90,209 research outputs found

### Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases

We prove regularity properties of the self-energy, to all orders in
perturbation theory, for systems with singular Fermi surfaces which contain Van
Hove points where the gradient of the dispersion relation vanishes. In this
paper, we show for spatial dimensions $d \ge 3$ that despite the Van Hove
singularity, the overlapping loop bounds we proved together with E. Trubowitz
for regular non--nested Fermi surfaces [J. Stat. Phys. 84 (1996) 1209] still
hold, provided that the Fermi surface satisfies a no-nesting condition. This
implies that for a fixed interacting Fermi surface, the self-energy is a
continuously differentiable function of frequency and momentum, so that the
quasiparticle weight and the Fermi velocity remain close to their values in the
noninteracting system to all orders in perturbation theory. In a companion
paper, we treat the more singular two-dimensional case.Comment: 48 pages LaTeX with figure

### The Anderson Model as a Matrix Model

In this paper we describe a strategy to study the Anderson model of an
electron in a random potential at weak coupling by a renormalization group
analysis. There is an interesting technical analogy between this problem and
the theory of random matrices. In d=2 the random matrices which appear are
approximately of the free type well known to physicists and mathematicians, and
their asymptotic eigenvalue distribution is therefore simply Wigner's law.
However in d=3 the natural random matrices that appear have non-trivial
constraints of a geometrical origin. It would be interesting to develop a
general theory of these constrained random matrices, which presumably play an
interesting role for many non-integrable problems related to diffusion. We
present a first step in this direction, namely a rigorous bound on the tail of
the eigenvalue distribution of such objects based on large deviation and
graphical estimates. This bound allows to prove regularity and decay properties
of the averaged Green's functions and the density of states for a three
dimensional model with a thin conducting band and an energy close to the border
of the band, for sufficiently small coupling constant.Comment: 23 pages, LateX, ps file available at
http://cpth.polytechnique.fr/cpth/rivass/articles.htm

### Perturbation Theory around Non-Nested Fermi Surfaces I. Keeping the Fermi Surface Fixed

The perturbation expansion for a general class of many-fermion systems with a
non-nested, non-spherical Fermi surface is renormalized to all orders. In the
limit as the infrared cutoff is removed, the counterterms converge to a finite
limit which is differentiable in the band structure. The map from the
renormalized to the bare band structure is shown to be locally injective. A new
classification of graphs as overlapping or non-overlapping is given, and
improved power counting bounds are derived from it. They imply that the only
subgraphs that can generate $r$ factorials in the $r^{\rm th}$ order of the
renormalized perturbation series are indeed the ladder graphs and thus give a
precise sense to the statement that `ladders are the most divergent diagrams'.
Our results apply directly to the Hubbard model at any filling except for
half-filling. The half-filled Hubbard model is treated in another place.Comment: plain TeX with postscript figures in a uuencoded gz-compressed tar
file. Put it on a separate directory before unpacking, since it contains
about 40 files. If you have problems, requests or comments, send e-mail to
[email protected]

### Migrants, immigrants and welfare from the Old Poor Law to the Welfare State

Under the Old Poor Law internal migrants moved from one jurisdiction to another when they crossed parochial boundaries. Following the Poor Law Amendment Act of 1834 central government took an enlarged and expanding part in welfare. As it did so, the entitlement to welfare of immigrants from overseas was scrutinised at a national level in a way that was analogous to the manner in which the status of internal migrants had previously been scrutinised at a parochial level. Having established this analogy, the essay asks whether the entitlement to welfare of outsiders improved or deteriorated over time and seeks to account for the broad trends

### Distribution-Independent Evolvability of Linear Threshold Functions

Valiant's (2007) model of evolvability models the evolutionary process of
acquiring useful functionality as a restricted form of learning from random
examples. Linear threshold functions and their various subclasses, such as
conjunctions and decision lists, play a fundamental role in learning theory and
hence their evolvability has been the primary focus of research on Valiant's
framework (2007). One of the main open problems regarding the model is whether
conjunctions are evolvable distribution-independently (Feldman and Valiant,
2008). We show that the answer is negative. Our proof is based on a new
combinatorial parameter of a concept class that lower-bounds the complexity of
learning from correlations.
We contrast the lower bound with a proof that linear threshold functions
having a non-negligible margin on the data points are evolvable
distribution-independently via a simple mutation algorithm. Our algorithm
relies on a non-linear loss function being used to select the hypotheses
instead of 0-1 loss in Valiant's (2007) original definition. The proof of
evolvability requires that the loss function satisfies several mild conditions
that are, for example, satisfied by the quadratic loss function studied in
several other works (Michael, 2007; Feldman, 2009; Valiant, 2010). An important
property of our evolution algorithm is monotonicity, that is the algorithm
guarantees evolvability without any decreases in performance. Previously,
monotone evolvability was only shown for conjunctions with quadratic loss
(Feldman, 2009) or when the distribution on the domain is severely restricted
(Michael, 2007; Feldman, 2009; Kanade et al., 2010

### Learning DNF Expressions from Fourier Spectrum

Since its introduction by Valiant in 1984, PAC learning of DNF expressions
remains one of the central problems in learning theory. We consider this
problem in the setting where the underlying distribution is uniform, or more
generally, a product distribution. Kalai, Samorodnitsky and Teng (2009) showed
that in this setting a DNF expression can be efficiently approximated from its
"heavy" low-degree Fourier coefficients alone. This is in contrast to previous
approaches where boosting was used and thus Fourier coefficients of the target
function modified by various distributions were needed. This property is
crucial for learning of DNF expressions over smoothed product distributions, a
learning model introduced by Kalai et al. (2009) and inspired by the seminal
smoothed analysis model of Spielman and Teng (2001).
We introduce a new approach to learning (or approximating) a polynomial
threshold functions which is based on creating a function with range [-1,1]
that approximately agrees with the unknown function on low-degree Fourier
coefficients. We then describe conditions under which this is sufficient for
learning polynomial threshold functions. Our approach yields a new, simple
algorithm for approximating any polynomial-size DNF expression from its "heavy"
low-degree Fourier coefficients alone. Our algorithm greatly simplifies the
proof of learnability of DNF expressions over smoothed product distributions.
We also describe an application of our algorithm to learning monotone DNF
expressions over product distributions. Building on the work of Servedio
(2001), we give an algorithm that runs in time \poly((s \cdot
\log{(s/\eps)})^{\log{(s/\eps)}}, n), where $s$ is the size of the target DNF
expression and \eps is the accuracy. This improves on \poly((s \cdot
\log{(ns/\eps)})^{\log{(s/\eps)} \cdot \log{(1/\eps)}}, n) bound of Servedio
(2001).Comment: Appears in Conference on Learning Theory (COLT) 201

### Feminist science and epistemologies: Key issues central to GENNOVATE's research program

This methodological brief offers a window into GENNOVATEâ€™s innovative collaborative research initiative to promote gender equality in agricultural and natural resource management. It addresses questions such as 1) Why is it important to distinguish among epistemology, methodology, and methods?; 2) What is feminist epistemology?; 3) What can researchers of gender, agriculture, and innovation learn from engaging the contributions of feminist epistemology?; and 4) How has GENNOVATE integrated lessons from feminist methods and feminist epistemics about gender relations, agricultural change, and innovation

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