Geometric and Algebraic Topology

Differential Forms in Algebraic Topology

Accurate normalization of real-time quantitative RT-PCR data by geometric averaging of multiple internal control genes

Consensus Problems in Networks of Agents With Switching Topology and Time-Delays

Predicting transmembrane protein topology with a hidden markov model: application to complete genomes11Edited by F. Cohen

A Global Geometric Framework for Nonlinear Dimensionality Reduction

THE VALUATION OF RISK ASSETS AND THE SELECTION OF RISKY INVESTMENTS IN STOCK PORTFOLIOS AND CAPITAL BUDGETS**This paper is another in a series of interrelated theoretical and statistical studies of corporate financial and investment policies being made under grants from the Rockefeller Foundation, and more recently the Ford Foundation, to the Harvard Business School. The generous support for this work is most gratefully acknowledged. The author is also much indebted to his colleagues Professors Bishop, Christenson, Kahr, Raiffa, and (especially) Schlaifer, for extensive discussion and commentary on an earlier draft of this paper; but responsibility for any errors or imperfections remains strictly his own.[Professor Sharpe's paper, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Journal of Finance, September 1964) appeared after this paper was in final form and on its way to the printers. My first section, which parallels the first half of his paper (with corresponding conclusions), sets the algebraic framework for sections II, III and VI, (which have no counterpart in his paper) and for section IV on the equilibrium prices of risk assets, concerning which our results differ significantly for reasons which will be explored elsewhere. Sharpe does not take up the capital budgeting problem developed in section V below.]

Geometric Theory of Semilinear Parabolic Equations

Toward Defining the Course of Evolution: Minimum Change for a Specific Tree Topology

Algebraic Geometry

Topology Optimization: Theory, Methods, and Applications

Algebraic Representation of Thermodynamic Properties and the Classification of Solutions

Geometric Measure Theory

The Algebraic Eigenvalue Problem

Algebraic decay in hierarchical graphs

Algebraic Graph Theory

Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems

Topology of the human and mouse m6A RNA methylomes revealed by m6A-seq

Voronoi diagrams—a survey of a fundamental geometric data structure

On the network topology of variance decompositions: Measuring the connectedness of financial firms

Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples