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I would like to thank my advisor, Prof. Jaroslav Neˇsetˇril, for his lead, patience and for
fixing sometimes unbelievable mistakes I was doing (seemingly) intentionally and perpetually.
I would like...
High-dimensional covariance estimation based on Gaussian graphical models
High-dimensional covariance estimation Gaussian graphical models
2010/12/15
Undirected graphs are often used to describe high dimensional distributions. Under sparsity
conditions, the graph can be estimated using ℓ1-penalization methods. We propose and study
the follo...
Species abundance distributions in neutral models with immigration or mutation and general lifetimes
Species abundance distribution Crump–Mode–Jagers process splitting tree branching process
2010/12/15
We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d.
lifetime durations, which are not necessarily exponentially distributed, and each individual
gives birth inde...
A sufficient condition to test identifiability of a nonlinear delayed-differential model with constant delays and multi-inputs
Identifiability Nonlinear delayed-differential models
2010/12/1
In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given.
We consider percolation in a multiscale Boolean model. This model is defined as the union of scaled independent copies of a given Boolean model. The scale factor of the nth copy is −n. We prove...
True nature of long-range order in a plaquette orbital model
Rigorous results in statistical mechanics Classical phase transitions
2010/12/9
We analyze the classical version of a plaquette orbital model that was recently introduced and studied numerically by S. Wenzel and W. Janke.
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Topological expansion of beta-ensemble model quantum algebraic geometry sectorwise approach
2010/12/14
We solve the loop equations of the β-ensemble model analogously to the solution found for the Hermitian matrices β = 1. For β = 1, the solution was expressed using the algebraic spectral curve of equa...
Convex Optimization In Identification Of Stable Non-Linear State Space Models
Convex Optimization Identification Stable Non-Linear State Space Models
2010/12/1
A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined ...
Emergence and annihilation of localized structures in a phytoplankton-nutrient model
Emergence annihilation of localized structures phytoplankton-nutrient model
2010/12/15
Co-limitation of marine phytoplankton by light and nutrient leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlo...
On the Accuracy of the Wyner Model in Cellular Networks
Accuracy Wyner Model Cellular Networks
2010/12/14
The Wyner model has been widely used to model and analyze cellular networks due to its simplicity and analytical tractability. Its key aspects include fixed user locations and the deterministic and ho...
Fokker-Planck Asymptotics for Traffic Flow Models
Traffic Flow Modeling Fokker–Planck Equations
2010/12/6
Starting from microscopic interaction rules we derive kinetic models of Fokker–Planck type for vehicular traffic flow. The derivation is based on taking a suitable asymptotic limit of the correspondin...
The Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray-Scott Model
matched asymptotic expansions spots self-replication logarithmic expansions eigenvalues,
2010/12/15
The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity " of one...
On a spectral analogue of the strong multiplicity one theorem
spectral analogue strong multiplicity one theorem
2010/11/29
We prove spectral analogues of the classical strong multiplicity one theorem for newforms. Let 1 and 2 be uniform lattices in a semisim-ple group G. Suppose all but finitely many i...
Learning Latent Tree Graphical Models
GraphicalModels Hidden Variables Latent Tree Models Structure Learning
2010/12/15
We study the problem of learning a latent tree graphical model where samples are available
only from a subset of variables. We propose two consistent and computationally efficient algorithms for lear...
Almost sure localization of the eigenvalues in a gaussian information plus noise model. Applications to the spiked models
localization eigenvalues gaussian information plus noise model
2010/12/14
Let §N be a M ×N randommatrix defined by §N = BN +σWN where BN is a uniformly bounded deterministicmatrix andwhereWN is an independent identically distributed complex Gaussianmatrix with zeromean and ...