Publications related to MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Phase Transitions in the Pooled Data Problem

In this paper, we study the {\em pooled data} problem of identifying the labels associated with a large collection of items, based on a sequence of pooled tests revealing the counts of each label within the pool. In the noiseless setting, we identify an ex ...

2017

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

Michaël Unser, Martin Kurt Storath

We study jump-penalized estimators based on least absolute deviations which are often referred to as Potts estimators. They are estimators for a parsimonious piecewise constant representation of noisy data having a noise distribution which has heavier tail ...

Oxford University Press2017

Gaussian versus Sparse Stochastic Processes

Julien René Pierre Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

Statistical physics approaches to subnetwork dynamics in biochemical systems

Barbara Bravi

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a l ...

Iop Publishing Ltd2017

Friction law and hysteresis in granular materials

Matthieu Wyart, Eric DeGiuli

The macroscopic friction of particulate materials often weakens as the flow rate is increased, leading to potentially disastrous intermittent phenomena including earthquakes and landslides. We theoretically and numerically study this phenomenon in simple g ...

National Academy of Sciences2017

Multiresolution Subdivision Snakes

Michaël Unser, Daniel Andreas Schmitter, Virginie Sophie Uhlmann, Anaïs Laure Marie-Thérèse Badoual

We present a new family of snakes that satisfy the property of multiresolution by exploiting subdivision schemes. We show in a generic way how to construct such snakes based on an admissible subdivision mask. We derive the necessary energy formulations and ...

2017

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Colin Neil Jones, Milan Korda

We study the convergence rate of the moment-sum-of-squares hierarchy of semidefinite programs for optimal control problems with polynomial data. It is known that this hierarchy generates polynomial under-approximations to the value function of the optimal ...

Elsevier Science Bv2017

How does one compute the noise power to simulate real and complex GNSS signals?

Cyril Botteron, Jérôme Leclère

Simulation of GNSS signals is very important to test and validate algorithms. With some algorithms, such as acquisition or tracking, we do not need to simulate a realistic constellation with actual ranges, Doppler or navigation data. We can simply simulate ...

2016

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

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Phase Transitions in the Pooled Data Problem

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

Gaussian versus Sparse Stochastic Processes

Statistical physics approaches to subnetwork dynamics in biochemical systems

Friction law and hysteresis in granular materials

Multiresolution Subdivision Snakes

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

How does one compute the noise power to simulate real and complex GNSS signals?

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Phase Transitions in the Pooled Data Problem

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Statistical physics approaches to subnetwork dynamics in biochemical systems

Gaussian versus Sparse Stochastic Processes

Jump-Penalized Least Absolute Values Estimation of Scalar or Circle-Valued Signals

Friction law and hysteresis in granular materials

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

How does one compute the noise power to simulate real and complex GNSS signals?

Multiresolution Subdivision Snakes