If Coyote comes to you… you can expect lessons. They may not be what you want and you may or may not like it. Coyote often shows up when we are taking ourselves too seriously. Laughter is powerful in the teachings of Coyote. He can best be seen as the Wise fool. Coyote Medicine Empowerment was channeled by Lisa "Ladywolf" Center.
Coyote is represented in the Tarot by the Fool. This is the card of new beginnings. It urges you to take the adventurous path. Follow your instincts. Ask yourself in what situation in your life would you benefit greatly in taking a leap of faith? It could be quitting your job and starting your own business, it could be asking for a raise or getting married…..the fool card encourages you to jump.
Coyote prints are very similar to dogs and wolves but there is a difference. The hind leg prints are smaller than the front paws. They also tend to travel in a straight line. Wolves and dogs are prone to wandering off in other directions. Coyote remains focused on destination in mind.
Coyotes are also very social. They travel in packs and communicate their feelings, warnings and general announcements with others. Its haunting cry touches something primal and deep within the human heart that opens to Coyote medicine…..Coyote calls…..what lesson does it hold for you?


I know this lady quite well, so I also know she's not making any money to speak of.
She stumbles over a client here and there, yet always undercharges them.
Then she spends what she gets, way before the end of the month.
All that feelgood stuff is a great foundation.
But imagine how great she'd feel if she actually had a scalable, sustainable client attraction process.
PS – If you want to see what my client attraction process looks like – it's right here.


text:
Q: Java client for XtreemFS I am building a Java web application which will require storing and retrieving large files. I would like to be able to scale the application for the future so I was planning on using XtreemFS http://www.xtreemfs.org/ as a distributed file system. It provides the redundancy and speed I need.
I'm hoping to find a direct client for it for Java but having a little bit of trouble finding one. There are some advanced features of XtreemFS which allow controlling the level of redundancy and by making files read-only can reduce locking overhead.
If I cannot find a Java client, then I will just mount the XtreemFS data store on my servers, treat it just like I would local storage, and use basic java.io.* classes to read and write files from it as if it were just files on the disk.
Any suggestions on the best practices for using XtreemFS?

redpajama_set_name: RedPajamaStackExchange


text:
using NQuery.Authoring.Outlining;
using NQuery.Authoring.Outlining.Outliners;

namespace NQuery.Authoring.Tests.Outlining.Outliners
{
    public class SelectQueryOutlinerTests : OutlinerTests
    {
        protected override IOutliner CreateOutliner()
        {
            return new SelectQueryOutliner();
        }

        [Fact]
        public void SelectQueryOutliner_FindsSelectQuery()
        {
            var query = @"
                {SELECT  *
                FROM    Employees e
                WHERE   e.City = 'London'}
            ";

            AssertIsMatch(query, "SELECT");
        }

        [Fact]
        public void SelectQueryOutliner_DoesNotTriggerForSingleLineQueries()
        {
            var query = @"
                SELECT  1, 2, 3
            ";

            AssertIsNoMatch(query);
        }

        [Fact]
        public void SelectQueryOutliner_DoesNotTriggerForOrderedQueries()
        {
            var query = @"
                SELECT  *
                FROM    Employees e
                WHERE   e.City = 'London'
                ORDER   BY 1
            ";

            AssertIsNoMatch(query);
        }
    }
}

redpajama_set_name: RedPajamaGithub


text:
stroke & neurological physiotherapy
Stroke & Neurological Conditions
Recent Strokes (within the last 6-months)
Long-term Strokes
Neuropathies – Polyneuritis and Other Polyneuropathies
Balance and Dizziness Problems
Adults with Cerebral Palsy
Other Neurological Conditions
We are a team of specialist neurological physiotherapists and trained advanced Bobath therapists. We are all members of the Chartered Society of Physiotherapists (CSP) and registered with the Health Professional Council (HPC).
As qualified neurological physiotherapists we are all committed to on-going training to keep abreast of new techniques and the latest developments, supporting and learning from one another.
Helen Lindfield – Clinical Director and Owner of heads up!
Helen qualified as a physiotherapist in 1989 and quickly focused on neurological rehabilitation completing a MSc in Rehabilitation and Research in 1999. She went on to develop her clinical skills by training as a Bobath Tutor. She teaches nationally and internationally and at a number of Higher Education institutions.
She has worked in neurological rehabilitation for 20 years developing advanced clinical reasoning skills and is an expert clinician with skills in assessment, the use of spasticity management, splinting, orthotics and hands on approaches.
She has a clear understanding of the range of rehabilitation skills available to clinicians and more importantly recognition of how these approaches can be used to meet the needs of the individual.
Helen continues to work as a Consultant in a number of NHS hospitals. She is aware of the importance of evidence-based practice and supports the team at heads up! to develop skills in practice in the context of best practice guidelines and clinical expertise.
Emma Walters MCSP SRP
Emma qualified from the University of Brighton in 2000 with Bsc(Hons) Physiotherapy. She then worked at Maidstone Hospital where she completed her junior rotations and started to specialise in neurology.
In 2003 she moved to Wycombe Hospital where she worked as a Highly Specialised Neurological Physiotherapist covering neurological outpatients, inpatients and rehabilitation. She completed her Basic Bobath Training in 2005 and helped to set up the new stroke unit at Wycombe Hospital.
Emma joined heads up! In 2006 as a Clinical Specialist and has continued to treat patients with all types of neurological conditions both in the outpatient clinic and the community. She has attended numerous courses and training days including four Advanced Bobath Courses and continues to enjoy developing her learning and skills.
She is HCPC registered and a member of the CSP and ACPIN. Emma says that the best things about working at heads up! are the friendly team, the opportunity to learn and develop and the quality time spent treating patients.
Zoe Moyse MCSP SRP
Zoe worked for 4 years as a highly specialised neuro physiotherapist at the Wolfson Neuro Rehabilitation Centre, working intensively with people with a variety of neurological conditions, as part of a multidisciplinary team. Whilst at the Wolfson, Zoe ran a lower limb neuro orthotic clinic with an orthotist and has retained an interest in this field.
Zoe joined heads up! in 2012. She has attended numerous courses, training days and an Advanced Bobath Course. Zoe feels that working at heads up! has enabled her to spend focussed, quality time with her patients, working closely with them to achieve their goals with the aim of improving their quality of life. The team at heads up is friendly and very supportive, with a strong emphasis on continuing development. Working at heads up! has provided the opportunity to work in both the clinic and home environment, allowing for a much more focussed, realistic and empathetic approach.
She is a member of the CSP, ACPIN and is HPCP registered.
Claire Jenkins MCSP SRP
Claire qualified as a physiotherapist in 2006 from Cardiff University with a BSc (Hons), subsequently working at St George's Hospital from 2007 – 2013, with a period in between at Stanmore in 2009 – 2010. Claire has been treating complex neurological patients with a range of stroke and neurological conditions during her time at The Wolfson Neurological unit at St George's Hospital, London.
Claire is a member of the Chartered Society of Physiotherapists, is HCPC registered, and joined the heads up! team in October 2013.
Georgie Drinkall MCSP
Georgie qualified from the University of East Anglia in 2004 with BSc (Hons) Physiotherapy. She then worked for the NHS Lothian completing her junior rotations followed by completion of her senior rotations at Hillingdon Hospital.
In 2007 Georgie moved worked at Stoke Mandeville Hospital where she worked as a senior specialist in spinal injuries. In 2009 Georgie moved into working in the community providing physiotherapy for neurological patients in their home for Hertfordshire NHS Trust, Caterham Dene Hospital and for the last 2 years has been working for the Sussex Community NHS Foundation Trust.
Georgie Joined heads up! in January 2017 as a clinical specialist treating patients with all types of neurological conditions. She is HCPC registered and a member of the CSP and ACPIN.
Hilary Myall MCSP
Hilary studied for her BSc (Hons) degree in physiotherapy in St. George's Hospital Medical School, London, qualifying in 2003. Hilary has specialised in neurological physiotherapy for 12 years, working in acute hospital settings, the Wolfson Neurorehabilitation Centre and in the community.
Hilary has specialised in vestibular rehabilitation for the last 7 years and worked with the Audiovestibular physicians in St. George's Hospital to establish a specialist vestibular rehabilitation service. She has been a committee member of the specialist vestibular physiotherapy group and regularly provides training on vestibular rehabilitation to other clinicians. Hilary especially enjoys working with complex vestibular patients including those with migraine, Meniere's disease and dizziness problems following head injuries.
Hilary has also worked closely with specialist consultants providing complex care to patients with facial palsy, Hilary works hard with these patients to achieve the best possible outcomes for their individual circumstances.
Hilary is Bobath trained and uses a variety of treatment approaches to meet the varying needs of her clients and as the team lead for the neuro outpatient service at St. George's Hospital she has worked with clients to achieve their individual goals be that to return to sports or to participate more in their day to day activities.. Hilary is also trained in the use of acupuncture and uses this as an adjunct to her treatment of both neuro and vestibular patients. Hilary has completed a post graduate certificate in rehabilitation at St. George's, University of London.
Hilary is a member of various physiotherapy clinical interest groups and regularly attends lectures and courses for both neuro and vestibular physiotherapy to ensure her skills are up to date and she is able to provide her clients with up to date evidence based treatment.
Hilary is HCPC registered and is a member of the CSP, ACPIVR, ACPIN and Facial Therapy Specialist-UK.
Steph Anderson MCSP
After graduating from Birmingham in 1989, Steph joined the physiotherapy department at East Surrey Hospital, where she completed all her junior rotations. She then became a Senior Physiotherapist specialising in orthopaedics and musculo-skeletal conditions. More recently she has worked in the community treating patients in their own home, particularly working on rehabilitation following hospital admissions and prevention of falls.
She has a special interest in Pilates and has completed the Matwork series and small equipment Pilates training through the Australian Physiotherapy and Pilates Institute (APPI). She has 10 years' experience teaching Pilates classes mostly for rehabilitation and 1:1 Pilates tuition. Pilates really lends itself to those with a neurological condition. It promotes ease, quality and precision of movement. The exercises start from very small and minimal to large and more complex, the benefits of which are muscle strengthening, improved flexibility and improved balance.
Steph has also recently completed the PD Warrior course (level 1&2) This is a very different form of exercise from Pilates with dynamic, large and powerful movements aimed at improving the symptoms of Parkinson's Disease.
Steph is a member of the Chartered Society of Physiotherapy and is HCPC registered
Louisa Sweetman MCSP
Louisa qualified as a physiotherapist from the University of Birmingham in 2005. Louisa has been working as a specialist neurological physiotherapist for the last 10 years at St George's University Hospital NHS Trust, working in both acute and rehabilitation settings. For the last 8 years, Louisa has been a team lead for the Wolfson Acute Neurological Rehabilitation Unit. Louisa has a keen interest in gait rehabilitation and the use of orthotics in neurological patients, and jointly ran a MDT Orthotics Clinic with an Orthotist at Queen Mary's Hospital, working closely with the Gait Laboratory and Spasticity Clinic to ensure a holistic and patient centred treatment approach. Louisa is Bobath trained, and enjoys using a range of treatment approaches. Louisa has provided training to other clinicians on gait biomechanics and the use of splinting and casting in the upper and lower limb. Louisa has also given lectures to physiotherapy students at St George's University London.
Louisa enjoys working closely and collaboratively with her patients in order to encourage and empower them to achieve their goals. Louisa is enthusiastic and is keen in making the physiotherapy sessions both enjoyable and physically rewarding.
Louisa is HCPC registered, and a member of the CSP and ACPIN.
Sally Watt
Sally is our Practice Manager and will probably be the voice on the other end of the phone when you call. She joined the team in 2003 after 11 years at a local GP's practice. During her time there, she completed a Diploma in Practice Management at Carshalton College, gaining a distinction.
Come and work with us at Headsup! Neuro-Rehab. Call Sally on 01306 888171 or send us an email
Heads up! – Conditions treated
If you have any questions, or would like to arrange an appointment or speak to one of our physiotherapists, please call Sally Watt, Practice Manager on 01306 888171 or email us.
We look forward to welcoming you to heads up!
If you would like further information about organisations that offer help and advice for sufferers with neurological conditions, please see our useful links page.
Heads up! Stroke & Neurological Physiotherapy
The Clockhouse
Partridge Lane
RH5 5EE
Heads up! Recent blogs
Recognising vestibular migraine and tips on how to manage it.
What is Dystonia and tips on how to manage it
PD Warrior
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Helping you during the Lockdown: Video appointments
Specialist neuro-physiotherapy and vestibular rehabilitation via your screen to your home.
We are still open during Lockdown 2
We would like to reassure you that Heads Up Neuro Rehab will be continuing to deliver specialist neurological physiotherapy during the lockdown period announced by the Government this weekend.
The government's new guidance has not required Physiotherapy clinics to close and allows people to travel for medical appointments.
As many of you will have experienced, we have created a covid safe environment in our clinics and during home visits.
We are following our professional bodies and Public Health England's recommendations ensuring we are minimising the risk to our patient's and team during this pandemic situation.
We are monitoring guidance and will inform you if any changes are required to maintain our teams and our patient's safety.
Please do not hesitate to contact the office or talk to your therapist if you have any queries.

redpajama_set_name: RedPajamaCommonCrawl


text:
Euglypta immaculata är en skalbaggsart som beskrevs av Miksic 1982. Euglypta immaculata ingår i släktet Euglypta och familjen Cetoniidae. Inga underarter finns listade i Catalogue of Life.

Källor

Skalbaggar
immaculata

redpajama_set_name: RedPajamaWikipedia


It has been in the mid 50's this week where I live and so that means T-shirt weather! I am not the biggest fan of winter so I will take as many of these days as I can get.
This week for my outfit under $20 look, I went with something simple and easy. As a mom of an active little girl, I live for easy outfits that still look put together. A basic tee and some skinny's are a perfect way to pull that off with minimal effort. Also this t-shirt is one of my favorites and it is on sale right now at Old Navy for only $1.97.


text:
\section{Introduction}
How much information can a prescribed electromagnetic waveform transport in time and space? This basic question is of mathematical and physical interest, and has numerous engineering applications, including in communications, sensing, imaging, radar detection and classification systems. Information theory of wireless communication provides a partial answer, but assumes a stochastic model of the fading channel,  taking for granted the physical nature of the quantities which figure in its formalism. In this paper, we take the point of view that communication of information is the transmission of physical states from transmitters to receivers and, as such, it is subject to the laws of nature. We rigorously compute the physical limits for the transport of information by electromagnetic waves in terms of degrees of freedom, and discuss their significance  in an engineering context.

Our results build upon Landau's theorem~\cite{szego}, concerning the asymptotic behavior of the eigenvalues of a certain integral equation arising from the problem of simultaneous concentration of a function and its Fourier transform. This theorem asserts that, in a well defined sense, the eigenvalues undergo a sharp transition from values close to one to values close to zero, and the scale of this transition characterizes the asymptotic dimension of the space of bandlimited functions.
The problem was originally considered jointly by Landau, Pollak and Slepian in a series of papers~\cite{Slepian1,Slepian2,Slepian3,Slepian4,Slepian5}, of which \cite{SlepianS1} and \cite{SlepianS2} provide excellent tutorial reviews. The precise width of the transition  in the single-dimensional case has been first conjectured  by Slepian~\cite{Slepian}, and finally computed rigorously  by Landau and Widom~\cite{widom}. The theorem we refer here gives  only the first order characterization of the transition, but it describes concentration over arbitrary sets and in arbitrary dimensions. We provide  extensions of the original statement, and apply them  in certain geometric configurations arising in the context of information transport through electromagnetic propagation.

Consider a wireless network in which a set of users located in one region  of the network wishes to communicate with users located in an another region,  see Figure~\ref{fig:cutsetsp}. The number of channels available for communication is limited by  the dimensionality of the signal's space on the cut-set boundary through which electromagnetic propagation occurs.
\begin{figure}
\begin{center}
{
\scalebox{.7}{\includegraphics{cutset.eps}}}
\end{center}
\caption{Parallel channels consume spatial resource along the cut.}
\label{fig:cutsetsp}
\end{figure}
This corresponds to the minimum number of  basis functions required to represent the signal  on the cut-set boundary, and  is independent of the communication scheme employed. It  provides a bound on the amount of spatial  and frequency multiplexing achievable using arbitrary technologies and in arbitrary scattering environments. It essentially corresponds to the \emph{number of degrees of freedom} of the space-time field used for communication and is determined by the phase transition of the eigenvalues referred above.  Similarly, the number of independent features that can be extracted from a scattering system using a  probe signal for remote sensing, imaging, detection and classification systems is  limited by the  number of degrees of freedom of the field and characterized by the same phase transition.

We compute the  number of degrees of freedom of multiple scattered electromagnetic waves  in terms of Kolmogorov's $n$-width, and  provide a physical interpretation in terms of cut-set information flow. Our results extend the single frequency treatments of ~\cite{bucci1,bucci2,Miller1,Miller2,Poon,Kennedy,migliore1,migliore2} to signals of non-zero frequency bandwidth.
In a broader framework, they rigorously address the question of how much information does an electromagnetic waveform carry in time and space, first posed in  the early works of  Toraldo di Francia~\cite{Toraldo1, Toraldo2} and Gabor~\cite{Gabor1,Gabor2}.

The number of degrees of freedom of the field is also related to the information capacity of multi-user communication systems. Its application  to bound the Shannon capacity scaling of wireless networks is described in~\cite{migliore1} and \cite{migliore2}, and can be extended to signals with a non-zero frequency band using the results given here.

The  rest of the paper is organized as follows. The next section provides rigorous statements of the mathematical results.
Applications are discussed in Section~\ref{sec:application}.
Section~\ref{sec:conc} draws conclusions and mentions some possible future work. The proof of the main theorem
is given in Appendix~\ref{sec:proof}.
\section{Statement of the results}
We begin by presenting our results in two dimensions, as this  form better suits the application discussed in the next section. A more general statement appears at the end of this section.
Let $P$ and $Q$ be measurable sets in $\mathbb{R}^2$ with boundaries of measure zero.
For any  point $ \textbf{p} \in \mathbb{R}^2$, and
positive scalar $\beta>0$,
we indicate by $\beta (P+ \textbf{p})$ the set of points of the form $\beta({\bf{x}}+ \textbf{p})$ with ${\bf{x}}\in P$. Clearly, we have
\begin{equation}
m(\beta P)= \beta^2 m(P),
\end{equation}
where $m(\cdot)$ indicates Lebesgue measure.
Similarly, for ${\bf{x}}=(x_1,x_2)$, we have
\begin{equation}
m\{(\beta x_1,x_2):{\bf{x}}\in P\} =\beta \,m(P).
\end{equation}
For any two points ${\bf{x}}=(x_1, x_2)$, ${\bf{u}}=(u_1, u_2)$,  we let ${\bf{x}} \cdot {\bf{u}} = x_1u_1+  x_2 u_2$. For $f \in L^2(\mathbb{R}^2)$,   the Fourier transform of $f$ is
\begin{equation}
\mathcal{F} f =  \int_{\mathbb{R}^2} f({\bf{x}}) \exp(- i {\bf{x}} \cdot {\bf{u}}) d {\bf{x}}.
\end{equation}

Consider now two subspaces of $L^2(\mathbb{R}^2)$ consisting of the functions supported in $P$ and of those  whose Fourier transform is supported in $Q$, namely
\begin{align}
\mathscr{T}_P &= \{f \in L^2 : f({\bf{x}}) = 0, \;  {\bf{x}} \not \in P\}, \\
\mathscr{B}_Q &= \{f \in L^2 : \mathcal{F} f ({\bf{u}})=0, \; {\bf{u}} \not \in Q\}.
\end{align}

The  orthogonal projections  onto these subspaces are defined using the indicator function
\begin{equation}
\mathds{1}_Q({\bf{x}}) =  \left\{ \begin{array}{ll}
1 & \mbox{if ${\bf{x}} \in Q$},\\
0 & \mbox{otherwise},\end{array} \right.
\end{equation}
in the following way
\begin{align}
\mathcal{T}_P f &= \mathds{1}_P({\bf{x}}) f({\bf{x}}), \label{eq:rect} \\
\mathcal{B}_Q f &= \mathcal{F}^{-1} \mathds{1}_Q \mathcal{F} f =  \int_{\mathbb{R}^2} h({\bf{x}}-{\bf{y}}) f({\bf{y}}) d {\bf{y}}, \label{eq:sinc}
\end{align}
where
\begin{equation}
\mathcal{F} h = \mathds{1}_Q.
\end{equation}
We are interested in the behavior of the eigenvalues in the integral equation
\begin{equation}
\mathcal{T}_P \mathcal{B}_Q \mathcal{T}_P \varphi({\bf{x}}) = \lambda \varphi({\bf{x}}),
\label{fred}
\end{equation}
where the operator  $\mathcal{T}_P \mathcal{B}_Q \mathcal{T}_P$ is positive, self-adjoint, compact, and bounded by one. The eigenvalues are a countable set that characterizes the \emph{asymptotic dimension} of the subspace $\mathscr{B}_Q$. Namely, the number of eigenvalues above level $\epsilon$ corresponds to the dimension of the minimal subspace approximating the elements of $\mathscr{B}_Q$ within $\epsilon$ accuracy over the set $P$. A rigorous definition of asymptotic dimension is given in Section~\ref{sec:application}. To determine this number, Landau~\cite{szego}
considered the case where $Q$ is a fixed set, while $P$ varies over the family $\beta P'$, with $P'$ fixed, and determined  the number of eigenvalues significantly greater than zero as $\beta \rightarrow \infty$. It turns out that the eigenvalues arranged in non-increasing order undergo a transition from values close to one to values close to zero in an interval of indexes around $\beta^2$. The transition  is sharp, of width $o(\beta^2)$, so that the eigenvalues plotted as a function of their indexes appear as a step function  when viewed at the scale of $\beta^2$, see Figure~\ref{fig:eigtran}.
\begin{figure}
\begin{center}
{
\scalebox{.8}{\includegraphics{Sharpt2.eps}}}
\end{center}
\caption{Phase transition of the eigenvalues.}
\label{fig:eigtran}
\end{figure}
The asymptotic dimension of the space $\mathscr{B}_Q$ is given by the  transition point  of this step function, that  is of the order of $\beta^2$, when the support set $P$ is appropriately scaled by blowing-up all of its coordinates. Due to symmetry,  the asymptotic dimension of the space $\mathscr{T}_P$ can similarly be obtained by considering the operator $\mathcal{B}_Q \mathcal{T}_P \mathcal{B}_Q$ and scaling $Q=\beta Q'$ while keeping $P$ fixed.
The precise result is stated as follows:
\newtheorem{thm}{Theorem}
\begin{thm}
\label{th:landau}
(Landau). For any  $0<\epsilon<1$,  let $N_\beta(\epsilon)$ be the number of eigenvalues of $\mathcal{T}_{\beta P'} \mathcal{B}_Q \mathcal{T}_{\beta P'}$ not smaller than $\epsilon$, then we have
\begin{equation}
\lim_{\beta \rightarrow \infty} \frac{N_\beta(\epsilon)}{\beta^2} = (2 \pi)^{-2} m(P') m(Q).
\end{equation}
\end{thm}

In Landau's case, spectral concentration is achieved by scaling all coordinates  of one of the two  support sets. We prove the analogous result by scaling only one coordinate of both support sets.  While in Landau's case the scaling of the coordinates is uniform, in our case coordinates are scaled at independent rates.

Let $P$ and $Q$ be two fixed sets. We consider  the following families
\begin{equation}
P_\tau = \{ (\tau x_1, x_2): (x_1,x_2) \in P\}
\end{equation}
\begin{equation}
Q_\rho = \{ (x_1, \rho x_2): (x_1,x_2) \in Q\}.
\end{equation}
\begin{thm}
For any  $0<\epsilon<1$,  let $N_{\tau,\rho}(\epsilon)$ be the number of eigenvalues of $\mathcal{T}_{P_{\tau}} \mathcal{B}_{Q_{\rho}} \mathcal{T}_{P_{\tau}}$ not smaller than $\epsilon$, then we have
\begin{equation}
N_{\tau,\rho}(\epsilon)= (2 \pi)^{-2} m(P) m(Q) \tau \rho +o(\tau \rho),
\label{eq:uno1}
\end{equation}
as $\tau, \rho \rightarrow \infty$.
\label{th1}
\end{thm}
The proof is based on decomposing the operator using orthonormal functions, and then computing an integral that  differs from  the one of Landau, due to the different scaling of the space.
The result also extends to higher dimensions, where any combination of coordinates' scaling in the original or transformed domain can be performed. Our theorem can be stated for any invertible linear mapping of the support sets, subject to a limiting condition.
Let $P$ and $Q$ be measurable sets in $\mathbb{R}^N$ with boundaries of measure zero. For any real  matrix $\mtx{A}$ of size $N\times N$, we indicate by $\mtx{A}P$ the set of points of the form $\mtx{A} \mtx{x}$, where $\mtx{x}$ is the column vector composed of the elements of ${\bf{x}}\in P$. We also indicate  with $|\mtx{A}|$  the determinant of $\mtx{A}$, with $\mtx{A^T}$ the transpose of $\mtx{A}$, and with with $U$   the unit ball in $L^2(\mathbb{R}^N).$ We let $\mtx{A}=\mtx{A}(\tau)$ and $\mtx{B}=\mtx{B}(\rho)$ for real parameters $\tau$ and $\rho$. The case in which either matrix is constant, or depends on multiple parameters is completely analogous.
\begin{thm}
For any  $0<\epsilon<1$,  let $N_{\mtx{A},\mtx{B}}(\epsilon)$ be the number of eigenvalues of $\mathcal{T}_{\mtx{A}P} \mathcal{B}_{\mtx{B}Q} \mathcal{T}_{\mtx{A}P}$ not smaller than $\epsilon$.
If
\begin{equation}
\lim_{(\tau, \rho) \rightarrow (\tau_0,\rho_0)} \mtx{B^T}\mtx{A} U = \mathbb{R}^N,
\end{equation}
then
we have
\begin{equation}
\lim_{(\tau, \rho) \rightarrow (\tau_0,\rho_0)} \frac{N_{\mtx{A},\mtx{B}}(\epsilon)}{|\mtx{A}|\,|\mtx{B}|} = (2 \pi)^{-N} m(P) m(Q).
\end{equation}
\label{th:tre}
\end{thm}

\newtheorem{rmk}{Remark}
Landau's theorem is a special case where $\mtx{A}$ is a scalar matrix and $\mtx{B}$ is the identity. Its  two-dimensional version is stated in Theorem~\ref{th:landau}. Theorem
\ref{th1} corresponds to the special case
\begin{equation}
\mtx{A}= \left( \begin{array}{cc}
\tau & 0 \\
0 & 1
\end{array} \right) \; \;
\mtx{B}= \left( \begin{array}{cc}
1 & 0 \\
0 & \rho
\end{array} \right).
\end{equation}

\section{Application of the results}
\label{sec:application}
Landau~\cite{szego} does not mention the extensions  to his theorem described above, but no doubt that if asked he could have proved them effortlessly. Nonetheless, these results do not seem to appear anywhere. We believe that our main contribution is to point out their significance  in the context of communication and sensing using electromagnetic waves.

\subsection{The number of degrees of freedom}
When communication occurs through propagation of electromagnetic waves, the effective dimensionality, or \emph{number of degrees of freedom}, of the space-time field is a key information-theoretic quantity related to the capacity of any spatially distributed communication system~\cite{migliore1,migliore2}. This quantity can be computed by evaluating the number of significant eigenvalues in Theorems~\ref{th:landau}, \ref{th1}, or \ref{th:tre}.

Consider the space $\mathscr{S}$ of real space-time waveforms $f(s,t) \in L^2(\mathbb{R}^2)$ and equipped with the norm
\begin{equation}
||f||^2 = \left( \iint_{P} f^2(s,t)ds dt \right)^{1/2}.
\end{equation}
A subspace $\mathscr{B}_Q \subset \mathscr{S}$ is given by the space of functions $f(s,t) \in L^2(\mathbb{R}^2)$ of  spectral support $Q$. We assume their energy is normalized so that
\begin{equation}
\iint_{\mathbb{R}^2} f^2(s,t) ds dt \leq1.
\label{enbound}
\end{equation}

Given a level of accuracy $\epsilon>0$,  define the number of
degrees of freedom at level $\epsilon$ of the space $\mathscr{B}_Q$ in $\mathscr{S}$
\begin{equation}
\mathcal{N}_{\epsilon}(\mathscr{B}_Q) = \min\{n : d_n(\mathscr{B}_Q, \mathscr{S}) \leq \epsilon\},
\end{equation}
where $d_n(\mathscr{B}_Q, \mathscr{S})$ is the Kolmogorov $n$-width~\cite{Pinkus} of the space $\mathscr{B}_Q$ in $\mathscr{S}$.
Letting  $\mathscr{S}_n$ be an $n$-dimensional subspace of $\mathscr{S}$, this is defined as
\begin{equation}
d_n(\mathscr{B}_Q, \mathscr{S}) = \inf_{\mathscr{S}_n \subset \mathscr{S}} D_{\mathscr{S}_n}(\mathscr{B}_Q),
\end{equation}
where the deviation
\begin{equation}
D_{\mathscr{S}_n}(\mathscr{B}_Q) =\sup_{f \in \mathscr{B}_Q} \inf_{g \in \mathscr{S}_n}||f-g||.
\end{equation}
In words, the deviation represents how well $\mathscr{B}_Q$ may be uniformly approximated by the elements of an $n$-dimensional subspace of $\mathscr{S}$, while the $n$-width is the smallest of such deviations over all $n$-dimensional subspaces of $\mathscr{S}$.
The number of degrees of freedom
$N_\epsilon(\mathscr{B}_Q)$ represents the dimension of the minimal subspace representing the elements of $\mathscr{B}_Q$ within $\epsilon$ accuracy over the set $P$. A basic result in approximation theory (see e.g.\ \cite[Ch. 2,  Prop. 2.8]{Pinkus}) states that
\begin{equation}
d_n(\mathscr{B}_Q, \mathscr{S}) = \sqrt{\lambda_n},
\label{basic}
\end{equation}
where $\lambda_n$ is the $n$-th eigenvalue (arranged in non-increasing order) of  the Fredholm integral equation of the second kind in (\ref{fred}).
It now follows from~(\ref{basic}) that Theorem~\ref{th1}  allows to compute the number of degrees of freedom by scaling only one of the two coordinates of the space-time field, together with the  transformed version of the other.

The number of degrees of freedom defined in this way appears to be a principal feature of the mathematical model of the real world of transmitted signals, that is practically insensitive to small changes of a secondary feature of the model, such as the accuracy $\epsilon$ of the measurement apparatus with which the signals are detected. This is evident by rewriting (\ref{eq:uno1})  as
\begin{equation}
N_{\tau,\rho}(\epsilon) = (2 \pi)^{-2} m(P) m(Q) \, \tau \rho + o(\tau \rho) \;\;\; \mbox{as } \tau,\rho \rightarrow \infty,
\end{equation}
where the $\epsilon$-dependence  appears  hidden as a pre-constant of the second order term  $ o(\tau \rho)$  in the phase transition of the eigenvalues.

\subsection{Cut-set of two-dimensional circular domains}
Theorems~\ref{th:landau} and \ref{th1} can be applied to  evaluate the number of degrees of freedom of waveforms of a given frequency band over spatial cut-sets separating transmitters and receivers in a wireless communication setting, or separating scattering objects from sensing devices in imaging and sensing systems.

Consider the case  of a two-dimensional domain of  cylindrical symmetry,
\begin{figure}
\begin{center}
{
\scalebox{.95}{\includegraphics{radiator.eps}}}
\end{center}
\caption{Cut-set boundary of two-dimensional circular  domain.}
\label{fig:radiator}
\end{figure}
in which an electromagnetic field is radiated by a configuration of currents located inside a circular domain of radius $r$ of an arbitrary scattering environment, oriented perpendicular to the domain, and constant along the direction of flow. This can model, for example, an arbitrary scattering environment where a spatial distribution of wireless transmitters is placed inside the circular domain,  and
communicate to receivers placed outside the domain. The same model applies to a remote sensing system where  objects  inside the domain are illuminated by an external waveform, and the scattered field is recovered by sensors placed outside the domain. The radiated field away from the scattering system and measured at the receivers is completely determined by the field on the cut-set boundary   through which it propagates, see Figure~\ref{fig:radiator}.  On this boundary, we can refer to a  scalar field  $f(\phi,t)$ that is a function  of only two scalar variables: one angular and one temporal. The corresponding four field's representations, linked by Fourier transforms, are depicted in Figure~\ref{fig:repr1}, where the angular frequency $\omega$ indicates the transformed coordinate of the time variable $t$, the wavenumber $w$ indicates the transformed coordinate of the angular variable $\phi$, and $\mathcal{F}f(\phi,t) = \widehat{F}(w,\omega)$.
\begin{figure}
\begin{center}
\begin{picture}(140,100)
\put(0,0){$\widehat{f}(w,t)$}
\put(0,80){$f( \phi,t)$}
\put(100,80){$F( \phi,\omega)$}
\put(100,0){$\widehat{F}( w,\omega)$}
\put(15,40){\vector(0,1){30}}
\put(15,40){\vector(0,-1){30}}
\put(68,0){\vector(1,0){20}}
\put(68,0){\vector(-1,0){30}}
\put(68,80){\vector(1,0){20}}
\put(68,80){\vector(-1,0){30}}
\put(115,40){\vector(0,1){30}}
\put(115,40){\vector(0,-1){30}}
\end{picture}
\end{center}
\caption{Field's representations linked by Fourier transforms.}
\label{fig:repr1}
\end{figure}

For convenience, we let $r$ be normalized by the speed of light, so that both radius-frequency and time-frequency products are dimensionless quantities.
We wish to determine the  number of degrees of freedom of the space-time field $f(\phi,t)$ on the cut-set boundary,  that is radiated for $t\in[-T/2,T/2]$ and occupies a bandwidth $\omega \in [-\Omega,\Omega]$; it is observed over the interval $\phi \in [-\pi,\pi]$ and occupies a  wavenumber bandwidth $w\in[-W,W]$. Of course, these statements make little mathematical sense since a field satisfying above constraints would have bounded support in both the natural and transformed domain, so it would be zero everywhere. To make our considerations precise, we need to take appropriate scaling limits.

To determine the correct scaling laws for the support sets of the field, we introduce some geometric constraints. On the one hand, we limit the observation domain  to $\phi \in [-\pi,\pi]$, so that the spatially periodic field on the cut-set boundary is observed over a single period. On the other hand,
it is well known~\cite{bucci1}  that in this case the wavenumber bandwidth is related to the frequency of transmission in such a way that for any possible configuration of sources and scatterers inside the circular radiating domain, we have at most
\begin{equation}
 w =  \omega r +o(\omega r) \;\;\; \mbox{as } \omega r \rightarrow \infty.
\label{circular}
\end{equation}
It follows that we need to scale the support sets of the field  subject to the constraints  depicted in Figure~\ref{fig:PQ}.
\begin{figure}
\begin{center}
{
\scalebox{.7}{\includegraphics{PQ.eps}}}
\end{center}
\caption{Support sets in the natural and transformed domains.}
\label{fig:PQ}
\end{figure}
We can blow-up the spectral support $Q$ while keeping $P$ fixed by letting $\Omega \rightarrow \infty$. In this case, by Theorem~\ref{th:landau}   the number of degrees of freedom  over a fixed transmission time  and cut-set  interval of width $2 \pi$, in the wide band frequency regime is
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &= \frac{2 \Omega^2 r T 2 \pi}{(2\pi)^2} + o(\Omega^2) \nonumber \\
&= \frac{\Omega T}{\pi}  \frac{2 \pi r \Omega}{2\pi} +o(\Omega^2)  \;\;\; \mbox{as } \Omega \rightarrow \infty.
\label{eq:uno}
\end{align}
On the other hand, our geometric configuration does not allow to blow-up the support $P$ while keeping $Q$ fixed because the cut-set domain is limited to an angle $2\pi$. Landau's theorem in its original form is of no help here, but we can apply Theorem~\ref{th1}  to obtain the number of degrees of freedom over a fixed frequency band, by scaling the time coordinate of $P$ and  the coordinate of $Q$ corresponding to the size of the radiating system, and we have
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &= \frac{\Omega T}{\pi}  \frac{2 \pi r \Omega}{2\pi} + o(rT)  \;\;\; \mbox{as } T,r \rightarrow \infty .
\label{eq:due}
\end{align}

Equations (\ref{eq:uno}) and (\ref{eq:due}) show that the number of degrees of freedom is given by the product of two factors, each viewed in an appropriate asymptotic regime: one accounting for the number of degrees of freedom in the time-frequency domain, $\Omega T/\pi$, and  another accounting for the number of degrees of freedom in the space-wavenumber domain, $2 \pi r \Omega  /(2 \pi)$. The latter factor physically corresponds to the perimeter of the disc of radius $r$ normalized by an interval of wavelengths $2 \pi/\Omega$,  and can be interpreted as the spatial cut-set through which the information must flow.
The idea is that for any finite size system, the wavenumber bandwidth is a limited resource. Each parallel channel occupies a certain amount of spatial resource on the cut, proportional to the wavelength of transmission, and these channels must be sufficiently spaced along the cut for the corresponding waveforms to provide independent streams of information. The total number of channels  is then given by the total spatial resource, given by the cut-length $2 \pi r$, divided by the total occupation cost, given by the wavelength-interval $2 \pi/\Omega$.

\subsection{Comparison with the single-dimensional case}
\label{sec:comparison}
The number of time-frequency degrees of freedom of any  signal $f(t) \in L^2(\mathbb{R})$  bandlimited to $[-\Omega,\Omega]$, or  timelimited to $[-T/2,T/2]$,   is given by the time-bandwidth product
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_{\Omega}) = \frac{\Omega T}{\pi} +o(\Omega T)\;\;\; \mbox{as } \Omega T \rightarrow \infty.
\label{comb1}
\end{equation}
In this case, spectral concentration occurs by scaling either the transmission time $T$, or the frequency band $\Omega$. The work in~\cite{widom} gives the precise asymptotic order of the term $o(\Omega T)$, which is $\log (\Omega T) \log (1/\epsilon)$.

Similarly, letting $W= \omega r+o(\omega r)$, the number of space-wavenumber degrees of freedom of any  signal $f(\phi) \in L^2[-\pi,\pi]$ radiated with frequency $\omega$ from the interior of a circular domain of radius $r$ and observed on the circular perimeter boundary of angle $\phi \in[-\pi,\pi]$,  is given by the space-bandwidth product
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{T}_{2\pi}) = \frac{\omega 2 \pi r}{\pi} +o(\omega r) \;\;\; \mbox{as } r \omega \rightarrow \infty.
\label{comb2}
\end{equation}
In this case, spectral concentration occurs
by scaling either the size of the radiating system $r$, or the frequency of transmission $\omega$.

The results (\ref{eq:uno}) and (\ref{eq:due}) can be viewed as a combination of (\ref{comb1}) and (\ref{comb2}).
An heuristic way  to compute the total number of degrees of freedom of the space-time field $f(t,\phi)$ would be to integrate   over frequencies while accounting for the number of spatial degrees of freedom that every frequency component carries. This corresponds to
simply integrate (\ref{comb2}) over the  frequency bandwidth and, according to (\ref{comb1}), multiply the result by $T/\pi$
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &= \frac{T}{\pi} \int_{0}^{\Omega} \frac{\omega 2 \pi r}{\pi} d \omega, \nonumber \\
&= \frac{\Omega T}{\pi}  \frac{2 \pi r \Omega}{2\pi},
\label{eq:b}
\end{align}
which gives the correct result.  Of course, the problem of this heuristic is clear: it does not account for the possible accumulation of the error $\epsilon$ when computing the integral along the frequency spectrum. Thus, the need for the rigorous method presented in this paper arises.

\subsection{Cut-set of three-dimensional spherical domains}
We extend results to three dimensions by considering a spherical radiating system of radius $r$. In this case, the  surface of the sphere is interpreted as a cut-set  through which the information must flow and provides a limit on the amount of information that can radiate from the interior of the domain to the outside space. Each scalar component $f(\phi_1,\phi_2,t)$ of the vector field on the cut-set boundary is a function of two angular coordinates identifying a point on the surface and one temporal one, see Figure~\ref{fig:sphere}.
\begin{figure}
\begin{center}
{
\scalebox{.55}{\includegraphics{sphere.eps}}}
\end{center}
\caption{Cut-set boundary of three-dimensional spherical  domain.}
\label{fig:sphere}
\end{figure}
The support sets of each scalar field component are the ones depicted in Figure~\ref{fig:PQ1}, where we indicate with $w_1$ the transformed coordinate of the variable $\phi_1$, with $w_2$ the transformed coordinate of the variable $\phi_2$, and with $\Phi$ the solid angle subtended by the surface boundary at the center of the sphere.
\begin{figure}
\begin{center}
{
\scalebox{.6}{\includegraphics{3D.eps}}}
\end{center}
\caption{Support sets in the natural and transformed domains.}
\label{fig:PQ1}
\end{figure}

We then have
\begin{equation}
m(P)= 4 \pi T,
\label{sub1}
\end{equation}
\begin{equation} m(Q)= \frac{8}{3}\Omega^3 r^2.
\label{sub2}
\end{equation}
By Theorem~\ref{th:tre}, with Landau's type scaling
\begin{equation}
\mtx{A}= \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1  & 0 \\
0 & 0  &  1
\end{array} \right), \; \;
\mtx{B}= \left( \begin{array}{ccc}
\rho & 0 & 0 \\
0 & \rho & 0 \\
0& 0 & \rho
\end{array} \right),
\label{landauscale}
\end{equation}
and using (\ref{sub1}) and (\ref{sub2}),  it follows that the number of degrees of freedom in the wide band frequency regime is
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q) = 4 \pi r^2 \frac{\Omega^3 T}{3 \pi^3} +o(\Omega^3) \;\;\; \mbox{as } \Omega \rightarrow \infty,
\label{eq:rigor1}
\end{equation}
where $\Omega = \rho \Omega'$ with $\Omega'$ fixed and $\rho \rightarrow \infty$.
With the alternative scaling
\begin{equation}
\mtx{A}= \left( \begin{array}{ccc}
\tau & 0 & 0 \\
0 & 1  & 0 \\
0 & 0  &  1
\end{array} \right), \; \;
\mtx{B}= \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & \rho & 0 \\
0& 0 & \rho
\end{array} \right),
\label{alternativescale}
\end{equation}
we also have that the number of degrees of freedom over a fixed frequency band for large radiating systems and transmission time is
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q) = 4 \pi r^2 \frac{\Omega^3 T}{3 \pi^3} +o(r^2 T) \;\;\; \mbox{as } T,r \rightarrow \infty,
\label{eq:rigor2}
\end{equation}
where $T=\tau T'$, $r= \rho r'$, with $T',r'$ fixed and $\tau, \rho \rightarrow \infty$.

Above rigorous results can also be obtained using the heuristic method described in Section~\ref{sec:comparison}.
The number of space-wavenumber degrees of freedom of the  electromagnetic field radiated with frequency $\omega$ from the interior of a spherical domain of radius $r$ and observed  on the surface boundary of solid angle $\Phi \in[-2\pi,2\pi]$, is given by the space-bandwidth product~\cite{bucci1, bucci2}
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{T}_{4\pi})=\frac{\omega^2 4 \pi r^2}{\pi^2} + o[(\omega r)^2] \;\;\; \mbox{as } r \omega \rightarrow \infty.
\label{eq:narrow2}
\end{equation}
Integrating over the frequency bandwidth and multiplying the result by $T/\pi$, we obtain
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &=  \frac{4 \pi r^2}{\pi^2} \frac{T}{\pi} \int_{0}^{\Omega} \omega^2 d \omega \nonumber \\
& = 4 \pi r^2 \frac{\Omega^3 T}{3 \pi^3},
\label{h}
\end{align}
which is consistent with  the rigorous results in (\ref{eq:rigor1}) and (\ref{eq:rigor2}).

\subsection{Cut-set of general rotationally symmetric domains}
Results can be further generalized  considering a radiating system enclosed in a convex domain bounded by a surface with rotational symmetry. Consider a  cylindrical coordinate system $(r,\phi, z)$, a closed analytic curve $\zeta=\zeta(r,z)$ lying in the plane $\phi=0$ and symmetric with respect to the $z$ axis, and the surface of revolution obtained by rotating the curve about the $z$ axis, see Figure~\ref{fig:oblate}.
\begin{figure}
\begin{center}
{
\scalebox{.8}{\includegraphics{oblate.eps}}}
\end{center}
\caption{Cut-set boundary of three-dimensional rotationally symmetric domain.}
\label{fig:oblate}
\end{figure}
In this case, we can choose a pair of  coordinates $(\phi_1,\phi_2)$ on the surface such that any meridian curve covers a $2 \pi$ range, and the spatial bandwidth along the meridian is constant and  bounded by~\cite{savarese}
\begin{equation}
w_1= \omega \frac{\ell}{2 \pi}  +o(\omega \ell) \;\; \mbox{as } \omega \ell \rightarrow \infty,
\end{equation}
where $\ell$ is the Euclidean length of the curve, normalized to the speed of light so that $\omega \ell$ is dimensionless. This should be compared with the geometric constraint for circular curves given in (\ref{circular}). On the other hand, any latitude line is a circle of radius $r(z)$ that also covers a $2 \pi$ range, and the spatial bandwidth along this line is bounded by
\begin{equation}
w_2 = \omega r(z) + o(\omega r), \;\; \mbox{as } \omega r \rightarrow \infty.
\end{equation}
It follows that while the domain $P$ covers a solid angle $4 \pi$, the domain $Q$ varies along $z$ according to the meridian curve parametrization $\zeta=\zeta(r,z)$, and we have
\begin{equation}
m(P)=4 \pi T,
\label{eq:sub11}
\end{equation}
\begin{align}
m(Q) &= \frac{8 \Omega^3}{3} \ \frac{\ell }{2 \pi} \frac{\pi}{2} \int_\zeta r(z) dz  \nonumber \\
&= \frac{8 \Omega^3}{3}  \frac{\ell }{4 \pi}  \int_\zeta  \pi r(z)  dz  \nonumber \\
&= \frac{8 \Omega^3}{3} \frac{\mathcal{A}}{4 \pi},
\label{eq:sub22}
\end{align}
where $\mathcal{A}$ is the surface area of the radiating volume.

By Theorem~\ref{th:tre},  the scaling in (\ref{landauscale}), and using (\ref{eq:sub11}) and (\ref{eq:sub22}), we have that the number of degrees of freedom in the wide band frequency regime is
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q) = \frac{\mathcal{A}  \Omega^3 T}{3 \pi^3} +o(\Omega^3) \;\;\; \mbox{as } \Omega \rightarrow \infty,
\end{equation}
where $\Omega = \rho \Omega'$ with $\Omega'$ fixed and $\rho \rightarrow \infty$.
The analogous result is obtained by  letting the transmission time $T= \tau T'$, with $T'$ fixed and $\tau \rightarrow \infty$, and blowing-up all coordinates of the radiating volume, so that both $\ell = \rho \ell'$ and $r= \rho r'(z)$ tend to infinity with $\ell'$ and $r'$ fixed and $\rho \rightarrow \infty$. In this case,
by Theorem~\ref{th:tre} with the scaling in (\ref{alternativescale}), and using (\ref{eq:sub11}) and (\ref{eq:sub22}), we have
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q) = \frac{\mathcal{A}  \Omega^3 T}{3 \pi^3} +o(\mathcal{A}T) \;\;\; \mbox{as } T, \mathcal{A} \rightarrow \infty,
\end{equation}
where $\mathcal{A}= \rho^2 \mathcal{A'}$, with $\mathcal{A}'$ fixed and $\rho \rightarrow \infty$.
Finally, we can check that the result is consistent with the heuristic calculation:  starting with the
 number of space-wavenumber degrees of freedom per angular frequency $\omega$~\cite{migliore2, savarese}
 \begin{equation}
 \mathcal{N}_\epsilon(\mathscr{T}_{4 \pi}) = \frac{\mathcal{A} \omega^2}{\pi^2},
 \label{h1}
 \end{equation}
integrating over the frequency bandwidth and multiplying by $T/\pi$, the result follows.

\subsection{Degrees of freedom of modulated signals}
The results  can be extended to handle the case of modulated signals. Consider  the case of a real signal modulating a sinusoid of carrier  frequency $\omega_c$, occupying a bandwidth $\Delta \omega =[\omega_1,\omega_2]$ centered around $\omega_c$, see Figure~\ref{fig:modulation}.
\begin{figure}
\begin{center}
{
\scalebox{.7}{\includegraphics{PQMod.eps}}}
\end{center}
\caption{Support set of a modulated signal in the transformed domain.}
\label{fig:modulation}
\end{figure}
In the two-dimensional case,
following the same procedure of the previous sections, letting $T=\tau T'$, $r = \rho r'$, and $\rho, \tau \rightarrow \infty$, we obtain
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &=  \frac{T}{\pi}  \frac{2 \pi r}{\pi} \frac{(\omega_2^2-\omega_1^2)}{2} +o(r  T)  \nonumber\\
&=   \frac{T \Delta \omega}{\pi}  \frac{2 \pi r  \omega_c}{\pi} + o(r  T),
\label{f1}
\end{align}
as $r,T \rightarrow \infty.$

On the other hand, letting
$\Delta \omega = \rho \Delta \omega'$, $\omega_c = \rho \omega_c'$, and $\rho \rightarrow \infty$, we have
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q) = \frac{T \Delta \omega}{\pi}  \frac{2 \pi r  \omega_c}{\pi} + o(\omega_c \Delta \omega),
\end{equation}
as $\omega_c, \Delta \omega \rightarrow \infty$.
The number of degrees of freedom is proportional to the time-bandwidth product and to the  cut-set boundary normalized by  the radiating carrier.

For spherical domains, letting $T = \tau T'$, $r= \rho r'$, and $\tau, \rho \rightarrow \infty$, we have
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) &= \frac{T}{\pi}  \frac{4 \pi r^2}{\pi^2}  \frac{(\omega_2^3-\omega_1^3)}{3} + o(T r^2) \nonumber \\
& = \frac{T \Delta \omega}{\pi}   \frac{4 \pi r^2}{\pi^2}     \frac{(\omega_{2}^2+\omega_{1}^2 + \omega_1 \omega_2)}{3} + o(T r^2) \nonumber \\
& =  \frac{T \Delta \omega}{\pi}   \frac{4 \pi r^2 \omega_c^2}{\pi^2}  (1+\delta) + o(T r^2),
\label{f2}
\end{align}
as $T,r \rightarrow \infty$, where  $\delta$ is a constant that depends only on the ratio $\Delta \omega/\omega_c$. Analogously,  letting $\Delta \omega = \rho \Delta \omega'$, $\omega_c = \rho \omega_c'$,  $\rho \rightarrow \infty$, we have
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) & =  \frac{T \Delta \omega}{\pi}   \frac{4 \pi r^2 \omega_c^2}{\pi^2}  (1+\delta) + o(\omega_c^2 \Delta \omega ),
\label{f3}
\end{align}
as $\omega_c, \Delta \omega \rightarrow \infty$.

Results (\ref{f2}) and (\ref{f3}) can also be combined using the scaling matrices
\begin{equation}
\mtx{A}= \left( \begin{array}{ccc}
\tau & 0 & 0 \\
0 & 1  & 0 \\
0 & 0  &  1
\end{array} \right), \; \;
\mtx{B}= \left( \begin{array}{ccc}
\beta & 0 & 0 \\
0 & \rho \beta & 0 \\
0& 0 & \rho  \beta
\end{array} \right),
\label{combine}
\end{equation}
and letting $\tau \beta, \rho \beta \rightarrow \infty$, obtaining
\begin{align}
\mathcal{N}_\epsilon(\mathscr{B}_Q) & =  \frac{T \Delta \omega}{\pi}   \frac{4 \pi r^2 \omega_c^2}{\pi^2}  (1+\delta) + o(r^2   \omega_c^2 \Delta \omega  T),
\label{f4}
\end{align}
as $r \omega_c,  \Delta \omega  T\rightarrow \infty$.

Finally, for general rotationally symmetric domains, using (\ref{combine})  we have
\begin{equation}
\mathcal{N}_\epsilon(\mathscr{B}_Q)  =  \frac{T \Delta \omega}{\pi}   \frac{\mathcal{A} \omega_c^2}{\pi^2}  (1+\delta) + o(\mathcal{A}  \omega_c^2  \Delta \omega  T),
\label{f5}
\end{equation}
as $\mathcal{A} \omega_c^2, \Delta \omega T \rightarrow \infty$, where $\mathcal{A}= \rho^2 \mathcal{A}'$ with $\mathcal{A}'$ fixed.

For narrowband signals $\Delta \omega/\omega_c \ll 1$, and the constant $\delta$ can be made arbitrarily small,  so that the number of degrees of freedom in three dimensions is essentially given by the first term of (\ref{f5}),
which is the natural extension of  of the single-frequency result in~\cite{migliore2, savarese} and reported in  (\ref{h1}), accounting for a non-zero frequency band around frequency $\pm \omega_c$.
It follows that   the number of degrees of freedom per unit time and per unit frequency band is essentially given by
\begin{equation}
N_0=\frac{\mathcal{A} \omega_c^2}{\pi^2}.
\label{eq:highenergy}
\end{equation}

\section{Concluding remarks}
\label{sec:conc}
A key insight of our analysis is that the amount of information, in terms of degrees of freedom, scales with the surface boundary, rather than with the volume of the space. Clearly,  field theory allows for a much larger number of possible field configurations \emph{inside} the radiating volume. Think for example of the number of standing waves insides a black body. This grows with the volume of the space rather than with the surface area. Our results apply to the information that one can gather about these volumetric configurations, from the point of view of an external observer, through electromagnetic propagation. They  pose an information-theoretic limit in terms of degrees of freedom at the scale of the surface boundary through which the field propagates.
Physically, this is due to the Green's propagation operator relating source currents to the radiated field, that essentially behaves as a spatial filter,  projecting the number of observable field configurations  onto a lower dimensional space~\cite{bucci1}. The resulting wavenumber bandlimitation of the field  dictates the geometric constraints on the support sets depicted in Figures~\ref{fig:PQ}, \ref{fig:PQ1}, and \ref{fig:modulation}, leading to our results. The conclusion is that Nature  ``hides'' three-dimensional field configurations, and the world appears to an external observer as having only an apparent three-dimensional informational structure, subject to a two-dimensional representation. Like for Plato's prisoners in the cave, ``the truth would be literally nothing  but the shadows of the images.''

Another important observation is that for any fixed size system the amount of information scales with the radiated frequency. We can increase the number of degrees of freedom as high as we want by transmitting signals modulating larger and larger  frequencies.  In wireless networks, this has been used to identify regimes of linear capacity scaling with the number of users~\cite{kaist, ozgur}.  In the context of electromagnetic imaging,  this allows to increase the spatial resolution of the constructed image by increasing the illumination frequency.

Our results are based on a variation of Landau's theorem that allows to compute the number of degrees of freedom of square integrable, bandlimited fields in terms of Kolmogorov's $n$-width, using an alternative scaling of the space.  When degrees of freedom of electromagnetic signals are evaluated along a spatial cut-set boundary that separates transmitters and receivers in a wireless network, or between radiating elements and sensing devices in an electromagnetic remote sensing system, our results yield the effective number of parallel channels available through the cut-set boundary in the time-frequency and the space-wavenumber domain. Thus, they provide a bound on the amount of spatial  and frequency multiplexing achievable using arbitrary technologies and in arbitrary scattering environments.

Relations between the number of degrees of freedom studied here and the Kolmogorov's $\epsilon$-entropy and $\epsilon$-capacities is well known, and follow from  the application of Mityagin's theorem~\cite{lorentz}. Usage of the number of degrees of freedom  to bound the Shannon capacity scaling of wireless networks are described in~\cite{migliore1} and \cite{migliore2}. Our results are limited to linear scalings of the support sets.
Extensions  to  non-linear  scalings suitable to describe signals with sparse supports would also be of interest. In this case, a  non-linear mapping of the support sets would need to achieve spectral concentration while retaining a structure composed of many vanishingly small subdomains.  The work in~\cite{stark} provides one step in this direction, but it is limited to the study of the zeroth order eigenvalue, rather than the whole phase transition of the eigenvalues. More generally, one could  study spectral concentration under different  structural constraints on the support sets, beside bandlimitation.  In this context,  connections with undersampled signal representations~\cite{donoho1} and compressed sensing~\cite{donoho2} for electromagnetic applications need to be explored.

redpajama_set_name: RedPajamaArXiv


Sometimes in towns and cities, and generally even in a rural setting, one might come throughout a constructing which appears anachronistic – a constructing out of maintaining with its native atmosphere. Her daughters Ada, Laura, Constance and Leila bought some land and the house and contined to spent most of their grownup lives at Como. I do not assume the climate is the only purpose for the distinction in home costs nonetheless. My brother-in-regulation was promoting his place and the people who bought it was the identical people who bought our second home. Public transportation in the US is terrible, and P/T jobs pay so little, some don't even cover rent. Painting the stacks black attracts the sun to the dark shade and should help prevent ice buildup in the future. Preffing houses primarily based on perceived reputation, picture, or reputation generally is a enormous mistake and will result in lacking out on the right house for you. They were photos taken at Mandie's home the previous weekend and so they made me chuckle out loud.
If the salesman had bothered to look behind the property, he would have seen that the guttering needed changing, and that water was accumulating in a gulley behind the house. Angels, in Burnley, Lancashire, was first running house nights from the very early days in around 1987-88. After the home was offered, piles of used cigarettes and messes like like this have been left all around the home. She refuses to cope with the scenario in any respect and we have no idea what to can we would like to someday buy a home but with this home scenario it seems we'll never be capable of. Do you may have any thought what he can do as a result of he was informed he isn't liable by the divorce court docket. If the house is value $197,000 and also you owe $153,000, then you've gotten some equity. Now we have three loans on our home – 1st at $327,465 interest solely which can turn out to be adjustable subsequent January.
Once again, I cannot choose to go forward with something like a fast sale if it is a bad concept..we try to get forward, not dig a deeper hole. A brief sale is where the bank agrees to just accept lower than the total amount owed as fee in full on the mortgage with a purpose to get the house offered and avoid a foreclosures. Settlement could not be reached, so preparation for the brand new building took place anyway with excavations paying homage to those which surrounded the Chongqing nail house. Getting rid of dampness in your house sometimes means changing your individual habits and adjusting your life-style.
A three-bedroom terraced house within the Potteries area, in cities reminiscent of Stoke-on-Trent and Newcastle-Underneath-Lyme, can be purchased for as little as £55,000 to £sixty five,000. And their philosophy was that the Democratic Party is a big-tent get together — you accept liberals, you accept reasonable, conservative Democrats — but we're all Democrats. One bid of $1.5 million was rejected, with an extravagant demand by Austin for 5 to 10 instances that quantity, plus a request to be employed on the development. I call and name and call these locations, pleasing for an interview, only to get turned down…. I have been homeless for five months now.
Its finest to start gigs as soon as your vitality is totally full, because it will likely be easier to complete the gig and get 5 stars. Then it was again to the automobiles to hang around on the providers for however long it took to discover a party. Larger home plants might require two or more bulbs in order to provide adequate water while you're away. Tonight we go to accommodate to measure and make preparations to collect OUR fridge and located the house has a lockbox and locks were changed! With the sum of money needed to place into this house to not solely catch-up however to repair I am involved our funds here would end up being greater than we might afford, or inexpensive with no extra money to put into repairs.
← Anyone Acquired $250,000,000 For A Home?


A 29 year old female was presented with increased frequency of urination and tiny particles passing through urine.
5 5 cm x 5 cm size ill-defined heterogeneous area in the posterior wall of the urinary bladder which is thickened and measures upto 0.6 cm in thickness. Large solid calcific areas are noted in the thicknened portion of the wall urinary bladder. Suggestive of schistosomiasis of the urinary bladder (possibly with malignant change).
Lesion in the wall of the urinary bladder has increased in size. Calcific areas are noted. Urinary bladder malignancy ( confirmed by histopathology), possibly following schistosomiasis.
Genitourinary schistosomiasis is produced by Schistosoma haematobium, a species of fluke that is endemic to Africa and the Middle East, and causes substantial morbidity and mortality in those regions. It also may be seen elsewhere, as a result of travel or immigration.
Schistosoma haematobium, one of the five fluke species responsible for most human schistosomiasis, is the only species that infects the genitourinary system.
In the early stages, it involves the bladder and ureters; later, the kidneys and genital organs .
The larvae of Schistosoma haematobium are released from snails into water and penetrate human skin exposed to the infected water. These larvae travel to the lungs and liver where they reside and mature. After maturation, pairs of adult worm travel to the pelvic veins. Eggs are deposited in the bladder wall vessels and cause a granulomatous response resulting in polypoid lesions.
Ultrasound featrures : mucosal irregularity, polypoidal bladder wall thickening, inflammatory pseudopolyps (with increased vascularity on Doppler), ureteral and pelvicalyceal system dilatation (mainly if ureterovesical junction involved), stricture, curvilinear dense wall calcification. Later, bladder capacity may be reduced; rarely ureteritis cystica.
The calcification in bladder wall is due to calcification of the ova deposited in the bladder wall vessels. The calcification spreads around the bladder wall and may completely encircle the bladder, appearing as a curvilinear ring. The bladder wall becomes fibrotic and later bladder capacity may be reduced.
A bladder carcinoma may be considered when follow-up imaging shows an absence of wall calcification in areas that were previously calcified.
Heavy egg deposits in the bladder mucosa and submucosa act as a mechanical irritant to the urothelium, inducing chronic inflammatory lesions, which causes hyperplasia and squamous metaplasia and eventually carcinoma.
Many mechanisms have been proposed to explain the malignant change.
Acknowledgment:- I am thankful to Dr Anirudh Badade for the support and encouragement whenever I was in need.
2) Kuper H, Adami HO, Trichopoulos D. Infections as a major preventable cause of human cancer. J Intern Med. 2000;248:171-183.
3) Cheever A W. Schistosomiasis and neoplasia. J Natl Cancer Inst. 1978;61:13-18.
4) Cheever A W, Kuntz R E, Moore J A, Hang T C. Pathology of Schistosoma haematobium infection in the Capuchin monkey. Trans R Soc Trop Med Hyg. 1988;82:107-111.
8) Knowles M A, Williamson M. Mutation of H-ras is infrequent in bladder cancer: confirmation by single-strand-conformation-polymorphism analysis, designed restriction-fragment-length polymorphisms, and direct sequencing. Cancer Res. 1993;53:133-139.


text:
ANALYSIS <b>The Agency Business</b>: To satisfy clients, sometimes two firms are better than one
August 02, 2004 by Thom Weidlich
After working together on a project for Eddie Bauer, Clearpoint Agency and KS Promotions came to realize the added value to clients when agencies combine their specialties.
Strategic alliances are a good way for agencies, especially small ones, to offer clients services outside their bailiwick. An interesting example of such a coupling is that between Clearpoint Agency, a four-person PR and marcomms outfit in Solana Beach, CA, and KS Promotions, a four-person sweepstakes-marketing shop in Carlsbad, CA. Both companies are located just north of San Diego, 15 miles apart. In spring 2003, at the recommendation of a mutual client, KS tapped Clearpoint to handle an event tour around the sweepstakes promotion for the launch of Eddie Bauer's Sport Shop Clothing Collection. The tour included displays in 16 Seattle-area venues, such as concerts and ball games. "We needed someone who could do the events because we weren't staffed to do" that, says Kelly Strange, president of KS Promotions. The two agencies found they worked together easily. Bonnie Shaw, president of Clearpoint, says they reviewed estimates together and conducted weekly conference calls with the client. "Clearpoint would put together a weekly report, and we would share it with KS to see if they had any comments or questions." Simple, perhaps, but it's easy to envision a scenario where conflicts and jealousies would arise. The partnership also eased things for Eddie Bauer after the campaign was over. The two agencies created one report to show how the PR and sweepstakes worked together. "We were able to definitely show a spike in game-piece redemption in the areas where they had the tour, which was really beneficial to Eddie Bauer because they were able to see the benefits of having the event," says Strange. Shortly after the success of that campaign, the two began thinking of collaborating in a more formal way. "We looked at each other and said, 'Look, we're both small firms, and this alliance was a good experience for us,'" says Shaw. "We thought an alliance could really help us to expand our footprint." They sat down and hammered out an agreement. The document went into areas such as how they would present each other on their websites. They also devised a list of services each offers, which helped them understand the scope of what each did. Clearpoint handles the promotion of the alliance for free; it also does PR for KS but gets paid for that. (This is the first strategic alliance for KS; Clearpoint has several other affiliations with, for example, a web-development firm and a graphics firm, but Shaw says the KS alliance is the most formal arrangement.) The document also addressed how account management would be handled. The firm that brings in the client is the account manager and bills the client for both firms. The other agency will discount its fees to the lead agency, which would charge the client in full, so that the lead firm gets paid for the work involved in overseeing that account. The two decided to issue a news release in February "to make it more official," Shaw says. They split hard costs, such as putting the release out on Business Wire. The arrangement can mean working together or simply making referrals to each other. Obviously, a KS client wanting an event for its sweepstakes would be a candidate to also become a Clearpoint client. But Shaw says she has mentioned to Clearpoint clients that they may want to do contests. She has also mentioned to clients that they may want to provide prizes for KS' sweepstakes. "As we move along, we see more opportunities to work together," Shaw says. After they inked the formal alliance, the two firms worked on the concept for an Eddie Bauer Father's Day sweepstakes. They plan to pitch to "a major credit-card company," Strange says. "We went to Clearpoint and brainstormed some ideas that would benefit this promotion." Shaw and Strange say a formal alliance has advantages over pretending that you can do a certain kind of work and then outsourcing it. "We consider ourselves experts at public relations, marketing communications, and event management," says Shaw. "We really aren't the experts in sweepstakes. When we get the opportunity to put a sweepstakes or contest component into a campaign, we'd love to bring Kelly in because she is the expert."
PRWeek welcomes topic ideas for future Agency Business columns. Please send them to news@prweek.com. Developing an alliance Clearpoint Agency and KS Promotions offer the following tips:
Make sure your business philosophies are similar
Discuss and agree on financial arrangements early to avoid confusion later
Discount each other's work to allow the managing account to earn a share
Give each other billing on each company's website
Get out of the way if a client really just needs the services of one partner
Don't charge each other for work done to land accounts
Don't hide alliance partners or try to convince clients your company offers the services - clients will see through that quickly and never trust you again
Don't rely solely on any alliance to bring in business
Publicis Groupe reports 15% hike in first-half profit, but struggles in North America
Obama, Lyft alum Daniel Roberts joins Facebook
Miami Super Bowl Host Committee brings on Golin


text:
Walking in Morocco - Atlas to Atlantic
This walking trip takes you among the foothills of the majestic High Atlas Mountains to the windswept Atlantic coast.
This walking trip takes you among the foothills of the majestic High Atlas Mountains to the windswept Atlantic coast. Explore the beaches and valleys, dotted with fruit orchards and tiny villages. Discover ancient Marrakech and the lively craft markets of Essaouira. Riad - Spend four nights in traditional accommodation Berber people - Discover their homeland taking lunch with a family Essaouira - Relax in this laid back town sampling fresh fish
Meals – Breakfast Only
Breakfast: 7 Lunch: 2
2 nights comfortable hotel 1 nights premium hotel 4 nights comfortable riad
Day 1: Join trip in Marrakech
The trip starts today in Marrakech. Morocco's famous 'Red City', Marrakech is the spiritual heart of the country, a cultural melting pot of the mountain Berbers and the desert peoples of the south. Blessed with some of the most stunning architecture in Morocco, its mix of tradition, colour and history make it the ideal starting point for our week of walking and exploration of Morocco. For those arriving on time our Leader plans to meet you in the hotel reception at 6pm for the welcome meeting. There are no other activities planned today, so you are free to arrive in Marrakech at any time. If you would like to receive a complimentary airport transfer today, you'll need to arrive into Marrakesh Menara Airport (RAK), which is around 20 minutes' drive. If your flight arrives later in the evening, they will inform you of any essential information after breakfast on day two.
Day 2: Atlas Mountains hike through Berber villages; lunch with a local family
This morning we leave the bright lights of Marrakech behind and head to the small village of Ouirgane in the High Atlas Mountains . Located in the heart of Toubkal National Park, Ouirgane is surrounded by red earth hills and pine forests. On arrival we'll ravel to a nearby Berber village to have lunch in a local house, a great opportunity to sample traditional home-cooking and learn more about the Berber culture. In Morocco lunch tends to be the main meal of day, we'll have a fresh salad followed by a traditional Berber omelette cooked in a clay tagine blending eggs with delicious savoury spices. Following lunch we take a short drive out to the Bridge of Assiff Azdeb, from where we'll walk among the olive groves towards the village of Tikhfist. Stopping at a panoramic view point overlooking the valley we see Lalla Takerskout Lake shimmering below. Taking the path down to the villages of Torort and Anraz, we return to the hotel on foot, surrounded by the scent of juniper and pine. Our hotel tonight is set within an extensive landscaped garden with spectacular mountain views and a inviting outdoor swimming pool. The rustic rooms are traditionally decorated, arranged around the central courtyard. Today's eight kilometre walk is expected to take around three hours with 250 metres of ascent and descent.
Day 3: Walk to 12th century Tinmel Mosque, drive over Tizi 'n' Test Pass to Ouled Berhil
Today we continue our journey through the mountains, to Ouled Berhil, stopping off along the way to visit the 12th century Tinmel mosque. We take a short walk crossing the Oued Nfiss Valley to view the red brick fortress from above before entering the site. Tinmel is one of the only two mosques in Morocco open to non-Muslims and was once considered the centre of the powerful Almohades dynasty. You can admire the brick arches and elaborate Mihrab of the roofless building. Continuing by bus we take a breathtaking drive crossing the High Atlas Mountains over the Tizi n Test pass (2,092 metres) to the Souss Plain. This scenic road is winding and spectacular. Weaving its way up into the mountains through a series of switchbacks, you can take in the fabulous views back across to the Toubkal Massif. Descending to the Souss Valley, across the agricultural plain, past orange groves to arrive at Ouled Berhil. For the next two nights we'll be staying in a traditional Moroccan house known as a riad. Riad Hida was built in 1860 and the property boasts lush gardens with fountains, palms, fruit trees and an outdoor swimming pool, you may even spot peacocks roaming the grounds. The lounge and dining rooms feature several collectors items, with colourful mosaic adorning the walls and ceilings.
Day 4: Hike in the Afensou Valley and enjoy lunch in a village house
Today we take an excursion to the valley of Afensou, a scenic drive northwards into the Western High Atlas. Arriving at a view point overlooking the valley, we walk down to Afensou village passing along farm terraces, observing people at work in their gardens and collecting vegetables, affording us an insight into Berber life. We have lunch in Afensou at a family-run guest house, feasting on the famed Moroccan tagine, accompanied by freshly baked Khobz bread, a rounded bread that forms a staple of the local diet. This slow cooked savoury stew is named after the clay dish it's cooked in, bursting with the sweet and sour flavours of dates and spices. On the way back to Ouled Berhil we make a stop at Taroudante, a walled city in the Souss Valley known as 'Little Marrakesh'. This thriving market town is a meeting place for the mountain Berbers trading their locally produced food and crafts, there will be time to stroll around the Medina. Today's four kilometre walk is expected to take around two hours with 100 metres of descent.
Day 5: Depart the Atlas Mountains for Essaouria; hike Atlantic Coast beaches en route
We leave the Atlas Mountains behind us today as we head to Agadir on the coast and drive alongside the Atlantic Ocean to Sidi Mbarek. This beautiful drive, hugging the coast, takes us past small villages, banana plantations and beaches where you can spot camels and surfers. During the journey keep an eye out for the bizarre sight of goats grazing in the trees! In the south west of Morocco, cloven-hoofed goats climb Argan trees attracted by the fruits' pulp. This afternoon's walk takes us from the small village of Sidi Mbarek down to the beach, walking along the deserted sand, surrounded by sand dunes and vast ocean views. Arriving at the sleepy surf town Sidi Kaouki the bus will be waiting to take us on to Essaouira. Essaouira is a colourful coastal fishing town set within 15th century Portuguese fortifications. Whilst here we'll stay in the Riad Al Madina in a beautiful setting within the city walls. This former 19th Century palace has been carefully restored to retain the charm and elegance of its original splendour. Rooms lead off from a central courtyard filled with plants and fountains and there are great views over the city's Medina from the sun terrace. Today's 12 kilometre walk is expected to take around three hours, along a flat route.
Day 6: Walking tour in Essaouira. Explore this charming walled Kasbah with its many craft shops
This morning we take a walking guided tour of Essaouira. Entering the old walled Medina, passing through a narrow, highly decorated arch, we are greeted by a host of merchants selling local handicrafts and women carrying out their daily routines, veiled in their traditional dress. We'll walk along the impressive ramparts, admiring the view of the wild Atlantic Ocean, to the port area of the town. This bustling port is crammed with bobbing blue fishing boats. We can observe fishermen mending their nets and try some delicious freshly grilled sardines. The rest of day is left free for you to explore further at your leisure, strolling around the craft stalls and along the fine sandy beach.
Day 7: Return to Marrakech, discover the city's souks and Jamaa el Fna Square on a walking tour
After breakfast we return by bus to Marrakech and in the afternoon take a guided walking tour of the Old City. Marrakech is a feast for the senses and Djemmael- Fna Square is a spectacle not to be missed with many street performers to watch and enjoy. The 70m-high tower of the 12th-century, Koutoubia Mosque dominates the skyline. Prohibited from entering this mosque, we'll admire the architecture from the outside. We visit the ornate 19th century Bahia Palace, with its lush gardens, rooms decorated in elegant Moroccan style and a grand marble-paved courtyard. We see further examples of Moroccan opulence at the Saadian Tombs and the lavish Mausoleum of el Mansour built during the reign of Sultan Ahmad el Mansour during the Saadian dynasty. There will be time to further explore the souks independently, losing yourself in the maze of narrow streets.
Day 8: Trip ends in Marrakech
The trip ends after breakfast at our hotel in Marrakech . There are no activities planned today, so you are free to depart from Marrakech at any time. If your flight is departing later in the day, luggage storage facilities are available at our hotel. If you would like to receive a complimentary airport transfer today, you need to depart from Marrakesh Menara Airport (RAK). Depending on the schedule of your flights, you may have some additional time to wander in the souks of Marrakech or buy your last souvenirs before departure.
You will have the option to book your own flights independently with the operator.
15-May-2021 for 7 Nights 16 View live deal View live deal
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Touring with Explore
Explore have been creating award-winning adventures for over 35 years and are experts when it comes to unique travel experiences.
Their small group adventure holidays have been running since 1981 and today, Explore are one of the most trusted travel companies in the UK with over 600 trips to more than 130 countries. At Explore, they are passionate about travel and have developed a wide range of unique activities and experiences which gives their customers an unforgettable adventure with a team of award-winning Explore leaders .
With Explore, you'll get to see your destination from a whole new perspective that takes you away from the typical well-trodden tourist track. You'll have the chance to meet, dine and stay with local people, rest in authentic accommodation with other like-minded explorers and travel to must-see destinations with a unique Explore twist.
From family trips to holidays for solo travellers; cycling tours to wildlife safaris; trekking on mountains or exploring miles of scenic coastline; self-guided holidays or small group trips; there is something for every kind of traveller with Explore. They will provide their expert knowledge, exciting itineraries and outstanding service as part of their sustainable travel experiences which take you under the skin of the country you're visiting for the adventure of a lifetime.
This tour is operated by Explore!
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Group Size: 4 - 16
Suitable For: 14-99
Accommodation: Comfortable
Meals: Breakfasts:7 Lunches:2
Imperial Cities and Desert 14 Nights from pp
Grand tour of Morocco 19 Nights from pp
Highlights of Morocco 8 Nights from pp
Moorish Spain to Marrakech 12 Nights from pp
Toubkal Climb 7 Nights from pp
Southern Oasis Cycling 7 Nights from pp
Toubkal Long Weekend 4 Nights from pp
All About Spain & Morocco 16 Nights from pp
Exotic Morocco 9 Nights from pp
African Insight (South)-Accommodated 6 Nights from pp


text:
Nigerian Hackers to Represent Africa at Cyberlympics
11 months ago Anele
Two teams of cybersecurity professionals from Nigeria have been selected to represent Nigeria and Africa at the Global Cyberlympics, which is the Olympics for cybersecurity professionals and ethical hackers around the world.
The competition hopes to create an opportunity for ethical hacking to be accepted.
The teams — NaijaSecForce and Ek0 pwn3 rs — were chosen after emerging first and second at the elimination round of the Global Cyberlympics after a 12-hour competition that had over 134 teams from across the world,
The Nigerian team also came out winners in the African regional contest after beating 24 teams that competed in Africa.
They will be competing with the winners from other continents and the top cybersecurity professionals across the globe, "
The finals of the competition will be held in Atlanta, Georgia on September 13 this year.
Global CyberLympics is an international online cybersecurity competition, dedicated to finding the top computer network defense teams.
The event tests the skills of information assurance professionals in teams of 4 to 6 people in the areas of ethical hacking, computer network defense and computer forensics.
Each round serves as an elimination round until only winning teams remain. The top winning teams from every continent get invited to play the game live in person at the world finals.
Global CyberLympics, on its website, says it "aspires to create an opportunity for ethical hacking to be accepted, practised and demonstrated without any discrimination, across all geographical boundaries – for the purpose of understanding what it takes to protect and secure critical information and assets."
You May Also Like: Rwanda has the Cheapest Mobile Data Prices in Africa, Nigeria Ranked 11th
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GSMA: Sub-Saharan Africa Remains the Fastest-growing Mobile Region in the World
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1 week ago Anele
Meet Fathia, 12-year-old Nigerian Programmer Who Created a Robot that Folds Clothes


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A wine that superbly expresses the history of Friuli and its terroir.
The Vini Orsone from Friuli greets the nose with delicate fruity notes of mature pear and peach, wedded to mineral overtones and a commendable acidity conducive to a pleasantly mouth-watering effect. Alcohol: 13% vol.
Outstandingly versatile, this wine is an excellent complement for Friuli cured ham but also for seafood and fish dishes. It also makes a surprisingly suitable companion to spicy oriental dishes.
The Bastianich winery aims to interpret and evoke the history and culture of the magnificent Friuli region, creating fine wines rooted in their territory of origin but which also establish an identity of their own via their exceptional balance and confident structure. The Bastianich philosophy, in other words, combines originality with a vocation for transmitting the best of Friuli's cultural DNA.


text:
How Should We Be Unloading Our Groceries? The Latest Recommendations
Sarah Regan
mbg Spirituality & Relationships Editor
By Sarah Regan
Sarah Regan is a Spirituality & Relationships Editor, and a registered yoga instructor. She received her bachelor's in broadcasting and mass communication from SUNY Oswego, and lives in Buffalo, New York.
Image by Martí Sans / Stocksy
In our "new normal," we know it's best to limit our trips to the grocery store, keep our distance from others while we're there, and wash our hands once we get home. But what happens next? Do we need to be disinfecting our grocery hauls too? Can you even get the virus from food?
This topic seems to be on top of everyone's mind lately, so we dug into the official guidelines from the FDA1 and got our follow-up questions answered from immunologist Heather Moday, M.D. Here are the latest recommendations.
So, can we catch the coronavirus from food?
Short answer: no. All current evidence suggests you cannot actually contract COVID-19 from food itself, because it is a respiratory virus, not a foodborne one. In order to get sick, you need to breathe the virus in as opposed to ingest it. "There have been no known cases of food-to-human transmission," Moday explains, but, she says, there's a caveat: "One study in the 2New England Journal2 showed that the virus can live for up to 24 hours on cardboard and 72 on metal and plastic."
So, if you touch a hard packaging surface in the store that has been recently contaminated, there's a chance you could contract the virus if you then touch your mouth, nose, or eyes. But the FDA says3 this is not thought to be the main way the virus spreads. Being in close proximity to other people is still thought to present the largest risk.
"Limiting time in a store, touching only what you intend to buy, wearing gloves and masks, staying 6 feet away from others, and wiping down carts and baskets with sanitizer wipes is recommended," Moday summarizes. And once you get home, "always dispose of gloves properly4 and wash hands again."
Do I need to wash pantry staples like cans and jars when I get home?
Once you grab your essentials and head home, there are some additional precautions you can take to make sure your groceries are clean. Although Moday says there are no clear recommendations on wiping down cans and hard packaging, if you want to be on the safe side, you can feel free to do so with "either alcohol wipes or a mild 1% bleach solution."
She also advises unpacking groceries outside your door and then discarding your grocery bags. If you're using reusable cloth bags, you'll want to throw them in the washing machine (or your makeshift one) after every trip to the store. When that's all said and done, wipe down the counters where you unpacked your items and wash your hands with soap and water.
What about fresh produce?
Again, food doesn't seem to transmit the virus, so eating fresh produce is A-OK right now assuming you wash your hands before and after handling it, according to the Institute of Food Safety at Cornell. And Moday adds that you should still be washing your fruits and vegetables to get rid of pesticides and other germs. She recommends running them underwater and using a stiff brush on sturdier veggies like potatoes and thick-skinned fruits. "Using soap is not recommended as the residue left behind may make you sick," she says.
The bottom line.
Bottom line is, we've all gotta eat. And while it's easy to become paranoid about all the potential ways we might be exposed to the coronavirus, there are actionable steps we can take to limit our risk as much as possible: Follow social distancing guidelines while in the stores, wear masks and gloves, and clean hard surfaces as you're unloading your groceries, and you should be OK. And, of course, keep washing those hands!
Sarah Regan is a Spirituality & Relationships Editor, a registered yoga instructor, and an avid astrologer and tarot reader. She received her bachelor's in broadcasting and mass communication from State University of New York at Oswego, and lives in Buffalo, New York.
https://www.fda.gov/food/food-safety-during-emergencies/food-safety-and-coronavirus-disease-2019-covid-19
https://www.nejm.org/doi/10.1056/NEJMc2004973
https://www.fda.gov/consumers/consumer-updates/food-safety-and-availability-during-coronavirus-pandemic
https://www.cdc.gov/vhf/ebola/pdf/poster-how-to-remove-gloves.pdf


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This fresh and lively rosé Champagne is the palest copper in hue, offering pronounced notes of smoky mineral layered with hints of dried white cherry, singed orange peel and biscuit. Drink now. 20,833 cases made.


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Nancy Leilani Jouwe (Delft, 1967) is een Nederlands cultuurhistoricus en auteur. Zij doet onderzoek naar onder meer racisme en intersectionaliteit. Vanaf begin jaren '90 van de twintigste eeuw zet zij zich als woordvoerder, publicist en organisator in voor Papoearechten en vrouwenrechten.

Biografie
Nancy Jouwe is de jongste dochter van Papoealeider Nicolaas Jouwe en zijn tweede vrouw, Louise Leonara (Wiesje) Fisher (Solo, 1922 - Delft, 2011), een Indische apothekersassistente die in Den Haag woonde en werkte.

Jouwe studeerde vrouwenstudies en cultuurgeschiedenis aan de Universiteit Utrecht en in York. In de jaren '80 en '90 van de twintigste eeuw was zij betrokken bij krakers- en emancipatiebewegingen. Ze reisde veel in Zuidoost-Azië en de Pacific, onder andere om te lobbyen voor vrouwenrechten. In 2009 reisde zij met haar vader naar Indonesië. Deze reis werd vastgelegd in de documentaire Land zonder koning van Babette Niemel.

Jouwe werkte als junior-onderzoeker bij de Universiteit Utrecht en als adjunct-directeur bij Mama Cash. Daarna was zij tot 2010 directeur van Stichting Papua Cultureel Erfgoed (PACE) en tot 2013 programmadirecteur bij Kosmopolis Utrecht, een platform dat door middel van kunst en cultuur een dialoog tussen gemeenschappen tot stand wil brengen. Sinds 2019 is zij een van de twee voorzitters van het bestuur van Mama Cash. Zij heeft les gegeven aan de Universiteit Utrecht, SIT Study Abroad, de Willem de Kooning Academie, het Amsterdam University College, de Council on International Educational Exchange (CIEE) en de Hogeschool voor de Kunsten Utrecht. Ze is projectleider van Mapping Slavery, een transnationaal onderzoeksproject dat de Nederlandse rol in de slavernijgeschiedenis in kaart brengt. Zo deed ze onderzoek naar het slavernijverleden in Utrecht, in opdracht van de gemeente. Het onderzoek resulteerde in een boek, Slavernij en de stad Utrecht, uitgebracht in 2021.

Jouwe is vooral geïnteresseerd in vrouwenstudies, gender, etniciteit en misogynoir, Papoea-erfgoed en -identiteit, en transculturele kunstprojecten. Als onderzoeker, curator en projectmanager focust ze op culturele en sociale bewegingen in postkoloniaal Nederland. op 1 november 2014 sprak ze op de manifestatie '5 december voor iedereen' in Utrecht.

Met ingang van 15 februari 2023 werd Jouwe benoemd tot lid van de Raad voor Cultuur voor een periode van vier jaar.

Bibliografie
 Papua's? Oja, die bestaan echt, he? Een inventarisatie van de positie van papuavrouwen in Nederland, 1958-1992, met Marlise Mensink, Wetenschapswinkel Letteren Universiteit Utrecht, 1993
 Ethnocide is not unity, in Pacific Women Speak Out, 1998
 Women, the Environment and sustainable development. An annotated bibliography, 1998
 Caleidoscopische Visies. De zwarte, Migranten-en vluchtelingenvrouwenbeweging in Nederland, met Maayke Botman en Gloria Wekker, Koninklijk Instituut voor de Tropen, ISBN 9789068327137, 2000
 Paradijsvogels in de polder, Papoea's in Nederland, met Eva Prins, foto's van Bodil Anaïs, LM Publishers, ISBN 9789460221859, 2012
 Gids slavernijverleden Amsterdam / Slavery Heritage Guide, met Dienke Hondius, Dineke Stam, Jennifer Tosch en Annemarie de Wildt, LM Publishers, ISBN 9789460223686, 2014
 Dutch New York Histories: Connecting African, Native American and Slavery Heritage | Geschiedenissen van Nederlands New York, met Dienke Hondius, Dineke Stam en Jennifer Tosch, LM Publishers, ISBN 9789460224508, 2017
 Gids Slavernijverleden Nederland, met Dienke Hondius, LM Publishers, ISBN 9789460225048, 2019
 De slavernij in Oost en West. Het Amsterdam onderzoek, met Pepijn Brandon, Guno Jones en Matthias van Rossum, Uitgeverij Het Spectrum, ISBN 9789000372867, 2020
 Slavernij herbezien / Re-Visualizing Slavery (redactie, met Wim Manuhutu), LM Publishers, ISBN 9789460220111, 2021
 Slavernij en de stad Utrecht (redactie, met Matthijs Kuipers en Remco Raben), Walburg Pers, ISBN 9789462497689, 2021.

Nederlands schrijver
Nederlands anti-racismeactivist
Nederlands feminist


Meet the miniature sculptors that shape our ideas and dreams in miniature. Authentic artists of the miniature !!
Antonio is one of the best historical miniature sculptors.
His works can be found in several miniature companies and he's a twice Euromilitaire B.O.S. winner, amongst an endless number of worldwide awards.
Jose is the man behind the all-time classic Hidalgo- Beneito Miniatures. He is also Oniria Miniatures' mold maker and caster. We are lucky and proud on counting with his many years of experience in both sculpting and mold making/casting.
Even though not personally present in the social media, Both Antonio and Alvaro's talented work has been present in quite a few miniature companies over the years.
Being Bob probably the best 28mm horse sculptor in the market, it was quite obvious that we requested his talent.