Now showing items 1-20 of 383

    • The 2.1-D Sketch 

      Nitzberg, Mark; Mumford, David Bryant (IEEE Computer Society Press, 1990)
      A model is described for image segmentation that tries to capture the low-level depth reconstruction exhibited in early human vision, giving an important role to edge terminations. The problem is to find a decomposition ...
    • 2D-Shape Analysis Using Conformal Mapping 

      Sharon, E.; Mumford, David Bryant (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 ...
    • 4-Manifolds With Inequivalent Symplectic Forms and 3-Manifolds With Inequivalent Fibrations 

      McMullen, Curtis T.; Taubes, Clifford H. (International Press, 1999)
      We exhibit a closed, simply connected 4-manifold \(X\) 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 

      Elkies, Noam (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 ...
    • Abstract 2374: Reconstructing the evolutionary history of metastatic cancers 

      Reiter, Johannes; Makohon-Moore, Alvin P.; Gerold, Jeffrey; Bozic, Ivana; Chatterjee, Krishnendu; Iacobuzio-Donahue, Christine A.; Vogelstein, Bert; Nowak, Martin A. (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. Genome-wide sequencing data has enabled modern phylogenomic ...
    • Abundance Conjecture 

      Siu, Yum-Tong (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 

      Bozic, Ivana; Antal, Tibor; Ohtsuki, Hisashi; Carter, Hannah; Kim, Dewey; Chen, Sining; Karchin, Rachel; Kinzler, Kenneth; Vogelstein, Bert; Nowak, Martin A. (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 3-Manifold and the Thurston Norm on Cohomology 

      McMullen, Curtis T. (Elsevier, 2002)
      Let M be a connected, compact, orientable 3-manifold 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, \((K^2)= 9, p_g = q = 0\) 

      Mumford, David Bryant (Johns Hopkins University Press, 1979)
    • Amenability, Poincaré Series and Quasiconformal Maps 

      McMullen, Curtis T. (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 ...
    • Amplification on Undirected Population Structures: Comets Beat Stars 

      Pavlogiannis, Andreas; Tkadlec, Josef; Chatterjee, Krishnendu; Nowak, Martin A. (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 

      Traulsen, Arne; Shoresh, Noam; Nowak, Martin A. (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 ...
    • Antiretroviral dynamics determines HIV evolution and predicts therapy outcome 

      Rosenbloom, Daniel Scholes; Hill, Alison Lynn; Rabi, S. Alireza; Siliciano, Robert F.; Nowak, Martin A. (Nature Publishing Group, 2012)
      Despite the high inhibition of viral replication achieved by current anti-HIV drugs, many patients fail treatment, often with emergence of drug-resistant virus. Clinical observations show that the relationship between ...
    • Area and Hausdorff Dimension of Julia Sets of Entire Functions 

      McMullen, Curtis T. (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 ...
    • Asymptotic dynamics of nonlinear Schrödinger equations: Resonance-dominated and dispersion-dominated solutions 

      Tsai, Tai-Peng; Yau, Horng-Tzer (Wiley-Blackwell, 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 eigen-values satisfy some resonance condition. We prove that if the ...
    • Automorphisms of Even Unimodular Lattices and Unramified Salem Numbers 

      Gross, Benedict H.; McMullen, Curtis T. (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 \(2n\) ...
    • Automorphisms of projective K3 surfaces with minimum entropy 

      McMullen, Curtis T. (Springer Science + Business Media, 2015)
    • Automorphisms of Rational Maps 

      McMullen, Curtis T. (Springer, 1988)
    • Automorphy for Some \(l\)-Adic Lifts of Automorphic Mod \(l\) Galois Representations 

      Clozel, Laurent; Taylor, Richard; Harris, Michael (Springer Berlin / Heidelberg, 2008)
      We extend the methods of Wiles and of Taylor and Wiles from \(GL_2\) to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge-Tate numbers), minimally ...