Browsing FAS Scholarly Articles by FAS Department "Mathematics"
Now showing items 120 of 403

The 2.1D Sketch
(IEEE Computer Society Press, 1990)A model is described for image segmentation that tries to capture the lowlevel depth reconstruction exhibited in early human vision, giving an important role to edge terminations. The problem is to find a decomposition ... 
2DShape Analysis Using Conformal Mapping
(Springer Verlag, 2006)The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural ... 
4Manifolds With Inequivalent Symplectic Forms and 3Manifolds With Inequivalent Fibrations
(International Press, 1999)We exhibit a closed, simply connected 4manifold \(X\) carrying two symplectic structures whose ﬁrst Chern classes in \(H^2 (X, \mathbb{Z})\) lie in disjoint orbits of the diffeomorphism group of \(X\). Consequently, the ... 
The ABC's of Number Theory
(Harvard University, 2007)The ABC conjecture is a central open problem in modern number theory, connecting results, techniques and questions ranging from elementary number theory and algebra to the arithmetic of elliptic curves to algebraic geometry ... 
About Hermann Weyl’s “Ramifications, Old and New, of the Eigenvalue Problem”
(American Mathematical Society (AMS), 20120501) 
Abstract 2374: Reconstructing the evolutionary history of metastatic cancers
(American Association for Cancer Research (AACR), 2016)Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genomewide sequencing data has enabled modern phylogenomic ... 
Abundance Conjecture
(International Press, 2010)We sketch a proof of the abundance conjecture that the Kodaira dimension of a compact complex algebraic manifold equals its numerical Kodaira dimension. The proof consists of the following three parts: (i) the case of ... 
Accumulation of Driver and Passenger Mutations During Tumor Progression
(National Academy of Sciences, 2010)Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major ... 
The Alexander Polynomial of a 3Manifold and the Thurston Norm on Cohomology
(Elsevier, 2002)Let M be a connected, compact, orientable 3manifold with \(b_1(M)>1\), whose boundary (if any) is a union of tori. Our main result is the inequality \({\parallel \phi \parallel}_A \le {\parallel \phi \parallel}_T\) between ... 
An Algebraic Surface with \(K\) ample, \((K^2)= 9, p_g = q = 0\)
(Johns Hopkins University Press, 1979) 
Amenability, Poincaré Series and Quasiconformal Maps
(Springer Verlag, 1989)Any covering \(Y \rightarrow X\) of a hyperbolic Riemann surface\(X\) of finite area determines an inclusion of Teichmüller spaces \(Teich(X) \hookrightarrow Teich(Y)\). We show this map is an isometry for the Teichmüller ... 
Amenable Coverings of Complex Manifolds and Holomorphic Probability Measures
(Springer Verlag, 1992) 
Amplification on Undirected Population Structures: Comets Beat Stars
(Springer Nature, 2017)The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population. The fixation probability is a fundamental quantity of natural selection, and ... 
Analytical Results for Individual and Group Selection of Any Intensity
(Springer Verlag, 2008)The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic ... 
Another Realization of the Category of Modules Over the Small Quantum Group
(Elsevier BV, 200301)Let g be a semisimple simplyconnected Lie algebra and let Ul be the corresponding quantum group with divided powers, where is an even order root of unity. Let in addition u(l) subset of Ul be the corresponding "small" ... 
Antiretroviral dynamics determines HIV evolution and predicts therapy outcome
(Nature Publishing Group, 2012)Despite the high inhibition of viral replication achieved by current antiHIV drugs, many patients fail treatment, often with emergence of drugresistant virus. Clinical observations show that the relationship between ... 
Area and Hausdorff Dimension of Julia Sets of Entire Functions
(American Mathematical Society, 1987)We show the Julia set of \(\lambda\sin(z)\) has positive area and the action of \(\lambda\sin(z)\) on its Julia set is not ergodic; the Julia set of \(\lambda\exp(z)\) has Hausdorff dimension two but in the presence of ... 
Arithmetic on Curves
(American Mathematical Society (AMS), 19860401) 
Asymptotic dynamics of nonlinear Schrödinger equations: Resonancedominated and dispersiondominated solutions
(WileyBlackwell, 2001)We consider a linear Schrödinger equation with a nonlinear perturbation in ℝ3. Assume that the linear Hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition. We prove that if the ... 
Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers
(Elsevier, 2002)In this paper we study the characteristic polynomials \(S(x)=\det(xI−F II_{p,q})\) of automorphisms of even unimodular lattices with signature \((p,q)\). In particular, we show that any Salem polynomial of degree \(2n\) ...