Everyone's idea of comfort food is different—but whether it's Grandma's apple pie or Dad's macaroni and cheese, the key ingredient is nostalgia. Two new STL eateries are taking you back to the good old days with comfort foods both sweet and savory.
An upcycled retro cafe? in Carondelet, Melt (7700 Ivory Ave.) brings to the table a menu chock full of waffles, ice cream, specialty alcoholic drinks and milkshakes served in mason jars—perfect for an evening of going for the high score on the pinball machines.
Meanwhile, Southwest Diner (6803 Southwest Ave.) in Ellendale takes home-style cooking and adds some spice with a New Mexican twist. The diverse menu includes favorites like buttermilk cornmeal pancakes, biscuits with chorizo gravy and green chile cheeseburgers.


My painting "Flights of Fancy" is to be exhibited as part of the "Lust for Life" exhibition at the Menier Gallery this August.
The PV is this Thursday July 4th and it would be lovely to see some of you there. There will be a short talkat 7.00pm on PV night, given by Beatriz Acevedo.
I was contacted by Renee Rilexie the artist and curator from the Artists Pool last September, who let me know this exhibition was in the making. Coincidentally I had been working on some paintings inspired by the Argentine Giga, a giant hummingbird. I was also experimenting with the painting styles of Diego Rivera and Frida Kahlo. I was using the Giga as a metaphor for how inspiration travels. At the same time I had visited the Alexander McQueen retrospective at the V & A, and so, "Flights of Fancy" came into being.
I loved making this painting, It has many wonderful associations which are very close to my heart. I am also looking forward to seeing the work of the other artists involved, so many responses to Frida Kahlo all in one location.
News from Walking with The Waste Land July17th 2016.
The walk was designed by the walking research group following an invitation by The University of Kent to create a walk for a Sunday event for delegates at their symposium "Writing Buildings." The symposium brought together the schools of Architecture and Literature on a three day conference looking at the intersection of literature and architecture.
elspethpenfold@yahoo.co.uk and I will add you to the mailing list.
You can also follow this blog to receive updates.
I will be documenting this walk during a residency at the Sun Pier house gallery in Chatham in collaboration with the photographer Jennifer Deakin. The work will be on display until July 31st. and explores using ropes as a way of recording memories in the form of a "Quipu." Jennifer will be exhibiting her photographs which were taken during the walk. We hope you have time to visit!
A big thank you to those of you who came on Wednesday June 29th and gave so willingly of your time, knowledge, ideas, creativity and company. For those who couldn't make it, life does get in the way, and we missed you but hope to see you on July 17th. when we will be hosting delegates from the University of Kent symposium"Writing Buildings".
Special events in Margate, Kent.
In 1921 T.S Eliot wrote part of 'The Waste Land' in Margate whilst recuperating from a nervous breakdown. Join Turner Contemporary's Waste Land Research Group for a multi-sited reading of the poem responding to the geography of the town. Locating the poem experimentally within the architecture of Margate, passages of 'The Waste Land' will be read on a walk exploring participants' personal connections between the poem, the town and Eliot's time here.
The Waste Land Research Group is made up of members of the Community working with Turner Contemporary to develop the gallery's first major exhibition of 2018, A Journey with 'The Waste Land', which will explore the connections between the poem and the visual arts. Walking is being developed as a research method for understanding how the poem can be rooted experientially within the town.
Yesterday we walked in quite unfavourable weather, which is probably a good thing as who knows what will happen on the day. There are 10 locations which I had linked to the poem, many of these links came about as a result of the walks we have engaged in since last November. Yesterday the walking group walked to these and tested them out by reading the sections at the site and discussing afterwards. There was a general consensus that these worked well. After the walk we had a cup of tea (courtesy of lovely Margaret, thank you.) and discussed the way forward.
I am presently undertaking a residency at Sun Pier house gallery in Chatham and am using this opportunity to experiment with documenting the walk. Please feel free to visit.


The transformation of our national traffic safety culture is recognized as a necessary condition for achieving our nation's traffic safety goals (reducing injuries and fatalities) including the Toward Zero Deaths vision. However, current research and practices are not sufficient to implement a strategic program for cultural transformation. This project will develop a process and guidelines for developing, implementing, and evaluating strategic programs for cultural transformation that are integrated within existing traffic safety planning processes of traditional and non-traditional traffic safety partners. Several products will be created including a reference guide (handbook) for transforming culture across all levels of our society (including examples demonstrating the application of these guidelines) and a series of recorded workforce development video lectures to support the implementation of the handbook guidelines.
For more information, please visit TRB NCHRP 17-69.


It's no secret that when it comes to your cell phone, car radio and computer, you want the best of the best.
After all, electronics are no longer luxuries – they're necessities that speak volumes about your unique style and tastes. And when it comes to your style, you want the world to know that you're always on the lookout for the newest gadget, mobile phone, computer and radio speakers and amplifiers. Because let's face it: no one ever turned heads with an outdated cell phone or car radio speakers that barely make a sound.
You're not someone who is willing to settle for anything less than the highest-quality – but you also know that shouldn't have to be rich to enjoy the best electronics on the market today. So how can you enjoy the best electronics in Decatur without sacrificing your bank account balance for the privilege?
Simple: call the experts at Platinum Auto & Electronics & Cellular in Decatur, GA!
At Platinum Auto & Electronics & Cellular, we understand that you don't want to fork over an entire month's paycheck just to stay up-to-date with the latest mobile phones, computers and car radios. That's why we're proud to offer our clients flexible pricing on a wide range of the best electronic brands. From discount computers and cheap cell phones to the very best car radio speakers in the industry, you'll find everything you're looking for at Platinum Auto & Electronics & Cellular.
Your experience doesn't end when you walk out of our store; in fact, we pride ourselves on offering the best car radio installation and repair service in the greater Atlanta, GA area. Don't sacrifice incredible audio quality to inexperienced DIY installation; instead let our professional technicians install your car radio, speakers and amplifiers at a price that won't break the bank.
With such a wide range of high-quality products and services on offer, we know that we're the perfect electronics vendor in Decatur, Lithonia, Stone Mountain, and Conyers to suit all of your needs. So if it's time to upgrade that cell phone or take your ride to the next level with a set of impressive speakers, let the friendly and knowledgeable experts at Platinum Auto & Electronics & Cellular help you pick out exactly what you need.
Call 678) 661-7147 today – and start enjoying your electronics again!


A family walk in aid of Burncourt National School will take place on Sunday 2nd April. The walk will leave from Glengarra Woods car park at 2pm. Entry is five euro and all funds raised will go towards our school. Thank you!


text:
Q: Atomically incrementing counters stored in ConcurrentHashMap I would like to collect some metrics from various places in a web app. To keep it simple, all these will be counters and therefore the only modifier operation is to increment them by 1.
The increments will be concurrent and often. The reads (dumping the stats) is a rare operation.
I was thinking to use a ConcurrentHashMap. The issue is how to increment the counters correctly. Since the map doesn't have an "increment" operation, I need to read the current value first, increment it than put the new value in the map. Without more code, this is not an atomic operation.
Is it possible to achieve this without synchronization (which would defeat the purpose of the ConcurrentHashMap)? Do I need to look at Guava ?
Thanks for any pointers.

P.S.
There is a related question on SO (Most efficient way to increment a Map value in Java) but focused on performance and not multi-threading
UPDATE
For those arriving here through searches on the same topic: besides the answers below, there's a useful presentation which incidentally covers the same topic. See slides 24-33.

A: You're pretty close.  Why don't you try something like a ConcurrentHashMap<Key, AtomicLong>?
If your Keys (metrics) are unchanging, you could even just use a standard HashMap (they are threadsafe if readonly, but you'd be well advised to make this explicit with an ImmutableMap from Google Collections or Collections.unmodifiableMap, etc.).
This way, you can use map.get(myKey).incrementAndGet() to bump statistics.

A: Other than going with AtomicLong, you can do the usual cas-loop thing:
private final ConcurrentMap<Key,Long> counts =
    new ConcurrentHashMap<Key,Long>();

public void increment(Key key) {
    if (counts.putIfAbsent(key, 1)) == null) {
        return;
    }

    Long old;
    do {
       old = counts.get(key);
    } while (!counts.replace(key, old, old+1)); // Assumes no removal.
}

(I've not written a do-while loop for ages.)
For small values the Long will probably be "cached". For longer values, it may require allocation. But the allocations are actually extremely fast (and you can cache further) - depends upon what you expect, in the worst case.

A: In Java 8:
ConcurrentHashMap<String, LongAdder> map = new ConcurrentHashMap<>();

map.computeIfAbsent("key", k -> new LongAdder()).increment();

A: Guava's new AtomicLongMap (in release 11) might address this need.

A: Got a necessity to do the same.
I'm using ConcurrentHashMap + AtomicInteger.
Also, ReentrantRW Lock was introduced for atomic flush(very similar behavior).
Tested with 10 Keys and 10 Threads per each Key. Nothing was lost.
I just haven't tried several flushing threads yet, but hope it will work.
Massive singleusermode flush is torturing me...
I want to remove RWLock and break down flushing into small pieces. Tomorrow.
private ConcurrentHashMap<String,AtomicInteger> counters = new ConcurrentHashMap<String, AtomicInteger>();
private ReadWriteLock rwLock = new ReentrantReadWriteLock();

public void count(String invoker) {

    rwLock.readLock().lock();

    try{
        AtomicInteger currentValue = counters.get(invoker);
        // if entry is absent - initialize it. If other thread has added value before - we will yield and not replace existing value
        if(currentValue == null){
            // value we want to init with
            AtomicInteger newValue = new AtomicInteger(0);
            // try to put and get old
            AtomicInteger oldValue = counters.putIfAbsent(invoker, newValue);
            // if old value not null - our insertion failed, lets use old value as it's in the map
            // if old value is null - our value was inserted - lets use it
            currentValue = oldValue != null ? oldValue : newValue;
        }

        // counter +1
        currentValue.incrementAndGet();
    }finally {
        rwLock.readLock().unlock();
    }

}

/**
 * @return Map with counting results
 */
public Map<String, Integer> getCount() {
    // stop all updates (readlocks)
    rwLock.writeLock().lock();
    try{
        HashMap<String, Integer> resultMap = new HashMap<String, Integer>();
        // read all Integers to a new map
        for(Map.Entry<String,AtomicInteger> entry: counters.entrySet()){
            resultMap.put(entry.getKey(), entry.getValue().intValue());
        }
        // reset ConcurrentMap
        counters.clear();
        return resultMap;

    }finally {
        rwLock.writeLock().unlock();
    }

}

A: I did a benchmark to compare the performance of LongAdder and AtomicLong.
LongAdder had a better performance in my benchmark: for 500 iterations using a map with size 100 (10 concurrent threads), the average time for LongAdder was 1270ms while that for AtomicLong was 1315ms.

redpajama_set_name: RedPajamaStackExchange


text:
Q: MacOS - detect when camera is turned on/off I want to automate a personal workflow that is based on camera usage on my MBP.
Basically I want to know if any of the cameras (built-in or USB) has been turned on or off, so I can run a program or script I'll create.
I think it's OK if I need to poll for the cameras statuses but an event or callback based solution would be ideal

A: log stream --predicate 'eventMessage contains "Post event kCameraStream"' works up to macOS Big Sur, but not in macOS Monterey.  You'll have to use a slightly different predicate:
$ log stream --predicate 'subsystem contains "com.apple.UVCExtension" and composedMessage contains "Post PowerLog"'
Filtering the log data using "subsystem CONTAINS "com.apple.UVCExtension" AND composedMessage CONTAINS "Post PowerLog""
Timestamp                       Thread     Type        Activity             PID    TTL
2021-10-27 12:21:13.366628+0200 0x147c5    Default     0x0                  353    0    UVCAssistant: (UVCExtension) [com.apple.UVCExtension:device] UVCExtensionDevice:0x1234005d7 [0x7fe3ce008ca0] Post PowerLog {
    "VDCAssistant_Device_GUID" = "00000000-1432-0000-1234-000022470000";
    "VDCAssistant_Power_State" = On;
}
2021-10-27 12:21:16.946379+0200 0x13dac    Default     0x0                  353    0    UVCAssistant: (UVCExtension) [com.apple.UVCExtension:device] UVCExtensionDevice:0x1234005d7 [0x7fe3ce008ca0] Post PowerLog {
    "VDCAssistant_Device_GUID" = "00000000-1432-0000-1234-000022470000";
    "VDCAssistant_Power_State" = Off;
}

A: This seems to work.
❯  log stream | grep "Post event kCameraStream"
2020-12-01 14:58:53.137796-0500 0xXXXXXX   Default     0x0                  XXX    0    VDCAssistant: [com.apple.VDCAssistant:device] [guid:0xXXXXXXXXXXXXXXXX] Post event kCameraStreamStart
2020-12-01 14:58:56.431147-0500 0xXXXXXX   Default     0x0                  XXX    0    VDCAssistant: [com.apple.VDCAssistant:device] [guid:0xXXXXXXXXXXXXXXXX] Post event kCameraStreamStop
2020-12-01 14:58:56.668970-0500 0xXXXXXX   Default     0x0                  XXX    0    VDCAssistant: [com.apple.VDCAssistant:device] [guid:0xXXXXXXXXXXXXXXXX] Post event kCameraStreamStart

Some of the numbers in the output are redacted with Xs because I don't know what they mean. :)

A: As far as I know, you can poll for the camera usage with:
$ lsof -n | grep "AppleCamera"

or change "AppleCamera" with the driver name of an external camera.
Other relevant names to try are: "USBVDC" or "VDCAssistant" or "FaceTime" (or "iSight" in older Macs).
You should get one line with the name and pid of the process using the webcam or nothing, which means that it is not in use.
You could check for all of the keywords and decide that the camera is in use if any of these keywords give you something back.
The -n option is to skip resolving DNS names of IP connections and this speeds the command a lot.
As a side note, I use this app to know when any app is using the microphone and/or webcam: OverSight

A: In macOS Ventura I find this incantation works:
log stream --predicate 'sender contains "appleh13camerad" and (composedMessage contains "PowerOnCamera" or composedMessage contains "PowerOffCamera")'


text:
The Saint Louis Perfectos and the Lafayette Square Cyclones are Base Ball clubs playing by the rules and customs of the 1860's. It is the goal of the clubs to spread the game of Vintage Base Ball and to provide an entertaining and fun atmosphere for all. As member clubs of the Greater St. Louis Base Ball Historical Society, players of all ages (over 18) and skill levels are welcome to join.
The clubs are dedicated to the preservation and demonstration of the great game of base ball as it was played in the mid 19th Century. In a nutshell, that means they pitch underhanded, catch the ball barehanded, and swing wooden bats the size of telephone poles (well, some of us do). All of this is done in grassy meadows under the summer sun with some of the craziest and most fun people you'll likely ever meet.
The home field of both teams is in historic Lafayette Park. The teams feel it is important (and historically significant) to play home games in St. Louis, preferably at a public park where residents can enjoy watching and participating in these games. With its rich history, Victorian-era personality and a vibrant surrounding neighborhood, Lafayette Park is an ideal location for the team's home games.
They play in an unmarked field at the northwest corner of Lafayette Park (Missouri and Park Avenues). Look for our "Vintage Base Ball To-Day" sign. Please bring your own seating (e.g., lawn chair), because there is no "field seating" available.
For a schedule of all Lafayette Park activities, including Vintage Base Ball games, visit our Events Calendar page.

redpajama_set_name: RedPajamaCommonCrawl


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

Obtaining robust solutions against parametric variations in optimal control problems is a requirement in various applications, particularly in the fields of aerospace and robotics.
For many problems, it is essential that for a given performance criterion, one can also ensure minimal dispersion in the total cost, in spite of variations in the problem parameters.
A simple example would be the case of finding a minimum-time trajectory between two points (cities) on a map when a trajectory with travel time that is insensitive to traffic flow variations is desirable.
In this example, the trajectory designer is interested in finding a good trade-off between the minimum cost solution and a solution that is less sensitive to variations in the model parameters (the traffic flow in the previous example).
Solutions obtained by existing optimal control theory are model-dependent, and their resilience to variations in uncertain system parameters is not guaranteed.

A great deal of research has been performed in robust control that primarily focuses on the stabilization of systems under uncertainty and $H_\infty$ optimal control \cite{bhattacharyya1995robust,zhou1998essentials}.
Previous attempts have primarily aimed at stability and performance criteria defined over an infinite horizon~\cite{petersen2014robust, wang1992robust}.
Questions regarding the sensitivity of the trajectory (or the cost) explicitly and its implications on the performance have been largely overlooked.
In \cite{amato2001finite}, the authors have addressed the implications of parametric uncertainties over a finite horizon using linear matrix inequalities (LMIs), however, the problem does not address the sensitivity of the performance with respect to the parameters.
Traditionally, robust optimal control \cite{zhou1996robust, korkel2004numerical, Nagy2004411, lin1998optimalrobot} and feedback control synthesis \cite{HOROWITZ1963v} have been used to address the issue of parametric uncertainty, with an inherent trade-off between cost and robustness to
be decided.
Indeed, the increased cost is incurred due to
additional control effort, in magnitude or over time.
The main goal of \emph{desensitized optimal control}  (DOC) is to alleviate the additional effort induced onto the control feedback loop by, instead, picking a trajectory which is less sensitive to variations under parametric uncertainty.

Desensitization of a solution can include addressing the problem of minimizing variations:
a) in the optimal trajectory; b) in the final state; or c) in the optimal cost under variation in model parameters, for a given optimal control problem.
The former two cases were dealt with in our previous work \cite{ramana2018doc}.
Three different formulations that employ sensitivity functions were put forth which desensitize either entire trajectories or the state at a particular
time (e.g., final time).

An approach to desensitize the cost for an optimal control problem with fixed final time is presented in this paper.
To this end, we recall that the co-states in an optimal control problem are a measure of the sensitivity of the value function with respect to the states along the optimal trajectory \cite{bryson, Peterson1974}.
In this paper, we first prove that the co-states indeed capture sensitivity of the \emph{cost-to-go} function with respect to perturbations in the state given \emph{any} prescribed control law $u(t)$, not just the optimal one.
Using this fact, a new approach to solve the DOC problem is presented.

Early work on trajectory sensitivity design include those of Winsor and Roy \cite{Winsor1970}, who developed a technique to design controllers that provide assurance for system performance under mathematical modeling inaccuracy.
The feasibility of the technique was established with appropriate simulation results.
However, their work has been restricted to linear systems.
Following that work, several approaches including sensitivity-reduction for linear regulators, using increased-order augmented system \cite{SUBBAYYAN_sensitivity},
modification of weighting matrix \cite{VERDE_sensitivity_reduction}, feedback \cite{Zames_optisensitivity, Chang_optidist_red}, and an augmented cost function \cite{Tang_sensitivity_1990, cheli2006observer}, were all thoroughly analyzed.
The approach of using an augmented cost function was further tested on the linear quadratic regulator (LQR) problem, which was later applied for active suspension control in passenger cars \cite{cheli2006observer}.

The work by Seywald et al. on desensitized optimal control makes use of sensitivity matrices to obtain an optimal open-loop trajectory that is insensitive to first-order parametric variations \cite{seywald1996desensitized, seywald2019}.
The proposed approach elevates the parameters of interest to system states, and defines a sensitivity matrix that provides the first-order variation in the states at time $t$, given the variation in the states at some time $t'$ ($t' \leq t$).
An appropriate sensitivity cost is added to the existing cost function, and the dynamics of the sensitivity matrix is augmented in the system dynamics to solve the resulting optimal control problem.
The approach was later extended to optimal control problems with control constraints \cite{seywald2003desensitized}, and it was used to solve the Mars pinpoint landing problem \cite{shen2010desensitizing}.
Some extensions to the landing problem include considering uncertainties in atmospheric density and aerodynamic characteristics \cite{Xu2015}, and using direct collocation and nonlinear programming \cite{li2011mars}.
However, the sensitivity matrix based approaches \cite{seywald1996desensitized, seywald2019} requires propagating the original states, the targeted parameters, and the elements in the sensitivity matrix, resulting to a total of $(n+\ell)^2 + n + \ell$ number of states.
An alternative approach was presented in \cite{ramana2018doc} where the dimensionality of the state-space for the augmented problem is reduced to $n + n\ell$, using traditional sensitivity functions.
Also, techniques based on sensitivity matrices have close connections with covariance trajectory-shaping, which was studied by Zimmer \cite{zimmer2005reducing} and Small \cite{small2010optimal}.
A more detailed discussion on the existing methods for desensitized control can be found in \cite{weinmann2012uncertain}.

The contributions of this paper are summarized as follows:
First, we mathematically prove (Theorem \ref{thm:main}) the fact that for any given control law, the co-states of an optimal control problem capture the first-order variations of the cost-to-go function given the variations in the system states.
Second, we provide an approach to desensitize (reduce the variations of) the cost with respect to parametric variations by elevating the parameters to system states, and then penalizing the associated co-states of the optimal control problem.
Third, it is shown that the co-states and the sensitivity matrices (in Ref. \cite{seywald2019}) are related.
The approach is demonstrated on the Zermelo's navigation problem, and on a standard linear system thereby establishing its efficacy.

The rest of the paper is organized as follows.
Section~\ref{sec:motivation} presents some preliminaries and formulates the problem addressed in this work.
Section~\ref{sec:analysis} first presents a derivation of the relationship between the cost-to-go function and the co-states, and then provides an approach to solve the co-state based desensitized optimal control (C-DOC) problem.
Section~\ref{sec:examples} demonstrates the proposed approach with two examples.
It also contains important observations which point at some nuances of the approach.
Section~\ref{sec:relation} discusses the relation between co-states and sensitivity matrices.
Section~\ref{sec:conclude} concludes the paper with some directions for future work.

\section{Background and Preliminaries} \label{sec:motivation}

Consider a standard optimal control problem of the form
\begin{align}
    \inf_u~~ &\mathcal{J}(u,p) \triangleq \phi(x(t_f),t_f) + \int_{t_0}^{t_f}L(x(t),u(t),t) \, \diff{t},
\label{eq:cost}
\end{align}
subject to
\begin{subequations}
\begin{align}
\dot{x} = f(x,p,u,t),& \quad x(t_0) = x_0, \label{eq:ini-dynamics},\\
\psi(x(t_f),&t_f) = 0, \label{eq:subjectto}
\end{align}
\end{subequations}
where $t \in [t_0,\,t_f]$ denotes time, with $t_0$ being the initial time and $t_f$ being the final time (both assumed to be fixed),  $p \in \mathcal{P} \subset \mathbb{R}^\ell$ are $\ell$ unknown, possibly time-varying, model parameters, $x(t) \in \mathbb{R}^n$ denotes the state, with $x_0$ being the fixed state at $t_0$.
The control $u \in \mathcal{U}=\{ \text{Piecewise Continuous (PWC)},\,u(t) \in  U, ~ \, \forall\, t \in [t_0,t_f] \},$
with $U \subseteq \mathbb{R}^{m}$ being the set of allowable values of $u(t)$, $\phi:\mathbb{R}^{n}\times [t_0,t_f] \rightarrow \mathbb{R}$, the terminal cost function, and $L:\mathbb{R}^{n}\times\mathbb{R}^{m}\times [t_0,t_f] \rightarrow \mathbb{R}$, the running cost.
Finally, $\psi: \mathbb{R}^n \times [t_0,t_f] \rightarrow \mathbb{R}^k$ is a function representing $k$-number of constraint equations at the final time.
The above problem is to be solved by finding the optimal control $u^* \in \mathcal{U}$ that minimizes the cost function in (\ref{eq:cost}).
The solution involves the optimal trajectory $x^*(t)$, $t \in [t_0,t_f]$, determined from $\dot{x}^*(t) = f(x^*(t), p, u^*(t), t)$ subject to $x^*(t_0) = x_0$, and the optimal cost $\mathcal{J}^* = \phi(x^*(t_f),t_f) + \int_{t_0}^{t_f}L(x^*(t),u^*(t),t) \, \diff{t}$.

The system dynamics represented by the function $f(x,p,u,t)$ contains the model parameters $p$ which are assumed to be constant.
It is understood that the optimal solution (constituting the cost, and the trajectory) is model-sensitive and, if changes in the parameters $p$ occur at any time $t \in [t_0,t_f]$, then the optimality of the obtained solution is not guaranteed.
Consequently, the optimal control problem has to be resolved
for each new value of the parameter vector.
If the optimal solution $u^*$ is used despite the parameter variations, one can expect a dispersion in the optimal trajectory (and/or cost $\mathcal{J}^*$).
With a motivation to minimize the dispersion of the final state $x^*(t_f)$ of the optimal solution, under parametric uncertainties, Seywald and Kumar constructed an augmented cost function using sensitivity matrices~\cite{seywald1996desensitized}.
The approach goes as follows.

First, the parameters of interest and the corresponding entries in the sensitivity matrix are elevated to states, and the augmented state $[ \tilde{x}^\top~(\vecop S)^\top] ^\top$,  where $\tilde{x} = [x~p]^\top$,
along with the corresponding dynamics and initial conditions are derived.
The sensitivity of the vector $\tilde{x}(t)$\footnote{From time to time we will denote $\tilde x(t)$ as $\tilde{x}(t|t_0,\tilde x_0)$ to explicitly represent the dependency on the initial conditions $\tilde{x}_0 = [x(t_0)^\top ~p(t_0)^\top]$} at time $t$ with respect to perturbations in the initial state vector $\tilde{x}(t_0) = \tilde{x}_0$ is denoted as $S(t|t_0,\tilde x_0)$
That is,
\begin{equation} \label{Sey:SF}
S(t|t_0,\tilde x_0) = \frac{\partial \tilde{x}(t|t_0,\tilde{x}_0)}{\partial \tilde{x}_0}.
\end{equation}
The dynamics of the  state $\tilde x$ can be written as
\begin{align}
&\dot{\tilde{x}} = \tilde{f}(\tilde{x},u,t) = [f^\top(x,p,u,t)~~0_{1 \times \ell}]^\top, \nonumber \\
&\tilde{x}(t_0) = \tilde{x}_0 = [x^\top_0~~p^\top_0]^\top, \label{dynamics_augstate}
\end{align}
and
\begin{align}
\dot{S}(t|t_0,\tilde x_0) = \frac{\partial \tilde{f}}{\partial \tilde{x}}S(t|t_0,\tilde x_0), \quad S(t_0|t_0,\tilde x_0) = I_{(n+\ell)}, \label{dynamics_seywald}
\end{align}
where  $p_0$ is the nominal value of the parameter vector, and where $S(t|t_0,\tilde x_0)$ represents the sensitivity of the vector $\tilde{x}(t)$ at time $t$ with respect to perturbations in the initial state vector $\tilde{x}(t_0)$.

The augmented cost function, given in (\ref{eq:seywald_aug}) below, is then minimized to obtain an optimal solution with the final state being ``desensitized" with respect to the parameter variations
\begin{align}     \label{eq:seywald_aug}
\mathcal{J}_s(u,p) = \mathcal{J}(u,p) + \int_{t_0}^{t_f} \| \vecop \left( S(t_f|t_0,\tilde x_0) S(t|t_0,\tilde x_0)^{-1}\right) \|_{Q(t)}^{2} \Big) \diff{t},
\end{align}
with $Q(t) \geq 0,~\text{for all}~t \geq t_0$.
Note that the sensitivity matrix of Seywald in (\ref{Sey:SF}) has the form of a state transition matrix and its properties are exploited to construct the sensitivity of the final state with respect to the variations in the state at time $t\in [0, t_f]$, which is then plugged into the running cost (\ref{eq:seywald_aug}).
This is elaborated upon in Ref. \cite{seywald1996desensitized}. The approach achieves the desensitization of the final state.

\subsection{Problem Formulation}

In this work, we are interested in desensitizing the cost itself.
By denoting
\begin{align}
    \mathcal J(u,p)=\int_{t_0}^tL(x(s),u(s),s)\diff{t}+C(\tilde x(t),u,t),\\
    C(\tilde x(t),u,t)=\int_{t}^{t_f}L(x(s),u(s),s)\diff{t}+\phi(x(t_f),t_f),
\end{align}
we immediately notice that the parametric variation at time $t$, affects the total cost $\mathcal{J}(u,p)$ only through the cost-to-go $C(\tilde x(t),u,t)$.
Thus, the sensitivity of the total cost for a parametric variation at time $t$ from its nominal value $p_0$ can be captured through the term
\begin{align}\label{eq:d-cost}
   S_C(x(t),p_0,u,t)= \frac{\partial C}{\partial p}(\tilde x(t),u,t)\Big|_{p=p_0}.
\end{align}
There are several ways to capture the effect of the parametric variations on the cost, one of which is to consider the following sensitivity cost
\begin{align}
   \mathcal{J}_c(u,p_0)= \int_{t_0}^{t_f}\|S_C(x(t),p_0,u,t)\|^2_{Q(t)}\diff{t},
\end{align}
for some $Q(t)\ge 0$, for all $t\ge t_0$.

There are three major formulations relevant to the problem of cost-based desensitization, which are as follows.

\begin{problem} \label{prob:1}
Solve
\begin{subequations}
\begin{align}
    \inf_{u\in \mathcal{U}}~~ & \mathcal{J}(u,p_0)\\
    \mathrm{subject~to}~~&\mathcal{J}_c(u,p_0)\le D.
\end{align}
\end{subequations}
\end{problem}

\vspace{2ex}

Let us denote the solution of Problem \ref{prob:1} to be the ``cost-desensitization'' function $\mathsf{J}(D)$ which represents the optimal cost given a bound on the sensitivity metric.
A similar problem is to consider minimizing the sensitivity of the cost for a given bound on the performance index, as presented below.

\begin{problem} \label{prob:2}
Solve
\begin{subequations}
\begin{align}
    \inf_{u\in \mathcal{U}}~~ & \mathcal{J}_c(u,p_0)\\
    \mathrm{subject~to}~~&\mathcal{J}(u,p_0)\le J.
\end{align}
\end{subequations}
\end{problem}

\vspace{2ex}

Let us denote the solution of Problem \ref{prob:2} to be the ``desensitization-cost'' function $\mathsf{D}(J)$.
Finding analytical or numerical solutions to $\mathsf{J}(D)$ or $\mathsf{D}(J)$ are challenging.
However, $\mathsf{J}(D)$ or $\mathsf{D}(J)$ can be constructed by solving the following family optimization problems for all $\alpha\in [0,\infty)$.

\begin{problem} \label{prob:3}
Solve
\begin{align}
    \inf_{u\in \mathcal{U} }\mathcal{J}(u,p_0)+\alpha\mathcal{J}_c(u,p_0)
\end{align}
\end{problem}

\vspace{2ex}

By observing that the scalar $\alpha$ can be absorbed into the matrix $Q(t)$, we will rewrite the objetive function in Problem \ref{prob:3} as
\begin{align*}
    \mathcal{J}_s(u) =\mathcal{J}(u,p_0)+\mathcal{J}_c(u,p_0).
\end{align*}
When the sensitivity cost has zero weight ($Q(t)\equiv 0$), we solve problem \eqref{eq:cost} and retrieve $\limsup_{D\to \infty}\mathsf{J}(D)$, and as we increase the weight on the sensitivity cost (through $Q(t)$), we arrive at an optimal control whose performance is more insensitive to the variations in the parameters.
In the limit when $Q(t)\to \infty$ for all $t$, we retrieve $\limsup_{J\to \infty}\mathsf{D}(J)$.
In this work, we will focus on minimizing $\mathcal{J}_s(u)$.
Detailed analysis of $\mathsf{J}(D)$ and $\mathsf{D}(J)$ will appear elsewhere.

The new optimization problem  we are interested in solving is
\begin{subequations}
\begin{align}
    \inf_u ~~&\mathcal{J}_s(u) \\
    \text{subject to}~&\dot{x}=f(x,p_0,u,t),~~x(t_0)=x_0,\\
    &\psi(x(t_f),t_f)=0. \label{eq:ter_const}
\end{align}
\end{subequations}

The following section presents a formal proof for the fact that the co-states capture the sensitivity of the cost-to-go function for any given control input $\bar{u}(t)$, that satisfies the terminal constraint (\ref{eq:ter_const}) with nominal value of the parameter $p_0$.
The result would allow us to penalize a weighted norm of the co-states, with their dynamics obtained from the adjoint equations, that desensitizes the cost function with respect to the variations in the targeted parameters.

\section{Co-states and Desensitized Optimal Control} \label{sec:analysis}
In this section we characterize the cost-sensitivity $S_C(x(t),p_0,u,t)$ in terms of the co-state process associated with the optimal control problem given by \eqref{eq:cost}-\eqref{eq:subjectto}.
The following theorem shows that the sensitivity of the cost-to-go function with respect to the state at time $t$ can be represented by a co-state process $\lambda$ with certain boundary conditions at the final time $t_f$.
\vspace{1ex}
\begin{theorem} \label{thm:main}
	Consider the dynamical system $\dot x=f(x,u,t)$, evolving under a given control law $\bar{u} \in \bar{\mathcal{U}}\subseteq \mathcal{U}$, where
	\begin{align*}
	\bar{\mathcal{U}} =  \Big\{ \bar{u}:[t_0, t_f] \rightarrow \mathbb{R}^{m}  \; \text{is}  \; \text{PWC}, \; \bar{u}(t) \in U, \text{ such that } \psi(x(t_f),t_f)=0, \; x(t_f) =x_0 + \int_{t_0}^{t_f}f(x(t),\bar{u}(t),t) \, \diff{t}  \Big\}.
	\end{align*}
Then, for a cost-to-go function (associated with the cost functional \eqref{eq:cost}) with $x = x(t)$
	\begin{align}
	C(x,\bar{u},t) = \phi(x(t_f),t_f) + \int_{t}^{t_f} L(x(\tau),\bar{u}(\tau),\tau) \, \diff{\tau},
	\label{eq:cost-to-go}
	\end{align}
	under the control $\bar{u} \in \bar{\mathcal{U}}$, the sensitivity of the cost-to-go function with respect to the state $x$ at time $t$ is,
	\begin{equation}
	\lambda^{\top}(t) = \dfrac{\partial C}{\partial x}(x(t),\bar{u},t),
	\end{equation}
	which obeys the dynamics
	\begin{equation}
	\dot{\lambda}^{\top}(t) = - \frac{\partial H}{\partial x}(x(t),\bar{u},\lambda(t),t), \label{eq:thm_co-state_dyn}
	\end{equation}
	where
	\begin{align}
	H(x,u,\lambda,t) = L(x,u,t) + \lambda^{\top}f(x,u,t).
	\label{eq:Hamiltonian}
	\end{align}
	Furthermore, the terminal condition for (\ref{eq:thm_co-state_dyn}) is given by
	\begin{align}
	\lambda(t_f) = \frac{\partial \phi}{\partial x}(x(t_f),t_f). \label{trans_cond1

	\end{align}
\end{theorem}

\vspace{1ex}

\begin{proof}
    The proof is presented in Appendix \ref{Ap:proof}.
\end{proof}

\vspace{1ex}

It is interesting to note that the theorem holds not only for the optimal control (a result that follows directly from the maximum principle \cite{pontryagin2018mathematical}), but for any control law that is piecewise-continuous and ensures that the terminal constraint is met. The C-DOC problem can now be fully formulated using this result.

For the C-DOC problem the augmented state is $\tilde{x}=[x^\top,p^\top]$ with dynamics given in \eqref{dynamics_augstate}.
The Hamiltonian, defined in Theorem \ref{thm:main}, for this system, can be written as
\begin{align}
H(\tilde{x}, u, \lambda, \mu, t) &= L(x,u,t) + \lambda^\top \dot{x} + \mu^\top \dot{p} \nonumber \\
&= L(x,u,t) + \lambda^\top f(x,p,u,t),
\end{align}
where $\lambda$ and $\mu$ are the co-states corresponding to state $x$ and vector of parameters defined by $p$, respectively. The corresponding adjoint equations are given by
\begin{align}
\dot{\lambda}^\top &= -\frac{\partial H}{\partial x}(\tilde x, u,\lambda,\mu, t) = -\lambda^\top \frac{\partial f}{\partial x}(x,p,u,t)-\frac{\partial L}{\partial x}(x,u,t), \label{eq:dyn_lambda} \\
\dot{\mu}^\top &= -\frac{\partial H}{\partial p}(\tilde x, u,\lambda,\mu, t) = -\lambda^\top \frac{\partial f}{\partial p}(x,p,u,t). \label{eq:dyn_mu}
\end{align}
Since the co-states represent the sensitivity of the cost-to-go function for a given control input $u(t)$ (Theorem \ref{thm:main}), they can be expressed as
\begin{align}
\lambda(t)^\top &= \frac{\partial C}{\partial x}(\tilde x(t),u,t), \label{eq:lambdat}\\
\mu(t)^\top &= \frac{\partial C}{\partial p}(\tilde x(t),u,t), \label{eq:mut}
\end{align}
for a given control  $u\in \bar{\mathcal{U}}$, this results in the trajectory $x(t)$ for $t_0 \leq t \leq t_f$, where
\begin{align*}
C(\tilde x,u,t) = \phi(x(t_f),t_f) + \int_{t}^{t_f}L(x(\tau),u(\tau),\tau) \, \diff{\tau}.
\end{align*}
Note that $p$ is an augmented state in the given problem and affects the cost $\mathcal{J}$ through the state $x$, whose dynamics is a function of $p$.
Since we have used $\dot p=0$ and $p(t_0)=p_0$, we have ensured that $p(t)=p_0$.
Thus, by comparing equations (\ref{eq:d-cost}) and (\ref{eq:mut}), we obtain $\mu(t) = S_C(x(t),p_0,u,t)$.
Therefore, weighting the co-state in the existing cost function will ensure that the solution of the augmented problem minimizes the sensitivity of the cost $\mathcal{J}$ with respect to parametric variations. This results in an updated optimal control problem with an augmented cost, accounting for the sensitivity component, given by
\begin{align}
{\mathcal{J}}_s(u) &= \phi(x(t_f),t_f) + \int_{t_0}^{t_f}  \left[ L(x(t),u(t),t)  + \mu^\top(t) Q(t) \mu(t) \right] \, \diff{t}. \label{eq:desen_cost}
\end{align}
Minimizing the cost (\ref{eq:desen_cost}) subject to the dynamics (\ref{dynamics_augstate}), terminal constraint (\ref{eq:subjectto}), and the transversality conditions (\ref{trans_cond1}) with
\begin{align}
\mu(t_f) = 0,
\end{align}
yields a desensitized optimal control problem for the original problem. Here, $Q(t)\in \mathbb{R}^{\ell\times \ell}$ is a user-defined positive semi-definite weighting function and is generally of the form
\begin{align}
Q(t) \equiv \text{diag}(\alpha_1(t),\ldots, \alpha_{\ell}(t)).
\end{align}
  This co-state based approach requires formulating $2(n+\ell)$ number of states, as compared to the higher $2(n+\ell)^2 + n+ \ell$ states in \cite{seywald1996desensitized}, employing sensitivity matrices for an optimal control problem.
The resulting problem \eqref{eq:desen_cost} is typically solved by the off-the-shelf existing solvers.

\section{Numerical Examples} \label{sec:examples}

In many applications, the resulting trajectories should be insensitive with respect to perturbations and/or uncertainties within the model parameters at specified times along the trajectory. The following section presents some numerical examples that will aid in understanding the implementation of this technique and will elucidate its subtleties. The simulations are obtained using GPOPS-II \cite{Patterson2014}.

\subsection{Zermelo's Navigation Problem}

Consider a typical Zermelo's problem \cite{seywald1996desensitized} with currents parallel to the shore ($x_1$) as a function of $x_2$ such that
\begin{align}
v_{\text{current}} = p x_2,
\end{align}
where $p$ is a parameter, which is uncertain, and its nominal value is $p_0 = 10$. The problem has to be desensitized with respect to this parameter. The dynamics can be written as
\begin{align}
\dot{x}_1 &= \cos(u) + p x_2, \\
\dot{x}_2 &= \sin(u),
\end{align}
subject to the conditions
\begin{align*}
x_1(0)=0, \quad x_2(0)=0, \\
x_2(t_f)=0, \quad  t_f=1.
\end{align*}
For the case where the state $x_1(t_f)$ has to be maximized, the cost function can be expressed in the Mayer form as
\begin{align}
\min_{u} \mathcal{J}(u) = -x_1(t_f),
\end{align}
where $u \in \mathcal{U}=\left\lbrace \text{C}^0, u(t) \in  [0,2\pi), \; \forall\ t \in \left[0,1\right]\right\rbrace$ and is the control input.
Here, optimization of the trajectory is done with respect to parameter $p$, which is not precisely known.
In order to facilitate desensitization of the cost (in this case the final state $x_1(t_f)$)
with respect to variations in the parameter $p$ we first consider the augmented dynamics
\begin{align}
\dot{\tilde{x}} = \begin{bmatrix}
\dot{x}_1\\\dot{x}_2\\\dot{p}
\end{bmatrix}
=\begin{bmatrix}
\cos(u) + p x_2\\\sin(u)\\0
\end{bmatrix},
\end{align}
with boundary conditions
\begin{align}
\tilde{x}(0) = \begin{bmatrix}
x_1(0)\\x_2(0)\\p(0)
\end{bmatrix} = \begin{bmatrix}
0\\0\\p_0
\end{bmatrix}, \quad x_2(t_f) = 0.
\end{align}
\begin{figure}[htb!]
	\centering
	\subfigure[Optimal trajectories]{\includegraphics[width=0.4\textwidth]{zermelo_traj}}
	\subfigure[$\mu^2(t)$ - a measure of sensitivity]{\includegraphics[width=0.4\textwidth]{zermelo_mu2}} \\
	\subfigure[Monte-Carlo simulations]{\includegraphics[width=0.4\textwidth]{zermelo_mc}}
	\subfigure[Optimal Control ($u^*$)]{\includegraphics[width=0.4\textwidth]{zermelo_control}}
	\caption{Results obtained for the Zermelo's path optimization problem with different levels of desensitization}
	\label{fig:Zermelo}
\end{figure}
The Hamiltonian is given by
\begin{align}
H(\tilde{x},u,\lambda, \mu) &= \lambda_1 (\cos(u)+px_2) + \lambda_2 \sin(u),
\end{align}
and the adjoint equations are:
\begin{align}
\dot{\lambda}_1 &= -\frac{\partial H}{\partial x_1} = 0, \\
\dot{\lambda}_2 &= -\frac{\partial H}{\partial x_2} = -\lambda_1 p, \\
\dot{\mu} &= -\frac{\partial H}{\partial p} = -\lambda_1 x_2.
\end{align}
The cost for the desensitized optimal control problem is
\begin{align}
\min_{u} {\mathcal{J}}_s(u) = -x_1(t_f) + \int_{0}^{t_f} \alpha \mu^2(t) \, \diff{t}.
\end{align}

The weight parameter $\alpha$ is chosen between 0 and 10,000. Figure \ref{fig:Zermelo}(a) shows the optimal paths obtained for the five different values of $\alpha$ in the selected range.
As the value of $\alpha$ increases, the optimal solution moves closer to the shore, minimizing the effect of uncertainty in the current, which has an effect proportional to the distance $x_2$.
For $\alpha \rightarrow \infty$, the optimal path would be moving along the shore, i.e., along the $x_1$ axis.
The results obtained from the Monte-Carlo simulations are shown in Figure \ref{fig:Zermelo}(c) which confirm the expected desensitization of the cost $x_1(t_f)$, further substantiating the claims.
For the Monte-Carlo simulations, a time-constant parametric variation is enforced, and 100 different values between $[0.9p_0,1.1p_0]$ are randomly chosen to be $p$.
The trends of the integrand in the running cost $\mu^2(t)$ (Figure \ref{fig:Zermelo}(b)), show that its value is steadily decreasing and is almost zero for $\alpha = 10,000$.

\subsection{Linear Systems}

Consider an optimal control problem of minimizing a quadratic cost
\begin{align}
\mathcal{J}(u) = \int_{0}^{t_f} {\frac{1}{2}(x^\top R_1 x + u^\top R_2 u)} \, \diff{t},
\end{align}
given the $n$-dimensional linear dynamics with parameter vector $p$
\begin{align}
\dot{x} &= A(p)x + B(p)u,\\
\dot{p} &= 0,
\end{align}
with initial conditions
\begin{align}
x(0) = x_0, \quad p(0) = p_0,
\end{align}
where $x \in \mathbb{R}^n$, $u \in \mathbb{R}^m$, $p \in \mathbb{R}^\ell$, $A:\mathbb{R}^\ell \rightarrow \mathbb{R}^{n \times n}$, $B:\mathbb{R}^\ell \rightarrow \mathbb{R}^{n \times m}$, $R_1 \geq 0$, $R_2 > 0$, and $t_f$ is fixed. The goal is to desensitize the cost with respect to the parameter $p$. Following the steps to construct the cost term for desensitization, the Hamiltonian is given by
\begin{align}
H &= \frac{1}{2}(x^\top R_1 x + u^\top R_2 u) + \lambda^\top \dot{x} + \mu^\top \dot{p}, \nonumber \\
&= \frac{1}{2}(x^\top R_1 x + u^\top R_2 u) + \lambda^\top (A(p)x + B(p)u).
\end{align}
The adjoint equations are
\begin{align}
\dot{\lambda}^\top = -\frac{\partial H}{\partial x} &= -x^\top R_1 - \lambda^\top A(p),\\
\dot{\mu}^\top = -\frac{\partial H}{\partial p} &= - (x^\top \otimes \lambda^\top) \frac{\partial}{\partial p} \kvec(A(p)) - (u^\top \otimes \lambda^\top) \frac{\partial}{\partial p} \kvec(B(p)).
\end{align}
where $\lambda$ and $\mu$ are the co-states of $x$ and $p$, respectively.
Since the cost has to be desensitized with respect to $p$,
the augmented cost that has to be minimized for the C-DOC problem is given by
\begin{align}
{\mathcal{J}}_s(u) = \int_{0}^{t_f} {\frac{1}{2}(x^\top R_1 x + u^\top R_2 u + \mu^\top Q \mu)} \, \diff{t}.
\end{align}

\begin{figure}[htb!]
	\centering
	\subfigure[Optimal trajectories]{\includegraphics[width=0.4\textwidth]{LS_b_traj}}
	\subfigure[$\mu^2(t)$ - a measure of sensitivity]{\includegraphics[width=0.4\textwidth]{LS_b_mu2}} \\
	\subfigure[Monte-Carlo simulations]{\includegraphics[width=0.4\textwidth]{LS_b_mc}}
	\subfigure[Optimal Control ($u^*$)]{\includegraphics[width=0.4\textwidth]{LS_b_control}}
	\caption{Results obtained for an LQR problem with $B$ matrix being uncertain}
	\label{fig:LS_b}
\end{figure}

To demonstrate the results, we consider a one-dimensional
linear system with the dynamics
$\dot{x} = ax+bu$ with initial condition $x(0) = 1$, and let $R_1 = R_2 = 2$, $t_f = 20$.
We first analyze the case where $b$ is the uncertain parameter with its nominal value as $b_0 = 1$, and $a = -1$.
The solutions obtained for $Q = 0$ and $1,000$ are shown in Figure~\ref{fig:LS_b}.
Note that the sensitivity measure ($\mu^2(t)$) in Figure~\ref{fig:LS_b}(b) is lower for the desensitized solution.
Since $b$ is the source of uncertainty that perturbs the trajectory (and eventually the cost), by
introducing desensitization ($Q = 1,000$), it can be observed from Figure~\ref{fig:LS_b}(d) that the control goes to zero earlier compared to the non-desensitized solution.
By making the control zero, the source of uncertainty is removed from the system.
The results obtained from the Monte-Carlo simulations with $ b \in [0.8b_0, 1.2b_0]$ are shown in Figure~\ref{fig:LS_b}(c), which suggests that the variation in the cost for the desensitized solution is significantly lower.

\begin{figure}[htb!]
	\centering
	\subfigure[Optimal trajectories]{\includegraphics[width=0.4\textwidth]{LS_a-1_traj}}
	\subfigure[Optimal Control ($u^*$)]{\includegraphics[width=0.4\textwidth]{LS_a-1_control}} \\
	\subfigure[Monte-Carlo simulations]{\includegraphics[width=0.4\textwidth]{LS_a-1_mc}}
	\subfigure[Cost ($J$)]{\includegraphics[width=0.4\textwidth]{LS_a-1_mc_cost}}
	\caption{Results obtained for an LQR problem with a stable $A$ matrix being uncertain}
	\label{fig:LS_a}
\end{figure}

The results for the case where $a$ is the uncertain parameter with its nominal value as $a_0 = -1$ (stable), and $b = 1$ are shown in Figure \ref{fig:LS_a}.
Since $a$ is the source of uncertainty, by switching on the desensitization ($Q = 1,000$), it can be observed from Figure~\ref{fig:LS_a}(a) that the state approaches zero faster compared to the non-desensitized solution.
Consequently, from the Monte-Carlo simulations ($a \in [0.8a_0, 1.2a_0]$), it can be observed that the variations in the optimal trajectory (Figure \ref{fig:LS_a}(c)), and the cost (Figure \ref{fig:LS_a}(d)) are significantly lower for the desensitized solution, though the cost for the same is higher which is a trade-off.
The error bars in Figure \ref{fig:LS_a}(d) represent the minimum and the maximum costs obtained form the Monte-Carlo results where the corresponding grey bars represent the nominal costs with $a=a_0$.

\begin{figure}[htb!]
	\centering
	\subfigure[Monte-Carlo simulations]{\includegraphics[width=0.4\textwidth]{LS_a1_mc}}
	\subfigure[Cost ($J$)]{\includegraphics[width=0.4\textwidth]{LS_a1_mc_cost}}
	\caption{Results obtained for an LQR problem with an unstable $A$ matrix being uncertain (red: $Q = 0$, green: $Q = 1,000$).}
	\label{fig:LS_a1}
\end{figure}

\begin{figure}[htb!]
	\centering
	\subfigure[Monte-Carlo simulations]{\includegraphics[width=0.4\textwidth]{LS_a0_mc}}
	\subfigure[Cost ($J$)]{\includegraphics[width=0.4\textwidth]{LS_a0_mc_cost}}
	\caption{Results obtained for the LQR problem with $a = 0$ (red: $Q = 0$, green: $Q = 1,000$).}
	\label{fig:LS_a0}
\end{figure}

We also consider an unstable system with $a\in [0.8a_0,1.2a_0]$ being the uncertain parameter with $a_0 = 0.1$.
Figure \ref{fig:LS_a1}(a) shows the Monte-Carlo results, and the behavior is similar to the one in the previous example except that the trajectories are now divergent because the system matrix is unstable.

A more interesting case is a marginally stable system with $a_0 = 0$, and $a\in [-0.2,0.2]$.
The corresponding results can be found in Figure \ref{fig:LS_a0}.
In the previous cases, although a parametric variation in $a$ is studied, such variations did not change the stability of the system, i.e., if the nominal system is stable, then the system with parametric variation is stable as well.
Since $a$ can be both stable and unstable, the optimal control obtained for the nominal system without desensitization will be
less effective combating the instabilities compared to the desensitized solution, as can be seen from the dispersion in trajectories (and costs) in Figure~\ref{fig:LS_a0}.

\section{Discussion: Relation between the Sensitivity Matrix and co-states}
\label{sec:relation}

In this section we address the relationship between the sensitivity matrix defined in \eqref{Sey:SF} and the co-states $\lambda$.
Let us note that,
\begin{align}
\lambda^\top(t) = \frac{\partial C}{\partial x} (x(t),u,t),
\end{align}
which can be expressed as
\begin{align}
\lambda^\top(t) &= \frac{\partial C(x(t),u,t)}{\partial x_0}\left[ \frac{\partial x(t)}{\partial x_0}\right]^{-1} \nonumber  \\
&= \frac{\partial C(x(t),u,t)}{\partial x_0} S(t|t_0,x_0)^{-1}, \label{eq:co-state_sm_rel}
\end{align}
where $S(t|t_0,x_0) = \dfrac{\partial x(t)}{\partial x_0}$ is the sensitivity of the state at time $t$ along the trajectory with respect to variation in its initial condition $x_0$ \cite{seywald1996desensitized}.
Note that the dependency of $x(t)$, $t \geq t_0$ on $t_0$ and $x_0$ (initial conditions) is implicit.
The relationship between the co-state and the sensitivity matrix in (\ref{eq:co-state_sm_rel}) can be generalized to obtain the sensitivity of the solution with regards to the state at any other time $t'$ as

\begin{align}
\lambda^\top(t) &= \frac{\partial C(x(t),u,t)}{\partial x(t')}\frac{\partial x(t')}{\partial x(t)}, \\
&= \frac{\partial C(x(t),u,t)}{\partial x(t')} S(t|t',x(t'))^{-1}~\forall\ t,t' \in [t_0,t_f].
\end{align}
Therefore,
\begin{align}
\lambda(t) &= S(t|t',x(t'))^{-\top} \left[ \frac{\partial C(x(t),u,t)}{\partial x(t')} \right]^\top,\\
\left[ \frac{\partial C(x(t),u,t)}{\partial x(t')} \right]^\top &= S(t|t',x(t'))^{\top} \lambda(t).
\end{align}

From the above expressions, we observe that the sensitivity matrix $S(t|t',x(t'))^{\top}$ is essentially the transition matrix between the co-states $\lambda(t)$ and the partial of the cost-to-go function at time $t$ with respect to the state at time $t'$, i.e., the sensitivity of the cost-to-go function at time $t$ with respect to the state at time $t' < t$.

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

We attempt to exploit the co-states to obtain trajectories that are \emph{less sensitive} to parametric variations.
It is established that the co-states, defined by the Hamiltonian and the adjoint equations, capture the sensitivity of a cost-to-go function
for \textit{any} arbitrary control law.
This has led to the idea of inserting the co-states into the cost function and then studying its implications in the context of DOC.
In particular, this approach has been used to solve the problem of cost desensitization with respect to variation in system parameters.
The results suggest that variations to parametric uncertainty and optimality can be balanced using this approach through the choice of an appropriate weighting parameter.
The numerical simulations give promising results that validate the theory.
The proposed approach can be used to look at some other interesting problems, especially related to robust optimal control.
It is also of interest to closely study its connections with covariance-steering for stochastic dynamical systems~\cite{okamoto2018Optimal}.

\section*{Acknowledgment}

This work has been supported by NSF award CMMI-1662542.

\section*{Appendix}

\subsection{Proof of Theorem \ref{thm:main}} \label{Ap:proof}

For a fix control $\bar{u}$, the cost-to-go  from any state $x$ at time $t$  is
\begin{align*}
    C(x,\bar u,t)=&\phi(x(t_f),t_f)+\int_{t}^{t_f}L(x(s), \bar{u}(s),s)\mathrm d

\end{align*}
where $x(t)=x$.

Let the perturbed state at time $t$  be represented by $x(t,\alpha)=x(t)+\alpha \delta x (t)$ where $\alpha \in [0,\alpha_0)$ for some $\alpha_0>0$, and $\delta x (t)\in \mathbb R^n$.
With this perturbation the new cost-to-go is
\begin{align*}
C(x+\alpha \delta x,\bar{u},t)=  &  \phi(x(t_f,\alpha),t_f)+\\
&~~\int_{t}^{t_f}L(x(s,\alpha),\bar{u}(s),s)\mathrm ds
\end{align*}
where $x(s,\alpha)$ denotes the perturbed state at time $s\ge t$.
By denoting
\begin{align*}
    x(s,\alpha)=x(s,0)+\alpha \mathrm \delta x(s),
\end{align*}
for all $s\ge t$, we obtain
\begin{align*}
    \delta \dot{x}(s)=f_x(x(s,0),\bar{u}(s),s)\mathrm \delta x(s)+O(\alpha),
\end{align*}
where $O(\alpha)$ is such that $\lim_{\alpha\to 0}O(\alpha)=0$.
Consequently, $\delta x(s)=\Gamma(s,t)\delta x(t) +O(\alpha)$
where $\Gamma(s,t)$ is the state transition matrix corresponding to the matrix $f_x(x(s,0),u(s),s)$.

Therefore,
\begin{align*}
    C(x+&\alpha \delta x,\bar{u},t)-C(x,\bar{u},t)=
    \alpha\phi_x(   x(t_f,0), t_f) \Gamma(t_f,t)\delta x +\alpha\left[\int_{t}^{t_f}L_x(x(s,0),u(s),s)\Gamma(s,t)\mathrm ds\right]\delta x
    +O(\alpha^2)
\end{align*}
and thus,
\begin{align*}
    \lim_{\alpha\to 0^+}\frac{ C(x+\alpha \delta x,\bar{u},t)-C(x,\bar{u},t)}{\alpha} &= \Big[\phi_x(x(t_f,0),t_f)\Gamma(t_f,t)+ \int_{t}^{t_f}\,L_x(x(s,0),u(s),s)\Gamma(s,t)\mathrm ds\Big]\delta x,\\
   \implies C_x(x,\bar u,t)& =\phi_x(x(t_f,0),t_f)\Gamma(t_f,t) +\int_{t}^{t_f}L_x(x(s,0),\bar{u}(s),s)\Gamma(s,t)\mathrm ds.
\end{align*}
At this point, if we denote
\begin{align*}
    \lambda^{\top}\triangleq C_x(x,\bar{u},t).
\end{align*}
We then have
\begin{align*}
    \dot{\lambda}^{\top}=-\lambda^{\top}f_x-L_x,
\end{align*}
since $\dot \Gamma(s,t)=-\Gamma(s,t)f_x(x(t,0),u(t),t)$.
Furthermore,
$\lambda(s)$ satisfies the terminal condition $\lambda(t_f)=\phi_x(x(t_f),t_f)$.
Thus, if we define the Hamiltonian as $H=L+\lambda^{\sf T}f$, it follows that
\begin{align*}
    \dot{\lambda}^{\top}=-\frac{\partial H}{\partial x}
\end{align*}
and this $\lambda$ represents the first order variation in cost-to-go with boundary condition
\begin{align*}
    \lambda(t_f)=\phi_x(x(t_f),t_f).
\end{align*}
The result follows.
\hfill$\blacksquare$

redpajama_set_name: RedPajamaArXiv


I have been doing LC-MS/MS method development for almost 15 years and have used stable isotope internal standards for much of that time. Recently I have been asked to start to tutor other staff in my group on quantitative LC-MS/MS method development. I have been trying to find references for the use of stable isotope internal standards but have been unsuccessful. Does anyone know where I can find references for a detailed explanation of the calculations, consideration and propagation of errors that occur with the use of stable isotope internal standards? Specifically I am looking for information regarding internal standard recovery limits and the propagation of error if the internal standard recovery is too low or too high, impact of density on the calculation (standards by volume but samples by weight), limitations for correcting matrix effects, and limits for using the internal standard to correct for sample dilution or concentration during sample preparation.
One of the Waters Senior Applications Chemists in Chemistry Applied Technology wrote a document a while back that describes some of the limitations of stable isotope labeled internal standards when it comes to compensating for matrix effects. It has some references in it as well- again describing instances where SIL internal standards do not adequately compensate for matrix effects.
The literature code is 720002438en if that helps.
This provides some of the information. But for the most part the referenced articles are experimental discussions as to why dueterated compounds may or may not be suitable internal standards. While this has helped identify a few additional sources of error for a couple of the methods I am working on it does not address the more fundamental questions around the calculations of the internal standards and the errors that occur due to the partial recovery of the internal standard. What are the practical limits on using the internal standard to correct for sample losses and matrix effects? Can an internal standard be used to correct for a 95% loss of analyte during sample preparation without introducing significant and unrecognized error? How would I experimentally verify that the recovery (both low and over recovery) of the native compound is not incorrectly adjusted. Does the density of the solution impact the calculations? Can standards be prepared based on volume but sample prepared based on weight without a density conversion as the IS is added based on a final volume concentration or does this introduce additional error in the data manipulation.


text:
L'aéroport de Sievierodonetsk est un aéroport situé en Ukraine. Il est l'aéroport de l'oblast de Louhansk en remplacement de l'Aéroport international de Louhansk détruit par la guerre de 2014. Il est actuellement fermé à la suite de l'invasion de l'Ukraine.

Situation

Statistiques

Compagnies et destinations

Notes et références

Crédits

Liens externes

Sievierodonetsk
Transport dans l'oblast de Louhansk
Sievierodonetsk

redpajama_set_name: RedPajamaWikipedia


text:
kewinn.com
Lead to success
Simon Lichtenberg | TRAYTON GROUP | ZoomInfo.com
Simon Lichtenberg's "Downfalls"
An additional challenge happened when simon lichtenberg (http://www.zoominfo.com) received faulty products from the Zhenjing Leather Factory, eventually leading to him not winning a court case concerning the dispute of fair payment. He is now a success owing to him having to deal with his business difficulties with extraordinary determination and skill. How a hurdle is surmounted decides whether an athlete trips over or clears the barrier; this is similar to how a business may deal with obstacles. Simon Lichtenberg's pathway to success has not been so straightforward but, by adhering to his maxim "Never give up", he has arrived at his goal.
Educational Background of Simon Lichtenberg
Virtually all efficient entrepreneurs are high flyers educationally; this indicates that a solid education, alongside determination, is vital for realising one's objectives. In his teenage years, Simon Lichtenberg resided in Africa after his attendance at Danish Tvind (private) educational institutions. At Fudan University in Shanghai, he secured his diploma in Chinese Language in the year 1988. Simon Lichtenberg has succeeded in his academic endeavours and is considered a leading entrepreneur in the world at present.
Simon Lichtenberg in the World of Business
Challenges are to be found all over the business world; success is the result of conquering them. The wisdom he has learned from making mistakes in running his business paved the way for Simon Lichtenberg to become one of the most capable businessmen in the world today. Simon Lichtenberg became engaged in the furniture market after being in the timber business for some time.
Setting up their own company, into which they can pour all of their passion, hard work and commitment, is one of the finest accomplishments of business-minded individuals. Every accomplished establishment must not only work to make money but must also possess a good reason for its existence. Simon Lichtenberg's organisation is based in Shanghai; it also has other factories located in Zhejiang Jishan.
The Outstanding Accomplishments of Simon Lichtenberg
Simon Lichtenberg acquired his Chinese Language diploma at Fudan University in Shanghai, China. He entered into the timber trade after finishing his schooling in 1992. As a result of having greatly contributed to developing Shanghai, Simon Lichtenberg was presented with the Magnolia Silver Award by the Shanghai Municipal Government in the year 2006. For a lot of businessmen, their most prosperous years (during which they attain great things) become unforgettable as time passes.
Simon Lichtenberg: how to live and work in China
LinkedIn - Dr Marvin Edeas
Plan du site Contact
Business update Lead to success


text:
AWS Solutions
Cloud Migration and Support
Cloud Security and Compliance
Agile ATO for FedRAMP
Government Cloud Solutions
stackArmor is certified Public Sector and AWS GovCloud competency partner with FISMA and FedRAMP Security Authorization and Accreditation (SA&A) experience with multiple US Federal, State & Local and Global Public Sector customers. The US Federal Government has announced the availability of Commercial Cloud Services that meet the FedRAMP High Baseline Requirements. Previously, the FedRAMP authorization process was only designed for low and moderate impact systems; however, with the introduction of a high baseline, even more federal agencies with sensitive data concerns can leverage cost-efficient cloud services from major commercial cloud providers such as Amazon Web Services (AWS) amongst others. The FedRAMP Joint Authorization Board (JAB), comprised of the CIOs of GSA, the Department of Defense, and Department of Homeland Security, have provisionally authorized Amazon Web Services GovCloud Region for FedRAMP High applications. The new FedRAMP High baseline applies to non-classified technology systems under the Federal Information Security Management Act (FISMA), with "High" characterized as if the loss of confidentiality, integrity, or availability of that data could be expected to have a severe or catastrophic effect on organizational operations, assets, or individuals. For example, these more sensitive workloads may include sensitive patient records, financial data, or law enforcement data.
The FedRAMP High authorization applies to the AWS GovCloud (US) Region, including Amazon Elastic Cloud Compute (EC2), Amazon Virtual Private Cloud (VPC), Amazon Simple Storage Service (S3),Amazon Identity and Access Management (IAM), and Amazon Elastic Block Store (EBS). Launched in 2011, the AWS GovCloud (US) is an exclusive region designed to host sensitive workloads in the cloud for government customers. In addition to FedRAMP, AWS GovCloud (US) adheres to U.S. International Traffic in Arms Regulations (ITAR), Criminal Justice Information Services (CJIS) requirements, as well as Levels 2 and 4 for DoD systems.
The certified AWS Solution Architects and Information Assurance Experts at stackArmor have assisted large US Federal Agencies and clients design and implement FedRAMP compliant hosting solutions that comply with the following security requirements and standards:
National Institute of Standards and Technology (NIST) SP 800-53
NIST SP 800-171
The OMB Trusted Internet Connection (TIC) Initiative – FedRAMP Overlay (pilot)
The DoD Cloud Computing Security Requirements Guide (SRG)
NIST SP 800-53 security controls are generally applicable to Federal Information Systems, "…operated by an executive agency, by a contractor of an executive agency, or by another organization on behalf of an executive agency." These are typically systems that must go through a formal assessment and authorization process to ensure sufficient protection of confidentiality, integrity, and availability of information and information systems, based on the security category and impact level of the system (low, moderate, or high), and a risk determination. Security controls are selected from the NIST SP 800-53 Security Control Catalog, and the system is assessed against those security control requirements.
NIST SP 800-171 is generally applicable to Nonfederal Information Systems that store or process federal Controlled Unclassified Information (CUI), but must appropriately protect the confidentiality of the CUI data in accordance with CUI Federal Acquisition Regulation (FAR). These are typically businesses, educational institutions, and research organizations that legitimately store and process federal CUI on their own systems. NIST SP 800-171 and DFARS requires DOD and US Federal contractors and sub-contractors to meet 110 security controls. FedRAMP Moderate accredited cloud services can help accelerate compliance requirements at a reduced cost. Click here to learn more and download our Free eBook.
The OMB Trusted Internet Connection (TIC) Initiative is designed to reduce the number of United States Government (USG) network boundary connections, including Internet points of presence (POPs), to optimize federal network services, and improve cyber protection, detection, and response capabilities.[5] In its current form, a TIC-compliant architecture precludes direct access to applications running in the cloud. However, the TIC program recently proposed a draft Federal Risk and Authorization Management Program (FedRAMP)–TIC Overlay that provides a mapping of NIST SP 800-53 security controls to the required TIC capabilities. In May 2015, GSA and DHS invited AWS to participate in a FedRAMP–TIC Overlay pilot. The purpose of the pilot was to determine whether the proposed TIC overlay on the FedRAMP moderate security control baseline was achievable. In collaboration with GSA and DHS, AWS assessed how remote agency users could use the TIC overlay to access cloud-based resources, and whether existing AWS capabilities would allow an agency to enforce TIC capabilities.
The DoD Cloud Computing Security Requirements Guide (SRG) provides security requirements and guidance for the use of cloud services by DoD mission owners. It provides security controls implementation guidance for cloud service providers (CSPs) that wish to have their cloud service offerings (CSOs) accredited for use by DoD components and mission owners. In August 2014, AWS became one of the first CSPs to be granted a Provisional Authorization to Operate (P-ATO) to store and process DoD Impact Level 4 data. DoD mission owners that operate their workloads on AWS can use our P-ATO as part of the supporting documentation that their authorizing official (AO) uses to grant the workload a system Authorization to Operate (ATO).
AWS Architecture
The engineers at stackArmor have designed AWS GovCloud solutions for security focused US Federal and DOD customers and incorporate the following components and features:
AWS Identity and Access Management (IAM) configuration with custom (IAM) policies, with associated groups, roles, and instance profiles
Network segregation with external-facing Amazon Virtual Private Cloud (Amazon VPC) Multi-AZ architecture with separate subnets for different application tiers and private (back-end) subnets for application and database
Amazon Simple Storage Service (Amazon S3) buckets for encrypted web content, logging, and backup data
Standard Amazon VPC security groups for Amazon Elastic Compute Cloud (Amazon EC2) instances and load balancers used in the sample application stack
Three-tier Linux web application using Auto Scaling and Elastic Load Balancing, which can be modified and/or bootstrapped with customer application
A secured bastion login host to facilitate command-line Secure Shell (SSH) access to Amazon EC2 instances for troubleshooting and systems administration activities
Encrypted, Multi-AZ Amazon Relational Database Service (Amazon RDS) MySQL database
Logging, monitoring, and alerts using AWS CloudTrail, Amazon CloudWatch, and AWS Config rules
Host-based protection to include preventing, monitoring, logging, and alerting for anti-malware, web reputation, file integrity, IPS/IDS, and host firewall
The diagram below provides an overview of a standard three-tier web architecture depicting integration with multiple VPCs.
AWS Architecture Diagram with multiple Virtual Private Cloud (VPC) segregation for NIST FedRAMP Compliant Hosting Environment
You can download the NIST 800-53 Security Controls Mapping Excel workbook from AWS site by going to https://s3.amazonaws.com/quickstart-reference/enterprise-accelerator/nistv2/latest/docs/NIST-800-53-Security-Controls-Mapping.xlsx
fedramp-security-controls
Are you interested in a Free consultation with a stackArmor Solutions Architect on how you take advantage of the FedRAMP High Baseline on AWS GovCloud? We can help review your workload requirements, and also assist with your A&A package preparation including the SSP, and associated document. Contact us by sending us an email at solutions at stackarmor.com or fill our contact us form .
Delivering a FedRAMP or 800-171 compliant cloud solution on AWS
Meeting NIST SP 800-171 and DFARS Requirements
Achieving Compliance and Security on AWS cloud
Enter details below and we will contact you.


Pink Mash™ is the latest scientific innovation in soaked fibre feeding. With super-fibre, beetroot, micronised linseed, prebiotics and Protexin® probiotics, this super food nurtures and supports the hindgut health in all horses and ponies. Pink Mash™ can also be used for a partial hay/forage replacement and to restore hydration.


text:
#10 Midfielder - Texas Tech
6' 1" Height
Hometown: Colleyville, TX
High School: Fort Worth Christian High School
2012 Texas Tech 10 15 1 0 0 0 0 - 0
2011 Texas Tech 10 17 1 1 0 0 27 - 41
02/04/2012 Southern Methodist L 5-13 1 0 0 0 0
02/11/2012 @ Texas A&M L 4-13 0 0 0 0 0
02/12/2012 @ Sam Houston State L 4-15 0 0 0 0 0
02/17/2012 @ Oklahoma L 6-16 2 0 0 0 0
02/25/2012 Fort Lewis L 11-16 3 1 0 0 0
02/26/2012 @ University of New Mexico L 5-6 1 0 0 0 0
03/09/2012 @ Texas Christian L 4-12 1 0 0 0 0
03/10/2012 @ Tennessee L 6-17 1 0 0 0 0
03/11/2012 @ Ole Miss L 4-9 2 0 0 0 0
04/07/2012 North Texas W 12-11 4 0 0 0 0
02/12/2011 Oklahoma State W 15-1 2 0 0 0 0
02/19/2011 @ Texas State L 8-19 3 0 0 0 0
02/26/2011 @ North Texas L 4-9 0 0 0 0 0
03/05/2011 Texas Christian L 6-7 0 0 0 0 0
03/15/2011 Idaho L 8-16 5 0 0 0 0
03/18/2011 @ San Diego State L 2-14 3 0 0 0 0
03/26/2011 @ Southern Methodist L 6-13 0 1 0 0 0
03/27/2011 Sam Houston State L 4-12 2 0 0 0 0
04/02/2011 Oklahoma W 12-10 0 0 1 0 0
04/09/2011 @ Colorado Mines L 6-10 0 0 0 0 0
04/10/2011 @ Colorado L 1-18 1 0 0 0 0


text:
package com.cloud.bridge.model;

import java.io.Serializable;

import javax.persistence.Column;
import javax.persistence.Entity;
import javax.persistence.GeneratedValue;
import javax.persistence.GenerationType;
import javax.persistence.Id;
import javax.persistence.Table;

@Entity
@Table(name="usercredentials")
public class UserCredentialsVO{
	private static final long serialVersionUID = 7459503272337054299L;

	@Id
	@GeneratedValue(strategy=GenerationType.IDENTITY)
	@Column(name="ID")
	private Long id;

	@Column(name="AccessKey")
	private String accessKey;

	@Column(name="SecretKey")
	private String secretKey;

	@Column(name="CertUniqueId")
	private String certUniqueId;

	public UserCredentialsVO() { }

	public UserCredentialsVO(String accessKey, String secretKey) {
	    this.accessKey = accessKey;
	    this.secretKey = secretKey;
	}

	public Long getId() {
		return id;
	}

	private void setId(Long id) {
		this.id = id;
	}

	public String getAccessKey() {
		return accessKey;
	}

	public void setAccessKey(String accessKey) {
		this.accessKey = accessKey;
	}

	public String getSecretKey() {
		return secretKey;
	}

	public void setSecretKey(String secretKey) {
		this.secretKey = secretKey;
	}

	public String getCertUniqueId() {
		return certUniqueId;
	}

	public void setCertUniqueId(String certUniqueId) {
		this.certUniqueId = certUniqueId;
	}

	@Override
	public boolean equals(Object other) {
		if (this == other) return true;

		if (!(other instanceof UserCredentialsVO)) return false;

		// The cert id can be null.  The cert is unused in the REST API.
		if ( getAccessKey().equals(((UserCredentialsVO)other).getAccessKey()) &&
		     getSecretKey().equals(((UserCredentialsVO)other).getSecretKey()))
		{
			String thisCertId  = getCertUniqueId();
			String otherCertId = ((UserCredentialsVO)other).getCertUniqueId();

			if (null == thisCertId && null == otherCertId) return true;

			if (null != thisCertId && null != otherCertId) return thisCertId.equals( otherCertId );
		}
		return false;
	}

	@Override
	public int hashCode() {
		int hashCode = 0;
		String thisCertId = getCertUniqueId();

		// The cert id can be null.  The cert is unused in the REST API.
		hashCode = hashCode*17 + getAccessKey().hashCode();
		hashCode = hashCode*17 + getSecretKey().hashCode();
		if (null != thisCertId) hashCode = hashCode*17 + thisCertId.hashCode();
		return hashCode;
	}
}

redpajama_set_name: RedPajamaGithub


text:
Q: Kafka streams merging message I have a data payload, which is too big for one message. Consider an avro:
record Likes {...}
record Comments {...}
record Post {
  Likes likes;
  Comments comments;
  string body;
}

Assume, likes and comments are large collections and if pass them together with post, it will exceed max message size, which I suppose incorrect to increase up to 10-20 MB.
I want to split one message into three: post body, comments and likes. However, I want database insert to be atomic - so I want to group and merge these messages in consumer memory.
Can I do it with kafka-streams?
Can I have a stream without output topic (as the output message will again exceed max size).
If you have any ideas assuming the same inputs (one large message exceeding configured max message size), please share

A: Yes, you can do it with kafka-streams, merging the messaging in the datastore, and you can have a stream without output topic. You need to be sure that three parts go to the same partition (to go to the same instance of the application), so they probably will have the same key.
You may also use three topics, for each object and then join them. (Again with the same key).
But generally Kafka is designed to handle a lot of small messages and it does not work good with large messages. May be you should consider to send not the whole info in one message, but incremental changes, only information, which was updated.


Grab bag suits are based on competition sizing. The Classic Grab Bag is a fun and affordable way to get a high-quality suit at a very affordable price. Brands that can be found in the Classic Grab Bag are Nike, Dolfin, Adidas and Speedo Lycra.
Sample pictures may not be representative of the styles available.
A quantity of "1" = one suit.


text:
Lyudmyla Pushkina (; born October 2, 1965) is a female long-distance runner from Ukraine. She set her personal best (2:28:15) in the women's marathon on October 19, 2003 in Columbus, Ohio.

Achievements

References

marathoninfo

1965 births
Living people
Ukrainian female long-distance runners
Ukrainian female marathon runners


text:
Protecting citizens from COVID while granting refugee access, can be done: UNHCR
© UNICEF
Refugees and migrants gather at the Pazarkule border crossing near Edirne, Turkey, hoping to travel into Greece.
It is possible for countries to both protect public health and "ensure access" for vulnerable people forced to flee their homes, the UN refugee agency (UNHCR) said on Wednesday.
Opening a virtual session of UNHCR's annual Dialogue on Protection challenges, Assistant High Commissioner for Protection, Gillian Triggs, warned that "measures restricting access to asylum must not be allowed to become entrenched under the guise of public health",
Instead, she urged States to maintain access for asylum seekers and to safeguard the rights of refugees, together with displaced and Stateless people.
Measures restricting access to asylum must not be allowed to become entrenched under the guise of public health.
-@GillianTriggs https://t.co/ergL0D5gGh
— Kathryn Mahoney📸 (@MissMahoo) November 4, 2020
Ms. Triggs also spoke of the deep and hard-hitting impact on refugees of the coronavirus, including restrictions impeding access to asylum, spiraling gender-based violence, risks of unsafe returns, and the loss of livelihoods.
Participants – consisting of displaced people, non-governmental organizations and Government speakers from Asia, Africa, the Middle East and Europe – discussed how compassion and initiative could help ensure that asylum claims were considered during the pandemic, and protection services adapted to reach people in need during lockdowns.They also pointed to how the pandemic presented greater challenges for the protection of refugees, internally displaced and Stateless people, maintaining the need for solidarity and greater support.
"The pandemic has threatened the social and economic rights of the most vulnerable in society – among them refugees and those forcibly displaced who, all too often, depend on the informal economy", said the UN official. "They are among the first to suffer the economic impacts of a lockdown".
Moreover, UNHCR operations also report increasing incidents of discrimination, stigmatization and xenophobia against refugees and displaced people, "exacerbating tensions with local communities", he added.
UNHCR has been advocating for the urgent inclusion of refugees, displaced and Stateless people in the full range of responses to the pandemic, from public health to national social safety nets.
"The virus does not distinguish between legal status or nationality", Ms. Triggs reminded. "Access to health services should not depend on citizenship or restrictive visa conditions".
She upheld that "a realistic and practical opportunity for protection" lies in social inclusion and in non-discriminatory access to education, health and employment.
To illustrate the difficulties that refugees and internally displaced people face in the context of the pandemic, UNHCR also launched an interactive report called Space, shelter and scarce resources – coping with COVID-19, which highlights how acutely vulnerable displaced populations must contend with the pandemic.
The High Commissioner's Dialogue was established more than a decade ago for refugees, Governments, the private sector and international organizations to exchange views on global protection matters.
This year, discussions are being held through five virtual sessions spread over the last quarter of the year, with the closing session to take place on 9 December.
COVID-19|coronavirus
FROM THE FIELD: Protecting the displaced in the time of COVID-19
New guidance for protecting migrant workers during the coronavirus pandemic
COVID-19: Agencies temporarily suspend refugee resettlement travel
Beat back 'catastrophic effects' of COVID-19 on refugee education, urges UNHCR
While children in every country have struggled with the impact of COVID-19 on their education, refugee children have been particularly disadvantaged, the UN refugee agency (UNHCR) has said, amid fears many may not be able to resume their studies due to school closures, high fees or lack of access to technology to learn remotely.
Amid COVID-19 and climate change, UNHCR appeals for $186 million for Sahel refugee and displacement crisis
The UN refugee agency (UNHCR) has issued an urgent appeal for $186 million to provide lifesaving protection and assistance in the Sahel amidst fears that the conflict in the vast African region – exacerbated by the COVID-19 pandemic – will spread.


I think you're confusing the properties of these materials. You state that steel both stores more heat and conducts it faster than ceramic. Those two things seem to be contradictory. I agree with you on the second part but disagree with you on the first one. Ceramic works well in this scenario exactly because it holds its heat better than steel. Density is not the only measure of heat storage. Ceramic is a better insulated than steel so when you drop your pizza on the ceramic dish, the temp of the ceramic does not drop as quickly as it does with steel, that then needs to be reheated by the air around it, which has low heat heat transfer properties.
I think Modernist cuisine is using steel for indoor ovens because it quickly captures the heat coming off the broiler. It would take forever to do this with ceramic as the broiler cycles on and off. The downside of course is the steel quickly cools once the broiler stops but they must have found that this is a worthwhile trade-off.
I've spent some time this summer making pizzas on a $39 stone placed atop a $30 ceramic mount in an old kamado-style grill that costs me an additional $50. This whole setup cost less than half of your "hacked" grill plus $300 in accessories. I've found that the pizzas come out best when the grill is hovering around 700-800 with the stone at 500 or so. This produces an incredibly crispy crust and cooks a 12-13″ pizza in about 5-7 minutes.
Excellent article Scott. I love thermal diffusivity! Another aspect that i absolutely love about steel is that it can withstand extreme temperature changes. I have been using carbon steel since i first read it in Modernist Cuisine and my pizza continues to get better.
I may have to attempt this hacking of my grill, although my family may call in the fire department.
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Your video brings back a fond memory – an acquaintance found some similar steel (part of a B-52 bomber seat, if memory serves) and used it for a cooking surface on his wood fired grill. The steel got hotter then blazes. Then he'd grill steaks on it. It's been years since I had one of their steaks, and there are lots of variables in a steak… but fading memory suggests they were very good.
As to adding gluten to the dough, why not just start with a high gluten flour? All-Trumps unbleached and unbromated, King Arthur's high gluten, and Honeyville Farms high gluten flours are all around 14 – 15% protein and make a great dough.
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Is there any compelling reason to use stainless? I can get 1/4″ x 14″ x 20″ "pickled and oiled" steel for about $25 per piece. I realize I would need to cook off the oil and that there is the chance of rust but the price advantage is considerable.
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International Day Against Homophobia and Transphobia
The International Day Against Homophobia and Transphobia was created in 2004. We observe this day to bring more attention to the violence and discrimination that members of the LGBT community faces. We include (but do not limit such things to): lesbian, gay, bisexual, transgender, and other gender and sexuality diverse people. The International Day Against Homophobia and Transphobia is celebrated every year on May 17th.
All too often, we as a community face higher levels of violence and poor treatment because of who we are. However, statistics on such violence goes reported less than what actually happens. For this reason, we are observing this day in an effort to spur the collection of more data. If we can encourage more collection of such data around the world, then more can be known about how much discrimination we truly face.
When we collect more data, we will be able to affect positive change for ourselves and others like us. We can encourage greater social acceptance, more awareness about our community, and even legal and policy changes. Our hope for the future is to make the world a better place for people of diverse gender and sexual identities through such positive change.
We invite you to observe International Day Against Homophobia and Transphobia with us! To participate in our events, visit Changing2Gether.
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In the midst of the fallout from the deadly shooting in Parkland, Florida, MSNBC host Rachel Maddow paused for a moment to highlight stunning new reporting from both CNN and NBC News that more than 100 officials in the Trump administration do not have permanent security clearance.
According to the CNN report, among those officials who have yet to receive clearance are Trump daughter Ivanka Trump and son-in-law Jared Kushner.
Nearly a year into President Donald Trump's administration, senior-level staffers — including Ivanka Trump, Jared Kushner and Rob Porter — remained on interim clearances even as other senior advisers were granted full security access, according to information obtained by CNN from a US government official.
Having interim clearance can hamper a staffer's ability to perform essential functions of the job, a former administration official said. It requires those with full permanent clearances to remain vigilant about what information is shared with those still operating on an interim basis.
There were more than 100 staffers in the Executive Office of the President who were operating on interim clearances more than a year after Trump was elected, according to the information.
Keep in mind: Some of the same people that are now working in the White House without full security clearance spent an entire campaign season spewing nonsense about Hillary Clinton's email server and the supposed threat it posed to American national security.
This reporting just confirms the reality that the Trump administration is operating without a full deck of cards – not that we didn't know that already.


Legendary investor Kirk Kerkorian began rubbing his magic on stalled General Motors – instantly goosing its shares to their highest leap in 40 years.
Kerkorian shook the ailing stock out of its anemic slump yesterday by saying he's doubling his secret and already huge stake in the world's No. 1 automaker.
Shares shot up 18 percent, giving him a paper profit of $95 million even before he bought a single new share. GM stock closed at $32.80, up $5.03 on busy volume of 60 million shares.
Kerkorian, who's built most of his $9 billion fortune on casino investments, would become GM's third largest shareholder.
Industry sources say the 87-year-old investor is following the same strategy he used to gain power at the once-depressed Chrysler empire, which he ran through the wringer to make a multi-billion killing in the 1990s before agreeing to sell it to German auto giant Daimler-Benz.
Some analysts were puzzled why Kerkorian would jump onto GM, which has mammoth problems, including huge debt, a pension albatross, as well as a vanishing customer base – all of which could potentially force the $18.5 billion company into bankruptcy.
"What we know for sure is that he's bought some time for GM to keep his investment from falling any further," Schiff said.
GM's survival strategy in the past few years has been to sell off some of its richest assets, including DirecTV, its auto parts-maker Delphi and its armored-vehicle defense unit.
GM is working on a plan to spin off parts of its big finance arm, GMAC, the first piece being GMAC Mortgage. Proceeds would likely be used to buy back its debt and commercial paper, analysts say.
In a reorganization, investors would eye some of GM's far-flung assets such as its major stakes in European car makers Fiat and Saab, as well as Asian car makers Isuzu, Subaru, Suzuki and Daewoo – which GM hopes to use to build cars for booming China.
Kerkorian disclosed yesterday that he already owned 22 million GM shares, or 3.9 percent, and intends to offer $31 per share to boost his stake to 50 million shares. It wasn't disclosed what he paid for those previous shares.
Kerkorian faces a grueling turnaround for GM and its management. Its market share is the smallest in 80 years, and it posted a $1.1 billion loss in its last quarter.
Kerkorian supports GM's management team, led by CEO Rick Wagoner, said a Kerkorian spokesman, adding that his stake is a "strictly passive" investment. Kerkorian's stake is owned through his Tracinda Corp., which will begin its $31 a share offer in about a week.
Scorching hot GM shares jumped almost 20 percent on Kirk Kerkorian's move to pay about $870M to boost his share in the automaker to nearly 9 percent.