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Brad Goreski Named 'Exclusive Brand Stylist' for Kate Spade, Probably Cried When He Found Out
Sounds like Brad Goreski is poised to dominate in 2012. His new reality show It's a Brad, Brad World debuts Monday on Bravo and has already received a decent amount of press. In fact, life must be a constant stream of phone interviews for the L.A.-based stylist. He's been talking to many outlets (including us) about the show and his falling out with Rachel Zoe. Most recently, he talked to E!'s Mark Malkin about how his show will feature an "off the charts" number of "tears per episode." And, according to WWD, he was waiting to board a plane when they chatted with him about his latest gig: "exclusive brand stylist" for Kate Spade.
Dhani Mau
Brad styled the label's spring 2012 presentation during New York Fashion Week and must have done a really good job. Part of Brad's new gig, in addition to styling all press events, fashion presentations, ad campaigns and e-commerce shoots, will be to bring more awareness to the label's ready-to-wear offerings; which, while strong, don't get as much attention as the accessories Kate Spade has always been known for.
He told the trade, "We see so many people carrying the bags and the accessories. It's my hope to get the ready-to-wear out there and see it more on the streets and see people playing with it and making it their own."
Granted, we're not that familiar yet with Brad's styling repertoire, but the Kate Spade aesthetic is kind of a female version of his personal style, so it seems like it would be a good fit, right? It sounds like Brad's sense of humor also may have played a part in getting him the job. Lloyd told WWD,
I have been a fan of Brad's sense of style and spirit from afar for some time now. When I began to consider a stylist with whom I could really build an ongoing relationship and one whom I trusted, he was the first that came to mind. Besides being a great stylist, he is a joy to be around and a true gentleman. He keeps me laughing and keeps me on my toes
Another part of his job will reportedly be collaborating with the brand in social media efforts, so his large Twitter following also may have helped. Looks like he's already gotten a head start on that.
We also have to wonder--could this mean Brad might take up residence in NYC, where Kate Spade is based? He did tell us a while back that he'd consider it...
EntertainmentBrad GoreskiNews
10 Things We Learned About Brad Goreski From His New Book, Plus What He Told Us About Being 'Blacklisted' at Vogue and Becoming a Lady Gaga Backup Dancer
Brad Goreski's memoir Born to be Brad hit shelves yesterday (he's doing a signing at 5pm tonight at the FIT Barnes & Noble) and you're not alone in thinking there's no way Brad is old enough to be writing his memoir. We thought the same thing until we read it--and as it turns out, Brad has lived a pretty full life--perhaps even two of them. And as of today, that life is literally an open book--and a pretty juicy one at that. From his difficulties growing up gay in a small Canadian town, to a period of excessive partying, to being a 24-year-old Vogue intern, to becoming the assistant to a huge celebrity stylist and a reality TV star in one felll swoop, to how that job came to an end, he doesn't really leave anything out. And he clears up a lot of those rumors. We learned so much about the celebrity stylist-slash-reality television star that we almost didn't know what to ask him the other day when we chatted on the phone. Of course, we managed to find some good stuff to talk about. Click through for the 10 most interesting things we learned about the It's a Brad, Brad World star from his shiny new book, followed by a Q+A in which he discusses making it in the industry, still feeling like an outsider, his backup dancer ambitions and how his boyfriend Gary is amazing--not that we didn't already know that.
By Dhani Mau
Check Out Kate Spade's Fall 2011 Collection, Styled by Brad Goreski
Whether or not Brad Goreski poached Demi Moore from his former boss, Rachel Zoe, remains to be seen, but he has been racking up some noteworthy styling gigs lately. Namely, styling Kate Spade's adorable fall 2011 collection. Kate Spade likes bows, Brad likes bow ties, it's a perfect match! Take a look.
Brad Goreski To Get His Own Show on Bravo, It's a Brad Brad World
It was only a matter of time. Rachel Zoe's former assistant Brad Goreski, whose bow ties often stole a little of Zoe's spotlight on her own Bravo series, has landed his own show on Bravo called It's a Brad Brad World. According to the release we just received from Bravo, the show will follow Goreski "as he embarks on his new solo career as a stylist...and tries to maintain his personal life." Cameras will trail Goreski as he hits up Paris fashion week, Cannes, the men's runway shows and couture. Goreski has certainly stepped up his styling game since parting ways with new mommy Zoe.
Jessica Alba Left Stylist Brad Goreski for Emily Current and Meritt Elliott
Successful styling and denim-designing duo Emily Current and Meritt Elliott have confirmed to us that they are currently Alba's stylists. And as any It's a Brad Brad World fan knows, Alba's styling duties used to go to Brad Goreski. So why did she leave him?


We are on the ground floor of figuring out which companies are really the best at providing quality and inexpensive CBD oil for people to use. People choose to use Cannabis and CBD products to get away from the harsh chemicals and pesticides of big pharma and are usually searching or a more natural method to help with their health. Because the industry is so new, I have found many companies that say they have high quality products to only find they have never tested their products or did little testing to prove it is in fact HIGH QUALITY.
Our definition of High Quality is the demand that products and isolates are TESTED for Cannabinoid Profile & Potency, Pesticides, Heavy Metals, and Microbials. We also prefer companies who conduct TRIPLE LAB TESTING from 3rd PARTY Labs. We believe the company should be honest, have easy access to testing results, and efficiently communicate with it's current and potential customers. We developed a ranking system to use so that you may see why we give certain companies certain stars.
I promise to do my best in giving the most recent information I am given on specific products and companies and that all I do provide has been thoroughly researched. I allow the companies to contact me if they have new testing and I will update accordingly. I also promise to provide any contact information I have on the companies and the labs they used to test.
At the end of each company/product review, I will give my overall ranking based on the results from their above ranking.
Wanna see us doing laundry at the laundromat? See how awkward I get talking to my phone in public..i gotta get over it lol!
A Rant about CBD- Know What's In IT!
Today I went Live on Youtube to kind of rant about CBD companies that are popping up all over the place but most of the people either don't know what is actually in the CBD or that they even have choices! I am on the search for a CBD company that is 100% pesticide free, 100% GMO Free, HEAVY METAL FREE, and TRIPLE TESTED for Mold, mildew and other crap that could harm me if I take it. People do no switch to CBD from their regular medicine just to get more crap and chemical in their body. They do it because it is a more natural alternative. But no body should be paying an arm and a leg for their products either. There are a TON of growers and manufacturers out there, but if it does not clearly say PESTICIDE/GMO/Heavy Metal Free…it is not! I am on the search. Send me companies you know of and want me to research. Send me products you may have used. Let me find out what is in those products and maybe together we can find a good and inexpensive company to purchase CBD products from!


Foshan TaiFeng Furniture Accessories Co.,Ltd. is a collection of office chairs chassis development, production and sales in one of the modern enterprise.
Based on the Chinese furniture industry with the PRD important manufacturing center - Foshan.
To "high standards, high-tech, high-quality" as the up factories in principle. within the grasp of product improvement and improve product quality, grasping the market salesperson sales networks.
Constantly improve their own management, quality control system, optimizing the production process, in order to keep perfect product quality to customer satisfaction.
The company all kinds of office chairs chassis have passed ANSI / BIFMA5.1 testing and certification, widely recognized in the industry, attracting many overseas customers come here.


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Q: EJB 3.0 circular dependencies We have hundreds of EJBs. Recently created a new patch which doesn't deploy correctly in our JAS: JBoss 4.2 and gives errors like the following at deployment time:
--- MBeans waiting for other MBeans ---
ObjectName: jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=Locator,service=EJB3
  State: NOTYETINSTALLED
  I Depend On:
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=MaintenanceWorkLoadInterceptor,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=CustomerDao,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=DrilldownEquipmentActivityAction,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=GeoLocDao,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=PackageTaskForInfoTabDao,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=System.jar,name=AutomatedTestLogDao,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=ModstateHistoryDao,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=System.jar,name=TaskSchedulerCommandHandler,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=CommonSupportValidationController,service=EJB3
    jboss.j2ee:ear=Ear.ear,jar=Business.jar,name=AssetEventValidationController,service=EJB3
...hundreds more listed. In any case I believe this is due to a circular dependency. The problem is since we have literally hundreds of EJBs, manually searching through them to try to find where the circular dependency is - is extremely time consuming.
I was thinking about writing a tool to check / find circular dependencies, but not wanting to re-invent the wheel I tried to search google for such a tool but had no luck. I can't believe that there isn't already a tool out there.
What is the best way to find these problems and fix them when you have as many EJBs as we do without manually going through each one?

redpajama_set_name: RedPajamaStackExchange


Saad is an Economics graduate, with a keen interest in real estate as well as the financial markets. Following graduation, and after traveling around Thailand he began his career at one of London's corporate estate agencies, where he gained a wealth of experience.
Having spent a number of years building client relationships for the agency he then embarked on a new challenge and joined Martyn Gerrard to head up their Client Services department in 2017.
Outside of the office, Saad likes traveling, trying new cuisines and supporting his favorite football team – Manchester United!


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Home»Soccer»MLS»Sounders win West finals, are MLS Cup-bound
Sounders win West finals, are MLS Cup-bound
By Andrew Harvey November 27, 2016 3 Comments6 Mins Read
The Seattle Sounders celebrated in front of traveling fans after winning the MLS Western Conference finals in Commerce City, COL. / Seattle Sounders FC
After seven seasons and as many playoff opportunities, the Sounders are bound for the MLS Cup. Seattle dealt the Colorado Rapids their first home loss of the season in the second leg of the Western Conference Finals, 1-0 Sunday and 3-1 on aggregate, a remarkable feat in a season defined by improbable tranformation.
When the clock ran out, the Sounders celebrated with fans who traveled, raising the Western Conference trophy for the first time in club history. Now, they will play for the MLS Cup and complete the turnaround of their worst half-season in club history.
Brian Schmetzer, never one to look beyond the moment at hand, allowed himself a try at context.
"The significance of this, is that it's now," the first-year head coach and longtime Seattleite said. "We're creating these moments now. The moment that we've created for the 200-plus fans that drove or flew on a holiday weekend to Colorado, for the 40,000 we have every weekend in Seattle, it's significant.
"It's significant to the fans that were watching us back in Memorial Stadium in the 1970s. It is significant. It's another chapter, but we're not finished yet. We have to make sure that all of this culminates with something really big, that people will talk about for many years."
The big moment for Seattle is Dec. 10 against the winner of the Montreal-Toronto Eastern Conference final at 4 p.m. PT Wednesday. If Montreal, which holds a 3-2 aggregate lead after the first leg, wins, Seattle will have the chance to win the MLS Cup in front of a home crowd in the Emerald City because of the Sounders' 1-0 win in Seattle April 2. A Toronto triumph means a trip to Canada.
Reaching the final after the Sounders sank as low as they did at midseason induces head-scratching incredulity.
In a 3-0 loss to Sporting Kansas City July 24, they recorded a lone shot, not even on goal. The team tumbled to 6-12-2.
The loss was the last straw for Sigi Schmid, the only coach the club had known in the MLS era, and the league's all-time winningest coach, who was fired.
In stepped Schmetzer in an interim role, seeking to salvage the team's dignity. Bolstered by the addition of Uruguayan midfielder Nicolas Lodeiro and the healthy return of Panamanian center back Roman Torres, Schmetzer did much more than that, helping the club weave its way to the playoffs.
The team finished 8-2-4, making the most of Lodeiro's four goals and eight assists to earn a spot in the knockout round of the postseason.
After knocking out the Kansas City team that had embarrassed them in July, the Sounders used a 3-0 advantage from the first leg to advance past top-seeded FC Dallas in the semifinal for a shot at the No. 2 seed, Colorado. The Rapids were 11-0-6 at home during the regular season and conceded the fewest goals in the league.
Seattle had a 2-1 lead from the first leg, meaning that all they had to do was draw with the Rapids in the thinner air and the cold of Dick's Sporting Goods Park. The Rapids tested the Sounders in the first half, controlling 60 percent of the possession and smashing 11 shots toward keeper Stefan Frei, though none was on target.
The goal came just when Seattle's defense started to flag against Colorado's onslaught. In the 56th minute after a midfield Colorado turnover, striker Nelson Valdez trapped a ball with his chest and spun toward the net with a defender in pursuit. He poked the ball toward Jordan Morris, who found space in Colorado's back line.
Morris had had a bad week. In the days before the match, the forward had a stomach flu bug, and was still rehabbing a hamstring strained during the conference semifinals.
But he ignored the health problems and pursued the ball as keeper Zac MacMath came out to challenge him. Morris chipped with his right foot just before colliding with MacMath, and the ball bounced into the net as Morris grabbed his right knee in pain.
Stepping away from the jubilation in the locker room. Morris reflected on the changes since July.
"It's definitely a rollercoaster," he said. "It's funny, looking back. This team always believed that we were good enough to make it. We want to do it for us, do it for fans, and we did it."
Morris was not the only Sounder to spend time down in the second half. Several players spent extended time on the ground after the club had taken the lead, milking the clock as the home team grew increasingly desperate to score.
Whether some the Sounders' pain was genuine or theatrics, Osvaldo Alonso was lost for the final 16 minutes when the Cuban defensive midfielder came out after a left knee sprain.
The Rapids were thwarted in front of goal by a hard-nosed defensive performance featuring stellar minutes from Torres, who had recently returned from injury. Torres figured in a number of blocked shots, dispossessions and deflected crosses.
Frei was pleased.
"It wasn't our prettiest game, for our part.," the goalkeeper said. "They had a lot of possession, but they didn't have too many shots on frame. (It was important) for us to come here, and play defensive football.
"We find ourselves in the final. Very important to bend but not break."
The Sounders also benefited from a non-call in the 66th minute. Center back Chad Marshall slid to the ground to block a shot, but the ball struck his outstretched arm behind his body after hitting his legs. Rapids players screamed for a penalty, but referee Ricardo Salazar waved for play to continue.
Seattle's defense kept the Rapids from recording any shots on target over 90 minutes. As the game dragged on, Seattle packed greater numbers behind the ball, daring Colorado to break down its defense as it clung to a two-goal aggregate lead.
As time ran out, the Sounders reached the threshold of the feat done a year earlier by rival Portland — becoming the best team in North America.
Kirkland on November 28, 2016 8:26 pm
Many times I've seen a team just strife the opposing net but come away empty-handed, and then watch the opponents get just one half-chance and bury it. That's why I like to see teams develop accurate strikers, who don't need a ton of shots to get their goals. Morris is becoming that, and Colorado doesn't have one in the meantime.
What an escape. If Vegas took MLS bets, I think a $5 wager in July on the Sounders winning MLS Cup could chop the average person's mortgage down to size.
Justinejwalters on November 29, 2016 1:26 am
Google is paying 97$ per hour! Work for few hours and have longer with friends & family! !mj92d:
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Shellydinman on November 30, 2016 2:46 am
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redpajama_set_name: RedPajamaCommonCrawl


text:
New computer modelling tool could boost drug discovery and improve treatment
Scientists from Queen's University Belfast have developed a computer-aided data tool that could improve treatment for a range of illnesses. The computer modelling tool will predict novel sites of binding for potential drugs that are more selective, leading to more effective drug targeting, increasing therapeutic efficacy and reducing side-effects.
The data tool or protocol will uncover a novel class of compounds — allosteric drugs in G protein-coupled receptors (GPCRs). GPCRs are the largest membrane protein family that transduce a signal inside cells from hormones, neurotransmitters, and other endogenous molecules. As a result of their broad influence on human physiology, GPCRs are drug targets in many therapeutic areas, such as inflammation, infertility, metabolic and neurological disorders, viral infections and cancer. Currently, over a third of drugs act via GPCRs.
Despite the substantial therapeutic success, the discovery of GPCR drugs is challenging due to promiscuous binding and subsequent side-effects. Recent studies point to the existence of other binding sites, called allosteric sites, that drugs can bind to and provide several therapeutic benefits. However, the discovery of allosteric sites and drugs has been mostly serendipitous. Recent x-ray crystallography that determines the atomic and molecular structure, and cryo-electron microscopy that offers 3D models of several GPCRs, offer opportunities to develop computer-aided methodologies to search for allosteric sites.
The researchers developed a computer-aided protocol to map allosteric sites in GPCRs with a view to start rational search of allosteric drugs, presenting the opportunity for new solutions and therapies for a range of diseases. Dr Irina Tikhonova from the School of Pharmacy at Queen's University and senior author explained: "We have developed a novel, cost-effective and rapid pipeline for the discovery of GPCRs allosteric sites, which overcomes the limitations of current computational protocols, such as membrane distortion and non-specific binding.
"Our pipeline can identify allosteric sites in a short time, which makes it suitable for industry settings. As such, our pipeline is a feasible solution to initiate structure-based search of allosteric drugs for any membrane bound drug targets that have an impact on cancer, inflammation, and CNS diseases."
Progress on cancer survival at risk due to Covid disruption — Irish Cancer Society
Common antidepressant should no longer be used to treat people with dementia, study says


In the Philippines, many considered motorcycle as a dangerous vehicle. However, Angkas is set to change this mentality as it announced its plan to launch the country's first motorcycle ambulance service – which will be named as Angkas Buhay.
Angkas Buhay eyes to provide first aid on-the-spot for emergency cases, allowing doctors to immediately respond to their patients. With this, Angkas invites its driver-partners to train as volunteer paramedics.
Teaming up with Our Lady of Guadalupe Colleges (OLGC) and Victor R. Potenciano Medical Center (VRP) in Mandaluyong City, Angkas Buhay will have its pilot program providing intensive training course for Emergency Medical Technicians (EMT-certified) drivers.
Angkas Buhay, which is also dubbed as ambucycle, will be equipped with medical supplies and equipment to stabilize patients until secondary medical transport arrives. It will be an in-app "Emergency" feature to match the EMT driver nearer to the patient, too.
Angkas Buhay is expected to be available in mid-2019.


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\section{Introduction}
Neurons in the brain interact with each other in a heterogeneous and
asymmetric way~\cite{Nature-11}, producing complex neuronal dynamics
for information processing. In the past decades, there are a surge
of research interests in randomly connected neural
networks~\cite{Rajan-2010,Sompolinsky-1988,Vreeswijk-1996,Taro-2011,Ostojic-2014,Aljadeff-2014}.
Although their behavior is described by simple deterministic
equations, the resulting dynamics are rich, exhibiting fixed-point
behavior, limit cycles, or high-dimensional chaos. These networks
are capable of generating useful dynamic activity patterns after
appropriate learning~\cite{Sussillo-2009,Laje-2013}.

Simple models of neural
networks~\cite{Parisi-1986,Derrida-1987,Young-1988,Rieger-1989,Berg-1992,Crisanti-1993,Bastolla-1997,Amari-2013,Huang-2014}
have been explored to elucidate characteristics of their complex
dynamics. In these networks, connections between binary neurons are
independently drawn from an identical distribution, and the state of
a network is updated simultaneously in discrete time steps without
thermal noise. Thus, every initial configuration must evolve into an
attractor, which is either a fixed point or a limit cycle.  Because
a fixed point is a limit cycle of length $l=1$, the whole state
space is divided into separated basins of attractions with
heterogenous cycle lengths. Extensive numerical simulations were
carried out to analyze the typical cycle length and the number of
cycles~\cite{Young-1988,Nutzel-1991}. The typical length of the
cycles was observed to grow exponentially with the number of neurons
$n$ (such kinds of cycles are called chaotic attractors), and the
total number of attractors increases linearly with $n$. These
quantities were also analytically evaluated based on an empirical
assumption that the dynamics loses memory of its non-immediate
past~\cite{Bastolla-1997}.

In this work, we develop a dynamic mean-field theory to characterize
the attractors of the asymmetric neural network by extending the
state concentration concept~\cite{Amari-2013}, recently introduced
to characterize the robustness and quickness of network's transient
dynamics. Our analysis estimates the (cumulative) distribution for
the cycle length of attractors, the total number of attractors, and
the volume of attractors in the state space.

 We remark that our work has
three-fold contributions for understanding the statistical
properties of the dynamics of randomly connected neural networks.
First, a theoretical support for the Markovian property of state
concentration dynamics (termed the annealed approximation in
Ref.~\cite{Bastolla-1997}) is provided by computing the finite-size
effect of the mean-field theory by explicitly evaluating the
quenched randomness of network connections. Second, we provide a
detailed picture about how state concentration happens in randomly
connected neural networks. In particular, we quantify what is the
characteristic distance that typically leads to state concentration
and evaluate characteristic time scales underlying the state
concentration dynamics. Finally, our theory gives a good consistency
with numerical simulations on the distribution of the cycle length,
the typical cycle length, the number of cycles, and the total number
of states belonging to all attractive cycles. These three
contributions complement the previous
studies~\cite{Young-1988,Nutzel-1991,Berg-1992,Bastolla-1997,Amari-2013}
and provide deep insights towards the dynamics of randomly-connected
neural networks.

The paper is organized as follows. In Sec.~\ref{Model}, we define
the neural network model and its dynamics. Mean-field analysis is
presented in detail in Sec.~\ref{Theory}. Results on the state
concentration and statistical properties of attractors are discussed
in Sec.~\ref{Stcon} and Sec.~\ref{Att}, respectively. We summarize
our results in Sec.~\ref{Conc}.

\section{Model definition}
\label{Model}
 We consider randomly connected neural networks consisting of $n$
 neurons (units). Each unit interacts with all the other units with an
 asymmetric coupling. We use $J_{ij}$ to represent the coupling
 strength from unit $j$ to $i$, and $J_{ij}$ is independent
 of $J_{ji}$ (and others), and they follow the same Gaussian
 distribution with zero mean and variance $1/n$. The state of neuron
 $i\, (i=1,\dots,n)$ at time $t+1\, (t=0,1,\dots)$
 is set according to the parallel deterministic dynamics in
 discrete time steps by its input $h_i(t)$ as
 \begin{equation}\label{phi0}
\sigma_i(t+1)=\mbox{sgn} (h_i(t))=\begin{cases} +1, &\text{(active state)}\\
-1, &\text{(silent state)}
\end{cases}
\end{equation}
where the input is defined by
 \begin{equation}\label{paradyn}
h_i(t) = \sum_{j=1}^n J_{ij}\sigma_j(t).
\end{equation}
Therefore, by combining Eqs. (\ref{phi0}) and (\ref{paradyn}), the dynamics are summarized by
$\sigma_i(t+1)=\mbox{sgn}{\left(\sum_{j}J_{ij}\sigma_{j}(t)\right)}$ in
terms of the activity,  or equivalently by
$h_i(t+1)=\sum_{j}J_{ij}\mbox{sgn}(h_{j}(t))$ in terms of the input.

We later compare the dynamics of randomly connected neural networks
to that of random Boolean networks
\cite{Kauffman-1969a,Kauffman-1969b}, where each one of $2^n$ states
$\bm \sigma(t)=\{\sigma_i(t)|i=1,\dots,n\}$ is randomly mapped to another.

\section{Mean-field analysis}
\label{Theory} We study the dynamical evolution of the overlap
between two states along a trajectory, expecting that its
distribution across different realizations of $\{J_{ij}\}$ contains information about the structure of attractors.
Let us define the overlap of two states,
$\bm \sigma(t)=\{\sigma_i(t)|i=1,\dots,n\}$ and
$\bm \sigma(s)=\{\sigma_i(s)|i=1,\dots,n\}$ along the same trajectory at different times $t>s$, by
\begin{eqnarray}
  \label{eq:q}
  q_{ts}\equiv\frac{1}{n}\sum_{i=1}^n \sigma_i(t)\sigma_i(s).
\end{eqnarray}
This overlap takes $+1$ if two states are the same and $-1$ if one
is the sign-flip of the other. The overlap takes a discrete value for a finite size network,
but can be approximated as a continuous quantity in the large network size limit.
The mean-field theory provides the
dynamics of this overlap parameter and its fluctuation defined over the ensemble of random $\{J_{ij}\}$ (see Appendix~\ref{DynF}). The stochastic dynamics of
the overlap is well approximated for large $n$ by a Markovian
process
\begin{eqnarray}
  \label{eq:markov}
  P_{t+1,s+1}(q)\approx\int  W(q|q')P_{ts}(q') dq',
\end{eqnarray}
where $P_{ts}(q)\equiv \mbox{Prob}(q_{ts}=q)$ is the probability of
$q_{ts}=q$. The transition probability is approximated for large but
finite $n$ by a simple binomial distribution
\begin{eqnarray}
  \label{eq:W}
  W(q|q')&=&\binom{n}{n(1+q)/2}\left[\frac{1+\varphi(q')}{2}\right]^{\frac{n(1+q)}{2}}\left[\frac{1-\varphi(q')}{2}\right]^{\frac{n(1-q)}{2}}\nonumber\\
&\approx&\exp\left[n\left(H(q)+\frac{1+q}{2}\ln\frac{1+\varphi(q')}{2}+\frac{1-q}{2}\ln\frac{1-\varphi(q')}{2}\right)\right],
\end{eqnarray}
where $\varphi(q)\equiv (2/\pi)\arcsin q$ and $H(q)\equiv
-\frac{1+q}{2}\ln\frac{1+q}{2}-\frac{1-q}{2}\ln\frac{1-q}{2}$.  Note
that Eq.~(\ref{eq:W}) summarizes the probability that $n(1+q)/2$ out
of $n$ neurons take the same sign in state $\bm \sigma(t+1)$ and
$\bm \sigma(s+1)$, given that $n(1+q')/2$ out of $n$ neurons take the same
sign in the previous step. The binomial distribution in
Eq.~(\ref{eq:W}) suggests that the state overlap for each neuron is
approximately independent, occurring with probability
$(1+\varphi(q'))/2$ (see Appendix~\ref{DynF} for a support).

A similar expression is obtained for random Boolean networks by
replacing $\varphi(q)$ with $\varphi_{BN}(q)\equiv\delta_{q,1}$, simply
reflecting completely random nature of state transitions.

It is worth noting that, the dynamics of the overlap becomes
deterministic in the limit of large $n$ according to the central limit theorem, which is the so called distance
law~\cite{Derrida-1986c,Derrida-1986d,Derrida-1987b,Amari-1974,Kurten-1988},
$q_{t+1,s+1}=\varphi(q_{ts})$. In this equation, the equality
holds only at $q=0$ and $q=\pm 1$, and otherwise $|\varphi(q)| < |q|$. Hence, in the limit of large $n$, the
overlap monotonically converges to the stable solution of $q=0$,
implying that two distinct states would never converge. On the other
hand, for finite $n$, the overlap fluctuates with amplitude $\sim
1/\sqrt{n}$ about the deterministic solution (see detailed
explanations in Appendix~\ref{DynF}). Thus, the overlap can evolve
from $q<1$ to $q=1$ in time, indicating that system's state
eventually comes back to one of previously visited states in a
finite network.

The Markovian process of Eq.~(\ref{eq:markov}) sequentially provides
$P_{t+l,t}(q)$ for $t=1,2,\dots$ for some positive time difference
$l=t-s$ given an initial distribution at $t=0$. The initial distribution is
denoted by $P_{l,0}(q)\equiv {\rm Prob}(q_{l,0}=q)$. Since the
initial state, $\bm \sigma(0)$, is selected randomly and independently from
$\{J_{ij}\}$, we can set without losing generality the initial state
to be $\sigma_i(0)=1$ for all $i$ (see Appendix~\ref{INIT}). In this
case, the initial overlap of interest is expressed by
\begin{eqnarray}
\label{eq:ql0}
q_{l,0}&=&\frac{1}{n}\sum_{i=1}^n \sigma_i(l) \sigma_i(0)\nonumber \\
&=&\frac{1}{n}\sum_{i=1}^n \mbox{sgn}\left(h_i(l-1)\right).
\end{eqnarray}
If $l$ is small, $P_{l,0}(q)$ reflects the memory of the initial
state $\bm \sigma(0)$ and is hard to evaluate exactly.  However, if $l$ is
large, the mean-field result in Appendix~\ref{DynF} indicates that
$\{h_i(l-1)| i=1,2,\dots,n\}$ follows approximately a zero-centered
independent Gaussian distribution with unit variance in the large
network-size limit. This means that the state overlap of
Eq.~(\ref{eq:ql0}) approaches a distribution centered around zero
with variance $\sim 1/n$. In particular, $P_{l,0}(q)$ tends for
large $l$ to a binomial distribution
$\binom{n}{n(1+q_{l,0})/2}2^{-n}$, where the probability of
$q_{l,0}=\pm 1$ is approximately $2^{-n}$ in the large network-size
limit. We confirm this property later with numerical simulations.

\section{State concentration}
\label{Stcon} In this section, we consider how different states
concentrate in time. The Markovian dynamics of Eq.~(\ref{eq:markov})
are completely characterized by the eigenvalues and eigenvectors of
the transition probability $W$ \cite{Gal-2014}. Let
$f_a(q)$ and $\lambda_a \, (\le 1)$ respectively be the $a$th
eigenvector and eigenvalue of $W$.  We rank eigenvalues in a
descending order, {\it i.e.}, $\lambda_1\ge\lambda_2\ge\dots\ge\lambda_{n+1}$ (the number of possible values for $q$ is $n+1$). The
distribution of the overlap is expressed by a weighted sum of the
eigenvectors as
\begin{eqnarray}
  P_{t+l,t}(q) = \sum_{a=1}^{n+1} (\lambda_a)^t A_a f_a(q),
\end{eqnarray}
where $\{A_a\}$ is a set of initial coefficients that satisfies
$P_{l,0}(q)=\sum_{a}A_a f_a(q)$. Hence, as the time step increases,
$P_{t+l,t}(q)$ becomes progressively dominated by the components with
large eigenvalues.

It is easy to see that $W$ has two trivial eigenvectors
$f_1(q)=\delta_{q,1}$ and $f_2(q)=\delta_{q,-1}$ with degenerate
eigenvalues $\lambda_1=\lambda_2=1$. Note that $\delta_{q,q_0}$ is
the Kronecker delta function. The third eigenvector $f_3(q)$ is a
non-trivial one and its eigenvalue $\lambda_3\approx 1-\exp(-0.41n)$
exponentially approaches 1 with $n$ (see Fig.~\ref{fig:lam} for the
numerical result). The fourth eigenvalue converges to
$\lambda_4\approx0.67$ in the limit of large $n$. The half-decay
time of the $a$-th component is described by these eigenvalues and
given by $t_a\equiv (\ln 2)/(-\ln \lambda_a)$, or equivalently,
$(\lambda_a)^{t_a}=1/2$. There is a clear gap between the decay time
of the third and fourth eigen-components. This result indicates
that, for large $n$, the distribution of the overlap must approach
quickly a quasi-stationary state $P_*(q)\equiv\sum_{a=1}^3 A_a
f_a(q)$ at around $t_4\approx 1.73$ and stay unchanged until
$t_3\approx 0.69\exp(0.41n)$. In particular, the quasi-stationary
state is characterized solely by $f_3(q)$ except at $q=\pm 1$.

\begin{figure}[h!]
\includegraphics[scale=1.0]{figure01.eps}
\caption{ (Color online) The non-trivial eigenvalues $\lambda_3$ and
$\lambda_4$ of the transition matrix $W$.
  }\label{fig:lam}
\end{figure}

 This
analysis also suggests when the mean-field theory breaks down ---
the theory is not applicable once the third eigen-component
significantly decays at around $t_3$. That is, after an exponential
time of $\exp(0.41n)$, the distribution of the overlap becomes the
linear combination of $f_1(q)$ and $f_2(q)$, {\it i.e.}, every state
becomes either the same or the sign-flip of the others. However,
this never happens in a real system.

In the remaining part of this
section, we characterize in more detail the quasi-stationary state in large $n$ limit,
from which we extract the structure of attractors.

 We first introduce an
auxiliary notation
\begin{eqnarray}
  \label{eq:alpha}
  \alpha_{t+l,t}(q)\equiv \frac{1}{n}\ln P_{t+l,t}(q),
\end{eqnarray}
where $\int \exp(n\alpha_{t+l,t}(q))dq=1$ according to the
normalization constraint. With this notation, we can express the
dynamics of Eq.~(\ref{eq:markov}) by
\begin{eqnarray}
\label{eq:dalpha}
  \alpha_{t+l+1,t+1}(q)&=&\frac{1}{n}\ln \int W(q|q')P_{t+l,t}(q')dq'\nonumber\\
&\approx&
H(q)+\max_{q'}\left[\frac{1+q}{2}\ln\frac{1+\varphi(q')}{2}+\frac{1-q}{2}\ln\frac{1-\varphi(q')}{2}+\alpha_{t+l,t}(q')\right],
\end{eqnarray}
where the Laplace's method was applied in the second line assuming
large $n$. Note that, in the above expression, the maximizer $q'$ of
the second term is a function of $q$. In particular, the
well-defined asymptotic solution of Eq.~(\ref{eq:dalpha}), {\it i.e.},
\begin{eqnarray}
\label{eq:alphass}
  \alpha_*(q) =  H(q)+\max_{q'}\left[\frac{1+q}{2}\ln\frac{1+\varphi(q')}{2}+\frac{1-q}{2}\ln\frac{1-\varphi(q')}{2}+\alpha_*(q')\right],
\end{eqnarray}
with finite $\alpha_*(q)$ self-consistently provides the
quasi-stationary state. Note that Eq. (\ref{eq:alphass}) permits
arbitrary discontinuity of $\alpha_*(q)$ at $q=\pm 1$, reflecting
that $q=\pm 1$ is the sink of the Markovian process. However, in the
following analysis, we assume continuous $\alpha_*(q)$.

Next, we define index $\beta_{t+l,t}(q_{ts})\equiv \frac{1}{n}\ln
\mbox{Prob}(q_{t+l,t}|q_{t+l+1,t+1}=1)$ that characterizes the
probability that two states $\bm \sigma(t+l)$ and $\bm \sigma(t)$ have overlap
$q_{t+l,t}$ before converging in the next step ($q_{t+l+1,t+1}=1$).
This index is expressed, using the Bayes theorem, in terms of
$\alpha$ by
\begin{eqnarray}
  \label{eq:beta}
  \beta_{t+l,t}(q')&=&\frac{1}{n}\ln \frac{W(1|q')P_{t+l,t}(q')}{P_{t+l+1,t+1}(1)}\nonumber\\
  &=&\ln\frac{1+\varphi(q')}{2}+\alpha_{t+l,t}(q')-\alpha_{t+l+1,t+1}(1).
\end{eqnarray}
This means that, for large $n$, most of the trajectories that lead
to state concentration had an overlap specified by the peak location
of $\beta_{t+l,t}$, {\it i.e.}, $\arg\max_{q'}\beta_{t+l,t}(q')$, in the
previous step.

\begin{figure}[h!]
\begin{tabular}{ll}
{\bf (a)} & {\bf (b)}\\
\includegraphics[width=8cm]{figure02a.eps}&
\includegraphics[width=8cm]{figure02b.eps}
\end{tabular}
\caption{(Color online) The Markovian dynamics of
  $\alpha_{t+l,t}$ and $\beta_{t+l,t}$ in time.  (a) The index $\alpha_{t+l,t}$
  characterizes the dynamics of distribution $P(q_{t+l,t})$. The line
  color changes from the lowest curve (the orange curve at $t=0$, i.e., $\alpha_{l,0}$ or $\beta_{l,0}$)
  to the yellow, and finally to the gray (the top curve at $t=10$, i.e., $\alpha_{l+10,10}$ or $\beta_{l+10,10}$). (b)
  The index $\beta_{t+l,l}$ characterizes the dynamics of distribution
  $P(q_{t+l,t}|q_{t+l+1,t+1}=1)$. The result indicates that
  states concentrate mainly from $q\approx 0.5$ at the beginning
  but concentrate equally from $q\approx 0.75$ and $q=1$ at the quasi-stationary state.
  We used $\alpha_{l,0}(q)=H(q)-\ln 2$ as the initial condition assuming no correlations at starting points.
  The results hold for any $l\ge1$.
  }\label{fig:alpha_beta}
\end{figure}

In the case of randomly connected neural networks studied here,
$\beta_{t+l,t}(q)$ has two peaks. As shown in Fig.~\ref{fig:alpha_beta} (b), one peak is located at $q=1$ reflecting
the monotonic increase in $\ln \frac{1+\varphi(q)}{2}$ toward $q=1$ and the other peak is
located at $q<1$ reflecting the peak of $\alpha_{t+l,t}(q)$ at $q=0$ in Eq.~(\ref{eq:beta}).
The $q<1$ peak shifts to a larger positive value of $q$ and its amplitude loses the dominance over the $q=1$ peak
as $t$ increases because $\alpha_{t+l,t}(q)$ becomes blunt at large $t$ (Fig.~\ref{fig:alpha_beta} (a)).
The two peaks become comparable at around $t_4$. In finite-size
systems, the two peaks become indistinguishable once the difference
of the peak values becomes less than $1/n$. The result indicates
that states concentrate mainly from $q\approx 0.5$ at the beginning
but concentrate equally from $q\approx 0.75$ and $q=1$ at the
quasi-stationary state.

These dynamics of the state overlap reflects the specific structure of
attractors as we shall show below. In contrast to the above situation, for
trivial dynamical systems that converge to a unique fixed-point ({\it e.g.},
$h_i(t+1)=(1+h_i(t))/2$), $\beta_{t+l,t}(q)$ has a unique peak, which
tends to approach $q=1$ at large $t$, indicating that most
states concentrate from nearby locations. On the other
hand, in random Boolean networks, states concentrate randomly
from any overlap values. Because most states are orthogonal to each
other for large $n$, states mainly concentrate from $q\approx
0$ (see Appendix~\ref{RBN}).

\section{Statistical properties of attractors}
\label{Att} In this section, we analytically describe the
statistical properties of attractors for randomly connected neural
networks using the state concentration
probability~\cite{Amari-2013}. The state concentration probability
$p_{t+1,s+1}$ that characterizes the conditional probability of
$\bm \sigma(t+1)=\bm \sigma(s+1)$
 given that no states up to time $t$ along the trajectory are the same or the sign-flip of the
others. Because of the symmetry, $p_{t+1,s+1}$ also characterizes
the probability of $\bm \sigma(t+1)=-\bm \sigma(s+1)$ given the same condition.
Hence,
\begin{eqnarray}
  p_{t+1,s+1} &\equiv& \mbox{Prob}(q_{t+1,s+1}= \pm 1| \{q_{t',s'}\ne \pm 1 | t'\le t, s'<t'\}).
\end{eqnarray}
This state concentration probability is further approximated under
the Markovian approximation of Eq.(\ref{eq:markov}) by
\begin{eqnarray}
  p_{t+1,s+1} &\approx& \int_{q_{ts}\ne \pm1}  W(q_{t+1,s+1}=1|q_{ts}) P(q_{ts}) dq_{ts} \nonumber\\
&=& \exp(n \alpha_{t+1,s+1}(1)), \label{eq:scp}
\end{eqnarray}
which directly follows from Eq.~(\ref{eq:dalpha}). Note that, based
on the consideration of the previous section, we used in the second
line that the result is not sensitive to the exclusion of $q'=\pm 1$
from the integral for large $n$. This is because the $\max_{q'}$ in
Eq.~(\ref{eq:dalpha}) is insensitive to its argument at $q'=\pm 1$
unless the initial distribution $P_{l,0}(q)$ is sharply peaked at
$q=\pm 1$, which is not the case here ({\it c.f.}
Eq.~(\ref{eq:ql0})).

Hence, based on the Markovian property, the probability that the
dynamics starting from $\bm \sigma(0)$ comes back for the first time to
$\bm \sigma(0)$ after $l$ steps without visiting any sign-flip of
previously visited states is described for large $n$ by
\begin{eqnarray}
  \tilde{P}(l) &\equiv& \mbox{Prob}\left(\{q_{1,0}\ne \pm 1\}, \{q_{2,s}\ne \pm 1|s=0,1\},\cdots, \{q_{l-1,s}\ne \pm 1|s=0,1,\dots,l-2\}, \, q_{l,0}=1\right)\nonumber\\
&=& (1-2 p_{1,0})\prod_{s=0}^1(1-2 p_{2,s})\cdots\prod_{s=0}^{l-2}(1-2p_{l-1,s}) p_{l,0} \nonumber\\
&=& p_{l,0}\exp\left(\sum_{t=1}^{l-1}\sum_{s=0}^{t-1}\ln(1-2
p_{t,s}) \right). \label{eq:cyc_length}
\end{eqnarray}
Note that, in the second line of Eq.~(\ref{eq:cyc_length}), the
factor $\prod_{s=0}^{t-1}(1-2 p_{t,s})$ describes the probability
that the state makes a transition at time $t$ to a state distinct
from $\{\pm \bm \sigma(s)|s=0,1,\dots,t-1\}$. The final factor, $p_{l,0}$,
describes the probability of coming back to the initial state
$\bm \sigma(0)$ after $l$ steps.

\begin{figure}[h!]
\includegraphics[width=8cm]{figure03.eps}
\caption{There are two kinds of limit cycles if the cycle length $l$
  is even. (a) In the first kind of cycles, the cycle closes without
  ever visiting the sign-flip of previously visited states.  (b) In
  the second kind of cycles, the state first makes a transition to the
  sign-flip of the initial state after $l/2$ steps, {\it i.e.},
  $\bm \sigma(l/2)=-\bm \sigma(0)$. If this happens, the cycle must close after $l$ steps.
  }\label{fig:FigAttractor}
\end{figure}

Altogether, the probability that a certain state, $\bm \sigma(0)$, belongs
to a cycle of length $l$ (revisiting $\bm \sigma(0)$ for the first time
after $l$ steps) is described for large $n$ by \cite{Bastolla-1997}
\begin{eqnarray}
  P(l) &=& \left\{\begin{array}{cc}
    \tilde{P}(l), & (\mbox{odd $l$})\\
    \tilde{P}(l) + \tilde{P}(l/2).& (\mbox{even $l$})
    \end{array}\right.
\label{eq:cyc_length02}
\end{eqnarray}
Notably, the probability takes different expressions for odd and
even $l$. If $l$ is odd, Eq.~(\ref{eq:cyc_length}) directly gives
the probability. If $l$ is even, there are two separate kinds of
contributions depicted in Fig.~\ref{fig:FigAttractor}. The first
contribution is from cycles that close without ever visiting the
sign-flip of their history. The second contribution is from cycles
that involve a transition at step $l/2$ to the sign-flip of their
initial state, which then guarantees that the cycle closes in $l$
steps.

The final step is to evaluate the state concentration probability
$p_{t,s}$. The initial state concentration probabilities are simply
given by
\begin{eqnarray}
p_{l,0}\approx 2^{-n}\equiv p_{\rm init}
\label{eq:pinit}
\end{eqnarray}
for large $n$ and $l$ as discussed in Sec.~\ref{Theory}. Although
this approximation is inaccurate for $l<10$, it becomes accurate for
large $n$ over a wide range of $l$ that includes the typical cycle
length (Fig.~\ref{qL0}).

\begin{figure}[h!]
\includegraphics[bb=2 2 533 413, scale=0.45]{figure04.eps}
\caption{(Color online) Simulation results of the initial state
concentration probability $p_{l,0}$
 as a function of $l$ when $n$ varies.
 The results are obtained based on statistics collected
 from $2\times10^9$ networks. The initial state is always set to
 $\sigma_i(0)=1$ for all $i$ (see Appendix~\ref{INIT}).
 The sampling error increases with $n$ because of exponential increase
 of the state space. Note that $p_{1,0}=2^{-n}$ is an exact result.
  }\label{qL0}
\end{figure}

On the other hand, the
state concentration probability $p_{t+l,t}$ at $t\ge 1$ is computed
sequentially by Eqs.~(\ref{eq:dalpha}) and (\ref{eq:scp}). In
particular, this probability quickly converges within several steps
($t_c\approx 5$; see, Fig.~\ref{fig:alpha_beta} (a)) to the
quasi-stationary value of
\begin{eqnarray}
\label{eq:p}
  p_{\infty}&\equiv& \lim_{t\to\infty}p_{t+l,t} = \exp\left(n \alpha(1)\right)
\end{eqnarray}
for any $l\ge 1$, where $\alpha(1)=-0.46$ from Eq.~(\ref{eq:alphass}). That is, the state concentration
probability quickly converges in several steps from the initial value of $p_{\rm init}\approx\exp(-0.69n)$
to the asymptotic value $p_{\infty}\approx \exp(-0.46n)$.

Therefore, $\tilde{P}(l)$ of Eq.~(\ref{eq:cyc_length}) can be
further approximated using $p_{\rm init}$ and $p_{\infty}$ by
\begin{eqnarray}
  \tilde{P}(l) &=&  p_{\rm init}\exp\left[\sum_{t=1}^{l-1}\sum_{s=0}^{t-1}\ln(1-2p_{\infty}) + O\left(2t_c l\frac{p_{\infty}-p_{\rm init}}{1-2p_{\infty}}\right)\right]\nonumber\\
&\approx&  p_{\rm init}\exp\left[\frac{l^2}{2}\ln(1-2p_{\infty}) \right]\nonumber\\
&=&  p_{\rm init}\exp\left(-\frac{l^2}{\tau^2}\right),
\label{eq:cyc_length2}
\end{eqnarray}
where $\tau\equiv \sqrt{-2/\ln(1-2p_\infty)}$ is the characteristic
cycle length that grows exponentially with the system size,
consistent with the numerical observations~\cite{Nutzel-1991}. Note that, in the first line of
Eq.~(\ref{eq:cyc_length2}), we used the relationship that
$|p_{\infty}-p_{ts}|\le |p_{\infty}-p_{\rm init}|$ (for any $t$ and
$s$; see, Fig.~\ref{fig:alpha_beta}) to upper-bound the deviation of
$p_{ts}$ from $p_{\infty}$. To make the contribution of the
 $O\left(2t_c l\frac{p_{\infty}-p_{\rm init}}{1-2p_{\infty}}\right)$ negligible,
 the approximation in the second line assumes
\begin{eqnarray}
4 t_c \frac{p_{\infty}-p_{\rm init}}{-(1-2p_\infty)\ln(1-2p_\infty)}
\ll l \;\; {\rm and} \;\; l\ll
\frac{1-2p_\infty}{2t_c(p_\infty-p_{\rm init})}. \label{eq:cond}
\end{eqnarray}
 The first
condition in Eq.~(\ref{eq:cond}) requires that
$-\frac{l^2}{2}\ln(1-2p_{\infty})\gg2t_c l\frac{p_{\infty}-p_{\rm
init}}{1-2p_{\infty}}$, while the second condition ensures that
$2t_c l\frac{p_{\infty}-p_{\rm init}}{1-2p_{\infty}}\ll1$. The range
of $l$ specified by Eq.~(\ref{eq:cond}) is roughly $10 \ll l\ll
\exp(0.46n)/(2t_c)$
 at $n> 10$.
Hence, the characteristic cycle length $\tau\approx\exp(0.23 n)$ is
well within this range.
Incidentally, $\tau$ is known to also characterize the typical
transient time scale to enter a limit cycle~\cite{Bastolla-1997}.

\begin{figure}[h!]
\begin{tabular}{ll}
{\bf (a)} & {\bf (b)}\\
 \includegraphics[bb=58 24 743 541,width=8cm]{figure05a.eps}&
\includegraphics[bb=65 26 735 541,width=8cm]{figure05b.eps}
\end{tabular}
\caption{(Color online) (a) Probability distribution of cycle
lengths. (b) Cumulative distribution of cycle lengths. The numerical
data is obtained from $1000$ samples for $n=10$, $500$ samples for
$n=15$, and $200$ samples for $n=17$. The inset shows an enlarged
view at small cycle length.
  }\label{fig:cum}
\end{figure}

\begin{figure}[h!]
\begin{tabular}{ll}
{\bf (a)} & {\bf (b)}\\
 \includegraphics[bb=78 24 735
543,width=8cm]{figure06a.eps}&
\includegraphics[bb=49 23 737 542,width=8cm]{figure06b.eps}
\end{tabular} \caption{(Color online) The first (mean) and second moment of
the cycle length distribution. Theoretical predictions and numerical
simulations are compared. The results are averaged over many random
realizations of the networks (from $1000$ samples for $n=10$ to
$100$ samples for $n=18$).}\label{fig:cycle}
\end{figure}

The probability of observing a cycle of length $l$ is given by
$P(l)/(l Z)$ with a normalization constant $Z \equiv
\sum_{l=1}^{2^n} P(l)/l$. In this expression, the probability,
$P(l)$, of a state belonging to a cycle of length $l$ should be
divided by $l$ to provide the cycle length probability since all
states within a cycle share the same cycle length.  Note that the
normalization constant $Z$ represents the probability of a state
belonging to a cycle (attractor). Figure~\ref{fig:cum} (a) shows the
comparison of numerically obtained cycle length probability with its
theoretical estimate.  Numerical details to collect the statistics
of the attractors are given in the Appendix~\ref{NumS}.  The theory
nicely captures this probability at around the characteristic cycle
length, including the difference in probability for odd and even
cycle lengths, as $n$ becomes large. However, the deviation is large
for non-typical $l$ in finite networks. The cumulative distribution
of cycle length is similarly obtained by $F(l)\equiv
(1/Z)\sum_{l'=1}^l P(l')/l'\approx
\left(\int_{1}^{l}\tilde{P}(l')/l' {\rm d}l' +
\int_1^{l/2}\tilde{P}(l')/(2l') {\rm d}l'\right)/Z$ . The comparison
of $F(l)$ with the numerical results is shown in Fig.~\ref{fig:cum}
(b). The discrepancy tends to become small for larger $n$ (see the
inset of Fig.~\ref{fig:cum} (b)).

The first moment (mean value) and the second moment of the
distribution can be computed analytically as well. Their values are
given by:
\begin{eqnarray}\label{moments}
  \left<l\right> &=& \frac{4\sqrt{\pi}\tau\left[1-{\rm erf}(1/\tau)\right]}{3\int^{\infty}_{1/\tau^{2}}\frac{e^{-t}}{t}{\rm d}t}, \\
   \left<l^{2}\right> &=& \frac{2\tau^{2}e^{-1/\tau^{2}}}{\int^{\infty}_{1/\tau^{2}}\frac{e^{-t}}{t}{\rm
   d}t},
\end{eqnarray}
where ${\rm erf}(x)=\frac{2}{\sqrt{\pi}}\int_{0}^{x}e^{-t^{2}}{\rm
d}t$ and $\int^{\infty}_{1/\tau^{2}}\frac{e^{-t}}{t}{\rm
   d}t\simeq-\gamma_{{\rm E}}-\alpha(1)n$ in the large $n$ limit, where
   $\gamma_{\rm E}=0.5772$ is the Euler constant. The theoretical predictions are
   compared with the numerical results in Fig.~\ref{fig:cycle}. The
   exponential growth of the typical cycle length is verified, which
   suggests that chaotic attractors exist in the state space of a
   randomly connected neural network.

\begin{figure}[h!]
\begin{tabular}{ll}
{\bf (a)} & {\bf (b)}\\
\includegraphics[bb=90 35 738
537,width=8cm]{figure07a.eps}&
 \includegraphics[bb=67 20 740 545,width=8cm]{figure07b.eps}
 \end{tabular} \caption{(Color online) (a)
Linear dependence of the number of cycles on network size $n$. (b)
Entropy density of the attractive states defined by
$s=\frac{1}{n}\ln N_{{\rm att}}$. As $n$ increases, the numerical
data gets to the theoretical prediction.
  }\label{fig:entropy}
\end{figure}

Following the same spirit, one can derive the number of attractors
as $2^n Z \simeq-3\alpha(1) n/4-3\gamma_{\rm E}/4$, from which a
linear dependence~\cite{Young-1988,Berg-1992,Bastolla-1997} is
confirmed (see also Fig.~\ref{fig:entropy} (a), the linear fit gives
the slope $0.360\pm0.010$, compatible with the theoretical value
$0.342$). Another interesting quantity is the number of the
attractive states $N_{{\rm att}}$ belonging to all cycles (e.g., a
cycle of length $l$ has $l$ attractive states), which is expected to
grow exponentially with the network size $n$. This quantity is
evaluated by our theory as $N_{{\rm
att}}=2^{n}\sum_{l=1}^{2^n}P(l)$, and can be quantified as the
growth rate (entropy density)
$s=\lim_{n\rightarrow\infty}\frac{1}{n}\ln N_{{\rm att}}$.  In the
large $n$ limit, we obtain $s=-\alpha(1)/2$, which is compared with
the numerical results at finite $n$. As shown in
Fig.~\ref{fig:entropy} (b), as $n$ increases, $s$ decreases,
approaching the asymptotic limit $0.2277$.

The deviation at small $n$ (or at $l$ far from the characteristic
length, see Fig.~\ref{fig:cum}) comes from three approximations. One
is Eq.~(\ref{eq:pinit}), which becomes invalid at small $l$ where
$p_{\rm init}$ also depends on $l$, but Eq.~(\ref{eq:pinit}) becomes
reasonable for large $l$ (as occurs in our case where the typical
cycles are long). The second one is Eq.~(\ref{eq:cyc_length2}). This
approximation is valid in the range of $l$ specified by
Eq.~(\ref{eq:cond}). Note that this condition is consistent with the
numerical results shown in Fig.~\ref{fig:cum}. The last approximation is
Eq.~(\ref{eq:markov}), which breaks down for small $n$ at which two
or more time-steps memory should be considered. In the large network
size limit, these approximations become exact and the dynamics can
be described by a Markovian process in terms of the state overlap.
Thus, as we focus on the structure of attractors at a relatively
large but finite $n$, these effects are not significant.

\section{Conclusion}
\label{Conc} In this work, we studied the deterministic dynamics of
a randomly connected neural network and proposed a simple Markovian
stochastic process to describe the evolution of the overlap of two
states along the dynamics trajectories. The properties of the state
concentration can be studied by a mean field computation, and
furthermore, the theoretical cumulative distribution of cycle length
is compared with the numerical simulation results. The typical
length of cycles is predicted and observed to grow exponentially
with the network size. The number of attractive states on all cycles
has also an exponential growth with the network size, and its
typical value can also be predicted by our theory.

Our theory should have potential to be
generalized to treat more complex situations, e.g., couplings
between neurons are correlated, where one time-step memory is not
enough to describe the dynamics and strong memory effects induced by
retarded self-interaction could be incorporated by introducing a
back-action field (two time-steps memory)~\cite{Huang-2014}. The
current analysis is also restricted to the parallel type of dynamics,
whereas, the sequential
(asynchronous) dynamics seems to be more natural, and our current method may apply to this type of dynamics, although the
computation will become more complicated. However, the
statistical properties of attractors would not change
qualitatively, as expected from numerical simulations~\cite{Young-1988}.

Our work is expected to provide insights towards understanding how
the neural network processes information and stores temporal
sequences~\cite{Abbott-2005}, which will be left for future study.

\section*{Acknowledgments}

We are grateful to Ugo Bastolla, Naoki Masuda, Hiroyasu Ando, and
Shun-ichi Amari for useful discussions. This work was supported by
RIKEN Brain Science Institute and the Brain Mapping by Integrated Neurotechnologies for Disease
Studies (Brain/MINDS) by the Ministry of Education, Culture, Sports,
Science and Technology of Japan (MEXT).

redpajama_set_name: RedPajamaArXiv


text:
Michael Russell (* 10. Dezember 1920 in Loughmore, County Tipperary, Irland; † 12. Januar 2009 in Waterford, County Waterford, Irland) war römisch-katholischer Bischof des Bistums Waterford und Lismore.

Leben
Michael Russell erhielt seine Priesterausbildung in Maynooth und empfing am 17. Juni 1945 die Priesterweihe. 1948 wurde er in Kanonischem Recht promoviert und war Professor für Moraltheologie am St. Patrick's College in Thurles. Bis 1965 war er zudem Vizepräsident des St Patrick's College.

1965 ernannte ihn Papst Paul VI. zum Bischof von Waterford und Lismore. Die Bischofsweihe spendete ihm am 19. Dezember 1965 der Erzbischof von Armagh, William Kardinal Conway; Mitkonsekratoren waren Erzbischof Giuseppe Maria Sensi, Apostolischer Nuntius in Irland und späterer Kurienkardinal, und Thomas Morris, Erzbischof Cashel und Emly. Am 27. Mai 1993 wurde seinem altersbedingten Rücktrittsgesuch stattgegeben.

Weblinks
 Eintrag über Michael Russell auf catholic-hierarchy.org (englisch)
 Nachruf (englisch)

Moraltheologe
Römisch-katholischer Bischof (20. Jahrhundert)
Römisch-katholischer Bischof (21. Jahrhundert)
Römisch-katholischer Theologe (20. Jahrhundert)
Römisch-katholischer Theologe (21. Jahrhundert)
Ire
Geboren 1920
Gestorben 2009
Mann
Thurles
Hochschullehrer (Irland)

redpajama_set_name: RedPajamaWikipedia


text:
Dons hold on to Hodson
Right-back Lee Hodson has committed his future to the Dons.
The 23-year-old's contract was set to expire at the end of June but he will now remain at stadiummk until at least 2017 after putting pen-to-paper on a new two-year deal.
Speaking to mkdons.com, Hodson said: "There were a number of reasons why I wanted to stay – there's a good bunch of lads here, the manager is great and the fans have always been good to me.
"It's a chance to play Championship football again. I'm sure every player at the club wanted to take that next step up to this level and I'm no different - I'm really looking forward to next season.
He continued: "Last year wasn't great because of the injuries but now, with this new deal, I can work to get back as fit as possible and give it a right go."
Since joining from Watford in summer 2013, the Northern Ireland international has made 43 appearances while also contributing to 17 clean-sheets and scoring two goals, including a stunning strike against Colchester United last November.
Hodson also has experience of playing in the Sky Bet Championship, having featured 83 times in the second tier for his former club, the Hornets, between 2008 and 2012.
Dons boss Robinson said: "Lee had a difficult time last season with injuries but he proved when he was available what a quality player he is. He played over 80 games in the Championship during his time with Watford so he knows what it takes to compete at that level."


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"The writer who knows the craft of writing can't walk into a room and work with students unless there is some understanding of the craft of teaching. neither can teachers who have not wrestled with writing, effectively teach the writer's craft.
Join us on this amazing journey, through the New Hampshire Literacy Institutes and the Learning Through Teaching Program. You'll be part of a vibrant community of readers, writers and teachers thoughtfully considering and practicing their crafts. Come for the chance to work with our wonderful faculty, the camaraderie, the support, the laughter and the sense of UNH literacy history (see photos above of teacher and writer Don Murray with current Institutes instructor Tom Romano, and of Institutes instructor and founder Tom Newkirk).
Click on the brochure for course descriptions and program details.
If you are new to UNH, please send a completed course permission form. Returning students can request permission via email and then register through Webcat.
Campus housing/dining options are available through UNH Conferences and Catering.
Parking information is explained in the brochure.
Click on a workshop button below for the title you want to register. Credit card payments will guarantee your spot; check payments will not.
New participants will be prompted at checkout to create a Learn for Life account (this is not the same as Webcat). It is important to save your new username and password so that you may register for future events and view a historical record of your participation from this year forward.
Campus housing/dining options are available through UNH Conferences and Catering (see above).
Commentary by Thomas Newkirk, emeritus professor of English at the University of New Hampshire and founder of the New Hampshire Literacy Institutes. These pieces originally appeared in Education Week.
Like us on Facebook. Follow @UNHLit on Twitter & Instagram. Join the #UNHLit conversation!


Have you been called a worrier? Is your mind always racing? You may have anxiety or an anxiety disorder. Learn what you can do to cope and some practical strategies to help keep you feeling calmer. Find out about treatment options including therapy and medications.
Wednesday May 29th at 9-1030am Eating the Vegetarian Way Come join our Registered Dietitian for an in depth look into a vegetarian pattern of eating with emphasis on key nutrients, label reading, reliable resources and meal ideas. If you are a vegetarian, are considering adopting some vegetarian options or just curious, this tour is for you! Meet at the customer service desk.
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text:
Boxing NZ not confident over Olympic prospects
Boxing New Zealand President Keith Walker concedes it's going to be tough for our boxers to qualify for next year's Olympics.
Photo: Boxing NZ
The IOC has taken over the running of the boxing programme in Tokyo because of the shambles the International Boxing Federation is in and they've decided that Oceania will join Asia for one of the Olympic qualifying tournaments.
The AIBA won't be involved in the Tokyo event as the IOC wasn't happy with their governance and finance.
New Zealand last qualified a boxer for an Olympics in 2012.
Walker says because of a lack of recent international competitions he's not sure about the quality of Asian boxers.
It is likely that the top four from each division will qualify for the Olympics.
He says New Zealand's top prospect, the men's heavyweight David Nyika is going to find it tough finishing in the top four of his division.
"In Asia we have the strong nations like Uzbekistan, Kazakhstan, South Korea and China, so that will be very difficult, but in saying that David has actually coped in some of those competitions in the past."
"But each year there seems to be a new crop coming through, so we don't really have a good line because there hasn't been those top competitions, we don't really now what is about so we just have to wait and see who appears."
New Zealand has four women in their elite squad and Walker believes they may have a better chance of qualifying for Tokyo.
"Our women are coping very well with the competitions and that is probably not as strong or have the same depth in the women what there is in the men.
"Historically the women don't have the numbers in some of the top nations and we're hopeful it will be a lot easier pathway for them."
The four Olympic qualifying tournaments will be held between January and May next year.
No hint of Black Caps changes
Collection of emergency supplies for Tonga underway in Auckland


San Francisco, October 11, 2018—McKesson Corporation, a leading distributor of medications and medical surgical supplies, is prepared to meet the needs of customers, employees and communities impacted by Hurricane Michael and its aftermath.
McKesson is experienced in disaster preparedness and recovery efforts. McKesson has significant operations in the southeastern United States and has taken proactive steps to prepare for Hurricane Michael and its aftermath, despite the rapidity with which this storm developed. The company is uniquely qualified to meet the needs of healthcare organizations and communities during natural disasters because of its relationships with hospitals, clinics, pharmacies, nursing homes, doctors and more.
Here are some of the ways McKesson is supporting customers, patients, and first responders who depend on access to medications and supplies, as well as our own employees, throughout Hurricane Michael and during the recovery.
McKesson has warehouse and distribution operations in the areas of impact, including Florida, Atlanta, GA and more. To ensure service isn't disrupted, McKesson has safeguarded all locations by providing satellite phones and back-up generators that will sustain full operations throughout the storm. Employees from other U.S. facilities are always on standby to travel and support relief efforts as needed.
In addition, the company has coordinated with specialty couriers to plan for the eventuality of emergency shipments. Based on McKesson's experience in disaster preparedness, the company has increased on-hand inventory of medications, potable water, antibiotics, vaccines, insulin, dialysis equipment, and other supplies that are frequently needed following a storm at nearby warehouses and neighboring distribution centers.
Before Hurricane Michael made landfall, McKesson representatives were busy doing outreach to pharmacy, clinic and hospital customers in impacted areas to emphasize the importance of being prepared by, for example, ensuring they have sufficient inventory and critical medications on hand in case of road closures or unpredictable delivery schedules.
McKesson has activated the Get You to Safety grants, a part of the McKesson Taking Care of Our Own Fund. This grant is provided to McKesson employees who need to evacuate their residences during government-declared disasters. The grant assists employees with any evacuation-related costs such as food, water, shelter, clothing, transportation or medical assistance.
RelayHealth Pharmacy Solutions, a unit of McKesson, is participating in Healthcare Ready's Rx Open. This network helps patients find nearby pharmacies that are open for business in areas impacted by disaster. For the patient looking to fill an essential prescription in or nearby affected areas, this tool could be critical. RxOpen works by combining multiple sources of information from across the industry– including RelayHealth –and using Google Maps to display open pharmacies in the impacted area.


Draymond Green will not be suspended from Game 4 of the Western Conference Finals following his kick to the groin of the Thunder's Steven Adams, but according to the NBA's former dead of discipline that was the wrong decision.
Stu Jackson is the NBA's former executive vice president for basketball operations and under former commissioner David Stern, was responsible for reviewing on-court conduct and handing down discipline. He was a guest on ESPN Radio's "Mike & Mike" and says the new NBA regime got the Green ruling wrong and wonders if they are using a different set of rules for star players.
"I'm looking at the [NBA's press release] yesterday and it had all the feeling that the NBA backed into a desired outcome here, rather than arriving at a decision based upon the flagrant foul rule and the history of penalties with respect to flagrant fouls," Jackson said. "My release would have said that it would have been upgraded to a flagrant-foul, penalty 2, and he would have received a 1-game suspension."
According to Jackson, there are six criteria that are looked at when reviewing a foul of this nature and that Green's kick to the groin meets four of them, presumably the first four. It is also important to note that intent is not one of the criteria.
Was it reckless or was the player making a basketball play?
Was there windup and follow through with the action after contact was made?
Was there potential for injury?
Did the contact result in actual injury?
Did the incident lead to further conflict (i.e. a fight)?
"To me, with this particular act, you don't need intent to evaluate it," Jackson explained. "If you go through the criteria, it clearly meets four of the six criteria."
When Jackson was asked if the status of the player (Green is a star) and the game (conference finals) would play a factor in the decision, he said that was not the case when he was the dean of discipline because player safety came first. However, he is not convinced the same is true under new commissioner Adam Silver and his new executive vice president of basketball operations Kiki Vandeweghe.
"Given the ruling yesterday, it leads one to believe that there's this notion of a double-standard," said Jackson. "If you look at contact hits throughout this playoffs ... it leads you to believe that you're getting different treatment for different players in these playoff games. That stuff concerns me."
The NBA has long been accused of playing favorites with star players. But according to Jackson, that was not the case under his watch when player safety was involved and there were plenty of times when key players were suspended from important games for actions far less severe than what Green did. By not suspending Green, it appears that times are changing.


The real estate arm of Hong Kong-based investment manager PAG has reached the final closing of its latest opportunistic Asian real estate fund with $1.9 billion in investor commitments, topping its initial target of $1.5 billion.
The Secured Capital Real Estate Partners VI (SCREP VI) fund, which began formal fundraising in the third quarter of 2016, drew on strong interest from global institutional investors to hit its $1.9 billion hard cap, according to an announcement by PAG Real Estate.
The fund will focus on distressed debt and property investments in Japan, along with other opportunistic real estate assets in markets including China and South Korea.
The vehicle, which held its first close last December with $1.2 billion in capital commitments, has already closed eight deals totalling more than $400 million, including outstanding transactions in Japan, mainland China and Hong Kong.
SCREP VI is the seventh opportunistic fund launched by PAG Real Estate, which currently manages $5 billion in property assets across the region. The latest vehicle is about 65 percent focused on Japan, according to PAG's corporate website. The investment manager set up SCREP VI to build on the success of its SCREP V opportunity fund, which earlier this year was reported to be projecting internal rates of return of more than 50 percent.
For its most recent fund, PAG said it has raised money from strategic partners including major institutional investors based in North America, Europe and Asia. The backers include Canada Pension Plan Investment Board (CCPIB), which this past February revealed that Canada's largest pension fund had committed $375 million to take an approximate 25 percent stake in the PAG vehicle.
PAG, formerly known as Pacific Alliance Group, has invested over $25 billion into more than 6,700 properties across Asia, including value-add, core-plus and opportunistic deals. In July 2015, the alternative asset manager bought a $1 billion portfolio of office properties in Japan from GE through its PAG Real Estate Partners (PREP) core-plus fund.
PREP closed in June 2016 with $1.3 billion in capital commitments, after initially targetting a $1 billion close.


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Q: Select statement using 2 tables returns 4million reocrds instead of 500k I created a small mapping table to associate values with values from another table. When I perform the select I get back 4million reocrds~.
I know it has to be something trivial I'm doing. Would appreciate if someone could A) Tell me what I'm doing wrong and B) Tell me what literature I should be reading so I understand these issues :) (Websites, books etc.)
select u.uid,
       l.catid
  from usersmap u,
       locmapping l
 where u.prodid = l.prodid

Sorry as for the extra data I'm getting back I'm assuming its duplicated in some form. What the query is attempting to do is get a user id and product id. I'm trying to replace product id with a category id which is coming from the other table.
The database structure is as follows
locmapping (Table)

*

*id (int)

*catid (int)

*prodid (varchar25))

usermap (Table)

*

*id (int)

*prodid (varchar)

*uid (varchar)

The old situation I had was just to select prodid, uid from usermap
But now I'd like to make prodid equal to catid. I use the locmapping to create these mappings (In theory :) )

A: The SQL is semantically correct.  If you're getting more records back than you expect it's most likely because you need to add a second pair of columns to WHERE clause to further limit how records are "matched" between the two tables, or limit the records considered from one of the tables to a subset (perhaps the current or most recent record found).
Any further guess as to what's wrong is not possible without a more complete description of the problem, your table structure and ideally some sample data.

A: From these table structures it looks as though there is a many-to-many relationship between categories and products, and also between users and products.
If so, it would be possible for one user to map to one category via many products, which is why there are so many additional rows - in which case, the answer is simply to add DISTINCT to the query, like so:
select DISTINCT u.uid, l.catid
from usersmap u, locmapping l where u.prodid=l.prodid

A: If  SELECT prodid, uid FROM usermap produces 500K rows, but the SQL in your question produces 4 million rows, it means that each value of prodid is found (on average) in 8 rows of the table locmapping.  That is causing the original 500K rows to be multiplied by 8 and those rows are coming back with a variety of catid values.
If locmapping is intended to provide a single catid per prodid, you should protect the prodid column in that table with a UNIQUE index.

A: Go to SQL School:
http://www.w3schools.com/sql/default.asp
Without knowing how many rows are you the respective tables, it's hard to know if you're doing something wrong or not.  i.e. if you have 4 million records in table A, and they're also all in table B (according to the field that you're joining on), then you're going to get 4 million records!
Also, this is merely a SQL issue, and has nothing to do with websites.

A: Without a data model it's difficult to tell where the problem is. Perhaps you are misunderstanding how an inner join works?
Your query is using an inner join. This means there must be 4 million intersections. Usersmap could have 500,000 rows but if the prodid of one of those rows is contained in multiple rows  in locmapping then you will get a row for each intersection.


Pianist-Composer Michael Brown, winner of a 2015 Avery Fisher Career Grant, has been described by The New York Times as a "young piano visionary" and "one of the leading figures in the current renaissance of performer-composers." Selected by Sir András Schiff for his "Building Bridges" series in 2016-17, Brown will make debut solo recitals in Berlin, Frankfurt, Antwerp, Zurich, and New York's 92nd Street Y. Recent highlights include debuts with the Seattle and Maryland Symphony Orchestras and the New York Youth Symphony in Carnegie Hall's Stern Auditorium. Brown joined the roster of The Chamber Music Society of Lincoln Center's CMS Two program in 2015 and performs with the Society in Alice Tully Hall and on tour. A native New Yorker, he earned dual Bachelor's and Master's degrees in Piano and Composition from The Juilliard School.


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Jason McElwain continues to do great things
By LZ Granderson
(Archive | Contact)
Updated: July 21, 2008, 12:24 PM ET
LOS ANGELES -- Beauty is more than skin-deep -- a lesson taught to us as small, open-minded children, then quickly tested once we're teased for wearing the wrong jeans or carrying the wrong cell phone.
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AP Photo/Chris Carlson
Who could ever forget Jason McElwain's remarkable performance a couple of years ago that garnered him an ESPY award.
The concept of inner beauty seems particularly foreign in a city like L.A., where glitter and gold have replaced bricks and mortar, and nip/tucks seem as common as grabbing a latte.
But every now and then, real beauty -- the kind we were taught to look for as kids -- makes an unexpected appearance and reminds us of the power of love, hope and the human spirit.
I was reminded of this as I watched former Buffalo Bills tight end Kevin Everett -- a man who was told he would never walk again -- defy the odds and walk out on stage to accept the Jimmy V ESPY for Perseverance on Wednesday.
I was reminded of this during the acceptance speeches of John Carlos and Tommie Smith, who received the Arthur Ashe Courage Award.
And I was especially reminded of this during a recent conversation with another ESPY winner, Jason McElwain.
You probably know him better as J-Mac.
Two years ago, then-18-year-old Jason -- an autistic high school student from Rochester, N.Y. -- became a national sensation when video clips circulated of him scoring 20 points in the final four minutes of his first and only varsity basketball game. His story brought tears to the eyes of millions and the topic of autism -- a developmental disorder that impairs communication and social interaction -- to the fore.
Jason took home the ESPY for Best Sports Moment in 2006, beating out Kobe Bryant's 81-point game and George Mason's run to the Final Four. He has been on Oprah, met President George W. Bush and become buddies with Peyton Manning, and Magic Johnson is making a movie based on his life.
Today, Jason travels the country to help raise funds to battle autism. The importance of his work cannot be overestimated.
The Autism Society of America estimates that the lifetime cost of caring for a person with autism is between $3.5 million and $5 million, and the United States accumulates nearly $90 billion in autism-related expenditures annually. When you know that 47 million Americans are without health insurance and that 41 percent of uninsured people don't go to the doctor because of the cost, Jason using his celebrity status to address this need is not a quaint, happy ending to a heartwarming story. He's addressing an ongoing need. And although his mother, Debbie, admits it can be tiresome at times, she also recognizes the importance of the work.
"We didn't ask for any of this," she says. "We were just trying to be good parents and do what's best for all of our children. His brother got him into basketball, and years later, something very special happened because of it. If other parents like us can find some hope from this, then we want to be there for them."
This week, Jason is back in L.A. because he's receiving an award from the HollyRod Foundation, the brainchild of former NFL quarterback Rodney Peete and his wife, actress Holly Robinson Peete. The couple started the organization in 1997 to raise funds for research and care for those afflicted with Parkinson's disease, to which Holly's father succumbed in 2002. When their son, Rodney Peete Jr., was diagnosed with autism, the cause quickly came under their philanthropic umbrella.
AP Photo/Mark Duncan
McElwain continues to live life to the fullest, and is trying to help others along the way.
"It means a lot to me to be able to go out and help people see you can live a regular life," says Jason, who takes distance-learning courses, volunteers at the Indianapolis Colts' training camp and is the student assistant coach for his former school's junior varsity team. His goal is to be a varsity basketball coach one day. "Having autism doesn't mean you can't live your dreams," he says.
That's a message the Peetes say their 10-year-old son readily embraces.
"When we got the diagnosis, we were told a lot of nevers," Holly says. "They said he would never spontaneously say, 'What's up, Dad?' or 'I love you.' That's really hard for a parent to hear, and we were sitting in that doctor's office wondering what we were going to do. We had no sense of hope.
"If there was a magazine story we could've read while sitting there, that would have helped me so much. That's why we talk about our experiences as parents … to try to help others. And I know for a fact that Jason's story continues to help a lot of parents who are just now learning their child is autistic. He's helped us."
Holly says her son looks up to Jason and is helping present him with the award. "He says, 'I have autism -- autism doesn't have me,'" she says.
With all this chatter about Brett Favre and cheating refs and cheating baseball players and pop singers, it's good to know sports -- at its core -- still can bring out the best in us. When you know that Jason didn't start speaking until he was 5 years old or that in four years as team manager he missed only one game or that when the student body learned Jason might play in that final game, kids printed up pictures of him and held them up as they cheered, you can't help but draw upon the strength.
The spirit.
The beauty.
The kind of beauty we were taught as kids.
The kind that, thankfully, never fades.
LZ Granderson is a senior writer for ESPN The Magazine and a regular contributor to Page 2. He can be reached at l_granderson@yahoo.com.
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