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Global sensitivity analysis measures the importance of some input variables to a function f by looking at the impact on f of making large random
perturbations to subsets of those variables. Using mea...
This paper introduces some notions of e ective dimension for weighted
function spaces. A space has low e ective dimension if the smallest ball
in it that contains a function of variance 1, has no fu...
Wavelets and the theory of non-parametric function estimation
Pinsker’s theorem sparsity statistical decision problem
2015/8/20
Non-parametric function estimation aims to estimate or recover or denoise a function
of interest, perhaps a signal, spectrum or image, that is observed in noise and possibly
indirectly after some tr...
Constrained ordination analysis with flexible response functions
Canonical correspondence analysis Density estimation
2015/8/20
Canonical correspondence analysis (CCA) is perhaps the most popular multivariate technique used by environmental ecologists
for constrained ordination; it is an approximation to the maximum likelihoo...
Monoidal Functors, Species and Hopf Algebras
bilax monoidal functor Fock functor Hopf algebra
2015/8/14
The fact that α is a morphism of lax monoidal functors is the same as (6.4) and the
coassociativity of I in (6.8). The fact that λ and ρ are morphisms of lax functors
is the same as (6.6) and the c...
Following Radford’s proof of Lagrange’s theorem for pointed Hopf algebras,
we prove Lagrange’s theorem for Hopf monoids in the category of connected
species. As a corollary, we obtain necessary cond...
HOPF MONOIDS FROM CLASS FUNCTIONS ON UNITRIANGULAR MATRICES
Unitriangular matrix class function superclass function
2015/8/14
We build, from the collection of all groups of unitriangular matrices, Hopf
monoids in Joyal’s category of species. Such structure is carried by the collection of
class function spaces on those grou...
THE LOOPING CONSTANT OF Zd
LOOPING CONSTANT Zd
2015/8/14
The looping constant ξ(Zd) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Zd.Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilso...
WHAT IS a sandpile?
sandpile
2015/8/14
An abelian sandpile is a collection of indistinguishable chips distributed among the vertices of a graph. More precisely, it is a function from the vertices to the nonnegative integers, indicating how...
Subharmonic functions and performance bounds on linear time-invariant feedback systems
Harmonic function linear the performance of the single output system a linear control system the harmonic function
2015/8/13
In this paper we study multi-input multi-output (MIMO) linear time-invariant (LTI) control systems. We show that some well known constraints on the performance of single-input single-output (SISO) lin...
The l1 norm of a discrete-time system determines its peak gain, whereas its H_infinity norm determines its RMS gain. In many cases it may be desirable to make a certain map small in the peak gain sens...
Comparison of peak and RMS gains for discrete-time systems
Discrete time system the peak more income signal function
2015/8/13
A convolution system can have a frequency response which is small for all frequencies, yet still greatly amplify the peaks of signals passing through it. For finite-dimensional systems, the authors es...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
A Simple Proof of the Ahlswede-Csiszk One-Bit Theorem
Simple Proof Ahlswede-Csiszk One-Bit Theorem
2015/8/12
It is proved that if (X, Y) are two finite alphabet correlated sources with p(x, JJ) > 0 for all (x, v) E (XX g), and if a function F(X, Y) is a-sensitive, then the rate R of transmission from X to Y ...
Multiple Access Channels with Arbitrarily Correlated Sources
Multiple Access Channels Arbitrarily Correlated Sources
2015/8/12
Let {(q, r$)}#L* be a source of independealt identicauy distributed (i.i.d.) disc&e random variables with joint probability mass function p(u,o) and common part w-f(u)=g(u) in the sense of Witsenbawn,...