7,548 research outputs found
Lens spaces, rational balls and the ribbon conjecture
We apply Donaldson's theorem on the intersection forms of definite
4--manifolds to characterize the lens spaces which smoothly bound rational
homology 4--dimensional balls. Our result implies, in particular, that every
smoothly slice 2--bridge knot is ribbon, proving the ribbon conjecture for
2--bridge knots.Comment: 45 pages, 8 figures; accepted for publication in Geometry and
Topolog
Evolution or revolution? a study of price and wage volatility in England, 1200-1900
Using annual data 1209-1914, this paper examines whether there are structural breaks in the movements of prices and wages that correspond to the major ārevolutionsā identified in historical narratives. Econometric modelling of trend and volatility in prices and wages confirms the importance of the Commercial Revolution and the Glorious Revolution, but suggests that the Industrial Revolution may be better described in evolutionary terms. The evidence also points to a late medieval revolution at the time of the Good Parliament, shortly after the Black Death and just before the Peasantās Revolt. This supports Britnell and Campbellās commercialisation hypothesis - that the institutional pre-conditions for the Industrial Revolution began to develop at a very early date.Economic evolution; Economic revolution; Historical economics;
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The theory of international business: the role of economic models
This paper reviews the scope for economic modelling in international business studies. It argues for multi-level theory based on classic internalisation theory. It present a systems approach that encompasses both firm-level and industry-level analysis
On the slice genus of links
We define Casson-Gordon sigma-invariants for links and give a lower bound of
the slice genus of a link in terms of these invariants. We study as an example
a family of two component links of genus h and show that their slice genus is
h, whereas the Murasugi-Tristram inequality does not obstruct this link from
bounding an annulus in the 4-ball.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-30.abs.htm
Derivatives of Knots and Second-order Signatures
We define a set of "second-order" L^(2)-signature invariants for any
algebraically slice knot. These obstruct a knot's being a slice knot and
generalize Casson-Gordon invariants, which we consider to be "first-order
signatures". As one application we prove: If K is a genus one slice knot then,
on any genus one Seifert surface, there exists a homologically essential simple
closed curve of self-linking zero, which has vanishing zero-th order signature
and a vanishing first-order signature. This extends theorems of Cooper and
Gilmer. We introduce a geometric notion, that of a derivative of a knot with
respect to a metabolizer. We also introduce a new equivalence relation,
generalizing homology cobordism, called null-bordism.Comment: 40 pages, 22 figures, typographical corrections, to appear in Alg.
Geom. Topolog
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Modelling the medieval economy: money, prices and income in England, 1263-1520
This chapter presents a simple econometric model of the medieval English economy, focusing on the relationship between money, prices and incomes. The model is estimated using annual data for the period 1263-1520 obtained from various sources. The start date is determined by the availability of continuous runs of annual data, while the finishing date immediately precedes the take-off of Tudor price inflation. Accounts from the ecclesiastical and monastic estates have survived in great numbers for this period, thereby ensuring that crop yields can be estimated from a regionally representative set of estates
Filtering smooth concordance classes of topologically slice knots
We propose and analyze a structure with which to organize the difference
between a knot in the 3-sphere bounding a topologically embedded 2-disk in the
4-ball and it bounding a smoothly embedded disk. The n-solvable filtration of
the topological knot concordance group, due to Cochran-Orr-Teichner, may be
complete in the sense that any knot in the intersection of its terms may well
be topologically slice. However, the natural extension of this filtration to
what is called the n-solvable filtration of the smooth knot concordance group,
is unsatisfactory because any topologically slice knot lies in every term of
the filtration. To ameliorate this we investigate a new filtration, {B_n}, that
is simultaneously a refinement of the n-solvable filtration and a
generalization of notions of positivity studied by Gompf and Cochran. We show
that each B_n/B_{n+1} has infinite rank. But our primary interest is in the
induced filtration, {T_n}, on the subgroup, T, of knots that are topologically
slice. We prove that T/T_0 is large, detected by gauge-theoretic invariants and
the tau, s, and epsilon-invariants; while the non-triviliality of T_0/T_1 can
be detected by certain d-invariants. All of these concordance obstructions
vanish for knots in T_1. Nonetheless, going beyond this, our main result is
that T_1/T_2 has positive rank. Moreover under a "weak homotopy-ribbon"
condition, we show that each T_n/T_{n+1} has positive rank. These results
suggest that, even among topologically slice knots, the fundamental group is
responsible for a wide range of complexity.Comment: 41 pages, slightly revised introduction, minor corrections and
up-dated references, this is the final version to appear in Geometry and
Topolog
Revolutionary change and structural breaks: A time series analysis of wages and commodity prices in Britain 1264-1913
In this paper we empirically test the hypothesis that economic revolutions are associated with structural breaks in historical economic data. A simple test for structural breaks in economic time series is applied to British wage and price data from the medieval to the modern period. Evidence for structural change is found in nearly half of the series studied -- suggesting that structural breaks are an intrinsic feature of such historic data. Structural changes are most closely linked to the Commercial Revolution followed by the Agricultural Revolution and the Industrial Revolution, with changes linked to an underlying process of price stabilisation as measured by a decrease in the long-term level of volatility.historical economics; economic revolutions; structural breaks; price stabilisation
Knot Concordance and Higher-Order Blanchfield Duality
In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of
the classical knot concordance group C. The filtration is important because of
its strong connection to the classification of topological 4-manifolds. Here we
introduce new techniques for studying C and use them to prove that, for each
natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish
the same result for the corresponding filtration of the smooth concordance
group. We also resolve a long-standing question as to whether certain natural
families of knots, first considered by Casson-Gordon and Gilmer, contain slice
knots.Comment: Corrected Figure in Example 8.4, Added Remark 5.11 pointing out an
important strengthening of Theorem 5.9 that is needed in a subsequent pape
Performance metrics for characterization of a seizure detection algorithm for offline and online use
Purpose: To select appropriate previously reported performance metrics to evaluate a new seizure detection algorithm for offline and online analysis, and thus quantify any performance variation between these metrics. Methods: Traditional offline algorithms mark out any EEG section (epoch) of a seizure (event), so that neurologists only analyze the detected and adjacent sections. Thus, offline algorithms could be evaluated using number of correctly detected events, or event-based sensitivity (SEVENT), and epoch-based specificity (percentage of incorrectly detected background epochs). In contrast, online seizure detection (especially, data selection) algorithms select for transmission only the detected EEG sections and hence need to detect the entire duration of a seizure. Thus, online algorithms could be evaluated using percentage of correctly detected seizure duration, or epoch-based sensitivity (SEPOCH), and epoch-based specificity. Here, a new seizure detection algorithm is evaluated using the selected performance metrics for epoch duration ranging from 1s to 60s. Results: For 1s epochs, the area under the event-based sensitivity-specificity curve was 0.95 whilst SEPOCH achieves 0.81. This difference is not surprising, as intuitively, detecting any epoch within a seizure is easier than detecting every epoch - especially as seizures evolve over time. For longer epochs of 30s or 60s, SEVENT falls to 0.84 and 0.82 respectively and SEPOCH reduces to 0.76. Here, decreased SEVENT shows that fewer seizures are detected, possibly due to easy-to-detect short seizure sections being masked by surrounding EEG. However, detecting one long epoch constitutes a larger percentage of a seizure than a shorter one and thus SEPOCH does not decrease proportionately. Conclusions: Traditional offline and online seizure detection algorithms require different metrics to effectively evaluate their performance for their respective applications. Using such metrics, it has been shown that a decrease in performance may be expected when an offline seizure detection algorithm (especially with short epoch duration) is used for online analysis.Accepted versio
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