text:
\section{Introduction}

Many real-world applications involve the optimization of certain objectives such as
the minimization of costs, energy consumption, environment and the maximization of performance, efficiency and sustainability. In many cases, the optimization problems that can be formulated are highly nonlinear with multimodal objective landscapes, subject to a set of complex, nonlinear constraints. Such problems are challenging to solve. Even with the ever-increasing power of modern computers, it is still impractical and not desirable to use simple brute force approaches. Thus, whenever possible, efficient algorithms are crucially important to such applications. However, efficient algorithms may not exist for most of the optimization problems in applications. Though there are a wide range of optimization algorithms such as gradient-based algorithms, the interior-point method and trust-region method, most of such algorithms are gradient-based and local search algorithms~\citep{Boyd2004,YangBook2014}, which means that the final solutions may depend on the initial starting points. In addition, the computation of derivatives can be computationally expensive, and some problems such as the objective with discontinuities may not have derivatives in certain regions.

A recent trend is to use evolutionary algorithms such as genetic algorithm (GA)~\citep{Holland1975},
and swarm intelligence (SI) based algorithms. In fact, a wide spectrum of SI-based algorithms have emerged in the last decades, including ant colony optimization (ACO)~\citep{Dorigo1992},
particle swarm optimization (PSO)~\citep{Kennedy1995PSO}, bat algorithm (BA)~\citep{YangBat2010},
firefly algorithm (FA)~\citep{Yang2009FA}, cuckoo search (CS)~\citep{YangDeb2009CS} and others \citep{YangBook2014}. These nature-inspired algorithms tend to be global optimizers, using a swarm of multiple, interacting agents to generate the search moves in the search space. Such global optimizers are typically simple, flexible and yet surprisingly efficient,
which have been shown in many applications and case studies (Kennedy et al., 2001;
Engelbrecht, 2005; Yang et al., 2013; Yang, 2013; Yang, 2014). In the last three decades, significant progress has been and various applications have appeared. This paper will briefly summarize some of these important developments.

Despite the extensive studies and developments, there are still some important issues concerning swarm intelligence and nature-inspired algorithms. Firstly, there still lacks a unified mathematical framework to analyze these algorithms. Consequently, it lacks in-depth understanding how such algorithms may converge and how quickly they can converge. Secondly, there are many different algorithms and their comparison studies have mainly based on numerical experiments, and it is difficult to justify if such comparison is always fair. Thirdly, most of the applications in the literature concern small-scale problems, and it is not clear if such approaches can be directly applied to large-scale problems. Finally, it is not clear what are the conditions for the emergence of swarming and intelligence behaviour, even though the term `swarm intelligence' is used widely. All these mean that a systematical review and analysis is needed, and this paper is a preliminary attempt to analyze nature-inspired algorithms in a comprehensive and unified manner.

Therefore, this paper is organized as follows. Section 2 briefly review and summarize some of the recent SI-based algorithms, with the emphasis on their main characteristics. Section 3 focuses on the search mechanisms and their possible mathematical foundations. Section 4 attempts to highlight some of the main issues concerning nature-inspired algorithms from different perspectives, and outline some open problems and future research directions.

\section{Nature-Inspired Optimization Algorithms}

There are many nature-inspired algorithms in the current literature, it is estimated there are more than 100 different algorithms and variants (Reyes-Sierra and Coello Coello, 2006; Kennedy et al., 2001; Price et al., 2005; Fister et al., 2013; Yang and He, 2013; Alyasseri et al., 2018; Abdel-Basset and Shawky, 2019). It is not our intention to review all of them. Instead, our emphasis will be on the typical characteristics of algorithms and search mechanisms, and consequently we have selected only a few algorithms in our discussions here.  Though different algorithms can be described in different ways, it would be convenient for the discussions later if we can subdivide the descriptions of algorithms into two categories: procedure-based and equation-based.

\subsection{Procedure-Based Algorithms}

Though the genetic algorithm (GA) can have quite rigorous mathematical analyses~\cite{Holland1975,Goldberg1989}, it is mainly a procedure as an optimization algorithm.
Its main steps are carried out in an iterative manner, and its main procedure consists of three parts:
\begin{itemize}
\item Solution representations: A solution vector $\x$ to a $D$-dimensional problem is usually
represented or encoded as a binary string of a fixed length or a string of real numbers.

\item Solution modifications: Solutions can be modified by mutation or crossover. Mutation can be applied to a single solution at a single place or multiple places, while crossover is carried out over two parent solutions by mixing or swap relevant parts to form new solutions.

\item Solution selection: The fitness of a solution is evaluated, usually in terms of its objective value.  The selection of a solution among a population is carried out according to its fitness
    (higher values for maximization problems) and the best solutions are usually passed onto the next generation.

\end{itemize}
This iterative procedure is relative generic for many algorithms. For example, the evolutionary strategy (ES) can also fit into the above procedure, though crossover is not used in ES. In addition, the ant colony optimization (ACO)~\citep{Dorigo1992} can also fit into the above steps, though solution modifications are not by mutation or crossover. Chemical pheromone is used to represent the fitness of a solution, and the modification of solutions are by pheromone deposition and evaporation.

\subsection{Equation-Based Algorithms}
A vast majority of the recent nature-inspired algorithms for optimization are equation-based where all solution vectors $\x_i (i=1,2,...,n)$ are represented as a population set of $n$ solutions in a $D$-dimensional search space. In this sense, all different algorithms use the same type of vector representations of solutions.

In addition, the selection of the solutions is mainly based on their fitness values. The fittest solutions (higher objective values for maximization, or lower objective values for minimization) are most likely to be passed onto the next generation in the population. Though there some subtle form of selection, such as fitness-proportional elitism, the essence of solution selection is basically the same.

Consequently, the main differences among different nature-inspired optimization algorithms now are the ways of solution modifications, usually using different mathematical forms or search mechanisms. In general, a solution vector $\x_i^t$ at iteration or generation $t$ is a position vector, and the new solution $\x_i^{t+1}$ is generated by a modification increment or mutation vector $\Dx$. That is
\be \x_i^{t+1}=\x_i^t +\Dx, \ee
which dictates the main differences between different algorithms. Traditionally, this increment is a step size (or a step vector). In case of gradient-based algorithms such as the Newton-Raphson method, this step
is linked to the negative gradient
\be \Dx=-\eta \nabla f(\x), \ee
where $\nabla f$ is the gradient of the objective function $f(\x)$, and $\eta>0$ is the so-called learning parameter~\citep{Boyd2004,YangBook2014}.

In some nature-inspired algorithms, the modification in $\Dx$ is often related to the
increment of velocity modification $\Dv=\ff{v}_i^{t+1}-\ff{v}_i^t$ such as
\be \Dx  = \ff{v}_i^t \; \Delta t, \ee
where $\ff{v}_i^t$ and $\ff{v}_i^{t+1}$ are the velocity for the solution $i$ (particle, agent, etc.)
at iterations $t$ and $t+1$, respectively. Here, $\Delta t$ is the time increment. As all algorithms are iterative or time-discrete dynamical systems, the time step or increment $\Delta t$ is essentially the difference in the iteration counter $t$, which means that $\Delta t =1$
can be used for all these algorithms. Consequently, there is no need to worry about the units of these quantities and thus consider all quantities in the same units.

Now let us discuss the equations for modifying solutions in different algorithms.
\begin{itemize}

\item Differential evolution (DE): In differential evolution~\citep{Storn1997DE}, the main mutation is realized by
\be \x_i^{t+1}=\x_i^t + F(\x_j^t-\x_k^t), \ee
which can be written as
\be \x_i^{t+1}=\x_i^t + \Dx, \quad \Dx=F (\x_j^t-\x_k^t), \label{DE-equ-100} \ee
where $\x_i^t, \x_j^t$ and $\x_k^t$ are three distinct solution vectors from the population.
The parameter $F \in (0, 2)$ controls the mutation strength.

\item Particle swarm optimization (PSO)~\citep{Kennedy1995PSO}: The main inspiration of PSO comes from the swarming behaviour of birds and fish. The position and velocity of particle $i$ at any iteration or pseudo-time $t$ can be updated iteratively using
\be \ff{v}_i^{t+1}= \ff{v}_i^t  + \Dv, \label{pso-speed-100} \ee
\be \x_i^{t+1}=\x_i^t+ \Dx, \label{pso-pos-100} \ee
with
\be \Dx=\ff{v}_i^{t+1} \Delta t = \ff{v}_i^{t+1}, \ee
and \be
\Dv=\alpha \ff{\epsilon}_1 [\ff{g}^*-\x_i^t] + \beta \ff{\epsilon}_2 [\x_i^*-\x_i^t], \ee
where $\ff{\epsilon}_1$ and $\ff{\epsilon}_2$ are two uniformly distributed random numbers in [0,1]. Here,  $\ff{g}^*$ is the best solution of the population at iteration $t$, while $\x_i^*$ is the
individual best solution for particle $i$ among its search history up to iteration $t$.

\item Firefly algorithm (FA)~\citep{Yang2008Book,Yang2009FA}:  The main characteristics of FA are based on the attraction and flashing behaviour of tropical fireflies.
The position vector $\x_i$ of firefly $i$ at iteration $t$ is updated by
\be  \x_i^{t+1} =\x_i^t +\Dx, \label{FA-equ} \ee
and
\be \Dx= \beta_0 e^{-\gamma r^2_{ij} } (\x_j^t-\x_i^t) + \alpha \; \ff{\epsilon}_i^t, \ee
where $\beta_0>0$ is the attractiveness at zero distance, that is $r_{ij}=0$.
The scale-depending parameter $\gamma$  controls the visibility of fireflies,
while $\alpha$ essentially controls the strength of randomization in FA.

\item Bat algorithm (BA)~\citep{YangBat2010}: The main inspiration of BA is based on the
echolocation of microbats and the associated frequency-tuning characteristics in a range from $f_{\min}$ to $f_{\max}$, in combination with varying pulse emission rate and loudness~\citep{Altri1996,Colin2000Bat}.

The position of a bat is updated by
\be \ff{v}_i^{t} = \ff{v}_i^{t-1} +  \Dv, \label{f-equ-150} \ee
\be \x_i^{t}=\x_i^{t-1} + \Dx,  \label{f-equ-250} \ee
with
\be \Dv=(\x_i^{t-1} - \x_*) [f_{\min}+\beta (f_{\max}-f_{\min}) ],
\quad \Dx=\ff{v}_i^t \Delta=\ff{v}_i^t, \label{BA-equ-200} \ee
where $\x_*$ is the best solution among the population of $n$ bats, and $\beta$ is a random number in [0,1].

\item Cuckoo search (CS)~\citep{YangDeb2009CS}: CS was based on the aggressive reproduction
strategy of some cuckoo species and their interactions with host species such as warblers~\citep{Davies2011}. The eggs laid by cuckoos can be discovered and thus abandoned with a probability $p_a$, realized by a Heaviside step function $H$ with the use of a random number $\epsilon$ in [0,1]. The similarity of two eggs (solutions $\x_j$ and $\x_k$) can be roughly measured by their difference $(\x_j-\x_k)$. Thus, the position at iteration $t$
can be updated~\citep{YangDeb2014Rev} by
\be \x_i^{t+1}=\x_i^t +\Dx, \ee
where
\be \Dx= \alpha s \otimes H(p_a-\epsilon) \otimes (\x_j^t-\x_k^t). \label{CS-equ1} \ee
The step size $s$, scaled by a parameter $\alpha$ so as to limit its strength,
is drawn from a L\'evy distribution with an exponent $\lambda$~\citep{Pav2007Levy}.
The generation of this step size can be realized by some sophisticated algorithms such as the Mantegna's algorithm~\citep{Mantegna1994}.

\item Flower pollination algorithm (FPA) (Yang, 2012): The FPA was mainly based on the pollination processes and characteristics of flowering plants (Yang, 2012; Yang et al., 2013), including biotic and abiotic pollination as well as flower constancy~\citep{Waser1986}.
The solution vector $\x_i$ of a pollen particle $i$ can be simulated by
\be \x_i^{t+1}=\x_i^t + \Dx, \ee
and
\be \Dx=
\brak{\gamma L(\lambda) (\ff{g}_* - \x_i^t), & \textrm{ if } r<p, \\ \\
\epsilon (\x_j^t -\x_k^t), & \textrm{ otherwise.} }
 \ee
Here, $r$ is a uniformly distributed random number in [0, 1], and
$\gamma$ is a scaling parameter. $\ff{g}_*$ is the best solution found so far at iteration $t$. In the above equation, $L(\lambda)$ can be considered as a random number vector to be drawn from a L\'evy distribution with an exponent of $\lambda$~\citep{Pav2007Levy}.

\item Other Algorithms: There are many other nature-inspired algorithms, such as simulated annealing (Kirkpatrick et al., 1983), bacteria foraging optimization~\citep{Passino2002}, biogeography-based optimization~\citep{Simon2008BGO},
    gravitational search (Rashedi et al.,2009), charged particle system \citep{Kaveh2010ChSS},
    black-hole algorithm \citep{Hatamlou2012}, krill herd algorithm \\
    \citep{Gandomi2012Krill},
    eagle strategy \citep{Yang2012ES} and others. However, their main differences are in the ways of generating $\Dx$ and $\Dv$ from the population of the existing solutions.

    Most recently, new variants and applications are appearing regularly, including local ant system for allocating robot swarms~\citep{Khaluf2019}, hybrid ant and firefly algorithms~\citep{Goel2018}, usability feature selection by MBBAT~\citep{Gupta2017}, vehicle routing (Osaba et al., 2017; Osaba et al., 2019) and others (Alyasseri et al., 2018; Rango et al., 2018; Abdel-Basset and Shawky, 2019).

\end{itemize}

Though the expressions of $\Dx$ and $\Dv$ may be different and some algorithms do not use velocity at all, the detailed underlying search mechanisms may also be very different, even for seemingly similar expression of $\Dx$. For example, the mutation in Eq.~\eqref{DE-equ-100} of differential evolution seems to be similar to the form in Eq.~\eqref{pso-pos-100} for PSO. However, the former was done by random permutation, while the latter was done by a difference vector with perturbed directions using a uniform distribution. Similarly, the modification in Eq.~\eqref{BA-equ-200} in BA uses frequency tuning by varying frequencies, though it has some similarity to the mathematical term in Eq.~\eqref{pso-pos-100}. Therefore, in order to gain better insight, we should analyze the underlying search mechanisms and their mathematical or statistical foundations.

\subsection{Applications}

Before we discuss various search mechanisms in nature-inspired algorithms, let us briefly outline some of their recent applications. These algorithms have been applied in almost every area of science, engineering and industry, from engineering optimization (Cagnina et al, 2008; Deb et al., 2002;
Yang and Gandomi, 2012; Yang and Deb 2013; Gandomi and Yang, 2014; Chakri et al., 2017),
and deep learning (Papa et al., 2017) to the coordination of swarming robots (Rango et al., 2018; Palmieri et al., 2018) and the travelling salesman problem (Ouaarab et al., 2014; Osaba et al., 2016; Osaba et al., 2017; Osaba et al., 2019).

For comprehensive reviews, please refer to some recent review articles
(Blum and Roli, 2003; Reyes-Sierra and Coello Coello, 2006; Senthilnath et al., 2011;
Yang and He, 2013; Yang and Deb, 2014; Alyasseri et al., 2018; Abdel-Basset and Shawky, 2019)
and books (Kennedy et al., 2001; Yang et al., 2013; Yang, 2013).

\section{Search Mechanisms and Theoretical Foundations}

Different algorithms usually use different search mechanisms, and these search moves are
often based on the underly probability distributions. Though solution modifications or perturbations
are largely part of mutation, we now focus on their statistical foundations and underlying mechanisms. Loosely speaking, we can put the ways of modifying or perturbing existing solutions into five categories: gradient-guided moves (GGM), random permutation (RP),
direction-based perturbations (DBP),  isotropic random walks (IRW),
and long-tailed, scale-free random walks (LTRW).

\begin{table}[ht]
\centering
\caption{Position and velocity modifications in algorithms. \label{PV-tab-100}}
\begin{tabular}{|l|l|l|}
\hline
Algorithm & Position increment $\Delta \x$ & Velocity increment $\Delta \ff{v}$ \\ \hline
Newton-Raphson & GGM & None \\
PSO & DBP & DBP \\
DE & RP, DBP & None \\
CS & RP, DBP, LTRW & None \\
SA & IRW & None \\
FA & DBP, IRW & None \\
BA & RP, DBP & RP, DBP \\
FPA & DBP, LTRW & None \\

\hline
\end{tabular}
\end{table}

Gradient-guided moves are mainly used in gradient-based optimization algorithms such as the Newton-Raphson method. The modification is parallel to the gradient direction, and the step length can be controlled by a learning parameter.

Random permutation tends to mix up a set of $n$ solutions, and then $k \ge 1$ solutions are randomly selected to generate new solutions. Random permutations are used in many algorithms, such as DE and FPA.

Direction-based perturbations are used in many algorithms with the term
of $(\ff{g}_*-\x_i)$ or $(\x_j-\x_k)$. The difference between any two vectors such as
$\x_j$ and $\x_k$ determines a direction, but this direction is then perturbed by multiplying by a uniformly distributed random number $\epsilon$. Thus, the actual directions of the moves are randomly distributed within a cone.

\begin{table}[ht]
\centering
\caption{Nature-inspired algorithms and their search characteristics.\label{Alg-tab-100}}
\begin{tabular}{|l|l|l|}
\hline
Algorithm & Probability  & Search \\
          & Distribution & Characteristics \\
\hline
PSO & Uniform & Guided search towards $\ff{g}_*$ \\
DE & Uniform  & Auto-scaling search \\
   &  Permutation & Random mutation  \\
CS & L\'evy flights & Self-similar search moves \\
   & Long-tailed & Scale-free search  \\
FA & Gaussian, uniform & Nonlinear attraction \\
BA & Uniform & Frequency-tuning \\
   &         & Fitness-dependent switching \\
FPA & Uniform & Scale-free search \\
    & L\'evy flights  & Jumps biased towards $\ff{g}_*$ \\
\hline
\end{tabular}
\end{table}

Random walks are a general framework for solution perturbations~\citep{YangHe2019}.
If we consider the current solution $\x_i^t$ as the current state $S_t$ at
time $t$, the next state (or solution) can be achieved by a local move $w_{t+1}$
\be S_{t+1}=S_t+w_{t+1}. \ee
Here, we use the non-bold form to denote the state in the $D$-dimensional space,
and perturbations can be done in a dimension by dimension manner.
Here, $w_{t+1}$ can be an array of random numbers to be drawn from the Gaussian distribution
\be w_{t+1} \sim N(0, 1), \ee
which means that the random walk becomes a Brownian motion. Here, the notation `$\sim$' emphasizes that the random steps should be drawn from the probability distribution described by the right-hand side of the equation. As the iteration time is discrete, the pseudotime counter $t$ can
be replaced by the number ($N=t$) of steps, which means that the average distance $d_N$ covered by a Brownian random walk is \be d_N \; \propto \; \sqrt{N}. \ee
This square-root law is a typical feature for many diffusion phenomena~\citep{YangHe2019}.
If the steps are drawn from Gaussian distributions, the random walks are isotropic random walks.

However, some probability density distributions can have a long tail, or a heavy tail.
If the steps are drawn from a heavy-tailed or long-tailed distribution, the random walks can
 become non-isotropic, long-tailed random walks or even scale-free random networks.
A good example of heavy-tailed distributions is
the Cauchy distribution
\be p(x, \mu, \gamma)=\frac{1}{\pi \gamma} \Big[\frac{\gamma^2}{(x-\mu)^2+\gamma^2} \Big], \quad -\infty < x < \infty, \ee
with two parameters $\mu$ and $\gamma$. Both its mean and variance are infinite or
undefined~\citep{Grindstead1997,Bhat2002}.

Another important long-tailed distribution is the L\'evy distribution, which has been used
in nature-inspired computation. L\'evy flights are a very special random walk whose steps are drawn from the L\'evy distribution.

The rigorous definition of L\'evy probability distribution can be tricky, involving an integral~\citep{Gutow2001,Pav2007Levy}
\be p(x) =\frac{1}{\pi} \int_0^{\infty} \cos(k x) e^{-\alpha |k|^{\beta}} dk, \quad (0 < \beta \le 2), \ee
where $\alpha>0$. The case of $\beta=1$ is equivalent to a Cauchy distribution, while $\beta=2$ leads to a normal distribution. For the practical purpose, we can use the following approximations for large steps ($s$)
\be L(s) \ra \frac{\alpha \; \beta \; \Gamma(\beta) \sin (\pi \beta/2)}{ \pi |s|^{1+\beta}}, \quad s \gg 0,  \ee
where $\Gamma(\beta)$ is the standard gamma function. Comparing the variance of the Brownian random walks, the variance or the distance covered by L\'evy flights increases much faster~\citep{YangBook2014}. The mean distance covered by the L\'evy flights after $N$ steps is \be d_N \; \propto \; N^{(3-\beta)/2}. \ee
This power-law feature is typically for super-diffusion phenomena~\citep{Pav2007Levy}.

By analyzing nature-inspired algorithms in great detail, we can summarize the search mechanisms and
their underlying statistical characteristics in Tables~\ref{PV-tab-100} and \ref{Alg-tab-100}.
Most algorithms modify their solution population directly without using velocities as shown in Table~\ref{PV-tab-100}. However, even for the same types of probability distributions, their role and
effects on search characteristics can be subtly different, and we summarize their search characteristics loosely in Table~\ref{Alg-tab-100}.

\section{Challenges and Open Problems}

Despite the effectiveness of nature-inspired algorithms and their popularity, there are still
many challenging issues concerning such algorithms, especially from theoretical perspectives.
Though researchers know the basic mechanisms of how such algorithms can work in practice, it is not quite clear why they work and under exactly what conditions. In addition, all nature-inspired algorithms have algorithm-dependent parameters, and the values of these parameters can affect the performance of the algorithm under consideration. However, it is not clear what the best values or settings are and how to tune these parameters to achieve the best performance. Furthermore,
though there are some theoretical analyses of some nature-inspired algorithms (Clerc and Kennedy, 2003; Chen et al., 2018), it still lacks a unified mathematical framework to analyze all algorithms to get in-depth understanding of their stability, convergence, rates of convergence and robustness.

In the rest of this paper, we will highlight five open problems concerning nature-inspired algorithms: mathematical framework for stability and convergence, parameter tuning, role of benchmarking, performance measures for fair comparison, and large-scale scalability.

\subsection{Mathematical Framework}

As almost all algorithms for optimization are iterative, traditional numerical analysis tends to use fixed-point theorems to see if it is possible to show the conditions for such theorems are satisfied. Basically, an iterative algorithm means that a new solution $\x_{k+1}$ can be obtained from
the current solution $\x_k$ by an algorithm $A$ with a parameter $\alpha$ or a set of parameters.
That is
\be \x_{k+1} =A(\x_k, \alpha), \label{Alg-iter-100} \ee
If we omit the bold font and use the standard notations in numerical analysis, we can write the above
equation simply as
\be x_{k+1}=A(x_k), \ee
without stating $\alpha$ explicitly.
Using the properties of function composites, we have
\be x_{k+1}=A^{k+1}(x_0)=(A \circ A^k)(x_0), \ee
where $x_0$ is the initial starting point.

From the well-known Banach fixed-point theorem~\citep{Granas2003,Khamsi2001Kirk}, we know that a fixed point $x_*$ can exist if $A(x_*)=x_*$ under
the condition that certain distance metric $\rho(.,.)$
\be \rho\big(A(x_i), A(x_j)\big) \le \theta \; \rho(x_i, x_j), \quad 0 \le \theta < 1, \ee
for all $x_i$ and $x_j$. This requires that $\rho$ is a shrinking or contracting metric.
If a fixed point exists, it is possible to approach this point iteratively via
\be \lim_{k \ra \infty} x_{k+1}=\lim_{k \ra \infty} A^{k+1}(x_0)=x_*. \ee However, for most nature-inspired algorithms, this condition may not be true at all~\citep{YangHe2019}.

Alternatively, we can view the iterative system such as Eq.~\eqref{Alg-iter-100} as a dynamical
system, which allows us to analyze its behaviour in the framework of dynamical system theory.
For example, the analysis of PSO was first carried out using dynamical system theory~\citep{Clerc2002}.

In case when an algorithm is linear in terms of its position or  solution vectors. It is possible to write the updating equations as a set of linear equations as  a time-discrete linear dynamical system
\be x_{k+1}=B x_k, \ee
where $B$ becomes a linear mathematical operator on $x_k$~\citep{Khalil1996}.
Its solution can be written as
\be x(k) =B^k x_0. \ee
The Lyapunov stability requires that all the $n$ eigenvalues $\lambda_i$ of $B$
must satisfy
\be |\lambda_i| \le 1. \ee
If $|\lambda_i|<1$ (without equality), the algorithm or system
becomes globally asymptotically stable.

Using a dynamical system framework, Chen et al. (2018) studied an
extended bat algorithm system
\begin{eqnarray}
v_{k+1}& = & -\zeta x_k+\theta v_k+\zeta g, \\
x_{k+1}& = & x_k+\theta v_k+\zeta g-\zeta x_k,
\end{eqnarray}
where $v_k$ and $x_k$ are the velocity and position of a bat at iteration $k$. Here, $g$ is
the best solution found by the current population. $\zeta$ and $\theta$ are two parameters.

The above two equations can be rewritten compactly as
\begin{equation}
Y_{k+1} = C Y_k+M g,
\end{equation}
where
\begin{equation}
Y_k=\begin{bmatrix}
x_k \\ v_k
\end{bmatrix}, \qquad
C=\begin{bmatrix}
1-\zeta & \theta \\-\zeta & \theta \\
\end{bmatrix}, \qquad
M=\begin{bmatrix}
\zeta \\ \zeta
\end{bmatrix}.
\end{equation}
Their analysis obtained some stability conditions for the parameters so that
\begin{equation}\begin{cases}
-1 \le \theta \le +1, \\
\zeta \ge 0, \\
2\theta-\zeta+2 \ge 0.
\end{cases}
\end{equation}
They also used numerical experiments confirmed such stability (Chen et al., 2018).

Another common way for analyzing the probabilistic convergence is to use Markov chain theory.
There are some extensive studies in this area. For example, the convergence of the genetic algorithm has been analyzed in terms of Markov chains (Suzuki, 1995; Aytug et al., 1996; Greenhalgh and Marshal, 2000; Gutjahr, 2010), and
this framework has been applied to analyze the cuckoo search algorithm (He et al., 2018)
and the bat algorithm (Chen et al., 2018). However, these studies have focused on the probabilistic convergence, but there still lacks information about the rate of convergence.

From the Markov chain theory~\citep{Grindstead1997,Ghate2008}, we know that the largest eigenvalue of a proper Markov chain is $\lambda_1=1$, it is believed that the second largest eigenvalue $0<\lambda_2<1$ controls the error variations $||E||$ or the rate of convergence
\be ||E|| \le  C (1-\lambda_2)^k, \ee
where  $C>0$ is a positive constant, which depends on the exact forms of the chains.
In principle, the chain should converge as $k \ra \infty$, but it can be very challenging to figure out this eigenvalue $\lambda_2$. There is almost no literature on this topic in the context of nature-inspired algorithms. Thus, an open problem in this area is as follows:

{\bf Open Problem 1.} How to build a unified framework for analyzing all nature-inspired algorithms mathematically, so as to obtain in-depth information about their convergence, rate of convergence, stability, and robustness?

As we have seen from the above, it seems that this framework may require a multidisciplinary approach to combine different mathematical, stochastic and numerical methods so that we can study algorithms from different perspectives.

\subsection{Parameter Tuning}

All nature-inspired algorithms have algorithm-dependent parameters, though the number of parameters can vary greatly. For traditional algorithms such as quasi-Newton methods, the tuning of a single parameter can have rigorous mathematical foundations (Boyd and Vandenberghe, 2004; Bertsekas et al., 2003; Chabert, 1999; Zdenek, 2009). However, for nature-inspired algorithms, the tuning is mainly empirical or by parametric studies~\citep{Eiben2011}.

Loosely speaking, an algorithm with $m$ parameters $\ff{p}_m$=($p_1, p_2, ..., p_m$) can be written schematically as
\be \x_{k+1}=A(\x_k | p_1, p_2, ..., p_m, \epsilon_1, ..., \epsilon_s), \ee
where $\epsilon_1, ..., \epsilon_s$ are $s$ different random numbers, which can be drawn from different probability distributions. To a certain degree, all these random numbers are drawn iteratively, thus the tuning of an algorithm will mainly be about the $m$ parameters. Thus, we can compactly write the above as
\be \x_{k+1}=A(\x_k, \ff{p}_m). \ee
If we use an algorithm $B$ to tune this algorithm, how was algorithm $B$ tuned initially? If we used another algorithm $C$ to tune algorithm $B$, how did we tune $C$ in the first place? In principle, we should use a well-tuned algorithm (or an algorithm without any parameters) to tune a new algorithm.
Thus, a key issue is how to tune an unknown algorithm properly?

Systematical brute-force tuning can be very time-consuming if the number of parameters is large. In addition, there is no guarantee that a well-tuned algorithm works well for one type of problems can work well for a different type of problems. It may be the case that parameter settings of an algorithm can be algorithm-dependent and problem-dependent if we want to maximize the overall performance.
In addition, even if an algorithm is tuned, its parameters become fixed after tuning. However,
there is no reason that we cannot vary the parameter during iterations. In fact, some studies showed that the variations of a parameter can be advantageous, which leads to self-adaptive variants.
For example, self-adaptive differential evolution seems to work better than its original version (Brest et al., 2006).

One way of tuning algorithms is to consider parameter tuning as a bi-objective process
so as to form a  self-tuning framework (Yang et al., 2013), where the algorithm to be tuned can be used to tune itself. This can still be a very time-consuming approach. Now we have another open problem concerning parameter tuning and parameter control.

{\bf Open Problem 2.} How to best tune the parameters of a given algorithm so that it can achieve
its best performance for a given set of problems? How to vary or control these parameters so as to maximize the performance of an algorithm?

\subsection{Role of Benchmarking and No-Free-Lunch Theorem}

For any new algorithm, especially a new nature-inspired algorithm, an important study is
to use benchmark functions to test how the new algorithm may perform, in comparison with other algorithms. Such benchmarking allows researchers to gain better understanding of the algorithm in terms of its convergence behaviour, stability and advantages as well as disadvantages.
However, the key question is what benchmarks should be used.

In the current literature, the benchmarking practice seems to use a set of test functions with different properties (such as mode shapes, separability and optima locality), there are many such benchmark test functions~\citep{Jamil2013} and some test suites designed by different conferences or research groups. As these functions are typically smooth, defined on some regular domains, they can serve some purpose, but such benchmarking is not actually much use in practice.
There are many reasons, but we only highlight two here. One reason is that these functions are often well-designed and sufficiently smooth, while real-world problems are much more diverse and can be very different from these test functions.  Another reason is that these test functions are typically unconstrained or with simple constraints on regular domains, while the problems in
real-world applications can have many nonlinear complex constraints and the domains can be formed by
many isolated regions or islands. Consequently, algorithms work well for test functions cannot work well in applications.

For an algorithm to be validated properly, testing and validation should include test functions with
irregular domains, subject to various constraints. For example, if an algorithm has been tested for all the benchmarks in the literature, there is no guarantee that it can still be effective to solve other problems such as the following newly designed, seemingly simple, two-dimensional function $f(x,y)$
\be f(x,y)=\sum_{i=-N}^N \sum_{j=-N}^N (|i|+|j|) \exp\Big[-a (x-i)^2 - a(y-j)^2\Big], \ee
in the domain of
\be |x-i|+|y-j| \le b=\frac{1}{a}, \quad \forall i, j, \ee
where $i,j$ are integers, $N=100$ and $a=10$. This function has $4N^2$ local peaks, but it has four highest peaks at four corners; however, its domain is formed by many isolated regions, or $4N^2=40000$ regions.

In the current literature, there are many different optimization algorithms. A key question naturally arises:  Which is the best one to use? Is there a universal tool that can be used to solve all or at least a vast majority of optimization problems? The simple truth is that there are no such algorithms. This conclusion has been formalized by Wolpert and Macready in 1997 in their influential work on the no-free-lunch (NFL) theorem \citep{Wolpert1997}. The NFL theorem states that if an algorithm $A$ can outperform another algorithm $B$ for finding the optima of some objective functions, then there are some other functions on which $B$ will outperform $A$. In other words, both $A$ and $B$ can perform equally well over all these functions if their performance is averaged over all possible problems or functions.

But the conclusions from most studies in terms of benchmarking seem to indicate that some algorithms are better than others. In practice, we know that some algorithms are indeed better than others, and  the quicksort for sorting numbers is indeed better than a method based on simple pair-wise comparison. Now how do we resolve this seemingly contradiction? The key to resolve this issue lies in the keywords `all' and `average'. In practical problem-solving,  we are always concerned with a particular set of problems, not all problems. We are also concerned with the actual individual performance of solving a particular problem, not the averaged performance over all problems.
As result, benchmarking using a finite set of algorithms and a finite set of functions becomes a zero-sum ranking problem~\citep{Joyce2018,YangHe2019}. On the other hand, recent studies seemed to indicate that free lunches may exist~\citep{Auger2010FL,Corne2003FL}, especially for continuous optimization \citep{Auger2010FL},  multi-objective optimization \citep{Corne2003FL} or co-evolution \citep{Wolpert2005}. Therefore, we now have an open problem concerning benchmarking.

{\bf Open Problem 3.} What types of benchmarking are useful? Do free lunches exist, under what conditions?

\subsection{Performance Measures}

For the benchmarking comparison of different algorithms, the conclusions can be influenced by the performance metrics used. To make a comparison, researchers have to select appropriate performance measures. In the current literature, comparison studies are mainly concerned with the accuracy, computational efforts, stability, and success rates.

For a given set of problems and a few algorithms, the algorithms obtained the most accurate solutions in comparison with some known or analytical solutions are considered better. Obviously, this will depend on the accuracy level and the stopping criteria used. Obviously, if one algorithm runs longer than others, even an ineffective algorithm may be able to obtain sufficiently good results if allowed to run much longer. Thus, to be fair, all algorithms should use the same computational efforts, which is usually realized by fixing the number of function evaluations.

An alternative approach is to use a fixed accuracy and compare the number of function calls or evaluations as a measure of computational costs. Algorithms with the smaller numbers of function evaluations are considered better. Even for the same number $N$ of function calls, there are different ways of using this fixed budget. If one algorithm first runs half of $N$ (or any other values) evaluations and select solutions, and then feed them into the run of the second half of $N$ evaluations, the performance may be different from the execution of the same algorithm with a single run of $N$ evaluations. Such different ways of implementing the same algorithm may lead to mixed conclusions.

Due to the statistical nature of nature-inspired algorithms, results are not exactly repeatable, and thus multiple runs are needed so as to get meaning statistics. Thus, some researchers use the best objective value obtained at the final iteration, together with their means, standard deviations and other statistics. This may give a fuller picture about the algorithms. Though a smaller standard derivation may indicate that the algorithm is more robust, but this may be linked to the problem under consideration. In addition, the ways of initializing the population and the probability distributions used in the algorithm may also influence such results, though it is not clear how initialization may exactly affect the final results.

Another measure used for comparison is the success rate. For multiple runs ($N_r$), there may be $N_s$ times that an algorithm is able to find the optimal solution, which means that the success rate is
the ratio $N_s/N_r$. However, this depends the way of how the success is defined. For a function $f(x)$ with a known optimal solution $x_*$ and the minimization objective $f_{\min}(x_*)$, the success can be defined by either $|x-x_*| \le \delta$ or $|f(x)-f_{\min}| \le \delta$ for a given small neighborhood such as $\delta=10^{-5}$. This can be two very different criteria if the landscape is relative flat.

Some studies use one or more performance measures, but it is not clear if the above performance measures are truly fair measures for a fair comparison.

{\bf Open Problem 4.} What are the most suitable performance metrics for fairly comparing all algorithms? Is it possible to design a unified framework to compare all algorithms fairly and rigorously.

\subsection{Algorithm Scalability}

From the application point of view, the most important indicator of the effectiveness of an algorithm is how efficiently it can solve a wide range of problems. Apart from the constraints posed by the no-free-lunch theorem, the efficiency of a given algorithm for a given type of problems can be largely affected by the size of problem instances. A well-known example is the travelling salesman problem (TSP) where a visitor is required to visit each city exactly once so as to minimize the overall distanced travelling through $n$ cities. For a small number of cities (say, $n \le 5$),
it is an easy problem. For a moderate or large $n$, this problem becomes an NP-hard problem~\citep{Cook1983,Arara2009,Goldreich2008}.
In this case, an algorithm that works well for small-scale problem instances cannot be scaled up to solve large-scale problems in a practically acceptable time scale.

Despite the diverse range of applications concerning nature-inspired algorithms and evolutionary algorithms, the problem sizes tend to be small or moderate, typically under several hundred parameters. It is not clear if these algorithms can be scaled up, by parallel computing, high-performance computing or cloud computing approaches.

{\bf Open Problem 5.} How to best scale up the algorithms that work well for small-scale problems to solve truly large-scale, real-world problems efficiently?

There are other open problems concerning nature-inspired algorithms, including how to achieve the optimal balance of exploitation and exploration, how to deal with nonlinear constraints effectively, and how to use these algorithms for machine learning and deep learning.

Nature-inspired computation is an active area of research. It is hoped that the above five open problems we have just highlighted can inspire more research in this area in the near future.

redpajama_set_name: RedPajamaArXiv


weapons against the opposition, and he eventually falls, the prospect of an opposition bloodbath, which are already very high, i think it becomes overwhelming. megyn: before i let you go, just to reiterate, you don't think that bashar al-assad is incapable of this? when i speak of the torture -- we have seen the bodies lined up, people with their arms tied behind their back, murdered in cold blood -- children, 9-year-olds being shot in the head. as their parents watch. other children made to watch as their parents are murdered in front of them -- babies -- reports go on and on. too gruesome for 1:00 p.m. eastern time. they're just so our viewers know, you believe this man is capable of unleashing chemical weaponry upon his own people? >> absolutely. i think it would be second nature to him. megyn: ambassador bolton, thank you for being here.
>> and you. megyn: ed henry is at the white house briefing as this happens. this is stronger language. in the worst-case scenario, should syria deploy chemical weapons, and america is forced to take action, the pentagon estimates it would take 75,000 troops to seize all the regime's weapons. syria is one of eight countries that have not signed in 1992 convention banning chemical weaponry. other countries refusing to sign our israel and north korea and egypt. a u.n. conference in dubai is underway right now. new questions about internet freedom.
two dozen countries, including iran, syria, north korea, could be making decisions affecting communications worldwide. catherine herridge has more in washington. reporter: thank you, megyn, and good afternoon. the international telecommunications union, this conference in dubai is viewing rules established long before the internet became a primary method of communication. the u.n. body could impact every day vacation. >> this could affect every cell phone tablet personal computer in the world. pretty much every chip in every type of consumer devices have an ip address associated with them. therefore, there are proposals that the there be a registry for each of those computer chips. reporter: the u.s. is in support of what is called web neutrality.
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private and secret, in fact. and avoids any expression of the national media. there has been almost no discussion in the public press of the discussions that are of today in their second week. that is extraordinary. megyn: does he really made this approval or can he do what he wants the epa? -- so he can get cap-and-trade. we played the mark levin clip before you came in, he actually sued the administration before the election saying that we have reason to believe that they are getting ready to unleash epa regulations after the election and we have the right to know what they are now. here is an october 22 issue that we are fighting an administration that has no regard for the rule of law in my humble opinion.
wearing all tennis gear. now experts say the husband may not have been murdered at all. now experts say the husband may not have been murdered at all. >> i'm just thrilled and so thankful for the das office for dropping the charges and i would like to thank my family and friends and my attorneys. my goodness, they were fabulous. my investigator, just everyone that has been there supporting me everyday obligations, but obligatio. i need to rethink the core of my portfolio. what i really need is sleep. introducing the ishares core, building blocks for the heart of your portfolio. find out why 9 out of 10 large professional investors choose ishares for their etfs. ishares by blackrock. call 1-800-ishares for a prospectus which includes investment objectives, risks, charges and expenses. read and consider it carefully before investing. risk includes possible loss of principal.
united nations announced it is withdrawing all nonessential people there as the threat of chemical warfare looms. this is not the first time that we have gotten reports that they could be considering using these weapons. the last time it didn't come to anything. well, will this time be different? as assad seems to be losing control in his own country. we just got some additional intelligence in the last half-hour that suggest evidence that syria may not only be moving chemical weapons, but also preparing them. that would make this a very different scenario. we are looking into that, and we will have a live report at the top of the hour. white house press secretary jay carney is also being grilled this afternoon in addition to syria, about the white house fiscal cliff package. the white house's proposal to avoid the big tax hikes and spending cuts that are going to happen in january, unless something is done.
eligibility age, ask wealthier americans to pay higher medicare premiums. and possibly paring back the cost of living increases, giving to social security beneficiaries. those are three specific so we have heard so far from the gop side. what are your thoughts on that? >> i think that is a good thought. but mitch mcconnell and speaker boehner need to be more specific. that doesn't add up to more than two or three really dollars worth of cuts. the president proposed many more cuts than not. that is the beginning. this is a negotiation process. i am a lawyer and we settle cases by someone saying this or that and then they move to the middle. that is not what is going on, although mitch mcconnell name three things, that is more than the house republicans have done. again, the republicans are afraid to talk about where the cuts should come. because they're going to have to talk about medicare.
host accused of setting a guest hair on fire. it wasn't a trick or an accident. trace gallagher walks us through what it was. we just got the update from police. plus, new developments on a high-profile case of domestic violence this week. that is an understatement. when an one nfl player murdered his girlfriend and killed himself. nbc's bob costas used the tragedy as a springboard for an anti-gun lecture right in the middle of a football game. his remarks and the fierce debate are just ahead. hi. i'm henry winkler.
said that we are not going to fund it. you can say that you are going to bring these detainees and as long as you want, but we have the power and we are not giving you the money. so can he do this in any way other than getting democratic control of the house? >> well, he's done a lot of things extra legally and using this unitary executive power, even the purchase of the facility was in defiance of not only bipartisan opposition and opposition across the country, but particularly in defiance of what the house appropriations subcommittee that oversees it says. frank wolf had raised a lot of questions about this unilateral decision that obama had made. i think that people need to go back and this smells like another chicago crony deal.
it combines obama's war on terror with the chicago way. apparently they were discussing this on air force one in march. he had already greenlighted it. particularly where these detainees might be shifted at some point. he certainly is laying the groundwork for it. particularly it says that the facility would be open to people who were detained under the authority. megyn: any act of congress three that's right. let's not be stupid about this. who else were they talking about? megyn: final question. do you believe that there was any shift of opinion on this issue in the congress right now? he believed president has the support to make this change at the moment? >> he certainly does not.
although the release of the gal report is a way to try to open the door and you had dianne feinstein saying that if there is a political will to do it -- the thing is that they don't care about it. they are going to run roughshod and steamroll political will to have a chance to do so. megyn: in three minutes, a shocking video accused you turn for legal matters? maybe you want to incorporate a business. orrotect your family with a will or living trust. and you'd like the help of an attorney. at legalzoom a legal plan attorney is available in most states with every personalized document to answer questions. get started at legalzoom.com today. and now you're protected. is efficiently absorbed in small continuous amounts. citracal slow release continuously releases calcium plus d with efficient absorption in one daily dose. citracal slow release.
intentional. now it appears that the police agree. trace gallagher is live with more. >> he was actually on that tv show to promote his own magic television show. i have to warn you that the video is kind of hard to watch. it's pretty violent. we will show it to you in real time here, and then we will slow it down. the host took something called [inaudible name], it is used during rituals, and it is very highly flammable. he ignites the liquid in his hand and then he puts it on this guys head. check it out. there it is on his head. as you said, at first, they thought this was a prank or a skit that had gone bad. he suffered severe burns to his head and neck and face. he let leader said in a statement, i was not aware that he was going to do this. this was not a stunt or part of an act.
this was a criminal attack. the producers on the show say the host was simply trying to bless a way the magician's evil spirits. in the dominican journalists say how they were well known for using witchcraft. you said earlier that the host has an arrest warrant for him and the charges are still unclear. they are doing whatever it is meant to be ritually. megyn: and credible. that poor meanwhile, the battle rages over the nations finances. there is also concern that the national media may have concern about the fiscal cliff. we will take a look. and investigators search for a motive in a horrific murder suicide that rock the national football scene.
the social media backlash has not stopped since comments by bob costas. he went on prime time last night and was inspired by the tragedy to go on an antigovernment tirade. are the taxpayer? a fair and balanced debate is coming up next [ fishing rod casting line, marching band playing ] [ male announcer ] the rhythm of life. [ whistle blowing ] where do you hear that beat? campbell's healthy request soup lets you hear it... in your heart. [ basketball bouncing ] heart healthy. great taste. mmm... [ male announcer ] sounds good. it's amazing what soup can do.
gun control. costas paraphrase an article written by a kansas city-based writer for fox sports. >> handguns do not enhance our safety. they exacerbate our flaws and bait us to embrace confrontation rather than avoiding it. in the coming days jovan belcher's actions will be an lids. but i believe in jovan belcher didn't possess a gun, he and kasandra perkins would both be alive today. >> reporter: a lot of people criticizing costas for using a sporting event to is suppose a political view point. some people agree with costas, others asked what kel were weapon did ovmen -- did o.j. us.
loopholes simply doesn't add up to a serious proposal. we haven't heard which deductions they would cap or which loopholes they would close. megyn: guy benson is a fox news contributor. we are hearing from the gop side, that this was not an opener about it president in their belief, but the focus on not just raising taxes on the rich -- it can't just be getting rid of loopholes. the president is saying the rate has to go you have on the rich is about humiliatingup cans. how so? >> i think there are a couple things you have to look at. the offer the president put on the table was heavy on tax increases. $1.6 trillion with almost nothing specified or guaranteed on entitlements or reduction in spending.
to solve the problem. megyn: last night bob costas launched into an anti-gun tirade. it made national news when police arrested a well-known ref from tennis right before the u.s. open. now she has been released. all charges were dropped. dr. baden is here.
who said it so well with we may as well just paraphrase from the end of his article. our current gun culture he wrote insures that more and more domestic disputes will end in the ultimate tragedy and more convenience store confrontations over loud music will leave more teenaged boys bloodied and dead. handguns do not enhance our safety. in the coming days jovan's actions and their connect to football will be analyzed. but here, wrote jason whitlock. here is what i believe. if jovan belcher didn't possess he begun today he and kasandra perkins would be alive.
more likely to die if a gun is involved than if a knife is involved. so the fatality rate is different if a gun is involved. if you are sitting there and somebody walk up to you and they are going to attack would you prefer they have a knife or gun? megyn: i would prefer i had a gun. >> you are far more likely to die if a person has a gun. >> kirsten is wrong. she grew up in fairbanks. nobody would go outside the city limit and go on a walk on a trail without a pistol because of the natural threats there. in big cities where they ban gun ownership or reasonably restrict it. there are 20,000 you laws already. when you say you shouldn't be fired forecasting an opinion? ask don imus about that.
megyn: and hank williams. >> are we comparing wanting gun laws to saying racist things? megyn: controversial comments. >> there has to be an allowance for people to have opinions. megyn: hold that thought. we are going to take it back up on the other side of the break. thank you both. constipation, diarrhea, gas, bloating? yeah. one phillips' colon health probiotic cap each day helps defend against these digestive issues with three strains of good bacteria. approved! [ female announcer ] live the regular life. phillips'.
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jovan belcher through any means other than denying it to all people. when he said why did he own one? i just suggested to you hundreds of thousands times a year american citizens protect themselves and the ultimate purpose for putting it in the constitution was founding fathers who believed some day you might have a tran cal government. i know people don't like that suggestion. but that was the reason they put it in there. >> i think we all agree it's the person responsible for this crime is jovan belcher. you can argue about what led to the moment. but -- >> one last thought. would an nfl player of 225 pound his size have ended the life of the mother of his child without a gun. i would asking you he could have done it without a gun. that's a sad statement.
i feel for kasandra perkins. she is the real victim. maybe if she owned a gun she would be alive today. megyn: we are taking your thoughts on it, by the way. it's an issue on which people feel so strongly. follow me on twitter @megynkelly. is the media playing favorite in the showdown over the looming fiscal cliff? after the break a look at why that debate i getting new attention. a stunning reversal of fortune. it made national news when police arrested a well-known woman from the world of tennis. she was about to be the ref at the u.s. open when she dragged her away. after they charged her with murdering her 80-year-old husband. a complete about-face. they set her free and dropped all charges, and yet the investigation continues. and they still suspect murder.
we'll look into this case as dr. michael baden may have saved this woman's freedom.
megyn: new questions about the fight over the fiscal cliff and whether some media outlets are playing favorites.
tony said saying the president doesn't necessarily have a mandate. the american people voted. there was a contrast of ideas over what we do with our tax code and how we reform our tax code. and at the even of the date president got millions more in the popular vote than romney because americans think by and large their wealthier neighbors and wealthier americans should be paying a fairer share. it's not fair when you have the wealthiest among us paying a lower effective tax rate. megyn: is the media -- the media has been focused on the tax hikes and whether president obama is going to get them and not focused on spending cuts. is that because the republicans and the president agree the middle class needs those tax cuts and should get them.
arrogance or bias, anything inappropriate about the media being oh focused on the tax debate as opposed to where are the spending cuts? >> i don't think so. this is because there hasn't been any serious proposal for spending cuts and it's true of the republicans as well. you don't see republicans coming out saying they want to cut spending on specific things. the president put forward a plan that included a few spending cuts. now it's the republicans' turn to show what they are willing to cut spending on. megyn: before i go, the president came out with a $400 billion in proposed spending cuts from his last budget. mitch mcconnell came out with spending cuts when it comes to medicare, maybe adjusting the cost of living for social security. but they are too timid because this is an issue on which people vote and no one wants to talk about it. am i wrong?
arrested for her husband's murder. she has been released after dr. baden gets involved in the case.
disease shows there is a good reason for him to fall down. and there was no other injuries. there were no injuries to any other part of the body. there were no skull fractures. no brain damage. it was just a fall downstairs and falls in people who are blind downstairs can occur. megyn: i want 0 bring in our panel. lis weihl and mark eiglarsh. lis? >> i love dr. baden and think he's wonderful. i will say from a prosecutor's standpoint if you really leave you don't have the evidence what you do is you dismiss with prejudice. very clearly here they did not do that. they think there is something else they can find here megyn and we'll see going forward. megyn: the investigators are saying they still suspect murder. they say we have no other suspects in the case.
there was no forced entry. they were arguing for weeks ahead of time. they seem to be telling us we can't prove it was her but we still think it was her. >> it moms shocker. these are the same investigator hospital brought evidence so sufficient they thought to bring charges and october 3 they announce she's the one who committed first degree murder and they filed charges and 58 days later the charges are dropped. the investigators still think she might be guilty? megyn: that's extraordinary, isn't it? >> extremely. at one minute you are saying you are proof beyond a reasonable doubt. there is no reasonable hypothesis of innocence. megyn: as dr. baden points out. 80 years old with a heart arrhythmia who is legally blind. is that not plausible he fell count stairs?
>>it is plausible. that's why the prosecutors had it dismissed. dr. baden came in, gave this great analysis. a prosecutor's expert might be different. let's find out. megyn: stand by. but dr. baden goes into a lot oe and it doesn't make the prosecutors drop the charges. [ female announcer ] the humana walmart-preferred rx plan p-d-p gives you a low $18.50 monthly plan premium... and select generic hypertension drugs available for only a penny... so you can focus on what really matters. call humana at 1-800-808-4003.
megyn: you have law enforcement in california saying they suspect murder, but telling the "l.a. times" that some evidence might now suggest accident and the d.a. spokeswoman declined to elaborate on the new information. dr. baden, are you the new information? >> i'm not sure what the d.a.
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MIDDLEBURY – Warsaw's Delaney Wihebrink will have her hands full, but is in good position after Thursday's Northern Lakes Conference Girls Swimming Championship preliminaries.
Wihebrink enters Saturday's championship round the top seed in the breaststroke, but only by a little bit. Wihebrink posted a 1:08.03, but has plenty of company with Northridge's duo of Haley Dygert and Jenna Nethercutt both within four-tenths of a second behind. Wawasee's Rileigh Atwood is also in striking range, sitting at 1:09.51 and alive in the championship swim.
Wihebrink is also swimming in the finals of the individual medley, posting a 2:17.10 for the third seed. Northridge's Sydnee Emerson had the top qualifying swim in the IM at 2:09.08. Wihebrink's teammate, Taylor Gunter, is also alive in the IM championship after qualifying eighth.
Warsaw has seven other individual swims in the championship flight, Gunter qualifying for a second event by landing eighth in the butterfly. Olivia Herman was fifth in the 100 freestyle and sixth in the 50 freestyle and Laurel Moeller squeaked into both the 200 and 500 freestyles in eighth place. Bella Coffing and Lauren Kuhl were both eighth in qualifying, Coffing in the 50 free and Kuhl in the backstroke.
NorthWood's Kate Jarvis is alive in the 100 free after placing eighth and Wawasee had one other swimmer make the finals, Ella Park's fifth-place run in the 500 free.
All eight of the NLC member schools had their relays qualify in all three disciplines.
Northridge, as no surprise, is the team to beat after posting nine top times heading into Saturday. The Raiders were again undefeated in the round robin at 7-0 and will bring in a trio of divers that will also perch at or near the top of those standings. Sydnee Emerson (fly, IM), Elsa Fretz (100, 200), Lauren Miller (50) and Caitlin Clark (500) are the Northridge top seeds heading into Saturday, and Miller nearly took a second middle lane but was edged out by Concord's Maddisen Lantz by three-hundredths in the backstroke.
Diving begins at 9 a.m. Saturday at Northridge, with swim finals starting at 1 p.m. with the diving finals worked into the main event.


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The key is to moisturize and not let skin become too dry. When skin becomes too dry it leads to itching, which leads to an itch-scratch cycle.
Good moisturization starts with limited use of soap and using only mild soaps.
In the bath only use soap on "dirty" areas which include: neck, armpits, groin, feet, and hands.
Allow the rest of your body to be washed by the running water.
Soaking in a clean, lukewarm bath daily is hydrating to the skin, but soaps will cause drying.
Allow your children to play in the tub only until hands become wrinkled. At this time wash with a limited amount of soap and remove from the bath. It is not encouraged to soak in soapy water.
Do not use any bubbles or other bath products.
Dove sensitive skin is an excellent soap to use for those with eczema.
When getting out of the tub or shower pat dry with a towel, leaving some water on the skin. This will stop skin from becoming overly dry as well as evaporation. Be sure to coat the skin with a good moisturizing cream that does not contain alcohol.
Use your prescribed steroid cream on any active eczema patches before applying moisturizing creams.
If there are large areas of the skin that are bumpy, it is usually a sign of an eczema flare. Use a nickel to a quarter sized amount of steroid cream mixed with a moisturizing cream to apply to that area.
These moisturizers are recommended for use by patients with eczema: VaniCream, Cetaphil, CeraVe, Eucerin, Curel, and Aquaphor. These should be creams and not just lotions. Aquaphor also has an ointment that is a greasy product, which is recommended for those with eczema.
Avoid or limit use of perfume, body sprays, or other scents on the body or clothing.
Eczema can be very frustrating and requires vigilance even when skin appears to be healthy. This disease waxes and wanes and no treatment will "cure" the problem. The good news for parents is that most children will outgrow the more severe flares and eczema will become easier to control as they get older.
Because food can sometimes be a trigger for young children, allergy testing and a potential elimination diet may also help control symptoms.
Allergy testing can also reveal an indoor allergen, in which case removal or avoidance can also help control eczema.
Patients who are older and still experiencing significant eczema symptoms may benefit from starting allergy injections.
In some severe cases, especially those who have no found allergy triggers may also need to seek treatment from a dermatologist.


'Tis the season of over indulgence!
Perhaps you've been over-doing it a bit this festive season and are feeling the effects of heartburn reflux or Oesphageal Reflux Disease (GERD).
Any degree of reflux and heartburn is not only annoying but can be quite painful and debilitating.
The main trigger for heartburn and reflux is an over-full or distended stomach, and that my be why you are feeling it more than usual, perhaps a bit too much Christmas indulgence?
Reflux is not caused by excess stomach acid!
Reflux is not caused by excess stomach acid as is common belief. Drug companies are happy to perpetuate this myth as acid-reflux drugs including proton pump inhibitors (PPIs) like Nexium or Prilosec, and H2 Antoagonists like Zantac are big business. They are only meant for short term symptomatic relief, but many people end up on them long term, and often report that they don't work that great anyway.
Long-term use can potentially have some serious consequences, and even short-term use has some undesirable side-effects.
Extended use can lead to any number of nutritional deficiencies and consequences. For example calcium deficiency leads to poor bone density and risk of fracture, while poor iron or vitamin B12 absorption cause anemia and The risk of contracting infections goes up such as pneumonia, food born infection (bacterial, parasitic) and Clostridium Difficile infection. C diff is very serious as it is now resistant to even the most powerful antibiotics.
Lowering stomach acid even for just a short while has issues as well. A lack of stomach acid means that you can't digest your food properly. This can give rise to leaky gut, altered gut flora and the resultant food allegies and intolernaces.
There is a strong link between food allergy and allergic rhinitis (hay fever), as well as Chronic Rhinosinusitis (CRS), suffered by thousands of Australians. That annoying post nasal drip that won't go away is a sure sign. And did you know that 10-50% of asthma cases are also triggered by food allergy?
So what does cause reflux if it's not excess stomach acid?
Reflux is not caused by excess acid. It is caused by a malfunction of the lower esophageal sphincter (LES) valve separating the esophagus from the stomach. Stomach contents can flow back into the esophagus causing pain and discomfort. Poor motility of the oesphagus motility then means that the reflux is not quickly expelled.
The proper treatment for GERD is not acid suppression, but avoidance of stomach distension, improvement of esophageal motility and tightening of the the LES valve.
2. Relax while eating to normalise peristalsis and motility in the oesphagus so that any refluxing acid can be quickly expelled.
-Put the phone down, get of Facebook and turn off the TV. Take the time to sit and enjoy your food. Give thanks for the nourishment provided by you meal, and by slowing down. .
5. Don't lie down within 2 hours of eating, including any afternoon naps after a big lunch!
– You need to give the stomach a chance to empty. Lie on your left side so your stomach doesn't end up upside down!
8. Most importantly: identify your food allergies!
– Akaline water and calcium both sooth the oesphagus and upper stomach without suppressing stomach acid. Win-win!
Calcium is suggested, not because it buffers acid, but because it is needed by the cells that line the oesphagus to regulate motility, and it is needed to close the LES valve, thereby cutting off back flow of stomach juices into the throat. The calcium must be in solution to work, hence the use of powder mixed with water. Calcium citrate is the best form and you might need to get this from a health practitioner, as it may not be availableover the counter.
While you are there you might like to have a chat about the connection between reflux, IBS, sinus problems, hay fever, chest pain, weight gain etc. Everything in the body is connected. Antacid medications might releive your heartburn symptoms if you are lucky, but they are doing nothing about the cause, and might even be making other conditions worse.
According to Dr Leo Galland, author of "The allergy solution", there is a strong link between reflux, sinus problems, allergies and even weight gain. You might never have considered that food allergy could be causing your sinus congestion and post nasal drip, exacerbating your asthma, or causing insidious weight gain, but it is not only possible it is very likely!
Food sensitivity can come from a number of sources, and can happen anytime. You may be suddenly sensitive to a food now that never used to be a problem. It can happen due to stress, infection, antibiotic use, poor diet or toxin (pollution or chemical) exposure.
A relatively new disorder is Eosinophilic Esophagitis (EoE). This is a fancy name for inflammation of the esophagus caused by eosinophils. Eosinophils are a type of white blood cell that is activated by the immune system in response to allergens, including food allergens. Eosinophils cause inflammation of tissue (in this case in the oesophagus). They also play a major role in the permanent lung damage that occurs with chronic asthma.
EoE causes chest pain and difficulty swallowing. To heal from EoE you need to identify the food sensitivities or toxic exposures (pollutants, allegens) that are causing the painful inflammation, by either testing, or following a carefully considered food elimination diet and challenge.
A word of warning – Don't stop acid suppressing drugs suddenly!
If you do wish to get off your reflux drugs do so in consultation with your doctor or health practitioner who can help you come off gradually. Stopping all of a sudden can cause a painful condition called "Acid rebound".
When stomach acid production is turned off by drugs your stomach responds by increasing the number of acid-producing cells. Then when you stop the drug, all these extra cells are going to pump out excess stomach acid, then you really will have true hyper-acidity! It is far better and well advised to taper off the drug slowly, giving your body a a chance to adjust.
Heartburn and reflux are portrayed as minor medical conditions, but if you are a sufferer they are anything but! For true relief from symptoms and resolution of this annoying and inconvenient problem have a look at your diet.
I hope you found this info both interesting and timely! Please feel free to share or comment below.


A HEALTHIER YOU! We want to feel better, be stronger, have more energy, and a more positive outlook. Along with cleaning up our diets, we strive to exercise properly, sleep enough, and reduce our stress. Now more than ever, we also look to reduce our dependence on prescription drugs. And most importantly, we must make sure that our spine and nervous system are at their best, as our health depends on them.
Your nervous system is the key to your body working at it's best and it depends on a health spine. Your PCO chiropractor is committed to helping your spine and nervous system reach their optimum performance.
Take the steps necessary for better health and call for an appointment today. Our doctors and staff are happy to help you reach your goal of a healthier you!
Since 1962, Perrault Chiropractic has been providing quality chiropractic care in a friendly, comfortable environment. Our continuing professional goal is to provide natural health care services for patients with acute injuries, chronic conditions, and for those seeking wellness naturally through chiropractic care. We look to empower our patients with the knowledge they need to achieve their health care goals and make educated health care decisions.
Combined, our doctors have nearly 175 years of clinical experience.
Our doctors listen carefully to your health concerns, then conduct the indicated chiropractic evaluation to ensure you are an appropriate candidate for care here in our office. If you are accepted as a patient and you wish to be treated, you'll be educated on how your health condition relates to your spine before delivering the effective chiropractic care you need. Whether your goal is to get out of pain, to get better and stay well, maintain your health, or prevent problems in the future, our doctors look forward to working with you to achieve your health care goals for you and your entire family.
We are pleased to announce that since October 2008, massage therapy services have been available at our office. To learn more about massage availability, call the office at (978) 686-7791.
The human body has an amazing ability to maintain and heal itself. This ability is controlled and coordinated by way of the nervous system, allowing all the systems in our body to function fully. Interference to the nervous system interferes with this ability and therefore creates problems. Chiropractic care looks to clear away interference of the nervous system through specific treatment of the spine. Removing this interference allows your body to regain its normal function and be healthier.


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Meditation August 17, 2022 0 Comments
Retired NYPD Detective James Shanahan recently told me the story of a young man in a desperate situation. He was a former Navy officer and had been out of the service for a few years. He was living with his mother and suffering from PTSD. None of the medical or psychological interventions seemed to make a difference.
On this day, Detective Shanahan and this young man's lives intersected because he decided his life wasn't worth living. The young former Navy officer had climbed onto the ledge of a building and was threatening to jump. Detective Shanahan and his team's job was to help him see that he didn't need to die.
The lead negotiator, a man named Jack, realized after some conversation with the young man and his mother that he had probably not had any meaningful human contact in the many years since he had left the military. Because his PTSD created behaviors in him that would scare others, he had gone years without simple human touch. Apart from his mother, he had no other meaningful intimate connections. He was isolated, and in that isolation, began seeing his world through a traumatized and shame-filled lens.
"I want to thank you for your service, for the ways that you have given this country so much of yourself," the negotiator, Jack, said. "I imagine it has cost you deeply. As a cop, I can understand that. Sometimes, you just need a hug, you know? You just need to be reminded that you're not alone in the world. I could use a hug right now, in fact. I bet you could too."
After a little more conversation, the former Navy officer began opening up, sharing just the tiniest bit of his pain with Jack. Then, at just the right moment, Jack reached out his hand to the young man. The young Navy officer had a choice: he could choose connection, or he could jump. After a moment of hesitation, the young man took Jack's hand, and together they climbed through a window to safety.
As Detective Shanahan told me this story, he paused and said, "What do you think Jack did then?" I said, "Well, I hope he gave him a hug!"
"First," said Shanahan, "he closed the window. You have to be practical. And then he gave him a hug."
Without a connection to one another, we lose something essential about being human. Our health suffers. Our minds play tricks with our reality. We lose ourselves. My friend, who is in recovery from addiction, often says, "The opposite of addiction isn't sobriety. The opposite of addiction is community." So it is. Let's show up for each other with big hugs and open hearts. While it feels like so much drives us apart, in truth, we belong to each other.
We are in this together,
Rev. Cameron Trimble
Author of Searching for the Sacred: Meditations on Faith, Hope and Love
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I'm facilitating a 3 hour "Futures Lab" tomorrow focused on the future of denominations. If you're serving in denominational leadership, or simply interested in the question, you're welcome to join us. Here's a link for more information: ... See MoreSee Less
FuturesLab
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The global pandemic has fundamentally changed our future. It created deep shifts in our institutions. It invited new questions of spirituality and faith. It opened new possibilities for how humanity m...
Such a great podcast from Sounds True with my friend and colleague Elaine Carney Gibson about her new book "Your Family Revealed." I love Sounds True in general but this episode is definitely my favorite. ... See MoreSee Less
Elaine Gibson: Learning from Family Systems Theory - Sounds True
resources.soundstrue.com
How do you view your family of origin? Our family dynamics have a tremendous influence on how we feel about ourselves, show up in the world, and relate to others. When these dynamics are subconscious,...
I am super excited about this upcoming event with Christian theologian Matthew Fox and Buddhist teacher Isa Gucciardi, Ph.D. where we talk about salvation and liberation. Isa will teach about the states of mind that lead to enlightenment. Matthew will explore the un-learning we need to do in our understandings of salvation in order to find meaningful liberation. Can't wait! ... See MoreSee Less
Liberation & Salvation: Healing Teachings in Buddhism & Christianity
Both Buddhism and Christianity offer their own vision of hope to help us meet the challenges we are facing individually and collectively. They each offer a path to meaning that can help us navigate ou...

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How can I switch virtual environments with Spyder without going to preferences? I have been programming in Python using Spyder in combination with virtual environments for a while now. Before I started using virtual envs, I installed Spyder using pip. I am not very familiar with paths and environments, but this seemed the way to go when I repetitively ran into package compatibility issues. However, it has been bugging me that every time I want to switch environment, I need to change the working directory to the folder of the environment and I need to change the Python interpreter manually within Spyder.
When I was looking for a solution, I found that it is possible to install Spyder within a virtual environment. I did this and found out that opening Spyder from a virtual environment has the exact same working directory and interpreter as the standalone version (the one I started with). This means that I still have to change the interpreter and working directory manually... Am I doing something wrong or is the only way to switch environments by changing it in the preferences tab within Spyder?
Background info: Using Windows, Spyder 4.2.1, venv as described on https://docs.python.org/3/tutorial/venv.html

redpajama_set_name: RedPajamaStackExchange


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High Strangeness
Armed Forces reveal UFO presence in Chile
The Santiago Times
Thu, 08 Feb 2007 11:01 UTC
More than 1,000 enthusiasts and experts gathered in Viña del Mar on Tuesday and Wednesday this week for the Tenth International Ufology Conference, organized by the Chile's Ufology Investigation Group (Aion). The highlight of the meeting was a display of photographs taken by members of Chile's Armed Forces.
Ufology is the study of unidentified flying objects, or UFOs. While many ufology experts feel that the field is not taken seriously by scientists, participants at the conference in Viña del Mar said the presence of several members of the armed forces added legitimacy to the proceedings. Rodrigo Fuenzalida, director of Aion, said the military presence was important because of the well-known objectivity of their reports and the advanced technology that can be used to back up their observations.
The military photographs and videos were revealed late Tuesday evening. They included a photograph of a spherical metallic object captured flying over Antarctica and a video of Navy ships being pursued by a luminous object in 2000.
Also presented at the conference was a report by Rodrigo Bravo, Captain of the Army's Fifth Division, who talked to a rapt audience about his thesis, entitled "Observations of unidentified aerial phenomena identified by the Civil Air Force." While Bravo's talk was not technically representative of the institution's position on UFOs, he had been authorized to give it by his commander-in-chief.
"Captain Bravo gave his talk from the point of view of the importance of UFOs as a phenomenon," said Fuenzalida. "He talked about encounters such as that of three helicopters near La Unión, when a UFO was spotted parked on the ground, and what happened in 2000, when five people were pursued by a luminous object that did not show up on radar screens."
Fuenzalida denied the existence of "secret investigations" being carried out by the Armed Forces about extraterrestrial activity.
Also present at the conference was retired official Armando Valdés, who is noted for his involvement in one of Chile's first documented UFO abductions, which became known as the Valdés Case. On April 35, 1977, Valdés, along with five members of an army patrol, saw two bright objects descending from the sky. Valdés set out alone to investigate and, according to the men, simply vanished. Fifteen minutes later, they said, he reappeared, tried to speak and passed out. The date on his watch had been advanced five days, and he had about a week's growth of beard.
According to his comrades, when Valdes was beginning to regain consciousness he said: "You do not know who we are, nor where we come from. But I tell you that we will soon return."
System · 2007-02-08T11:48:46Z
of simple sightings to the news of an invasion?
Esta noticia se ha hecho pública muy ampliamente por la TV, la radio y los diarios.
¿Porqué están liberando esa información con el respaldo de las fuerzas armadas?
Creo que están preparando a la gente para noticias peores a un simple avistamiento de un objeto desconocido.
Traduction with google:
This news has become public very widely by the TV, the radio and newspapers. Because they are releasing that information with the endorsement of the Armed Forces? I believe that they are preparing to people for the worse news to a simple sighting of a unknown object.
From an expat observer
-- For many rural Chileans, especially in the north and south regions of the country, UFOs and other strange stuff - chupacabras, crop circles, etc. are just a part of life and take secondary importance in their priority of living like earning an income and family matters.
-- I suspect there is even an underwater base off the coast of central Chile from a story my landlord and other witnesses recounted.
-- Chupacabra investigations and stories have received national media coverage in the past.
Just my observations OSIT.
Yossarian · 2007-02-08T20:29:05Z
Secrets?
"Rodrigo Fuenzalida, director of Aion, Chile's Ufology Investigation Group (Aion)""Fuenzalida denied the existence of 'secret investigations' being carried out by the Armed Forces about extraterrestrial activity."
Duh, let's think about this a minute. Let's define the word secret. How would Fuenzalida know whether or not there were secret investigations, seeing as he is not in a position to be privy to such secrets as a civilian?
Even a high ranking military officer wouldn't know unless he happened to be in the "compartment" involved in the investigation--seeing as how all secrets worth two cents are compartmentalized. Then, if he did know and were to reveal what he knew, he would be breaking some military rule or law and subject to severe penalties--loss of job, jail, or worse--so how would he know whether or not there was a secret investigation????
That's why truth and lies are mostly leaked anonymously. Then, there's "plausible deniability."
LETS GO BRANDON - Rap [Link]
Dragnarr77


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Debello Law
Banking and Financial
Technology Media and Communications
Aviation Law Advice
Consumer Law Advice
Corporate Advisory and Governance
Dispute Resolution and Litigation
Author Archives: pvadmin
Article author pvadmin
Debello Law advises Nanosynth Group PLC on joint venture
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Nanosynth group is a technology business that originated in Nottingham from a partnership with the university to develop the application of nano particles. Debello Law advised the listed company in relation to its joint venture with the Volz Group.
Debello Law provides consumer law training to Carpetright
Carpetright is a leading flooring and bed provider and has firmly established itself as a household name. Debello Law has provided a unique online consumer law training course for the customer services team of the retailer.
Debello Law advises Infinity Reliance Limited on a debt raise
NewsBy pvadmin November 23, 2021
Infinity Reliance Limited (which trades as 'My First Years') is one of the UK's leading online baby and toddler retailers, specialising in bespoke goods. Debello advised the company on a debt raise.
Dean Dunham Named 'Consumer Lawyer of the Year for the fourth year in a row
Debello Law's senior partner, Dean Dunham, is one of the most recognised lawyers in the UK and is widely regarded as one of the leading authorities on consumer law. Dean was awarded Consumer Lawyer of the Year in 2018, 2018 and 2020. Debello Law is delighted to announce that Dean has now been awarded Consumer…
Debello Law provides legal submission to the Competition and Markets Authority
NewsBy pvadmin November 5, 2021
Debello Law has provided written legal submissions to the Competition and Markets Authority (CMA) in relation to the static caravan industry. Within the submissions, authored by Dean Dunham, it has been submitted that there are wide ranging breaches of consumer laws occurring within the sector, causing significant consumer detriment.
Debello Law appointed as advisors to Nanosynth Group PLC
NewsBy pvadmin September 6, 2021
Debello Law has been appointed on a retainer basis to provide 'in-house' style advice to the listed company on a wide range of legal matters, including; AIM and other applicable rules, other regulatory matters, commercial contracts, corporate advice and intellectual property.
Debello Law advises victim of HBOS Reading Fraud on first Foskett re-review case
NewsBy pvadmin March 28, 2021
The Foskett independent Re-Review Panel ("Panel") was established in 2020 to reassess the direct and consequential ('D & C') losses suffered by victims of the fraud committed at the 'HBOS Impaired Assets unit based at Reading and Bishopsgate ('IAR')'. The Panel was established following the conclusions of Sir Ross Cranston's report published in December 2019.…
Debello Law provides consumer law training to Harrods
NewsBy pvadmin August 22, 2019
Harrods is the Worlds leading luxury department store. Debello Law provided consumer law training to the customer service team and department heads a the retailer.
Debello Law advised management team on £160 million investment
Office Space in Town (OSiT), one of the UK's leading serviced office providers. Debello Law advised the management team on the £160 million investment by Kailong, a leading Chinese real estate asset manager, into the business. Kailong took a majority stake in in OSiT's first joint venture, LSOI, replacing global real estate investors, Forum Partners,…
Debello Law provides media advice to Sports Direct
NewsBy pvadmin June 18, 2018
Sports Direct is the UK's premier sports retailer. Debello Law provided advice to the retailer in relation to an undercover investigation carried out by BBC's Panorama and C4.


Jess Castle is running away. Again. This time she's running back home, like she swore she never would.
Castle Kidbury, like all small towns, hums with gossip but now it's plagued with murder of the most gruesome kind. Jess instinctively believes that the hippyish cult camped out on the edge of town are not responsible for the spate of crucifixions that blights the pretty landscape. Her father, a respected judge, despairs of Jess as she infiltrates the cult and manages, not for the first time, to get herself arrested.
Rupert Lawson, a schooldays crush who's now a barrister, bails her out. Jess ropes in a reluctant Rupert as she gatecrashes the murder investigation of DS Eden. A by-the-book copper, Eden has to admit that intuitive, eccentric Jess has the nose of a detective.
Perfect for fans of Midsomer Murders and MC Beaton, this is cosy crime at its most entertaining and enthralling.


Superb villa located on a plot of 17,000 m2 in Cala Vadella, in a very quiet location in the countryside with beautiful views.
This elegant property is ideal for a relaxing holiday with friends or family.
Room, Ground level. This bedroom has 1 double bed 140 cm. Bathroom ensuite, With shower.
Room, Ground level. This bedroom has 2 twin beds 90 cm. Bathroom ensuite, With shower.
Room, Ground level. This bedroom has 2 twin beds 90 cm configurable as a double bed. Bathroom ensuite, With shower.
The villa divided into different parts, on a total area of 250m2, all rooms are independent of the main house and has an independent access from the outside.
The villa has a similar design of charming country hotels.
Lounge with satellite TV (ASTRA), and stereo.
The main kitchen is fully equipped and outdoor by the pool. A large table is also at your disposal to accommodate 12 people.
Large terrace with swimming pool 15m x 7.5m.
Lounge areas and various sun loungers and parasols.
Outdoor parking for 6 cars: 4 cars at the main entrance and 2 covered parking spaces.
Beautiful tropical garden and lower terrace with fruit garden.
Only 5 minutes drive from the beaches of Cala Vadella, Cala Carbó and Cala d'Hort. Supermarket just 2 minutes. The village of San Jose is 10 minutes drive and Ibiza town 25 minutes by car. There is a path from the villa that leads directly to Cala Vadella beach, which you only takes 15 minutes on foot. The path to the villa is 1,5km, passable with a normal car but not asphalt.


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Cecil Brooks III (* 16. August 1961) ist ein US-amerikanischer Jazzschlagzeuger und -komponist.

Der Sohn des Schlagzeugers Cecil Brooks II und Enkel des Konzertpianisten Cecil Brooks I lernte schon als Kind die Musik von Philly Joe Jones und Art Blakey kennen, die in seinem Elternhaus verkehrten. Ende der 1980er Jahre arbeitete er u. a. mit Greg Osby, Geri Allen und Lonnie Plaxico. 1989 erschien mit The Collective sein erstes Album als Bandleader, dem sich in rascher Folge weitere anschlossen. Daneben wirkt er auch als Komponist und Musikverleger und betreibt einen Jazzclub in West Orange/New Jersey.

Diskographie
The Collective mit Geri Allen,  Greg Osby, Lonnie Plaxico, Gary Thomas, 1989
Hangin' With Smooth mit Justin Robinson, Kenny Davis, Craig Handy, Benny Green,  Philip Harper,  Peter Washington, 1990
Neck Peckin' Jammie mit Geoff Keezer, Justin Robinson, Craig Handy, Christian McBride, Terell Stafford, 1993
Smokin' Jazz mit Stephen Scott, Antonio Hart, Lonnie Plaxico, Jack Walrath,  Ravi Coltrane, 1993
For Those Who Love to Groove mit Don Braden, Bruce Williams, Radam Schwartz, Riley Mullins, 1999
Our Mister Brooks mit Stephen Scott, Geri Allen, Antonio Hart, Geoff Keezer, Greg Osby, Lonnie Plaxico, Gary Thomas, Jack Walrath,  Justin Robinson, Craig Handy, Benny Green, Philip Harper, Christian McBride, Terell Stafford, Peter Washington, Ravi Coltrane, 2000
Live at Sweet Basil mit John Hicks, Don Braden, Dwayne Dolphin, Riley Mullins, 2001
Double Exposure mit Gene Ludwig, 2006

Weblinks
 (englisch)
Porträt, All About Jazz (englisch)

Jazz-Schlagzeuger
Komponist (Jazz)
US-Amerikaner
Geboren 1961
Mann

redpajama_set_name: RedPajamaWikipedia


These per diem rates are set by the GSA and are used by Federal and local governments as well as many private-sector companies to reimburse employees for business travel expenses incurred within Vernon Parish, Louisiana (county borders are highlighted on the Louisiana map).
Generally, you will be entitled to one Lodging per-diem of up to $98.00 to cover your actual hotel costs and one Meals & Incidentals per-diem payment of $66.00 to cover food and incidentals like parking costs for each full day of travel within Vernon Parish. 75% of the normal M&IE per diem rates are generally issued for your first and last days of travel.
In the Continental United States (CONUS), per diems are assigned on a county-by-county basis. These rates apply to all cities, towns, and other areas that fall within the borders of Vernon Parish.
The Vernon Parish per diem rates listed on this page apply to business travel in the following cities: Ft. Polk Anacoco Kurthwood Rosepine Knight Hicks Neame Slagle New Llano Hornbeck Leander Hutton Pitkin Fullerton Simpson Leesville Evans Temple Burr Ferry Vernon Parish and other unincorporated areas within Vernon Parish boundaries.


Hindi GEC SAB TV is launching a new show Sajan Re Phir Jhoot Mat Bolo. The show, which is being produced by Optimystix Production, marks the comeback of actor Hussain Kuwajerwala to the channel. The actor has been away from fiction shows for the last eight years.
The show, which is a sequel to Sajan Re Phir Jhoot Mat Bolo, will also be a comeback for actress Sana Amin Sheikh, who was last seen as Aradhya in Colors' Krishnadasi.
However, Due to some creative differences the makers opted for Parvati over Sana. the makers have now finalized television actress Parvati Vaze to play the female protagonist.
As viewers would know, Parvati, last in Star Plus' Sapno Se Bhare Naina has been missing from TV space for more than five years. The actress will be paired opposite Hussain Kuwajerwala in her comeback vehicle.
Hussain, who had been hosting various reality shows in the last few years, will now play a male protagonist in the show 'Sajan Re Phir Jhoot Mat bolo' which is based on a hilarious conundrum created by lies.
Actor Tiku Talsania will be playing the role of a father to the male protagonist (played by Hussain Kuwajerwala) in the Sony SAB show.
The actor says he is glad to be part of the show. "I have played the role of a father before but this time my role is quite different from what I have portrayed before. The show has a very powerful storyline, which I am sure the audience will love," Tiku said in a statement.