Charles Swinburne, he concludes his own portrait of the poet—alternately admiring and exasperated—with this summary: "At any rate we can, whatever our verbal fastidiousness, be thankful for any man who kept alive some spirit of paganism and of revolt in a papier-mâché era, in a time swarming with Longfellows, Mabies, Gosses, Harrisons."1 "Paganism" and "revolt" are [End Page 403] watchwords for the small run of Swinburne scholarship this past year, a set of essays and chapters that sees our poet lending Aleister Crowley the formulae for versified sex "magick," pondering the limits of rational thought, and celebrating the erosion of the human world. Though the number of essays and chapters was small, these cover a fair range of the field's current interests. In the introduction to Decadent Ecology in British Literature and Art, 1860–1910: Decay, Desire, and the Pagan Revival (Cambridge: Cambridge Univ. Press, 2022), Dennis Denisoff turns to Swinburne's Poems and Ballads (1866)—"the main catalyst for literature having a voice in the formulation of British decadence" (p. 12)—in order to show how the era's decadent paganism produced an "expansive conceptualization of ecological reality" (p. 19). Victorian critics like Robert Buchanan (Thomas Maitland) had themselves described the "fleshly" poetry of Dante Gabriel Rossetti and Swinburne in ecological terms–as a biological threat to the moral health of the nation. Yet decadent writing, Denisoff argues, did not offer straightforward rebellion against "an artificial image of a stable society" but pursued instead images of "mutation, excess, and inconstancy" that joined human and nonhuman worlds: "Like biological decay, decadent culture is not a threat but an inherent aspect of an open ecology" (p. 11). In Denisoff's readings, paganism and decadence collaborate in portraying a world of "indeterminate, open . . . relationships" within which human beings are merely one set of coordinates rather than an organizing center (p. 19). Swinburne's neopaganism (represented, in this case, by "Hertha" and "The Garden of Proserpine") is treated rather briefly. Denisoff notes that Swinburne challenged the rigid moral vision of Victorian society by celebrating pagan divinities like the eponymous Hertha, who represents a "timeless" and "ongoing" force without being "tied to a narrative of progression and improvement" (p. 14). Denisoff devotes more attention to "The Leper," which he contextualizes with Victorian essays and poems on fungus and disease, drawing out the tendency in the era to represent decay not as a natural force but as a hostile (moral) agent. Against such habits of thought, "The Leper" exemplifies the perspective of decadent ecology by "contrasting the common impulse to shun the other—whether deemed abject, sickly, foreign, or unnatural—with the decadent drive for appreciative incorporation" (p. 19). Though Swinburne appears primarily to introduce the preoccupations of the book as a whole, Denisoff's discussion suggests the richness of Swinburne's work for ecocritical approaches to Victorian poetry and decadence. Swinburne's ecological imagination is also the focus of Keri Stevenson's "The Death of Birdsong, the Birdsong of Death: Algernon Charles Swinburne [End Page 404] and the Horror of Erosion" (in Fear and Nature: Ecohorror Studies in the Anthropocene, ed. Christy Tidwell and Carter Soles [University Park: Penn State Univ. Press, 2021], pp. 91–109). Stevenson treats the eroding landscapes in "A Forsaken Garden" and "By the North Sea" as examples of what Greg Garrard calls "disanthropic" literature—that is, literature that imagines a world without humans. The challenge or paradox of artistic disanthropy, Stevenson explains, involves forgetting that any such representation of the world is itself a human product, arranged and designed for our consumption. Stevenson's readings of Swinburne's poems explore the strategies by which he works through this challenge. Erosion is the principal figure here because Swinburne strives to render landscapes "free of the colonization of human minds and needs": "There is nothing here humans can use, want, name, or eat," writes Stevenson of Swinburne's gardens and seashores (p. 97). Conventional poetic images—birdsong, flowers, and trees—are offered not in the redemptive mode of pastoral. Rather, these objects survive our...

Eating the Empire: Food and Society in Eighteenth-Century Britain by Troy Bickham, and: British Orientalisms, 1759–1835 by James Watt

Reviewed by: Eating the Empire: Food and Society in Eighteenth-Century Britain by Troy Bickham, and: British Orientalisms, 1759–1835 by James Watt James Mulholland Troy Bickham, Eating the Empire: Food and Society in Eighteenth-Century Britain (London: Reaktion Books, 2020); distributed by Univ. of Chicago Press). Pp. 285, 85 halftones. $35 cloth. James Watt, British Orientalisms, 1759–1835 (Cambridge: Cambridge Univ. Press, 2019). Pp. 285. $99.99 cloth. One summer afternoon, while researching in the Manuscripts Room of the British Library, I came across a memorandum book of India's first Governor-General, Warren Hastings. He lived in India since the 1770s and was an enthusiastic sampler of South Asian culture (as well as an orientalist who combined colonial governance with cultural creation). Included among his drafts of poems, notes on weather, and accounts of meetings was a recipe for chicken kebabs—he called it "Kabaub Fowl"—which called for washing the chicken in salted water, rubbing it with "corriander seed, pepper and garlick" and "juice of ginger, chicory, and figs strained through a cloth" before stuffing it with "ghee and cloves" and roasting it over a gentle fire "until it is done, & looks red."1 Delicious, no doubt, and just as likely never prepared by Hastings himself. I thought of Hastings' recipe as I read Troy Bickham's capacious account of food and empire in the eighteenth century. Bickham's reads like a cross-over: a scholarly account that popularizes sharp expertise to knowledgeable non-academic readers. His book feels at times like the synthesis of accounts, among academic and popular writers alike, which tracked commodities and their effect on the globe, including salt (Salt: A World History [2003]), tea (A Thirst for Empire [2017]), sugar (Sweetness and Power [1986]; Sugar and Civilization [2015]), coffee (Uncommon Grounds [1999]), and curry (Curry: Cooks and Conquerors [2006]).2 As with many of these other accounts, Bickham sees in the preparation, consumption, and popular representation of food an image of how empire affected Britons and an indication of empire's extraordinary reach yet often ordinary effects. He describes empire as an "ever-moving umbrella" (10) of nearly incongruous activities, some of which were under British sovereignty but others that were negotiated with others. The middle grounds, translators, and imperial brokers that have become standard metaphors of twenty-first-century studies of empire are evident in how food connected domestic Britons to imperial dominion. Bickham describes the "abundance of choice" and the rituals it created as "a language" (17) that solidified "national and regional identities" (18) in Britain but also acted as a "tool for cultural critiques" (19). Doubleness of experience pervades Eating the Empire, which is also an explanation of how the foreign and exotic was made familiar and domestic. Bickham approaches foodways in the manner of an anthropologist or sociologist—as fundamentally about the interpersonal relationships forged by empire (9). In this way, his book is an elegantly interlocking story, and is extensively illustrated, typically with satirical prints that show commodities' imperial associations, making it an engaging overarching history of food and empire. At its most important, Eating the Empire describes the transformation of empire's goods from "rare luxuries to commonplace staples" across the eighteenth century (28), which necessarily altered diets, changed social practices, and arguably [End Page 556] made the current United Kingdom what it is, with teatime and biscuits but also curries and kebabs, of the type that Hastings encountered centuries ago. During the eighteenth century, consumer choice expanded rapidly, and what was a luxury in the seventeenth century was a staple one hundred years later (56). Then, as now, the rich censured the poor for the ingestion of what was seen as above their station (54), with anxieties about tea or coffee being replaced later with worries over carbonated drinks. Throughout Eating the Empire, Bickham touches on broad changes that are formative for the present: shopping (59–60), credit (61–65), fashion and fashionability (65), social visits and visiting (67), cook books (144), and in turn the evolution of politeness and manners, especially as related to the preparation and consumption of food. Some topics, such as coffee, are familiar to most eighteenth-century studies scholars, while...

Mukai duality via roofs of projective bundles

We investigate a construction providing pairs of Calabi–Yau varieties described as zero loci of pushforwards of a hyperplane section on a roof as described in Kanemitsu (Preprint, arXiv:1812.05392, 2018). We discuss the implications of such construction at the level of Hodge equivalence, derived equivalence and L ${\mathbb {L}}$ -equivalence. For the case of K3 surfaces, we provide alternative interpretations for the Fourier–Mukai duality in the family of K3 surfaces of degree 12 of (New trends in algebraic geometry (Warwick, 1996), Lond. Math. Soc. Lecture Note Ser., vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 311–326). In all these constructions, the derived equivalence lifts to an equivalence of matrix factorizations categories.

Ireland, Enlightenment and the English Stage, 1740–1820 by David O’Shaughnessy

Reviewed by: Ireland, Enlightenment and the English Stage, 1740–1820 by David O’Shaughnessy Misty G. Anderson David O’Shaughnessy, ed., Ireland, Enlightenment and the English Stage, 1740–1820 (Cambridge: Cambridge Univ. Press, 2019). Pp. 282; 21 b/w illus., 5 tables. $99 cloth. What did Irish theatre, Irish playwrights and actors, and the idea of Irishness in the anglophone theatrical world contribute to Enlightenment values? David O’Shaughnessy, serving as both academic editor and impresario, has answers. His collection brings together some of the top voices in eighteenth-century theater studies to make visible what has been a submerged Irish influence and to consider its collective impact on Enlightenment ideas. Rejecting the “barometer” metaphor [End Page 403] Michael Brown uses in The Irish Enlightenment (2016) to contain theater as reflective, O’Shaughnessy and his contributors read for mediations that shape the anglophone Enlightenment imagination. These essays paint a picture of Irish theatrical contributions that move far beyond Teagues and brogues to show how Irish actors, playwrights, and sensibilities were not peripheral but central. The claim, well substantiated, is that a deep bench of Irish talent, including Catherine Clive, Peg Woffington, Charles Macklin, Oliver Goldsmith, Arthur Murphy, Richard Brinsley Sheridan, and John O’Keeffe, defined Georgian theater. Part of the magic of this collection is the conversation O’Shaughnessy has hosted, most directly in the two accounts of London-based Irish actor John Johnstone’s influence, but also through the gracious references to other essays in the volume, evidence of true collaboration that models the values of the cosmopolitan Irish Enlightenment O’Shaughnessy maps out. The three sections of the collection draw our focus first to performance, then place, then political perspective, in ten essays that leave the reader with no doubt about the central function of Irish players and playwrights in eighteenth-century theater and with a new working thesis about an Irishness without borders, figuring and performing the migrant in the metropole that makes so many of these plays “‘excentrically’ cosmopolitan” (Burke, 248). It is fitting that the conclusion, which frames out the overarching thesis, comes from Helen Burke, the theater scholar who has contributed the most to our understanding of Irish influence and representation in the long eighteenth century.1 O’Shaughnessy’s own introduction reflects the partly reparative mission of this collection: to show that Irish plays, playwrights, and influence are everywhere. That celebratory trend, which could drift into encomium, stays within O’Shaughnessy’s deft control, beginning with his introductory, non-exhaustive, yet still impressive overview of a missing Irish theater history. His critical intervention in this volume is to explore why it’s been hiding in plain sight, in bodies and bodies of work that often blurred Irish difference but that collectively defined the Georgian theater world from within the London metropole. Performance and Irishness serve twinned functions in this collection, recalibrating an Irish Enlightenment that is not limited by, or to, negative Irish stereotypes but instead defined by a positive Irish influence on Enlightenment values of mobility, self-improvement, knowledge, and equality. Michael Brown’s “door-stopping” The Irish Enlightenment grounds O’Shaughnessy’s approach, both because it acknowledges theater’s productive work in a field of print Enlightenment studies and because the centering of Irishness or, more accurately, multiple types of Irishness that embody the principle of civility in action, shows how the Irish were fundamental to the Enlightenment concept of civilization. His attachment to the concept of Enlightenment risks what Al Coppola calls “Enlightenolatry” and the need to think through Enlightenment’s Cold War (rather than Kantian) production and twenty-first-century pop culture re-animation. But the notion of a “thick” Enlightenment that isn’t over yet (as Joseph Roach has argued) comports with the overarching vision of a more capacious geography of Enlightenment ideals within imperial Britain, starting at home.2 O’Shaughnessy argues that performances between London and Dublin crossed borders through an Irish Enlightenment that was “energized by its national kinesis and the cosmopolitan environs of London” (13), an Irishness not merely but always peripatetic, always translating, always mediating. This collection is structurally and intellectually engaged with a capacious notion of Enlightenment oriented around political justice, even...

The First of the Modern Ottomans: The Intellectual History of Ahmed Vasif by Ethan Menchinger

Reviewed by: The First of the Modern Ottomans: The Intellectual History of Ahmed Vasif by Ethan Menchinger Dženita Karić Ethan Menchinger, The First of the Modern Ottomans: The Intellectual History of Ahmed Vasif (Cambridge: Cambridge Univ. Press, 2017). Pp. 356. $103.99 cloth. Ethan Menchinger's monograph The First of the Modern Ottomans: The Intellectual History of Ahmed Vasif is an impressive and ambitious biography of one of the key, yet neglected figures of the eighteenth-century Ottoman administrative and intellectual scene: Ahmed Vâsıf (d. 1806), chancery officer and court historian. The book not only follows Vâsif's personal and professional trajectory in detail but also provides insightful analysis of the intellectual discussions and wider political and social context of a turbulent period. Thus, through the biography of Ahmed Vâsıf and Menchinger's powerful narration, we are drawn into the complex Ottoman world of the eighteenth century and its military, bureaucratic, and intellectual dealings. The book moves progressively from the beginnings of Vâsıf's life through eight chapters: "Out of the East: Early Life (ca. 1735–1768)"; "At War (1768–1774)"; "Years of Faction and Reform (1774–1787)"; "Honorable Exile: In Spain (1787–1788)"; "At War (1788–1792)"; "Vâsıf and the New Order (1792–1800)"; "The Height of Fame (1800–1806)"; and "Epilogue: Vâsıf as Ancient and Modern." The book also contains a Dramatis Personae, a chronology, a glossary, and an appendix that discusses Vâsıf's potential authorship of the "Final Word to Refute the Rabble" (Hulâsatü'l-Kelâm fî Reddi'l-'Avamm), a treatise that aimed to dispel misconceptions of the reforms of Sultan Selim III. As the chapter titles suggest, much of Vâsıf's life and career was marked by the frequent wars in which the Ottomans engaged and by his rise to service as a high-ranked Ottoman official. In many ways, Ahmed Vâsıf's life presents the "Ottoman dream" story: hailing from Baghdad, which by Vâsıf's time had been reduced to a provincial city, Vâsıf climbed the scholarly and administrative ranks partly supported by his family background (his father was a minor scholar), but much more by the relentlessly ambitious nature that led him to a continuous pursuit of posts and social status. Ahmed Vâsıf's career was thus marked by mobility, both social and physical, as he served the Ottoman Empire from the battlefronts on the Danube, to imprisonment in St. Petersburg, to posts and exile in Spain and Belgrade. Ahmed Vâsıf's administrative rank steadily rose: he began as a treasury scribe and rose through the positions of private secretary to Abaza Mehmed Paşa, clerk in the correspondence office, military secretary, fortifications officer, director of the outer documentation office, court historian (several times), galley scribe, temporary head of the suspended payments office, ambassador to Spain, head of the Anatolian accounts office (several times), head of the general accounts office, chief of the daily ledger, and chancellor (several times)—to his highest position, chief scribe. As Menchinger's painstaking attention to detail in numerous sources makes clear, Ahmed Vâsıf also engaged in a range of other pursuits. He was a poet and lexicographer and an "inordinately vain" editor of court histories (173); he was also active in many aspects of the printing process. Wide-ranging as were his travels, the most significant locale of Vâsıf's aspirations was certainly Istanbul, where he steadily sought both to influence Ottoman foreign politics and to amass wealth. Menchinger positions Ahmed Vâsıf against the background of a larger canvas of the eighteenth century, which saw increased Ottoman struggles with other [End Page 411] European powers and numerous territorial losses that forced the Ottoman Empire into rounds of negotiations and prolonged reassessments of its own internal affairs. Moreover, according to Menchinger's research, these self-assessments extended to reexamination of the ideological foundations of the Empire itself. In this regard, the major questions posed by intellectuals regarded realities of war and peace in the face of predestined eternity of the Ottoman Empire: how were...

Analysis of Pseudo-spectral Methods Used for Numerical Simulations of Turbulence

Events in turbulent flows computed by direct numerical simulation (DNS) are often calibrated with properties based on homogeneous isotropic turbulence, advanced by Kolmogorov, and given in Turbulence, U. Frisch, Cambridge Univ. Press, UK (1995). However, these computational procedures are not calibrated using numerical analyses in order to assess their strengths and weaknesses for DNS. This is with the exception in "A critical assessment of simulations for transitional and turbulence flows- Sengupta, T.K., In Proc. of IUTAM Symp. on Advances in Computation, Modeling and Control of Transitional and Turbulent Flows, 491-532, (eds. Sengupta, Lele, Sreenivasan, Davidson), WSPC, Singapore (2016)", where such a calibration has been advocated for numerical schemes using global spectral analysis (GSA) for the convection equation. In recent times, due to growing computing power, simulations have been reported using pseudo-spectral methods, with spatial discretization performed in Fourier spectral space and time-integration by multi-stage Runge-Kutta (RK) methods. Here, we perform GSA of Fourier spectral methods for the first time with RK2 and other multistage Runge-Kutta methods using the model linear convection and convection-diffusion equations. With the help of GSA, various sources of numerical errors are quantified. The major limitations of the RK2-Fourier spectral method are demonstrated for DNS and alternate choices are presented. We specify optimal parameters to achieve the best possible accuracy for simulations. There is a one-to-one correspondence of numerical solutions obtained by linear convection-diffusion equation and nonlinear Navier-Stokes equation with respect to numerical parameters. This enables us to investigate the capabilities of the numerical methods for DNS.

7. /aI/-Raising on the U.S. East Coast

Research Article| December 01 2021 7. /aI/-Raising on the U.S. East Coast: Resurgence, Retreat, and Resilience Natalie Schilling Natalie Schilling natalie schilling is professor of linguistics at Georgetown University. She specializes in language variation and change in American English, including ethnicity based and stylistic variation. She also conducts research, training, and case work in forensic linguistics. She is coauthor (with Walt Wolfram) of American English: Dialects and Variation (3rd ed., Blackwell, 2016); coeditor (with J. K. Chambers) of The Handbook of Language Variation and Change (2nd ed., Blackwell, 2013), and author of Sociolinguistic Fieldwork (Cambridge Univ. Press, 2013). She currently serves as editor of the Publications of the American Dialect Society (PADS) monograph series. Email: ns3@georgetown.edu. Search for other works by this author on: This Site Google Publication of the American Dialect Society (2021) 106 (1): 147–170. https://doi.org/10.1215/00031283-9551332 Cite Icon Cite Share Icon Share Twitter Permissions Search Site Citation Natalie Schilling; 7. /aI/-Raising on the U.S. East Coast: Resurgence, Retreat, and Resilience. Publication of the American Dialect Society 1 December 2021; 106 (1): 147–170. doi: https://doi.org/10.1215/00031283-9551332 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsAmerican Dialect SocietyThe Publication of the American Dialect Society Search Advanced Search The text of this article is only available as a PDF. Copyright © 2021 American Dialect Society2021 Article PDF first page preview Close Modal You do not currently have access to this content.

Semimartingales and shrinkage of filtration

We consider a complete probability space (Ω,F,P), which is endowed with two filtrations, G and F, assumed to satisfy the usual conditions and such that F⊂G. On this probability space we consider a real valued G-semimartingale X. The purpose of this work is to study the following two problems: A. If X is F-adapted, compute the F-semimartingale characteristics of X in terms of the G-semimartingale characteristics of X. B. If X is a special G-semimartingale but not F-adapted, compute the F-semimartingale characteristics of the F-optional projection of X in terms of the G-canonical decomposition and the G-semimartingale characteristics of X. In this paper problem B is solved under the assumption that the filtration F is immersed in G. Beyond the obvious mathematical interest, our study is motivated by important practical applications in areas such as finance and insurance (cf. Structured Dependence Between Stochastic Processes (2020) Cambridge Univ. Press).

The Cambridge History of the Gothic. Vol. 1: Gothic in the Long Eighteenth Century ed. by Angela Wright and Dale Townshend, and: The Cambridge History of the Gothic. Vol. 2: Gothic in the Nineteenth Century ed. by Dale Townshend and Angela Wright

Reviewed by: The Cambridge History of the Gothic. Vol. 1: Gothic in the Long Eighteenth Century ed. by Angela Wright and Dale Townshend, and: The Cambridge History of the Gothic. Vol. 2: Gothic in the Nineteenth Century ed. by Dale Townshend and Angela Wright JoEllen Mary DeLucia Angela Wright and Dale Townshend, eds., The Cambridge History of the Gothic. Vol. 1: Gothic in the Long Eighteenth Century (Cambridge: Cambridge Univ. Press, 2020). Pp. 516; 16 b/w illus. $155.00 cloth. Dale Townshend and Angela Wright, eds., The Cambridge History of the Gothic. Vol. 2: Gothic in the Nineteenth Century. (Cambridge: Cambridge Univ. Press, 2020) Pp. 541; 14 illus. $155.00 cloth. Defining the Gothic has been a perennial problem. Is it a literary genre, an aesthetic, or a style? As a historical marker, does it refer to the liberty-loving Goths of pre-Roman Britain, a medieval chivalric culture, or is it a negative definition of modernity? During the long eighteenth-century, Gothic was used as an adjective to describe architecture, political values, and, later, literary texts; in the nineteenth century, the term largely disappeared. In the twentieth century, Victorian studies adapted the Gothic as a “retrospective construct” (II:15)—a category used to group everything from Bram Stoker’s Dracula to the Kelmscott Press’s The Works of Geoffrey Chaucer under the same umbrella. The Gothic’s search for a clear referent has had the sometimes frustrating but also liberating effect of evacuating the term of any clear meaning. Dale Townshend and Angela Wright, the editors of the first two volumes of The Cambridge History of the Gothic, argue that instead of linking the Gothic to a historical period, discipline, or set of formal characteristics, we should understand it as a “mode.” Mode in these volumes means something close to a method or approach, an active means of both interrogating dominant histories and writing “counter-history” (I: 6). The discontinuities and the unevenness in the application of the term Gothic make the case for it as an approach or process. As Robert Miles argues, the Gothic might best be understood as “a temporal contrast . . . between the premodern world of ghosts (timeless, circular, repetitious, with porous boundaries between the self and other, this world and the next), and the empty, chronometric, homogenous time of modernity” (I: 449); or, as Tom Duggett persuasively suggests, “a zeitgeist term—a word in the process of becoming, through contestation and self-contradiction” (II: 105). One of the great strengths of Townshend and Wright’s turn to mode instead of form is that they are able to develop a truly interdisciplinary collection of essays, putting literature, history, art, architecture, and drama into conversation with one another. At the same time, the constraints of the linear history demanded by the form of a three-volume Cambridge History, with separate volumes dedicated to the long eighteenth century, the nineteenth century, and a yet to be published volume on the twentieth century, work against the Gothic mode itself. As I read, I sometimes wished that the essays were grouped in a non-linear fashion, interrogating instead of replicating progressive historical form. Despite these formal constraints, the collected essays provide a fascinating interdisciplinary and transnational look at the Gothic, which almost always begins its story with Horace Walpole’s Castle of Otranto (1764); those in eighteenth-century studies would find these volumes most useful as a means of building a counternarrative of our period’s influence, one that contests the aesthetic and philosophical tenets of the neo-Classical and Enlightenment impulses that still dominate understandings of the eighteenth century; in addition, the collection would aid eighteenth centuryists in responding to recent calls to think and teach beyond the traditional boundaries of period and [End Page 1012] discipline and track the echoes of issues central to the eighteenth century across periods and national traditions. With the third volume yet to be released, this review only considers the first two volumes, which are dedicated to the long eighteenth and nineteenth centuries; they include an impressive forty-one essays from forty-two scholars writing from different disciplinary and national perspectives. In keeping with the Gothic mode, the essays are best read...