Some babies and toddlers barely seemed bothered by their erupting teeth. They sleep well, eat well and suddenly one day some adorable little chiclets appear in their mouth, but that's not the case for many babies, including mine. If you have a little one who is drooling profusely, gnawing on everything, and all out of sorts, there is a good chance they are teething. Some of the other symptoms babies experience are red cheeks, decreased appetite, loose bowel movements, diaper rash, red swollen gums, disrupted sleep and generally clingy behaviour. Sounds like fun eh? Well I'm here to help. Here is a roundup of my favourite ways to help support your little one through teething. As always, try to remember, this too shall pass.
2. Feeder With Frozen Fruit: If your little one is old enough to eat complimentary foods (approximately 6 months and beyond Learn more), fill up your silicone or mesh feeder with any type of frozen fruit and let baby enjoy a nice numbing sweet treat.
3. Frozen Wash Cloth: Wet a baby wash cloth and place it in the freezer. Once it's frozen it can be removed for baby to chew on. Before giving to baby always make sure there are no sharp edges of ice, and allow the cloth to thaw for a few minutes to soften if necessary. You can also use the frozen wash cloth to gently massage your baby's gums if that provides them relief.
4. Frozen Pineapple Core: This one is a win win for parents and baby. Simply cut all edible pineapple off the core to eat and enjoy. Then take the tough fibrous core and slice it into wedges approximately 1" wide x 3" long. Toss them in a container or baggie in the freezer and pull out a wedge of frozen pineapple core when baby is needing some relief. The great thing about it is that the core is so hard baby can't chew through it, and it's relatively mess free. Always ensure your baby is being attended while enjoying their frozen pineapple core.
5. Clove Oil: Essential oils are something that I've started to explore in the last year. When we were having some epic non-stop teething pain with Penny a few months ago, and she refused all pain medications, we decided to try clove oil. We diluted 2 drops of clove oil in 1 Tablespoon of coconut oil and rubbed a small amount on her gums. It seemed to provide some good relief and Penny didn't mind it. *Please Note: Clove oil should never be ingested directly and should always be mixed with a carrier oil to dilute it. Always test on yourself before applying to baby's gums and always ensure you are buying high quality food grade oils.
6. Camilla: With all of my babies I have found homeopathic Camilla by Boiroin to be a nice option to help with their irritability. There is no solid research to support homeopathic remedies, but I'm open to trying anything that is safe and within reason. After all, I don't claim to know all, and I don't think that we can prove everything with research studies. Camilla doesn't contain any alcohol or sugar and is safe to be used in combination with over the counter pain medications.
It's important to remember that numbing agents that are typically used for tooth pain are not safe for use on babies. Over the counter pain medications such as acetaminophen and ibuprofen are safe options, but should be reserved for occassions when baby really needs them. Pain medications should not be used for long periods of time, and teething can go on for several weeks at a time...for several months...for several years. It's super fun ;) Good Luck!
*Note: There has been a lot of attention in the news in recent months about the safety of Hylands Homeopathic Teething Tablets. There has not been any concern about Boiron homeopathic products and there have been no issues within Canada. Homeopathic remedies should never be dangerous to your health, and all companies (whether traditional pharmaceuticals or homeopathics) should have stringent checks in place to ensure their product is being produced safely. More from Health Canada.


MSSQL: The rowset was using optimistic concurrency and the value of a column has been changed after the containing row was last fetched or resynchronized.
Sometimes you may get the above error when dealing with openquery updates and linked servers.
"XXXXXXXXX" could NOT UPDATE TABLE "[MSDASQL]".
[SQLSTATE 01000] (Error 7412). The step failed.
A solution is to go to the SQL server that links to MySql, go to configure screen of the MySql ODBC connection in the linked server. Open Details, click on Cursor/Results tab and check the "Return matched rows instead of affected rows".


"A company not worried about employee retention"
The jobs and what is expected of you is clear. After working in an entry level role you can interview in different departments that interest you.
"Worked there for about a year and a half."
Benefits package is excellent, campus is beautiful, and there were a number of excellent team leaders and managers.
Protocol at the company can feel entrenched in its ways, and management at times felt unwilling to make big changes.
Discover more reviews about Fisher Investments.


Advantages of LEDWhy choose FX Luminaire integrated LED lighting?
About FX LuminaireWhen the effect, control, longevity, and simplicity are important factors, FX Luminaire is the best option.
The JB is FX Luminaire's original LED Down Light. The JB solves the problem of changing lamps in complicated areas by providing long-life LEDs. The pure color of the LED allows you to add the supplied blue lens to create a natural moonlight effect.
FX Luminaire is an industry-leading manufacturer of landscape and architectural lighting products with a focus on the advancement of LED Landscape Lighting technology and digital lighting control with zoning, dimming and color adjustment capabilities.


text:
Q: Evaluating the integral $\int_0^\infty \frac{\ln(x)}{e^x+1}$ I'm interested in evaluating the integral of
$$ \int_0^\infty \frac{\ln(x)}{e^x+1}\ $$
TLDR: How do you evaluate $ \eta'(1) $?
I found and adapted this integral from this video, unfortunately, they didn't fully evaluate the integral and I'm interested in the result.
This question is similar to this, but my question goes more in-depth on the way that I tried to evaluate this integral.
This was solved by @J.G. in the answers, and by @Zacky in the comments.
I'll run through what I did and what the video did to evaluate the integral
$$ I =\int_0^\infty \frac{\ln(x)}{e^x+1}$$
Multiplying by $ \frac{e^{-x}}{e^{-x}}\ $ results in
$$ = \int_0^\infty\frac{e^{-x}\ln(x)}{e^{-x}+1} $$
Expanding the denominator into a geometric sum results in
$$ = \int_0^\infty\ e^{-x}\ln(x)\sum_{k\ge0}{-e^{-x^k}} $$
Interchanging our signs of integration of summation and simplifying results in
$$ \sum_{k \ge 0}(-1)^k \int_0^\infty\ e^{-x(k+1)}\ln(x) $$
Substituting $ x(k+1) = t $ and $ dx = \frac{dt}{k+1} $ results in
$$ \sum_{k \ge 0} (-1)^k \int_0^\infty e^{-t}\ln(\frac t{k+1})\frac{dt}{k+1} $$
Expanded and simplified you get
$$ \sum_{k \ge 0} \frac{(-1)^k}{k+1} (\int_0^\infty \ln(t)e^{-t}dt - \ln(k+1)\int_0^\infty e^{-t}dt) $$
Once again simplified we can see that our first integral is the $ \mathcal L\{\ln(t)\} $ at $s = 1$ and our second integral is $\Gamma(1)$ in total this results in.
Where $ \mathcal L $ is the Laplace transform and $\Gamma$ is the Gamma function.
$$ \sum_{k \ge 0} \frac{(-1)^k}{k+1}(\mathcal L\{\ln(t)\}-\ln(k+1)\Gamma(1)) $$
This then simplifies to
$$ \sum_{k \ge 0} \frac{(-1)^k}{k+1}(-\gamma-\ln(k+1)) $$
With $ \gamma $ being the euler-mascheroni constant
Increasing our lower bound on our summation we get
$$ \sum_{k \ge 1} \frac{(-1)^{k-1}}k(-\gamma-\ln(k)) $$
Realizing that the Dirichlet Eta function is defined as
$$ \eta(s) = \sum_{k \ge 1} \frac{(-1)^{k-1}}{k^s} $$
We can then see that our equation is
$$ \eta(1)(-\gamma-\ln(k)) $$
Knowing that $ \eta(1) = \ln(2) $ we can then distribute our eta to get
$$ -\gamma\ln(2)-\ln(k)\eta(1) $$
Which is
$$ -\gamma\ln(2) - \sum_{k \ge 1} \frac{(-1)^{k-1}}k\ln(k) $$
Taking the derivative of the eta function we can see that this is
$$ -\gamma\ln(2)+\eta'(1) $$
According to Wikipedia $ \eta'(1) $ is equal to $ \gamma\ln(2)-\frac{\ln(2)^2}2$
Meaning that our integral $I$ will evaluate to
$$ I = -\frac{\ln(2)^2}2$$
But how can we evaluate $ \eta'(1) $ without encountering the pole at $s = 1$ of the Zeta function?
Are there any other interesting ways to evaluate this integral not using the eta function?
Thank you for your time and patience!

A: For $s\approx1$, $\zeta(s)\approx\frac{1}{s-1}+\gamma$ and $\zeta^\prime(s)\approx\frac{-1}{(s-1)^2}$, so$$\begin{align}\eta^\prime(s)&=2^{1-s}\ln2\cdot\zeta(s)+(1-2^{1-s})\zeta^\prime(s)\\&\approx(1+(1-s)\ln 2)\ln2\left(\frac{1}{s-1}+\gamma\right)-\frac{\ln 2}{s-1}+\frac12\ln^22\\&=\gamma\ln 2-\frac12\ln^22.\end{align}$$Note we only need to expand $2^{1-s}$ to $O(1-s)^2$ viz.$$2^{1-s}=1+(1-s)\ln 2+\frac12(1-s)^2\ln^22+o((1-s)^2)$$in the $\zeta^\prime$ term.

redpajama_set_name: RedPajamaStackExchange


text:
HomeNew ZealandPrime Minister welcomes Royal visit
Prime Minister welcomes Royal visit
December 18, 2011 MelW New Zealand, United Kingdom 0
Prime Minister John Key has welcomed the news of a planned visit to New Zealand by the Prince of Wales and the Duchess of Cornwall next year.
"I am pleased New Zealand will be able host the Prince of Wales and the Duchess of Cornwall as part of the Queen's Diamond Jubilee celebrations," says Mr Key.
"Prince Charles, heir to the throne, will be visiting New Zealand on the Queen's behalf."
The Palace has announced that family representatives will make official visits in 2012 to all 15 countries outside the United Kingdom of which Queen Elizabeth is Sovereign. The Prince of Wales will also visit Australia, Papua New Guinea and Canada.
The Prince of Wales last visited New Zealand in 2005. This will be the Duchess of Cornwall's first visit here.
Further details regarding next year's visit will be made available in due course.
Blair cancels London book signing over protest fears
'Severe' 6.3 earthquake strikes NZ East Coast - Geonet blames ghost
The Ian Wishart Radio Show 14 February 2014 segment 1 podcast
RuggedAustralia
UK Green Police raid home of climate blogger, seize computers
21st Century IT System for Immigration

redpajama_set_name: RedPajamaCommonCrawl


text:
#ifndef GLES2Texture_h__
#define GLES2Texture_h__

#include "ES2Prerequisites.h"
#include "Texture.h"

namespace Demi
{
    class DI_GLES2_API DiGLES2TextureDrv : public DiTextureDrv
    {
    public:

        DiGLES2TextureDrv(DiTexture* parent);

        ~DiGLES2TextureDrv();

    public:

        void          CreateTexture();

        void          Release();

        void*         LockLevel(uint32 level, uint32 surface = 0, DiLockFlag lockflag = LOCK_NORMAL);

        void          UnlockLevel(uint32 level, uint32 surface = 0);

        void          Bind(uint32 samplerIndex);

        void          CopyToMemory(const DiBox &srcBox, const DiPixelBox &dst);

        void          CopyFromMemory(const DiPixelBox &srcBox, const DiBox &dst, uint32 level, uint32 surface = 0);

        void*         GetSurfaceHandle();

        void          Upload(const DiPixelBox &src, const DiBox &dst, uint32 level, uint32 surface = 0);

        void          Download(const DiPixelBox &data, uint32 level, uint32 surface);

        void          BindToFrameBuffer(GLenum attachment, uint32 level, uint32 surface);

    private:

        void          AllocateBuffer();

        void          DeallocateBuffer();

    private:

        DiLockFlag    mCurrentLockFlag;

        DiPixelBox*   mBuffer;

        GLenum        mGLFormat;

        GLenum        mGLOriginFormat;

        GLenum        mGLTextureType;

        GLuint        mTextureID;

        uint32        mImageSize;

        uint32        mFinalMipmaps;
    };
}
#endif // GLTexture_h__

redpajama_set_name: RedPajamaGithub


text:
Last edited by Faebei
Wednesday, August 5, 2020 | History
5 edition of Liza found in the catalog.
Ivan Sergeevich Turgenev
by Ivan Sergeevich Turgenev
Published 1997 by J.M. Dent in London, Toronto .
Statement by Ivan S. Turgenev ; translated from the Russian by W.R.S. Ralston.
Series CIHM/ICMH Microfiche series = CIHM/ICMH collection de microfiches -- no. 87157, Everyman"s library -- no. 677.
Pagination 3 microfiches (128 fr.)
1. Results-driven sessions. My straightforward, well-researched, sessions instill confidence in delegates to strive for excellence, unfazed by obstacles. Oct 02, · Lindas Book Obsession Reviews "Code Girls The Untold Story of the American Women Code Breakers of World War 11" by Liza Mundy, Hachette Books Kudos to Liza Mundy, Author of "Code Girls The Untold Story of the American Women Code Breakers of World War 11" for the Historical research and vivid descriptions of the unsung heroines that /5(13).
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Soviet Russian literature
Reentry of the Offender Into the Community.
Sources Brtsh/Irsh Ecmc Hty
Politics and government in Israel
History of the county palatine and duchy of Lancaster.
Liza by Ivan Sergeevich Turgenev Download PDF EPUB FB2
View the profiles of people named Liza Liza. Join Facebook to connect with Liza Liza and others you may know. Facebook gives people the power to share. LIZA ON DEMAND follows the chaotic misadventures that ensue as the eponymous character takes on various tasks and odd jobs, as she tries to get ahead in the gig economy.
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The film premiered on the Liza Koshy Too YouTube channel and Oculus VR on November 15, Walk Me Home by Liza Kendall is the 1st book in her new Silverlake Ranch novel.
We meet our heroine, Charlie Nash, who has just returned to Silverlake, Texas to be a bridesmaid for her cousin's wedding. Charlie and her family left Silverlake years before, after a tragic fire destroyed their home, and caused the death of her grandmother/5.
Nov 16, · Liza Klaussmann is the author of Tigers in Red Weather, an international bestseller Liza book which she won a British National Book Award, the Elle Grand Prix for Fiction and was named Amazon UK's Rising Star of the Year in A former journalist, Klaussmann was born Brooklyn, New York and spent ten years living in Paris/5().
Liza Mundy is the New York Times bestselling author of The Richer Sex: How the New Majority of Female Breadwinners Is Transforming Sex, Love and Family and Michelle: A ecole-temps-danse.com was a long-time reporter at the Washington Post and has contributed to numerous publications including The Atlantic, TIME, The New Republic, Slate, Mother Jones, and Politico.
Dec 04, · Liza Lou And The Yeller Belly Swamp [Mercer Mayer] on ecole-temps-danse.com *FREE* shipping on qualifying offers. With her quick thinking Liza Lou manages to outwit all the haunts, gobblygooks, witches, and devils in the Yeller Belly Swamp/5(97). Sep 23, · At two and a half, Liza grew up on the MGM lot and made her first appearance in her mother's musical In the Good Old ecole-temps-danse.com the time she was 19, Liza was already on Author: Bio Staff.
Scandinavia's undisputed queen of crime fiction, Liza Marklund is the No. 1 international bestselling author of the Annika Bengtzon series.
Liza Marklund was born in in the small village of Pålmark, close to the Arctic Circle in Sweden/5. The two authors behind the pen name Liza Kendall have been friends for years.
But writing a book together is a wholly different endeavor. In this piece, the two women behind Liza Kendall share how they teamed up to write their first romance together, Walk Me Home. Liza Soberano Biography - Affair, In Relation, Ethnicity, Nationality, Salary, Net Worth, Height | Who is Liza Soberano.
Liza Soberano is Filipino-American citizenship. She is a television and film actress. Also, she is a model and endorser. Liza is best known for her work with the Filipino television network ABS-CBN.
Liza Soberano: Early Life, Childhood, and Education Talking about herHeight: Meter. The hit pair of Liza and Gil then went on to create magic in the Theodore Boborol directed Filipino teen romantic comedy-drama film 'Just The Way You Are' that released on June 17, The film was based on the Wattpad book titled 'The Bet' and succeeded at the box-office.
Looking for books by Liza Marklund. See all books authored by Liza Marklund, including The Postcard Killers, and The Bomber (Annika Bengtzon (Chronological Order) #4), and more on ecole-temps-danse.com Liza established Liza Dawson Associates following a successful year career in book publishing, including posts as executive editor of Putnam Publishing and executive editor at William Morrow.
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He was the only one of the family to survive what Francois Maurois, in his introduction, calls the "human holocaust" of the persecution of the Jews, which began with the restrictions, the singularization of the yellow star, the enclosure within the ghetto, and went on to the mass deportations to the ovens.
Liza's Roots. In his Newbery Acceptance speech, Neil Gaiman reveals that Chapter 4, the chapter that introduces Liza, was the first chapter he wrote.
Liza's inspired by a grave in the graveyard Gaiman played in as a child in Sussex, England. As a kid, Gaiman thought witches were buried in that grave. Nov 18, · National Book Award winner Andrew Solomon has this to say about The Price of Silence: " In this courageous, determined, radical book, Liza Long exposes the dearth of alternatives for parents of kids with mental illnesses, the shame that attends their perceived failures, and the hope that such families may find their collective voice and.A comparison between Liza Koshy and iisuperwomanii.
VS. IISUPERWOMANII Liza Koshy. Lilly Singh (born September 26, ) is an Indo-Canadian YouTube.I'm looking forward to going on book tour for Code Girls; see the calendar below for a schedule of upcoming events.I also give talks on various related topics–women in the workplace, women in tech–at conferences, networking events, leadership seminars, universities, alumni groups, and corporate retreats.
ecole-temps-danse.com - Liza book © 2020


text:
\section{Introduction}

Sampling designs that optimise one or more specified utility functions are valuable in many applied contexts, since they facilitate the intelligent collection of data.
That is, an optimal design results in greater information efficiency, reduced sampling cost and improved estimation.
However, such schemes remain challenging to develop for spatial processes with complex covariance structures, such as those found in natural ecosystems.
Moreover, sampling at the exact design point can be difficult in practice within these systems due to practical challenges associated with the collection of samples and accessibility of the sites.
In this case, a more flexible sampling scheme that identifies windows with near-optimal design efficiency can be highly useful.

Data collected by environmental monitoring programs are essential for understanding patterns, trends and vulnerabilities in ecological and environmental systems.
Here, we focus on river network and coral reef systems, and develop optimal sampling regions given non-standard spatial relationships.
The covariance across locations on a branching river is particularly complex, since the network topology is embedded in a 2D terrestrial landscape, with directional water flow, and disparities between flow volume.
Furthermore, monitoring programs are notoriously expensive in terms of monetary, human and technological resources \citep{Lind2010the,Roelf2010calibration}.
Balancing short- and long-term requirements, as well as practical constraints of data collection can add further complication to the design process \citep{kang2016bayesian}.
Our aim is to develop a more flexible design approach within a Bayesian framework while achieving two goals: 1) the determination of a set of optimal sampling locations based on a discrete set of available locations, and 2) the formation of sampling windows within a specified region where difficulties due to access or otherwise may be encountered.

Experimental design problems are commonly viewed as optimisation problems.
In the classical framework, optimal experimental designs are often derived using utilities based on the expected Fisher information matrix \citep[e.g.][]{atkinson1992optimum}.
Such designs have been shown to depend on assumed values for model parameters, so approaches have been proposed to remove some of this dependence.
For example, \cite{pronzato1985robust} optimised a design criterion over a prior probability distribution for the model parameters; the so-called `pseudo-Bayesian' design approach.
While pseudo-Bayesian designs are more robust for the choice of parameter values, the prior information is not utilised in subsequent analysis (i.e. computation of the utility).
A fully Bayesian framework provides a unified approach for incorporating prior information and rigorously handling uncertainty about the model parameters and the statistical model when forming a design and analysing the resulting data (see \cite{chaloner1995bayesian, ryan2016review}).

Various approaches to finding sampling intervals, so-called windows, are presented in the statistical literature relating to pharmacokinetics (e.g. \cite{bogacka2008d, foo2012general,mcgree2012sequential}).
These intervals provide flexibility in the timing of sample collection, while
assuring a high level of information efficiency.
An approach for stratified random sampling in a geostatistical simulation study by \cite{lin2011modeling} uses Latin Hypercube sampling to find the optimal sub-sampling of pre-specified regions (for a given spatial stratification).
However, to our knowledge no approaches have been developed to form sampling windows for spatial processes in the statistical literature.

We present a Bayesian approach, using a Gaussian process emulator to approximate the utility surface in high-dimensions.
Our method builds on the approach to stochastic optimisation employed in the Approximate Coordinate Exchange (ACE) \citep{overstall2017bayesian} algorithm.
We also demonstrate how to derive design efficiency contours using sampling windows, which can then be used to guide highly efficient and flexible sampling of complex spatial processes.
The new approach is applied to substantive real-world case studies, described below.

\subsection{Motivational Case Studies}

Example 1: Water temperature is considered a ``master" variable in river ecosystems because it affects the metabolic rates of aquatic organisms, life history events related to reproduction, hatching and maturation, and restricts the distribution and abundance of ectothermic species \citep{isaak2017norwest}.
Water temperature is often monitored to understand the impacts of climate change and land management on thermal habitats \citep{isaak2016slow, jackson2018spatio} and is also used as the basis for regulatory actions \citep{todd2008development}.
The recent proliferation of inexpensive \emph{in-situ} sensors has dramatically increased the potential for monitoring and data-enabled management decisions \citep{isaak2017norwest}.
Nevertheless, comprehensive monitoring on river networks using in-situ sensors remains costly and complex in terms of balancing short- and long-term priorities.
Optimal sensor placement must be assessed when sensors are initially deployed, new sensors are added to an established monitoring program or the number of in-situ sensors must be reduced.
In addition, field conditions can be unpredictable; some sites are inaccessible due to steep terrain, a lack of network reception for data streaming, or private landholders refusing access.
This motivates two considerations: the design of a global optimal sampling scheme across the river network, and a more targeted approach to identify finer-scale sampling regions that provide near-optimal design efficiency.

In river networks, spatial relationships are characterised in part by their topology (e.g. branching network structure, connectivity).
There have been numerous advances in statistical modelling used to describe spatial covariance in data collected on branching river networks based on distance travelled along the river, directionality in water flow and differences in flow volume \citep{ver2006spatial, ver2010moving, peterson2013modelling, santos2021bayesian}.
The ability to model this spatial component and more accurately predict conditions throughout a river network often provides a better understanding of habitat suitability \citep{isaak2016slow} and leads to more effective management decisions \citep{fig2021guiding,sharma2021dendritic}.
Frequentist sampling methods for river networks have been developed \citep{som2014spatial,wang2020designing}, as well as pseudo-Bayesian approaches \citep{falk2014sampling, pearse2020ssndesign}.
However, a fully Bayesian design framework for river networks is currently unexplored.

Example 2: Coral reefs are inextricably linked by the symbiotic relationships formed between corals and the organisms around them \citep{richmond1993coral}.
In particular, deep reefs have the capacity to act as refugia and to assist in the recovery of more vulnerable shallow water reefs following a disturbance.
However, major challenges remain in understanding the extent of and managing the vast marine estate for Australia, as well as for many other maritime nations.
Insights into remote reefs are beginning to emerge due to data captured using new technologies such as remote and autonomous underwater vehicles.
With limited resources to invest in research and monitoring, there is a need to optimise in-field activities to collect data that will most efficiently achieve research and management goals.

Hard coral cover is an indicator commonly used to infer the health and condition of a coral reef \citep{ltmp2022}.
In this example, we consider deep reefs, or mesophotic coral ecosystems, with data collected between 12 to 50 metres in depth.
The extent to which important ecological processes change along depth gradients in a reef is not well understood and is a critical knowledge gap for developing future reef policies and management practices \citep{kang2016bayesian}.
Monitoring coral reef environments often relies on a series of images taken underwater, along a transect line.
As such, collecting data from submerged shoals can be costly given the specialised skills of those undertaking the monitoring and the cost of equipment and running a ship.
Motivating our second design scenario, we consider the optimal placement of transect lines across a submerged shoal taking into account the spatial nature of the process.
In practice, underwater sampling along these lines can be challenging and unpredictable due to water currents.
Thus, a more practical solution would be to define sampling regions, as proposed here, offering more flexibility and assurance in sampling.

The following section provides details about the general statistical modelling used in both case studies, then outlines specific details in each case.
In Section 3, the Bayesian optimal design approach is described.
Our proposed approach to finding sampling windows is given in Section 4, along with the concept of design efficiency contours.
Finally, Section 5 illustrates the results of these two examples and demonstrates the scope of applicability of Bayesian design and sampling windows for spatial processes.

\section{Model}
\subsection{Bayesian Spatial Generalised Linear Models}

We start with a general description of spatial linear models and then extend this to models for data collected on river networks and coral reefs.
Let $\textbf{d} = (d^1, ..., d^\gamma)$ denote a design, that is, a set of locations in the physical or parameter space.
Consider a linear mixed model with $n \times 1$ response $\textbf{Y}$, and the $n \times p$ design matrix $\textbf{X}$ of explanatory variables spatially indexed at locations, $\textbf{d}$,
\begin{equation}
    \textbf{Y} = \textbf{X} \boldsymbol{\beta} + \textbf{z} + \boldsymbol{\epsilon}, \label{linearmodel}
\end{equation}

\noindent with spatially correlated random effects $\textbf{z} \sim \mathcal{N}(\bf{0}, \boldsymbol{\Sigma_z})$ and independent residuals $\boldsymbol{\epsilon} \stackrel{iid}{\sim} \mathcal{N}(0, \sigma_0^2)$ yielding a covariance of $\boldsymbol{\Sigma} = \mbox{Cov}[\textbf{Y}] = \boldsymbol{\Sigma}_z + \sigma_0^2 \textbf{I}$ \noindent where \textbf{I} is the $n \times n$ identity matrix and $\sigma_0^2$ is the nugget effect. Typically, we express $\boldsymbol{\Sigma_z}$ as a function based on distance $h$ between locations $\textbf{d}$, and covariance parameters, $\boldsymbol{\theta}_z$. We define the set of all parameters as $\boldsymbol{\theta} = (\boldsymbol{\beta}, \boldsymbol{\theta}_z)'$.

There are many covariance models that describe how the dependence between observed data at two spatial locations decays with distance. A common example is the exponential function,
\begin{equation}
    C(h|\boldsymbol{\theta}_z) = \sigma_1^2 \mbox{exp}\Big(\frac{-3h}{\alpha}\Big),
\label{eq:exp}
\end{equation}

\noindent where the partial sill, $\sigma_1^2$, represents the magnitude of variance and the range parameter, $\alpha$, describes how fast the covariance decays with an appropriate measure of distance between the locations, $h$.

The generalised linear modelling (GLM) framework provides a unified approach to analyse data for which some function of the mean response (link function) may vary linearly with the predictors rather than the mean response itself.
We denote the linear predictor by $\textbf{X} \boldsymbol{\beta} = \boldsymbol{\eta} = \beta_0 + \sum\limits^{p}_{j=1}\textbf{X}_{j} \beta_j$.
A link function $g(\cdot)$ relates the linear predictor to the mean of the outcome variable $g(\mathbb{E}(\textbf{Y}|\textbf{X})) = \boldsymbol{\eta}$.
In a GLM, $\textbf{Y}$ is assumed to be generated from a distribution in the exponential family, where the probability density (or mass) function is written as,
\begin{equation*}
    p(y_i) = \mbox{exp}\Bigg(\frac{y_i \psi_i - b(\psi_i)}{a_i(\phi)} + c(y_i, \phi) \Bigg),
\end{equation*}
where for observation $i$, $\psi_i$ is the location parameter, $\phi$ is the scale parameter and $a_i(\cdot)$, $b(\cdot)$ and $c(\cdot,\cdot)$ are known functions.\\

\noindent \emph{Example 1: Model for River Networks}

\noindent Consider data collected on a river network exhibiting complex patterns of spatial dependence due to multi-scale processes occurring within and between the aquatic and terrestrial environments \citep{peterson2013modelling}.
Two points $d^k$ and $d^s$ on the river network are said to be \emph{flow-connected} if water flows from an upstream site to a downstream site. They are \emph{flow-unconnected} if they reside on the same river network and share a common junction downstream, but do not share flow.
Following \cite{ver2010moving}, we estimate autocorrelation between points $d^k$ and $d^s$ by constructing random variables as the integration of a moving-average function over a white-noise random process.
The tails of these moving-average functions are unilateral and spatial autocorrelation only occurs when the tails of the functions overlap.
If the tail points upstream, it is referred to as a \emph{tail-up} model and by construction, these models restrict correlation to flow-connected locations. Stream networks are dendritic and so weights are used to proportionally allocate (i.e. split) the tail-up moving average function at river junctions.
Tail-up models are particularly useful for modelling organisms or materials that flow passively downstream (e.g. water pollutants).
Conversely, when the tail of the function points downstream it is referred to as a \emph{tail-down} model. These models allow spatial correlation between both flow-connected and flow unconnected locations and may be more suitable for modelling organisms such as fish that actively move both up and downstream \citep{peterson2003upstream}.

A mixed modelling approach is often used for modelling river network data since it allows for more complex patterns of spatial dependence to be described within a single model \citep{peterson2010mixed}. Variance components are used to expand the spatially dependent random variable $\textbf{z}$ into several zero-mean random variables,
\begin{equation}
\textbf{Y} = \textbf{X} \boldsymbol{\beta} + \textbf{z}_{_{EUC}} + \textbf{z}_{_{TU}} + \textbf{z}_{_{TD}} + \boldsymbol{\epsilon},
\label{eq:mixed}
\end{equation}

\noindent with correlation structure described using Euclidean (EUC), tail-up (TU) and tail-down (TD) covariance models.
As the notation suggests, the general covariance matrix can be formulated by a combination of such covariance models,
\begin{align}
\boldsymbol\Sigma &= \mbox{Cov}(\textbf{z}_{_{EUC}}) + \mbox{Cov}(\textbf{z}_{_{TU}}) + \mbox{Cov}(\textbf{z}_{_{TD}}) + \mbox{Cov}(\boldsymbol{\epsilon}) \nonumber\\
&= \textbf{C}_{_{EUC}}(h_{_{EUC}}|\boldsymbol{\theta}_{\textbf{z}_{EUC}}) +  \textbf{C}_{_{TU}}(h_{_{H}}|\boldsymbol{\theta}_{\textbf{z}_{TU}}) +  \textbf{C}_{_{TD}}(h_{_{H}}|\boldsymbol{\theta}_{\textbf{z}_{TD}}) + \sigma_0^2 \textbf{I}, \label{eqsigma}
\end{align}
\noindent where $h_{_{EUC}}$ is the Euclidean distance and $h_{_{H}}$ represents the hydrological distance, that is, distance \emph{along} the river.
Note that, distance considered can depend on flow-connectivity of sites and the appropriate covariance function but for brevity we denote this as $h_{_{H}}$, see \cite{santos2021bayesian} for further details.
See Appendix A.1 for the specification of the covariance matrices $\textbf{C}_{_{EUC}}$, $\textbf{C}_{_{TU}}$ and $\textbf{C}_{_{TD}}$, as well as distance $h_{_{H}}$.

The generalised linear mixed model for river networks we consider is of the form,
\begin{align}
   \textbf{Y} &\sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol\Sigma)\label{eqlinear}\\
   p(\textbf{y}|\boldsymbol{\theta}, \textbf{d}) = (2\pi)^{-\frac{k}{2}}\mbox{det}(\boldsymbol\Sigma)^{-\frac{1}{2}}&\mbox{exp}\big(-\frac{1}{2}(\textbf{y}-\boldsymbol{\mu})^T\boldsymbol\Sigma^{-1}(\textbf{y}-\boldsymbol{\mu})\big),\nonumber
\end{align}

\noindent with link function as the identity $g(\boldsymbol{\mu}) =\textbf{X}\boldsymbol{\beta}$ and $\boldsymbol\Sigma$ as defined by Equation \eqref{eqsigma} at a collection of locations $\textbf{d}$ on the network.

\vspace{0.5cm}
\noindent \emph{Example 2: Coral Reef Modelling}

\noindent Estimates of hard coral are generally obtained using a number of images, $N$, of the reef floor at locations $s_k$ collected along a transect.
In order to define transect placement, design parameters are introduced: the midpoint of a transect using Easting and Northing coordinates, $E^j$ and $N^j$, the angle of the transect, $\alpha^j$ in degrees, and the length of the transect, $l^j$ in meters (m).
Transects can therefore be fully specified by design parameters $d^j = (E^j, N^j, \alpha^j, l^j)$ for transect $j$ (see Figure \ref{fig:transect}).
Let $s_k = (e_k, n_k)$ denote the geographic coordinates of image $k$ specified by a collection of transects $\textbf{d}$.
Another parameter, $r^j$, is introduced to create a transect \emph{region}. For radius $r^j > 0$, points disperse across the geographic plane to $\hat{s}_k = (\hat e_k, \hat n_k) = (e_k + \delta_{k}^1, n_k+ \delta_{k}^2)$, with $\delta_{k}^1,\delta_{k}^2 \sim \mbox{Unif}(-r^j, r^j)$.

For each image a number, $n_k$, of randomly selected points are placed on image, $k$, and classified as hard coral, or not.
The number of points within an image that contain hard coral, $y_k$, are assumed to have a binomial distribution
\begin{align}
   \textbf{Y} &\sim \mbox{Binomial}(\textbf{q},\textbf{n}) \nonumber\\
   p(\textbf{y}|\boldsymbol{\theta}, \textbf{d}, \textbf{z}) &= \prod^N_{k=1} { n_k \choose y_k}  q_k^{y_k} (1-q_k)^{n_k-y_k}.
\label{eqn:logit}
\end{align}
where $\textbf{q} = \mathbb{E}(\textbf{Y}|\textbf{X}, \boldsymbol{\theta}, \textbf{z})$, with spatially correlated random effects $\textbf{z} \sim \mathcal{N}(\bf{0}, \boldsymbol{\Sigma_z} + \sigma_0^2 \textbf{I})$ where the matrix $\boldsymbol{\Sigma_z}$ has entries of the form in Equation \eqref{eq:exp} or some other covariance matrix.
The expected value of coral cover $q_k$ on image $k$ leads to the specification of a logistic regression model with link function denoted by $g(\textbf{q}) = \mbox{log}(\textbf{q}/(1-\textbf{q}))$, so that $\textbf{q} = \mbox{logit}^{-1}(\boldsymbol{\eta} + \textbf{z}) = \mbox{exp}(\boldsymbol{\eta} + \textbf{z})/(1 + \mbox{exp}(\boldsymbol{\eta} + \textbf{z}))$ with $\boldsymbol{\eta} = \textbf{X} \boldsymbol{\beta}$.

\begin{figure}
\includegraphics[width=0.9\textwidth]{images/Easting-Northing-transect-plots_final.png}
\caption{Data is sampled at each geographic point $s_k$ along the transect defined by $d^j = (E^j, N^j, \alpha^j, l^j)$ (left). A transect region with radius $r^j$ is shown, where data is collected at the stochastic sample locations $\hat{s}_k$ within the region (right).}
\label{fig:transect}
\end{figure}

\subsection{Bayesian Framework}

Let $p(\boldsymbol{\theta})$ denote the prior distribution on $\boldsymbol{\theta}$, and consider the joint posterior distribution,
\begin{equation}
p(\boldsymbol{\theta}, \textbf{z}| \textbf{y}, \textbf{d}) = \frac{p(\textbf{y} | \boldsymbol{\beta}, \textbf{d}, \textbf{z}) p(\boldsymbol{\theta} ) p(\textbf{z}|\boldsymbol{\theta}_z) }{p(\textbf{y}|\textbf{d})} \propto p(\textbf{y} | \boldsymbol{\beta}, \textbf{d}, \textbf{z}) p(\boldsymbol{\theta} ) p(\textbf{z}|\boldsymbol{\theta}_z),
\label{eqn:joint}
\end{equation}

\noindent where $p(\textbf{y}|\textbf{d}) = \int_{\theta} p(\textbf{y}, \boldsymbol{\theta})\ d\boldsymbol{\theta}= \int_{\theta} p(\textbf{y} | \boldsymbol{\theta}, \textbf{d} ) p(\boldsymbol{\theta})\ d\boldsymbol{\theta}$ is the marginal distribution of $\textbf{y}$.
Unless the likelihood and spatial random effect are analytically tractable, that is, $\int_{\textbf{z}} p(\textbf{y} | \boldsymbol{\beta}, \textbf{d}, \textbf{z})p(\textbf{z}|\boldsymbol{\theta}_z)\ d\textbf{z} = p(\textbf{y}|\boldsymbol{\theta}, \textbf{d})$ has a closed form solution, the spatial random effect must be integrated out numerically.
We describe the approach taken in the next section.

\section{Bayesian Optimal Design for Spatial Models}

Optimal design problems are commonly viewed as an optimisation framework with respect to an experimental aim. A utility function is defined to quantify the worth of a design, which may be to control systematic error (bias), reduce random variation, increase the precision of parameter estimates, make predictions about future observations or discriminate between competing models.
Formally, we denote the utility function as $u(\textbf{d}, \boldsymbol{\theta}, \textbf{y})$ which depends on model parameters $\boldsymbol{\theta}\sim p(\boldsymbol{\theta})$ and the data we might observe under that statistical model $\textbf{y} \sim p(\textbf{y} | \boldsymbol{\theta}, \textbf{d})$ at design points $\textbf{d}$ from the design space $\mathcal{D}$.
We establish the notation for a design as follows, $\textbf{d}_i = (d_i^1, ..., d_i^\gamma)$, and use $d_i^j$ to refer to the $j$th coordinate of design $\textbf{d}_i$ throughout the paper.

The aim is to maximise the expected utility, $U(\textbf{d}) = \mathbb{E}[u(\textbf{d}, \boldsymbol{\theta}, \textbf{y})]$ over the entire parameter space $\Theta$ and all conceivable data sets $\mathcal{Y}$. The Bayesian optimal design $\textbf{d}_*$ can therefore be expressed as,
\begin{align}
\textbf{d}_* &= \mbox{arg max}_{\textbf{d} \in \mathcal{D}} \mathbb{E}[u(\textbf{d}, \boldsymbol{\theta}, \textbf{y})] \nonumber \\
&= \mbox{arg max}_{\textbf{d} \in \mathcal{D}} \int_{\textbf{y} \in \mathcal{Y}} \int_{\boldsymbol{\theta} \in \Theta} u(\textbf{d}, \boldsymbol{\theta}, \textbf{y})\ p(\boldsymbol{\theta}, \textbf{y}| \textbf{d}) \ d\boldsymbol{\theta}\ d\textbf{y} \label{eq2} \\
&= \mbox{arg max}_{\textbf{d} \in \mathcal{D}} \int_{\textbf{y} \in \mathcal{Y}} \int_{\boldsymbol{\theta} \in \Theta} u(\textbf{d}, \boldsymbol{\theta}, \textbf{y})\ p(\textbf{y} | \boldsymbol{\theta}, \textbf{d})\ p(\boldsymbol{\theta})\ d\boldsymbol{\theta}\ d\textbf{y}. \nonumber
\end{align}

Unfortunately, the integral in Equation \eqref{eq2} is analytically intractable for most applications, and indeed the linear mixed-model in Equation \eqref{linearmodel}. In practice, a commonly used method is Monte Carlo integration, where the expected utility can be approximated by the empirical mean, that is,

\begin{equation}
\hat U(\textbf{d}) = \frac {1}{M} \sum^{M}_{m=1} u(\textbf{d}, \boldsymbol{\theta}^{(m)}, \textbf{y}^{(m)})
\label{eq:monte}
\end{equation}

\noindent with draws from the prior $\boldsymbol{\theta}^{(m)} \sim p(\boldsymbol{\theta})$ and then the likelihood $\textbf{y}^{(m)} \sim p(\textbf{y} | \boldsymbol{\theta}^{(m)}, \textbf{d})$.
In order to accurately estimate $\hat U(\textbf{d})$, $M$ needs to be large.
In some cases, the median $\tilde U(\textbf{d}) =  \mbox{median}(u(\textbf{d}, \boldsymbol{\theta}^{(m)}, \textbf{y}^{(m)}))$ may be preferred to the arithmetic mean in Equation \eqref{eq:monte}, since it is less sensitive to tail behaviour when the target distribution is asymmetric.
We explore this comparison further in the following sections.

A commonly used utility function is the Kullback-Liebler (KL) divergence \citep{kullback1951information} of the posterior from the prior distribution,
\begin{align}
\label{eqn:kld}
u(\textbf{y}, \textbf{d}) &= D_{KL}[p(\boldsymbol{\theta} | \textbf{y}, \textbf{d})||p(\boldsymbol{\theta})] \nonumber \\
&=  \int p(\boldsymbol{\theta} | \textbf{y}, \textbf{d}) \log \frac{p(\boldsymbol{\theta} | \textbf{y}, \textbf{d})}{p(\boldsymbol{\theta})} \ \mbox{d}\theta.
\end{align}

\noindent The intuition behind Equation \eqref{eqn:kld} is that a large $D_{KL}$ divergence from posterior to prior implies that the data in $\textbf{y}$ reduces entropy (randomness or uncertainty) in $\theta$ and hence the data are more informative at design points $\textbf{d}$. As suggested by \cite{lindley1956measure}, this utility can be used in the interest of maximising the expected information gain on the model parameters (or functions of these) when performing experiments at design points $\textbf{d}$. When both the prior and the posterior distributions follow multivariate normal distributions, that is, $\boldsymbol{\theta} \sim  \mathcal{N}(\boldsymbol{\mu}_{0},\boldsymbol{ \Sigma_{0}})$ and $\boldsymbol{\theta} | \textbf{y}, \textbf{d} \sim  \mathcal{N}(\boldsymbol{\mu}_{1}, \boldsymbol{\Sigma_{1}})$, respectively, then the KL divergence becomes
\begin{equation*}
u(\textbf{y}, \textbf{d}) = \frac{1}{2} \Big[(\boldsymbol{\mu}_{0} - \boldsymbol{\mu}_{1})^T \boldsymbol{\Sigma_{0}}^{-1}(\boldsymbol{\mu}_{0} - \boldsymbol{\mu}_{1}) + \text{tr}(\boldsymbol{\Sigma_{0}}^{-1}\boldsymbol{\Sigma_{1}}) - \text{ln}\frac{|\boldsymbol{\Sigma_{1}}|}{|\boldsymbol{\Sigma_{0}}|} - {\kappa} \Big],
\end{equation*}

\noindent where $\boldsymbol{\mu}_{0},\ \boldsymbol{\mu}_{1} \in \mathbb{R}^{\kappa}$ and $\boldsymbol{\Sigma_{0}},\ \boldsymbol{\Sigma_{1}} \in \mathbb{R}^{{\kappa} \times {\kappa}}$ \citep{duchi2007derivations}.

Note that in Bayesian design, the utility is always a function of the posterior distribution, which generally means that inference is performed many thousands of times since the posterior $p(\boldsymbol{\theta} | \textbf{y}, \textbf{d})$ must be evaluated for each future data set $\{\boldsymbol{\theta}^{(m)}, \textbf{y}^{(m)}\}$ that is drawn from the joint distribution $p(\boldsymbol{\theta},\textbf{y}| \textbf{d})$.
As a computationally efficient approximation to the posterior distribution, we employ the Laplace approximation which has the following form:
\begin{equation}
    \boldsymbol{\theta} | \textbf{y}, \textbf{d} \sim  \mathcal{N}(\boldsymbol{\theta}, \textbf{H}(\boldsymbol{\theta}^{*})^{-1}),
\end{equation}
where $\boldsymbol{\theta}^* = \mbox{arg max}_{\boldsymbol{\theta} \in \Theta}\{\mbox{log } p(\textbf{y}|\boldsymbol{\theta}, \textbf{d}) + \mbox{log }p(\boldsymbol{\theta})\}$ and $\textbf{H}(\boldsymbol{\theta}^{*})$ is the Hessian matrix defined as:
\begin{equation*}
    \textbf{H}(\boldsymbol{\theta}^{*}) = \left.\ffrac{-\partial^2 \{\mbox{log } p(\textbf{y}|\boldsymbol{\theta}, \textbf{d}) + \mbox{log }p(\boldsymbol{\theta})\} }{\partial\boldsymbol{\theta}\partial\boldsymbol{\theta}^{'}}\right\rvert_{\boldsymbol{\theta}=\boldsymbol{\theta}^{*}}.
\end{equation*}

This approximation requires evaluation of the full data likelihood.
Thus, the full data likelihood used in forming the Laplace approximation is replaced with a numerical approximation to the posterior for $\boldsymbol{\theta}$,
\begin{equation}
p(\boldsymbol{\theta} | \textbf{y}, \textbf{d}) \propto p(\boldsymbol{\theta} ) \int_{\textbf{z}} p(\textbf{y} | \boldsymbol{\beta}, \textbf{d}, \textbf{z})  p(\textbf{z}|\boldsymbol{\theta}_z)\ d\textbf{z}.
\label{eqn:fulllikelihood}
\end{equation}

Finally, an approach for the maximisation required in finding the Bayesian optimal design in Equation \eqref{eq2} needs to be specified.
It is common to use a Coordinate Exchange (CE) algorithm to search a discrete space, by exchanging coordinates in the design, $\textbf{d}$, with other points in the design space, in a sequential manner.
Formally, denote a proposal design by $\textbf{d}^{j\curvearrowright} = (d^1, ..., d^{j-1}, d^{\curvearrowright}, d^{j+1}, ..., d^\gamma)$, obtained by exchanging the $j$th design coordinate for some other design point $d^{\curvearrowright} \in \mathcal{D} \setminus \textbf{d}$.
Given the stochastic nature of the utility approximation, illustrated by draws of the prior and likelihood in Equation \eqref{eq2}, the search algorithm needs to accommodate different realisations of $\tilde{U}(\textbf{d})$.
For this, an acceptance probability $p^*$ can be used to compare a proposed design $\textbf{d}^{j\curvearrowright}$ to the current best design $\textbf{d}$.
The Approximate Coordinate Exchange (ACE) algorithm \citep{overstall2017bayesian} is a commonly used stochastic CE algorithm with acceptance probability defined by

\begin{equation*}
p^* = 1- T_{2B -2}\Big(- \dfrac{B\hat{U}(\textbf{d}^{j\curvearrowright}) - B\hat{U}(\textbf{d})}{\sqrt{2B\hat{v_b}}}\Big),
\end{equation*}
and
\begin{equation*}
\hat{v_b} = \dfrac{\sum^B_{l=1} \big[ u(\textbf{d}^{j\curvearrowright}, \boldsymbol{\theta}^{(l)}, \textbf{y}^{(l)}) - \hat{U}(\textbf{d}^{j\curvearrowright})\big]^2 + \sum^B_{l=1} \big[ u(\textbf{d}, \boldsymbol{\theta}^{(l)}, \textbf{y}^{(l)}) - \hat{U}(\textbf{d})\big]^2}{2B -2}
\end{equation*}
with large $B$ and random draws $\{\boldsymbol{\theta}^{(l)}, \textbf{y}^{(l)}\}$ from $p(\boldsymbol{\theta}, \textbf{y} | \textbf{d})$. However, this acceptance criteria relies on the assumption of a normally distributed utility (at least approximately).

We propose an alternative version of the stochastic Coordinate Exchange algorithm (see Appendix Algorithm \ref{stochastic_search}) with a non-parametric acceptance criterion defined as $$p_W^* = 1- W(U(\textbf{d}^{j\curvearrowright}), U(\textbf{d}))$$ where $W$ is the p-value of the one-sided Wilcoxon rank sum test (equivalent to the Mann-Whitney test).
In this case, the null hypothesis is that the distributions of the proposed design utility, $U(\textbf{d}^{j\curvearrowright})$, and the current best design utility, $U(\textbf{d})$, differ by a location shift of $\mu=0$ and the alternative hypothesis is that $\mu > 0$. The `one-sided' specifies that $U(\textbf{d}^{j\curvearrowright})$ is shifted to the right of $U(\textbf{d})$. We explore the proposed non-parametric stochastic Coordinate Exchange algorithm in comparison to the ACE in the Appendix, both with median and mean central tendency measure.

\section{Sampling Windows}

As mentioned previously, optimal design methods have been used to determine sampling windows for experiments in pharmacokinetics \citep{foo2012general, bogacka2008d}.
For spatial processes, sampling windows would allow the experimenter some flexibility in the sampling location, while preserving a minimum required efficiency for the design utility.
In order to define sampling windows, we define the utility in a continuous domain.
Consider the design space $\mathcal{D} \subseteq \mathbb{R}^q$ across $q$ windows.
We first introduce Gaussian processes (GP) and illustrate their flexibility and capability as a multi-dimensional utility smoothing technique.
Based on the smoothing GPs provide, we then show how design efficiency contours can be derived.

GPs generalise the concept of Gaussian distributions over discrete random variables to the function space.
In the Bayesian context, GPs can be seen as a prior over the function space, where inference takes place. Let $f(\textbf{x})$ denote the target value of interest where $\textbf{x} \in \mathbb{R}^{q}$ is a $q$-dimensional random vector containing predictor values such as spatial locations.
We write $\mathcal{GP}(m(\textbf{x}), k(\textbf{x}, \textbf{x}^{'}))$ to denote a GP characterised by a mean function $m(\textbf{x})$ and a covariance function $k(\textbf{x}, \textbf{x}^{'})$.
Consider a GP model with kernel,
\begin{equation}
k(\textbf{x}_p, \textbf{x}_s) = \sum\limits^{q}_{j=1} \exp(-\zeta_j * \mbox{dist}_j(\textbf{x}_p, \textbf{x}_s))
\label{eq:kernel}
\end{equation}
with hyperparameters $\boldsymbol\zeta$ and distance measure defined as $\mbox{dist}_j(\textbf{x}_p, \textbf{x}_s) = |x_{p}^j - x_{s}^j|$, for $j=\{1,...,q\}$. Using a finite collection of inputs $\{\textbf{x}_1,...,\textbf{x}_n\}$ and the function above, we construct the kernel matrix $\textbf{K}(\cdot)$ over the parameter space.

Details of the proposed Sampling Windows Algorithm are presented in Algorithm \ref{gp}, using design notation. We begin by defining a design space for windows (line 2), this may differ from the design space searched in the discrete stochastic CE algorithm.
We fit a GP (line 4) to the criterion of interest, here, the median utility $\tilde U(\textbf{d}_i)$ computed at each input $\textbf{d}_i$ (line 3), assuming a zero-mean GP prior, $f \sim \mathcal{GP}(\textbf{0}, \textbf{K}(\textbf{D},\textbf{D}) + \zeta_0 \textbf{I})$.
Inclusion of the nugget $\zeta_0 > 0$ ensures that every $f$ has some magnitude of variance with itself only (independent noise), so that the Monte Carlo approximations of the median utility surface will be smoothed, not interpolated.
Hyperparameters $\boldsymbol\zeta = (\zeta_0,...,\zeta_{\kappa})$ are determined (line 5) by minimising cross-validation error of the GP,
\begin{align}
\hat{\boldsymbol{\zeta}} &= \underset{\boldsymbol{\zeta}}{\mathrm{arg\ min}}\ CV(\boldsymbol{\zeta}|f,\textbf{D}) \text{, with }\\
CV(\boldsymbol{\zeta}|f,\textbf{D}) &= \ffrac{1}{\gamma_1} \sum\limits^{\gamma_1}_{i=1} \Bigg(\ffrac{\tilde{U}(\textbf{d}_i|\textbf{d}_c) - f(\textbf{d}_i)}{1 - S_{ii}}\Bigg)^2
\label{eqn:cv}
\end{align}
where $\textbf{S} = \textbf{K}(\textbf{D},\textbf{D})[\textbf{K}(\textbf{D},\textbf{D}) + \zeta_0 \textbf{I}]^{-1}$.

The posterior predictive mean of $f$ used as an emulator (in line 6) is,
\begin{equation}
\bar f = \textbf{K}(\textbf{d}_{\star}, \textbf{D})[\textbf{K}(\textbf{D},\textbf{D}) + \zeta_0 \textbf{I}]^{-1}\tilde{U}(\textbf{D}|\textbf{d}_c)
\end{equation}
for arbitrary inputs $\textbf{d}_{\star}$ derived using standard results on the conditional distribution of normal random variables.
Finally, computing the design efficiency (line 7) is achieved by normalising the functional utility to
\begin{equation}
eff(\textbf{d}_{\star j}) = \ffrac{\bar f(\textbf{d}_{\star j}|\textbf{D},\hat{\boldsymbol{\zeta}})}{\bar f(\hat{\textbf{d}}_{*j}|\textbf{D},\hat{\boldsymbol{\zeta}})}
\label{eqn:eff}
\end{equation}
where $\hat{\textbf{d}}_{\star j} = \underset{\textbf{d}_{\star j} \in \textbf{D}_{\star}}{\mathrm{arg\ max}}\ \bar f(\textbf{d}_{\star j}|\textbf{D},\hat{\boldsymbol{\zeta}})$. Output design efficiency contours (line 8) as the set of prediction points above threshold value $t$.

\LinesNumbered
\begin{algorithm}
\SetAlgoLined

If existing, let $\textbf{d}_c = (\textbf{d}_{c1}, \textbf{d}_{c2},...,\textbf{d}_{c\gamma})$ be the current design. Specify $\tilde{U}(\textbf{d}|\textbf{d}_c)$ as appropriate and define prior $p(\boldsymbol{\theta})$ and likelihood $p(\textbf{y}|\boldsymbol{\theta}, \textbf{d})$. \\

\nonl\emph{Phase I - Construct $q$-dimensional utility grid} \\

Define design space $\mathcal{D} \subseteq \mathbb{R}^q$ across $q$ windows, sample $\textbf{D} = (\textbf{d}_1, ..., \textbf{d}_{\gamma_1})$ with $\textbf{d}_i \in \mathcal{D}$ for training and $\textbf{D}_{\star} = (\textbf{d}_{\star 1}, ..., \textbf{d}_{\star \gamma_2})$ with $\textbf{d}_{\star j} \in \mathcal{D}$ for predictions.

Compute median utility $\Tilde{U}(\textbf{d}_i)$ for each point $\textbf{d}_i$\\

\nonl\emph{Phase II - Functional utility surface} \\

Fit a GP; hyperparameters are determined by minimising cross-validation error\\
$\hat{\boldsymbol{\zeta}} = \underset{\boldsymbol{\zeta}}{\mathrm{arg\ min}}\ CV(\boldsymbol{\zeta}|f,\textbf{d})$ with CV defined in Equation \eqref{eqn:cv}

Evaluate predicted mean values $\bar f$ at each prediction point $\textbf{d}_{\star j}$ as
$\bar f(\textbf{d}_{\star j}|\textbf{D},\hat{\boldsymbol{\zeta}}) = \sum\limits^{\gamma_1}_{i=1} k(\textbf{d}_{\star j}, \textbf{d}_i| \hat{\boldsymbol{\zeta}})\alpha_i $ for $\boldsymbol{\alpha} = [\textbf{K}(\textbf{D},\textbf{D}) + \hat\zeta_0 \textbf{I}]^{-1} \tilde{U}(\textbf{D}|\textbf{d}_c)$\\

\nonl\emph{Phase III - Design Efficiency contours} \\

Normalise utility surface to yield efficiencies
$eff(\textbf{d}_{\star j})$ as per Equation \eqref{eqn:eff} for each prediction point $\textbf{d}_{\star j}$

Output set of points where $eff(\textbf{d}_{\star}) > t$ for threshold values $t = [0,1]$

\caption{Sampling Windows Algorithm}\label{gp}
\end{algorithm}

\section{Case Studies} \label{sec:casestudy}

\subsection{Example 1: River Network Design}

The design problem in this case study is motivated by a costly and complex balance of priorities, that is, short-term interest in monitoring particular river segments (e.g. wildfire impacts on juvenile fish habitat), while maintaining the ability monitor efficiently at established locations throughout the region.
In this example, we use a water temperature dataset from the Clearwater River Basin, USA, with observation sites located from 500m up to 46km apart (Figure \ref{fig:clearwater}).
Temperature data were collected at 15 spatial locations using in-situ sensors that recorded measurements at 30 minute intervals \citep{isaak2018principal}.
The response variable is mean temperature for July 1, 2013, with stream slope, elevation, watershed area, and air temperature used as covariates \citep{santos2022ssnbayes}.
Note that spatial variation in temperature often constitutes the largest proportion of total variation, since temporal correlation among sites is strong \citep{isaak2017norwest}.
A tail-down covariance function was found to be the most suitable covariance function for describing this spatial dependence.

\begin{figure}
\includegraphics[width=1\textwidth]{images/clearwater_network_optimal_colour_final.png}
\caption{A total of 15 observation sites located in the Clearwater River Basin, USA. Average daily water temperature for July 1, 2013. The width of the stream line is proportional to Shreve's stream order \citep{shreve1966statistical}. The optimal and non-optimal design locations using the proposed stochastic Coordinate Exchange search are represented by filled and unfilled dots, respectively.}
\label{fig:clearwater}
\end{figure}

There are 15 existing monitoring sites in the Clearwater River Basin and the design problem is to find the best 5 among them.
In addition, wildfires occurred near two segments that provide cold water refugia for juvenile fish and sensors are to be deployed to monitor impacts on water temperature.
For convenience, we define search neighbourhoods along the river network, that is, any continuous line along the branching river network and specify Neighbourhood 1 (N1) and Neighbourhood 2 (N2) in Figure \ref{fig:windowsnetwork}.

\begin{figure}
\includegraphics[width=0.5\textwidth]{images/stochastic_wilcox_trace_median_final.png}
\includegraphics[width=0.5\textwidth]{images/stochastic_all_densities_final.png}
\includegraphics[width=0.5\textwidth]{images/stochastic_wilcox_acceptance_median_final.png}
\includegraphics[width=0.5\textwidth]{images/stochastic_best_density_final.png}
\label{figutility}
\caption{Trace plot for the coordinate exchange algorithm using Wilcoxon acceptance criteria and median utility (top-left); proposal probability using Wilcoxon acceptance criteria, $p^*_W$ (bottom-left); every 50th utility distribution in the proposed CE algorithm (top-right); and the optimal utility distribution (bottom-right).}
\end{figure}

The stochastic Coordinate Exchange approach outlined in Algorithm \ref{stochastic_search} (Appendix) was computed with $K = 5$ random starts and $T=15$ outer iterations.
Figure \ref{figutility} shows a selection of the utility distributions found in the proposed search algorithm, then the distributions of the optimal design, noting the non-normality of these distributions.
The optimal design was found to be at locations, $\textbf{d}_* = (167, 169, 172, 174, 183)$ with a median utility of 3.6805.
These optimal locations cover a wide range for each of the covariate values, in particular, optimal locations include the maximum and minimum value for air temperature.
The set of locations $(167, 169, 174)$ are clustered at a river confluence and the most downstream location of all sites, $169$, is included in the design (Figure \ref{fig:clearwater}).
These characteristics agree with optimal designs found using previous pseudo-Bayesian approaches for river networks \cite{falk2014sampling}.
We also benchmark the performance of the proposed Coordinate Exchange algorithm against other variations; a comparison of acceptance criteria (Wilcoxon vs. ACE), as well as central tendency measure (mean vs. median) is provided in the Appendix.
The choice of the median as a preferred measure is supported by the apparent skewness and long tails of the distributions of the utilities (Figure \ref{figutility}).

Recall the specification of neighbourhoods N1 and N2 within the river network for sensor deployment.
The proposed Sampling Windows Algorithm (Algorithm \ref{gp}), is applied.
Consider the design space $\mathcal{D} \subseteq \mathbb{R}^2$ with design points $d_i^1 \in N1$ and $d_i^2 \in N2$ for each design $\textbf{d}_i = (d_i^1, d_i^2)$.
The current design $\textbf{d}_c$ is set as the optimal points $\textbf{d}_*$ from the downsizing regime previously found.
In Phase I, the median utility is computed as $\tilde{U}(\textbf{d}_i | \textbf{d}_c) = \tilde{U}(\textbf{d}_i \cup \textbf{d}_c)$ for each $\textbf{d}_i$ in the grid, $\textbf{D}$, sampled from neighbourhoods 500m apart.
Covariate values at $\textbf{d}_i$ for air temperature are interpolated using 3 nearest neighbours based on Euclidean distance, whereas the remaining covariate values (stream slope, elevation and watershed area) are unique to each river segment.
In Phase II, a GP is fit assuming a kernel function defined by Equation \eqref{eq:kernel}, where the distance measure $\mbox{dist}_j(\textbf{d}_s, \textbf{d}_p) = |d_s^j - d_p^j|$ for $j=1,2$ is equivalent to stream distance (along dimension $j$).
Results from Phase III indicate that N1 is more sensitive to location placement than N2, as shown in Figure \ref{fig:windows}.

From an applied standpoint, these design outputs allow decisions to be made in the field (e.g. placement around specific location $n_{15}$ in N1, but anywhere convenient on the main branch in N2).
This provides support for greater flexibility in sensor placement when access issues arise, without having to rerun a full discrete optimal design search.
A practical approach, given the design efficiency contours as a roadmap, would be to visit N1 first; should $n_{15}$ be inaccessible then move along the river to deploy the in-situ sensor where possible, say $n_{14}$.
Take the line segment corresponding to $eff(\textbf{D}_*|n_{14})$ to inform deployment in N2, in this case, $n_{24}$, to retain $98\%$ optimal utility.

\begin{figure}
\includegraphics[width=1\textwidth]{images/clearwater_network_windows_final.png}
\caption{Existing sites (red dots) and potential sites within search neighbourhoods N1 and N2 (gray dots) located on the river network. A discrete set of points were sampled from both neighbourhoods spaced at 500m stream distance apart.}
\label{fig:windowsnetwork}
\end{figure}

\begin{figure}
\includegraphics[width=1\textwidth]{images/windows_3_final.png}
\caption{Phases of the proposed Sampling Windows Algorithm; constructed median utility grid (left), Gaussian process mean predictions (middle), and normalised contours of design efficiency (right). A sensor close to $n_{15}\in$N1 will yield high design efficiency, while more flexibility can be afforded for the choice of sensor placement in N2.}
\label{fig:windows}
\end{figure}

\subsection{Coral Reef Design}

The Australian Institute of Marine Science (AIMS) has monitored the condition of coral reefs around Australia for decades.
We considered data collected in 2013 from the Barracouta East submerged coral reef off the north-west coast of Australia \citep{heyward2013montara}.
The design problem is to find the best regions to sample underwater images in.
We propose a two step approach using the methods described above: first, a global search for the optimal transect lines with $n=3$, the total number of transects, using the proposed stochastic CE algorithm in a discrete design space; then, a continuous search for the optimal radius of each transect region with $q=3$, the number of sampling windows centred at each transect.

Coral cover is assessed using images of the reef floor taken every 5m along a transect, where $n_k = 20$ random points on image $k$ are analysed, leading to the consideration of the logistic regression model described in Equation \eqref{eqn:logit}.
Exploratory analyses showed a strong linear relationship between the response variable, $\textbf{q}$, and depth of the reef floor which was used as the only covariate.
Note that depth was interpolated using 3 nearest neighbours based on Euclidean distance from the survey data.
To reduce the design space and thus the complexity of the search, angles are discretised to $\alpha^j = \{0, 45, 90, 135\}$, $E^j$ and $N^j$ are defined by a discrete set of points. Length remains fixed at $l^j=500$ so that each transect compromises of 100 images.

The proposed Stochastic Coordinate Exchange algorithm with the Wilcoxon acceptance criteria and median utility (Algorithm \ref{stochastic_search}) was applied to find the optimal transect lines across the shoal.
When computing the utility, the Laplace approximation to the posterior requires evaluating the full data likelihood, as shown in Equation \eqref{eqn:fulllikelihood}.
Accordingly, the spatially correlated random effect, $\textbf{z}$, needs to be integrated out.
For this, we chose to use Monte Carlo integration with $M_z=50$ draws from the marginal likelihood due to computational restraints.
The Monte Carlo integration for the median utility in Equation \eqref{eq:monte} is evaluated with $M=350$ and $B=600$ draws from the prior and full likelihood for the evaluation of $\hat{U}(\textbf{d}^{j\curvearrowright})$ and $p^*_W$, respectively.

\begin{figure}
\includegraphics[width=0.48\textwidth]{images/coral_stochastic_wilcox_combined_final.png}
\includegraphics[width=0.52\textwidth]{images/coral_transects_depth_final.png}
\caption{Trace plot of proposed stochastic coordinate exchange algorithm (top-left), acceptance probability (bottom-left), and optimal transect design in geographic space (right).}
\label{fig:optimal_transect}
\end{figure}

Spatial covariance is characterised by exponential decay, defined in Equation \eqref{eq:exp}.
To further ease the computational burden, we construct a spatial grid (10 $\times$ 10) over the entire shoal, with $h_{_{EUC}}$ the Euclidean distance between grid centre points (a lower-dimensional surrogate to the $N \times N$ distance matrix using coordinates $\textbf{x}_k$).
This grid size is a compromise; not so small that the computational gains are marginal, but not so large that the spatial relationships are not captured between grid rectangles.
Results in Figure \ref{fig:optimal_transect} show the optimal placement of transects $\textbf{d}_* = (d_*^1, d_*^2, d_*^3)$ in the shallower areas of the reef, each with varying depth gradients.
Thus, it would seem reasonable to sample in along these transects to estimate coral cover.

The proposed Sampling Windows Algorithm (Algorithm \ref{gp}) is applied over the parameter space $r$, with the kernel function defined by Equation \eqref{eq:kernel} and distance $\mbox{dist}_j(r_s, r_p) = |r_s^j - r_p^j|$ for $j=1,2,3$.
In the first step, the optimal transect design previously found is fixed, while the design space $\mathcal{D} \subseteq \mathbb{R}^3$ is constructed for radius parameter, $r$, corresponding to each transect.
Since stochasticity is introduced in the choice of geographic locations, $\hat{s}_k$, we average median utility across 3 location samples for a given radius, each with $M=600$ Monte Carlo draws from the prior and likelihood.
The 3-dimensional design contours are shown in Figure \ref{3dwindows}.
Optimal design efficiency, $eff(\textbf{D}_*) = 101\%$, is achieved at $r_* = (44, 0, 44)$.
This implies optimality when sampling within a region for the shallower areas, and more strictly across the transect $d_*^2$ in the deeper area of the reef.
Generally, these contours can be used to guide decision making on the field, for example, sample $d_*^2$ when conditions are good, whereas sampling in $d_*^1$ and $d_*^3$ can be done with stronger underwater currents.

\begin{figure}
\includegraphics[width=\textwidth]{images/windows_3_coral_final.png}
\caption{The median utility (left); Gaussian process mean predictions of median utility (middle), and normalised contours of design efficiency (right) found at each phase of the proposed Sampling Windows Algorithm. The radius parameter, $r^j$, specifies a radius for transect $d^j_*$ for $j = \{1,2,3\}$.}
\label{3dwindows}
\end{figure}

\section{Discussion}

Coral reefs and freshwater ecosystems are biodiversity hotspots that are particularly sensitive to anthropogenic impacts of climate change, water pollution and over-exploitation, among other factors, resulting in rapid population declines \citep{strayer2010freshwater, tickner2020bending, wagner2020coral}.
Informative data are needed to support critical and timely conservation decisions, but various practical constraints make precise sampling difficult or even impossible.
In this paper, we have considered Bayesian optimal design for collecting data where greater flexibility is needed in the design outputs.
To this end, we proposed a spatial Sampling Windows Algorithm using Gaussian process emulation to estimate design efficiency contours.
While we focused on two important environmental systems, such an approach is also applicable to a broad range of complex systems that require rigorous design.
For example, optimal design methods for sub-sampling can be used as a computationally efficient way to analyse Big Data \citep{drovandi2017principles}. Rather than extracting optimal design points from the Big Data set, which may or may not exist, points could be selected within windows.

There are several novel aspects to the approaches described here.
Statistical models for branching river networks use distance travelled along the river network, directionality, and flow volume to describe spatial relationships.
There is novelty in the application of Bayesian design for river network systems, as of yet to be presented in the statistical literature.
Since utility distributions were not normally distributed, we also proposed the use of a non-parametric acceptance probability in the stochastic Coordinate Exchange, based on the one-sided Wilcoxon Rank Sum Test.
We successfully demonstrated how Bayesian design works in complex spatial settings and introduced a method to find sampling windows, facilitating intelligent data collection.

The novel methodological advances presented here provide practical solutions to common monitoring challenges.
Results from the proposed Sampling Windows Algorithm highlighted in the river network case study showed that design efficiency was best achieved around a smaller range in Neighbourhood 1, while almost agnostic to choice in Neighbourhood 2; recalling that neighbourhoods are any continuous line along the river.
In particular, the design efficiency contours identify which, and quantify how much, design points are sensitive to precise sampling.
Similarly, results in the coral reef case study showed high design efficiency around regions in shallow areas of the reef compared to deeper regions with less hard coral.
Providing fine-scale information about optimality allows practitioners in the field to make informed judgements on jointly optimal variables based on physical conditions not included in the utility (e.g. accessibility, safety, etc.), without the need to re-run time consuming optimisations.

There are also numerous opportunities for future research in this space.
One useful extension would be to incorporate additional monitoring objectives related to cost into the utility function.
For example, the optimal deployment of a combination of high-cost sensors that produce high-quality data and lower-cost sensors that produce less reliable data.
Sampling and monitoring costs are a core consideration for any monitoring program, but it is especially true in remote locations.
In such cases, it would also be useful to consider the travel time between sampling locations in the optimal design.
New Bayesian spatio-temporal models for river networks \citep{santos2021bayesian} provide the opportunity to extend the approach developed here for spatio-temporal sampling windows.
This would allow practitioners to make more effective use of mobile in-situ sensors for spatio-temporal data collection.
Thus, the novel methods presented here (along with future extensions) facilitate more efficient data collection; providing insights into spatial (and spatio-temporal) processes which can be used to better inform data-enabled management decisions in complex and vulnerable ecosystems.

\section*{Acknowledgments}

This project was supported by the Australian Research Council (ARC) Linkage Project (LP180101151) ``Revolutionising water-quality monitoring in the information age".
We thank Dan Isaak and Dona Horan from the US Forest Service Rocky Mountain Research Station for sharing the data and creating the SpatialStreamNetwork object used in the river network case study.
We also acknowledge the Seascape Health and Resilience team of the Australian Institute of Marine Science (AIMS) for the curation and provision of data towards the coral reef case study.

\section*{Code Accessibility}

The computations were performed using the R package bayesDesign, which contains functions for fitting models, optimisations and visualising design domains. The code can be found online at \url{github.com/KatieBuc/bayesDesign}. Note that the code relies on high performance computing infrastructure.

\bibliographystyle{rss}

redpajama_set_name: RedPajamaArXiv


text:
Tampa Bay Buccaneers' Mike Evans ends national anthem protest against Trump
Joseph McCormick November 21, 2016
An American football player in Tampa, Florida has ended his protest against President-elect Donald Trump.
Tampa Bay Buccaneers wide receiver Mike Evans had sat during the national anthem, refusing to stand last week.
He said his protest was over Donald Trump's divisive statements on minorities, women and LGBT+ people.
But he stood on Sunday for the national anthem ahead of a game against the Kansas City Chiefs.
Evans had previously vowed to sit during the national anthem "as long as Trump is President-elect".
But he has issued several apologies for refusing to stand, and has now ended his protest.
Last week's game had been the Buccaneers' Salute to Service game, and his refusal to stand had upset many.
"If I had to do it over again, I would have done it differently, but I would still use my platform to help," Evans said.
"On the field, I'm going to continue to do what I do — play hard. I'm playing hard because I've got this right — freedom, because of the vets," Evans added.
"I'm going to reach out to organisations, organisations that I feel are doing the best job to help the minority … women, LGBT, African Americans, Latinos, people that are in fear of Donald Trump and his presidency."
More: mike evans, US


© 2018, © 2018 Engineers Australia. With the rapid population growth and scarcity of developable space, especially in large cities, there is a need for increased density in both commercial and residential housing, and hence a strong demand to maximise floor space by constructing not only tall, but also slender buildings. This study considers different structural systems available for constructing slender high-rise buildings and evaluates their feasibility in terms of the lateral deformation being one of the key governing design criteria for very tall buildings. To examine the performance of different structural systems in buildings of varying height and floor plan, this study applies finite element analyses in a parametric study to compare nine different building configurations under static loading with heights varying from 80 to 460 m. The study shows that buildings with square footprints can achieve greater heights over rectangular footprints with the same area and that multiple towers when connected structurally at one or more levels can achieve even greater heights.


« IVF #3 is officially on!
1. The way my dog sleeps when she sneaks onto the bed in the middle of the night. She starts out at my feet, just curled up into a tiny ball, but by the time my alarm rings in the morning, she's almost always sprawled across me, with her head resting under my chin.
2. Hot shower on a cold morning. Duh.
3. Looking through a veritable mound of seed catalogs in January. I used to have a serious garden in Utah. Here in Brooklyn, we have a yard, but it's the size of the proverbial postage stamp. And it's mostly taken up by a couple of trees. It gets almost no sun. But I still dream of what flowers and vegetables will go where. And I still buy too many seeds & starts each year. Are you sensing a "giddy optimism even in the face of certain disappointment" theme in my dealings with life?
4. My favorite pen. It's a gel retractable, and I bought a ton of them when they first came out, which is a good thing, since I don't like the new ones so much. I still have a handful of my favorite pens from my place of employment almost 6 years ago. Best ballpoints ever.
5. Bagels warm from the oven. Yum. Heading to the bagel shop right now for my subway breakfast.
Yes! I adore seed catalogs in the winter! I spend hours looking through them and planning a fabulous garden, full of heirlooms and yummy new treats. Most years, I end up with a few dying tomato plants (boring Whoopers) in July and some crazy, overgrown zucchini. In January, I never fully realize how hot it will be July and how much I won't want to go out in that heat to water a garden. But, a girl can dream.
What a nice reminder of the little things in life! Happy Friday!
may I begin a list as well? i love it.


text:
New Markets for Old Furniture and Utensils Ready- Dubai
September, 25th 2017
Dubai will soon open new markets for used building materials and electrical appliances, and used furniture and utensils following the completion of the construction of their buildings.
Director General of Dubai Municipality, Hussain Nasser Lootah, recently visited the buildings of the new markets, which have been completed and handed over to the municipality by the contractors, the civic body said in a press release. The opening dates for the buildings will be announced soon.
The objective of the project is to have all used furniture, electrical appliances and household utensil showrooms in one location rather than allowing them to spread randomly in an unorganized way within the city, making it cumbersome for the majority of the public and re-export companies to purchase and locate the appropriate items and transport them.
The scrap market for building materials and electrical appliances in Warsan includes a main building consisting of 71 shops with public services, fast food outlets, market administration office, a mosque for men and women, 80 parking lots for trucks, 53 outdoor display outlets, loading and unloading areas and 760 parking spaces for visitors.
Built at a cost of Dh100 million, the market has a building area of 43,000 square metres on a land area of 11 hectares, the municipality said.
The used utensils and furniture market in Nad Al Sheba 3, includes 120 shops, half of them for the sale of furniture and the rest to sell utensils. It also includes an external plaza, market administration office, restaurant area for selling snacks, service buildings, toilets and other facilities.
The market, has a building area of 28,800 square meters on a land area of 17 hectares and is built at a cost of Dh77 million,
Lootah pointed out that these projects are part of the efforts of the Government of Dubai to complement the specialized market projects offered by the emirate, in line with the growth and development, the two streams that have made Dubai a prominent city competing with the world's finest cities.
Source: bizmap


Get lyrics of Single lil wayne song you love. List contains Single lil wayne song lyrics of older one songs and hot new releases. Get known every word of your favorite song or start your own karaoke party tonight :-).
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Hello, PlayStation Now fans! Today we're adding nine new games to the PlayStation Now library of more than 750 games in all, including hits from Konami and Codemasters. Check out Metal Gear Solid V: The Phantom Pain, DiRT 4, and more, available starting today! Subscribers can stream any game in the service to PS4 and PC, and download any PS4 game and PS2 game in the service directly to their PS4.
For a change of pace, take things offroad with DiRT 4 for some rally, rallycross, and landrush action. With over 50 iconic rally vehicles from throughout the history of rally motorsports, courses in the US and Europe, and a custom driver/team creator, get your rally on with DiRT 4 for PS4 (stream or download).
We're also adding three classic Star Wars PS2 games to the PS Now library to stream or download. Take to the skies in Star Wars: Jedi Starfighter, become Jango Fett in the 3rd person shooter Star Wars: Bounty Hunter, and test your Podracing skills in Star Wars: Racer Revenge.


text:
Heidi Roy of the Cariboo Jade Shop in Cache Creek with the boulder that was stolen from outside their shop on Dec. 19. The rock has been recovered intact, but with a few battle scars. (Photo credit: Submitted)
Jade boulder recovered intact after daring theft in Cache Creek
Suspects have been identified and police say investigation is ongoing
Barbara Roden
Ashcroft RCMP have recovered a jade boulder weighing more than 2,850 pounds that was stolen from outside the Cariboo Jade Shop in Cache Creek on Dec. 19.
"The jade boulder was recovered intact," says Sgt. Darren Angman, CO of the Ashcroft detachment. "We have identified suspects, and the investigation is still ongoing."
Angman says that no arrests have been made and that the investigation is ongoing, as police are still trying to tie the theft to the suspects.
Heidi Roy, whose family owns the Jade Shop and whose father Ben installed the boulder outside the shop in 1985, is thrilled that it has been recovered.
"We are so happy to have it back in one piece, although with a few scars from its adventure," she tells the Journal. "Thank you to all of you who have been keeping an eye out and sending in tips, as well as kind words of sympathy and encouragement received from across the country.
"It is clear that this stone meant a lot to many more people than we realized."
Two Ashcroft residents who were returning from Kamloops spotted a pickup truck towing a flat-deck trailer with an excavator on it leaving the Jade Shop parking lot at 11:55 p.m. on Dec. 19. They saw the boulder on the flat-deck and pursued the truck, which was heading east on Highway 1 toward Kamloops. They called 9-1-1 to report the incident, but turned around after a man thought to be associated with the theft threw a boulder at them near the Ghost of Walhachin pullout east of Cache Creek.
Jarrett Fitzpatrick, who was driving the vehicle, says that although the damage to his vehicle "sucked", he would do it again to try to catch the thieves. He wants to give a big thanks to Bill Elliott and the Cariboo Jade Shop, who contacted him to say that they would pay his deductible for the repairs.
"The fact that I was going to have to pay my deductible really sucked right before Christmas (what a way to end the worst year ever lol)," he wrote in a message to the Ashcroft Journal. "However Bill and the Jade Shop have stepped up and phoned me to let me know that they will be covering it for me.
"To some people it might not seem like much but to someone like me it is so appreciated."
Police have now determined that at 9:45 p.m. on Dec. 19 the pickup truck, trailer, and excavator were at a hotel parking lot next door to the Jade Shop. At approximately 11:05 p.m. a man was seen walking to the truck, which then drove to the Jade Shop, where the excavator was used to lift the jade boulder onto the trailer.
The suspect vehicle was later seen turning around on the Deadman-Vidette Road, approximately 32 kilometres off Highway 1 west of Savona. Kamloops RCMP later found the trailer abandoned in that area, but the excavator and boulder were gone. On Monday, Dec. 21 Chase RCMP located an abandoned truck matching the pickup truck used in the theft.
The boulder has been a much-loved and -photographed attraction in Cache Creek since it was installed outside the Jade Shop. Despite its size, its commercial value is minimal, as it is composed of low-quality jade. Roy, however, says that it is of great historic and sentimental value to Cache Creek.
"I'm seeing comments from all over the province and the world from people who took a picture of the rock, saying how much it meant to them," she said, shortly after the boulder was stolen."To us it's priceless."
Police are asking for the public's assistance with the investigation. Anyone with information about the incident, who was in the area at the time, or who has dash cam footage is asked to contact the Ashcroft RCMP at (250) 453-2216. If you wish to remain anonymous, contact Crime Stoppers at 1-800-222-TIPS (8477).
editorial@accjournal.ca
Cache Creek
The jade boulder stolen from outside the Cariboo Jade Shop in Cache Creek on Dec. 19, pictured in May 2020. (Photo credit: Barbara Roden)
GALLERY: British Columbians celebrate triumphs during a trying year
Addressing mental-health issues linked to pandemic looming issue in 2021, Bains says
Tweedsmuir Ski Hill wrecked by sledders for second time this season
The Club is respectfully requesting snowmobilers stay off the ski hill
COVID-19 cases climb to 52 as first vaccinations to begin Jan. 19
VCH has indicated vaccines will be available for off-reserve elders, but has not provided specifics
COVID-19 exposure confirmed at Nusatsum Elementary School
The exposure was in grade 5 and took place Jan. 6, 2021
Bella Coola's community paramedic can now test people for COVID-19
Jeffery Snow became certified to offer COVID-19 testing on Jan. 13, 2021
COVID-19 cases climb to 25 in Bella Coola
The first cases were reported by the Nuxalk EOC on Jan. 7
Explore Coast Mountain News
Bella Coola News
Bella Coola Classifieds
© 2021, Coast Mountain News and Black Press Group Ltd.


text:
Bayern Munich Youth
Transfer news and rumors
Bayern Munich's first Chinese player Liu Shaoziyang is determined to make his mark
Being Bayern Munich's first Chinese player comes with a responsibility, and Liu Shaoziyang is determined to do his best.
By Phillip Quinn@philneezy Jan 2, 2022, 8:00pm CET
Share All sharing options for: Bayern Munich's first Chinese player Liu Shaoziyang is determined to make his mark
Anytime a big European power signs a player from a non-major power, certain fans and pundits immediately turn the discussion to "They're just trying to market to the fans in that country!" and almost immediately dismisses the player as a marketing afterthought. Back in December, when Bayern Munich announced the signing of Liu Shaoziyang, the club's first player from China, that was the first thing out of the lips of many. The player, however, is determined to show that he's more than that.
"I want to assert myself in the team and play a lot of games," Shaoziyang, who signed a contract through 2025, said in an interview with FCBayern.de.
Before the signing, Shaoziyang had been on trial at the Bayern Campus for weeks living at the boarding school and in training with Bayern's U-19 side and Bayern II. "I think my technique has improved the most," Shaoziyang said regarding his training with U-19 goalkeeping coach Tom Starke. "Both when catching and with the ball on the foot. The structure of the game is also a central element in our daily work."
Everyone remembers Starke for his dutiful job as Manuel Neuer's backup for years, but what about him as a coach?
"For me, Tom is the best goalkeeping coach and a great person to relate to. He helps me everywhere: whether on or next to the pitch. And because we both speak Spanish, he also regularly helps me to communicate. It's usually faster than with the German language."
Servus, Liu!
18-year-old goalkeeper Liu Shaoziyang becomes first Chinese player at FC Bayern, joining @fcbayerncampus from partner club FC Wuhan Three Towns on a contract through 2025. ✍✅ pic.twitter.com/BmMFc56nPm
— FC Bayern US (@FCBayernUS) December 16, 2021
Learning German, as anyone who has tried to learn it can attest, is a work in progress for Shaoziyang. "It's a difficult language, but I've been in class for many weeks and I can understand a lot. Speaking is a little more difficult."
What does Bayern think about Shaoziyang's on-the-field skills? They rate him so highly that they're not willing to let the 18-year-old sit around and wait. According to a report, they're sending him out on loan to Austria Klagenfurt in the Austrian Bundesliga to get professional minutes under his belt.
Shaoziyang may not ever become a first team player at Bayern or even a Bundesliga player; however, it's not going to be because he wasn't willing to put in the work.
Daily Schmankerl: Chelsea eyeing Bayern Munich's Robert Lewandowski; No one peed on Ricardo Pepi at FC Augsburg; Liverpool wants Denis Zakaria; The latest on Niklas Süle and Corentin Tolisso; plus MORE!


text:
autocommit on;
create table t(i int);
insert into t values(1),(2),(1);
select 8 as col0 from t group by col0;
select 8 as i from t group by i;
select 8 i from t group by i;
drop table t;


Join us on Saturday March 16 at 8pm to Party With Marty McKernan. It's our St. Patrick's Day Party.
Marty McKernan is an incredible one man band who plays bass keyboard, percussion while playing guitar or banjo as he sings and plays harmonica. Covering originals and your favorite bluegrass, country, blues, Irish and Rock classics.
I never thought I was wasted, but I probably was.


text:
M&S and Aldi are again locked in a legal spat- this time over a bottle of gin, Wedlake Bell comment
M&S has gone to the High Court seeking an injunction against alleged infringement of its gin bottle design. The retailer says Aldi's blackberry and clementine gin liqueur is "strikingly similar" to its own Light Up gin.
Commenting on the story, Charlotte Wilding, Partner and Head of Trade Marks at Wedlake Bell said:
"It is rare for retailers to have two fights ongoing in the same year, but perhaps unsurprising given that, arguably, a number of Aldi products walk the line between copying and taking inspiration from a third-party product. This 'copycatting' is a legal grey area and certainly results in interesting court actions – if it gets to that point. Whilst 'Caterpillargate' concerns trademark infringement, this action focuses on design infringement and the similarities between the two retailers 'light up' gin products, namely the shape of the bottle, integrated light feature at the bottom of the bottle, gold leaf flakes within the product and the winter forest graphic.
Trademarks and patents tend to be the more well-known and favoured IP right but design rights provide for a real and effective IP right so should not be overlooked. Another point to note is Aldi's clever use of social media and marketing to its advantage with the hashtag 'Free Cuthbert' trending on Twitter in April, including Cuthbert being arrested in the Christmas advert and renaming Marks & Spencer to 'Marks & Snitches'. It will be interesting to see what Aldi create this time and whether M&S are now more prepared for an equally clever response. Although success in a court action and / or settlement removing the similarities between products is the end goal, retailers must also be careful not to lose public favor."
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The Nixie speedo is designed to fit into a stock P200 housing and use the stock speedo cable. The nixies are IN-12's and the driver board contains an atmega8u2, a Taylor Edge high voltage driver, and a bunch of BSS131 FETs. A hall effect pickup for calculating speed.
Principle of operation: The speedo cable is driven from a gear in the front wheel hub. The rotating speedo cable spins a magnet inside the speedo housing. To calculate speed, a latching hall effect sensor is used to detect the rotating magnet. The rate at which the magnet is rotating is proportional to the rate of the front wheels rotation. Based on the diameter of the front wheel, the speed can be calculated. The nixies are all low side driven via the BSS131 FETs.
Updates to follow: Formula for calculating speed, source code, and some additional images of the speedo housing.