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624
The exact MSSM spectrum from string theory,” JHEP 0605
, 2006
"... We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E8 ×E8 heterotic superstring on a smooth CalabiYau threefold with an SU(4) gauge instanton and a Z3 × Z3 Wilson line. Specifically, the ..."
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Cited by 88 (40 self)
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We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E8 ×E8 heterotic superstring on a smooth CalabiYau threefold with an SU(4) gauge instanton and a Z3 × Z3 Wilson line. Specifically, the observable sector is N = 1 supersymmetric with gauge group SU(3)C × SU(2)L × U(1)Y × U(1)B−L, three families of quarks and leptons, each family with a righthanded neutrino, and one Higgs–Higgs conjugate pair. Importantly, there are no extra vectorlike pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slopestable.
Stability of Travelling Waves
, 2002
"... An overview of various aspects related to the spectral and nonlinear stability of travellingwave solutions to partial differential equations is given. The point and the essential spectrum of the linearization about a travelling wave are discussed as is the relation between these spectra, Fredholm p ..."
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Cited by 85 (8 self)
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An overview of various aspects related to the spectral and nonlinear stability of travellingwave solutions to partial differential equations is given. The point and the essential spectrum of the linearization about a travelling wave are discussed as is the relation between these spectra, Fredholm properties, and the existence of exponential dichotomies (or Green's functions) for the linear operator. Among the other topics reviewed in this survey are the nonlinear stability of waves, the stability and interaction of wellseparated multibump pulses, the numerical computation of spectra, and the Evans function, which is a tool to locate isolated eigenvalues in the point spectrum and near the essential spectrum. Furthermore, methods for the stability of waves in Hamiltonian and monotone equations as well as for singularly perturbed problems are mentioned. Modulated waves, rotating waves on the plane, and travelling waves on cylindrical domains are also discussed briefly.
Theory of multivariate statistics
, 1999
"... Our object in writing this book is to present the main results of the modern theory of multivariate statistics to an audience of advanced students who would appreciate a concise and mathematically rigorous treatment of that material. It is intended for use as a textbook by students taking a first gr ..."
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Cited by 78 (0 self)
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Our object in writing this book is to present the main results of the modern theory of multivariate statistics to an audience of advanced students who would appreciate a concise and mathematically rigorous treatment of that material. It is intended for use as a textbook by students taking a first graduate course in the subject, as well as for the general reference of interested research workers who will find, in a readable form, developments from recently published work on certain broad topics not otherwise easily accessible, as, for instance, robust inference (using adjusted likelihood ratio tests) and the use of the bootstrap in a multivariate setting. The references contains over 150 entries post1982. The main development of the text is supplemented by over 135 problems, most of which are original with the authors. A minimum background expected of the reader would include at least two courses in mathematical statistics, and certainly some exposure to the calculus of several variables together with the descriptive geometry of linear
Nonparametric Kernel Regression Subject To Monotonicity Constraints
 Annals of Statistics
, 1999
"... . We suggest a biasedbootstrap method for monotonising general linear, kerneltype estimators, for example local linear estimators and NadarayaWatson estimators. Attributes of our approach include the fact that it produces smooth estimates, that is applicable to a particularly wide range of estimat ..."
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Cited by 67 (2 self)
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. We suggest a biasedbootstrap method for monotonising general linear, kerneltype estimators, for example local linear estimators and NadarayaWatson estimators. Attributes of our approach include the fact that it produces smooth estimates, that is applicable to a particularly wide range of estimator types, and that it can be employed after the smoothing step has been implemented. Therefore, an experimenter may use his or her favourite kernel estimator, and their favourite bandwidth selector, to construct the basic nonparametric smoother, and then use our technique to render it monotone in a smooth way. Since our method is based on maximising fidelity to the conventional empirical approach, subject to monotonicity, then if the original kernel smoother were monotone we would not modify it. More generally, we would adjust it by adjoining weights to data values so as to make least possible change, in the sense of a distance measure, subject to imposing the constraint of monotonicity. KEY...
AlphaProlog: A Logic Programming Language with Names, Binding, and AlphaEquivalence
, 2004
"... There are two wellknown approaches to programming with names, binding, and equivalence up to consistent renaming: representing names and bindings as concrete identifiers in a firstorder language (such as Prolog), or encoding names and bindings as variables and abstractions in a higherorder langua ..."
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Cited by 56 (10 self)
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There are two wellknown approaches to programming with names, binding, and equivalence up to consistent renaming: representing names and bindings as concrete identifiers in a firstorder language (such as Prolog), or encoding names and bindings as variables and abstractions in a higherorder language (such as LambdaProlog). However, both approaches have drawbacks: the former often involves stateful namegeneration and requires manual definitions for alphaequivalence and captureavoiding substitution, and the latter is semantically very complicated, so reasoning about programs written using either approach can be very di#cult. Gabbay and Pitts have developed a new approach to encoding abstract syntax with binding based on primitive operations of nameswapping and freshness. This paper presents AlphaProlog, a logic programming language that uses this approach, along with several illustrative example programs and an operational semantics.
Bifurcation from Relative Equilibria of Noncompact Group Actions: Skew Products, Meanders, and Drifts
, 1996
"... We consider a finitedimensional, typically noncompact Riemannian manifold M with a differentiable proper action of a possibly noncompact Lie group G: We describe Gequivariant flows in a tubular neighborhood U of a relative equilibrium G \Delta u 0 ; u 0 2 M , with compact isotropy H of u 0 ; ..."
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Cited by 47 (16 self)
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We consider a finitedimensional, typically noncompact Riemannian manifold M with a differentiable proper action of a possibly noncompact Lie group G: We describe Gequivariant flows in a tubular neighborhood U of a relative equilibrium G \Delta u 0 ; u 0 2 M , with compact isotropy H of u 0
Dynamics of spiral waves on unbounded domains using centermanifold reduction
 J. Differential Equations
, 1997
"... An equivariant centermanifold reduction near relative equilibria of Gequivariant semiflows on Banach spaces is presented. In contrast to previous results, the Lie group G is possibly noncompact. Moreover, it is not required that G induces a strongly continuous group action on the underlying funct ..."
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Cited by 44 (18 self)
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An equivariant centermanifold reduction near relative equilibria of Gequivariant semiflows on Banach spaces is presented. In contrast to previous results, the Lie group G is possibly noncompact. Moreover, it is not required that G induces a strongly continuous group action on the underlying
On the Structure of Spectra of Modulated Travelling Waves
 MATH. NACHR.
, 2001
"... Modulated travelling waves are solutions to reaction–diffusion equations that are time–periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential instabilities from pulses or fronts. In this article, a framework for the stability analysis of such solut ..."
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Cited by 48 (28 self)
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Modulated travelling waves are solutions to reaction–diffusion equations that are time–periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential instabilities from pulses or fronts. In this article, a framework for the stability analysis of such solutions is presented: the reaction–diffusion equation is cast as an ill–posed elliptic dynamical system in the spatial variable acting upon time–periodic functions. Using this formulation, points in the resolvent set, the point spectrum, and the essential spectrum of the linearization about a modulated travelling wave are related to the existence of exponential dichotomies on appropriate intervals for the associated spatial elliptic eigenvalue problem. Fredholm properties of the linearized operator are characterized by a relative Morse–Floer index of the elliptic equation. These results are proved without assumptions on the asymptotic shape of the wave. Analogous results are true for the spectra of travelling waves to parabolic equations on unbounded cylinders. As an application, we study the existence and stability of modulated spatially–periodic patterns with long–wavelength that accompany modulated pulses.
A mad day’s work: from Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry
 Bull. Amer. Math. Soc. (N.S
, 2001
"... To add to the chorus of praise by referring to my own experience would be of little interest, but I am in no way forgetting the facilities for work provided by the Institut des Hautes Études Scientifiques (IHES) for so many years, particularly the constantly renewed opportunities for meetings and ex ..."
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Cited by 48 (0 self)
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To add to the chorus of praise by referring to my own experience would be of little interest, but I am in no way forgetting the facilities for work provided by the Institut des Hautes Études Scientifiques (IHES) for so many years, particularly the constantly renewed opportunities for meetings and exchanges. While there have
Results 1  10
of
624