You've probably heard legends about "rat kings": rats whose tails are tangled to form a super-rodent more fearsome even than the pizza rat. While many doubt the existence of these skittery monarchs, there has officially, without a doubt, been a squirrel king.
We like to think we speak for everyone when we say: what.
This is a real thing that happened in Milwaukee last week. According to Fox 6 Now, five juvenile gray squirrels -- siblings, no less -- were brought to the Wisconsin Humane Society's Wildlife Rehabilitation Center with their tails tangled into a "Gordian Knot." Their tails were reportedly "entangled with long-stemmed grasses and strips of plastic their mother used as nest material."
Almost more unbelievably, the whole family was saved. After anesthetizing the understandably distressed squirrels, the center slowly went about snipping the grass and plastic off the tails over the course of 20 minutes.
As you might imagine, all five had tissue damage from impairment to their circulation. But as of now, they're safe and are being monitored to make sure the rest of the recovery process goes smoothly.
All hail the squirrel king, and may it be the last one ever.


text:
© Martin Hajek
Everything We Know About The iWatch So Far
Amos Kwon
If you've just crawled out from under a rock, we'll find it in our hearts to forgive you for not knowing much about wearable technology. OK, so you've heard of Google Glass, but we're talking about gear that doesn't make you look like an old Tomorrow's World prediction of What People Will Look Like In The Year 2000.
From fitness monitors to posture sensors and smart watches, the tide of socially acceptable wearable tech is growing, seemingly by the month. One of the most anticipated smart watches, if not the most, is the much-speculated-upon Apple iWatch — the supposed "next big thing" from the Cupertino innovation juggernaut, who ironically hasn't churned out a new, original product since way back in the prehistoric era known as 2010. Timing, as you know in the tech world, is nearly everything, and it would befit Apple to do something quickly, since there are more than a handful of smart watches out on the market already. It was supposed to have emerged sometime back in 2013, but that came and went. Could 2014 be the year?
Though we know that the iWatch, or whatever it's eventually named, is likely to show up on the market before the end of the year, we have just about zero indication as to what it will look like. Suffice to say that design is Apple's strongest suit, next to its ability to create an impressive level of device utility as exemplified in the ubiquitous iPhone. From various news sources, here is what we do know so far about the iWatch — though as always, this information is subject to change as the weeks pass and more information comes over the channels.
It looks like Apple will adorn its iWatch with one of a few glass options. The first, which was rumoured some time ago, is a scratch-resistant, high-quality sapphire glass face, great news for watch lovers everywhere (or at least those who will dare to wear the iWatch). The second is Corning's Willow Glass, which is a super-futuristic flexible glass that can be moulded in a curved shape, something that would lend itself nicely to a smart watch. The third option would be a flexible OLED plastic "glass" from LG. If the iWatch gets another rumoured feature, a slap band-style strap, it makes sense to go with one of the last two options. Plus, it will knock the iWatch into the stratosphere of cool with that level of glass tech.
Also, Apple gets the personalisation game, so it's likely that the iWatch will show up in various versions. Similar to rumours of differing iPhone 6 sizes, the iWatch will supposedly be offered in two different sizes, 1.3 and 1.5 inches. It's also possible that the iWatch will have an even greater array of personalisation options, such as swappable bands and faces. It's all part of the game in making mass high-tech more individualistic. That, and it appeals to analogue watch lovers, who just might be brought to the dark side with new ways to get addicted.
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The New iPhone Is Likely To Be Called The 'iPhone SE', But What Does That Mean?

redpajama_set_name: RedPajamaCommonCrawl


Im soo sorry for the long hiatus but I did tried to upload pictures but I dont understand why InternetExplorer doesnt allow me to do so and when I use Chorme I can only upload but not view the photos -.- So, now I have yo use 2 browser to get my pictures up and going.
Did quite a no. of nails during CNY and am pretty satisfied that everyone is happy with the nails I created. (: And I brought in quite a no. of products. I have 35 new gel colours into my collection and more glitter flakes/disco balls to spice up the nails. And I am sourcing for new crystals which cant be found in Singapore. I cant wait to embark myself into 2014 as I try to create more art and prettier designs for you.


Leo is currently an undergraduate student at the University of Sydney with majors in mathematics and chemistry. His mathematical interests include category theory, knot theory, and ergodic theory, and he would like to know more about representation theory. In 2018 he is planning to pursue Honours in pure mathematics.


A Class 40 hull undergoing final assembly at Maine Yacht Center.
The pressure of competition often pushes forward overall boat design and system development. Though high-end sail racing machines seem to bear little resemblance to voyaging boats, the results of racing's rapid development cycles often find their way into the hands of cruisers.
One racing class undergoing this rapid development cycle are the Class 40 boats. The U.S. importer for Class 40s is Akilaria Import LLC, which does its commissioning work at Maine Yacht Center (MYC) in Portland, Maine. These Class 40 boats are an international effort. The hulls and decks are built in Tunisia, the masts are produced in Romania and the keels and rudders originate in France.
The navigation console is mounted under the mast and can pivot to either side.
The main water ballast transfer pipe on the Akilaria Class 40s is much larger in diameter than those found on earlier models, allowing for faster tacks.
One way the Class 40 hulls meet this requirement is with five watertight compartments that can be sealed off via watertight doors. Another method is to use buoyant foam in many of the vessel's empty spaces. With added buoyancy and with watertight bulkheads, the Class 40 boats are designed to withstand some level of hull damage and still stay afloat. The reason for this is clear in the Category 0 description above. The boat and its driver may find themselves in situations where there is little to no chance of outside assistance.
Still, even though they must be tough to withstand tough conditions, Class 40s are still lightweight race boats designed to go fast. Sitting on the 40-foot hull is a 62-foot carbon fiber mast that can carry more than 2,800 square feet of sail. And that rig is driving a 40-foot hull weighing in at 9,900 pounds (4.9 tons). A 37-foot Island Packet 370, by comparison, has a standard displacement of 23,800 pounds (11.9 tons) with a 54-foot tall mast.
Even for a class as young as the Class 40s, there has been plenty of small design changes to produce ever faster boats. The overall hull shape of the Class 40 is similar to the Open 60s pioneered for the Vendée Globe and other shorthanded round-the-world races: plumb bow and narrow entry that widens to flat sections aft. This design gives the boat substantial form stability aft, which is further augmented in the bigger boats by canting keels that can get the keel bulb well out to windward. The Class 40 boats are prohibited from using canting keels. Instead, they use a deep fixed keel ballast bulb.
A nearly complete Class 40 in the water at Maine Yacht Center after launching.
Harris and crew are putting together some of the incremental changes designers are using to squeeze even more speed from these sleds. Harris pointed out that while the first versions of Class 40s had a right angle at the gunwale where the hull meets the deck, the Class 40 boats now have eliminated that right angle for a flat area that joins the hull and deck — as if that gunwale corner had been shaved off. The idea is simple: less hull material means less weight and thus a better power to weight ratio.
The Class 40s make use of water ballast for stability, with two ballast tanks, one on either side of the hull. Experience with the water ballast on Class 40s and other classes of race boats has led to refinements in the way the water is handled. Older vessels used smaller transfer pipes, but racers found that the smaller pipe impeded flow and meant that transferring water ballast between tanks took longer than desired. The present Class 40s, on the other hand, have a wide, six-inch diameter main transfer pipe that can move water between tanks much faster and thus speed up the time required to complete a tack.
Even the spartan interiors of these boats have become more spare. For the nav station, previous Class 40s used a gimbaled chair and desktop that adjusted as a single unit when the vessel heeled. This arrangement has been superseded, however, by a nav pod mounted on a vertical pivot below the mast. Racers can pivot this pod to port or starboard. And instead of a fixed seat, the new Class 40s have an oversized bean bag that the race crew are free to reposition depending on heel, etc., to get the most comfortable arrangement. The result is a reduction in weight, allowing the boat to go faster.
Some of these design ideas may find their way to voyaging boats in one form or another. Or they may become design dead ends (it's hard to imagine cruisers giving up berths for a bean bag!). When and if these design ideas are adopted, you can be sure that the race boat designers will be on to the next fastest thing.


text:
Liverpool Move One Step Closer to Premier League Title With Crystal Palace Win
Liverpool are now within touching distance of a first domestic title in 30 years after a comfortable win over Crystal Palace on Wednesday.
Jurgen Klopp's side are running away with the Premier League title and required just four points to make certain and they got three of those points with a standard win over Crystal Palace, managed by former Liverpool boss Roy Hodgson.
Goals from Trent Alexander-Arnold, Mohamed Salah, Fabinho and Sadio Mane gave the Anfield side a 4-0 win and means that should Manchester City fail to beat Chelsea on Thursday, then Liverpool will be named champions of England.
Liverpool have been in awesome form since the season kicked off, winning 28 of 31 matches thus far, and look likely to break all manner of records before the 2019-20 season is completed.
Klopp has seen his superb attacking trio of Salah, Mane and Roberto Fimino cause all sorts of problems in the final third but it's arguably their backline that has proven the real reason that they have seen off Manchester City this season.
Brazilian keeper Alisson has been amazing between the goalposts and the likes of Virgil van Dijk and full-backs Alexander-Arnold and Andrew Robertson have made the Merseyside club almost unbeatable.
Though the title race may be over there is still a lot to consider when making your Premier League bets this season, with the race for the top four and relegation being red hot with only a matter of weeks to go.
NBA Restart: Lakers Set to Replace Bradley With Smith
Two Sacramento Kings Stars Test Positive for Coronavirus


1. Entity Framework allows you to code your POCO classes first, then use a Context object to manage the database persistance.
But because databases have peculiarities, such as keys and identity columns, some control over how EF implements your data object in the database may be required. EF allows you to do this in a couple of ways: a Fluent API lets you do it in code, or the simpler way using Data Annotations, which we'll use here.
Now we know databases, and we know a few things about how this needs to be implemented in a database - we could go create a new table called Pupils, with 4 columns, the PupilId column will be the Primary Key and will be a generated identity column. Name and the DOB fields will have to be not nullable, but PrimarySchool can be optional. We would decide to implement max lengths on the nvarchar fields for Name (say 100 chars) and PrimarySchool (say 200 chars). But instead of creating it by hand, we can Annotate the fields in the class to do all these things and EF will create it for us.
3. Firstly we can deal with the Primary Key. There is a [Key] attribute we can put on the field we want as the key.
When the database is created from this data object, the column created for PupilId will be set as the Primary Key.
4. Secondly, we can set the non-nullable fields by using the [Required] attribute on the three columns we want non-nullable.
5. Now we can set the max char lengths on the two string fields suing the [StringLength] attribute.
6. Finally, we can set the primary key as an identity column using the DatabaseGenerated attribute.
Note this hasn't changed our class in any way, it's still just a POCO class, all the annotations have done is provide Entity Framework with enough information to create the database when it comes to do it.
7. To bind this model to an actual database table, we need to create a new class to hold the DbContext for our School application and make it inherit from DbContext.
This class creates an inherited instance of DbContext, which we call here SchoolContext, and defines a DbSet as a member. This generic object takes a type contructor, and by passing our Pupil object, we are basically telling Entity Framework to bind the object to a database table.
8. Because Entity Framework can bind to any data store, or to existing database tables for instance, we don't want the default behaviour to be that it creates the table if it doesn't exist. EF defaults to creating the tables to support the models if you are using SQLEXPRESS, but for production databases it isn't so bold, and you have to make it do it.
This tells Entity Framework, that for the SchoolContext object, it must always Drop and Recreate the tables every time. This may be a bit extreme, since dropping the tables will remove all data each time the application is restarted. The other options are more usual: DropCreateDatabaseIfModelChanges and CreateDatabaseIfNotExists. It's usual for developers to use these options while they are developing the system, to propagate their DB changes to the database, but then to remove them once in production and the databases are established.
9. All this holding ourselves apart from the database layer and letting EF do the dirty work means we've not thought about how EF knows which database to connect to - we have to supply it a database connection string. As usual, there are two ways to do it, one convention, one configuration.
By default, EF looks in the ConnectionStrings section of web.config for a ConnectionString named after the DbContext you've used in your code. Since we created a SchoolContext, all we have to do is add a named ConnectionString in web.config and the rest is magic.
10. Now we run our application, and go look in the named database to see our lovely tables. What? Theyre not there?
Now after you run this, you should be able to see that it's created a Pupils table (note the pluralisation of your entity name) with the correct columns, keys, etc. And with any luck, you'll have one row in it, with your new Pupil.
And that's the basics of Entity Framework code-first with Data Annotations.


text:
A group of 14 young musicians drawn from Ceoltóirí Drumlin, the local branch of Comhaltas Ceoltóirí Eireann, travelled to Carhaix on Friday, May 14th. Their teacher Francis Mc Mahon from Tullycorbet, Branch Chairman Breen Jackson from Carrickmacross, Mary Kerr-Conlon Mayor of Carrickmacross, Michael Mc Mahon Chairman Carrickmacross/Carhaix Town Twinning Association and parents Orla Mhic Shuibhne, Paul Quinn and Gerard Mc Guirk accompanied the highly talented teenagers.
Saturday afternoon was largely spent rehearsing with a group of Celtic musicians known as Castle Céilí from the Carhaix Ecole de Musique du Poher under the leadership of internationally renowned uillinn piper Patrick Molard. At 8.30pm Castle Céilí took the stage first to entertain the international audience of Dutch, English, French and German guests who were there to celebrate the 40th Anniversary of the town Twinning of Carhaix and German town Waldkappel. Ceoltóirí Drumlin then took over and played samples of practically every type of Irish music including a most beautiful traditional Irish solo song. The climax was in the second part of the concert when the two groups played together and brought the house down. At the end of the set the insatiable and appreciative audience shouted for more and more. The evening's entertainment concluded with some Breton and Irish dancing, the highlight of which was a unique performance by Francis Mc Mahon.
The outstandingly enjoyable weekend was overshadowed a little when the return Ryan Air flight was cancelled on Monday. The day was saved however when Marie Louise Huiban, President of Carhaix Town Twinning Association did trojan work to book a passage home for the group on Irish Ferries. Ceoltóirí Drumlin showed the breath and depth of their talent by playing for the passengers from 8pm to nearly midnight. Copies of their latest CD Turas Ceoil were in big demand and lots of people expressed the hope of visiting Carrickmacross as a result of the positive way the town was presented to international audiences in France and on the boat home. Every cloud, even an ash cloud, has a silver lining.


text:
Q: How to configure SNMP Trap? I knew that SNMP Trap is event sent from Agent to Manager.
But how can I setup so that the Agent know where to send the trap message?
Do I setup in the snmpd.conf
Or I inform the Agent where to send via a Set Request from the Manager?

redpajama_set_name: RedPajamaStackExchange


It's my favorite day of the year!
It's #NationalLipstickDay and I'm feeling bright and happy wearing NYX Cosmetics soft matte lip cream in colors Tokyo and Addis Ababa. I love giving my pouty lips their own Summer signature color. I first applied Tokyo and then Addis Ababa gently on top. Afterwards, I blended them nicely over lips to make sure the color was even with a lip brush.
Don't be afraid to mix colors. You might just love what you come up with! What do you think? Good color for a summer day? I think so!
Hey! Excellent blog! I prefer how well you reviewed Celebrating National Lipstick Day with NYX Cosmetics.
I LOVE NYX and love that you mixed these colors. So cute Shannon!


text:
\subsubsection*{References}}
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\title{A general framework for defining and optimizing robustness}

\author{
  Alessandro Tibo\\
  Aalborg University, Institut for Datalogi\\
  \texttt{alessandro@cs.aau.dk}\\
  \And
  Manfred Jaeger \\
  Aalborg University, Institut for Datalogi\\
  \texttt{jaeger@cs.aau.dk}\\
  \And
  Kim G.~Larsen \\
  Aalborg University, Institut for Datalogi\\
  \texttt{kgl@cs.aau.dk}
}

\begin{document}
\maketitle

\begin{abstract}
  Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area
  lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible
  framework for defining different types of robustness properties for classifiers.
  Our robustness concept is based on postulates that
  robustness of a classifier should be considered as a property that is independent of accuracy, and that it should be
  defined in purely mathematical terms without reliance on algorithmic procedures for its measurement.
  We develop a very general robustness framework that is applicable to any type of classification model, and that
  encompasses relevant robustness concepts for investigations ranging from safety against adversarial attacks to
  transferability of models to new domains. For two prototypical, distinct robustness objectives we then
  propose new learning approaches based on neural network co-training strategies for obtaining image classifiers
  optimized for these respective objectives.
\end{abstract}

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

Machine learning models have reached impressive levels of performance for solving various types of classification problems.
Famously, convolutional neural networks  \cite{fukushima1980neocognitron,lecun1989backpropagation},
are the state-of-the-art method for image classification (see, e.g., \cite{szegedy2017inception,xie2019self,kolesnikov2019large}).
However, the phenomenon of \emph{adversarial examples} \cite{szegedy2013intriguing,goodfellow2014explaining} has raised
serious concerns about the reliability of these machine learning solutions, especially in safety-critical applications.
Autonomous driving and counterfeit bill detection are  two intuitive examples where safety concerns play a fundamental role.
The vulnerability of machine learning models to adversarial examples is widely interpreted as a lack of
\emph{robustness} of these models, and a large amount of recent work investigates robustness properties, with a
strong focus on deep neural network models. Research in this area has been pursued both from the perspective
of formal verification with its traditional objective of rigorously proving safety properties of hard- and software
systems~\citep{ruan2018reachability,ehlers2017formal,dvijotham2018dual,bunel2018,Cisse-etal-2017,wicker2020probabilistic},
and from the perspective
of machine learning with its traditional objective of optimizing expected values of performance measures~\citep{madry2017towards,hein2017formal,elsayed2018large,sinha2019harnessing,su2019one}.

The original motivation derived from adversarial examples led to a focus on robustness against small
adversarial perturbations.
As noted by \cite{gilmer2019adversarial}, this needs to be distinguished
from  robustness under larger scale distribution shifts.
The former is a particular
concern in order to guard against vulnerability to targeted attacks, whereas the latter is
important for applications where the characteristics of test cases may (eventually) differ from
the original training data.

In most works, the focus is on one of two separate issues: either \emph{assessing} the robustness properties
of a given model, or \emph{improving} the robustness properties of learned classifiers by developing new training
techniques. Works with a background in formal verification mostly focus on the first issue, while in the field
of machine learning the second  plays a larger role. However, in machine learning, too, the problem
of assessing robustness has received a lot of attention, especially in connection with designing adversarial
attacks \cite{goodfellow2014explaining,madry2017towards,hein2017formal,su2019one}.

The underlying concept of robustness used in different works
often only is implicit in a proposed loss function and/or the
experimental protocol used to evaluate robustness properties. As a result,  there does not yet
appear to be a common full understanding of what robustness actually is, and how it relates to other
properties of classification models. For example, \cite{tsipras2018robustness} have argued that the objectives
of robustness and accuracy are in conflict with each other, whereas \cite{stutz2019disentangling} come to
somewhat opposite conclusions: they argue that robustness and generalization capabilities are in conflict
only when robustness is designed to defend against ``off-manifold'' attacks, i.e., adversarial examples that
do not follow the data distribution, whereas they are consistent with each other in the scenario of
``on-manifold'' adversarial examples.
Similarly, there exist somewhat conflicting results with regard to the question whether robustness
against adversarial examples and against distribution shifts are in conflict with each other, or whether
these two objectives can be aligned~\citep{gilmer2019adversarial,rusak2020simple}.

Underlying these differences are not so much theoretical or empirical
discrepancies, as conceptual differences about what one wants to capture with robustness. In this paper we first
aim to put the analysis of robustness properties on a more solid foundation by  developing
a general framework for the specification
of different robustness concepts that captures most of the concepts previously used (implicitly or explicitly)
in the literature, and that helps to clarify their basic structural differences.
We propose a  flexible framework that captures in a coherent manner different robustness concepts
ranging from safety against adversarial attacks to the ability to adapt to distribution changes.
In this manner, we draw a direct link between the goals of learning robust and safe classifiers on
the one hand, and the traditional objectives of transfer learning on the other hand.

We then use our robustness definitions as the conceptual basis for developing robust learning
techniques in two protypical application settings: learning neural network classifiers that are
robust against small adversarial perturbations, and learning image classifiers that are robust
with respect to larger distribution shifts.
Like most of previous research on robustness which focusses on neural network technology for image
classification problems, we, too, use readily available image benchmark datasets and
standard neural network architectures
to evaluate our methods. However, it is one of our core objectives that the conceptual framework is
generally applicable to all types of classification models, and the developed techniques are not specifically
tied to image data.

The key contributions of this paper are:
\begin{itemize}
\item A general analysis and specification framework for robustness concepts for classification models.
\item Development of robust learning techniques for two prototypical instantiations of the
  robustness framework covering two very different points in the robustness spectrum.
\end{itemize}

\section{A Robustness Framework}
\label{sec:shades}
We are considering classification problems given by an input space
$\mathcal{X}$, a label space $\mathcal{Y}= \{0,\ldots,K-1\}$, and a data distribution consisting of
an input distribution $P(X)$, and a conditional label distribution $P(Y|X)$. A classifier is any
mapping $f:\mathcal{X}\rightarrow \mathcal{Y}$. By as slight abuse of notation we also use $Y$ to
denote the \emph{true labeling functions} $Y: \mathcal{X}\rightarrow \mathcal{Y}$ defined by
$Y(x):=\argmax_y P(Y=y|X=x)$.
Most existing notions of robustness require that $\mathcal{X}$ is endowed with a metric.
Usually, ${\mathcal X} \subseteq \mathbb R^d$ for some $d\geq 1$, with a metric induced by
one of the standard norms on $\mathbb R^d$. In the following we will assume that ${\mathcal x}$ is
of this form.

Underlying our robustness framework are the  following two postulates:

\begin{description}
\item[P1.]  Robustness is orthogonal to accuracy (or generalization). In particular, a constant classifier with
  $f(x)=y$ for some fixed $y\in\mathcal{Y}$ and all $x\in \mathcal{X}$ always is maximally robust.
  This does not entail that robustness and accuracy are necessarily in conflict; only that they are
  separate, distinguishable objectives.
\item[P2.]   Robustness of a model $f$ is defined only in terms of $f$ itself, and the given classification problem.
  In particular, robustness is not dependent on specific (algorithmic) tools for assessing robustness.
\end{description}

P1 makes our concept of robustness different from robustness metrics used  e.g. by
\cite{tramer2019adversarial} or \cite{gilmer2019adversarial}, where robustness measures are directly
tied to accuracy. These differences notwithstanding, the measures we propose are consistent with these
earlier proposals in that they arguably extract their pure robustness components.
P2 implies that e.g. \emph{success rates} of particular adversarial example generators as used e.g.
in~\cite{su2018robustness},  or the CLEVER scoring algorithm of~\cite{weng2018evaluating}
are not robustness measures in our sense per se, but rather tools for approximate evaluations of
proper robustness measures.

P2 can be refined to a hierarchy of robustness concepts reflecting their dependence
on different elements: we distinguish three types of robustness concepts, according to whether
robustness is defined in terms of
\begin{description}
\item[Type 1:] only the classifier $f$,
\item[Type 2:] the classifier $f$, and the input distribution $P(X)$
\item[Type 3:] $f, P(X)$, and the label distribution $P(Y|X)$
\end{description}

We now develop a  flexible framework  that can accommodate a wide
range of robustness concepts of all three types. In the following,
${\cal A}({\cal X})$ denotes the $\sigma$-algebra of Borel sets on ${\cal X}$.

\begin{definition}
\label{def:robustnessfct}
(Basic $Q$-Robustness Measure)
Let $f$ be a classifier and
\begin{equation}
  \label{eq:Qkernel}
  \begin{array}{llll}
    Q: & {\cal X}\times{\cal A}({\cal X})  & \rightarrow & [0,1] \\
    & (x,A) & \mapsto & Q(A|x)
  \end{array}
\end{equation}
 a transition kernel on ${\cal X}$.
The function
  \begin{equation}
    \label{eq:basicrobustnessfct}
    \begin{array}{rcl}
     \rho_{Q}^f:\ \  \mathcal{X} & \rightarrow & [0,1] \\
      x & \mapsto & Q( \{ x' : f(x')=f(x)  \} |x)
    \end{array}
  \end{equation}
  is called the \emph{basic robustness measure} of $f$ with respect to $Q$.

\end{definition}

In conjunction with a distribution $P()$ on ${\cal X}$, a kernel $Q$ defines the probability measure
$\int_{\cal X} Q(\cdot|x)dP(x)$ on ${\cal X}$. We denote this measure as $Q\circ P$.

\begin{example}
  \label{ex:Qepsilon}
  Let $\epsilon >0$. We denote with $B_{\epsilon}(x)$ the open $\epsilon$-ball around $x$ (according
  to a chosen metric on ${\cal X}$).
  Let  $Q_{\epsilon}( \cdot | x)$ be the uniform distribution on $B_{\epsilon}(x)$ ($x\in {\cal X}$).
  $\rho_{Q_{\epsilon}}^f(x)$ then is the probability that a perturbation of $x$ with a uniform random noise
  vector of length $\leq \epsilon$ is assigned by $f$ the same label as $x$.
\end{example}

The basic robustness measure measures the stability of the classifiers output
when examples $x$ are randomly perturbed according to the distribution $Q(\cdot|x)$.
Integrating $\rho_{Q}^f(x)$ over $x$  gives an overall robustness
score for $f$ relative to  $Q$-perturbations.
However,
simply taking the integral over $\rho_{Q}^f$ is too crude to encode many important versions of
robustness. We therefore generalize the basic robustness measure by adding functions that allow
to extract specific features of $\rho_{Q}^f$.

\begin{definition}
  ($Q,H,G$-Robustness Function)
  Let $H:[0,1]\rightarrow \mathbb R^+$ be a monotone increasing function, and
  $G: {\cal X}\rightarrow \mathbb R^+$. Then
  \begin{equation}
    \label{eq:robustnessfct}
    \begin{array}{rcl}
      {\rho}_{Q,H,G}^f:\ \  \mathcal{X} & \rightarrow & \mathbb R^+ \\
      x & \mapsto & H(\rho_{Q}^f(x))G(x)
    \end{array}
  \end{equation}
  is the \emph{robustness function} of $f$ defined by $Q,H$ and $G$.

\end{definition}

Integrating the robustness function then gives a robustness score for a classifier:

\begin{definition} \label{def:Qrobscore}
    ($Q,H,G$-Robustness Score)
	For a given $f$, $Q$,   $H$, and $G$ we define the $Q,H,G$-robustness score
	\begin{equation}
         \label{eq:Qrobscore}
		R_{Q,H,G}^f = \int_{\mathcal{X}} {\rho}^f_{Q,H,G}(x) dx.
	\end{equation}
\end{definition}

We note that for a constant classifier $f(x)=i\in{\cal Y}\ (x\in{\cal X})$ we have
$\rho^f_Q(x)=1$ for all $x$, and by the monotony of $H$ then also
$H(\rho^f_Q(x))$ is the maximal possible value for all $x$. This implies that for all
$Q,H,G$,
$R_{Q,H,G}^f$ is maximal for a constant classifier, i.e., postulate P1 is satisfied.

The robustness score of Definition~\ref{def:Qrobscore} only relates to a single perturbation
model $Q$. Often, one will want to consider different forms of perturbations, possibly weighted by
a probability distribution.

\begin{definition} \label{def:QQrobscore}
    (${\cal Q},H,G$-Robustness Score)
  Let ${\cal Q}$ be a family of transition
  kernels $Q_{{\boldsymbol \lambda}}$ parameterized by  ${\boldsymbol \lambda}\in A\subseteq \mathbb R^k$.
  Let ${\cal Q}$ be equipped with a probability distribution defined by a density function
  $q_{\cal Q}$ on $A$. Let $H$ and $G$ as in Definition~\ref{def:Qrobscore}. Then we define the
  ${\cal Q}$-robustness score as
  \begin{equation}
         \label{eq:QQrobscore}
		R_{{\cal Q},H,G}^f = \int_A  R_{Q_{{\boldsymbol \lambda}},H,G}^f   q_{\cal Q}({\boldsymbol \lambda})  d{\boldsymbol \lambda} .
	\end{equation}
\end{definition}

We next illustrate how the general robustness concepts introduced by
Definitions~\ref{def:robustnessfct}-\ref{def:QQrobscore} can be instantiated to obtain previously proposed
and novel robustness concepts of types 1-3.
 To simplify descriptions, from now on we assume that $\mathcal{X}$ is the $m$-dimensional unit hypercube,
  and we denote with $d =  \sqrt{m}$ its diameter.
  In this paper, we will consider for $H$ only  the two functions

  \begin{displaymath}
    \begin{array}{llll}
\label{eq:Hindicator}
H(p) & = &{\mathbf{1}}(p) & := \indicator{p=1}, \ \ \mbox{and}\\
H(p) & = & {\mathit id}  (p) & :=  p
\end{array}
  \end{displaymath}

with $\indicator{\cdot}$ the indicator function. Thus, with $H={\mathbf{1}}$ we are only interested in whether
the predicted label of $x$ will be almost surely preserved under the perturbation $Q(\cdot|x)$, which
leads to robustness concepts related to safety guarantees under adversarial perturbations, wheras
$H= {\mathit id}  $ leads to robustness concepts concerned with preservation of predictive accuracy.

\begin{example}
  \label{ex:geometry}
  (Geometry of decision regions; type 1.)
  For $\epsilon > 0$ let $Q_{\epsilon}$ be defined as in Example~\ref{ex:Qepsilon}. Define
  \begin{displaymath}
    {\cal Q}_{[0,d]} := \{ Q_{\epsilon} | \epsilon\in [0,d]\}
  \end{displaymath}
  and let $q_{ {\cal Q}_0}$ be the uniform density on $[0,d]$.
  Let $H={\mathbf{1}}$,
  and $G(x)\equiv 1$. Under mild regularity conditions on
$f$\footnote{e.g. that $f(x)$ be defined as the argmax of a set of continuous discriminant
  functions  $f_y$ ($y\in{\cal Y}$)} we then have that
\begin{equation}
  \label{eq:indicator}
  {\mathbf{1}}(\rho^f_{Q_{\epsilon}}(x))=\indicator{\forall x'\in B_{\epsilon}(x): f(x')=f(x) },
\end{equation}\
i.e. the probabilistic statement $Q_{\epsilon}(\ldots)=1$ can be sharpened into a categorical ``for all'' statement.
Then
\begin{equation}
  R^f_{{\cal Q}_{[0,d]}, {\mathit id}  ,1}=
  \int_0^d \int_{\cal X} \rho^f_{Q_{\epsilon},{\mathbf{1}},1}(x) dx d\epsilon
  =  \int_{\cal X}\int_0^d\rho^f_{Q_{\epsilon},{\mathbf{1}},1}(x) d\epsilon dx.
  \label{eq:exgeometry}
\end{equation}
The inner integral on the right is equal to the minimum distance from $x$ to a
decision boundary of $f$, i.e., the classifier margin at $x$.
Integrating over ${\cal X}$ then gives that $R^f_{{\cal Q}_{[0,d]}, {\mathit id}  ,1}$ is the average margin
for points $x\in {\cal X}$. This robustness measure only depends on the geometric complexity
of the decision regions of $f$.
\end{example}

\begin{example}
  \label{ex:succrates}
  (Margin curves; type 2.)

  Let ${\cal Q}_{[0,d]}$ be as in Example~\ref{ex:geometry}. Assume that $P(X)$ has a density function
  $p(x)$ relative to the uniform distribution, and let $G(x):=p(x)$. Then, under the same
  regularity assumptions as in Example~\ref{ex:geometry},
  $R_{Q_{\epsilon},{\mathbf{1}},p}$
  is the probability that a point $x$ sampled according to $P(X)$ has no adversarial example at
  distance $\leq \epsilon$. Empirical estimates of this integral based on a number of test points
  $x_i$ correspond to robustness scores in terms of success rates of adversarial example generators
  (where the precision of the estimate then also is affected by the effectiveness of the generator).
  Seen as a
  function of $\epsilon$,  $R^f_{Q_{\epsilon},{\mathbf{1}},p}$ defines the \emph{margin curves}
  of~\cite{gopfert2019adversarial}
  (up to a $1-\ldots$ inversion).
  Integrating  over $\epsilon\in[0,d]$ yields $R^f_{{\cal Q}_{[0,d]},{\mathbf{1}},p}$, which measures robustness as the
  area under the margin curve.
\end{example}

\begin{example}
  (label aware; type 3.)
  Label-aware (type 3) robustness functions can be obtained by conditioning the perturbation
  distribution $Q_{\epsilon}(\cdot | x)$  also on the label of $x$. Thus we let
  \begin{displaymath}
    Q_{\epsilon,Y}(\cdot | x):= Q_{\epsilon}(\cdot |x)| \{ x': Y(x')=Y(x) \},
  \end{displaymath}
  where we use the general notation $P|A$ to denote a probability distribution $P$ conditioned on
  an event $A\in {\cal A}({\cal X})$.
  With $H$ and $G$ as in Example~\ref{ex:succrates}, one now
  obtains the robustness concept implicitly (through the definition of
  the \emph{expected adversarial loss} function) used in~\cite{tsipras2018robustness}
  and adapted in~\cite{gopfert2019adversarial}.
\end{example}

In all the preceding examples the data distribution $P(X)$ was only used to weigh the contribution
of points $x\in {\cal X}$ to the overall robustness score. It was not used in the definition of
the perturbation model ${\cal Q}$.
The resulting robustness models then capture scenarios where datapoints generated by $Q\circ P$ can
be  off-manifold  in the sense of~\cite{stutz2019disentangling}. For the more conservative setting of
robustness with respect to
on-manifold adversarial examples, one can also use $P()$ in the definition of $Q$ by letting
  \begin{displaymath}
    Q_{\epsilon,P}(\cdot|x):=P | B_{\epsilon}(x).
  \end{displaymath}
  In all preceding examples, we can substitute $Q_{\epsilon,P}$ for $Q_{\epsilon}$, and thereby obtain
  on-manifold versions of the given robustness concepts. The question of whether an off-manifold or on-manifold
  concept of robustness is more appropriate is quite subtle. The former is more relevant when robustness
  against malicious attacks or substantial distribution changes is required; the latter may be sufficient
  when only robustness against distribution changes is required that are induced e.g. by changing
  observation biases, but do not modify the underlying nature of the sampling population.

None of the preceding definitions and examples takes the accuracy of the model $f$ into account, i.e., we
never considered whether $f(x)=Y(x)$. This is in line with our stipulation that robustness as a
concept is orthogonal to accuracy. Obviously, one  ultimately wants robustness to lead to accuracy
gains under some conditions. In order to link robustness to accuracy, we first give and
explicit definition for an assumption that usually  implicitly made for
adversarial perturbations or common corruptions.

\begin{definition}
  Let $P$ be a distribution on ${\cal X}$ with density function $p()$,
  and $\epsilon>0$. A kernel $Q$ is $(P,\epsilon)$-\emph{label preserving} if
  \begin{displaymath}
    \int Q(\{x': Y(x') = Y(x) | x\})p(x)dx \geq 1-\epsilon
  \end{displaymath}
\end{definition}

Viewing $Q$ as a formal model for adversarial perturbations or corruption mechanisms,
standard assumptions in the literature would translate into an assumption that
$Q$ is $(P,0)$-label preserving.
We can  now formulate the following trivial but noteworthy relationship between robustness and
accuracy:

\begin{proposition}
  \label{prop:accpreservation}
  Let $f$ have accuracy $\alpha$ on data sampled according to the distribution $P$. Let $Q$ be
  $(P,\epsilon)$-\emph{label preserving}, and assume that $R^f_{Q, {\mathit id}  ,p}= 1-\delta$.
  Then $f$ has accuracy on data sampled according to $Q\circ P$ of at least $\alpha-\epsilon-\delta$.
\end{proposition}

\begin{proof}
  Let $A=\{x | f(x)=Y(x)\}$ be the set of inputs on which $f$ makes correct predictions. Then
  $P(A)=\alpha$. Using that $Q(\cdot|\cdot)$ is non-negative, and therefore the integral of
  $Q(\cdot|x)$ over the full space is always greater or equal the partial integral over $A$, we
  obtain:
  \begin{multline}
    (Q\circ P)(A)=\int Q(A|x)p(x)dx\geq \int_A Q(A|x)p(x)dx\\
    \geq  \int_A Q( \{ x':Y(x')=Y(x)  \}\cap\{ x': f(x')=f(x)\}   |x)p(x)dx \\
    \geq  \int_A (1-Q( \{ x':Y(x')\neq Y(x)  \}|x)-Q(\{ x': f(x')\neq f(x)\}   |x))p(x)dx \\
    =\alpha - \int_AQ( \{ x':Y(x')\neq Y(x)  \}|x)p(x)dx - \int_AQ(\{ x': f(x')\neq f(x)\}   |x)p(x)dx \\
    \geq \alpha - \int Q( \{ x':Y(x')\neq Y(x)  \}|x)p(x)dx - \int Q(\{ x': f(x')\neq f(x)\}   |x)p(x)dx
    \geq \alpha-\epsilon-\delta.
  \end{multline}
\end{proof}

\section{Optimizing a Given Robustness Measure}\label{sec:methodology}

In this section we consider the case where a target robustness version is fully specified in terms
of specific ${\cal Q}, H, G$. An important case of this nature is the one described in Example~\ref{ex:succrates},
which has been quite extensively considered for neural network classifiers.
We therefore  also focus in this section on neural network classifiers  $f$.
We assume that classification is performed
by taking the $\argmax$ over an output layer produced by a softmax function. We denote with
$\hat{f}(x)\in[0,1]^K$ the network output for input $x$; $\hat{f}(x)[j]$ denotes the $j$th component of
$\hat{f}(x)$.

\subsection{Robust co-training for  $R^{\lowercase{f}}_{{\cal Q}_{[0,{\lowercase{d}}]},{\lowercase{{\mathbf{1}}}},{\lowercase{p}}}$}\label{sec:ouradvgenerator}

Existing approaches for training $f$ with high $R^f_{Q_{\epsilon},{\mathbf{1}},p}$ scores include data augmentation
with adversarial examples~\cite{madry2017towards} and the use of customized regularization terms in the loss
function~\citep{hein2017formal}. The construction of adversarial examples is computationally expensive,
especially when it has to be repeated in each iteration of the training loop for $f$. We therefore
propose a hybrid approach that employs computationally cheap adversarial example generation to
define a regularization term in the loss function for $f$.

\begin{figure}[b]
\centering
\centerline{\includegraphics[width=0.3\columnwidth]{./images/robustnessFramework.pdf}}
\caption{Co-training of classifier $f$ and adversarial generator. Solid arrows represent
input/output relations; dashed arrows represent dependence of the loss function.}
\label{fig:robustness-framework}
\end{figure}

Concretely, our approach consists of co-training the classifier $f$, and a generator $g$ that
maps inputs $x$ to approximate adversarial examples $g(x)$. Given a (current) classifier $f$, our
loss function for $g$ for a training example $x$ is
\begin{equation}\label{eq:proposed:reg}
{\cal L}_g(x,\theta_g) =  \frac{1}{2} \| g(x;\theta_g ) - x \|^2 +
\max(\hat{f}(g(x;\theta_G))[i] - \hat{f}(g(x;\theta_G))[j],\ 0) ,
\end{equation}
where $\theta_g$ are the trainable parameters of $g$, $i=f(x)$ is the label associated with $x$ by $f$,
and $j\in{\cal Y}$  is the label with the second highest value in $\hat{f}(g(x;\theta_G))$.
The first term of the loss function enforces that $g(x)$ is close to $x$.
The second term is equal to zero if $f(g(x))\neq f(x)$, i.e., $g(x)$ is adversarial in the sense
that it is labeled differently from $x$.

Given a (current) generator $g$, the classifier $f$ is trained using the following loss function
for a labeled training example $(x,y)$:
\begin{equation}
  \label{eq:final:loss:ex:1}
  {\cal L}_f(x,\theta_f) = -\log( \hat{f}(x)[y]  ) +
  \lambda\frac{CE(\hat{f}(x),\hat{f}(g(x))}{1+ \parallel x-g(x)\parallel^2  }.
\end{equation}
The first term here is the standard log loss. The second term is our robustness regularizer.
It is essentially inversely proportional to how successful the generator $g$ is: the loss increases
if $g$ finds close adversarial examples, i.e. $\parallel x-g(x)\parallel^2$ is small, and it
increases when the output of $f$ at $g(x)$ is very different from the output of $f$ at $x$, as
measured by $CE(\hat{f}(x),\hat{f}(g(x))$.

The models $f$ and $g$ are co-trained by an alternating stochastic gradient descent as
shown in Algorithm~\ref{alg:reg:training}.

\begin{algorithm}
\SetAlgoLined
 {\bfseries Input:} $D$, $f$, $g$, batchsize\;
 Randomly initialize $f$ and $g$\;
 \While{not converged}{
  $\{I^{(f)}_1,\ldots,I^{(f)}_K \}$ = shuffle(D)  //create $K$ mini-batches according to batchsize\;
  $\{I^{(g)}_1,\ldots,I^{(g)}_K \}$ = shuffle(D)\;
  \For{$i=1$ {\bfseries to} $K$}{
  	$x'_j = g(x_j) \quad \forall \ j = 1,\ldots, |I^{(f)}_i| $\;
  	Perform SGD update on $f$ using augmented mini-batch $\{x_j,x'_j \ | \ j=1, \ldots, |I_i^{(f)}| \}$\;
  	Perform SGD update on $g$ using inputs from $I_i^{(g)}$\;
  }
 }
 \caption{Regularization Training for $R^f_{{\cal Q}_{[0,d]},{\mathbf{1}},p}$}\label{alg:reg:training}
\end{algorithm}

\subsection{Robustness Evaluation}\label{sec:robeval}

Having learned a classifier $f$, we want to evaluate its $R^f_{{\cal Q}_{[0,d]},{\mathbf{1}},p}$ score. To obtain
an empirical estimate based on a set of test points $x^{(i)}$, one would ideally determine precisely
the classifier margin at each $x^{(i)}$. Since this is infeasible, we resort as usual to
the distance between $x^{(i)}$ and an adversarial example for $x^{(i)}$ as an upper approximation
of the margin. For this purpose we could re-use the generator model $g$ constructed in our
robust training approach. However, this would lead to an unfair advantage of our models in comparsion
to models learned using other robust training approaches.
For scoring, we therefore construct adversarial examples $x^*$ using an ensemble approach,
where we consider a set of state-of-the-art strategies for generating adversarial examples, FGSM~\cite{goodfellow2014explaining}, PGD~\cite{madry2017towards}, and BG~\cite{hein2017formal}. Starting from
a trained model $f$, for each $x$ in the test set, we construct the set $Adv(x)=\{ x_{FGSM}, x_{PDG}, x_{BG}\}$, where its elements are generated according to the strategies mentioned above. Then, for each
$x' \in Adv(x)$ we consider $\hat{x} = x + \epsilon_{x'} (x' - x)$, where $\epsilon$
is the smallest positive real number such that $f(x + \epsilon (x' - x)) \neq f(x)\}$.
In practise $\epsilon$ is estimated by a binary search under the assumption that there is only
one decision boundary on the line between $x$ and $x'$.
Finally, we select from among $\hat{x}_{FGSM}$, $\hat{x}_{PDG}$, $\hat{x}_{BG}$ the one that lies closest to
$x$ as the adversarial example $x^*$.

\begin{figure}[ht]
\centering
\centerline{ \includegraphics[width=0.4\columnwidth]{./images/cartoonRobEval.pdf}}
\caption{Ensemble approach for adversarial example construction. Shown are the decision boundary,
  a test point $x$, the adversarial examples generated for $x$ by the methods BG, PGD, FGSM, their
  associated points $\hat{x}$, and the finally selected $x^*$.}

\label{fig:rob:eval:cartoon}
\end{figure}

\subsection{Experimental results}\label{sec:experiments}

\begin{figure*}[t]
\centering
\centerline{\includegraphics[width=\textwidth]{./images/gopfert_curves.png}}
\caption{Qualitative and quantitative robustness results for the MNIST, CIFAR-10, SVHN, and F-MNIST. The legends report the area under the curves as quantitative measure of robustness. Higher areas corresponds to more robust models.}
\label{fig:gopfert}
\end{figure*}

We evaluated the proposed training approach for Example~\ref{ex:succrates} on 4 datasets: MNIST~\cite{lecun1998gradient}, CIFAR-10~\cite{krizhevsky2009learning}, SVHN~\cite{netzer2011reading}, and F(ashion)-MNIST~\cite{xiao2017fashion}.
MNIST contains $28\times 28$ pixel gray scale handwritten digits uniformly distributed over $10$ classes, divided in $60,000$ and $10,000$ examples for training and test respectively. SVHN contains $32 \times 32$ pixel RGB images of street view house numbers uniformly distributed over $10$ classes, divided in $73,257$ and $26,032$ examples for training and test respectively. CIFAR-10 contains $32 \times 32$ pixel RGB natural images uniformly distributed over $10$ classes, divided in $50,000$ and $10,000$ examples for training and test respectively. Finally F-MNIST is a dataset of Zalando's article $28\times 28$ images, consisting of a training set of $60,000$ examples and a test set of $10,000$ examples, uniformly distributed within $10$ classes.

For each dataset we compared 3 neural networks $f$ which share the same structure: a model trained without any robustness regularization, a model trained with the regularization penalty from~\cite{hein2017formal}
, and a model trained according to our proposed regularization penalty defined in Equation \ref{eq:final:loss:ex:1}, in conjunction with the adversarial generator described in Section~\ref{sec:ouradvgenerator}.

For MNIST, SVHN, and F-MNIST we used for  $f$ the same convolutional neural network architecture.
For CIFAR-10, we used instead the state-of-the-art model ResNet 20 described in \cite{he2016deep}.
The generator $g$ is another convolutional neural network, whose structure is the same for all the datasets (with the exception of the filters of the last layer that depend whether the input picture is grayscale or RGB). The  implementation details of $f$ and $g$ are described in the supplementary material.
We  first trained the models without any robustness regularization, obtaining  accuracies as
shown in the first column of Table~\ref{tab:accuracies}. We then trained using the robustness regularizer of
\cite{hein2017formal} (in the following referred to as {\sc Hein} method) and our approach using different
values of the $\lambda$ parameter that trades off accuracy vs. robustness (cf.
Equation~\ref{eq:final:loss:ex:1}; {\sc Hein}
has a corresponding parameter).
We report in the following the results that were obtained with the  $\lambda$ parameter value that matched
most closely the learning without robustness regularization in terms of test set accuracy.
The second and third column of Table~\ref{tab:accuracies} show the obtained accuracies.
Note that here we are not so much interested in improving the state of the art in terms of accuracy,
but in improving robustness of reasonably accurate models.
Therefore, we  compare the robustness scores on models that have similar accuracies.

\begin{table}[ht]
\caption{Classification accuracies for the three setups for all the datasets.}
\label{tab:accuracies}
\begin{center}
\begin{small}
\begin{sc}
\begin{tabular}{lcccr}
\toprule
Data set & No Reg. & Hein & Ours \\
\midrule
MNIST     & 99.42\% & 99.12\% & 99.49\% \\
CIFAR-10 & 91.15\% & 90.61\% & 90.38\% \\
SVHN    & 92.64\% & 92.08\% & 92.33\% \\
F-MINST    & 93.47\% & 92.80\% & 93.57\%  \\
\bottomrule
\end{tabular}
\end{sc}
\end{small}
\end{center}
\end{table}

For evaluating the robustness of the models, we used the adversarial example construction described in Section \ref{sec:robeval}.
In Figure \ref{fig:gopfert} we plot the $R^f_{Q_{\epsilon},{\mathbf{1}},p}$ scores against $\epsilon$-values.
These are essentially the  marginal curves defined by \cite{gopfert2019adversarial}. The areas under these
curves, i.e. our $R^f_{{\cal Q}_{[0,d]},{\mathbf{1}},p}$ score are reported in the legends, denoted with $R$.
The results suggest that our proposed method allows to learn more robust models while keeping the accuracy almost unchanged. We also evaluated the effectiveness of the three methods BG, FGSM and PGD
for generating adversarial examples. Due to the space limitation this analysis is reported
in the supplementary material.

\section{Unknown, large distribution shifts}
In contrast to the adversarial robustness considered in the previous section,
robustness under distribution shift or common corruptions~\citep{rusak2020simple}
addresses the situation where new test cases may differ substantially from the
original training data, which in our framework means that the conditional distribution
$Q(\cdot | x)$ is not concentrated in an $\epsilon$-neighborhood of $x$.
Without such a locality assumption on $Q$, it is then very difficult to encapsulate
a sufficiently general robustness requirement by the specification of a specific
family ${\cal Q}$ in analogy to ${\cal Q}_{[0,d]}$ of the previous section.

Recent investigations on distribution shift robustness are mostly based on image
benchmark datasets, where an existing collection of labeled images is extended
with additional test sets consisting of original test images that are modified by
different types of corruptions, such as blurring, rotations, or change in brightness.
Corrupted test sets of this kind have been introduced for the MNIST character recognition
set~\citep{mu2019mnist}, and for ImageNet~\citep{hendrycks2018benchmarking}. The goal
then is to train a model on original, uncorrupted, training data, such that it maintains
high accuracy on the corrupted test images.
Trying to obtain robustness in this setting by robust training
techniques developed for adversarial robustness has met with limited
success~\citep{mu2019mnist,rusak2020simple}. Current state-of-the-art approaches for
corruption robustness are based on training set augmentation, where additional
training instances are generated from a mixture of pre-defined image perturbations~\citep{hendrycks2019augmix},
or added Gaussian noise sampled from a noise distribution optimized by co-training the
classifier and the noise generator~\citep{rusak2020simple}.

Most existing approaches are quite tightly linked to image data and neural network classifiers.
We propose a  general method that is not based on any specific properties of image data, and that
can be combined with any type of classifier. Seeing that in this context a preservation of
accuracy is the goal (not resistance to adversarial attacks), we are aiming for robustness as
measured by  $R^f_{Q, {\mathit id}  ,p}$ (cf. Proposition~\ref{prop:accpreservation}). However, the transition kernel
$Q$ modeling the shift in the data distribution is not known a-priori. Our general idea is
to
\begin{description}
\item[1.] learn a classifier $f$ from labeled training examples $(x,y)$ sampled from $P(X)P(Y|X)$;
\item[2.] from original data points $x$, and new unlabeled examples $\tilde{x}$ sampled from $Q\circ P$, learn  a
  \emph{transfer mapping} $T$ that approximates an inversion of the transition
  $x\mapsto  \tilde{x} \sim Q( | x)$;
\item[3.] classify new test instances $\tilde{x}$ as $f(T(\tilde{x}))$.
\end{description}

The learning of $f$ and $T$ are completely separate, which allows the method to be used in conjunction with
any type of classifier. Since in step 2. we are using examples from  $Q\circ P$, this approach
does not follow the strict condition that all training has to be done on the original, uncorrupted
training set. However, the approach reflects a realistic application scenario, where one
modifies an original classifier $f$ to a classifier $f\circ T$ adapted to a changing data distribution.
It is important to note that for this adaptation we neither require labeled examples $(\tilde{x},y)$, nor
do we use  supervision in the form of given pairs $(x,\tilde{x})$ for which $\tilde{x}\sim Q(\cdot| x)$.
In effect, our approach can be seen as a type of \emph{transductive  transfer learning}
in the sense of~\citep{pan2009survey}.

Our approach for constructing a transfer model $T$  follows
a paired auto-encoder architecture that in similar form has previously
been used for the quite different application of deep fake generation~\citep{DBLP:journals/corr/abs-1909-11573}.
We jointly train a pair of autoencoders to reconstruct
samples of original points $x$, and corrupted points $\tilde{x}$.
The two autoencoderes share
the same encoder $E$, but have different decoders,
$D_1$ and $D_2$, as depicted
in Figure~\ref{fig:deepfake} (left) for the case of clean and corrupted MNIST digits.
The transfer function $T$ then is defined as
$T(\tilde{x})=D_1(E(\tilde{x}))$
(see Figure~\ref{fig:deepfake} (right)).

\begin{table*}[ht]
  \caption{Classification accuracies for NN and SVM models using different robust
    robust training techniques.
For both models, the first row reprents the average accuracy over the
15 different corruption types. The second row shows the accuracy on the
original MNIST test set. The standard deviation are estimated by training
the models (including the autoencoders) with 5 different weight initializations.
}
\label{tab:cmnist:svm:nn}
\begin{center}
\begin{small}
\begin{sc}
\setlength\tabcolsep{3.0pt}
\begin{tabular}{cccccccccc}
\toprule
\multirow{2}{*}{Model} & \multirow{2}{*}{Plain} & \multirow{2}{*}{Gauss} & \multicolumn{4}{c}{Transfer-Separate} & \multicolumn{3}{c}{Transfer-Joint} \\
 \cmidrule(lr){4-7}
 \cmidrule(lr){8-10}
 & & & 0 & 128 & 1024 & 30k & 128 & 1024 & 30k \\
 \cmidrule(lr){1-1}
 \cmidrule(lr){2-2}
 \cmidrule(lr){3-3}
 \cmidrule(lr){4-4}
 \cmidrule(lr){5-5}
 \cmidrule(lr){6-6}
 \cmidrule(lr){7-7}
 \cmidrule(lr){8-8}
 \cmidrule(lr){9-9}
 \cmidrule(lr){10-10}

\multirow{2}{*}{NN} & 86.3$\pm$0.52 & 88.5$\pm$0.38 & 86.4$\pm$0.87 & 88.5$\pm$0.44 & 91.1$\pm$0.16 & 92.8$\pm$0.09 & 88.5$\pm$0.17 & 91.5$\pm$0.05 & 92.1$\pm$0.15 \\
& 99.1$\pm$0.03 & 99.3$\pm$0.05 & 99.1$\pm$0.03 & 99.0$\pm$0.02 & 99.0$\pm$0.04 & 99.1$\pm$0.01 & 99.0$\pm$0.01 & 99.1$\pm$0.05 & 99.1$\pm$0.01\\
\midrule
\multirow{2}{*}{SVM} & 69.7 & 70.6$\pm$0.07 & 70.7$\pm$0.74 & 81.0$\pm$0.89  & 86.2$\pm$0.41 & 87.8$\pm$0.30 & 83.1$\pm$0.67 & 85.4$\pm$0.41 & 85.4$\pm$0.40 \\
& 98.4 & 97.9$\pm$0.02 & 98.3$\pm$0.06 & 98.3$\pm$0.06 & 98.2$\pm$0.02 & 98.3$\pm$0.03 & 98.2$\pm$0.07 & 98.3$\pm$0.05 & 98.3$\pm$0.03 \\

\bottomrule
\end{tabular}

\end{sc}
\end{small}
\end{center}
\end{table*}

We evaluate our method using the
C-MNIST~\citep{mu2019mnist} suite of 15 corruptions
applied to the MNIST training and test sets.
We consider two different classifers:
a Neural Network (NN), and a support vector machine (SVM) with RBF kernel.
For the NN we used the same architecture as used
by~\cite{mu2019mnist}. The details regarding the structure
and the training of $f$, $E$, $D_1$, and $D_2$ are reported
in the supplementary material.
We use  two  different evaluation setups:
\begin{itemize}
\item \textsc{Transfer-Separate}: we train and test transfer models with data of one of the
  15 corruption types at a time. Hence, in total
  we construct 15 different pairs of autoencoders. Corrupted test images
  are classified using the transfer model learned from examples of the corresponding
  corruption type.
  \item \textsc{Transfer-Joint}: for training, we  pool all the 15
    corruption types into one set for training a single  pair of autoencoders.
    Test images with all corruption types are classified using the same resulting transfer model.
\end{itemize}
For both \textsc{Transfer-Separate} and \textsc{Transfer-Joint}
we use for training $N_o=60k-15N_c$ examples $x$ from the original MNIST
dataset and $N_c \in \{0, 128, 1024, 30k\}$ examples $\tilde{x}$ for each of
the 15 corruption classes  from the
C-MNIST training set. We ensure that none of the $\tilde{x}$  used for training
is the corrupted  version of a clean $x$ also used for training.
The case $N_c=0$, means that we only train
one autoencoder consisting of $E$, and $D_1$ which then still can be used as a transfer
model for new, corrupted examples. There is no difference between \textsc{Transfer-Joint}
and \textsc{Transfer-Separate} in this case.

\begin{figure}[h]
\centering
\centerline{ \includegraphics[width=0.5\columnwidth]{./images/deepfake.png}}
\caption{Transfer by paired auto-encoders}
\label{fig:deepfake}
\end{figure}

As baselines we consider \textsc{Plain} classifiers wich are obtained by standard
training on clean images, and then used without modifications to classify noisy images.
As a second baseline we used data augmentation
by adding Gaussian noise to the original MNIST pictures. The Gaussian noise centered
in 0 with standard deviation of 0.1, was applied independently for each pixel.
NN and SVM classifiers were
then learned from a mix of clean and noisy examples.

Table~\ref{tab:cmnist:svm:nn} shows a summary of results\footnote{More detailed results
are contained in the supplementary material}.
For each classifer we report the accuracy on corrupted test images,
averaged over the 15 corruption types,  and the accuracy for the original MNIST test set
We first observe that adding a robust training approach nowhere leads to a significant
decrease in the clean data accuracy. Both the \textsc{Plain} NN and SVM models are
significantly less accuracte on the noisy than the clean data, where the gap is even
more pronounced for SVM than NN. The \textsc{Gauss} baseline for robust training
in this experiment only led to a minor improvement. This is in contrast to findings
by \cite{rusak2020simple}, who reported  that Gaussian noise augmentation can be
quite effective. However, they also show that a very careful calibration of the Gaussian
noise generation is required.
The results for both \textsc{Transfer} approaches show a significant improvement of classification
accuracy for the corrupted examples as the number of noisy training examples increases.
This improvement is consistent for the NN and SVM models. Most remarkably, perhaps,
the results for \textsc{Transfer-Separate} and \textsc{Transfer-Joint} are very similar,
showing that a single transfer model $T$ can handle a wide range of different data
transformations.

\cite{mu2019mnist} reported an accuracy
of $91.91\%$ for what should correspond exactly to our \textsc{Plain} NN model.
We were unable to reproduce their results, and only obtained the  $86.30\%\pm0.52$
shown in the table.
\cite{rusak2020simple} report and accuracy of $92.2\%$ for their trained Gaussian noise
augmentation approach. However, these results are not directly comparable, since
\cite{rusak2020simple} use a different neural network architecture.

\section{Conclusions}
We have introduced a general framework for defining robustness of classifiers.
Our framework allows flexible definitions for different types of robustness that in a uniform manner
permit to calibrate robustness objectives with respect to different assumptions on the nature of
adversarial attacks or distribution changes that one wants to protect against. Our framework
establishes a natural link between the recent work in robustness, and more established
work in the area of transfer learning. Considering two specific robustness concepts,   we have
developed new training methods for image classifiers for these robustness objectives.
Our results show particularly promising results in a learning setting where a classifier can
be incrementally trained to become more robust by being exposed to novel, unlabeled examples.

While being greatly motivated by the conceptual framework, our algorithmic solutions are not directly
linked to the formal foundations we laid in this paper. A possible line of future work can be the
development of more generic training methods that can then be simply instantiated for a given
robustness objectives. On the theoretical side, an interesting question would be to what extent
robustness for a given measure $R_{Q,H,G}$ implies lower bounds on the robustness according to
another  measure $R_{Q',H',G'}$, and, thus, whether one type of robustness as a training objective
typically leads to models that are robust in a wider sense.

\clearpage
\input{main_arxiv.bbl}
\clearpage

redpajama_set_name: RedPajamaArXiv


following your blog. this would be ideal thing to win as my little lady is teething and just got her 1st 2 teeth through yesterday.
Am following via GFC as viviennej, email address is viviennej@hotmail.com. Fingers crossed!


I have been asked to create a world map for a Flat Earther's community but having trouble setting up the projection. Can someone please explain which spheroid I should use?
Steve, I'm not sure on the technicalities, but I'm guessing it would be one that had USA right in the middle of the map.
Correct, but remember to use the Mar-a- Lago datum.
Sometimes, it feels like the internet was a mistake.
Absolutely. On the 364 days of the year that are not April Fools day! On April Fools day it makes perfect sense.


text:
Q: How to initiate a change event for a TreeModel in Java? Suppose you got a JTree with a model that implements TreeModel, and all nodes implement TreeNode.
Suppose then that something happens in the background with the model (not through the GUI) like a CRUD-event, that update the model and should update the JTree.
Since the model is CRUD-affected from other views it does not seems like a good idea to use the DefaultTreeModel for this task, correct me if I'm wrong.
I guess you need to signal the change to the TreeModel in somehow, like fire some event in some way?
Btw I have not managed to implement the methods:
public void addTreeModelListener( TreeModelListener l )
public void removeTreeModelListener( TreeModelListener l )

I guess these methods need to be implemented for such a feature.

A: I like to use this kind of generic ListenerList:
public class ListenerList {
    private final List<Object> list = new ArrayList<Object>();

    public ListenerList() {
    }

    public void addListener(Object listener) {
        list.add(listener);
    }

    public void removeListener(Object listener) {
        list.remove(listener);
    }

    public <T> T getNotifier(Class<T> intf) {
        ClassLoader cl = intf.getClassLoader();
        return intf.cast(Proxy.newProxyInstance(cl, new Class[] {intf},
                (Object proxy, Method method, Object[] args)
                        -> actualInvoke(method, args)));
    }

    private Object actualInvoke(Method method, Object args[]) {
        Object result = null;
        for (Object listener: list) {
            try {
                result = method.invoke(listener, args);
            } catch (IllegalAccessException e) {
                LOG.error("Error invoking listener method", e);
            } catch (InvocationTargetException e) {
                LOG.error("Error invoking listener method", e);
            }
        }
        return result;
    }
}

That I use in my model class:
public class MyTreeModel implements TreeModel {
    private final ListenerList listeners = new ListenerList();
    private final TreeModelListener notifier = listeners.getNotifier(TreeModelListener.class);

    public void addTreeModelListener( TreeModelListener l ) {
        listeners.addListener(l);
    }

    public void removeTreeModelListener( TreeModelListener l ) {
        listeners.removeListener(l);
    }

    protected void fireTreeNodesChanged(TreeModelEvent e) {
        notifier.treeNodesChanged(e);
    }

    protected void fireTreeNodesInserted(TreeModelEvent e) {
        notifier.treeNodesInserted(e);
    }

    protected void fireTreeNodesRemoved(TreeModelEvent e) {
        notifier.treeNodesRemoved(e);
    }

    protected void fireTreeStructureChanged(TreeModelEvent e)
        notifier.treeStructureChanged(e);
    }

    ...
}


text:
Pitino leaves Greece, seeking return to the NBA
Rick Pitino is leaving Panathinaikos, the team he coached to a Greek League championship this season, he told ESPN on Friday.
The Hall of Famer said he turned down an offer to return as the franchise's president and head coach in order to pursue a job in the NBA, either in coaching or in a player personnel or advisory role.
Pitino, 66, was fired after a long run at Louisville following an FBI probe into college basketball recruiting. He coached the Cardinals from 2001 until the end of the 2016-17 season, taking the program through three conference changes (Conference USA, Big East and ACC) while posting a 416-143 record.
Pitino, who also coached at Hawaii, Boston University, Providence and Kentucky, has 770 career college victories over 1,041 games, winning an NCAA title in 1996 with Kentucky and 2013 with Louisville.
Back in October, Pitino first expressed his interest in returning to the NBA: "I just want to be a part of an organization," he told ESPN. "I want to develop young players. I want to be part of a team. I miss it terribly. I'm using this time to really study the NBA. If something opens up with a young basketball team, I'd have deep interest in it."
"I think the league is going to get younger and player development will become even more important to every organization. That's my forte. I believe I can help an organization find a pathway to success."
Pitino has not worked in the NBA for almost two decades. He compiled a 192-220 record as head coach of the New York Knicks (1987-89) and Boston Celtics (1997-2001).
With the Celtics, Pitino also was handed personnel control and the title of team president. He said he wouldn't insist on a front-office role this time around.
"I'm not looking for any of that at this stage of my life," Pitino told ESPN in October. "I want to develop teams and develop players and build a winner. I value analytics. I want to fit into an organization. At this stage, that's all I'm interested in."
[Reuters]
Showing no sign of remorse, Giorgos Roupakias, the man charged with the murder of rapper Pavlos Fyssas in September 2013, described the incident as a "simple homicide" that has been "blown out of proportion" in his testimony Thursday before a panel of judges in a packed Athens courtroom.


A sense of TRUE VALUE. We will always have your "best interests at heart," and deliver the best result(s) possible.
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text:
Philip Brent Carter
By Editor | February 17, 2021
GENEVA, Fla. – Philip Brent Carter, 69, of Geneva, Fla., passed away on Feb. 7, 2021.
Phil was born in Sharpsville on July 3, 1951 to W. Dean and Evelyn Carter.
He is survived by his wife, brother, six children and 13 grandchildren.
Phil had a long career as a basketball player and coach. He was an alumnus of Jacksonville University, Class of 1974. He began his coaching career at Episcopal High School in Jacksonville, Fla. He then coached at Daytona Beach Community College (76-80), followed by Baptist College in Charleston, S.C. 980-83), Hardin-Simmons University in Abilene, Texas (83-85), University of Central Florida (85-89) and finished his collegiate coaching career at Lake Sumter Community College in Leesburg, Fla.
After a long career in coaching, Phil went on to own and work for several auto dealerships, working for Sanford Auto Dealers Exchange and Adesa Auto Auction.
Sports remained an integral part of Phil's life. He enjoyed time on the golf course with friends, coaching his children and grandchildren's teams or simply watching the game at home with family.
In lieu of flowers, the family asks that donations be made to charity in Phil's memory. Sports related charities for children or agencies funding research for the treatment of colon cancer and multiple myeloma would have been close to his heart.


text:
Canalul Panama (spaniolă: Canal de Panamá) este un canal important care traversează istmul Panama în America Centrală, legând oceanele Atlantic și Pacific. Construcția canalului a reprezentat unul dintre cele mai mari proiecte de inginerie întreprinse vreodată. A avut un impact enorm asupra navigației, deoarece navele nu mai trebuie să treacă pe drumul periculos prin Pasajul Drake și Capul Horn în punctul cel mai sudic al Americii de Sud. O navă care pleacă de la New York către San Francisco, dacă trece  prin canal, parcurge în total 9.500 km, mult sub distanța de 22.500 km pe care o presupunea ruta ocolitoare pe la Capul Horn (strâmtoarea Magellan).

Deși conceptul unui canal în Panama datează de la începutul secolului al XVI-lea, prima încercare de construcție a avut loc începând cu 1880 sub conducerea francezului Ferdinand de Lesseps. După ce această încercare a eșuat, lucrul a fost terminat în cele din urmă de Statele Unite, și canalul s-a deschis în 1914. Construcția canalului, de o lungime de 77 km, a fost presărată de probleme, cum ar fi bolile (în special malaria și febra galbenă) și enormele alunecări de teren. Se estimează că la construcția canalului au murit până la 27 500 de muncitori.

De la deschidere, canalul a avut un succes enorm, și este în continuare un element indispensabil al navigației internaționale. În fiecare an prin canal trec mai mult de 14 000 de nave, transportând mai mult de 20378 milioane de tone de marfă.

Descriere

Canalul Panama face legătura între Golful Panama din cadrul Oceanului Pacific cu Marea Caraibelor și Oceanul Atlantic. Din cauza formei de S a istmului Panama, canalul pleacă din sud-est, din capătul dinspre Pacific, către nord-vest, la capătul dinspre Atlantic; pentru a evita orice confuzie, autoritățile au clasificat tranzitul prin canal ca spre nord (din Pacific în Atlantic) și spre sud (din Atlantic în Pacific).

Prin canal pot trece vase, de la iahturi private mici până la nave comerciale destul de mari. Dimensiunea maximă a vaselor care pot folosi canalul este cunoscută sub numele de Panamax; tot mai multe nave moderne depășesc această limită, ele fiind cunoscute ca nave post-Panamax. O traversare obișnuită a canalului de o navă comercială ia în jur de nouă ore. 14 011 vase au trecut prin canal în 2005, cu o capacitate totală de 278,8 milioane tone, cu o medie de aproape 40 de vase pe zi.

Plan

Canalul e format din două lacuri artificiale, câteva canale artificiale și trei seturi de ecluze. Un alt lac artificial, Lacul Alajuela, are rol de rezervor pentru canal. Dispunerea canalului, din punctul de vedere al unei nave care îl traversează din Pacific către Atlantic, este cum urmează:

Datorită geografiei locale, principala direcție de navigație este către nord-vest, însă direcția în general din Pacific către Atlantic este spre est.
 De la începutul intrării în canal, marcată cu balize, navele navighează 13,2 km pe canal, până la ecluzele Miraflores trecând pe sub Podul Americilor
 Sistemul de ecluze cu două trepte de la Miraflores, incluzând peretele de apropiere, are 1,7 km lungime, cu o diferență totală de altitudine de 16,5 m la jumătatea mareei.
 Lacul artificial Miraflores este următoarea etapă, de 1,7 km lungime, și aflat la 16,5 m deasupra nivelului mării
 Ecluza Pedro Miguel, cu o singură treaptă, are 1,4 km lungime, și ridică navele cu 9,5 m, până la nivelul principal al canalului.
 Tăietura Gaillard (Culebra) taie 12,6 km prin istm, la o altitudine de 26 m, și trece pe sub Podul Centenar.
 Râul Chagres (Río Chagres), un curs de apă natural, modificat prin construcția unui baraj al lacutului Gatún, curge către vest circa 8,5 km, vărsându-se în Lacul Gatun.
 Lacul Gatun, un lac artificial format prin costruirea Barajului Gatun, duce navele pe o distanță de 24,2 km
 Ecluzele Gatún, un set de ecluze în trei trepte, de 1,3456 km lungime, coboară navele înapoi la nivelul mării.
 Un canal de 3,2 kilometri lungime reprezintă secțiunea premergătoare a ecluzelor din partea atlantică
 Golful Limón (Bahía Limón), un port natural uriaș, reprezintă un loc de ancorare pentru unele nave aflate la intrarea în canal, și se întinde pe 8,7 kilometri până la Oceanul Atlantic.

Lungimea totală de la canalul de intrare în Pacific până la ieșirea în Atlantic este de 76,9 km. Cea mai mare diferență de maree înspre Oceanul Pacific este de la +3.35 metri până la -3.20 metri; prin urmare, înălțimea câștigată la Miraflores variază între 13,1 metri la flux și 19,7 la reflux. Diferența de maree pe partea atlantică nu depășește 60 tone . Nivelul normal al mării la capătul dinspre Pacific al canalului este în medie cu 20 cm mai înalt decât cel dinspre Atlantic.

Golful Limón, pe partea atlantică, este un loc de ancorare adăpostit, protejat de un dig; totuși, spațiul din interiorul golfului nu mai este adecvat pentru numărul și dimensiunea navelor care folosesc canalul, și multe nave așteaptă la ancoră în afara golfului. Locul de ancorare în partea pacifică este deschis, deși este protejat de topografia închisă a Golfului Panama.

Ecluze

Cea mai impresionantă parte a canalului e dată de ecluzele sale. Secțiunile ecluzelor au o lățime de 33,53 metri și o lungime folosibilă de 304,8 metri. Adâncimea apei în ecluze este variabilă, însă cea mai mică adâncime este de 12,55 metri în partea sudică a ecluzelor Pedro Miguel. Aceste dimensiuni determină mărimea maximă a navelor care pot tranzita prin canal; această mărime este cunoscută sub numele de Panamax. Toate ecluzele din canal sunt perechi; există două seturi paralele de ecluze în fiecare loc, permițând în principiu trecerea a două nave în direcții opuse simultan. Navele mari, însă, nu pot traversa în siguranță pe la Tăietura Gaillard; în practică traficul naval se desfășoară alternativ, folosind fiecare "bandă" a ecluzelor într-o singură direcție la un moment dat.

Fiecare secțiune a ecluzei necesită 101 000 metri cubi de apă pentru a se umple; această apă intră cu ajutorul gravitației, printr-o rețea de conducte sub fiecare cameră a ecluzei. Navele sunt transportate prin ecluze de mici locomotive numite mulas (asini, numite astfel după animalele care înainte trăgeau barjele), mergând pe șine pe pereții ecluzelor; navele mai mici, cum ar fi iahturile private sau vaporașele, nu sunt transportate tot cu locomotivele, ci de remorchere.

Lacurile Gatún și Alajuela

Lacul Gatún și râul Chagres, (Río Chagres), canalizat, sunt componente de bază ale canalului, transportând navele pe o distanță apreciabilă peste istm. Lacul are de semenea rol de rezervor, stocând apa pentru a permite funcționarea ecluzelor și în timpul sezonului secetos. Formarea lacului și adâncirea și lărgirea râului s-au făcut prin construcția Barajului Gatun pe râul Chagresr. Acest lucru a inundat valea împădurită inițială; aproape un secol mai târziu, cioturile vechilor arbori încă mai pot fi văzute ridicându-se din apă, constituind un pericol pentru navele care se îndepărtează de canalele marcate.

Există o mică "scurtătură" prin canal, numită "Tăietura Banana", care permite un drum ușor mai scurt; ea este folosită de navele aparținând canalului și de iahturi, precum și pentru a evita traficul naval greu. Mai multe insule se află în cadrul secțiunii Lacului Gatún din Canalul Panama, cum ar fi Insula Barro Colorado, unde se află cunoscutul Smithsonian Tropical Research Institute (STRI).

Volumul apei utilizată de navele care trec prin ecluze, împreună cu natura sezonieră a ploilor în Panama, face dificilă menținerea nivelului apei Lacului Gatún, în special în sezonul secetos. Din acest motiv, a fost construit un alt baraj, Barajul Madden, peste râul Chagres, deasupra Lacului Gatun. Acest baraj a creat Lacul Alajuela — numit și Lacul Madden — care asigură mai multă apă pentru canal.

Puncte de traversare

Există mai multe puncte de traversare peste canal. La capătul dinspre sud (Pacific), se află Podul Americilor, un pod rutier important deschis în 1962; pentru mult timp, acesta a fost singurul punct de trecere a canalului. Înainte de construcția sa, erau folosite feriboturi pentru traversare. Către nord, la ecluzele Miraflores, există un pod rutier/feroviar culisant, deschis în 1942, însă nu poate prelua traficul decât atunci când nu circulă nicio navă, fiind astfel foarte rar folosit. În același punct, un mic pod rutier culisant este construit în structura ecluzelor Miraflores; acesta este de asemenea rar folosit.

Cel mai nou pod este Podul Centenar, care traversează Tăietura Gaillard la nord de ecluzele Pedro Miguel; acest pod rutier cu șase benzi a fost terminat în 2004, deși a fost deschis traficului abia în 2005. În sfârșit, un alt pod rutier culisant a fost construit în structura ecluzelor Gatún; acest pod este folosibil numai când ecluzele sunt închise și are o capacitate foarte redusă.

În afară de traversările deschise publicului, lucrătorii canalului pot traversa și pe porțile ecluzelor, atunci când sunt închise.

Noul canal
După 6 ani de studii de fezabilitate, eficiență economică și impact asupra mediului, în septembrie 2007 au început lucrările la un nou canal, paralel cu cel vechi. Dacă vechiul canal permitea trecerea navelor care transportă maximum 5000 TEU, noul canal va permite nave cu capacitatea de 13.000-14.000 TEU, dublând astfel capacitatea totală de traversare a sistemului de canale Panama.

Referințe

Legături externe

 Panama Canal Sailing Guide by CaptainWiki.Com
 Official website of the Panama Canal Authority — are o simulare care prezintă funcționarea canalului
 Canal Zone Brats — informații ample despre canal și despre zona în care se află
 History of the Canal Zone — including much canal information, from CZ Brats
 Latin Business Chronicle  — Panama Canal: Chinese Control?
 Panama Canal Webcams
 Time Lapse Video of the Canal  (created using one week of webcam footage).
 TeddyRoosevelt.com: Omul care a costruit Canalul Panama
  Dr. Alonso Roy's short essays on Panama Canal History
 Judicial Watch, Inc. v. Panama Canal Commission case (archived)
 Satellite view in Google Maps
 informații generale despre Canalul Panama
 Structurae: Panama Canal
 Canalul Panama: drumul de ape care leagă două oceane, 25 iulie 2013, Nicu Pârlog, Descoperă
 Panama - canalul construit cu sânge , 11 iulie 2007, Gabriel Tudor, Revista Magazin

Vezi și
 Listă de superlative geografice

Canalul Panama

redpajama_set_name: RedPajamaWikipedia


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Drop Off Locations
How Can Kids Help?
Forever Foster
By Kristina Millman-RinaldiDecember 15, 2020No Comments
Detroit came to us from a dilapidated sanctuary where he was held for years in a kennel so rusted that it wouldn't even open. One of our loving foster families took Detroit in and now this guy is enjoying car rides, kisses and naps while he gains weight and receives medical care.
What started as an animal sanctuary became an overwhelmed dumping ground for senior dogs. Sadly, the dogs were in deplorable conditions, lacked medical care, were surrounded by feces and some cages were so rusted shut that they had to be opened by extreme force.
The property was covered in living and dead rats, maggots filled the moldy food bowls, and the dogs were exposed to extreme weather and sun. It quickly became apparent that this was an emergency rescue mission. All 165+ dogs were removed from the property and thanks to Animal Rescue Corps, the dogs were able to do a legal hold and quarantine until they were able to legally cross state lines with health certificates and documentation.
Thanks to the collaboration that Bissell Pet Foundation provides, each shelter leader agreed to take in some of the dogs in an effort to aid in this emergency.
On Wednesday some of the dogs arrived in Detroit. Although Detroit Dog Rescue focuses on the rescue and rehabilitation of Detroit's dogs, it's in times like these that we need to collaborate across borders to aid others the way they aid Detroit. This was a massive effort spanning several shelters.
The dogs that DDR took on are extreme cases, they need the resilience and spirit of Detroit. All except one of these rescue dogs are senior dogs. They need dental treatments, orthopedic treatments and possible surgery and full medical work ups. We believe they deserve to live out the time they have making the memories they deserved, but were never given.
Kristina Millman-Rinaldi
Kristina Millman-Rinaldi has been changing the face of animal welfare in Detroit for well over a decade. The nonprofit organization is Detroit's first and only no-kill shelter, which finds homes for neglected dogs and animals who are victims of violent crimes. As Detroit Dog Rescue's Executive Director, Kristina worked closely with Detroit Mayor, Mike Duggan's administration to create Detroit's first animal welfare committee. This partnership resulted in new leadership and policies for the city's municipal animal shelter. Detroit now works harder to find alternatives to euthanasia due to overpopulation, while focusing on public safety. Kristina has been a part of several documentaries, news stories, and reality shows highlighting Detroit's stray dog epidemic and she has raised millions of dollars to fund initiatives that support animals, especially ones who are victims of violent crimes. In the past, Kristina has been the recipient of the Mackinac Humanitarian Award, Beaumont Hospital's President Award for Community Giving, and has been named WDVD's "Woman of the Year" for her ability to create solutions in underserved communities.
Detroit Dog Rescue
St. Clair Shores, MI 48080
support@detroitdogrescue.com
Want to help the dogs of Detroit?
Detroit Dog Rescue is a non-profit 501(c)3 organization regulated by the Michigan Department of Agriculture and Rural Development.
© 2020 Detroit Dog Rescue. All Rights Reserved.
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Члопа:

 Члопа — город в Польше, входит в Западно-Поморское воеводство, Валецкий повят.
 Члопа — гмина (волость) в Польше, входит в Валецкий повят, Западно-Поморское воеводство.


How to watch Liverpool v Chelsea LIVE in Nigeria. The TV channels that will broadcast the premier league match live includes DSTV, GOtv, EIR Sport 2, Premier SportsSelect 2 or Select 3, Kwesetv, Startime, NTAsport, Sky sports, Fox sport and Eurosport.
SuperSport 3 Nigeria will be available for the live coverage of the match. Most West African fans and South African can hoop up with SuperSport different channels to watch the match between Liverpool and Chelsea.


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Mountain Walks
Fell Walks
Coast Walks
Pilgrim Walks
Other Walks
Narrowboating
The Barn
Hiking Statistics Picos de Europa Guide Colletts Mountain Holidays
Glassby Family History
Komagatake - September 2009
When I came to extend my stay at the Toko City Hotel I had a problem! The Japanese Government has changed the date of Respect for the Aged Day (which now seems to be called "Respect for the Elderly Day") and has moved it to the third Monday in September, and for the first time this led to 5-days of holiday. Whilst the Japanese have Golden Week in April, they now have "Silver Week" in September. Whilst this is good news for them, it meant that all the hotels were full and millions of people were travelling to enjoy the five day break! The 5-day consecutive holiday break will occur every 6 years, the next one being 2015.
The Toko City Hotel had a room for me for Friday night, but they were full for Saturday and Sunday. Hence my top prioirty was to go back to the Tourist Office at the station to try to find a room for Saturday and Sunday, and to reconfirm my flight. Having got all my travel and hotel reservations confirmed I was ready for another day in the mountains. Because of Silver Week, the fact that my rucksack was pretty heavy and the fact that my right knee was giving me some pain, I wanted a walk where I could gain height effortlessly but at the same time be at the 3,000 m level. The answer was Komagatake, 2,956 m, in the Central Alps.
It was quite a warm day as I set off at 6 a.m. on the Saturday morning…….. the temperature indicator at Matsumoto Station indicated 16 deg C already. I bought a Yen 1,110 rail ticket Matsumoto – Komagane and took the 6-32 a.m. train to Okaya, arriving at 6-59 a.m.
Here I changed to the Iida Line, and had to wait for the 7-28 a.m. train to Komagane.
Komagane train at "Platform 0", Okaya
The Iida line is a very nice single track railway that winds its way up the valley beneath the high mountains, and the train arrived at Komagane at 8-52 a.m. I was soon out of the station and on the bus (Yen 1,000 each way) waiting to take me to Shirabidaira, 1,662 m above sea level.
Along the Iida Line
The bus went through central Komagane before climbing up a valley via an incredible number of hairpin bends until it reached Shirabidaira, the lower station of the Komagatake Ropeway. This cable car, built in 1967 and rebuilt in 1998, takes you to 2,612 m above sea level to the upper station of Senjojiki Col. This is at the foot of a cirque directly below Hokendake, 2,931 m. The vertical lift is 950 m, which they claim to be the largest of any cable car in Japan. The ride takes just under 8 minutes, and each gondola can carry 61 people. The fare is Yen 2,200 return for an adult.
I arrived at Senjojiki at 10-05 a.m., and the temperature was already 12 deg C. It was going to be a beautiful day on the peaks.
I exited the cable car station, had the obligatory photograph taken, and headed up the trail to the left towards Gokurakudaira. The path is man-made and is not too steep, and there are ropes to keep people off the side of the track to protect the alpine flowers that grow there. I reached Gokurakudaira at 10-55 a.m.
Path to Gokurakudaira
Looking back down to the cable car station
Gokurakudaira
From Gokurakudaira you have majestic views of the surrounding valleys and mountains. Fuji-san could just be seen in the distance behind the Southern Alps chain, and nearer by Mt. Ontake stood proud of the surrounding plain standing isolated on its own. The ridge to Hokendake went off to the right, and after a fairly flat bit turned into an exposed ridge of broken rock.
Mt Ontake in the distance
It looked quite challenging ahead, but there are numerous chains and footholds that have been put in place to help you over the difficult bits. At one point, which is quite exposed, you have to jump from one rock to another a short distance away, relying on an overhead chain for security!
The trail leading to Hokendake along the ridge
A hiker in red can be seen half way down the peak
A tricky bit, where you have to jump from one rock to another with the aid of a chain
Hokendake 2,931 m
Fuji-san can just be seen in the distance
I reached the top of Hokendake, 2,931m by 12 noon, and began the descent down the other side to the col over quite steep rock slabs. The path traverses a very narrow exposed ledge, but again you are assisted by chains for security. I reached the col and the two lodges located there, Tengu Sanso and Hoken Sanso, at 12-30 p.m.
Tengu Sanso and Hoken Sanso with Nakadake and Komagatake peaks ahead
Looking back to Hokendake from Nakadake
Up from the lodges is a peak named Nakadake, and the trail falls away the other side to another col with another lodge
View of Komagatake from Nakadake
Nakadake
The trail then makes the final climb to Komagatake, 2,956 m. I reached Nakadake by 12-45 p.m., and Komagatake by 1-15 p.m. I stayed there for 10 minutes or so taking photographs and looking at the shrine, and then made my way back to the col where the two lodges are located.
Komagatake 2,956m
Komagatake Shrine
Lads in the small shop atop Komagatake
Looking back from Komagatake towards Nakadake, with Hokendake in the background
It was by now 1-45 p.m. as I started to descend down a steep twisting path down towards the cable car station. After a while the path levels out and traverses across the cirque towards the cable car station.
View back towards Nakadake
Mt. Fuji visible in the distance
I was back at the top of the ropeway at 2-25 p.m., and after a short wait took the cable car down. I was back at Shirabidaira by 2-50 p.m. The 3-10 p.m. bus took me back to Komagane Station, and I was there by 4 p.m. Ahead of schedule, I was able to take the 4-25 p.m. train instead of the 5-25 p.m. one, and reached Tatsuno Station by 5-11 p.m. Here I had to wait until 5-53 p.m. for the train to Matsumoto, and I got back by 6-31 p.m.
Monkeys on the road down from Shirabidaira
What a wonderful day out. In approximately 12 hours I had been able to visit the Central Alps and scale a peak (with assistance from the cable car!) of 2,956 m height and enjoy four and a half hours ridge walking