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#### A computational systems biology approach for elucidating molecular features of primary and metastatic melanoma

Malignant melanoma, a cancer arising from melanocytes, is reported to have one of
the fastest growing incidence rates worldwide, and is considered to be one of the most
aggressive human malignancies. According to the ...

#### On the Kobayashi geometry of domains

In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects:
Estimates for holomorphic images of subsets in convex ...

#### Sparse bounds for various spherical maximal functions

Harmonic analysis mainly deals with the qualitative and quantitative properties of functions
and transforms of those functions. It has applications in various areas of Mathematics like PDE,
Differential geometry, Ergodic ...

#### Geometric invariants for a class of submodules of analytic Hilbert modules

Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ...

#### Correlation Functions in the Finite Toom Model

This thesis is divided into four chapters. In Chapter 1, we give some basic definitions and
results that we need throughout the thesis. In Chapter 2, we describe the pn0;n1q-Toom model
and prove some known results about ...

#### Decomposition of the tensor product of Hilbert modules via the jet construction and weakly homogeneous operators

Let ½ Cm be a bounded domain and K :£!C be a sesqui-analytic function. We show
that if ®,¯ È 0 be such that the functions K® and K¯, defined on £, are non-negative
definite kernels, then theMm(C) valued function
...

#### A Study of Some Conformal Metrics and Invariants on Planar Domains

The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants
near a smooth boundary point of a domain in the complex plane. We will be interested
in the invariants associated to the ...

#### Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space

Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand
the concept of holomorphicity of a complex-valued function. Suppose a function f defined
on O takes values in a locally convex ...

#### Characterization of Brain Signals Across Scales Using Temporally Modulated Visual Stimuli

Electrical signals from the brain can be recorded at several different scales, ranging
from spiking activity to local field potential (LFP) in animals to scalp
electroencephalogram (EEG) in humans. Each signal represents ...

#### Trace Estimate For The Determinant Operator And K- Homogeneous Operators

Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! ...