The tail of the logarithmic degree
distribution of networks decays linearly with respect to the logarithmic degree
is known as the power law and is ubiquitous in daily lives. A commonly used
technique in modeling the power law is preferential attachment (PA), which
sequentially joins each new node to the existing nodes according to the
conditional probability law proportional to a linear function of their degrees.
Although effective, it is tricky to apply PA to real networks because the
number of nodes and that of edges have to satisfy a linear constraint. This
paper enables real application of PA by making each new node as an isolated
node that attaches to other nodes according to PA scheme in some later epochs.
This simple and novel strategy provides an additional degree of freedom to
relax the aforementioned constraint to the observed data and uses the PA scheme
to compute the implied proportion of the unobserved zero-degree nodes. By using
martingale convergence theory, the degree distribution of the proposed model is
shown to follow the power law and its asymptotic variance is proved to be the
solution of a Sylvester matrix equation. These results give a strongly
consistent estimator for the power-law parameter and its asymptotic normality.
This talk will review the theory of this new modeling approach and will
illustrate how to use it to big network analysis.

Pain is a subjective and multidimensional
experience, encompassing the sensory-discriminative, affective-motivational,
and cognitive-evaluative dimensions. Acute pain is adaptive and protects
individuals from further damage. However, chronic pain is often maladaptive and
leads to functional neuroplasticity changes and structural reorganization. We
focus on primary dysmenorrhea (PDM), which is menstrual pain in the absence of
identifiable pathology. The dual characteristics of PDM thus serves as a
genuine clinical model of chronic pain.

Functionally, pain perception occurs in the
brain and emerges from neural information processing at varying spatial and
temporal scales. By using nonlinear multiscale sample entropy (MSE) analysis,
we studied the irregularity/uncertainty of brain signals across different time
scales, which can be regarded as brain complexity and reflects the adaptability
of the nervous system. Loss of complexity is thus considered as a
representation of pathologic dynamics.

In this talk, I will first introduce
chronic pain, the clinical significance of studying primary dysmenorrhea (PDM),
and the use of PDM as a clinical model of chronic pain. Secondly, I will
outline our recent findings on genetic neuroimaging studies in PDM. Lastly, I
will briefly share the perspectives from pain experts and the International
Association for the Study of Pain (IASP) on the search for human pain
biomarkers.

In Multi-Class Classification (MCC), each
label is attached with a possibly high dimensional and large sized point-cloud.
I will start from nonparametrically building a label embedding tree, and then
deriving a label predictive graph. Both label embedding tree and predictive
graph reveals the nature of information content of (MCC): Heterogeneity. This
is the platform for Data-driven Intelligence (D.I.). D.I. is shown to achieve
nearly perfect, if not perfect, predictions. We then argue that achieving perfect
prediction is indeed the prerequisite of all data analysis in general.
Throughout our computational developments, data from PITCHf/x database is used.
I will also mention how to scale our algorithmic paradigm in the setting of
Extreme MCC involving with many hundreds or thousands of labels.

At the end, if time allows, I will mention
issues related to Multi-Label Classification (MLC) and Multiple Response
problem in order to shed some lights on the future competition between D.I and
A.I. (Artificial Intelligence).

During analyzing functional data process,
the presence of outliers can greatly influence the results on modeling and
forecasting of functional data, which may lead to the inaccurate conclusion.
Hence, detection of such outliers becomes an essential task. Visualization of
data not only plays a vital role in discovering the features of data before
applying statistical models and summary statistics but also is an auxiliary
tool in identifying outliers. The research involved visualization and
sensitivity analysis for functional data has not yet received much attention in
the literature to date. Thus, this becomes the focus of this paper. To this
end, we propose a method combined influence function with the iteration scheme
motivated by Zou et al.(2012) for identifying outliers in functional data, and
develop new visualization tools for displaying features and grasping the
outliers in functional data. Furthermore, comparisons between our proposed
methods with the existing methods are also investigated. Finally, we illustrate
these proposed methods with simulation studies and real data examples .

A regression tree method for count data
called CORE is introduced. Besides a Poisson regression, a count regression
such as negative binomial, hurdle, or zero-inflated regression which can
accommodate over-dispersion and/or excess zeros is fitted at each node.
Likelihood function is used to guide the selection of split variables and split
sets. We then use node deviance in the tree pruning process to avoid
overfitting. CORE is free of variable selection bias. It is shown to have an
edge over the existing methods in the simulation and real data studies.