10,860 research outputs found
An Induction Principle for the Weighted p-Energy Minimality of x/|x|
In this paper, we investigate minimizing properties of the map from
the Euclidean unit ball to its boundary ,
for the weighted energy functionals . We establish the following induction
principle: if the map
minimizes among the maps satisfying on , then the map
minimizes
among the maps
satisfying on . This result enables us to enlarge
the range of values of and for which minimizes
.Comment: 8 page
On the Approximation of Toeplitz Operators for Nonparametric -norm Estimation
Given a stable SISO LTI system , we investigate the problem of estimating
the -norm of , denoted , when is only
accessible via noisy observations. Wahlberg et al. recently proposed a
nonparametric algorithm based on the power method for estimating the top
eigenvalue of a matrix. In particular, by applying a clever time-reversal
trick, Wahlberg et al. implement the power method on the top left
corner of the Toeplitz (convolution) operator associated with . In
this paper, we prove sharp non-asymptotic bounds on the necessary length
needed so that is an -additive approximation of
. Furthermore, in the process of demonstrating the sharpness of
our bounds, we construct a simple family of finite impulse response (FIR)
filters where the number of timesteps needed for the power method is
arbitrarily worse than the number of timesteps needed for parametric FIR
identification via least-squares to achieve the same -additive
approximation
Conceptualizing interdependences between regulatory and monetary policies. Some preliminary considerations
In this paper we investigate the interplay between regulatory and monetary policies. We analyze how changes in institutional settings modify the functioning of various channels of monetary transmission. The paper begins with a brief presentation of the main channels of monetary transmission, including credit channel, exchange rate channel, Tobin q theory, and the credit channel. After that we define a positive institutional change and we check how such adjustments can be put into the logic of monetary transmission. We show that the most profound way institutions impact the monetary transmission is via its effect on the elasticity of investments to changes in interest rates.monetary transmission channels, monetary policy, regulatory policy, institutional change, financial globalization
A note on -axially symmetric harmonic maps from to minimizing the relaxed energy
For any n>1 we give an explicit example of an n-axially symmetric Cartesian
current in B^3 x S^2 with non-trivial vertical part and non-constant graph part
minimizing the relaxed Dirichlet energy among the n-axially symmetric Cartesian
currents with the same boundary. This stands in sharp contrast with a results
of Hardt, Lin and Poon for the case n=1.Comment: 17 page
Criticizing the critique. Some methodological insights into the debate on the state of economic theory in the face of the post 2008 crisis
The aim of this paper is to investigate the current debate on the state of economics from a methodological perspective. We claim that the majority of contributions criticizing modern economics are not based on clear methodological principles and thus many of them are not correct. We show this with respect to such issues as the problem of realisticness of models and their assumptions, the role of mathematics in economics, the way we conceptualize the relation between economics (theory) and economy (empiria), as well as the general problem of comparing theories. In doing so we use the research apparatus taken form the philosophy of science and also we benefit a lot from recent developments in the philosophy of economics. Finally, we show one of the paradoxes of that debate, namely that many critics of economics accuse economists of using the wrong language (mathematics) while they do not use proper language themselves while criticizing economics, namely the apparatus taken from the philosophy of science.methodology of economics, mathematization, assumptions, theories of explanation, global economic crisis
The history of transaction cost economics and its recent developments
The emergence of transaction cost economics (TCE) in the early 1970s with Oliver Williamsonâs successful reconciliation of the so called neoclassical approach with Herbert Simonâs organizational theory can be considered an important part of the first cognitive turn in economics. The development of TCE until the late 1980s was particularly marked by treating the firm as an avoider of negative frictions, i.e., of transaction costs. However, since the 1990s TCE has been enriched by various approaches stressing the role of the firm in creating positive value, e.g., the literature on modularity. Hence, a second cognitive turn has taken place: the firm is no longer only seen as an avoider of negative costs but also as a creator of positive knowledge.transaction cost economics, Oliver Williamson, theory of the firm, modularity literature, cognitive turn
Beating Randomized Response on Incoherent Matrices
Computing accurate low rank approximations of large matrices is a fundamental
data mining task. In many applications however the matrix contains sensitive
information about individuals. In such case we would like to release a low rank
approximation that satisfies a strong privacy guarantee such as differential
privacy. Unfortunately, to date the best known algorithm for this task that
satisfies differential privacy is based on naive input perturbation or
randomized response: Each entry of the matrix is perturbed independently by a
sufficiently large random noise variable, a low rank approximation is then
computed on the resulting matrix.
We give (the first) significant improvements in accuracy over randomized
response under the natural and necessary assumption that the matrix has low
coherence. Our algorithm is also very efficient and finds a constant rank
approximation of an m x n matrix in time O(mn). Note that even generating the
noise matrix required for randomized response already requires time O(mn)
The Noisy Power Method: A Meta Algorithm with Applications
We provide a new robust convergence analysis of the well-known power method
for computing the dominant singular vectors of a matrix that we call the noisy
power method. Our result characterizes the convergence behavior of the
algorithm when a significant amount noise is introduced after each
matrix-vector multiplication. The noisy power method can be seen as a
meta-algorithm that has recently found a number of important applications in a
broad range of machine learning problems including alternating minimization for
matrix completion, streaming principal component analysis (PCA), and
privacy-preserving spectral analysis. Our general analysis subsumes several
existing ad-hoc convergence bounds and resolves a number of open problems in
multiple applications including streaming PCA and privacy-preserving singular
vector computation.Comment: NIPS 201
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