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Maximal Volume of Curved Folding Boxes
"... 12.08> 1 sin at with a # (0,#/2], the volume V (f) takes the maximal value # 0.7414 when a # 1.2215, a result of N. Reed [4]. The feature of cut squares are shown in Figures 1, 2 and 3. For the general problem, we obtain the following solution. Solution. The volume V (f) takes the maximal ..."
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12.08> 1 sin at with a # (0,#/2], the volume V (f) takes the maximal value # 0.7414 when a # 1.2215, a result of N. Reed [4]. The feature of cut squares are shown in Figures 1, 2 and 3. For the general problem, we obtain the following solution. Solution. The volume V (f) takes the maximal value (4/3)# 2 # 0.7757 when the function f is in the form f(t)=# 1 sn(#t, # 2) cn(#t, # 2) ,#= #/2 agm(1, # 2) # 1.3110, (1) where agm(1, # 2) is the arithmeticgeometri
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k
Fast Folding and Comparison of RNA Secondary Structures (The Vienna RNA Package)
"... Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and bas ..."
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Cited by 812 (119 self)
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and base pairing probabilities. An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment. All computer codes are written in ANSI C. They include
The use of the area under the ROC curve in the evaluation of machine learning algorithms
 Pattern Recognition
, 1997
"... AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multilayer Percept ..."
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Cited by 664 (3 self)
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AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multi
Creative Commons Attribution RESEARCH ARTICLE Optimal design of curved folded plates
"... The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip meth ..."
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The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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’ of holomorphic curves of higher genus curves in Calabi–Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N = 2
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves
The Vocabulary Problem in HumanSystem Communication
 COMMUNICATIONS OF THE ACM
, 1987
"... In almost all computer applications, users must enter correct words for the desired objects or actions. For success without extensive training, or in firsttries for new targets, the system must recognize terms that will be chosen spontaneously. We studied spontaneous word choice for objects in five ..."
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Cited by 551 (8 self)
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. For example, the popular approach in which access is via one designer's favorite single word will result in 8090 percent failure rates in many common situations. An optimal strategy, unlimited aliasing, is derived and shown to be capable of severalfold improvements.
Alternative isoform regulation in human tissue transcriptomes
 Nature
, 2008
"... Through alternative processing of premRNAs, individual mammalian genes often produce multiple mRNA and protein isoforms that may have related, distinct or even opposing functions. Here we report an indepth analysis of 15 diverse human tissue and cell line transcriptomes based on deep sequencing of ..."
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Cited by 525 (4 self)
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specific read densities indicated that a majority of AS and of alternative cleavage and polyadenylation (APA) events vary between tissues, while variation between individuals was ∼2 to 3fold less common. Extreme or ‘switchlike ’ regulation of splicing between tissues was associated with increased sequence
The Cyclical Behavior of Equilibrium Unemployment and Vacancies
 American Economic Review
, 2005
"... This paper argues that a broad class of search models cannot generate the observed businesscyclefrequency fluctuations in unemployment and job vacancies in response to shocks of a plausible magnitude. In the U.S., the vacancyunemployment ratio is 20 times as volatile as average labor productivity ..."
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Cited by 839 (20 self)
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of the model. I show that a shock that changes average labor productivity primarily alters the present value of wages, generating only a small movement along a downward sloping Beveridge curve (unemploymentvacancy locus). A shock to the job destruction rate generates a counterfactually positive correlation
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