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Two Time Physics with a Minimum Length
, 2008
"... We study the possibility of introducing the classical analogue of Snyder’s Lorentzcovariant noncommutative spacetime in twotime physics theory. In the free theory we find that this is possible because there is a broken local scale invariance of the action. When background gauge fields are present ..."
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We study the possibility of introducing the classical analogue of Snyder’s Lorentzcovariant noncommutative spacetime in twotime physics theory. In the free theory we find that this is possible because there is a broken local scale invariance of the action. When background gauge fields are present, they must satisfy certain conditions very similar to the ones first obtained by Dirac in 1936. These conditions preserve the local and global invariances of the action and leads to a Snyder spacetime with background gauge fields. 1
A sentimental education: Sentiment analysis using subjectivity summarization based on minimum cuts
 In Proceedings of the ACL
, 2004
"... Sentiment analysis seeks to identify the viewpoint(s) underlying a text span; an example application is classifying a movie review as “thumbs up” or “thumbs down”. To determine this sentiment polarity, we propose a novel machinelearning method that applies textcategorization techniques to just the ..."
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Cited by 589 (7 self)
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the subjective portions of the document. Extracting these portions can be implemented using efficient techniques for finding minimum cuts in graphs; this greatly facilitates incorporation of crosssentence contextual constraints. Publication info: Proceedings of the ACL, 2004. 1
Innocuous Implications of a Minimum Length in Quantum Gravity
, 2008
"... A modification to the timeenergy uncertainty relation in quantum gravity has been interpreted as increasing the duration of fluctuations producing virtual black holes with masses greater than the Planck mass. I point out that such virtual black holes have an exponential factor arising from the acti ..."
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A modification to the timeenergy uncertainty relation in quantum gravity has been interpreted as increasing the duration of fluctuations producing virtual black holes with masses greater than the Planck mass. I point out that such virtual black holes have an exponential factor arising from the action such that their contribution to proton decay is suppressed, rather than enhanced, relative to Planckmass black holes. frampton@physics.unc.edu In a remarkable paper Sakharov [1] not only provided his wellknown requirements for baryogensis in the early universe but also made the first theoretical estimate of the proton lifetime. Ignoring all factors of order O(1), as I shall do throughout, his formula had the form τp ∼ M4 Planck M 5 p (1) and gives a value τp ∼ 10 45 y. This contains only the contribution of quantum gravity and the lifetime in Eq. (1) is far too long for practical measurement. The present emprical lower bound [2] on τp is only τp ∼ 5 × 10 33 y. Although Sakharov did not use the language of spacetime foam, the Euclidean path integral approach to quantum gravity provides the means to make a similar estimate of the proton lifetime [3]. The amplitude for producing a black hole through a fluctuation of the spacetime metric leads to a density of Plancksize black holes of order one, in dimensionless units. The estimate for the proton decay rate arises from looking at virtual black holes (hereafter VBHs) with masses in the vicinity of the Planck mass. VBHs underly, from this viewpoint, the proton lifetime formula found by Sakharov as in Eq.(1). To arrive at Eq.(1) employing parallel methods to insights in [3], there is, in general, an exponential tunneling factor [4]. When the VBH has a mass close to the Planck mass, the exponential factor is of order one, O(1), and so does not survive in Eq.(1). For the case of VBHs which are significantly heavier than the Planck mass, MV BH = ηMPlanck with η ≫ 1 there was recently an interesting paper [5] which merits further study. It arrives at the following formula for the proton lifetime
Computing Minimum Length Paths of a Given Homotopy Class
 Comput. Geom. Theory Appl
, 1991
"... In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides reveal ..."
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Cited by 93 (6 self)
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revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified lineartime algorithms for shortest path trees, for minimumlink paths in simple polygons, and for paths restricted to c given orientations. 1 Introduction
New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface
, 1994
"... Abstract Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude (M), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resultin ..."
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Cited by 524 (0 self)
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Abstract Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude (M), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event
Independent Minimum Length Programs to Translate Between Given Strings
"... A string p is called a program to compute y given x if U (p; x) = y, where U denotes universal programming language. Kolmogorov complexity K(yjx) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(xjempty string) (Kolmogorov complexity of x) and let ..."
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Cited by 26 (0 self)
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A string p is called a program to compute y given x if U (p; x) = y, where U denotes universal programming language. Kolmogorov complexity K(yjx) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(xjempty string) (Kolmogorov complexity of x
Hitting Set, Spanning Trees, and the Minimum Length Corridor Problem
, 2008
"... 1 Introduction We consider a problem that is a combination of hitting set and minimum spanning trees that generalizes the minimum length corridor problem. In the minimum length corridor problem, we are given a rectangle aligned with the axes in the plane that is subdivided into smaller rectangles al ..."
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1 Introduction We consider a problem that is a combination of hitting set and minimum spanning trees that generalizes the minimum length corridor problem. In the minimum length corridor problem, we are given a rectangle aligned with the axes in the plane that is subdivided into smaller rectangles
MinimumLength Polygons of FirstClass Simple CubeCurve
 In Proc. Computer Analysis Images Patterns, LNCS 3691
, 2005
"... Abstract. We consider simple cubecurves in the orthogonal 3D grid. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve’s length is defined to be that of the minimumlength polygonal curve (MLP) fully contained and complete i ..."
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Cited by 2 (2 self)
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Abstract. We consider simple cubecurves in the orthogonal 3D grid. The union of all cells contained in such a curve (also called the tube of this curve) is a polyhedrally bounded set. The curve’s length is defined to be that of the minimumlength polygonal curve (MLP) fully contained and complete
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