The South-East Asia One Health University Network (SEAOHUN) encourages participation of students and academic staff in One Health-focused national and international meetings, conferences and workshops. SEAOHUN supports participation by providing travel awards to students and academic staff to deliver presentations and share updated knowledge/ experiences at such venues.
Applicant must be a staff member (permanent or contracted), or a student from one of the SEAOHUN member faculties in Indonesia, Malaysia, Thailand and Vietnam, or one of the SEAOHUN expansion countries, namely Cambodia, Lao PDR, Myanmar and Bangladesh.
The applicant must have been already accepted for oral or poster presentation by the conference.
The attending conference must be related to One Health and taken place within 30 September 2017.
Application must be submitted to SEAOHUN Foundation at least 45 days prior to the conference date.
The applications time of Travel Awards 2017 will be closed on 31st August 2017 (application DEADLINE).
The attending conference must be taken place within 30th September 2017.
Completed the "TRAVEL AWARD APPLICATION FORM" (using format as attached). The application must be endorsed and signed by the Head of Department or Faculty Dean.
Once travel awardee has accepted the travel grant from SEAOHUN and the grant has already been transferred, the awardee cannot cancel the commitment on the travel award.
The travel awardee must attend the whole event of the conference.
All international travel will be subject to final travel approval from USAID/Washington DC. Travel Awardee must not incur any costs, including registration fee, prior to USAID approval.
SEAOHUN and USAID must be acknowledged in the awardee's oral and poster presentation.


Swartz, S.; Arogundade, E.; Bockarie, A.; Breakey, J.; Nyamnjoh, A.
Swartz, S., Arogundade, E., Bockarie, A., Breakey, J. & Nyamnjoh, A. (2016) Cultivating moral eyes: bridging the knowledge-action gap for privilege and injustice. (Paper presented at the 42nd Annual Meeting of the Association for Moral Education, Harvard University, Cambridge, 8 December).


Last Month in this post I introduced you to a wonderful company, Artterro, who produces over 12 great eco-friendly art kits for kids and adults! I'm pleased to be having a giveaway for your choice of one of their their Gorgeous kits! There are so many kits including: Bubble Wands, Paint with Wool, Wool Felt Bugs, Bookmaking, Garden Art, and more.... I'm reviewing their Wire and Bead kit in this post, but take a look at all there other kits here. At the end of this post find out how to enter!!!
The Wire and Bead Kit comes with twistable wire of many colors, unique beads, and marbles!! All you need to include is some wire cutters (or nail clippers) and some pliers.
C jumped right in making a bracelet before I even got a chance to look at the kit! She definitely needed help, but she could easily string the beads and bend some wire!
Here are our creations! So much Creative FUN! These kits are for ADULTS too....so if you are a creative Mom Like me you'll Love these kits!!! Pick one for yourself to win or buy one!!! If you choose to buy a kit all Chocolate Muffin readers can use the special discount code of TREE20 for 20% off your order until Janauary 31, 2012!!! Go to www.arterroecoartkits.bigcartel.com/ to use the special code!
Visit Artterro Site here and pick out a Kit (under $20.00) that you would like to win!
Leave the name of the kit in my comment section below!!!
Winner will be selected January 31st at 10pm EST.
I like the creativity kit!
My son would love to make bugs with the wool felt bug kit. I love their packaging!
What a great giveaway! I think my daughter would love the Creativity Kit. Thanks for the opportunity Melissa!
My son and I would love the bubble Wand kit!! fun!
my girls would love the Art Doll kit.
I "liked" Artterro on Facebook.
I've been waiting for this giveaway! I know my oldest would love the wool felt wearables kit!!
The art journal for my little artist!
The paint with wool kit would be great for my preschool class.
I would have picked Paint With Wool but after seeing the pictures of your wire creations, I'm awfully tempted.
I like the wire and bead art! Hope my boys would too!
Related note...my kids got the Art Journal Kits for Christmas. We LOVE them and I highly recommend them!
Love the Wire & Bead kit!
So hard to pick, but I think the Bookmaking kit.
I like Artterro on Facebook.
These are very cute! I like the art journals!
Sooooo hard to choose only one of these fabulous kits! I think the creativity kit would have to be it though, since it contains a variety of fun activities.
My daughters would love the Art Dolls kit! I'll have to remember to tell our relatives about these kits for my daughters' birthdays.
They are all wonderful, but I really love the art doll kit!
The Creativity Kit is my favorite!
I love, love, love these kits! I would love the Canvas Storybook kit for my daughters!
We would LOVE the bubble wand kit!
I like the paint with wool. These are adorable and fun!
I love their kits. So creative!
You make the Wire and Bead kit look the MOST fun but they all look fantastic. Thank you for the chance to win a kit! Love your blog.
The felt bug kit looks great for spring. Thanks for the chance to win.
id love the art journal kit.
I love the bookmaking, as well as the creativity kit- it's a tie!


text:
EA/05556/2020 & EA/05553/2020
Promulgation date: 12 Sep 2022
Publication date: 27 Sep 2022
(Immigration and Asylum Chamber) Appeal Number:
UI-2022-001718 (EA/05556/2020)
Heard at Field House
On the 30 August 2022
On the 12 September 2022
UPPER TRIBUNAL JUDGE CANAVAN
MAAME EFUA PESSEH
First Appellant
JEREMIAH FRIMPONG
Second Appellant
For the appellant: Mr J. Dhanji, instructed by
For the respondent: Mr E. Tufan, Senior Home Office Presenting Officer
1. The appellants are citizens of Ghana who appealed the respondent's decision date 29 September 2020 to refuse to issue residence cards recognising a permanent right of residence under EU law. The appeals were brought under regulation 36 of The Immigration (European Economic Area) Regulations 2016 ('the EEA Regulations 2016') on the ground that the decision breached their rights under the EU Treaties in respect of entry into or residence in the United Kingdom.
2. It is not necessary to give detailed reasons for my decision because Mr Tufan accepted on behalf of the respondent that the First-tier Tribunal decision involved the making of an error of law and that on a correct interpretation of the law the decisions should be remade and the appeals allowed. Having discussed the legal framework with the legal representatives at the hearing I was satisfied that this was a correct concession.
3. The appellant's entered the UK on 09 March 2014 with a family permit recognising their right of residence as the direct descendants of an EEA national's spouse (their mother) (regulation 7(1)(b)). On 26 October 2014 they were issued with residence cards recognising the same right of residence, which were valid for five years. Their mother's marriage to the EEA national broke down and I am told that the divorce was finalised on 22 December 2016. On 21 March 2017 their mother was issued with a permanent residence card based on a retained right of residence. The appellants applied for permanent residence on 05 September 2019. The respondent refused the applications in decisions dated 29 September 2020 on the ground that they did not meet the requirements of regulation 10 of the EEA Regulations 2016.
4. First-tier Tribunal Judge Young-Harry ('the judge') dismissed the appeals in a decision promulgated on 18 October 2021. The judge found that it was arguable that the appellants ceased to be family members of the EEA national when their mother divorced in 2016. She concluded that the appellants were not entitled to retain their rights of residence and did not meet the requirements of regulation 10. As such, they were unable to show that they had resided in the UK in accordance with the regulations for a continuous period of five years in order to qualify for permanent residence under regulation 15.
5. At the hearing before the Upper Tribunal the parties were in agreement as to the relevant law. Neither party had been able to find any authority from the European Court of Justice on the point, but Mr Tufan had clear instructions that the point made by Mr Dhanji in his grounds of appeal was correct.
6. Mr Dhanji argued that the wording of Article 13(2) of the Citizens' Directive (2004/38/EC) was not transposed accurately into regulation 10(5). The Article 13(2) states:
'(2) Without prejudice to the second subparagraph, divorce, annulment of marriage or termination of the registered partnership referred to in point 2(b) of Article 2 shall not entail the loss of the right of residence of a Union citizen's family members who are not nationals of a Member State where:
(a) prior to initiation of the divorce or annulment proceedings or termination of the registered partnership referred to in point 2(b) of article 2, the marriage or registered partnership has lasted at least three years, including one year in the host Member State;
Before acquiring the right of permanent residence, the right of residence of the persons concerned shall remain subject to the requirement that they are able to show that they are workers or self-employed persons or that they have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State during their period of residence and have comprehensive sickness insurance cover in the host Member State, or that they are members of the family, already constituted in the host Member State, of a person satisfying these requirements. 'Sufficient resources' shall be defined in Article 8(4).
Such family members shall retain their right of residence exclusively on personal basis.' [emphasis added]
7. It is clear from the use of the plural 'family members' that the retention of a right of residence is not confined to the non-EEA national spouse but also to any other family members who have been recognised as having a right of residence prior to the initiation of divorce proceedings. At the point when their mother retained a right of residence so too did the appellants. The judge erred in finding that they ceased to have a right of residence.
8. At the hearing it was argued that the wording of regulation 10(5) of the EEA Regulations 2016 focussed solely on the non-EEA national whose marriage has come to an end. At the date of the decision regulation 10(5) and (6) stated:
(5) The condition in this paragraph is that the person ("A")—
(a) ceased to be a family member of a qualified person or an EEA national with a right of permanent residence on the initiation of proceedings for the termination of the marriage or civil partnership of A;
(b) was residing in the United Kingdom in accordance with these Regulations at the date of the initiation of proceedings for the termination;
(c) satisfies the condition in paragraph (6); and
(d) either—
(i) prior to the initiation of the proceedings for the termination of the marriage or the civil partnership, the marriage or civil partnership had lasted for at least three years and the parties to the marriage or civil partnership had resided in the United Kingdom for at least one year during its duration;
(6) The condition in this paragraph is that the person—
(a) is not an EEA national but would, if the person were an EEA national, be a worker, a self-employed person or a self-sufficient person under regulation 6; or
(b) is the family member of a person who falls within paragraph (a).' [emphasis added]
9. On a closer reading of regulation 10 there is some provision for family members of the non-EEA national who has retained a right of residence in the wording of regulation 10(6). However, the parties are correct to point out that regulation 10 requires both conditions in sub-paragraphs (5) and (6) to be satisfied. If the appellants had made applications to retain rights of residence alongside their mother it is possible that they could have been dealt with together. As stand alone applications, the appellants could not meet the initial condition of regulation 10(5) because it is focussed on the initiation of divorce proceedings of 'the person' who was married to the EEA national.
10. Mr Tufan accepted that regulation 10 appeared to provide a narrower interpretation of EU law than the Directive. The respondent accepts that EU law has direct effect and is binding. He also accepted that the wider scope of the Directive included family members of the EEA national that could include the direct descendants of the non-EEA spouse who had been recognised as having a right of residence prior to the initiation of divorce proceedings.
11. The residence card applications were made and decided before 31 December 2020, when for legal purposes the UK left the European Union ('IP Completion Day'). Since this appeal is decided after that date the appellants can no longer be issued with permanent residence cards. Mr Tufan said that an application for settlement under domestic law should be made and will be honoured in light of the outcome of this appeal.
12. For the reasons given above, I conclude that the First-tier Tribunal decision involved the making of an error on a point of law. The decision is set aside. The decisions breached the appellants rights under the EU Treaties relating to entry into and residence in the United Kingdom.
The First-tier Tribunal decision involved the making of an error on a point of law
The appeals are ALLOWED under the EEA Regulations 2016
Signed M. Canavan Date 30 August 2022
NOTIFICATION OF APPEAL RIGHTS
1. A person seeking permission to appeal against this decision must make a written application to the Upper Tribunal. Any such application must be received by the Upper Tribunal within the appropriate period after this decision was sent to the person making the application. The appropriate period varies, as follows, according to the location of the individual and the way in which the Upper Tribunal's decision was sent:
2. Where the person who appealed to the First-tier Tribunal is in the United Kingdom at the time that the application for permission to appeal is made, and is not in detention under the Immigration Acts, the appropriate period is 12 working days (10 working days, if the notice of decision is sent electronically).
3. Where the person making the application is in detention under the Immigration Acts, the appropriate period is 7 working days (5 working days, if the notice of decision is sent electronically).
4. Where the person who appealed to the First-tier Tribunal is outside the United Kingdom at the time that the application for permission to appeal is made, the appropriate period is 38 days (10 working days, if the notice of decision is sent electronically).
5. A "working day" means any day except a Saturday or a Sunday, Christmas Day, Good Friday or a bank holiday.
6. The date when the decision is "sent' is that appearing on the covering letter or covering email

redpajama_set_name: RedPajamaCommonCrawl


The brand new GametimeCt New Haven Register Top 10 High School Football Poll has been released and the results are the same.
Darien sits at the top once again.
Here is the Top 10 Poll with this week's opponent.
Don't forget, it's a 2 game Broadcast Week for me and the HS Football Crew.
Plus, you can WATCH both games, with the Audio Play by Play, by going to 960WELI.com, go to On Air, click on High School Sports. Or you can watch them on the 960WELI Facebook Page.
Another edition of my Podcast Show, "Strictly High School" will be taped on Tuesday night and posted. You can listen to any episode of the show by going to 960WELI.com, go to Podcasts, and click on Strictly High School.
Week 7 will be here before you know it - full speed ahead to the finish line!


← CONGRATULATIONS NEW ROCHELLE HS BEST BUDDIES!
SEPTA is New Rochelle's Special Education PTA. SEPTA fosters support for all children in our district that may be facing academic, physical, and/or social challenges. The programs we support certainly help those children with a formal review and defined services– but our involvement extends beyond that and helps any child with any type of a need.
SEPTA communicates, funds, and assists in supporting programs that help children to accept and understand each other.
We understand that it takes a village and SEPTA highlights the actions of those in our community that work to ensure our challenged children are actively included as important, contributing members of our community through our "We Are One" awards dinner. Look for invites in March – it's really the best night in New Rochelle!
If there's an intervention you believe your child may need or a challenge your child is facing, a program you don't understand – please know that you can reach out to SEPTA and we'll offer our resources, knowledge, and energies to help you. It's a great district-wide network and resource.


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text:
\section{\label{sec:Intro}Introduction}

Networks are the underlying principle for countless physical systems and information processing concepts.
Particularly in computing, they support a wide range of powerful algorithms such as Hopfield \cite{Hopfield1982} and neural \cite{McCulloch1943} networks as well as in Ising machines \cite{Utsunomiya2011}.
Especially neural networks have recently resulted in a revolution of modern computing \cite{LeCun2015}.
By now, deep neural networks achieve super-human performance in computational tasks previously deemed un-solvable by computers.
They are now established as indispensable and as the current disruptive computing technology.

A fundamental aspect of neural networks is the propagation of information between nodes along weighted connections, making parallelism essential in neural network computing concepts.
However, our digital computing architectures are serial and spatially separate memory from the location of information transformation.
As each of a neural network's connection-weight corresponds to one value of memory, the ratio between floating point operations (FLOP) and memory access (byte) is fundamentally skewed when compared to classical computing.
As a consequence, high-performance neural network computing is today performed on special-purpose integrated circuits (SAICs) such a graphic processors (GPU) or Google's tensor processing unit (TPU) \cite{Jouppi2017}.

Maximal computing performance can therefore only be achieved if neural networks are fully hardware implemented.
In such systems, the overhead due to serial communication is avoided: each neuron corresponds to a simple nonlinear component, each connection to a direct physical link.
Motivated by the potential benefits, research activity along these lines has lately exploded.
Novel physical components such as lasers \cite{Brunner2013a}, memristors \cite{Tuma2016} and spin-torque oscillators \cite{Torrejon2017} have been shown to serve as excellent analogue neurons.
Simultaneously, mostly optical concepts for parallel networks based on holography \cite{Psaltis1990}, diffraction \cite{Bueno2018,Lin2018}, integrated networks of Mach-Zehnder modulators \cite{Shen2016b} and wavelength division multiplexing \cite{Tait2017} have been demonstrated.
Several review articles summarize various trends inside this area \cite{VanderSande2017,Tanaka2019,Schuman2017,Hasler2013}.

It is equally clear that, besides the potentially large benefits, such parallel and analogue hardware platforms face new, fundamental challenges.
Among the most basic differences to digital circuits, is that the noise of individual components propagates along the network.
Consequently, an important concern is that such systems might ultimately succumb to the detrimental impact of noise, rendering computing impossible.
Regardless of its relevance, no previous study analyses this aspect in detail, but focus on noise propagation in serial analogue circuits \cite{Sarpeshkar1998} and the interaction between noise and learning \cite{Murray1991}.
Here, we study fundamental properties of noise and propagation along connections of networks, considering feed forward neural networks (FNNs) as well as recurrent neural networks (RNNs).
We consider correlated and uncorrelated, multiplicative and additive noise present in individual neurons and use noise amplitudes extracted from a physical experiment \cite{Bueno2018}.
This covers a large range of noise sources possibly encountered in analogue hardware neural networks.
We assume linear neurons in order to exclusively focus on the mixing of noise due to network-connections.
Analytical dependencies of noise propagating are derived, providing a clear understanding of the relevant processes.
Finally, we provide guidelines for hardware architectures and identify the critical points where such systems are most vulnerable.

\section{\label{sec:ANN}Analogue hardware neural networks}

Neural networks can be found in multiple configurations which can be categorized by their connectivity.
 In general, a neuron's internal state $x$ sums input from other neurons according to connectivity weights $\mathbf{W}$.
 The internal state is then mapped onto its output $y'$.
 Figure \ref{fig:one_node}(a) schematically illustrates such a unit, also referred to as a perceptron.
 For neuron $i$, the set of governing equations is
\begin{eqnarray}
x_i =& \sum_{j}^{I} W_{i,j} x_j + b_i, \\ \label{eq:simplNeuron}
y'_i =& f\left( x_i \right). \label{eq:NodeSelectB}
\end{eqnarray}
\noindent In this simple description the number of neurons is $I$, and $b_{i}$ is a constant bias offset.
 As previously mentioned, we will restrict this work to a linear mapping according to $f(x)=\alpha x$.
 Importantly, if the neuron is located in the first layer, then its input $x_j$ is replaced by th system's input signal $u$.

This set of equations forms the basis of our description.
 It will be adopted to different architectures, while neurons will include sources of noise.
 Typically, we normalize connection matrices to their largest eigenvalue, which (i) maintains the signal amplitude for FNNs, or (ii) makes RNNs more comparable to FNNs.
 In FNNs, connections $\mathbf{W}$ are established in a cascaded manner, connecting the neurons of a layer to the neurons of a previous layers.
 In RNNs, connections $\mathbf{W}$ of a hidden layer establish connections between neurons from the same layer.
 This introduces a temporal context in the RNNs state, and such systems feature short term memory and can be employed to process temporal information \cite{Jaeger2002ShortNetworks}.

In addition, we restrict our treatment to connection matrices with purely positive connections.
 This was (i) motivated by our hardware-system, and (ii) corresponds to a restriction commonly found in optical networks \cite{Psaltis1990}.
 Finally we only utilize single neurons in the first (input) and final (output) layer.

\subsection{\label{sec:ANN_noise}Different sources of noise}

For simplicity we start by considering sources and the impact of noise upon a single neuron.
 A schematic illustration of the relevant processes are shown in Fig.~\ref{fig:one_node}(a).
 After a neuron's internal state $x$ has been mapped onto its noiseless output $y'$ according to Eq. (\ref{eq:NodeSelectB}), the signal becomes perturbed by noise operator $\mathbf{\hat{N}}$:
\begin{equation}\label{eq:one_neuron}
y=y'+\mathbf{\hat{N}}(y').
\end{equation}
\noindent  We focus on two noise families, see Fig. \ref{fig:one_node}(b).
 For additive noise, operator $\mathbf{\hat{N}}$ does not depend on incoming signal $y'$, i.e. has properties and characteristics independent of the neuron's internal state.
 If, however, noise is multiplicative, then operator $\mathbf{\hat{N}}$ depends on $y'$ and hence on $x$.

\begin{figure}[t]
\center{\includegraphics[width=1\linewidth]{one_node.pdf}}
\caption[]{Schematic diagram showing the signal propagation through one noisy neuron.}
\label{fig:one_node}
\end{figure}

In this work we consider only white Gaussian noise sources according to:
\begin{equation}
\begin{array}{l}
\text{additive noise: } \mathbf{\hat{N}}(y')=\sqrt{2D_A}\xi_A \nonumber\\
\text{multiplicative noise: } \mathbf{\hat{N}}(y')=y'\cdot\sqrt{2D_M}\xi_M,
\end{array}
\end{equation}
where $\xi_A$ and $\xi_M$ are sources of white Gaussian noise with zero expectation value and a variances of 1.
 The variance of the noise operator is controlled by noise intensities $D_A$ and $D_M$.

In our description, each $\xi$ value can depend on four indexes: (i) - time $t\in[1,T]$ ($T$ is the length of the input sequence), (ii) - repetition number $k\in[1,K]$ (needed for SNR calculation), (iii) - layer number $n\in [1, N]$ and (iv) - a neuron's index $i\in [1,I_n]$ in a layer $n$.
 At this stage we need to contemplate about the potential impact typical hardware circuitry can impose.
 Most fundamentally speaking, component (neuron) internal processes will be locally unique and hence result in noise which is different for each neuron at each instant in time.
 The describing term depends on each index $t,k,n,i$ and hence we refer to this type as \textit{uncorrelated noise}.
 A schematic circuit noise-model for uncorrelated noise is illustrated in Fig. \ref{fig:one_node}(b).
 In the present work we denote uncorrelated noise by the letter $'U'$.
 Uncorrelated additive noise, for example, is governed by $\xi^U_A=\xi^U_A(t,k,n,i)$ with $D^U_A$ as its noise intensity.

Another feature commonly encountered in hardware circuits is that a few elements impact / control the overall circuit's state.
 A simple example would be a circuit's supply voltage or its temperature.
 Noise in such central components will perturb large fractions of the circuit in a comparable manner.
 In our considerations such noise is the same inside one layer and therefore only depends on time $t$, number of repetition $k$ and the layer's number $n$.
 It is therefore correlated across neuron populations, and \textit{correlated noise} is denoted by the letter $'C'$.
 A schematic circuit noise-model for correlated noise is illustrated in Fig. \ref{fig:one_node}(b).
 Correlated additive noise, for example, is governed by $\xi^C_A=\xi^C_A(t,k,n)$ with $D^C_A$ as its corresponding noise intensity.

Each noisy neuron can therefore exhibit four different types of noise: correlated additive $\xi^C_A$ and correlated multiplicative $\xi^C_M$, as well as uncorrelated additive $\xi^U_A$ and uncorrelated multiplicative $\xi^U_M$.
 In the presence of both types of noise the output signal emitted by a single neuron at time $t$ is
\begin{equation}\label{eq:one_neuron_noise}
\begin{array}{c}
y^t_{n,i}=y'^t_{n,i}\cdot\big( 1+\sqrt{2D^U_M}\xi^U_{M n,i}\big)\big( 1+\sqrt{2D^C_{M}}\xi^C_{Mn}\big) + \\
\sqrt{2D^U_A}\xi^U_{An,i}+\sqrt{2D^C_A}\xi^C_{An},
\end{array}
\end{equation}
\noindent Crucially, the introduced four noise classes were motivated by findings during the careful characterization of our experiment \cite{Bueno2018}.
 We found that the different components exhibit and induce different noise characteristics.
 The camera, for example, mostly contributed uncorrelated multiplicative noise, which we attributed to timing-jitter in the device's clock.
 The illuminating laser, on the other hand, influences all neuron-states simultaneously and results in correlated multiplicative noise.
 The same type of noise is induced by the spatial light modulator, and importantly it is of significantly larger intensity and hence dominates over the laser's contribution.
 The SLM also contributed uncorrelated, additive noise, and so does the system's readout-detector.
 We have characterized each of these sources individually and in detail.
 Noise intensities used on the following are based upon the values we obtained.

\subsection{\label{sec:ANN_SNR}Signal to noise ratio}

To quantify the corruption of a signal by noise, we employ the signal-to-noise ratio (SNR)
\begin{equation}\label{eq:SNR_general}
\text{SNR}(y^t)=\frac{E(y^t)}{\sigma(y^t)},
\end{equation}
 where $y$ is the noisy signal, $E(\cdot)$ and $\sigma(\cdot)$ are the signal's mean value and standard deviation, respectively.

There are many other well-known method for noise analysis, for example autocorrelation, cross-correlation and consistency based analysis.
 However in the present article, we (i) know the temporal characteristics of the noise-sources, and (ii) are more interested in signal amplitude-related effects which enable a first interpretation of results with respect to a system with nonlinear neurons.
 We therefore break the overall SNR down into its values at different amplitudes $E(y)$.
 This allows to associate system performance to potential modifications by nonlinearities.
 It furthermore illustrates the importance of exploiting a hardware system's entire dynamical amplitude range.

We follow that strategy and procedure for characterizing deep FNNs as well as RNNs.
 The network's input signal at time $t$ is $u^t$, leading to network output $y^t$.
 We repeat the same input sequence $u^t$ for several repetitions $k\in[ 1, K]$ and obtain the sequence of the output values $y^t_k$.
 We average the obtained sequence across all $k$s and obtain the mean-response $E(y^t)=1/K\sum^K_{k=1}y^t_k$.
 The standard deviation of sequence $\sigma(y^t_k)$ is obtained following the same strategy.

\begin{figure}[tbp]
	\center{\includegraphics[width=1\linewidth]{one_node_noise.pdf}}
	\caption[]{Signal-to-noise ratio for one neuron in the case of only additive noise (blue points) with intensity $D^U_A=10^{-4}$, only multiplicative noise (green points) with intensity $D^U_M=10^{-3}$ and mixed noise (orange points) with both types of noise of the same intensities. Parameters: $\alpha=1$, $b=0.02$.}
	\label{fig:SNR_one_node}
\end{figure}

We first consider the impact of additive and multiplicative noise ($D^U_A=10^{-4}, D^U_M=10^{-3}$) on the SNR of a single neuron.
 Figure \ref{fig:SNR_one_node} shows the SNR depending on the mean output values $E(y^{t})$ for the cases of only additive (blue points), only multiplicative (geen points), as well as a combination of both noise types, hence mixed noise (orange points).

A single-neuron's SNR has features which form the basis for interpreting more complex systems.
 Due to the zero expectation value for the input signal and all noise sources, the mean value of the neuron's output is $E(y^t)=f(x)=u^t$.
 As derived in Appendix~\ref{sec:Appendix_A}, the variance of the noisy output sequence is $\text{Var}(y^t)=\sigma^2(y^t)\approx 2D^U_A+2D^U_M f(x)^2$, leading to $\text{SNR}(y^t)=E(y^t)/\sqrt{2D^U_A+2D^U_M (E(y^t))^2}$.
 For the case of only multiplicative noise this simplifies to $ \text{SNR}(y^t)=1/\sqrt{2D^U_M}$, which is constant for each output signal.
 As shown by the green data in Fig.~\ref{fig:SNR_one_node}, noise output signal level increase both linearly and the SNR is constant.
 For the case of additive noise only, the SNR becomes $ \text{SNR}(y^t)=E(y^t)/\sqrt{2D^U_A}$, and the SNR of additive noise therefore increases linearly with $E(y^t)$ according to slope $1/\sqrt{2D^U_A}$, see blue data in Fig.~\ref{fig:SNR_one_node}.
 Finally, the SNR for mixed noise combines both features.
 For small output values it coincides with the SNR for additive noise, while for larger output values the SNR is limited by the constant SNR of multiplicative noise.

Before we can apply the single neuron nomenclature to networks, we need to introduce a final tool.
 Each node of an artificial neural network can exhibit some bias $b$.
 In particular for the here considered linear system with only uni-polar (positive) connection weights, this bias can accumulate during its propagation through network layers, creating a constant output signal offset.
 For deep FNNs, this offset increases with the number of layers.
 According to unfolding in time \cite{Williams1989}, a RNN can be mapped onto a FNN, linking the strength of a RNN's internal coupling too the depth of a corresponding FNN.
 Similar offset accumulation is therefore found when increasing a RNN's internal connection strengths.
 This offset is constant and does therefore not contribute to information processing, yet it would increase $E(y^t)$ and hence induce artefacts in $\text{SNR}(y^t)$.
 We calculate the system's response without noise on a zero-input signal $0$, and by that isolate the contribution of the constant biases.
 We refer to this value as the \textit{shifting constant} $C$, which needs to be subtracted from each output value before calculating the SNR.
 We are able to analytically describe this step for FNNs and RNNs and hence maintain the generality of our analysis.

\section{\label{sec:FNN}Noise in deep feed-forward networks}

\begin{figure}[tbp]
\center{\includegraphics[width=.8\linewidth]{FNN_scheme.pdf}}
\caption[]{Schematic representation of a simple feed-forward neural network (FNN) consisting of $N=4$ layers.
	The central two layers are referred to as hidden layers, which each hosts $I_2=I_3=200$ neurons.
	The first and final layers consist of single neurons, $I_1=I_4=1$.}
\label{fig:FNN_scheme}
\end{figure}

We consider the FNN schematically illustrated in Fig.~\ref{fig:FNN_scheme}.
 The network consists of four layers, with one neuron in the first and last layer $I_1=I_4=1$, and $I_2=I_3=200$ neurons in the two hidden layers. The neuron in the first layer is connected to the system's input $u^t$.

 The system's evolution is governed by
\begin{eqnarray}
x^t_{n,i} =& \sum_{j=1}^{I_{n-1}} W^n_{i,j} y^t_{n-1,j} + b_i, \\ \label{eq:NeuronFNN}
y'^t_{n,i} =& f\left( x^t_i \right), \label{eq:NodeOutFNN}
\end{eqnarray}
\noindent and the structure of Eq. \ref{eq:NeuronFNN} connects neurons of layer $n$ exclusively to neurons in layer $n-1$.
 For generality, we focus on global coupling between each layer with equal weights.
 The impact of inter-layer connectivity is discussed in Section \ref{sec:depth}.
 The connections from layer $n-1$ to layer $n$ is determined by matrix $\mathbf{W}^n$ of size $I_{n-1}\times I_n$ and for global coupling $W^n_{i,j}=1/I_{n-1}$.
 For sake of clarity we label $\mathbf{W}^2$ and $\mathbf{W}^N$ as input $\mathbf{W}^{\rm in}$ and output $\mathbf{W}^{\rm out}$ matrices, respectively.

For a FNN with such a topology, the shifting constant in the last layer is
\begin{equation}\label{eq:shift_const}
C_4=b+\alpha(b+\alpha(b+(0+b)))=b(1+2\alpha^2) + \alpha b,
\end{equation}
\noindent where $(0+b)$ is the signal coming from the first layer, and transformations $\alpha(b+\cdots)$ are made in each hidden layer.
 For the more general case of an unknown number of layers $N\ge 4$, the shifting constant is
\begin{equation}\label{eq:shift_const_general}
C_N=b(1+2\alpha^{N-2}) + b\sum\limits_{j=1}^{N-3}\alpha^j.
\end{equation}

\subsection{Correlated and uncorrelated noise}\label{sec:FNN_corr_uncorr_noise}

Within our framework, the state of each noisy neuron inside a hidden layer of a FNN exhibits two multiplicative and two additive noise sources, see Eq. (\ref{eq:one_neuron_noise}).
 Figure \ref{fig:FNN_corr_uncorr_noise} shows the numerically obtained SNR for exclusively uncorrelated noise in panel (a), and for exclusively correlated noise in panel (b).
 Both panels are identically scaled, and the detrimental impact of correlated noise compared to uncorrelated noise is clearly visible.
 However, corresponding dependencies do not differ qualitatively.
 Furthermore, there is little quailitative difference between a single node perturbed by noise, Fig. \ref{fig:SNR_one_node}, and a FNN's output, Fig. \ref{fig:FNN_corr_uncorr_noise}.
 From this comparison, we can conclude that additive, multiplicative and mixed noises have a very comparable effect on a FNN's and on a single noise neuron's output signal.
 The only notable difference is the contribution of multiplicative noise for small $E(y^t)$ values, which is due to shifting constant $C_4$.

In general, the overall SNR is reduced by the network.
 However, the accumulation of noise is very little: a single noisy neuron has less than twice the SNR compared to the collective of over 400 noisy neurons.
 In particular for the case of uncorrelated noise the reduction in SNR is moderate.

\begin{figure}[tbp]
\center{\includegraphics[width=1\linewidth]{FNN_noise.pdf}}
\caption{SNR dependences for uncorrelated noise (a) and correlated noise (b). Blue points correspond to only additive noise of intensity $D^U_A=D^C_A=10^{-4}$, green points indicate to only multiplicative noise with intensities $D^U_M=D^C_M=10^{-3}$, orange points match mixed noise with combination of both noise intensities. Parameters: $\alpha=1$, $b=0.02$.}\label{fig:FNN_corr_uncorr_noise}
\end{figure}

As the connection between the FNN layers is global, each neuron is driven by an averaged-state of the previous layer, a mean-field so to speak.
 This is where a network inherently aids keeping the influence of noise in check.
 Uncorrelated noise is different for each neuron of a preceding layer, and the influence of these different, uncorrelated noise-terms is efficiently averaged out by the network's connections.
 For correlated noise the situation is different.
 This term is identical for all neurons in preceding layers, averaging cannot curb the propagation of correlated noise.
 This is an essential insight: in analogue neural networks an optimal network connectivity does not only address best the task it is proposed to solve, but also will depend on the network's very own noise properties.

Similar considerations also highlight the importance of neurons located in the first and last layers.
 The first layer spreads its noise across the entire system, and hence induces an additional form of correlated noise.
 The system's output, on the other hand, is the position where the computational results is presented to the outside world, and no averaging by network-connections is suppressing suppressing its uncorrelated noise.

\subsection{Signal to noise ratio}\label{sec:FNN_analytics}

The previous line of argument can be formulated analytically.
 Here we focus on the main results, the full derivation is given in Appendix~\ref{sec:Appendix_A}.

The mean value and variance of the the first layer are
\begin{eqnarray}
E(y^t_1)= E(y'^t_1)= u^t+b, \\\label{eq:FNN_mu_1}
\text{Var}(y^t_1)= \sigma^2_{add}+E^2(y^t_1)\cdot\sigma^2_{mult},\label{eq:FNN_var_1}
\end{eqnarray}
with $\sigma^2_{add}$ is the combined perturbation due to additive noise $\sigma^2_{add}=2D^U_A+2D^C_A$, and for multiplicative noise $\sigma^2_{mult}=2D^U_M+2D^C_M+4D^C_M D^U_M$.

Due to the here imposed symmetric topology, we find that
\begin{equation}\label{eq:FNN_mu_n}
E(y^t_{n,i})=E(y'^t_{n,i})=E(y'^t_n)=\alpha(E(y'^t_{n-1})+b)
\end{equation}
This formula is valid for any hidden layer.
 The variable $y'^t_n$ does not contain the noise of $n$th layer but has all the noise from previous layers.
 The corresponding variance can be approximated according to
\begin{equation}\label{eq:FNN_var_n}
\begin{array}{c}
 \text{Var}(y'^t_n) \approx \alpha^2 \big[ 2D^C_A + 2D^C_M E^2(y'^t_{n-1}) +\\
(1+2D^C_M) \text{Var}(y'^t_{n-1}) \big] , \ \ 2<n<N.
\end{array}
\end{equation}
\noindent Equation (\ref{eq:FNN_var_n}) is used until $n=2$.
 The variance for the 2nd layer is $ \text{Var}(y'^t_{2,n})=\alpha^2  \text{Var}(y^t_1)$.
 Equations (\ref{eq:FNN_mu_n}) and (\ref{eq:FNN_var_n}) are recursively defined in function of the network's depth.
 From these relationships it becomes clear that the variance of hidden layers does not contain uncorrelated noise-contributions originating from the previous hidden layers.

Finally, the $N$th layer mean signal and variance, hence of the output signal are
\begin{eqnarray}
E(y^t_N)= E(y^t_{N-1})+b \\\label{eq:FNN_mu_N}
\begin{array}{c}
\text{Var}(y^t_N) \approx \sigma^2_{add}+E^2(y^t_N)\cdot\sigma^2_{mult} + \\
(1+\sigma^2_{mult})\cdot \text{Var}(y'^t_N).\label{eq:FNN_var_N}
\end{array}
\end{eqnarray}
Equations (\ref{eq:FNN_var_1}) and (\ref{eq:FNN_var_N}) confirm that the first and last layer add both, correlated and uncorrelated noise to the output signal.

Based on these considerations, we arrive at the system's final SNR
\begin{equation}\label{eq:FNN_SNR_N}
\text{SNR}(y^t_N)=\frac{E(y^t_N)}{\big(\text{Var}(y^t_N)\big)^{1/2}},
\end{equation}
\noindent which only requires knowledge of individual component's noise properties.
 Figure \ref{fig:FNN_corr_uncorr_noise} shows analytically derived dependencies as dashed lines.
 The agreement between the numerical simulation and the analytical description is excellent.
 The noise of hardware neurons inside a network can be characterized in model systems, while the properties of input as well as the desired output signals are typically known for most tasks.
 The here derived analytical description is therefore of important predictive value for estimating hardware-linked performance limits in future analogue neural networks.

\section{Noise in recurrent networks\label{sec:RNN}}

Following the previously developed techniques, we now turn to propagation of noise through RNNs.
 Figure \ref{fig:RNN_scheme_realization}(a) shows the general scheme of such a network.
 In our case, the network contains one input and one output neuron (orange circles), while the single hidden layer hosts $I_{2}=200$ neurons.
 As for the case of the feed-forward network, the additional bias constant acts for all network nodes.
 The evolution of neurons in the hidden-layer is given by
\begin{equation}\label{eq:RNN_network}
y'^{t+1}_{2,i}=f\big( \gamma\mathbf{W}^{\rm in} y^{t+1}_1  + \beta\mathbf{W} \mathbf{y}^t_2 + b \big),
\end{equation}
\noindent The output signal of our RNN is
\begin{equation}\label{eq:RNN_yout}
y'^{t+1}_3=\mathbf{W}^{\rm out} \mathbf{y}^{t+1}_2 + b.
\end{equation}
\noindent Matrices $\mathbf{W}^{\rm in}$ and $\mathbf{W}^{\rm out}$ define  the connections between the hidden layer to the input and output neurons, respectively.
 In contrast to FNNs, the system's state does not only depend on input signal $u^{t+1}$, but also on the hidden layer's state at previous times according to $\mathbf{W}$ in Eq. \ref{eq:RNN_network}.
 There is only one recurrent layer, so the index $n$ is not used for RNN.
 Parameters $\beta$ and $\gamma$ can be interpreted as balancing coefficient between the system's previous state $x^{t}$ or the current input signal $u^{t+1}$.
 If $\beta=0$ and $\gamma=1$ the network has a FNN topology with a single hidden layer.
 For $\gamma=\beta=0.5$ the input signal and the recurrent signal have equal force.

\begin{figure}[tbp]
\center{\includegraphics[width=1\linewidth]{RNN_scheme.pdf}}
\caption[]{Schematic representation of simple recurrent neural network (1) consisting of input and output neurons (orange circles) and hidden (recurrent) layer (gray circles) of $I_2=200$ nodes. The panel (b) illustrates the output signal for $\gamma=0.5$, $\beta=0.9$. The panel (c) depicts shifts of output signal range (gray points) and focusing mean value (red line). The coupling is global, $\alpha=1$, $b=0.02$.}
\label{fig:RNN_scheme_realization}
\end{figure}

As in FNNs, it is important to consider the impact of constant signal accumulation in an RNN.
 However, the interplay between recurrence and input signal leads to a nonlinear modification of an RNN's output signal.
 As the nodes are linear and we normalized all matrices to their largest eigenvalue, a FNN's output range depends only on the input signal's range.
 In a RNN, this limit is fundamentally harder to obtain.
 Figure \ref{fig:RNN_scheme_realization}(b) shows a RNN's output signal for $\alpha=1$, $\beta=0.9$ and $\gamma=0.5$, indicating the problem's temporal sensitivity via a short initial transient.
 After this transient, the network's signal is dispersed around some mean value.
 However, due to the recurrence output range depends not only on the input signals amplitude range, but also on its temporal characteristic.
 As before, we drive the system with a random signal uniformly distributed within interval $u^{t}\in(0,\cdots,1)$.
 Figure \ref{fig:RNN_scheme_realization}(c) shows the mean output signal as a red line for different strength of the network internal coupling $\beta$.

As expected, for $\beta$ approaching 1 the system destabilizes, and the offset quickly diverges towards infinity (with its pole at $\beta=1$).
 In a nonlinear system, this is the point were chaos due to sensitivity to initial conditions would start to arise.
 However, as we lack nonlinearity, resulting dynamics are not bound through nonlinear stretching and folding.
 However, we can approximate the amplitude-range of the output if the input signal is known. The mean value of the output signal $E(y^t_3)$ can be found for each time $t$.
\begin{equation}\label{eq:RNN_mu_y}
\begin{array}{c}
E(y^t_3) = E(y'^t_2)+b, \ \ \ \text{where} \\
E(y'^t_2) = \alpha\Big( \gamma(u^t+b) + \beta E(y'^{t-1}_2) +b \Big).
\end{array}
\end{equation}
The full technique is given in Appendix B. Based on this technique, we obtain:
\begin{equation}
\begin{array}{c}\label{eq:RNN_range}
y_{min}=min\big( E(y^t_3) \big) \\
y_{max}=max\big( E(y^t_3) \big).
\end{array}
\end{equation}
They will be employed for normalizing output signal $y^t_3$ in order to keep it within the range $y^t_3\in(0,\cdots,1)$.

\subsection{Correlated and uncorrelated noise}

Figure \ref{fig:RNN_SNR}(a) and (b) show the SNR for $\beta=\gamma=0.5$ for exclusively uncorrelated and correlated noise, respectively.
 Noise intensities are identical to the once of the FNN-section, and the resulting SNR has overall similar properties and scale as the one found for the 4-layer FNN.
 Again, correlated noise significantly reduces the system's performance when compared to uncorrelated noise, which indicates that the temporal averaging in an RNN suppresses uncorrelated noise in a similar fashion as in deep FNNs.

Increasing $\beta$ confirms this general observation, see Fig. \ref{fig:RNN_SNR}(a) and (d) for exclusively uncorrelated and correlated noise at for $\beta=0.9$ and $\gamma=0.5$, respectively.
 The increased contribution of the recurrent signal has multiple consequences.
 On one hand $\beta$ improves the additive SNR, but then on the other hand significantly reduces the multiplicative SNR.
 Ultimately, the output's SNR is dominated by the latter contribution, and hence increasing $\beta$ increases the RNN's susceptibility to noisy neurons.

\begin{figure}[htbp]
\center{\includegraphics[width=1\linewidth]{RNN_noise.pdf}}
\caption[]{SNR dependences for uncorrelated noise (left panels) and correlated noise (right panels). Blue points correspond to only additive noise of intensity $D^U_A=D^C_A=10^{-4}$, green points indicate to only multiplicative noise with intensities $D^U_M=D^C_M=10^{-3}$, orange points match mixed noise with combination of both noise intensities. Top panels were prepared for $\beta=0.5$, bottom panels correspond to $\beta=0.9$. Other parameters are: $\gamma=0.5$, $I_2=200$, $\alpha=1$.}
\label{fig:RNN_SNR}
\end{figure}

\subsection{\label{sec:RNN_analytics}Noise in recurrent networks}

Here, we face the same challenge as when deriving the RNN's output amplitude range: the analytical SNR description requires some knowledge of the input signal's temporal nature.
 As before we will focus on the final form of the equations; the complete derivation can be found in Appendix \ref{sec:Appendix_B}.

For a noisy RNN, the mean value is (\ref{eq:RNN_mu_y}). The noise-induced variance of its output signal is given by
\begin{equation}\label{eq:RNN_var_y}
\begin{array}{l}
 \text{Var}(y^t_3) = \sigma^2_{add} + \sigma^2_{mult} E^2(y^t_3) + (1+\sigma^2_{mult})\times \\
 \big[ 2D^C_A + 2D^C_M E^2(y'^t_2) + (1+2D^C_M)  \text{Var}(y'^t_2)  \big].
\end{array}
\end{equation}
\noindent Variables $\sigma^2_{add}$ and $\sigma^2_{mult}$ are identical to the once previously introduced in Sec.~\ref{sec:FNN_analytics}.
 Furthermore, $y'^t_2=y'^t_{2,i}$ contains the averaged signal passed on from the recurrent layer of previous time ($t-1$) to the output neuron for the case of global coupling.
 Its variance is
 \begin{equation}\label{eq:RNN_y2_var}
\begin{array}{c}
 \text{Var}(y'^t_2)\approx \alpha^2\gamma^2  \text{Var}(y^t_1) + \alpha^2\beta^2 \big[ 2D^C_A + \\
2D^C_M E^2(y'^{t-1}_2) + (1+2D^C_M)  \text{Var}(y'^{t-1}_2)  \big].
\end{array}
\end{equation}
with mean value
\begin{equation}\label{eq:RNN_y2_mean}
E(y'^t_2)=E(y^t_{2,i}) = \alpha \big( \gamma E(y^t_1) + \beta E(y'^{t-1}_2) +b  \big) \\
\end{equation}
Again the uncorrelated noise comes only from the input and output neurons.
 The nodes from the recurrent layer transmit only their correlated noise. It means that, as with FNN, the main noise effect comes from the input and output neuron.
 Equations (\ref{eq:RNN_mu_y})--(\ref{eq:RNN_y2_mean}) demonstrate good correspondence with the numerical simulation (Fig.~\ref{fig:RNN_SNR} black points).

\section{\label{sec:coupling}Noise propagation versus connectivity}

Previously we considered networks were connectivity in all matrices was 100$~\%$ and uniform.
This enabled a clean derivation of analytical models, however, it does not correspond to typical topology-statistics of neural networks.
In the following sections we will replace the fully connected matrices by matrices consisting of random entries and with a certain fraction of non-zero connections, i.e. connectivity.

\subsection{Connectivity in FNNs}\label{sec:FNN_coupling}

We will again focus on the case of a deep FNN with a single input and output neuron, $I_1=I_4=1$, and hosting with $I_2=I_3=200$ neurons in the hidden layers.
Matrices $\mathbf{W}^{in}\in\mathbb{R}^{1\times I_2}$ and $\mathbf{W}^{out}\in\mathbb{R}^{I_3\times 1}$ determine the system's connection to the in and output, respectively.
Coupling between hidden layers is given by $\mathbf{W}^{\rm 3}\in\mathbb{R}^{I_2\times I_3}$.
All matrices have a percentage of $\rho$ non-zero entries, which are drawn from a random distribution.
Finally, matrices are normalized to their largest eigenvalue.
For $\rho=100~\%$ we would again obtain global coupling, however now according to random weight distributions.

Figure \ref{fig:FNN_coupling_hidden} shows the SNR for uncorrelated and correlated noise in panels (a) and (b).
The orange (blue) data have been obtained using $\rho=1~\%$ ($\rho=100~\%$) connectivity of $\mathbf{W}^{\rm 3}$, i.e. between the two hidden layers, while $\mathbf{W}^{\rm 2}$ and $\mathbf{W}^{\rm 4}$ were fully connected.
The dashed line was obtained based on the analytical SNR description based on Eqs. (\ref{eq:FNN_mu_N})-(\ref{eq:FNN_SNR_N}), crucially dervide under the assumption of symmetric and full connectivity.
From the data it is clear that the SNR's dependency on the connectivity between both hidden layers is very weak.
Furthermore, for correlated as well as uncorrelated noise the analytical SNR description perfectly agrees with the numerically obtained data.
This leads to an interesting conclusion: attenuation of uncorrelated noise is already established by averaging tue to input and readout matrices $\mathbf{W}^{\rm 2}$ and $\mathbf{W}^{\rm 4}$.

\begin{figure}[h]
\center{\includegraphics[width=1\linewidth]{FNN_hidden_connection.pdf}}
\caption{Signal-to-noise ratio in the last layer of FNN for the case with multiplicative correlated noise of intensity $D^C_M=10^{-3}$ (b) and without it (a). Other parameters are $D^U_A=10^{-4}$, $D^U_M=10^{-3}$. Blue points correspond 100\% connection and orange ones to 1\% connection between hidden layers. Both dependences are almost the same.}\label{fig:FNN_coupling_hidden}
\end{figure}

For this reason, we now turn our attention to the SNR's dependency upon the readout connectivity.
The corresponding SNR, see Fig.~\ref{fig:FNN_coupling_out} was obtained for $\rho=1~\%$ of $\mathbf{W}^{\rm 3}$ and $\rho=100~\%$ of $\mathbf{W}^{in}$, while orange (blue) data corresponds to $\rho=1~\%$ ($\rho=100~\%$) connectivity for $\mathbf{W}^{out}$, respectively.
Only in the case of a final layer connectivity of $\rho=1~\%$ we obtain a reduction of the SNR-function for uncorrelated noise, hence a reduced suppression of such.
Such a low final layer connectivity is unlikely for most applications.

\begin{figure}[h]
\center{\includegraphics[width=1\linewidth]{FNN_out_connection.pdf}}
\caption{Signal-to-noise ratio in the last layer of FNN for the case with multiplicative correlated noise with intensity $D^C_M=10^{-3}$ (b) and without it (a). Other parameters are $D^U_A=10^{-4}$, $D^U_M=10^{-3}$. Blue points correspond 100\% connection and orange ones to 1\% connection in the output matrix $\mathbf{W}^{\rm out}$. The matrix between hidden layers has 1\% connection.}\label{fig:FNN_coupling_out}
\end{figure}

\subsection{Coupling in RNN}\label{sec:RNN_coupling}

Guided by the previous FNN-results we can immediately focus on the connectivity of the RNN's readout layer.
Crucially, we have confirmed that, as for the FNN, $\rho$ of the RNN's hidden layer $\mathbf{W}^{out}$ has negligible impact upon the system's SNR.
However, there is a fundamental difference when discussing the RNN's connectivity.
Besides the percentage of non-zero connections $\rho$, parameter $\beta$ greatly influences the system's sensitivity as well as its connection topology, and is therefore included in our considerations.

For each noise-type and final layer connectivity we investigate two $\beta$-values.
In Fig.~\ref{fig:RNN_coupling_out} we show the SNR for $\beta=0.5$ and final layer connectivity $\rho=1~\%$ ($\rho=100~\%$) as orange (blue) data.
Data for $\beta=0.9$ and final layer connectivity $\rho=1~\%$ ($\rho=100~\%$) is shown in gray (green).
For uncorrelated noise, panel (a), we find that for both, connectivity as well as $\beta$ have a strong impact.
Again, higher connectivity suppresses propagation of uncorrelated noise, while larger $\beta$'s increase the system's sensitivity.
As expected, we find very little impact of the final layer's connectivity upon the suppression of correlated noise for $\beta=0.5$.
For $\beta=0.9$ we find that connectivity has no positive effect upon correlated noise suppression; a $\rho$ of the final layer beyond $\sim10~\%$ is sufficient for that purpose.

\begin{figure}[h]
\center{\includegraphics[width=1\linewidth]{RNN_out_connection.pdf}}
\caption{Signal-to-noise ratio in RNN for the case with multiplicative correlated noise with intensity $D^C_M=10^{-3}$ (b) and without it (a). Other parameters are $D^U_A=10^{-4}$, $D^U_M=10^{-3}$. Blue points ($\beta=0.5$) and green points ($\beta=0.9$) correspond 100\% connection and orange ($\beta=0.5$) and gray ($\beta=0.9$) ones are for 1\% connection in the output matrix $\mathbf{W}^{\rm out}$. The connectivity of the hidden (input) layer is 1~$\%$ (100~$\%$).}\label{fig:RNN_coupling_out}
\end{figure}

\begin{figure}[h]
\center{\includegraphics[width=1\linewidth]{RNN_SNR_ratio_connection.pdf}}
\caption{SNR ratio for RNN. SNR dependences are normalized to SNR for corresponding $\beta$ and nose intensities but for global coupling in all the matrices.}\label{fig:RNN_SNR_ratio_conn}
\end{figure}

\section{\label{sec:depth} Impact of depth}

The final topological consideration in our work will be the impact of a FNN's and RNN's depth upon the SNR.
 The feed-forward network in the simplest case has only one hidden layer ($N=3$), and its SNR for exclusively uncorrelated noise ($D^U_M=10^{-3}$, $D^U_A=10^{-4}$) will serve as the reference for deeper FNNs.
 Figure~\ref{fig:depth}(a) illustrates the SNR's dependency upon the number of layers for five cases: without correlated noise (black data), with additive correlated noise (light red ($D^C_A=10^{-4}$) and light blue ($D^C_A=10^{-3}$) data) and with multiplicative correlated noise (dark red ($D^C_M=10^{-4}$) data and dark blue ($D^C_M=10^{-3}$) data).
 In general, the FNN is more resilient against multiplicative noise, and while the FNN's depth certainly has an impact, it requires approximately 20 layers for the SNR to be reduced to half of the single hidden layer system.

\begin{figure}[tbp]
\center{\includegraphics[width=1\linewidth]{FNN_RNN_depth.pdf}}
	\caption{SNR ratio for different number of layers in FNN (a) and different recurrency impact $\beta$ in RNN (b). The color scheme is the same for both panels. Black lines correspond to the case without correlated noise. Other lines correspond to different correlated noise intensities: dark blue -- $D^C_M=10^{-4}$, dark red -- $D^C_M=10^{-3}$, light blue -- $D^C_A=10^{-4}$, light red -- $D^C_A=10^{-3}$. Fixed parameters are $D^U_A=10^{-4}$, $D^C_M=10^{-4}$, $D^U_M=10^{-3}$, $\alpha=1$, $b=0.02$. }\label{fig:depth}
\end{figure}

Figure~\ref{fig:depth}(b) illustrates the RNN's dependency upon its internal coupling strength $\beta$ for the same five configurations of noise.
 The SNR reference was obtained for the case without correlated noise and $\beta=0$, black data.
 As mentioned before, the internal coupling strength can be linked to the depth of a corresponding mapping of the RNN upon an FNN via the unfolding in time technique.
 For $\beta=1$ the depth of such a system becomes infinity, and it is hence not surprising that for this case the SNR drops to zero for all noise-configurations.
 Here we would like to point out a difference we expect for the case of nonlinear RNNs.
 For $\beta>1$ the nonlinearity results in characteristic dynamical regimes, and for the case of periodic orbits we expect that the system will still preserve a large degree of its noise-resilience \cite{Marquez2018}.
 Apart from the SNR when approaching the critical value of $\beta=1$ we find that the system has an ideal operational point for maximum noise mitigation.
 The particular value of the optimal $\beta$ depends on the type and amplitude of noise.

\section{\label{sec:Startegies}Strategies for noise mitigation}

In the previous sections we have continuously encountered two essential aspects of a analogue neural networks sensitivity to noise.
 The first is that uncorrelated noise can efficiently be suppressed through averaging by the numerous network's connections.
 And second is that the global SNR dependencies of FNN's and RNN's share strong similarities.
 We will now use these features for devising first strategies for boosting neural network noise mitigation.

The first argument in the previous paragraph leads the way to an intuitive strategy.
 The fact that the first layer neuron acts as drive for all other neurons morphs this particular element into the ultimate source of globally correlated noise.
 We therefore attempt to de-correlate this impact and increase the number of input neurons where each of the input neurons receives the same input signal.
 Figure \ref{fig:I1_with_noise4} illustrates the system's SNR for identical noise conditions for different $1 \leq I_1 \leq 200$.
 Panel (a) shows the impact of this strategy upon a FNN, panel (b) for a RNN ($\gamma=\beta=0.5$).
 For the FNN, the impact of increasing $I_1$ is significant and improve the SNR by $\sim30~\%$ for $I_1 \gtrsim 10$.
 For the RNN we do not find significant impact.

\begin{figure}[tbp]
\center{\includegraphics[width=1\linewidth]{change_I1_with_noise4.pdf}}
\caption{Signal-to-noise ratio of the output signal in FNN (a) and RNN (b) for the case different numbers of nodes in the input layer and noiseless neurons in the final readout layer. Parameters are $D^U_A=10^{-4}$, $D^C_M=10^{-4}$, $D^U_M=10^{-3}$, $\alpha=1$, $b=0.02$, $\beta=0.5$. }\label{fig:I1_with_noise4}
\end{figure}

The relevance of the last layer is due to the fact that fundamentally there its no further averaging taking place after.
 The most immediate conclusion is therefore to place substantial effort on low-noise last layer neurons in the fabrication and design of an analogue neural networks.
 In the case of the systems as in \cite{Bueno2018}, this corresponds to the selection of a low-noise detector in the output.
 Figure \ref{fig:I1_no_noise4} shows the great effectiveness of this strategy.
 In both cases, for the FNN, panel (a), and RNN, panel (b) ($\gamma=\beta=0.5$), the benefit upon the system's SNR is significant when combined with multiplexing of the first layer input neurons.
 Based on noise-less readout neurons and duplicating the input-neuron to around 10 copies approximately doubles the system's SNR.
 Most importantly, we have also analysed the situation for only uncorrelated noise.
 There, the SNR can be increased close to 10 times following this strategy.

\begin{figure}[tbp]
\center{\includegraphics[width=1\linewidth]{change_I1_no_noise4.pdf}}
\caption{Signal-to-noise ratio of the output signal in FNN (a) and RNN (b) for the case different numbers of nodes in the input layer and turned off noise in the output layer. Parameters are $D^U_A=10^{-4}$, $D^C_M=10^{-4}$, $D^U_M=10^{-3}$, $\alpha=1$, $b=0.02$, $\beta=0.5$. }\label{fig:I1_no_noise4}
\end{figure}

In some types of networks, it is impossible to alter the neuron type. Then the idea of turned off noise can be transformed to the next way. Previously the feed-forward network with four layers of nodes $I_1$, $I_2$, $I_3$, $I_4$ with $I_4=1$ has been considered. Now we remove the last layer and read out all the signal from each node of the 3rd layer. Then we average this set of signals over the number of nodes in the third layer $I_3$ and get almost the same effect of noise reduction. The same can be made for RNN.

\section{\label{sec:Conclusion}Conclusion}

To conclude, we have analysed the interplay between noise and network connections in great detail.
 We have considered a large variety of networks topologies and parameters are have analysed their output susceptibility to noisy neurons.
 We find that the in general the networks are quite resilient towards such noise units.

The principle results of our work are confirmed by analytical descriptions.
 They identify the fundamental laws with govern the propagation of noise across future hardware implementations.
 Based on the gain insight identify noise which is correlated across populations of neurons together with the noise present in input and output neurons as the main nuisance in such systems.
 Our work identifies the fundamental importance of stability in global parameters, for example in the stability of a analogue neural network's power supply.
 Individual neurons, on the other hand, can be of lesser quality as their local noise will largely be averaged out by the network itself.

We directly leverage this insight and propose noise mitigation strategies which have a great effect.
 Under good conditions this approach can results into an SNR improvement by up to one order of magnitude.

Our work focused on networks of linear components.
 By that it highlighted the fundamental interaction between noisy neurons and network connections.
 However, we presented a large fraction of our results as a SNR dependency against the average output amplitude.
 This allows for a first, heuristic mapping of our findings onto nonliear system's for which the nonlinearity is known.
 An important task is now to include such nonlinear noisy neurons and to understand their role inside the noisy orchestra in detail.

\begin{acknowledgments}

The authors acknowledge the support of the Region Bourgogne Franche-Comt\'{e}.
This work was supported by the EUR EIPHI program (Contract No. ANR-17-EURE- 0002), the BiPhoProc project (Contract No. ANR-14-OHRI- 0002-02), by the Volkwagen Foundation (NeuroQNet).
N.S. is supported by Vernadski scholarship of the French Government.
X.P. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 713694 (MULTIPLY).

\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


In 2015 actress, director and photographer, Esther Anderson, received THE VOICE OF A WOMAN - DISTINCTION AWARD FOR OUTSTANDING CONTRIBUTIONS TO FILM in a career that has spanned over 50 years.
As seen in the photo above she co-starred with actor Sydney Poitier in the film "A Warm December" which he also directed. Shot in 1973 entirely on location in the UK "A Warm December" is a love story, with Anderson playing Catherine, an African Princess. At the time Ms. Anderson was one of the first Black actresses working in the British film/television industry since her arrival to London in the early 60's.
Anderson born in Jamaica moved to London in 1961 where she began modeling for the artist Aubrix Rix, an illustrator for Woman's Own magazine. At the same time as working as a model she studied drama at the Actor's Workshop. She was offered a role in a documentary film by Jo Menell, who was a producer for television's Panorama. In addition to a modeling and acting career she danced with her sister Tiffany Anderson, for such bands as: The Rolling Stones, The Animals, The Walker Brothers, Sonny and Cher, Cathy McGowan and Donovan.
Already a success in film and television in the UK, Anderson began to develop the Jamaican music label Island Records in the early 1960s with Chris Blackwell selling Jamaican records in London from a Mini Cooper, writing lyrics, taking stock, and promoting and managing all the Jamaican artists signed to the label, including Millie Small, Jimmy Cliff and Bob Marley and the Wailers. Anderson's iconic photographs and grooming of Bob Marley along with their writing collaborations, helped to launch his international career in 1973.
In parallel with her photography and work with Island Records, Anderson continued to develop her career as an actress. She secured roles in a number of early 1960s British television shows, including Dixon of Dock Green and The Avengers. She played roles in movies such as Henry Levin's Genghis Khan for Columbia Pictures. Robert Freeman's The Touchables for Twentieth Century Fox, Ted Kotcheff's Two Gentlemen Sharing, Jerry Lewis's One More Time for United Artists, and Sidney Poitier's A Warm Decemeber for First Artists.
She helped to launch the film industry in Jamaica, acting as co-producer of the film The Harder They Come, encouraging the other producers and director Perry Henzell to give the lead role to a new Jamaican talent, Jimmy Cliff, instead of to Johnny Nash. She coached Cliff for the part, partly autobiographical, and he gave a formidable performance. Anderson also organised the finance for the soundtrack, bringing in Chris Blackwell to put up the US$5,000 needed to complete the film, plus a music distribution deal.
Anderson continues to develop her work as a photographer and documentary maker. She has been exhibited by "La Tete Gallery" in Paris curated by Galaad Milinaire, the Photographers' Gallery in London, the Stephen Bulger Gallery in Toronto, Canada, and in the Caribbean by Niki Michelin in Antigua. Her portraits include as subjects: Louise Bennett, Marlon Brando, Amanda Lear, Catherine Deneuve, Charles Prince of Wales, Denzel Washington, Jacques Chirac. Her photographic collection has been exhibited at The Photographer's Gallery in London. She is also represented by Bill Gates' agency Corbis and the Stephen Bulger Gallery in Toronto.
As a filmmaker, Esther Anderson's first film, Short Ends, was an official selection at the 1976 Edinburgh Film Festival. She researched the lives of people of colour at the Library of Congress, Washington, DC, developing the idea of making films on positive role models. The first of these films, The Three Dumas (the story behind The Count of Monte Cristo) was produced in collaboration with architect Gian Gody under the banner of Trenhorne Films (UK), a dramatised documentary about novelist Alexandre Dumas and his ancestors: the grandson of the French Marquis de la Pailleterie and an enslaved African, Dumas overcame all the obstacles of prejudice to become a role model of contemporary literature. Anderson herself portrays General Toussaint L'Ouverture, leader of the Haitian Revolution. The avant-premiere of The Three Dumas took place in 2005 in France at Villers-Cotterets, birthplace of Dumas, to coincide with the inauguration of a statue of him in the presence of the French Minister of Culture. The UK premiere took place in 2007 at the Museum of London Docklands, coinciding with the inauguration of the new Sugar and Slavery Gallery during the bicentenary commemorations of the 1807 Abolition of the Slave Trade Act. Other screenings around the world include the British Film Institute, Canadian Museum of Civilization, McCord Museum, Massachusetts Historical Society, McCormick Tribune Freedom Museum, University of Leeds, University of Nottingham, University of Birmingham, Centro Cultural Palacio La Moneda, V&A, and an Official Selection at the Portobello Film Festival. Bob Marley: The Making of a Legend had its London premiere at the British Film Institute (NFT1) and screened again at THE VOICE OF A WOMAN FILM FESTIVAL in October 2015.


text:
exegetes.eu.org
Les exégètes amateurs
Legal working group shared by French Data Network (FDN), La Quadrature du Net (LQDN) and the Federation of non-profit Internet access providers (Fédération FDN). Since December 2014.
Legal Action against the French Surveillance Law!
In June 2015, French newspaper Le Figaro titled: "Opponents to the Surveillance Law make their last-ditch effort"1. Not so! Since the partial validation of the Surveillance Bill by the French Constitutional Council last summer, we have been working to lodge a complaint with the French Council of State.
This Friday, we filed several new documents with the help of the Spinosi-Sureau law firm. These documents detail all of our arguments against French surveillance. Three years after the start of the Snowden revelations, while the Rule of Law buckles a little more each month under the battering of the Police State, we are now turning to judges to enforce our fundamental rights.
What is the scope of these actions?
On 30 November 2015, the Federation of non-profit Internet service providers (FDN Federation), La Quadrature du Net and the French Data Network2(FDN), intiatied proceedings against the first three decrees implementing the Surveillance Law(s)3.
Later on, following the publication of two additional decrees, two new challenges were introduced (one of which was filed by Igwan, a non-profit Internet access provider in the Antilles, member of the FDN Federation).
The goal of these actions is to demonstrate that those five decrees are contrary to our fundamental rights. To do so, we directly question the validity of the law they are meant to implement. This enables us to question the entire Surveillance Law(s).
Within which context do these actions take place?
This strategy is a direct extension of the one initiated after the adoption of the law in June 2015. At that time, we sent to the Constitutional Council an amicus curiae [FR] including numerous constitutional arguments against the law. The current action before the Council of State carries on this work, now with arguments based on the Charter of Fundamental Rights of the EU and the European Convention on Human Rights.
In parallel with our efforts, many complaints have been lodged before the European Court of Human Rights (ECHR) by organisations of journalists and lawyers. We strongly welcome these legal actions perfectly complementary to ours - our goal being primarily to obtain the enforcement of European law. Where are we in the proceedings?
The first applications initiating the proceedings date back five months. They were only intended to meet the time limits for referring cases and therefore included a small portion of the arguments to raise.
We have developed these arguments over these last five months and submit them today to the French Council of State as supplementary statements. For their part, the French Prime Minister and the Defence Minister have already begun to respond. Hence, the exchange of arguments will continue.
What are our arguments?
Put it simply: our strategy is to mobilise the European Court of Justice's (ECJ) case law, which has made landmark rulings concerning privacy protection these last months (see in particular the Digital Rights case and the Schrems case)). With this in mind, if the French Council of State were to refuse to directly apply this case law, we would suggest it several preliminary rulings that it would then have to be referred to the ECJ.
All our arguments can be found in our writings [FR], but these documents are voluminous (for example the main document is around 90 pages). Our goal here is to give a synthetic overview.
It was already one of the arguments raised in the amicus brief [FR] that we filed before the French Constitutional Council last summer: the Surveillance Law allows the services to spy on the population for various reasons which are neither sufficiently restricted nor precise enough (the main interests of France's foreign policy; the accomplishment of its European and international commitments; its main economical, industrial and scientific interests; preventing the organisation of illegal or incompletely declared demonstration; or preventing access or use of narcotics for personal consumption).
Being secret surveillance measures, this inaccuracy is extremely worrying and is, in our opinion, directly in violation with the Schrems ruling, which requires in particular "purposes which are specific, strictly restricted and capable of justifying the interference".
The law merely regulates the conditions of data collection (collection authorised not only for intelligence services but also for dozens of other administrative authorities, whose actual aggregate exceeds 45 000 persons). However, it says nothing about how access to information gathered is organised internally, paving the way for arbitrary uses. This lack of legal framework is clearly contrary to the ECJ's Schrems case).
So-called "international" surveillance
The provisions on international surveillance legalise the vast Internet traffic collection system implemented by the DGSE (French foreign intelligence services) since 2008 to catch up with the NSA and the GCHQ in this area. It is very large-scale surveillance: the Prime Minister is to designate the submarine cables and other networks on which the DGSE can connect and authorises it to set up mass interceptions of the traffic.
This indiscriminate surveillance of communications constitutes a frontal attack on the Rule of Law that is contrary to the case law of the ECJ and the ECHR, which require to specify the existence of a reasonable suspicion against the persons whose communications are intercepted. On this matter, the Dutch MEP Sophie in't Veld just challenged [FR] those provisions before the CNCTR4.
Finally, as the French Constitutional Council has validated, citizens under surveillance have no legal remedy to challenge the so-called international surveillance measures, which is blatantly violating European conventions.
Exchanges of data with foreign intelligence services
The Snowden documents have shown the growing importance of the cooperation agreements between Western intelligence agencies, which provide massive exchanges of data between services. But the Surveillance Law prohibits the oversight Commission, the CNCTR, access to data held by the French services that has been transmitted by their foreign counterparts. This way, it also prevents any oversight by the Council of State.
As we have put in our writings, "the British GCHQ and the German BND can collect the communications of French residents in application of provisions which, in their national law, fall under the surveillance of international communications, and can transfer them to their French counterparts of the DGSE, who therefore escape any supervision and control over the use of such personal data." By disarming the CNCTR's oversight, the Surveillance Law allows services to bypass the meagre safeguards applicable for national surveillance and deprive citizens of the right to an effective remedy against the collection and use of this data.
Last year, during the parliamentary debate of the Surveillance Law, the "black boxes" sparked heated debates. They did so for a good reason: the intelligence services can now force Telecoms operators and hosting providers to install tracking devices on their infrastructure for real-time scanning of all traffic, hoping to identify "weak signals" of terrorist activities . These "black boxes" would thus imply to scrutinise the communications of nearly the entirety of the population.
Again, this indiscriminate surveillance is contrary to EU law. But this provision also violates the spirit and letter of the 2000 European directive on the information society services (eCommerce Directive), which prohibits national authorities from imposing on Telecom operators and hosting providers "a general obligation [...] to monitor the information which they transmit or store, nor a general obligation actively to seek facts or circumstances indicating illegal activity".
Oversight by the CNCTR
This has been said time and again: the CNCTR only issues non-binding opinions on the permissions that the French Prime Minister delivers to the intelligence services to recourse to surveillance measures. Because this is optional, it carries tangible risks of abuse. By the same token, last year, the president of the former Commission highlighted that almost one quarter of negative opinions issued during the first term of 2015 had not been followed [FR]. However, European case law is clear: it requires collection and secret use of personal data to be subject to prior authorisation by an independent entity. Such is not the case in France.
Judicial remedy
The right to a judicial remedy before a special chamber of the Council of State was presented as a major advance provided by the Surveillance Law. This is actually a fool's game, which brings reason of State and its secrecy in French law without providing the minimum guarantees necessary for a fair trial. Indeed, all the documents submitted by the administration during the proceedings remain secret; the plaintiff and his/her lawyer will not have access to them. The jurisprudence of the Council of State itself will remain secret, and it will be impossible for an individual to know whether he/she was under surveillance. Again, these special rules are contrary to European case law concerning the right to a fair trial.
But there is more!
Back to the Constitutional Council? (surprise!)
We just asked for a priority preliminary ruling on issues of constitutionality (QPC5) that will have to pass the French Council of State's scrutiny and will, hopefully, be referred to the Constitutional Council.
But why going back before the constitutional judges, when they have already largely deliberated on the Surveillance Law [FR], rejecting most criticisms that we, as many others, submitted?
One key provision had, seemingly, been overlooked.
As for so many other discoveries, it was chance that brought our attention to it: on 12 April, like many people, we learnt from the French newspaper Le Monde how the DGSE [FR] had put politician Thierry Solère under surveillance in 2012, probably by using article 20 of the 1991 law. We did remember this article 20, which had been denounced as soon as in 2001 as being a potential basis for a vast surveillance system. Nevertheless, maybe unconsciously, we had assumed that its existence would end with the new Surveillance Law, whose objective, according to the Government, was precisely to put an end to unclear "a-legal" regimes, which this kind of provision had let flourish.
Hunting for this article 20, we found it as such, unchanged for the last 25 years, with merely a new numbering in the Surveillance Law as article L. 811-5 [FR - see the unofficial translation above] of the Internal Security Code.
This article specifies that "measures taken by public authorities to monitor and control wireless communications for the specific defense of national interests are not subject to the provisions of this book".
For a start, the notion of "wireless communications"6 might not be clear for everybody, and it is useful to provide a few examples. It might concern, for instance, all information sent:
between a mobile phone and its relay antenna (GSM/3G/4G);
between a WiFi hotspot and a computer, smartphone or tablet;
by a laptop using a 3G or 4G dongle;
between two Bluetooth devices (wireless microphones, etc);
between a cordless phone and its station;
between two ham radio practitioners or two walkie-talkies, etc.;
by users of Satellite, WiMax, WiFi etc.;
between an instant pay card and its station;
by a GPS beacon;
between an NFC chip (which you find in credit cards, or various other cards) and the reader.
Therefore, all "public authorities" - all state services (ministers, prefects, DGSE, DGSI, independent authorities, etc.) - may have recourse to any technique allowing "monitor and control" of these wireless transmissions, in the name of "the defence of national interests".
Finally, and most importantly, these techniques are "not subject to the provisions" of the book VIII of the Internal Security Code which, being derived from the Surveillance Law, supervises all surveillance activities in France. That is to say, this wireless transmissions monitoring is a loophole, not covered by any binding legal framework.
Thus, the lawmaker leaves the door open for all sorts of surveillance measure by state services.
Should a person's phone calls be destroyed after a set time once intercepted? Does an independent authority verify that the emails sent from a smartphone have been intercepted for a legitimate reason? What legal remedies are offered to citizens under surveillance? Nothing is specified on these matters.
Thus, all wireless communications are de facto excluded from the scope of the - still insufficient - control procedures established by intelligence techniques. In other words, while the Government claimed to supervise intelligence techniques, it merely did so for a few wired communication techniques. What is even more shocking is that during the legislative debates on the Surveillance Law, our attention was particularly drawn to the IMSI catchers. But these intelligence techniques are essentially not covered by the Surveillance Law, since they apply exclusively to wireless communication.
In the face of such a lack of safeguards, we can only expect the French Constitutional Council to follow its own case law and to censure this provision for "negative incompetence"7, as it had done so with the Surveillance Law by censoring the provisions pretending to regulate international surveillance. Apart from this legal action, whose delays are strictly limited, we will certainly have to be patient since the Government will most likely run out the clock and try to avoid that any case be brought before a European jurisdiction. Three years after the beginning of the Snowden revelations, and facing the inertia of the European Parliament, it is now the judges' turn to have the final say. Let us hope they will overcome the temptation of following the reason of State.
Source: Le Figaro, 23 June 2015 [FR].↩
The oldest French non-profit Internet access provider still active.↩
La Quadrature du Net has translated these two laws. This translation is not official, but is the only one available.↩
National Oversight Commission for Intelligence-Gathering Techniques.↩
The QPC is a French Constitutional Law procedure allowing persons involved in a pending case to ask the Constitutional Council to assess the constitutionality of the laws relating to the case at hand.↩
« [T]ransmissions empruntant la voie hertzienne » in French.↩
The notion of "negative competence" is a French Constitutional Law one, referring to cases where the legislator has overlooked his competence derived from the principle of legality (art. 34 of the French Constitution). The omission of this principle leaves the regulatory power with the task of regulating cases which should have been regulated in the law.↩
Hosted by FDN. Legal information


This is a largess competition. Each entrant will make 5 pieces of largess, similar in nature but they do not have to be exactly the same. Each piece will need to be tagged with the entrants name and description of the piece. Each entrant will get to choose a piece of largess to take home. The rest will be given to Their Excellencies of Fontaine to gift as largess, as they see fit. We will also have a populace vote on this competition as well.


text:
Q: Duplicate in key (Muenchian Grouping) it may sound strange, but is it the case that, for example, if we group it based on 3 things and also want to see a recurrence of a certain element in the key? Can anyone give a simple example if this exists? Although I searched for previous solutions, I only found one where duplicates were deleted.
I finally have my example.
My XML:
<?xml version="1.0" encoding="UTF-8"?>
<invoices>
    <invoice buyer="Company_1">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="1878.95"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_1">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="0.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_1">
        <invoicenumbers>
            <invoicenumber name="5678"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="1900.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_1">
        <invoicenumbers>
            <invoicenumber name="5678"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="0.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_2">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="1900.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_2">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_2"/>
        </cost>
        <amounts>
            <amount localamount="2700.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_2">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_3"/>
        </cost>
        <amounts>
            <amount localamount="500.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_3">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_1"/>
        </cost>
        <amounts>
            <amount localamount="0.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_3">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_2"/>
        </cost>
        <amounts>
            <amount localamount="100.00"/>
        </amounts>
    </invoice>
    <invoice buyer="Company_3">
        <invoicenumbers>
            <invoicenumber name="1234"/>
        </invoicenumbers>
        <cost>
            <COSTGROUP name="Group_3"/>
        </cost>
        <amounts>
            <amount localamount="5000.00"/>
        </amounts>
    </invoice>
</invoices>

My XSLT:
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform" xmlns="urn:schemas-microsoft-com:office:spreadsheet" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:x="urn:schemas-microsoft-com:office:excel" xmlns:ss="urn:schemas-microsoft-com:office:spreadsheet" xmlns:html="http://www.w3.org/TR/REC-html40">
    <xsl:output method="xml" encoding="UTF-8" indent="yes"/>

    <xsl:key name="Muenchian_Grouping"
        match="/invoices/invoice"
        use="concat(@buyer, '|', invoicenumbers/invoicenumber/@name)"/>

    <xsl:key name="Muenchian_Grouping_by_costgroup"
        match="/invoices/invoice"
        use="concat(@buyer, '|', invoicenumbers/invoicenumber/@name, '|', cost/COSTGROUP/@name)"/>

    <xsl:template match="/">
        <Workbook>
            <Worksheet ss:Name="Report">
                <xsl:call-template name="ws_table"/>
            </Worksheet>
        </Workbook>
    </xsl:template>

    <xsl:template name="ws_table">
        <Table>
            <xsl:call-template name="columns"/>
            <xsl:call-template name="columnHeader"/>

            <xsl:apply-templates select="invoices/invoice[generate-id() = generate-id(key('Muenchian_Grouping',
                concat(@buyer, '|', invoicenumbers/invoicenumber/@name))[1])]" mode="invoices"/>
        </Table>
    </xsl:template>

    <xsl:template name="columns">
        <Column ss:Width="269.25"/>
        <Column ss:Width="218.25"/>
        <Column ss:Width="291.75"/>
        <Column ss:Width="276.75"/>
        <Column ss:Width="276.75"/>
    </xsl:template>

    <xsl:template name="columnHeader">
        <Row>
            <!-- buyer -->
            <Cell>
                <Data ss:Type="String">buyer</Data>
            </Cell>
            <!-- invoicenumber -->
            <Cell>
                <Data ss:Type="String">invoicenumber</Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">Group1_localamount</Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">Group2_localamount</Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">Group3_localamount</Data>
            </Cell>
        </Row>
    </xsl:template>

    <xsl:template match="invoice" mode="invoices">

        <xsl:variable name="Group1_data" select="key('Muenchian_Grouping_by_costgroup',
            concat(@buyer, '|', invoicenumbers/invoicenumber/@name, '|', 'Group_1'))"/>

        <xsl:variable name="Group2_data" select="key('Muenchian_Grouping_by_costgroup',
            concat(@buyer, '|', invoicenumbers/invoicenumber/@name, '|', 'Group_2'))"/>

        <xsl:variable name="Group3_data" select="key('Muenchian_Grouping_by_costgroup',
            concat(@buyer, '|', invoicenumbers/invoicenumber/@name, '|', 'Group_3'))"/>

        <Row>
            <!-- buyer - when group1 is not exists -->
            <Cell>
                <Data ss:Type="String">
                    <xsl:value-of select="$Group1_data/@buyer | $Group2_data/@buyer | $Group3_data/@buyer"/>
                </Data>
            </Cell>
            <!-- invoicenumber - when group1 is not exists -->
            <Cell>
                <Data ss:Type="String">
                    <xsl:value-of select="$Group1_data/invoicenumbers/invoicenumber/@name | $Group2_data/invoicenumbers/invoicenumber/@name | $Group3_data/invoicenumbers/invoicenumber/@name"/>
                </Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">
                    <xsl:value-of select="$Group1_data/amounts/amount/@localamount"/>
                </Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">
                    <xsl:value-of select="$Group2_data/amounts/amount/@localamount"/>
                </Data>
            </Cell>
            <!-- Group1_localamount -->
            <Cell>
                <Data ss:Type="String">
                    <xsl:value-of select="$Group3_data/amounts/amount/@localamount"/>
                </Data>
            </Cell>

        </Row>
    </xsl:template>
</xsl:stylesheet>

So as you can see in the XML the "Company_1" has a duplicate value at "invoicenumber name="1234"" and at "invoicenumber name="5678"", and the question is how can i see both in the output excel file?
EDIT:
Expected result:
enter image description here

redpajama_set_name: RedPajamaStackExchange


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Q: DIY small light pipe I need a small (3 cm), 90° angled lightpipe to redirect a 0.5cm LED.
I'm looking for a DIY solution using common materials I already have at home. (Even if it won't redirect all the light it is still OK).

A: Whatever material you use, the rule of thumb is that the bend radius should be no smaller than 15 times the fiber diameter to avoid loss of light.  My experience is that loss is pretty big when you bend too far.
https://www.youtube.com/watch?v=wGaJMVQt7qc

A: Not knowing what common materials you have at home, I'd say use nylon monofilament fishing line, or clear weed-whacker string, or a nylon guitar string.

A: Depending on what you have available, clear acrylic will give you a solid lightpipe while clear tubing can work reasonably well. Either reflecting the light down the tube, or get thick-walled tubing and cut a solid section to use total internal reflection for the piping.

A: Dollar store for a piece of suitable plexiglass. cut into a triangle with flat instead of pointy end points. Use a nail file to shape until light is acceptable. A piece of foil covering the sides the light shouldn't escape from helps reflect more of it.
Otherwise, dollar store for a optical fiber toy.
Hot glue sticks, either as is, cut down, or melted into shape using a small mold.


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Q: Redirect to new url ends session even if end response is false On our asp.net site we use Response.Redirect(url, false) to redirect user to payment provider. Before redirect, we store some data in session, because we need it for postback. Immediately when we make our redirect, the session is ended and on postback new session with the same id is created. Our stored data is of course - gone.
Does anyone know why redirect ends session even if parameter endResponse is set to false? When I'm using different payment provider (redirect to different url), the session is not terminated and I don't lose data that was stored in session.


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The Lady-Draft May Be In Our Future
Katie J.M. Baker
Filed to:women in the military
We're not sure if the title of the Associated Press's report on whether women will be drafted now that they'll be fighting on the front lines — "Listen Up Ladies! Uncle Sam Might Want You Too" — is patronizing or sarcastic or what. (It'd make sense on a blog but seems a bit weird coming from the AP.) It skews towards patronizing, with phrases like "Tennnnnn-hut, ladies! The next time Uncle Sam comes calling, he's probably going to want you, too" and "but if you're worried a draft notice is going to soon be in your mailbox, take a deep breath. There is no looming national crisis that makes a military draft likely." Uh, thanks?
That's pretty much the gist right there: if there's a draft in our future, women will probably be drafted, but no one thinks that will happen anytime soon. But is there any good reason for why women shouldn't women be drafted? The military's women don't think so:
Maj. Mary Jennings Hegar, a California Air National Guard pilot who served three tours in Afghanistan, said excluding women from a draft reinforces a stereotype that they are less capable than men and need to be protected. Not every woman can handle a close combat job, she said, and neither can every man.
But they can contribute in other ways if a crisis demands their service, said Hegar, who received a Purple Heart for wounds she suffered when her Medevac helicopter was shot at during a mission near Kandahar, Afghanistan.
"You can't pick and choose when equality should apply to you," Hegar said. "Making generalized statements like, 'Women are capable of being in combat' or 'Women are incapable of being in combat,' are equally ignorant. People are either competent or they're not competent."
Word. The most interesting parts of this article are about draft controversy in general, not whether women should sign up:
For baby boomers in particular, talk of conscription stirs memories of the social and political upheaval of the late 1960s and early 1970s caused in large part by the unpopularity of the Vietnam war and the perceived unfairness of the draft. Research published in the late 1970s showed that men from low-income or disadvantaged backgrounds were more likely to fight in Vietnam than men from middle- and high-income families who could avoid being drafted by going to college or finding a slot in a stateside National Guard unit.
"The American people lost confidence in the draft as a means of raising an army when it ceased to require equal sacrifice from everyone that was eligible to serve," said Bernard Rostker, a former director of the Selective Service System and the author of "I Want You! The Evolution of the All-Volunteer Force."
Lawmakers (and most of the nation) recoiled in horror when Jimmy Carter once tried to get young women to sign up for the draft, and surely many conservatives would still consider drafting women "unfeminine" today. But as Hegar pointed out, women are either equal or they're not. Let's go with "they are."
[AP]


Hong Kong, as small as it is, has a number of venomous snakes you should be aware of if walking through the forest, or even at night in a suburban neighborhood. If you are not a snake expert, please do not attempt to move, touch, catch, or kill one of the following snakes – it's just too dangerous, and not worth the risk.
Not sure if the Rhabdophis genus in Hong Kong is considered venomous and dangerous, or not. I've included it on the list as precautionary. At any rate, do not let one of these snakes bite down on you repeatedly or for any length of time (over 5-seconds). In some countries, R. subminiatus is considered deadly.