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160025244eb6ca66e9066ee22b67c7093c110d6b | subsection | 114 | 144 | Rescaling classes | Since the image of _{[\Delta ]}^f is contained in F^\textup {found}, the rescaling class of [\Delta ] comes from a class of an F^\textup {found}-matroid [\Delta ^{\prime }] that is represented by a Grassmann-Plücker function \Delta ^{\prime }:\binom{E}{r}\rightarrow F^\textup {found}.Thus \Delta and \circ \Delta ^{\pri... | {
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c4bb2cb403a40caa63953495eabcff5f3d3cbf6c | subsection | 115 | 144 | Foundations of binary matroids | A binary matroid is a matroid that is representableSince fields are perfect pastures, cf. Remark REF , it does not matter here if we talk about weak or strong representability. over the finite field {\mathbb {F}}_2 with two elements. In this section, we classify the foundations of binary matroids, and draw conclusions ... | {
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aeffa4d4b0a9a7f851bb2dfd878ac21189e354f7 | subsection | 116 | 144 | Foundations of binary matroids | An example of such a matroid is the Fano plane, which is not representable over any field of characteristic different from 2, cf. .In fact, it is a classical result that a binary matroid fails to be regular only if it contains the Fano plane as a minor, cf. . Thus binary matroids are either representable over every fie... | {
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a882e9a8c6905a2ecac981c6d100929af68b6d8e | subsection | 117 | 144 | Foundations of binary matroids | Thus M is binary by Theorem REF .Conversely, let M be a binary matroid that is represented by a Grassmann-Plücker function \Delta :\binom{E}{r}\rightarrow {\mathbb {F}}_2, i.e. \Delta (I)=1 if I is a basis of M and \Delta (I)=0 otherwise. A 3-term Plücker relation is satisfied over {\mathbb {F}}_2 if and only if an eve... | {
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5886683ab29ec029f24b62ff87cd56c764db72a4 | subsection | 118 | 144 | Foundations of binary matroids | By Corollary REF , the classes in {\mathcal {X}}^f_M(F) correspond bijectively to the morphisms k_M^f\rightarrow F. For both possibilities of k_M^f, there is at most one such morphism. Thus the theorem. | {
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661d70d35c45956faf415d23db02831ce54ab01d | subsection | 119 | 144 | Foundations of regular matroids | Our results on binary matroids lead to a short proof of Tutte's characterization of regular matroids. While Tutte's original proof was based on his homotopy theory for matroids, cf. and , shorter and more elementary proofs were found later on, cf. and .Our proof has some ingredients in common with these latter approach... | {
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f4a9db3e9ac420c9290ffb38b85dd12dec93bdca | subsection | 120 | 144 | Foundations of regular matroids | A regular matroid is binary and thus has precisely one rescaling class over every pasture by Corollary REF .Conversely, assume that M is a matroid that has exactly one rescaling class over every pasture. Then M is, in particular, representable over every pasture. Thus M is regular by Theorem REF .Corollary 3.37 Let M b... | {
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34f9369f452a1e1c104d66db4a26013faeac6189 | subsection | 121 | 144 | Foundations of regular matroids | Since both {\mathbb {S}} and {\mathbb {F}}_q (for q odd) are pastures with 1\ne , we reobtain the following well-known consequences of Tutte's characterization of regular matroids (cf. 7.52 in ) as immediate consequences of Theorem REF .Corollary 3.34
A matroid is regular if and only if it is binary and orientable.Cor... | {
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10833174e68078d8924ad5b276fc8e1ef38b3dab | subsection | 122 | 144 | Uniqueness for rescaling classes over | A matroid is called ternary if it is representable over the field {\mathbb {F}}_3 with 3 elements. Brylawski and Lucas show in that every ternary matroid has a unique rescaling class over {\mathbb {F}}_3. We find the following short proof of this result, employing the foundation of a matroid.Theorem 3.38
Every matroid... | {
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830d538e37dae8e137a43cd281d1af500ea0b0eb | subsection | 123 | 144 | Uniqueness for rescaling classes over | Since f maps nonzero elements of k_M^f to {\mathbb {F}}_3^\times , we encounter the following possibilities. If a=0, then f(a)=0. If b=0, then a=^{i+1} and f(a)=(-1)^{i+1} is determined by i. If both a and b are nonzero, then f(a) and f(b) are units in {\mathbb {F}}_3 and f(a)+f(b)+(-1)^i=0. This is only possible if f(... | {
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6600c95b0f863072e2f3c4263096e4323364ef1e | subsection | 124 | 144 | The bracket ring and the universal partial field | In , Pendavingh and Van Zwam introduce new techniques for establishing representability theorems for matroids. Their central tools are the bracket ring and the universal partial field. We will explain in this section how these two objects relate to the weak universal pasture and the foundation.In , Pendavingh and Van Z... | {
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c3cc8edb15bcca0b16efb29718ed4912c0fdccad | subsection | 125 | 144 | The bracket ring | Pendavingh and van Zwam's bracket ring is a variation of White's bracket ring from . We recall the definition from .Definition 3.40 Let M be a matroid with representing Grassmann-Plücker function \Delta :\binom{E}{r}\rightarrow {\mathbb {K}}. Let\textstyle {\mathcal {B}}\ = \ \big \lbrace \, I\in \binom{E}{r} \, \big |... | {
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91542bf8b3272e6ee4b0a8d8646fc138fc937cde | subsection | 126 | 144 | The bracket ring | Analogously, we define the partial degree-0 bracket field of M as P_{M,0}=(B_{M,0}^\times ,_{P_{M,0}}) where _{P_{M,0}}:{\mathbb {Z}}[B_{M,0}^\times ]\rightarrow B_{M,0} is the restriction of _{P_M} to the degree-0 elements.Pendavingh and van Zwam's bracket ring is a variation of White's bracket ring from . We recall t... | {
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81b19abbfcfa11bfc38c4dd6d23a72264142ad4f | subsection | 127 | 144 | The bracket ring | Analogously, we define the partial degree-0 bracket field of M as P_{M,0}=(B_{M,0}^\times ,_{P_{M,0}}) where _{P_{M,0}}:{\mathbb {Z}}[B_{M,0}^\times ]\rightarrow B_{M,0} is the restriction of _{P_M} to the degree-0 elements. | {
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8415fa3408c2517be28f63a6ac83842837369d0e | subsection | 128 | 144 | Relation to the weak universal pasture | We briefly recall from section that there are two ways to realize a partial field as an ordered blueprint. These two embeddings reflect the difference between the weak universal pasture and the partial bracket field, or between the foundation and the universal partial field, and provide a suitable language to compare t... | {
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2564b7e16d456d89f958bead2a0a0321c0ce930d | subsection | 129 | 144 | Relation to the weak universal pasture | Remark REF .Lemma 3.41
Let M be a matroid whose set of bases is {\mathcal {B}}. Let k_M^w be its weak universal pasture and P_{M,0} its partial degree-0 bracket field. Then k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\simeq P_{M,0}^\textup {blpr} and there are natural bijections{\mathcal {X}}_M(P^\textup ... | {
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f57aed0d3b4aa08c30042ba97190be701e256474 | subsection | 130 | 144 | Relation to the weak universal pasture | The last bijection follows from the isomorphism k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\simeq P_{M,0}^\textup {blpr} and the fact that (-)^\textup {oblpr}:\operatorname{{PartFields}}\rightarrow \operatorname{{OBlpr}}^\pm is fully faithful.As a consequence of Lemma REF , we can reprove Theorem 4.6 from... | {
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14535b175b81ac12f5406f4c1ff48e8576e2f869 | subsection | 131 | 144 | Relation to the weak universal pasture | By Corollary REF , such matroids are characterized by the property that their bracket ring is trivial. Since such matroids exist, for instance the Vámos matroid, this means that there are matroids M with trivial bracket ring B_M.On the other hand, the (weak) universal pasture is always nontrivial. This shows, in partic... | {
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4d657301aea584e0b2a900e2a960ad5a76f5f84c | subsection | 132 | 144 | Relation to the weak universal pasture | Note that we can recover the ambient ring of P as R_P=(P^\textup {oblpr}\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}})^+=(P^\textup {blpr})^+; recall from section the notation B^+ for the ambient semiring of an ordered blueprint B.Recall from section REF the definition of the weak universal pasture k_M^w of M as... | {
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f733a41ed722dd6058aed4582803bcc7c22e030f | subsection | 133 | 144 | Relation to the weak universal pasture | The underlying monoids of both k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}} and P_{M,0}^\textup {blpr} are generated by the terms \pm x_J^{\pm 1}. Thus k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\simeq P_{M,0}^\textup {blpr}.We turn to the proof of the second claim. A partial field is a doubl... | {
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257654c661d392061fbc40a9aed7025a378b7554 | subsection | 134 | 144 | Relation to the weak universal pasture | Thus {\mathcal {X}}_M(P^\textup {oblpr}) is nonempty and M is representable over the partial field P_M.The following fact shows that the class of representable matroids does not change if we ask for representability over fields or partial fields. This was already observed in . Note that for a partial field, strong and ... | {
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a9ff8a87f822fd338dc6eb0799388293b065ef4f | subsection | 135 | 144 | The universal partial field | The universal partial field of a matroid M was introduced by Pendavingh and van Zwam in as a device for proving representability theorems for matroids over partial fields. The definition in is somewhat technical, which is perhaps an inevitable consequence of their approach to matroid representations over partial fields... | {
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045ea039d8221a8531ad0fc2421ef495c0711428 | subsection | 136 | 144 | The universal partial field | The second bijection comes from applying -\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}} and (-)^{\textup {ppos}} to the morphism sets, cf. the proof of Lemma REF . The third bijection follows from k_M^f\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\simeq {\mathbb {P}}_{M}^\textup {blpr} and the fact that (... | {
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99860ae2ad6b65137ddaa0901d5a64213a78a2f5 | subsection | 137 | 144 | The universal partial field | Using the isomorphisms k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\rightarrow P_{M,0}^\textup {blpr} from Lemma REF and k_M^f\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\rightarrow {\mathbb {P}}_M^\textup {blpr} from Lemma REF , we obtain a sequence of isomorphismsP_{M,0}^\textup {blpr}\ \simeq \ ... | {
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3a2f022526a3fe35efc7007817e4aef64abc2945 | subsection | 138 | 144 | The universal partial field | Thus all operations that generate the strong equivalence relation come from scaling columns of a (non-truncated and possibly non-normalized) matrix representation A of M. This corresponds to the torus action appearing in the definition of rescaling classes.Let A be a truncated and normalized matrix representation of M.... | {
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b7e51015c665682e05d320cb58249ed33d3e54a1 | subsection | 139 | 144 | The universal partial field | Recall from Lemma REF that the canonical morphism k_M^w\rightarrow P_{M,0}^\textup {oblpr} induces an isomorphism k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\rightarrow P_{M,0}^\textup {blpr}. The following lemma recovers in a more concise form.Lemma 3.46
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5b24cf9e972163112a5328e7eb56f23ef13ed0f0 | subsection | 140 | 144 | The universal partial field | Then we define P[T_1^{\pm 1},\cdots ,T_s^{\pm 1}] as the partial field (P^\times \times \lbrace \prod T_i^{e_i}\rbrace _{e_i\in {\mathbb {Z}}}, \hat{}_P) where\textstyle \hat{}_P: \ {\mathbb {Z}}[P^\times ][T_1^{\pm 1},\cdots ,T_s^{\pm 1}] \ \longrightarrow \ R_P[T_1^{\pm 1},\cdots ,T_s^{\pm 1}]is the extension of _P t... | {
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eb9978b5e59a0d2d78b23cbd669d9bbfa216411e | subsection | 141 | 144 | The universal partial field | Using the isomorphisms k_M^w\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\rightarrow P_{M,0}^\textup {blpr} from Lemma REF and k_M^f\otimes _{{\mathbb {F}}_1^\pm }{{\mathbb {F}}_{1^2}}\rightarrow {\mathbb {P}}_M^\textup {blpr} from Lemma REF , we obtain a sequence of isomorphismsP_{M,0}^\textup {blpr}\ \simeq \ ... | {
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14cf44e0f94fc144457edab032a8a62044afaed6 | subsection | 142 | 144 | The universal partial field | Thus all operations that generate the strong equivalence relation come from scaling columns of a (non-truncated and possibly non-normalized) matrix representation A of M. This corresponds to the torus action appearing in the definition of rescaling classes.Let A be a truncated and normalized matrix representation of M.... | {
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317116924d811e7a053ff2af83d96b90da7431d1 | subsection | 143 | 144 | The universal partial fields of binary and regular matroids | Our classification of binary and regular matroids in terms of their foundation, cf. section REF and REF , yields a classification of such matroids in terms of their universal partial fields.Corollary 3.50
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61f22206aa5e16b7e4e99d92d008fa1dff959eaa | abstract | 0 | 29 | Abstract | Over the past decade, Airbnb has emerged as the most popular platform for
renting out single rooms or whole apartments. The impact of Airbnb listings on
local neighborhoods has been controversially discussed in many cities around
the world. The platform's widespread adoption led to changes in urban life, and
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5c28faa6d87e7a40b60c0c37b482160dc6d2b080 | subsection | 1 | 29 | Introduction | Airbnb, the largest digital peer-to-peer distribution platform for accommodations, operates in about 81,000 cities in 191 countries, offering 4.5 million rooms, apartments, houses, and other types of accommodation .
The widespread adoption of Airbnb led to changes in urban life and in particular urban tourism.
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8877d7d6e5a67f0030e8d54baf425e79fe3d32ca | subsection | 2 | 29 | Introduction | With regard to the CSCW community, he argues that the concept of place has been widely adapted to inform location-based technologies, whereas implications of a “discursive place shaping” on online platforms have not been considered yet.
With our research, we try to fill this gap.
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ae47633e374854fd0c587ebddc7a6c352b82c82f | subsection | 3 | 29 | Introduction | Moreover, we analyzed which practices are encouraged in the listings (see Sections REF , REF , REF ) and investigated how places named by Airbnb hosts and visitBerlin, the city's destination management and marketing organization (DMO), differ (see Sections REF and REF ).This paper provides a twofold contribution:
From... | {
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fc91d236edff55705f72c648552aad74760f512b | subsection | 4 | 29 | Theoretical Background | Understanding space and place on a conceptual level is a central goal of geography.
Much empirical work, however, deals with natural or cultural phenomena happening in distinct places.
Considering the nature of space just became popular again after the “spatial turn” in social sciences from the late 1960s onwards .
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a34b8a22ba69a3197a23525f30339053a0ecb1e7 | subsection | 5 | 29 | Traditional Understandings of Urban Tourism Space | Traditionally, tourism space, in the sense of a tourist destination, has been defined as a geographical area , that contains agglomerations of tourism-related attractions, facilities, and services , .
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417dfc7e8aed0c2e1522b5dccba5233ea6a1bbbd | subsection | 6 | 29 | Traditional Understandings of Urban Tourism Space | At the same time, increasing affluence, more leisure time, and the ubiquitous proliferation of the car and the rise of the airplane as a means of transportation enabled people to travel not only to the countryside but also to urban destinations .
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in Two Berlin Neighborhoods | [
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603b6bd71fdd089dcaa21c3b8456acb4a1c043fc | subsection | 7 | 29 | Constructing New Urban Tourism Space | Tourism in general and tourist behavior in particular have changed.
Tourists are no longer staying within the confines of the central tourist zone with major sights in walking distance and gastronomic infrastructure just around the corner.
Instead, many of them are now venturing into residential neighborhoods.
Urban to... | {
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4728792ed0c8c337df8d9fa7b81e47b691a86af0 | subsection | 8 | 29 | Constructing New Urban Tourism Space | Following Dourish’s point of view , we establish that such technologies influence the way people move through the city and encounter urban space.
Moreover, information on online platforms is no longer solely provided by the city's DMO.
Due to social web applications, many people can now produce content online, for exam... | {
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d9ff1e8247dfdfafee18962aacd227618814cc99 | subsection | 9 | 29 | Constructing New Urban Tourism Space | We argue that through the means of digital technologies, local people are now empowered to participate in the discourse producing and reproducing urban space.
[Figure: Overview of our conceptual approach: Airbnb hosts perceive their city and neighborhood and capture this perception in their listing descriptions. Guests... | {
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} | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
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e2ebda746ce8eea79b869b233acfa32dd881252c | subsection | 10 | 29 | From Theoretical Concepts to Empirical Research | The city depiction in Figure REF represents the city in its multitude of dimensions.
It stands for buildings and infrastructure, but likewise for people, for flows of information and capital, for images and feelings associated with it, for its various representations in pictures and discourses, and for everyday practic... | {
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7d3a12adfd90116dbd5a9d25e4caf7b3c91ec4be | subsection | 11 | 29 | From Theoretical Concepts to Empirical Research | We have theoretically motivated the relation of those digital descriptions to the physical world, that is the neighborhood and the city, and peoples' performances in that environment.
We consider it to be an important direction for future work to also analyze Airbnb from a user perspective.
On the one hand, one could e... | {
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} | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
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b126ba15270c6aecb146051a626a5c7376ad10e1 | subsection | 12 | 29 | Research Design | As motivated above, our goal was to analyze and compare how the two neighborhoods Kreuzkölln and City West are constructed as tourism spaces in Airbnb listing descriptions (RQ1 and RQ2).
For our analysis, we deliberately chose two very different neighborhoods.
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37526259e2b9e4a4d94e7d6c462d3a02f028da54 | subsection | 13 | 29 | Data Collection | To retrieve the Airbnb listings in the two neighborhoods, we utilized Tom Slee's airbnb-data-collection toolhttps://github.com/tomslee/airbnb-data-collection.
On March 22, 2017, we collected all listings within two bounding boxes encompassing the Kreuzkölln and City West areas.
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1ee5eec371e0b8a46723234883ebfe27aecfb515 | subsection | 14 | 29 | Data Collection | The retrieval failed for three hosts.
There is no universally accepted threshold for the number of listings that a host must provide to be considered professional.
Nevertheless, we observed that most hosts (80%) in the two areas provide only one listing.
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"raw": "visitBerlin. 2018e. Neukölln: Lively and bustling - and vibrantly diverse. (2018). https://www.visitberlin.de/en/districts/neukolln",
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7c5723a0cdb2c6de18cbc9946d64f170a3d0b25f | subsection | 15 | 29 | Qualitative Data Analysis | Figure REF shows an exemplary Airbnb listing from the Kreuzkölln neighborhood and visualizes where the information we analyzed is located on the Airbnb website.
The median length of the listing descriptions (including house rules) was 138.5 words for Kreuzkölln and 117.5 words for City West; the median title length was... | {
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4f56af36fb491cc089147a81625b66844d6e497a | subsection | 16 | 29 | Quantitative Data Analysis | After we finished our qualitative analysis of the listing descriptions, we used the resulting coding schema to compare those descriptions to the borough descriptions of visitBerlin (RQ3).
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1086d7e971a1689a4834e3bcd2d75d9f6b13851e | subsection | 17 | 29 | Results | In this section, we summarize key findings from our qualitative and quantitative data analyses. As described above, the four high-level concepts places, facilities, adjectives, and practices emerged from the qualitative data.
Table REF shows the number of listings in which particular places in the neighborhood or other... | {
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} | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
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4a8016d35355e0e359b99819bfa8237995828950 | subsection | 18 | 29 | Places and Facilities | To spatially reference the location of an Airbnb room or apartment in the city, it was common for hosts to name specific places in the neighborhood or in the city.
This is particularly true for the short listing headlines, which we analyzed first.
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8cf85cb32d775e72a0c9e0d78f79374d254a92b3 | subsection | 19 | 29 | Places and Facilities | In doing so, they contribute to the public discourse , , , , framing the neighborhood as a trendy and upcoming area, a so-called Szenekiez.
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da8d0a2b441a59556e180d02972455f162e5298a | subsection | 20 | 29 | Streets and Squares | Large streets and squares structure the urban fabric of a neighborhood.
In our case study, for each neighborhood one important street emerged from the listing descriptions.
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2562304aa155be0891bbb47a85074c0d08eb4984 | subsection | 21 | 29 | Sights, Parks, and Markets | Sights and other attractions, such as museums or art galleries, are often considered to be facilities that are primarily tourism-related and attract visitors.
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a0779145cf425a6f7561ef42c8658233aea2ecd4 | subsection | 22 | 29 | Sights, Parks, and Markets | Instead of gazing upon Landwehrkanal, hosts encouraged other practices.
They invited guests to “take a bike ride along the tree-lined Landwehr Canal” (4243519), to “stroll” along (6089778), to “hang out” (879602), or to “jog or take walks” (16462941).
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4f8b4752a6583950b1320de308725fc31b8e0fa6 | subsection | 23 | 29 | Sights, Parks, and Markets | This mix of people visiting it, and the offers that are still primarily dedicated to the local residents, mark it as an authentic place—a place that is not artificially designed to meet only visitors' needs.
[Table: Places mentioned by visitBerlin, the city's DMO, in their borough descriptions of Neukölln and Charlotte... | {
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} | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
in Two Berlin Neighborhoods | [
"Natalie Stors",
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0b11c8d418b5989221b3928641a94a26f94fc1f1 | subsection | 24 | 29 | Comparison with DMO Website | After extracting the places mentioned in visitBerlin's description of the two boroughs in which the neighborhoods Kreuzkölln and City West are located (see Section REF ), we first compared those places with the places frequently mentioned by Airbnb hosts (gray background in Table REF ).
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"raw": "visitBerlin. 2018e. Neukölln: Lively and bustling - and vibrantly diverse. (2018). https://www.visitberlin.de/en/districts/neukolln",
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d2ef8ca904405da0c4ac01e96e0b61167a9e7cc6 | subsection | 25 | 29 | Discussion | Questions regarding the conceptual nature of space and place have been addressed in both CSCW and human geography research.
For CSCW scholars, the main motivation to use spatial metaphors has long been to transfer spatial structures from the physical world into the digital realm .
Examples include the organization of t... | {
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"raw": "Steve Harrison and Paul Dourish. 1996. Re-Place-ing Space: The Roles of Place and Space in Collaborative Systems. In 1996 ACM Conference on Computer Supported Cooperative Work (CSCW 1996), Mark S. A... | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
in Two Berlin Neighborhoods | [
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211944b695d4423be98852619ed9a9687ab77afe | subsection | 26 | 29 | Discussion | Hosts encourage their guests to buy typical food in order to experience the neighborhoods' multicultural atmosphere.
As a result of these neighborhood descriptions, certain space images are collaboratively constructed and (re-)produced by Airbnb hosts.
In the case of Kreuzkölln, a residential area and its prevalent loc... | {
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"raw": "DWIF Consulting. 2017. 12 mal Berliner Leben, 12 mal Berlin erleben: Konzept für einen stadtverträglichen und nachhaltigen Berlin-Tourismus 2018+. (2017).",
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a8eb63220fe7b3c8a73b84d0cd0e2eee34cd3412 | subsection | 27 | 29 | Discussion | We thus hypothesize that digital information sharing platforms are more important in the production of new urban tourism areas than the city's DMO.Our finding that, through digital representations of space in Airbnb listing descriptions, mundane places can gain significance for visitors and thus transform into tourist ... | {
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"raw": "Jingfu Chen and Ningning Chen. 2016. Beyond the everyday? Rethinking place meanings in tourism. Tourism Geographies 19, 1 (2016), 9–26.",... | 10.1145/3274435 | 1809.03398 | Constructing Urban Tourism Space Digitally: A Study of Airbnb Listings
in Two Berlin Neighborhoods | [
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b48e447d8d200b59f46a68e2b50cef0e0ea1b817 | subsection | 28 | 29 | Conclusion and Future Work | In this paper, we illustrated how urban tourism space is (re-)produced digitally and collaboratively on online platforms.
In particular, we investigated how Airbnb hosts construct their neighborhoods as touristic places in their listing descriptions.
We followed a constructionist notion of space, building on existing r... | {
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"raw": "Edward W. Soja. 2009. Vom Zeitgeist zum Raumgeist: New Twists on the Spatial Turn. In Spatial Turn, Joerg Doering and Tristan Thielmann (Eds.). Transcript, Bielefeld, Germany, 241–262.",
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f015f28a62d61a1bd3126b5df0ef8cfa4be7f9be | abstract | 0 | 45 | Abstract | We consider the control of a three-dimensional thin liquid film on a flat
substrate, inclined at a non-zero angle to the horizontal. Controls are applied
via same-fluid blowing and suction through the substrate surface. We consider
both overlying and hanging films, where the liquid lies above or below the
substrate, re... | {
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} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
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88ed737c913fd1432e595209b9a27c2f23a067f3 | subsection | 1 | 45 | Introduction | The dynamics of thin liquid films in various physical situations form a range of classical and important problems in fluid mechanics, attracting a lot of attention from researchers in the field (see , and the references therein). In this work, we study the optimal control problem for a gravity-driven, thin, viscous liq... | {
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"Ruben J. Tomlin",
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989517d6df4e1eb90280f61987b9b4d8dbf76c28 | subsection | 2 | 45 | Introduction | This partial differential equation (PDE) exhibits a range of dynamical behaviours in windows of the bifurcation parameter L, including steady and travelling waves, time-periodic and quasi-periodic solutions, and full spatiotemporal chaos , , . It has been observed that (REF ) possesses a finite-dimensional global attra... | {
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4cb5f1428bf74003f3f529df3231f7e53602f0ac | subsection | 3 | 45 | Introduction | In a related study, Lin and Kondic considered the case of a non-wetted substrate with numerical simulations of a Benney equation, and observed that fluid fronts were unstable to a transverse fingering instability. Thin rivulets form with approximately equal width in the spanwise direction, with fast moving “drop-like" ... | {
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... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
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6222261e7f82bbe6d384ef633c97fb53fe83d26d | subsection | 4 | 45 | Introduction | The current paper is organised as follows: In section , we present the physical problem, and discuss the hierarchy of models culminating with (REF ). In section , we consider purely transverse controls, \zeta = \tilde{\zeta }(y,t). Seeking an optimal control of this form reduces to a linear quadratic regulator (LQR) pr... | {
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} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
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5b358f41eb5feed46f394c12561a5a2de221f9c0 | subsection | 5 | 45 | Physical problem and governing equations | We consider a Newtonian fluid with constant density \rho , dynamic viscosity \mu , and kinematic viscosity \nu , flowing under gravity along a flat infinite 2D substrate inclined at a non-zero angle \theta to the horizontal – the schematic of the problem is presented in Figure REF . Same-fluid blowing and suction contr... | {
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106120208792f939eba29e27d58acf9470b60326 | subsection | 6 | 45 | Physical problem and governing equations | The non-dimensional Navier–Stokes equations for this problem are{\operatorname{\mathit {R\hspace{-1.99997pt}e}}} \left( {u}_t + ({u} {\cdot } {\nabla } ){u} \right)= & - {\nabla } p + {\nabla }^2 {u} + 2 {\overline{g}} ,\\
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
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bee46026b3cf25873cb93b360bab4419b26d71f0 | subsection | 7 | 45 | Fully nonlinear Benney equation | In order to reduce the Navier–Stokes formulation to a forced evolution equation for the film thickness, we make a long-wave assumption.
The details of the following derivation are omitted since they are similar to those in for the case of a fully 3D model of an electrified thin film, and the derivation for the 2D case ... | {
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5ec115a6a7e66ed2171e2a8afec2219cdc823b00 | subsection | 8 | 45 | Fully nonlinear Benney equation | As observed by a number of authors , , , the uncontrolled 1D simplification (no spanwise variation) of this Benney equation exhibits finite-time blow-ups in numerical simulations. The existence of an optimal control for (REF ) is an open problem (lack of analytical results for the uncontrolled equation is problematic),... | {
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0019102381118a1e5893727c3b4254279d11e114 | subsection | 9 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | We seek to analyse the evolution of a sufficiently small perturbation about the non-dimensional exact constant solution to (REF ) given by H=1, F=0. For this, we substitute H = 1 + \delta \eta and F = 4 \delta ^2 \zeta into equation (REF ) where \eta , \zeta are O(1) quantities, and also assume that \cot \theta is O(1)... | {
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} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
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1c61c9cbba42df9d995ca9991f2eb29708ab445f | subsection | 10 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | Note that the rescaling (REF ) involves a Galilean transformation, so (REF ) is in a moving reference frame. For our investigation of optimal controls with actuators at every point on the substrate, the advection term makes no difference and the result in the moving frame can be translated back into the “lab" frame wit... | {
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c91361e770e1d2337fc6bf869569f544a4324455 | subsection | 11 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | The controls considered in this work can thus be thought of as moving fluid from one location to another, without changing the total fluid volume.From the ODE description (REF ), it can be observed that the dynamics of the transverse modes (i.e. k_1 = 0) are linear, being governed by\frac{\mathrm {d}}{\mathrm {d}t} \ti... | {
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af6ad15b90b4f2d84dac1e3cc3e0eb2ca26f8bb5 | subsection | 12 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | When \kappa = 0, the film is vertical, and the canonical equation (REF ) reduces to a forced version of the thin film equation obtained by Nepomnyashchy , ,\eta _t + \eta \eta _x + \eta _{xx} + \Delta ^2 \eta = \zeta .Without controls, this equation has been studied both analytically and numerically by a number of auth... | {
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"doi": "",
"end": 218,
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"raw": "A. A. Nepomnyashchy. Periodical motion in tridimensional space of fluid films running down a vertical plane. Hydrodynamics, Perm State Pedagogical Institute, 7:43–54, 1974.",
"source_ref_id": ... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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4842062f6f6afe19281a3b0c2978ba2cbf78a294 | subsection | 13 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | We denote the three components of the cost functional by \mathcal {C}_{s,\gamma }^{(1)}, \mathcal {C}_{s,\gamma }^{(2)}, and \mathcal {C}_{s,\gamma }^{(3)}, respectively. The optimal control \zeta ^* and associated optimal state \eta ^* (which solves the KSE (REF ) with \zeta = \zeta ^*) are defined as minimisers of th... | {
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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7a59983a8063dd6eabc1f0f76a53b3ef3303fac3 | subsection | 14 | 45 | Weakly nonlinear evolution: 2D Kuramoto–Sivashinsky equation | These schemes were utilised for the corresponding 1D optimal control problem by Gomes et al. , and their applicability was checked for similar multi-dimensional problems in (including a convergence study) and for a non-local problem. In order to perform computations, we truncate the Fourier series (REF ) to |k_1| \le M... | {
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"raw": "S. N. Gomes, D. T. Papageorgiou, and G. A. Pavliotis. Stabilizing non-trivial solutions of the generalized Kuramoto–Sivashinsky equation using feedback and optimal control. IMA J. Appl. Math., pages... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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c8505c064ce1d5ef8ea1e1118f2e33adb40763ed | subsection | 15 | 45 | Optimal transverse control for hanging films | We first consider controlling the transverse instabilities present for hanging films (\kappa < 0) by applying controls of the form \zeta = \tilde{\zeta }(y,t) (with \tilde{\zeta }_{0} = 0). We work under the assumption that the dynamics of
(REF ) are bounded if the linear growth in the spanwise dimension is controlled.... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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81866335c50289b77761a33de38982173e1376f8 | subsection | 16 | 45 | Optimal transverse control for hanging films | The desired state is taken to be the orthogonal projection \overline{\eta } = (I -\tilde{P}_{\Xi }) \eta = \eta - \tilde{\eta }_{\textrm {u}}, with no components of unstable transverse modes. It is important to note that due to the slaving of the streamwise and mixed modes to the transverse modes, \overline{\eta } is n... | {
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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e4e6b1ec6cf7ea53537bcba18f9efc14e6b1d369 | subsection | 17 | 45 | Optimal transverse control for hanging films | The optimal control (derived in appendix ) is given by
\tilde{\zeta }_{k_2}^* = r_{k_2}\tilde{\eta }_{k_2}^* (with stars denoting optimality) where r_{k_2} satisfies a Riccati equation and final time boundary condition\frac{\mathrm {d}}{\mathrm {d}t}r_{k_2} = - r_{k_2}^2 + 2 (\kappa \tilde{k}_2^2 + \tilde{k}_2^4) r_{k_... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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76ca3dda322bc9424467bc01c99711cf7884cf8a | subsection | 18 | 45 | Optimal transverse control for hanging films | Substituting back into (REF ) yields the solution\tilde{\eta }_{k_2}^* = \exp \left( - t \; \sqrt{ (\kappa \tilde{k}_2^2 + \tilde{k}_2^4)^2 + |\tilde{k}_2|^{2s}/\gamma } \right)\tilde{v}_{k_2},where the optimal control is defined by \tilde{\zeta }_{k_2}^* = \lambda _{-} \tilde{\eta }_{k_2}^*.
[Figure: Application of op... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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ed0348da4679ae920b1673c5a1603a56801eb48c | subsection | 19 | 45 | Optimal transverse control for hanging films | With the application of the optimal transverse controls, the H_0^2-norm of the unstable modes and the L_0^2-norm of the control decay exponentially as shown in Figure REF (c), and the energy of the full solution remains bounded as desired with a modal steady state (dominated by the (m,2m)-modes for m\in \mathbb {Z}) em... | {
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
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"physics.flu-dyn"
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00e62d8b54c3630497bdc21b5471d5340c725bee | subsection | 20 | 45 | Optimal transverse control for hanging films | With the length parameters L_1 = 40 and L_2 = 27, as in case (ii), we find mostly chaotic dynamics as \kappa is decreased to -0.44, below which a time-periodic attractor emerges. This behaviour dominates until \kappa = -0.58 when steady modal waves dominated by the (m,3m)-modes for m\in \mathbb {Z} appear – this is sim... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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cf83dab8865106bf1780ee6ba49323a88bc0ebc3 | subsection | 21 | 45 | Full optimal control | In this section, we consider the general optimal control problem for the 2D KSE (REF ), where the set of admissible controls F_{\textrm {ad}} is a non-empty, closed, convex subset of L^2(0,T;L_0^2). We consider the existence of an optimiser for our problem, and then give the methodology for numerical simulations. In co... | {
"cite_spans": [
{
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"raw": "J.L. Lions. Quelques méthodes de résolution des problèmes aux limites non linéaires. Etudes mathématiques. Dunod, 1969.",
"source_ref_id": "c6d6eed7a2bf97ea6b43... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
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cd48b1c39b1a851d34331b1bcda3e52ebb2b4354 | subsection | 22 | 45 | Full optimal control | The optimal control problem can thus be recast as the problem of finding the minimiser of \tilde{\mathcal {C}}_{s,\gamma }(\zeta ) over F_{\textrm {ad}}. It makes sense to check that there exist \zeta \in F_{\textrm {ad}} which give a finite value of \tilde{\mathcal {C}}_{s,\gamma }. The boundedness of the first and la... | {
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"raw": "F. Tröltzsch. Optimal Control of Partial Differential Equations: Theory, Methods, and Applications. American Mathematical Society, 2010.",
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"Ruben J. Tomlin",
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835a2d2d578f725707bc41e0cc40e5fa78900fea | subsection | 23 | 45 | Full optimal control | Then, the sequence \lbrace \zeta ^{(n)}\rbrace _{n=1}^{\infty } \subseteq K has a weakly convergent subsequence \zeta ^{(n)} \rightharpoonup \zeta ^* for the topology of L^2(0,T;L_0^2) (not relabelled for simplicity) with weak limit \zeta ^* \in K \subseteq F_{\textrm {ad}}. For more general forms of cost functional, i... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
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31072317c9a7de01d17ca702b1b7efec5c121492 | subsection | 24 | 45 | Full optimal control | To deal with the nonlinearity, we use the estimate\Vert \eta ^{(n)} \eta ^{(n)}_x \Vert _{H_0^{-1}} \le \frac{1}{2} \Vert (\eta ^{(n)})^2 \Vert _{L_0^{2}} \le \frac{1}{2} \Vert \eta ^{(n)} \Vert _{L^{\infty }} \Vert \eta ^{(n)} \Vert _{L_0^{2}} \le \widehat{C}\Vert \eta ^{(n)} \Vert _{H_0^2} \Vert \eta ^{(n)} \Vert _{L... | {
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
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c7221cdce42b6c680478a6399b94d6b5da218905 | subsection | 25 | 45 | Full optimal control | With this and the weak convergence result (REF a), it follows from Thm 8.1 in (a compactness result) that\eta ^{(n)} \rightarrow \eta ^* \; \textrm {strongly in} \; L^2(0,T;H_0^s), \textrm { for } s < 2.We now check that the weak limits satisfy the control-to-state map, \eta ^* = \eta (\zeta ^*;v) – the pair (\eta ^*,\... | {
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"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
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8696994960a00b60552187e13e41dda9edea5e43 | subsection | 26 | 45 | Full optimal control | Since \lbrace \eta ^{(n)}_t \rbrace _{n=1}^{\infty } is bounded uniformly in L^2(0,T,H_0^{-2}) \subset L^2(0,T,(H_0^{2})^*), it is weakly convergent, and furthermore by a density argument we can conclude that the weak limit is \eta _t^*. Since the sequence
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"Ruben J. Tomlin",
"Susana N. Gomes",
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90c0bab22ee976e5241e616d7e3ac3e187489e8a | subsection | 27 | 45 | Full optimal control | The first-order conditions of optimality for a local optimiser (\eta ^*, \zeta ^*, p^*) consist of the governing equation (REF ), an adjoint equation, and a variational inequality. The governing equation arises from the functional (Fréchet) derivative of \mathcal {L} with respect to the adjoint variable p, and taking t... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
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f449a19dc44d18fbcec785a0bdcee419c85bf826 | subsection | 28 | 45 | Full optimal control | Note that (REF ) may be written in the form- p_t + \mathcal {A}p = \mathcal {B}^{\prime }(p;\eta ,\overline{\eta }), \qquad \mathcal {B}^{\prime }(p;\eta ,\overline{\eta }) = (I - P_{{0}}) \eta p_x + (-\Delta )^s(\eta - \overline{\eta }) + cp,where \mathcal {A} is defined by (REF a). Thus, the BDF methods outlined in s... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
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61e10f65a3bde72ad5f2d9719bfb35d664a9b942 | subsection | 29 | 45 | Full optimal control | \mathcal {C}_{s,\gamma }(n+1) \ge \mathcal {C}_{s,\gamma }(n)
c^{(m)} = c^{(m)}/2 for m \ge n.
Update control \zeta ^{(n+1)} =(1 - c^{(n)})\zeta ^{(n)} - c^{(n)} p^{(n)}/\gamma .
\eta ^{(n)}, \zeta ^{(n)}.
The returned values (\eta ^{(n)},\zeta ^{(n)}) are a minimising sequence as in Theorem REF , with limit approxim... | {
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{
"arxiv_id": "",
"doi": "10.1201/9781420011418",
"end": 905,
"openalex_id": "https://openalex.org/W231975775",
"raw": "Suzanne Lenhart and John T Workman. Optimal control applied to biological models. Crc Press, 2007.",
"source_ref_id": "caea40e69bd2a528998d4... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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b40eaee2cc8b152c30619dfe2200d149c6116686 | subsection | 30 | 45 | Full optimal control | The dotted lines are with points at half-integers represent the gradient descent steps which resulted in larger costs, resulting in step-halving; the faded dashed line taking values on the right axis is the step c^{(n)}.]For the first numerical experiment, we take L_1 = L_2 = 21, and cover the three different dynamical... | {
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"doi": "10.1017/jfm.2017.250",
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"raw": "R. J. Tomlin, D. T. Papageorgiou, and G. A. Pavliotis. Three-dimensional wave evolution on electrified falling films. Journal of Fluid Mechanics, ... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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91b8da5b10d95512c5b0041c135d94ef1d15adb4 | subsection | 31 | 45 | Full optimal control | Rows 2 to 4 correspond to the uncontrolled case, with cost components \mathcal {C}_{0,1}^{(1)}, \mathcal {C}_{0,1}^{(2)} (note that \mathcal {C}_{0,1}^{(3)} = 0 for \zeta = 0) and total cost \mathcal {C}_{0,1} – these are observed to be decreasing functions of \kappa . The next four rows give the optimal cost and its b... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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5af71b328e2b19a8844cd1dc375ada51e5d767ea | subsection | 32 | 45 | Full optimal control | We consider three cases, (i),(ii), and (iii), of initial conditions and time-dependent desired states,v = \sin \left(\frac{4\pi x}{L_1} \right) + \delta _{\textrm {(ii)}}\cos \left(\frac{2\pi x}{L_1} + \frac{2\pi y}{L_2} \right), \quad \overline{\eta } = \sin \left(\frac{2\pi (x - t)}{L_1} \right) + \delta _{\textrm {(... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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05676a2f49c4d7438d8ce5ea18d3e41c67403557 | subsection | 33 | 45 | Full optimal control | For these two cases, the L_0^2-norms of the projections \tilde{P}(\eta ^* - \overline{\eta }) and \tilde{P}\zeta ^* are included in Figure REF (c,d), and visualisations of the time evolution are given in Supplementary Movies 2 (available at https://youtu.be/V24mi-C8n1g) and 3 (available at https://youtu.be/hfcmplP83fQ)... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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1ac08e0a36631e7b3725bc8d9842136601e89957 | subsection | 34 | 45 | Transverse mode effects | In this section, we briefly examine the extent to which controlled transverse modes can affect the streamwise and mixed modes through the nonlinear coupling – see the ODE system of Fourier coefficients (REF ). In this way, purely transverse controls (such as those studied in section ) may be thought of as indirect cont... | {
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{
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"raw": "R. J. Tomlin, A. Kalogirou, and D. T. Papageorgiou. Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space di... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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525a333633d23fb044704738b851e987c26b62e1 | subsection | 35 | 45 | Transverse mode effects | Another appealing property of a controlled system would be the regularisation of chaos.The appropriate choice of desired state for this study is \overline{\eta } = (I - \tilde{P}_{\Sigma }) \eta + \tilde{\psi }(y,t), where \Sigma is the set of transverse Fourier modes which we can force (\tilde{P}_{\Sigma } is a projec... | {
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{
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"raw": "R. J. Tomlin, A. Kalogirou, and D. T. Papageorgiou. Nonlinear dynamics of a dispersive anisotropic Kuramoto–Sivashinsky equation in two space d... | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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ee1eceea4f16c344a7be2a236d826d3dd9585416 | subsection | 36 | 45 | Transverse mode effects | Panel (a) shows that an increase in A results in decay of the energy density of \eta - \tilde{\eta } (this decrease is monotonic in most cases). Furthermore, we find that the chaotic dynamics are eventually regularised for a sufficiently large value of A, and the transverse wave eventually becomes nonlinearly stable wh... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
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34f0b3408ca62659d3ea818b04658ddf2443a10e | subsection | 37 | 45 | Transverse mode effects | In terms of the infinite-dimensional system of Fourier modes, the linearisation of (REF ) about \eta = \tilde{\eta } = \tilde{\psi } for a general \tilde{\psi }(y,t) is\frac{\mathrm {d}}{\mathrm {d}t}\eta _{{m}} = - i\tilde{m}_1 \sum _{l_2\in \mathbb {Z}} \eta _{(m_1, m_2 - l_2)} \tilde{\psi }_{l_2} + \left[ (1-\kappa ... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
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d245b7391955d88ec46d7a7c96881f496ecdb1af | subsection | 38 | 45 | Conclusions | In this paper we considered the distributed control of a Kuramoto–Sivashinsky equation for gravity-driven thin film flow overlying or hanging from a 2D flat substrate. Blowing and suction controls applied at the substrate surface appear as a forcing term in the weakly-nonlinear evolution equation.For hanging films (\ka... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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86c85dc37b3d7d06ce5080ea5d736aa1ca8a2938 | subsection | 39 | 45 | Conclusions | With extensive numerical simulations, we found that small amplitude sinusoidal transverse waves yielded a decrease in the average energy of the fluid interface, with large amplitude waves being nonlinearly stable, regularising the chaotic dynamics.A large motivation for this paper and current work by the authors is in ... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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e3886b6015720aade7df771fa228a00ce1767a91 | subsection | 40 | 45 | Derivation of optimal transverse control | We now give a brief derivation of the optimal control for an LQR tracker problem for the transverse system (REF ). We consider the general desired state\overline{\eta } = (I -\tilde{P}_{\Sigma }) \eta + \tilde{\psi }(y,t), \qquad \tilde{\psi }(y,t) = \sum _{k_2 \in \Sigma } \tilde{\psi }_{k_2}(t) e^{i\tilde{k}_2 y}.Her... | {
"cite_spans": []
} | 1805.08236 | Optimal control of thin liquid films and transverse mode effects | [
"Ruben J. Tomlin",
"Susana N. Gomes",
"Grigorios A. Pavliotis",
"Demetrios T. Papageorgiou"
] | [
"physics.flu-dyn"
] | 2,018 | en | Physics | [
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