text:
Jacob Dafni, PhD - Marine biologist ; ד"ר יעקב דפני - ביולוג ימי
P.O.box 6469, Eilat, Israel 88105 * 88105 אילת ,6469 ת.ד.
Telefax: 972-8-6372383 טלפקס * Mobile: 972-53-909104 טלפון נייד
E-mail: jdafni@netvision.net.il
To the Hebrew Version ** לגירסה העברית
Scientific interests
Pneumatic nature of the echinoid skeletons
Sea-urchin skeletons (tests) are unique among vertebrates and invertebrates alike: They are formed as an outer shell, containing inner fluid. It has been suggested that the test is affected by mechanical forces, exerted by inner -- thethering mesenterial threads -- and outer -- tubefeet muscles and the mechanical properties of the collagen fibers that connect the test plates. Under low mechanical activity the test tends to be globular, while under strong adherence the test is flat.
A chemically decalcified dead sea-urchin retains its shape, proving that the overall shape of the sea-urchin is supported by the pneumatic properties of the soft tissue.
A special emphasis in my studies were observations and experiments dealing with the skeleton growth and calcification of the test, trying to demonstrate the influence of mechanical pressure and forces applied by the contractile and -- tissues on the final shape. I showed that even without the support of the hard plates, the sea urchin form retains it typical shape, due to the soft tissue envelope, which acts as a matrix to the calcium carbonate plates. An evidence to the pneumatic hypothesis is the "soap-bubble" curvature pattern of the plates' edge, indicating that inner pressure and outer surface tension of the plates' envelope are primary to the calcification process. This and other evidence urged me to propose a "bio- mechanical" model for the growth and morphogenesis of sea urchins (ref. 10). The model was tested experimentally by various scientists.
Left: the reversal curvature pattern of echinoid skeletal plates, showing in the plate edge and earlier growth-lines. Right: a gap between two neighboring plates in a living test, induces rapid growth of needle-like 'trabeculae', proving that available space enhances rapid growth. Middle: graphic presentation of the "mechanical model".
Two types of deformed T. gratilla under pollution
Deformities of sea-urchin under pollution conditions.
Mass-deformities (up to 70% urchins were affected) of two types were shown in Tripneustes gratilla under pollution conditions, in the Gulf of Eilat. The apparent cause seems to be chemicals aiming to prevent calcium carbonate clogging of pipe systems in a local power-plant (ref. 2) or hotel laundry (6). The deformities are believed to result from less calcification and softening of the mechanical tissues - inter-plate collagen fibers, inner muscles etc. These observations seem to support the proposed model.
The biology of marine mollusca
The Gulf of Eilat (Aqaba) has a typical Indo-Pacific fauna, with large amount of endemism. Pollution in the northern part of the Gulf limits the number of living species. I have followed the Gulf mollusc fauna for over thirty years, and published semi-popular reports and lists. I have also made a webguide to the mollusca of the region. .
The effect of pollution on the species diversity
I studied the species diversity of invertebrate community on dead stony corals, aiming to demonstrate the influence of pollution on the community (ref. 11).
Guiding and teaching nature
I have served many years as warden and guide in the Nature Conservation organization, the Society for the Protection of Nature, I dedicated much effort to the develope a didactic approach to field teaching and study. I wrote many articles -- in Hebrew -- on this topic.
Invertebrate web guides
I wrote several web guides to the invertebrates of the Gulf of Eilat (Aqaba) all included in Dafni-sites:
Corals - https://www.dafni.com/corals/index.htm
non-coral coelenterates - https://www.dafni.com/non-corals/index.htm
Echinodermata - https://www.dafni.com/echinodermata/index.htm
mollusca - https://www.dafni.com/mollusca/index.htm
Crustacea - https://www.dafni.com/crustacea/index.htm
Tunicates - https://www.dafni.com/tunicata/index.htm
Worms - https://www.dafni.com/vermes/index.htm
Sponges - https://www.dafni.com/spongia/index.htm
Sea plants - https://www.dafni.com/plants/index.htm
Fishes - https://www.dafni.com/fish/index.html
1979-2010 = PDF העתקי
Ben-Eliahu, N. & J. Dafni (1979) A new reef building serpulid genus and species from Elat and the Red Sea, with notes on other gregarious tube worms from Israeli waters.Isr. J. Zool. 28:199-208.
Dafni, J.(1980) Abnormal growth patterns in the sea urchin Tripneustes cf. gratilla (L.) under pollution (Echinodermata: Echinoidea). J. Exp. Mar. Biol. Ecol., 47:259-279.
Dafni, J. (1982) Skeletal deformations in the sea urchin Tripneustes gratilla (L.) under pollution conditions in the Gulf of Eilat, Red Sea. in: Echinoderms - Proceeding of the Fourth International Conference,Tampa Bay, September 1981 (Ed. J.M. Lawrence), A.A. Balkema, Rotterdam. pp. 69.
Dafni, J.& J. Erez (1982) Differential growth in Tripneustes gratilla (Echinoidea). in: Echinoderms: Proceeding of the Fourth Intenational Conference, Tampa Bay, September 1981(Ed. J.M. Lawrence), A.A. Balkema, Rotterdam. pp . 71-75.
Dafni, J. (1983a) A new sub-species of Tripneustes gratilla (L.) from the northern Red Sea (Echinodermata: Echinoidea: Toxopneustidae). Isr. J. Zool., 32:1-12.
Dafni, J.(1983b) Aboral depressions in the tests of the sea urchin Tripneustes cf. gratilla (L.) in the Gulf of Eilat, Red Sea. J. Exp. Mar. Biol. Ecol., 67:1-15
Dafni, J.& A. Diamant (1984) School-oriented mimicry, a new type of mimicry in fishes. Mar.Ecol. Prog. Ser., 20:45-50.
Dafni, J. (1985) Effect of mechanical stress on the calcification pattern in regular echinoids. in: Echinodermata - Proceeding of the Fifth International Echinoderm Conference, Galway, September 1984 (Eds. B.E. Keegan and B.D.S. O'Connor), A.A. Balkema, Rotterdam. pp. 233-236.
Dafni, J. (1986a) A biomechanical model for the morphogenesis of echinoid tests. Paleobiology, 12:143-160.
Dafni, J. (1986b) Echinoid Skeletons as Pneu Structures. Konzepte SFB 230, Universitat Tubingen und Stuttgart. Stuttgart, 13:9-96.
Dafni, J.& L. Fishelson (1986) Effect of pollution on the community structure of animals associated with dead corals in Eilat (Gulf of Aqaba, Red Sea). In: Environmental Quality and Ecosystem Stability, Proc. Third Intern. Conf. of the Israeli Ecological Society, (Ed. Z. Dubinsky & Y. Steinberger). Bar Ilan University Press, Ramat Gan, Israel. Vol III/B; pp. 849-858.
Dafni, J.& R. Tobol. (1986/87) Population structure patterns of a common Red Sea echinoid (Tripneustes gratilla elatensis)/Isr. J. Zool., 34:191-204.
Dafni, J.& J. Erez (1987a) Skeletal calcification patterns in the sea urchin Tripneustes gratilla elatensis: I. Basic patterns. Mar. Biol. 95:275-287.
Dafni, J.& J. Erez (1987b) Skeletal calcification patterns in the sea urchin Tripneustes gratilla elatensis: II. Effect of various treatments. Mar. Biol. 95:289-297.
Dafni, J. (1988) A biomechanical approach to the ontogeny and phylogeny of echinoids. in: C.R.C. Paul & A.B. Smith (Eds.)Echinoderm Phylogeny and Evolutionary Biology. Oxford University Press, Oxford. pp. 175-188.
Dafni, J. (1992) Growth rate of the sea urchin Tripneustes gratilla elatensis. Isr. J. Zool., 38:25-33.
Dafni, J. (1995) The need for Damaged Reef Reclamation and Restoration. In: Proc. International Conference: The Ecosystem of the Gulf of Aqaba in Relation to the enhanced Economical Development and the Peace Process II - Eilat, Jan 30th - Feb 2nd, 1995, 84-86
Dafni, J. (2001) Reduced biodiversity in the northern Gulf of Eilat. Paper prepared for the evaluation committee and presented at the IUI seminars on May 2, 2001. 7 pp.
Dafni, J. (2008) Diversity and Recent Changes in the Echinoderm Fauna of the Gulf of Aqaba with emphasis on the Regular Echinoids. in: F. D. Por (Ed.) Aqaba-Eilat, the Improbable Gulf : Environment, Biodiversity and Preservation. Magnes Press Jerusalem 2008 pp. 226-234.
Dafni, J. (2010) Pollution induced mass-deformities in Tripneustes: Biomechanical aspects. in: Echinoderms: Durham Proceedings of the 12th International Echinoderm Conference, Durham, New Hampshire, USA, 7-11 August 2006 (Eds L.G. Harris, S.A. Bottger, C.W. Walker and M.P. Lesser), CRC Press, A Balkema Book,ISBN 978-0-415-40819-6, pp.601-607.
. " Routes and Trails in the Eilat Region"
Gefen Publications, Jerusalem (1995).
A guide book describing 30 foot and car trails in the mountains of Eilat Region:
. "Strange is their middle name - Echinodermata
inernet book (PDF) describing the Echinoderms, and the story of a study made by the author in the years 1979-1988"
"Gulf of Eilat from the Red Sea to the Red Line..."
Cherikover, Tel Aviv (2000).
A comprehensive description of the Gulf of Aqaba-Eilat Gulf including Geology, Biology, history and environmental aspects, (in Hebrew only)
. " Eilat's Coral Reefs"
Yeela Books, Eilat (2008).
A guide and description of the coral reefs of Eilat, showing > 500 species of corals, invertebrates and fishes


THEKEY (CURRENCY:TKY) traded 2.4% lower against the dollar during the twenty-four hour period ending at 10:00 AM E.T. on April 15th. THEKEY has a total market capitalization of $14.98 million and $241,428.00 worth of THEKEY was traded on exchanges in the last 24 hours. One THEKEY token can now be purchased for approximately $0.0030 or 0.00000057 BTC on major cryptocurrency exchanges including Coinrail, Bit-Z, LBank and LATOKEN. During the last seven days, THEKEY has traded 0.9% higher against the dollar.
CryCash (CRC) traded 13.1% higher against the dollar and now trades at $0.0378 or 0.00000731 BTC.
THEKEY is a token. Its genesis date was October 29th, 2017. THEKEY's total supply is 9,795,844,687 tokens and its circulating supply is 5,060,038,287 tokens. The Reddit community for THEKEY is /r/THEKEYOFFICIAL and the currency's Github account can be viewed here. THEKEY's official Twitter account is @thekeyvip and its Facebook page is accessible here. The official website for THEKEY is www.thekey.vip.
THEKEY can be traded on the following cryptocurrency exchanges: HitBTC, Kucoin, Bit-Z, LATOKEN, Coinrail, LBank and Switcheo Network. It is usually not possible to purchase alternative cryptocurrencies such as THEKEY directly using US dollars. Investors seeking to trade THEKEY should first purchase Bitcoin or Ethereum using an exchange that deals in US dollars such as Gemini, Coinbase or GDAX. Investors can then use their newly-acquired Bitcoin or Ethereum to purchase THEKEY using one of the exchanges listed above.


SOBERLINK, Inc. signs with premiere facial recognition technology company, bolstering their unrivaled level of automation for alcohol monitoring programs. SOBERLINK, Inc., a leading innovator in mobile alcohol monitoring, has signed an agreement with a prominent facial recognition software provider to further enhance the automation of their alcohol monitoring system. This new feature will substantially reduce the workload of verifying participant photos.
BI Incorporated became the exclusive master distributor of the SL2 for the criminal justice market in July 2013. BI is the leading provider of electronic monitoring technology and monitoring services for community corrections and immigration agencies. As part of the agreement, BI assumed all existing reseller relationships within the United States with the exception of Texas and Oklahoma.
Reliable results and seamless integration with SOBERLINK's user-friendly monitoring platform was a high priority. The company spent most of 2013 vetting facial recognition software companies in order to find the most trusted technology. After several months of Beta testing with top Biometric companies, SOBERLINK selected a company that has nearly 20 years of experience developing facial recognition software for security sensitive agencies and has over 2,000 customers and services in more than 100 countries.
The SOBERLINK Breathalyzer has an embedded high-resolution camera that takes a picture of the participant during the breath alcohol test. The point-in-time photograph is then spatially analyzed by the software in comparison to an adaptive template of a group of photos of the participant. This level of software intelligence is unique to SOBERLINK and ensures increased accuracy, as opposed to being limited to one master photo which can cause false readings. SOBERLINK has aptly termed their automated facial recognition feature AFR (TM), standing for Adaptive Facial Recognition. This new feature rounds out a growing list of automated features that have helped SOBERLINK become one of the fastest growing devices in electronic monitoring today.
Casey Hanrahan, SOBERLINK's Vice President of Design, states, "The facial recognition feature is the final step in making our system completely automated. This is just one more addition in a long line of industry leading features that will ensure SOBERLINK continues to be the most convenient and effective alcohol monitoring technology on the market." SOBERLINK will release the new feature to all customers in early 2014.


Life isn't perfect, and neither is software creation and delivery. And that's where DevOps comes in, representing a fundamental shift in the way many organizations are developing and delivering applications to users and customers. While DevOps isn't new, more organizations are building it into the way they deliver IT and experts expect that trend to continue next year.
Organizations that are new to the DevOps concept are grappling with how to get their distinct IT operations and development organizations to embrace it, where the two collaborate and build more automation into their systems to make it easier to deploy apps more dynamically.
The two described from both the IT pro and developer points of view on how to move to a DevOps culture in a keynote address at Live! 360, which took place in Orlando, Fla. The conference is produced by 1105 Media, which is also the parent company of Visual Studio Magazine.
Cooperation: Successful DevOps also requires a measure of cooperation.


text:
1. [Overview](#overview)
2. [Module Description](#module-description)
3. [Setup](#setup)
    * [What Puppet EOS affects](#what-puppet-eos-affects)
    * [Setup requirements](#setup-requirements)
    * [Beginning with NetDev EOS Providers](#beginning-eos)
4. [Usage - Configuration options and additional functionality](#usage)
5. [Reference - An under-the-hood peek at what the module is doing and how](#reference)
6. [Limitations - OS compatibility, etc.](#limitations)
7. [Development - Guide for getting started developing the module](#development)
8. [Contributing - Contributing to this project](#contributing)
9. [License](#license)
10. [Release Notes](#release-notes)

## Build status

Style/Lint/build/docs: [![Start Build Status](https://revproxy.arista.com/eosplus/ci/buildStatus/icon?job=puppet-eos_start&style=plastic)](https://revproxy.arista.com/eosplus/ci/job/puppet-eos_start)

System tests spec/coverage: [![Spec Build Status](https://revproxy.arista.com/eosplus/ci/buildStatus/icon?job=puppet-eos_spec&style=plastic)](https://revproxy.arista.com/eosplus/ci/job/puppet-eos_spec)

## Overview

The Arista EOS module for Puppet provides a set of types and providers for
automating Arista EOS node configuraitons.  The module allows for configuration
of EOS nodes using the Puppet agent running native in EOS.

The Puppet EOS modules are freely provided to the open source community for
automating Arista EOS node configurations using Puppet.  Support for the
modules is provided on a best effort basis by the Arista EOS+ community.
Please file any bugs, questions or enhancement requests using [Github
Issues](http://github.com/arista-eosplus/puppet-eos/issues)

## Module Description

This module provides network abstractions for configuring network services on
Arista EOS nodes.  The module provides a set of types and providers to serve as
building blocks for automating the configuration of Arista EOS nodes.  This
module extends Puppet's capability to configure network devices including node
system services, access services and trunk side services of EOS nodes running
EOS 4.13 or later with the Puppet agent installed.  The Puppet agent running on
the node will use pluginsync to download the types and providers from the Puppet
master and uses the Ruby Client for eAPI (rbeapi) to interface with the nodes
configuration.

## Setup

### What Puppet EOS affects

The types and providers in this module provide native abstractions for
configuring Arista EOS nodes.

### Setup Requirements

This module requires pluginsync in order to synchronize the types and providers
to the node.  This module also requires the [Ruby Client for eAPI](rbeapi) to
be installed on the master and nodes.

### Beginning with eos

 1. Install the module on the Puppet master
 2. Install the rbeapi gem on the Puppet master [See Ruby Client for eAPI](rbeapi)
 3. Install the rbeapi gem on the switch [See Ruby Client for eAPI](rbeapi)
 4. Run the puppet agent on the switch to synchronize the types and providers
 5. List the types by running `bash sudo puppet resource --types | grep eos`
    from the EOS CLI enable mode
 6. Verify the providrs by running `bash sudo puppet resource <resource>` from
    the EOS CLI enable mode

```
Arista$ bash sudo puppet resource eos_vlan
eos_vlan { '1':
  ensure    => 'present',
  enable    => 'true',
  vlan_name => 'default',
}
eos_vlan { '100':
  ensure    => 'present',
  enable    => 'true',
  vlan_name => 'TEST_VLAN_100',
}
```

## Usage

See the [Documentation](http://puppet-eos.readthedocs.org/en/master/)

## Reference

See the [Type reference](http://puppet-eos.readthedocs.org/en/master/types.html) in the documentation

## Limitations
* Puppet 3.6 or later
* Ruby 1.9.3 or later
* [Arista EOS 4.13.7M or later](arista)
* [Ruby Client for eAPI 0.4.0 or later](rbeapi)

## Development

This module can be configured to run directly from source and configured to do
local development, sending the commands to the node over HTTP.  The following
instructions explain how to configure your local development environment.

This module requires one dependency that must be checked out as a Git working
copy in the context of ongoing development in addition to running Puppet from
source.

 * [rbeapi][rbeapi]

The dependency is managed via the bundler Gemfile and the environment needs to
be configured to use local Git copies:

    cd /workspace
    git clone https://github.com/arista-eosplus/rbeapi
    export GEM_RBEAPI_VERSION=file:///workspace/rbeapi

Once the dependencies are installed and the environment configured, then
install all of the dependencies:

    git clone https://github.com/arista-eosplus/puppet-eos
    cd puppet-eos
    bundle install --path .bundle/gems

Once everything is installed, run the spec tests to make sure everything is
working properly:

    bundle exec rspec spec

Finally, configure the eapi.conf file for rbeapi [See rbeapi for
details][rbeapi] and set the connection enviroment variable to run sanity tests
using `puppet resource`:

    export RBEAPI_CONNECTION=veos01

## Contributing

Contributions to this project are gladly welcomed in the form of issues (bugs,
questions, enhancement proposals) and pull requests.  All pull requests must be
accompanied by spec unit tests and up-to-date doc-strings, otherwise the pull
request will be rejected.

## License
Copyright (c) 2014-2015, Arista Networks EOS+
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice, this
  list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright notice,
  this list of conditions and the following disclaimer in the documentation
  and/or other materials provided with the distribution.

* Neither the name of Arista Networks nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

## Release Notes

See the [Release Notes](http://puppet-eos.readthedocs.org/en/master/release-notes.html)
in the official documentation.

[rbeapi]: https://github.com/arista-eosplus/rbeapi
[arista]: http://www.arista.com

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
Environment monitoring and control in smart factory scenarios are mission-critical applications in 5G and beyond, where sensors, meters, and monitors generate and upload data to a central controller with real-time ultra-low latency.
In particular, for real-time monitoring and control, the elapsed time since the data was generated is a key factor for the control performance.
Such time duration is referred to as the \emph{age of information} (AoI).
If the AoI of the controller's available data grows unexpectedly, the outcome of the real-time environmental monitoring and control will be poorly degraded \cite{zhou2020age}.
The impact of AoI-aware resource allocation has been investigated in various communication systems \cite{zhou2020age,Liu_2019,8904450,8766741,8969641}.
In \cite{zhou2020age}, a mean-field game approach was proposed in a dense IoT monitoring system.
The work \cite{Liu_2019} considered a multi-sensor industrial IoT (IIoT) scenario with finite blocklength transmission in which the controller instructs all devices to sample and upload environment data based on its AoI records.
The objective therein was to minimize the sensors' power consumption.
Aiming at minimizing the average AoI and average peak AoI using a Markov decision process.
The work \cite{8904450} investigated the tradeoff between AoI and energy cost and proposed an action policy for devices.
In \cite{8766741}, the authors assumed that the devices could not upload data while wirelessly harvesting energy from the base station.
As a result, the AoI exponentially increases during the energy harvesting period.
Finally, the authors in \cite{8969641} considered a remote monitoring problem trading off the expected AoI and the AoI threshold violation probability.

While reducing the AoI in a centralized manner, the proposed resource allocation approaches in \cite{zhou2020age,Liu_2019,8904450,8766741,8969641} incurred not only supernumerary power for statistical information exchanging but also tremendous signaling overheads, which are not negligible in ultra-low latency real-time monitoring, e.g., industrial automation.
Under the ultra-low latency constraints, delegating the transmission decisions to the sensors provides a more realistic avenue, especially when the data-sampling time is uncertain.
Therefore, while accounting for the AoI threshold violation and the threshold-exceeding events, our work aims at proposing a decentralized and proactive power allocation scheme by minimizing the sensors' entropic risk measure energy consumption \cite{8936848}.
We further leverage \textit{extreme value theory} at the sensor to characterize the AoI exceedances over a threshold using the locally observed historical data.
However, the accuracy of characterization is limited by the amount of the sensor's data.
To improve the accuracy under limited data availability, we resort to \emph{federated learning} (FL),  a collaborative and distributed model training framework \cite{park2019wireless,park2020communicationefficient}, and propose an FL-based distributed power allocation algorithm along with Lyapunov optimization. Numerical results show that the proposed approach is on par with the centralized baseline while consuming less system energy for data transmission and model training.

\vspace{-.4em}
\section{System Model and Problem Formulation\vspace{-0.3em}}
\begin{figure}[t]
	\begin{center}
	\includegraphics[width = \columnwidth]{scenario}
	\caption{Sensor-Controller system architecture.}
	\label{fig:simple_scenario}
	\end{center}
\end{figure}
As shown in Fig.~\ref{fig:simple_scenario}, we consider an industrial IoT network with a set $\mathcal{K}$ of $K$ intelligent sensors that monitor distinct and independent (but of the same type) environments and transmit the sampled data to a controller.
We assume that the sensors' sampling operations are event-triggered by the environmental changes without any available statistical information.
After the sensor samples the status data, the new data is immediately transmitted to the controller if the previous data's uploading procedure has been completed. Otherwise, the (new) data is queued in the buffer.
Such a queueing time is called the procrastinated time in this paper.
Let us index the sequentially sampled data of each sensor by $i\in\mathbb{Z}^{+}$ and denote the procrastinated time of the $i$th data of sensor $k\in\mathcal{K}$ as $\eta_k(i)\geq 0$.
Then to send the $i$th data with size $N$, sensor $k$ allocates transmission power $p_k(i)$ over its dedicated bandwidth $B$ with the transmission time
\begin{equation}\label{Tx_time}
    t_k(i) = \frac{N}{B\log_2\big(1+\frac{h_k(i)p_k(i)}{N_0 B}\big)},
\end{equation}
in which $h_k(i)$ is the channel gain, including path loss and channel fading, between sensor $k$ and the controller, and $N_0$ is the power spectral density of the additive white Gaussian noise. Further, assume that the controller issues control commands to the actuator right after receiving the status data. Hence, we focus on the AoI of the time instant at which the status data is fully received at the controller. In this regard, we express the concerned AoI of the $i$th data as $a_k(i) = \eta_k(i) + t_k(i)$ which incorporates the elapsed procrastinated and transmission time.
The data sampling and transmitting instances are schematically illustrated in Fig.~\ref{fig:AoI_example}. Therein, $\tau_k(i)$ denotes the sampling time instant of the $i$th data, and the procrastinated time is shown as the overlapping period.
From Fig.~\ref{fig:AoI_example}, we can straightforwardly find $\eta_k(i)=[\tau_k(i-1) + a_k(i-1) - \tau_k(i)]^{+}$ with $[x]^+=\max\{x,0\}$ and rewrite the AoI in a recursive manner as
\begin{equation}\label{AoI}
    a_k(i) = [\tau_k(i-1) + a_k(i-1) - \tau_k(i)]^{+}+ t_k(i).
\end{equation}
Since the information ages in consecutive transmissions are entangled as per \eqref{AoI}, we should proactively account for the impacts of the allocated power on future AoI.

Note that the factory environment varies continuously, in which the stale information can degrade the control system performance.
As a remedy, we impose a set of constraints on the AoI in terms of the weighted expectation, AoI outage probability, and AoI exceedance.
We firstly introduce a staleness function from \cite{staleness_function} as
$f_k(i) = \frac{[a_k(i)]^{(1-\beta)}}{1-\beta}$
for the AoI staleness with a predetermined value $\beta \leq 0$ and then consider a long-term time-averaged constraint for every sensor $k$, i.e.,
\begin{equation}\label{AoI_loss_bound}
    \lim\limits_{I \to \infty} \frac{1}{I}\sum^I_{i=1} \mathbbm{E}[f_k(i)] \leq f_0,\forall k \in \mathcal{K},
\end{equation}
where $f_0$ is a pre-defined threshold. Additionally, we impose a probabilistic constraint on the AoI for each sensor $k$ as
\begin{equation}\label{outg}
 \lim\limits_{I \to \infty} \frac{1}{I}\sum^I_{i=1}\Pr\{f_k(i)>f_0\} \leq \epsilon, \forall  k \in \mathcal{K},
\end{equation}
in which $\epsilon\ll 1$ is the tolerable threshold violation probability.
Although a very low occurrence probability of the AoI exceedance is ensured in \eqref{outg}, the uploaded data with an extremely large age can hinder the control performance.
To mitigate this effect, a constraint on the AoI exceedances $q_k(i) = f_k(i)-f_0>0$ is imposed as follows:
\begin{equation}\label{extreme_AoI}
   \lim\limits_{I \to \infty} \frac{1}{I}\sum^I_{i=1} \mathbbm{E}[q_k(i)] \leq e_0, \forall k \in \mathcal{K}.
\end{equation}
Here, we define the set of AoI exceedance of sensor $k$ as $\mathcal{Q}_k \triangleq \{q_k(i)|\mathbbm{1}_{\{q_k(i)>0\}}, \forall i\}$, and $e_0$ is a pre-defined threshold.
Finally, taking into account the sensors' limited-energy, we aim at minimizing not only the sensors' average energy consumption but also the variance for data uploading to reduce superabundant energy between each sensor.
To this end, we invoke  the entropic risk measure $\frac{1}{\rho}\ln(\mathbbm{E}_{X}[\exp({\rho X})])$,
which incorporates the mean, variance, and higher-order statistics of $X$ \cite{8936848}, in our global objective, and formulate the studied optimization problem as follows:
\begin{subequations}\label{origin}
 \begin{IEEEeqnarray}{cl}
 \mathop{\text{minimize}}\limits_{p_k(i)}
 &~~ \frac{1}{\rho}\ln\bigg( \lim\limits_{I \to \infty} \frac{1}{I}\sum^I_{i=1} \frac{1}{K}\sum_{ k\in\mathcal{K}}\exp({\rho E_k(i)})\bigg)\label{main_problem}\\
 \text{subject to}
 &~~0\leq p_k(i) \leq p_{max}, \forall i \in \mathbb{Z}^+, k \in \mathcal{K}, \label{PW_max}\\
 &~~ \eqref{AoI_loss_bound}, \eqref{outg},\mbox{and\,} \eqref{extreme_AoI}, \nonumber
 \end{IEEEeqnarray}
 \end{subequations}
 %
 %
 %
 where $E_k(i)=p_k(i)t_k(i)$ denotes sensor $k$'s energy consumption for transmitting its $i$th data,
 $\rho>0$ reflects the weights of the variance and higher-order statistics in risk minimization, and $p_{max}$ is the sensor's data transmission power budget.
Moreover, in the objective \eqref{main_problem}, we take the average over time and sensors instead of expectation in the entropic risk measure.
In the next section,  we will utilize Lyapunov optimization techniques  \cite{Lyopunov} to solve problem \eqref{origin} since the objective \eqref{main_problem} and constraints \eqref{AoI_loss_bound}, \eqref{outg}, and \eqref{extreme_AoI} are long-term time-averaged functions.
\begin{figure}[t]
	\begin{center}
	\includegraphics[width = \columnwidth]{AoI_example}
	\caption{The AoI instances with data sampling and transmission. \small Since only $\eta_k(i+2)>0$, we have $a_k(i)=t_k(i)$, $a_k(i+1)=t_k(i+1)$, and $a_k(i+2)=\eta_k(i+2)+t_k(i+2)$.}
	\label{fig:AoI_example}
	\end{center}
\end{figure}

\section{FL-Based Distributed Power Allocation}\label{proposed_scheme}
\subsection{Lyapunov Optimization Framework}
In order to ensure the time-averaged constraints by Lyapunov optimization, we first introduce the virtual queues
\begin{align}
    \Gamma_k(i+1)&=[\Gamma_k(i)+f_k(i)-f_0]^+,\label{Virtual_queue_1}
\\    \Upsilon_k(i+1)&=[\Upsilon_k(i)+[q_k(i)-e_0]\mathbbm{1}_{\{q_k(i)>0\}}]^+,\label{Virtual_queue_2}
\end{align}
 for constraints \eqref{AoI_loss_bound} and \eqref{extreme_AoI}, respectively. Additionally, by applying $\Pr\{f_k(i)>f_0\}=\mathbb{E}[\mathbbm{1}_{\{q_k(i)>0\}}]$ and scaling both sides of \eqref{outg} as $\lim\limits_{I \to \infty}\frac{1}{I}\sum_{i=1}^I f_k(i) \mathbb{E}[\mathbbm{1}_{\{q_k(i)>0\}}] \leq \lim\limits_{I \to \infty}\frac{1}{I}\sum_{i=1}^I f_k(i)\epsilon$, the virtual queue
 %
 %
 %
\begin{equation}\label{Virtual queue 3}
    \Lambda_k(i+1)=[\Lambda_k(i)+(\mathbbm{1}_{\{q_k(i)>0\}}-\epsilon)f_k(i)]^+
\end{equation}
is considered for the constraint \eqref{outg}.
Due to the fact that minimizing $\lim\limits_{I \to \infty} \frac{1}{IK}\sum^I_{i=1}\sum_{ k\in\mathcal{K}}\exp(\rho E_k(i))$ is equivalent to minimizing \eqref{main_problem}, we consider the conditional Lyapunov drift-plus-penalty
\begin{multline}\label{Lyapunov}
\frac{1}{K}\sum_{k \in \mathcal{K}}\mathbb{E}\Big[\frac{1}{2}\boldsymbol{\Phi}_k(i+1)\boldsymbol{\Phi}_k(i+1)^{\rm T}-\frac{1}{2}\boldsymbol{\Phi}_k(i)\boldsymbol{\Phi}_k(i)^{\rm T}\\+V\exp(\rho E_k(i))\Big],
\end{multline}
where $\boldsymbol{\Phi}_k(i)=[\Gamma_k(i),\Upsilon_k(i),\Lambda_k(i),\forall k \in \mathcal{K}]$ is the combined queue vector for notational simplicity, and $(\cdot)^{\rm T}$ represents the transpose of a vector.  Subsequently, by applying $([Q+y]^+)^2\leq Q^2+2Qy+y^2$, we can derive the inequality
\begin{equation}\label{L_d_bound}
\eqref{Lyapunov}\leq
\frac{1}{K}\sum_{k \in \mathcal{K}}\mathbb{E}\big[\Delta_0+F_k(i)+V\exp(\rho E_k(i)) \big],
\end{equation}
in which
$  F_k(i) = \theta^1_k(i)[f_k(i)]^2 + \theta^2_k(i)f_k(i)$
with
$\theta^1_k(i)=\frac{1}{2}(1+\epsilon^2)+(1-\epsilon)\mathbbm{1}_{\{q_k(i)>0\}}$ and
$\theta^2_k(i)=\Gamma_k(i)-f_0-\epsilon\Lambda_k(i)
+[\Lambda_k(i)+\Upsilon_k(i)-f_0-e_0]\mathbbm{1}_{\{q_k(i)>0\}}$.
Additionally, $\Delta_0=\frac{1}{2}[f^2_0-\Gamma_k(i)+[(f_0+e_0)^2-\Lambda_k(i)(f_0+e_0)]\mathbbm{1}_{\{q_k(i)>0\}}$ is a constant.
Note that the solution of \eqref{origin} can be obtained by minimizing the derived upper bound on the conditional Lyapunov drift-plus-penalty function  \cite{Lyopunov}, i.e.,  \eqref{L_d_bound}, in each transmission $i$ by optimizing over the transmit power $p_k(i)$.
Furthermore, $V \geq  0$ is the tradeoff parameter between the lengths of the virtual queues and the optimality of the energy consumption in \eqref{origin}.

\vspace{-0.4em}
\subsection{Distributed Power Allocation with Federated Learning for AoI Exceedances \vspace{-0.3em}}
Obtaining the optimal solution of minimizing the upper bound \eqref{L_d_bound} requires the global information about $\boldsymbol{\Phi}_k(i), \forall k$.
However, centrally allocating power (i.e., the centralized model-training (CENT) scheme in Section \ref{Numerical}) consumes tremendous power overheads on queue state information exchanges.
To improve power efficiency, we propose a decentralized FL-Based scheme, wherein each sensor $k\in\mathcal{K}$ locally allocates its transmit power for each transmission $i\in\mathbb{Z^{+}}$ by minimizing the individual upper bound of \eqref{L_d_bound},
 \begin{align}\label{L_form}
 \underset {p_k(i)}{\text{minimize}}
 ~V\exp(\rho E_k(i)) +F_k(i)
 ~~\text{subject to}
 ~\eqref{PW_max}.
 \end{align}
In \eqref{L_form}, we can straightforwardly prove the convexity of $F_k(i)$, but $\exp(\rho E_k(i))$ is non-convex with respect to $p_k(i)$.
In order to tractably solve the non-convex problem \eqref{L_form}, we adopt the notion of the convex-concave procedure (CCP) \cite{CCP} by which we iteratively convexify the non-convex part $\exp(\rho E_k(i))$ by the first-order Taylor series expansion with respect to a reference point $\hat{p}_k$ as
\begin{equation*}
    \textstyle \exp(\rho E_k(\hat{p}_k))\left[t_k(\hat{p}_k )\left(1-\frac{\hat{p}_k h_k t_k(\hat{p}_k )}{ N(\hat{p}_k h_k+N_0 B)\ln2}\right)(p_k-\hat{p}_k)+1\right]
\end{equation*}
and solve the convexified problem. Specifically, given the reference point $\hat{p}_k^{r}$ in the $r$th iteration, we focus on
\begin{subequations}\label{CCP_r}
 \begin{IEEEeqnarray}{cl}
 \mathop{\text{minimize}} \limits_{\hat{p}_k^{r+1}}
 &~~ VJ(\hat{p}_k^{r})\hat{p}_k^{r+1} + F_k(\hat{p}_k^{r+1})\label{CCP_r_obj}\\
 \text{subject to}
 &~~ 0\leq \hat{p}_k^{r+1} \leq p_{max},
 \end{IEEEeqnarray}
\end{subequations}
in which $J(\hat{p}_k^{r})=\exp(\rho E_k(\hat{p}_k^{r}))t_k(\hat{p}_k^{r})\big[1-\frac{\hat{p}_k^{r} h_k t_k(\hat{p}_k^{r})}{N(\hat{p}_k^{r} h_k+N_0 B)\ln 2}\big]$.
The optimal solution to \eqref{CCP_r} is subsequently used as the reference point $\hat{p}_k^{r+1}$ in the next iteration.
The initial reference point $\hat{p}_k^0$ is randomly selected from $(0,p_{max}]$. When $|\hat{p}^{r}_k-\hat{p}^{r-1}_k|\to 0$ after a number of iterations, sensor $k$ uses the transmit power $p^*_k(i)=\hat{p}^{r}_k$ to upload the $i$th data and then updates \eqref{AoI} and all virtual queues \eqref{Virtual_queue_1}, \eqref{Virtual_queue_2}, and \eqref{Virtual queue 3}.

However, since the AoI exceedance happens rarely, the deviation of virtual queue \eqref{Virtual_queue_2} between each sensor becomes severe with local statistics only.
To address this issue, we invoke results from extreme value theory and the principles of FL.
Let us rewrite the virtual queue $\Upsilon_k(i)$ in \eqref{Virtual_queue_2} as
    \begin{align*}
        \textstyle\Upsilon_k(i+1)&=\sum^{i}_{j=1}[q_k(j)-e_0]^+\mathbbm{1}_{\{q_k(j)>0\}}
        \\
        & \textstyle \geq \left [ \sum^{i}_{j=1}[q_k(j)-e_0]\mathbbm{1}_{\{q_k(j)>0\}} \right ]^+
        \\
        &\textstyle \stackrel{(a)}{=}\left[ \frac{\sum^{i}_{j=1}q_k(j)\mathbbm{1}_{\{q_k(j)>0\}}}{\sum^{i}_{j=1}\mathbbm{1}_{\{q_k(j)>0\}}}-e_0 \right ]^+\sum^{i}_{j=1}\mathbbm{1}_{\{q_k(j)>0\}}
    \end{align*}
in which the first term in $(a)$ represents the empirical average, which may have large variance due to limited historical data of the excess AoI.
Nevertheless, if the mean of the AoI exceedance is available, we can estimate the steady-state average length of the virtual queue \eqref{Virtual_queue_2}.
\begin{theorem}[Pickands–Balkema–de Haan theorem\cite{Coles2001}] \label{thm1}
Given a random variable $A$ with the cumulative distribution function $F_A(a)$ and a threshold $a_0$, as $a_0 \to F^{-1}_A(1)$, the excess value $Q=A-a_0>0$ can be approximately characterized by a generalized Pareto distribution (GPD) with the scale  $\sigma>0$ and shape $\xi\in\mathbbm{R}$ parameters.
The mean of the GPD is $\frac{\sigma}{1-\xi}$.
\end{theorem}
Leveraging the results in Theorem \ref{thm1}, we characterize the statistics of $q_k(j)$ as a GPD whose parameters $\sigma$ and $\xi$ (i.e., the mean) can be estimated using maximum likelihood estimation.
Given a sufficient amount of historical data, the GPD model (i.e., scale and shape parameters) of the excess AoI can be trained.
However, owing to the sparsity of the excess AoI data at the sensor, it is time-consuming for each sensor to train the GPD model independently.
To overcome this hurdle, we utilize the FL framework in which
all sensors periodically update their locally-trained model to the controller.
Then the controller aggregates the updated local models and feeds back the aggregated model to the sensors.
Our FL-based model training is detailed as follows.

Assume that the local-model updating time interval is $M$, and each interval is indexed by $m \in \mathbb{Z}^+$.
In every updating time interval, each sensor trains its model locally.
In order to have sufficient independent data for local training, we set $W$ observation time windows within which the sensor selects the largest excess AoI as a training sample.
The observation time windows are indexed by $w\in\mathbb{Z}^{+}$, and the window size is $O$ with $M/O=W\in\mathbb{Z}^{+}$, which should be sufficiently large to minimize the correlation between the selected data while being sufficiently small to prevent filtering out the data overmuch.
Moreover, the selected extreme data at sensor $k$ in the $w$th time window of the $m$th time interval is denoted by $\hat{q}^{m,w}_k=\max_{\tau_k(i) \in\mathcal{T}^{m,w}}\{q_k(i)|\mathbbm{1}_{\{q_k(i)>0\}}\}$, where $\mathcal{T}^{m,w}\in [M(m-1)+O(w-1),M(m-1)+Ow]$.
The selected data set within the $m$th time interval is denoted by $\mathcal{Q}^m_k=\{\hat{q}^{m,w}_k\}^{W}_{w=1}$.
After collecting the samples $\mathcal{Q}^m_k$, we train the sensor $k$'s GPD model $\theta^m_k = \{\sigma^m_k, \xi^m_k\}$ via \textit{tilted empirical risk minimization} (TERM) \cite{li2020tilted}, i.e.,
\begin{multline}
 \underset{\theta^m_k}{\mbox{minimize}} ~   \tilde{\mathcal{L}}(\theta^m_k|t,\mathcal{Q}^m_k)
 \\ \equiv \underset{\theta^m_k}{\mbox{minimize}}~\frac{1}{t}\ln \bigg (\frac{1}{|\mathcal{Q}^m_k|}\sum_{\mathcal{Q}^m_k} G(\theta^m_k|\mathcal{Q}^m_k)^{-t} \bigg).\label{TERM}
\end{multline}
Here, $G(\sigma,\xi|q)= \frac{1}{\sigma}\big( 1+ \frac{\xi q}{\sigma}\big )^{-(\frac{1}{\xi}+1)}$ is the GPD's likelihood function while $t$ is the tilted factor used to leverage the effects of the outliers in model training.
In this regard, by setting $t<0$ in \eqref{TERM}, we can account for the outliers and other extreme events.
Subsequently, based on the global model $\theta^{m-1}=\{\sigma^{m-1},\xi^{m-1}\}$ received in the $(m-1)$th interval, each sensor $k$ updates the local model parameters as per
\begin{equation}\label{para_update}
    \theta^m_k=\theta^{m-1}-\delta_{\theta}\nabla_{\theta^m_k}\tilde{\mathcal{L}}(\theta^m_k|t,\mathcal{Q}^m_k),
\end{equation}
with the initial value  $\theta^0$ and sends $\theta^m_k$ to the controller. In \eqref{para_update}, $\delta_{\theta}$ is the step size. The gradient of $\tilde{\mathcal{L}}(\theta^m_k|t,\mathcal{Q}^m_k)$ with respect to $\theta^m_k$ is given by
\begin{align}\label{gradient}
    &\nabla_{\theta^m_k}\tilde{\mathcal{L}}(\theta^m_k|t,\mathcal{Q}^m_k)= \notag
    \\&\frac{-\sum_{\mathcal{Q}^m_k} \nabla_{\theta^m_k}G(\theta^m_k|\mathcal{Q}^m_k)\times G(\theta^m_k|\mathcal{Q}^m_k)^{-t-1}}{\sum_{\mathcal{Q}^m_k} G(\theta^m_k|\mathcal{Q}^m_k)^{-t}},
\end{align}
and
\begin{align*}
  \textstyle \frac{\partial G(\theta|\mathcal{Q})}{\partial\sigma}=&\textstyle \frac{Q-\sigma}{\sigma^3}\left(1+\frac{\xi Q}{\sigma}\right)^{-2-\frac{1}{\xi}} ,
\\ \textstyle \frac{\partial G(\theta|\mathcal{Q})}{\partial\xi}=& \textstyle
  \frac{(1+\frac{\xi Q} {\sigma})^{-1-\frac{1}{\xi}}}{\sigma\xi}\left(\frac{-(\xi+1)Q}{\sigma+\xi Q}+\frac{\ln(1+\frac{\xi Q}{\sigma})}{\xi}\right).
  \end{align*}
Here, the notations $m$ and $k$ are neglected for simplicity.
The controller then calculates the global model of the $m$th updating time interval as
\begin{equation}\label{global_para}
    \theta^m = \frac{\sum^{K}_{k=1}\left (|\mathcal{Q}^m_k|\theta^m_k\right )}{\sum^{K}_{k=1}|\mathcal{Q}^m_k|}.
\end{equation}
Finally, after receiving the global feedback model $ \theta^m $, each sensor $k$ replaces the virtual queue value with
\begin{equation}\label{Upsilon_update}
    \Upsilon_k(\hat{i}+1)=\left[ \frac{\sigma^m}{1-\xi^m}-e_0\right]^+\mathbbm{E}_{ \mathcal{K}}\left[\sum^{\hat{i}}_{j=1}\mathbbm{1}_{\{q_k(j)>0\}}\right],
\end{equation}
in which $\hat{i} = \arg \min \limits_{\forall i} \{\tau_k(i)-Mm\geq0\}$,
and proceeds with the next local-model training $\theta^{m+1}_k$.
The proposed FL-based distributed power allocation is outlined in Algorithm \ref{alg}.
Therein, each sensor $k \in \mathcal{K}$ iteratively optimizes the transmission power $p_k(i_k)$ for each local-sampled data $i_k$ based on the time instance $\tau_k(i_k)$ and the FL updated virtual queue states $A(i_k),\Gamma_k(i_k),\Lambda_k(i_k),\Upsilon_k(i_k)$.

\captionsetup[algorithm]{font=footnotesize}
\begin{algorithm}[t]\footnotesize
\caption{FL-Based Distributed Power Allocation Mechanism}\label{alg}
\textbf{Input:}  $\tau_k(i_k)~\forall k\in \mathcal{K}$, \text{transmission parameters in (\ref{Tx_time})}, $\beta, \theta^0, \delta_{\theta}, M, O.$\\
\textbf{Output:} $p^*_k(i_k),A(i_k),\Gamma_k(i_k),\Lambda_k(i_k),\Upsilon_k(i_k) ~\forall i_k,~\forall k\in \mathcal{K}.$\\
\textbf{Initialize:} \text{create $i_k$ for data indicator, $i_k=1,  \forall k,$}\\ $a_k(0)=0,\eta_k(1)=0, \tau_k(i_k|i_k=0,1)=0,\forall k,\\ \{A_k(1),\Gamma_k(1),\Lambda_k(1),\Upsilon_k(1)\} = 0.$
\begin{algorithmic}[1]
\For {$m=1,2,...$} \textit{// for global model updating interval}
\For {$k=1,...,|\mathcal{K}|$}
\State {$w=1, \mathcal{Q}^m_k=\{\},$} \textit{// check each observation window}
\If {$\tau_k(i_k)\leq Mm \quad\&\&\quad w \leq W$}
\While {$\tau_k(i_k)\leq M(m-1)+Ow$}
\State \text{update} $\eta_k(i_k), \theta^1_k(i_k), \theta^2_k(i_k), \theta^3_k(i_k),$
\State \text{form $u_k(i_k)$ by \eqref{L_d_bound} and solve $p^*_k(i_k)$ by CCP.}
\State \text{count $t^*_k(i_k)$ by \eqref{Tx_time}, $E^*_k(i_k), a_k(i_k), f_k(i_k), q_k(i_k),$}
\State \text{update state $A(i_k),\Gamma_k(i_k),\Lambda_k(i_k),\Upsilon_k(i_k),$}
\State $i_k = i_k + 1,$
\EndWhile
\State \text{Count $\hat{q}^{m,w}_k$, update $\mathcal{Q}^m_k=\{\mathcal{Q}^m_k,\hat{q}^{m,w}_k\},$}
\State \text{$w=w+1,$}
\Else \text{$\mathcal{Q}^m_k=\{\},$}
\EndIf
\State \text{train $\theta^m_k$ with \eqref{para_update}, \eqref{gradient} by $\mathcal{Q}^m_k$ and update them to Controller,}
\EndFor
\State \text{Controller updates $\theta^m$ with $\theta^m_k$ by \eqref{global_para}, and broadcasts to IDs,}
\State \text{$\forall k, \Upsilon_k(i_k)$ is replaced with $\theta^m$ by \eqref{Upsilon_update}}.
\EndFor
\end{algorithmic}
\end{algorithm}

\section{Numerical Results}\label{Numerical}
We simulate a factory environment with $K=50$ sensors with $50$\,Hz data-sampling frequency in Poisson.
The considered path loss model is $32.45+31.9\log20+20\log3.5$ (dB) given $3.5$\,GHz carrier frequency and a $20$-meter sensor-controller distance \cite{nokia_spec}.
The wireless channel experiences Rayleigh fading with unit variance.
The remaining simulation parameters are $N=3000$\,bytes, $B= 180$\,kHz, $N_0=-174$\,dBm, $p_{max}=23$\,dBm, $\beta=-2$, $f_0=5\times10^{-4}$, $e_0 = 10^{-4}$, $\epsilon=2\times10^{-3}$, $M=30$\,ms, $O=10$\,ms, $\theta^0=[0.0002,0.02]$, $\delta_{\theta}=[10^{-9},10^{-3}]$, and $t=-0.1$.
For performance comparison, we consider four baselines: \emph{i)}
\textbf{Centralized model-training} (CENT) scheme which trains the extreme staleness GPD model at the central controller with all sensors' AoI exceedance data;
\emph{ii)} \textbf{Local model-training} (LOCAL) scheme in which the sensors only train the GPD model individually without any information exchange;
\emph{iii)} \textbf{Non-model-training} (NonT) scheme which directly solves problem \eqref{L_form} without renewing the virtual queue $\Upsilon_k(i)$ in \eqref{Virtual_queue_2} via the training result of GPD model;
\emph{iv)} \textbf{Excess staleness-agnostic} (ESA) scheme which does not take extreme staleness into consideration, i.e., neglecting constraints \eqref{outg} and \eqref{extreme_AoI} in problem \eqref{origin}.
In addition to the performance of the objective \eqref{main_problem}, we further investigate the expected
system energy consumption $\mathbbm{E}[E_{sys}]=\mathbbm{E}[E_k] + \mathbbm{E}[E^{train}_{comp.}]+\mathbbm{E}[E^{train}_{tx}]$, including the sensor's monitored data-updating energy $E_k$, the computation energy in GPD-model training $E^{train}_{comp.}=10^{-27} f^2_{cpu} N_{tr}l_{req}$, and the energy consumption in model-uploading $E^{train}_{tx}=p_{max}N_{tr}/\big(B\log_2\big(1+\frac{h_kp_{max}}{N_0 B}\big)\big)$.
Here, $f_{cpu}=2\times10^{11}$ cycle/s and $f_{cpu}=10^{9}$ cycle/s are the controller's and sensor's computation capabilities for model training \cite{8936848}. $N_{tr}=30$\,bytes is the single-data size in GPD-model training, and $l_{req}=87.8$ cycle/bit is the required computation frequency.
\begin{figure}[t!]
     \centering
     \begin{subfigure}[b]{0.43\textwidth}
         \centering
         \includegraphics[width=\textwidth]{objective_V}
         \caption{Value of objective \eqref{main_problem}}
         \label{fig:objective_V}
     \end{subfigure}
     \begin{subfigure}[b]{0.43\textwidth}
         \centering
         \includegraphics[width=\textwidth]{energy_V}
         \caption{System energy $\mathbbm{E}[E_{sys}]$}
         \label{fig:energy_V}
     \end{subfigure}
        \caption{Energy consumption versus $V$ with $\rho=2$.}
        \label{fig:multi_V}
\end{figure}

The impact of the tradeoff parameter $V$ in the Lyapunov optimization on energy consumption is shown in Fig.~\ref{fig:multi_V}.
We first examine the performance of the objective \eqref{main_problem} in Fig.~\ref{fig:objective_V} as a function of $V$.
Note that the objective is a decreasing function of $V$ since the importance of energy reduction increases with increasing $V$.
Although CENT outperforms the other schemes across various $V$ values due to the GPD model training, the performance of our proposed scheme is close to CENT with $0.48\%-11.26\%$ increments in the objective.
Compared with LOCAL and NonT, the proposed FL scheme decreases the objective cost up to $5.45\%$ and $5.56\%$, respectively, showing the benefit of FL model training.
In addition, LOCAL outperforms NonT, manifesting the advantage of model training even without any information exchange.
Being agnostic to extreme staleness, ESA may incur a high instantaneous AoI, resulting in larger energy consumption.
In this regard, ESA has a higher objective cost (up to $44.75\%$ increase) than the cost of the proposed scheme.
\begin{figure}[t!]
     \centering
     \begin{subfigure}[b]{0.43\textwidth}
         \centering
         \includegraphics[width=\textwidth]{objective_rho}
         \caption{Value of objective  \eqref{main_problem}}
         \label{fig:objective_rho}
     \end{subfigure}
     \begin{subfigure}[b]{0.43\textwidth}
         \centering
         \includegraphics[width=\textwidth]{energy_rho}
         \caption{System energy $\mathbbm{E}[E_{sys}]$}
         \label{fig:energy_rho}
     \end{subfigure}
        \caption{Energy consumption versus $\rho$ with $V=10^{-5}$.}
        \label{fig:multi_rho}
\end{figure}

In Fig.~\ref{fig:energy_V}, we further verify the advantages of our proposed approach in terms of the expected system energy consumption.
In CENT, all sensors have to deliver every observed extreme staleness data to the controller, consuming high energy for information exchange.
Note that as $V$ increases, all schemes tend to save more power in environmental data transmission based on the  Lyapunov optimization framework but increases the occurrence chance of extreme staleness. In this situation, the CENT sensors have to consume more energy to upload more model-training data to the controller. Therefore, the expected system energy of CENT grows gradually with $V$ in Fig.~\ref{fig:energy_V}.
In the proposed FL-based approach, since the sensors train the GPD models locally and only upload the model parameters to the controller, the energy consumption is significantly reduced.
In this regard, our approach can save up to $64.11\%$ in system energy compared to CENT. In contrast with NonT and LOCAL, our approach spends extra energy on FL model training and information exchange.
Nevertheless, our energy-saving benefit with respect of $\mathbbm{E}[E_k]$ compensates this expenditure.
The proposed scheme can save up to $5.82\%$ and $6.21\%$ in system energy then LOCAL and NonT.
The objective performance and expected system energy consumption by varying $\rho$ are shown in Fig.~\ref{fig:multi_rho}.
As per \eqref{L_form}, all the schemes put more focus on energy deduction as $\rho$ grows.

\begin{figure}[t!]
	\begin{center}
	\includegraphics[width = .9\columnwidth]{Energy_vs_EAoI}
	\caption{Extreme AoI versus average transmission energy with $\rho=2$.}
	\label{fig:Energy_vs_EAoI}
	\end{center}
\end{figure}
\begin{figure}[t!]
	\begin{center}
	\includegraphics[width = .9\columnwidth]{extreme_GPD}
	\caption{CCDF of extreme AoI with $\rho=2$ and $V=10^{-5}$.}
	\label{fig:extreme_GPD}
	\end{center}
\end{figure}

The capability of extreme staleness control is manifested in Fig.~\ref{fig:Energy_vs_EAoI}.
Given a specific amount of expected status-updating energy $\mathbbm{E}[E_k]$, the proposed approach, CENT, and LOCAL benefited from the GPD-model training showcase the lowest excess staleness values. In contrast, ESA, which is agnostic to the extreme AoI, has much higher excess staleness. However, if we further consider the energy consumption in model training, our proposed approach (compared with CENT and LOCAL) consumes less energy while achieving the same extreme staleness performance.

Finally, we discuss the performance of GPD-model training in terms of the complementary cumulative distribution function (CCDF) of extreme staleness in Fig.~\ref{fig:extreme_GPD}.
As shown, the predicted extreme staleness mean $\sigma/(1-\xi)$ is always higher than the empirical one. The reason is that the predicted extreme staleness mean values in both schemes are leveraged to suppress the extreme staleness further.
The more precise the estimation is, the more accurate the decision.
The centralized approach, i.e., CENT, estimates the GPD model closer to the empirical one, saving more energy to control the extreme staleness.
In this regard, the proposed FL scheme and CENT, respectively, yield $2.33\times10^{-5}$ and $1.08\times10^{-5}$ in terms of
estimation-statistic mean surplus (ESMS) value between the trained model and empirical curve.
On the other hand, the localized approach, i.e., LOCAL, has the highest ESMS $8.36\times10^{-5}$ due to the lack of global estimation.
Such results reflect on the least objective performance in Fig. \ref{fig:objective_V} and \ref{fig:objective_rho}.
However, the mean extreme staleness from the proposed scheme is $3.54\%$ higher than CENT, underscoring that increasing transmission energy based on inaccurate predictions cannot effectively suppress extreme values.

\section{Conclusions}
We studied an industrial IoT network in which the sensors autonomously and proactively allocate transmit power for uploading monitored status data.
To avoid stale data delivery hindering the monitoring performance, we have formulated an entropic risk-minimizing problem for energy consumption subject to data staleness constraints.
By applying extreme value theory results, we trained an GPD model to obviate extreme staleness regimes and have further proposed a distributed FL-based scheme to improve the power efficiency versus its centralized counterpart.
Numerical results have shown that the proposed FL scheme is on par with the centralized model-training scheme while consuming significantly less system energy.
Future work will extend the current framework towards a system that can jointly optimize the data transmission power and sampling rate rather than obey a default number.

\section*{Acknowledgments}
This work is funded by the Ministry of Science and Technology (MOST) of Taiwan under the Graduate Students Study Abroad Program grant 109-2917-I-002-007 and supported by the CHIST-ERA LeadingEdge
and CONNECT projects.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


Will Gold Price Continue to Decline?
Gold price is now trading at 1220 which is lower than the neckline of the head and shoulder pattern. Should traders expect a decline in price? Gain insight into the following XAUUSD analysis.
17 October, OctaFX – Wall Street gained yesterday after earnings data overshadowed recent news about a slowing economy and interest rates. The Dow, Nasdaq, and S&P gained by 547, 214, and 60 points respectively.
These results were helped by Goldman Sachs, Morgan Stanley, BlackRock and Johnson & Johnson. In the aftermarket, results from Netflix showed that revenues and earnings had beaten analysts' forecasts leading to a sharp increase in the stock price.
Today, the Asian markets followed Wall Street with the Nikkei, Hang Seng, and China A50 gaining by 331, 17, and 43 points respectively. In Asia-Pacific, the Australian ASX gained by 63 points.
Last week, the XAUUSD pair jumped sharply to 1230, which was the highest level since July. This was as traders moved to safe havens following the worries of a slowed economic growth and high interest rates.
This week, the pair has remained closer to these levels as the focus on global growth cools down. It is now trading at 1220, which is lower than the neckline of the head and shoulder pattern.
This is an indication that the pair will likely continue to move lower. This is confirmed by the slow change of direction of the 14 and 28-day EMAs.


She may have lived in the United States for the past 23 years, but Dr Wee Hong Ling, 47, says she is always thinking of ways to give back to Singapore and is proud to represent Singapore at international ceramics competitions.
"My sculptural work always focuses on home and my longing for home," she said, referring to the tiny ceramic houses which are signature Wee Hong Ling pieces.
Recent exhibitions here have played on the theme. In 2013, her show at the Arts House was titled Sojourn, while an earlier 2011 exhibition at Sculpture Square was called No Place Like Home.
Interestingly, the New York- based artist said it was the 9/11 terrorist attacks which "formed the foundation" of her Singapore identity.
"I was living in New York and the first phone call I got after the attack was from the permanent mission of Singapore to the United Nations," she said. "I felt that my people were looking out for me."
With a scientist's eye for detail, Dr Wee explains the process of shaping, glazing and firing clay - not surprising as the singleton had been a National Aeronautics and Space Administration research fellow before embracing ceramic art.
Her first brush with clay came in 2000, when her friend arranged for her to take a class.
"I was awful at it," she exclaimed, but it flicked an artistic switch in her and she was hooked. "It was so clear to me. I want to rush to the studio to make work. I never rush to the lab to turn on computers," she said.
She plunged into ceramics full time after completing her PhD in geography in 2005 and gave herself five years to see where she could go with her art, living on money she had saved as a doctoral student.
In 2006, she won first prize at the Ceramics Biennial organised by the New Hampshire Institute of Art.
"It was very helpful, because my choice was validated," she said.
But it was not always plain sailing. "In the beginning, I would sell two pieces a year," she said, but she stuck it out. Now, her pieces are part of the permanent collection of the National Gallery of Singapore and the Guangxi National Art Centre, among others.
Her big project this year is to organise a Singapore arts festival called Something to Write Home About, to showcase Singaporean creatives based in the US and Singapore. She says it will be her tribute to SG50.
Singaporeans are finding novel ways to make it in the US. Watch their stories as told by Straits Times reporter Melissa Sim at http://str.sg/ELK.


Interpolation is basically just the creation of intermediate points between two points. In games, this is quite often used to move an object smoothly from one place to another over several frames.
This basically represents a straight line segment between p0 and p1, with t representing how far along the line we are.
This form does have some possible performance advantages. First, there is only one multiplication to perform. Second, since p0 and p1 are constants, it is also possible to pre-compute the subtraction.
This basic formula also works for vectors, so p0 and p1 can be single floating point values, 2D or 3D points, or vectors of any other size.
This is such a common and basic function that it is an intrinsic function in shader languages.
Quite often you will find that the values you want to use as the interpolation amount (t) are not between 0 and 1.
Suppose we have three points, p0, p1, and p2. We can interpolate between p0 and p1, and then from p1 to p2. This allows us to follow a path through multiple points, but the results are usually not very satisfactory. For motion of an object, changes in speed and direction are very abrupt and unnatural.
One easy way to smooth out these transitions is to modify the value of t before doing the interpolation. The main advantage to this is the ability to reuse the basic linear interpolation function for various non-linear interpolation methods.
Because t' (the first derivative) is zero at t0=0 and t0=1, there will be less apparent discontinuity as we pass through each point.
The second derivative is still non-zero at t0=1, which may still be perceived as a discontinuity. In terms of physics, this would be the same as having zero velocity at the end point, but non-zero acceleration.
This function is common enough to be, like lerp, implemented in shader languages. Implementations for smoothstep typically also include the normalization step, so t = smoothstep(0, 1, t0) is equivalent to the basic smoothstep function.
This will have first and second derivatives equal to zero at t0=0 and t0=1.
There are many other possible functions that you may find useful, depending on the circumstances. In general, any function that gives output values in the range [0,1] for input in the range [0,1] will work.
I have found it useful to have all of these curves available (and their derivatives and integrals) available in a general-purpose library.
Hopefully there is some useful information here that helps you with your own programming!


The American Swedish Historical Museum offers a variety of educational programs for all audiences. From school programs, to Swedish language classes to Swedish genealogy, the Museum has something for learners of all ages.
It's never too early to introduce world culture to preschoolers! The American Swedish Historical Museum is excited to offer specially designed programs for Pre-K students that build and reinforce early learning skills. The My 1st Museum program engages children through interactive stories, music, games, art, and museum exploration. Children will get a personal introduction to museum culture. Each program conforms to specific Pennsylvania pre-kindergarten learning standards with preprogram materials available to assist teachers get students ready for their experience.
Cost: $5.00 per child, minimum and maximum attendance rules apply, call for details.
Children will learn about adaptations of animals native to the cold climate of Sweden.
Children will reinforce their knowledge of the five senses through interactive stories and music movement. Toddlers will visit five rooms in the museum and test each of their senses.
Enter the unique world of Swedish born author Astrid Lindgren and her famous character Pippi Longstocking. Children will be introduced to Pippi through hands on exploration of our interactive exhibit.
Colors, Shapes, and Sculpture, Oh My!
This art inspired program will reinforce knowledge of shapes and color through interactive songs and stories. Children will discover that art isn't just on paper during this interactive lesson introducing sculpture.
Bring the program that engages children through interactive stories, music, games, art, and museum exploration to your preschool. Children will get a personal introduction to museum culture. Each program conforms to specific Pennsylvania pre-kindergarten learning standards with preprogram materials available to assist teachers get students ready for their experience.
Cost: $100.00 for groups within 20 miles. Additional travel costs apply for further distances.
If your preschool provides subsidized care for students, inquire about becoming a program partner with ASHM to receive financial aid towards the program fee and transportation.
Children will discover the wonderful world of textiles and learn how wool from a sheep is made into new clothes.
Children will explore all modes of transportation and see at how people get around both in the U.S and Sweden.
Sweden is a leader when it comes to recycling. Children will learn resources can be reused instead of thrown away by playing games and making art with recycled materials.
ABCs & 123s Svenska Style!
Children will build those language and math skills by reinforcing their knowledge of the alphabet and learn how to count in English and Swedish.


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