498 research outputs found
Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems
The full approximation storage (FAS) scheme is a widely used multigrid method
for nonlinear problems. In this paper, a new framework to design and analyze
FAS-like schemes for convex optimization problems is developed. The new method,
the Fast Subspace Descent (FASD) scheme, which generalizes classical FAS, can
be recast as an inexact version of nonlinear multigrid methods based on space
decomposition and subspace correction. The local problem in each subspace can
be simplified to be linear and one gradient descent iteration (with an
appropriate step size) is enough to ensure a global linear (geometric)
convergence of FASD.Comment: 33 page
Nonhuman Rights to Personhood
2012 Dyson Distinguished Lecture, delivered April 26, 2012 at Pace Law School. Introduction by Prof. David N. Cassuto. Video available here
The Evolution of Animal Law since 1950
Over the last half century, the law has assumed an increasingly important place in animal protection even as it has begun to point in the direction of true legal rights for at least some nonhuman animals. In this chapter I briefly discuss five aspects of the law: anti-cruelty statutes; the necessity of obtaining standing to litigate on behalf of the interests of nonhuman animals; evolving protections for great apes; the movement toward legal rights for at least some nonhuman animals; and the state of legal education concerning animal protection
The Entitlement of Chimpanzees to the Common Law Writs of Habeas Corpus and de Homine Replegiando
In this Article, I claim that humans enslave chimpanzees and thereby deprive them of their bodily liberty and that chimpanzees should be entitled to use the common law writs of habeas corpus and de homine replegiando and to bring their common law claims to bodily liberty before courts. In Part I, I demonstrate that chimpanzees are genetically highly similar to humans and quite cognitively and socially complex. In Part II, I argue that flexibility is part of the common law\u27s basic structure, that legal personhood is one of the common law\u27s basic values, that the structure of the common law requires it to permit such a cause of action to go forward on its merits, and that the claim of chimpanzees to common law legal personhood should always be subject to common law re-evaluation. In Part III, I show that post-Conquest English villeins used writs that allowed them, under certain circumstances, to be declared free. In Part IV, I trace the history of the common law writ of de homine replegiando in England and America and argue that individual chimpanzees are entitled to use it to bring their claims to bodily liberty before common law courts. In Part V, I set out the history of the common law writ of habeas corpus in England and America and argue that individual chimpanzees are entitled to use that common law writ to bring their claims to bodily liberty before common law courts
The Entitlement of Chimpanzees to the Common Law Writs of Habeas Corpus and de Homine Replegiando
In this Article, I claim that humans enslave chimpanzees and thereby deprive them of their bodily liberty and that chimpanzees should be entitled to use the common law writs of habeas corpus and de homine replegiando and to bring their common law claims to bodily liberty before courts. In Part I, I demonstrate that chimpanzees are genetically highly similar to humans and quite cognitively and socially complex. In Part II, I argue that flexibility is part of the common law\u27s basic structure, that legal personhood is one of the common law\u27s basic values, that the structure of the common law requires it to permit such a cause of action to go forward on its merits, and that the claim of chimpanzees to common law legal personhood should always be subject to common law re-evaluation. In Part III, I show that post-Conquest English villeins used writs that allowed them, under certain circumstances, to be declared free. In Part IV, I trace the history of the common law writ of de homine replegiando in England and America and argue that individual chimpanzees are entitled to use it to bring their claims to bodily liberty before common law courts. In Part V, I set out the history of the common law writ of habeas corpus in England and America and argue that individual chimpanzees are entitled to use that common law writ to bring their claims to bodily liberty before common law courts
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
We present and analyze finite difference numerical schemes for the Allen
Cahn/Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential.
Both the first order and second order accurate temporal algorithms are
considered. In the first order scheme, we treat the nonlinear logarithmic terms
and the surface diffusion term implicitly, and update the linear expansive term
and the mobility explicitly. We provide a theoretical justification that, this
numerical algorithm has a unique solution such that the positivity is always
preserved for the logarithmic arguments. In particular, our analysis reveals a
subtle fact: the singular nature of the logarithmic term around the values of
and 1 prevents the numerical solution reaching these singular values, so
that the numerical scheme is always well-defined as long as the numerical
solution stays similarly bounded at the previous time step. Furthermore, an
unconditional energy stability of the numerical scheme is derived, without any
restriction for the time step size. The unique solvability and the
positivity-preserving property for the second order scheme are proved using
similar ideas, in which the singular nature of the logarithmic term plays an
essential role. For both the first and second order accurate schemes, we are
able to derive an optimal rate convergence analysis, which gives the full order
error estimate. The case with a non-constant mobility is analyzed as well. We
also describe a practical and efficient multigrid solver for the proposed
numerical schemes, and present some numerical results, which demonstrate the
robustness of the numerical schemes
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