We formulate a system of integro-differential equations to model the dynamics of competition in a two-species community, in which the mortality, fertility and growth are sizedependent. Existence and uniqueness of nonnegative solutions to the system are analyzed. The existence of the stationary size distributions is discussed, and the linear stability is investigated by means of the semigroup theory of operators and the characteristic equation technique. Some sufficient conditions for asymptotical stability / instability of steady states are obtained. The resulting conclusion extends some existing results involving age-independent and age-dependent population models.

Numerous researchers have applied the martingale approach for models driven by
L′evy processes to study optimal investment problems. This paper considers an insurer who
wants to maximize the expected utility of terminal wealth by selecting optimal investment and
proportional reinsurance strategies. The insurer’s risk process is modeled by a L′evy process
and the capital can be invested in a security market described by the standard Black-Scholes
model. By the martingale approach, the closed-form solutions to the problems of expected
utility maximization are derived. Numerical examples are presented to show the impact of
model parameters on the optimal strategies.

A credit-linked note (CLN) is a note paying an enhanced coupon to investors for
bearing the credit risk of a reference entity. In this paper, we study the counterparty risk on
CLNs under a Markov chain framework, and introduce a Markov copula model to describe joint
defaults between the reference entity underlying the CLN and CLN issuer. Assuming that the
respective default intensities are directly and inversely proportional to the interest rate, which
follows a CIR process, we obtain the explicit formulae for CLN values through a PDE approach.
Finally, credit valuation adjustment (CVA) formula is derived to price counterparty credit risk.

In this paper we prove a global attractivity result for the unique positive equilibrium
point of a difference equation, which improves and generalizes some known ones in the existing literature. Especially, our results completely solve an open problem and some conjectures proposed in [1, 2, 3, 4].

Mixture of Experts (MoE) regression models are widely studied in statistics and
machine learning for modeling heterogeneity in data for regression, clustering and classification.
Laplace distribution is one of the most important statistical tools to analyze thick and tail
data. Laplace Mixture of Linear Experts (LMoLE) regression models are based on the Laplace
distribution which is more robust. Similar to modelling variance parameter in a homogeneous
population, we propose and study a new novel class of models: heteroscedastic Laplace mixture
of experts regression models to analyze the heteroscedastic data coming from a heterogeneous
population in this paper. The issues of maximum likelihood estimation are addressed. In
particular, Minorization-Maximization (MM) algorithm for estimating the regression parameters
is developed. Properties of the estimators of the regression coefficients are evaluated through
Monte Carlo simulations. Results from the analysis of two real data sets are presented.

This paper is concerned with multidirectional associative memory neural network
with distributed delays on almost-periodic time scales. Some sufficient conditions on the existence, uniqueness and the global exponential stability of almost-periodic solutions are established. An example is presented to illustrate the feasibility and effectiveness of the obtained results.

In this paper, the approximate solutions for two different type of two-dimensional
nonlinear integral equations: two-dimensional nonlinear Volterra-Fredholm integral equations
and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre
wavelet method. To do this, these two-dimensional nonlinear integral equations are transformed
into a system of nonlinear algebraic equations in matrix form. By solving these systems, unknown coefficients are obtained. Also, some theorems are proved for convergence analysis.
Some numerical examples are presented and results are compared with the analytical solution
to demonstrate the validity and applicability of the proposed method.

In statistical parameter estimation problems, how well the parameters are estimated
largely depends on the sampling design used. In the current paper, a modification of ranked set
sampling (RSS) called moving extremes RSS (MERSS) is considered for the estimation of the
scale and shape parameters for the log-logistic distribution. Several traditional estimators and
ad hoc estimators will be studied under MERSS. The estimators under MERSS are compared
to the corresponding ones under SRS. The simulation results show that the estimators under
MERSS are significantly more efficient than the ones under SRS.

K-mer can be used for the description of biological sequences and k-mer distribution
is a tool for solving sequences analysis problems in bioinformatics. We can use k-mer vector as
a representation method of the k-mer distribution of the biological sequence. Problems, such as
similarity calculations or sequence assembly, can be described in the k-mer vector space. It helps
us to identify new features of an old sequence-based problem in bioinformatics and develop new
algorithms using the concepts and methods from linear space theory. In this study, we defined
the k-mer vector space for the generalized biological sequences. The meaning of corresponding
vector operations is explained in the biological context. We presented the vector/matrix form of
several widely seen sequence-based problems, including read quantification, sequence assembly,
and pattern detection problem. Its advantages and disadvantages are discussed. Also, we
implement a tool for the sequence assembly problem based on the concepts of k-mer vector
methods. It shows the practicability and convenience of this algorithm design strategy.

Tracy-Widom distribution was first discovered in the study of largest eigenvalues
of high dimensional Gaussian unitary ensembles (GUE), and since then it has appeared in a
number of apparently distinct research fields. It is believed that Tracy-Widom distribution
have a universal feature like classic normal distribution. Airy2 process is defined through finite
dimensional distributions with Tracy-Widom distribution as its marginal distributions. In this
introductory survey, we will briefly review some basic notions, intuitive background and fundamental properties concerning Tracy-Widom distribution and Airy2 process. For sake of reading,
the paper starts with some simple and well-known facts about normal distributions, Gaussian
processes and their sample path properties.