That's right, you read the title correctly. Your library card grants you access to books, movies, music, astronomy binoculars, GoPros, and now….selfie sticks!
You might be asking yourself, "why in the world would a library circulate selfie sticks?" It's a fair question. But before I answer I should clarify that we're not just circulating any old selfie stick. We are circulating the state of the art Flexion Wireless Selfie Stick with Bluetooth technology, compatible with most smartphones.
This selfie stick allows a variety of adjustments for those looking to experiment with selfie angles, and the phone harness can be removed so you can attach other devices like digital cameras, camcorders, or even microphones. With a little brainstorming you can see how this simple retractable stick can be used as an extension arm for all sorts of creative purposes!
So why does the library have selfie sticks? As our mission states, we want the library to be a place where you are connected "to resources and experiences that educate, enrich, and inspire." Sometimes these resources can take unexpected forms. We circulate digital equipment so our community can learn through hands-on access to technology and be inspired to use the library for creative projects. You might not think a selfie stick could possibly enrich or inspire, but they are a popular technology accessory similar to other tech gear that people are curious to try, like the camera tripods and GoPro headstraps we circulate. They are accessories for creativity and often the intended usage is only the beginning.
1. You want a group photo that includes YOU!
You might cringe at the thought of being the tourist constantly taking selfies in front of every landmark, but what about the occasion where you want that perfect family shot and there's no one else around to take the picture? You might be surprised how well a selfie stick works for this purpose. I know I was!
It doesn't even look like a selfie!
2. You need a quick and cheap headshot for promotional purposes.
Need a new LinkedIn profile pic? Looking for a job and want a better look for Facebook or Twitter? You can use a selfie stick to get a more professional looking headshot that doesn't look like you're stretching your arms out as far as they'll go. You can take as much time and as many photos as you need until you get it perfect and also, you don't need to awkwardly ask a friend or relative to take photos of you. Of course, a selfie stick doesn't guarantee you'll get a great picture, but with some good lighting, a plain background, and some nice clothes, it can do the trick in a pinch.
3. Fashion a DIY on-the-go boom mic.
Are you a budding filmmaker? Do you want to experiment with getting better sound in your movie? Maybe you've heard that most filmmakers utilize something called a boom mic that someone holds out of the camera's range directly over the actors to get better sounding dialog. You've also heard the library circulates ZOOM handy recorders (more on this in a later post). Well, whaddaya know! The microphone can be screwed onto the end of the selfie stick and voila! You've got yourself a quick and portable boom mic thanks to a selfie stick.
A selfie stick boom mic? Now I've seen everything!


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text:
On Gilbert
By Evan Dunlap Updated Jun 20, 2011, 8:01am EDT
Share All sharing options for: On Gilbert
Dwight Howard has expressed his displeasure with the way the Orlando Magic used Gilbert Arenas last season. "I just felt like he didn't get the opportunity to play his style but also play with me," Orlando's franchise cornerstone told Jorge Sierra of HoopsHype.com. "I think he needed to. I think he got a couple of opportunities to do it in the playoffs, but it was kind of too late."
Arenas, who finished no worse than seventh in the league in scoring for three straight seasons earlier in his career, arrived in Orlando via a trade with the Washington Wizards last December. Brought in to bolster Orlando's offense, he faltered, shooting 34.4 percent from the field while shooting more often, per minute, than every Magic player apart from Howard. Though he showed aptitude in pushing the pace in transition and running the high pick-and-roll, Arenas did precious little else well, committing too many turnovers and proving to be a liability on defense.
Yet perhaps he, more than any Magic player other than Howard, might be the key to Orlando's future, according to not a few analysts, as well as Magic fans who've tweeted me. Orlando's biggest issue going forward is its lack of dynamic perimeter scoring, which Arenas can provide in spurts if healthy. Indeed, in his last injury-free season, Arenas averaged 28.4 points, good for third in the league. That's the good news. The bad is that it was five years ago, in the 2006/07 campaign. That was the year, you may recall, wherein Darko Milicic was a rotation player for Orlando. Yup.
What are we to make of Howard's claims? And can Arenas return to a form approximating his former self?
First, we need to unpack what Howard means by "his style." Arenas' is to dominate the ball and try to break defenses down off the dribble, usually going toward the basket, potentially to draw fouls. He is what one might call a classic scoring point guard. When at his best, he doesn't even need the help of a screen to get to where he wants to go.
But the whole "dominate the ball" thing isn't part of coach Stan Van Gundy's offense, which instead preaches spacing and quick, smart ball movement to create open shots. The Magic haven't employed a player who so desperately needs the ball, as Arenas does, during Van Gundy's tenure. Moreover, Van Gundy's previous backup point guards tended to be game-manager types. He tasked Carlos Arroyo, Anthony Johnson, Jason Williams, and (briefly) Chris Duhon to run the offense, distribute, and shoot only when necessary. Keyon Dooling proved to be the exception, with Van Gundy using him as the go-to scorer for his second unit in 2007/08.
Of course, Otis Smith didn't trade for Arenas expecting him to play like Anthony Johnson. He traded for Arenas to play like Gilbert Arenas. Arenas tried to oblige--as I said, he shot more frequently on a per-minute basis than all Orlando players save for Howard--but only saw the court for 21.8 minutes per game, on average. Obviously, he played miserably, and perhaps that word works two ways: "miserably" as in "poorly," and "miserably" as in "sad."
It's possible for score-first point guards to thrive in reserve roles. Look at Louis Williams (13.7 points in 23.3 minutes) in Philadelphia, Leandro Barbosa (13.3 points in 24.1 minutes) in Toronto, or J.J. Barea (9.5 points in 20.6 minutes) in Dallas. The problem for Arenas is adjusting to that role. It's perfectly reasonable that he'd struggle to adapt. He'd come off the bench just 26 times in his nine seasons prior to the last one, and 17 of those were in his rookie year. Then, boom, he arrives in Orlando and comes off the bench 47 times out of 49.
There is something to be said about the difference between starting and coming off the bench. J.J. Redick, Arenas' teammate in the reserve backcourt, has commented on it as well. Starters tend to have more freedom: they usually play more total minutes, and play longer stints than their backups as well. Time is on their side, in multiple ways.
If Arenas' challenge is to adapt to playing fewer minutes, then Van Gundy's is to figure a way to maximize Arenas' skills. Good luck with that.
Arenas has never been a great outside shooter, so spotting up isn't something Van Gundy can count on him to do. And the three operations he's had on his left knee have robbed Arenas of the athleticism which made him a great finisher and foul-drawer. Despite that, I do believe he has to continue driving to the basket; those flat-footed long twos off the dribble are simply hopeless, and the fewer he takes, the better.
Nobody knows quite yet what Arenas is capable of, but if his last four seasons are any indication, it isn't much. Perhaps we ought to give him the benefit of the doubt. Between his injuries, legal issues, and personal problems, he's had to deal with a lot these last few years. I believe there's middle ground between Arenas and Van Gundy. If the two can strike a satisfactory balance, perhaps he can challenge Jameer Nelson for the starting point guard job, which is something Smith has said he'd like to see happen.
What we do know, however, is this: if those two don't meet each other halfway, somehow, and Arenas is again mired on the bench and/or playing ineffective ball next season, Orlando is in a heap of trouble. With no particularly enticing trade assets or salary-cap room, the Magic almost certainly have to improve their offense from within. A bounce-back season from Arenas is their last, best hope of that.
Having laid all that out, it'd be unfair not to mention that Orlando tends to play fairly well with Arenas on the court, and that he's a great passer. His biggest problems pertain to shooting percentage, shot-selection, and defense. The first two, one hopes, can be remedied. The last one, however, may not be, given his loss of athleticism. Even a full commitment on that end of the floor may not be enough to make him serviceable there.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: How to keep section heading on the same page as a floating image in a landscape layout without getting kicked to the next page? I need to set up a landscape layout (preferably an environment) for one page in conjuncture with an image scaled to the page's width, and there must be a chapter heading always sitting on the same place. Problem is: The chapter heading can't stay put; it either goes off to the next page or its starting position isn't consistent (it has to).
Another small issue: Maybe it's because of the landscape environment, but the image doesn't scale properly (sometimes). Hence why I tried minipages (but the results aren't very consistent...)
\documentclass{memoir}
\usepackage{geometry}
\usepackage{xcolor}
\usepackage{pagecolor}
\usepackage{pdflscape}

\usepackage{graphicx}
\usepackage{float}
\begin{document}
\newpagecolor{black}
\thispagestyle{empty}
\newgeometry{left=0cm,right=0cm,bottom=0cm,top=0cm}
\begin{landscape}
    \begin{figure}
    \centering
        \begin{minipage}{1\paperheight}
        \includegraphics[keepaspectratio,width=1\textwidth,height=\textheight]{example-image}
        \caption{caption here}
        \end{minipage}
        \begin{minipage}{1\textheight}
        \color{white}\chapter{chapter here}
        \end{minipage}
    \end{figure}
\end{landscape}
\restoregeometry

\end{document}

Here is what the code looks like:

If I remove minipage it would become like this:

What I want is this (intended end result):
EDIT:
I tried using Tikzpicture's positioning feature Positioning relative to page in TikZ to stack a text node but since it is also considered to be a float it still got back down to the next page, sigh.
My next bet is trying to overlay the heading text Tikzpicture's by overlaying upon the whole page (Tikz: overlay png or pdf image over another pdf figure), not sure if it'll work though.

A: To avoid the "gross hack" you can redefine the memoir class hook \clearforchapter. By default this just clears the page at the start of \chapter, but it can do anything, for example include the graphic.
I also used the memoir \legend command which can put a pseudo-caption anywhere in the document (though it won't appear in any "contents" section like "list of figures" unless you explicitly add a contents line).
\begin{document}
\newpagecolor{black}
\thispagestyle{empty}
\newgeometry{left=0cm,right=0cm,bottom=0cm,top=0cm}
\begin{landscape}
  \renewcommand{\clearforchapter}{%
    \openany % or \openleft or \openright
    \centering
    \includegraphics[width=\linewidth,
    height=.9\textheight % just needed here, as example-image fills the whole page
    ]{example-image}
    \color{white}
    \legend{CAPTION HERE}
    \vspace{-0.3\textheight} % adjust as required to overlap the chapter with the image
  }
\chapter{chapter here}
\end{landscape}
\restoregeometry

\newpagecolor{white}
\chapter{Another chapter here}

\end{document}

A: If I understand correctly you want something like

You certainly never want a chapter heading inside a float, so I removed  that, I also removed the minipage around the image which wasn't doing much. I left one around the chapter heading, just to stop it stating a new page (which is a gross hack but still...)
\documentclass{memoir}
\usepackage{geometry}
\usepackage{xcolor}
\usepackage{pagecolor}
\usepackage{pdflscape}
\usepackage{capt-of}
\usepackage{graphicx}
\usepackage{float}
\begin{document}
\newpagecolor{black}
\thispagestyle{empty}
\newgeometry{left=0cm,right=0cm,bottom=0cm,top=0cm}
\begin{landscape}
    \centering
        \includegraphics[width=\linewidth,
  height=.7\textwidth % just needed here as example-image is too tall for the heading
]{example-image}

 \begin{minipage}{\linewidth}% just to stop \chapter starting a page
 \color{white}
 \captionof{figure}{caption here}
\chapter{chapter here}
\end{minipage}
\end{landscape}
\restoregeometry

\end{document}

redpajama_set_name: RedPajamaStackExchange


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text:
Mexican Migration Field Research Program
Community-action research at the US-Mexico border
Student Bios: 2022-2023
Federal Police and the National Guard
Retraumatization Series: Blog 1
When Central American migrants enter Mexico, one might hope that local authorities would provide some safety along their journey. Governmental institutions theoretically operate according to standards of treatment and "respect for human rights," particularly when it comes to migrants. However, this government mission to treat people with dignity is often violated once the federal police and national guard are out in the field.
Similarly, the mission statement of the Federal Police, of the National Guard of Mexico believes that it is important to:
Safeguard life, integrity, security, goods and rights of the people, along with preserving their liberties.
Contribute to the generation and preservation of the public order and social peace.
Safeguard the goods and resources of the nation.
Participate in the collaboration and coordination with federal entities and municipalities.
While both of these governmental entities take pride in doing all that is possible to maintain the wellbeing of their country, many migrants we interviewed described the opposite.
For instance, "N" a 28-year-old male migrant from El Salvador recounted how he would not want his family to travel and take the same route he did, because it was too dangerous, and the police did a poor job at providing safety. He explained:
El camino en que tu vienes …hay muchos policías… que cuando tu vienes…la policía de México casi todos son corruptos. Ellos te ven, se te quedan viendo, y si ellos tienen sospecha que eres inmigrante, te paran, te quitan lo que tienes.
On the path that you take … there are many policemen… when you are on your way … the Mexican police are almost all corrupt. They see you, they watch you, and if they suspect that you are a migrant, they stop you, they take what you have.
– N, 28-year-old man from El Salvador
"N's" encounter with the police is similar to the encounters that other migrants had. Not only was being harassed by the police retraumatizing but it made migrants distrust Mexican officials.
"M," a 21-year-old female from Honduras, was interviewed at the shelter Ejercito de Salvación. Her decision to leave her home country was influenced by the lack of support she received from her family members throughout her pregnancy. Along her way through Mexico she had encounters with governmental officials who exploited her and physically abused her. The following quote is illustrates the treatment she received from government officials:
Bueno tuvimos problemas, allí en Arriaga, en la marina … me trataron muy mal, este, llegó otro de la federal. Me golpeó, me quería quitar mis documentos, que le pagara $2,000 (pesos) para que yo procesalmente que viniera.
Well we had problems, there in Arriaga, the Mexican marines … they treated me very badly, and an agent from the federal police arrived. He hit me, he wanted to take my documents, he wanted me to pay $2,000 (pesos) so that I could continue with my journey.
– M, 21-year-old woman from Honduras
M's vivid depiction highlights her shock and disbelief at being beaten and asked for money by Mexican authorities to continue on her journey. Not only is it surprising, but it serves as example to show how corrupt the officials are.
"A," a 47-year-old male who was also from Honduras, shared that he has dealt with discrimination since living in his home country due to his identity as an indigenous man from the Garifuna community. He felt that his identity as an indigenous man amplified the stigma he faced in his journey through Mexico. Throughout his interview, he shared that he was constantly confused for being a "pollero" – a smuggler, and that immigration officials would ask for his documents to determine where he was from. This constant occurrence made him feel vulnerable and persecuted by immigration officials. He described:
Mire, me siento perseguido, me siento discriminado, me siento – o sea – vulnerable a los ojos de cualquiera gente policía inmigración lo que sea.
Look I feel persecuted, I feel discriminated against, I feel – I mean – I feel vulnerable in the eyes of any people from the police or immigration or whatever.
– A, 47-year-old man from Honduras
A's reaction to immigration officials had not been easy and had put him in vulnerable positions several times. The treatment he received has caused him a lot fear, distrust, and stress throughout his journey.
In sum, all three of these examples show a recurring themes of being taken advantage of by Mexican officials. Indeed, in most of the interviews we conducted with asylum seekers, they described being exposed to this type of treatment. Things were especially bad at cities on or near the border between Guatemala and Mexico such as Tapachula, Ciudad Hidalgo, and Ciudad Tecún Uman. These tend to be places where the Policia Federal and the Guardia Nacional concentrate to block immigration flows coming from the south.
The police in such cities are aware that migrants are desperate to cross through Mexico so they can attempt to reach the United States. Many migrants travel with little money – barely enough to feed themselves and their family members. Even though money is constantly confiscated by officials, governments also sometimes seize migrants' documents, including evidence for their asylum cases. These quotes emphasize the extent to which the police take advantage of migrants and their vulnerability. They highlight the fear that migrants experience towards Mexican law enforcement as an institution.
Among the people that I had the chance to interview at the Casa del Migrante, many them had discriminatory and tense encounters with either the Policia Federal and Guardia Nacional. Most of the time it occurred when they were traveling on a bus from city to city in Mexico. Typically, they were asked to show a form of identification that would verify that they were legally traveling through Mexico. It was in instances like these that police would often ask for money, especially if the migrant did not have proper documentation. Speaking to a number of migrants showed us that interaction with the Federal Police and National Guard is common, and that their lack of work ethic, corruption and lack of respect contributes to the retraumatization of migrants.
Both the Federal Police and the National Guard represent the Mexican government. However, the behavior adopted by officials in these agencies contradicts their mission statements to enforce the safety of the country. The act of stealing and discriminating against migrants from Central America or any other foreign country condones violence and does not promote the human rights of migrants. Most importantly, the behavior of the police adds to the trauma that migrants experience throughout their journey to the US-Mexico border.
Mexican Migration Field Research Program, Website Powered by WordPress.com.


Jones graduates from Northside a week from today. The following day, he'll travel to Athens to begin his life at Georgia after signing with the Bulldogs in February.
Jones said he begins freshman orientation June 1. His summer calendar will be filled with classes and workouts as he prepares for the beginning of practice in August.
One of Jones' new classmates, quarterback Aaron Murray of Tampa, Fla., received the Bobby Dodd National High School Back of the Year award from the Touchdown Club of Atlanta in February.
Jones is the first Middle Georgia football player to receive either the lineman or back honor in the 21-year history of the Touchdown Club award.


text:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CompanyName.ProductName.Provider.Betfair
{
    public class BetfairMarket
    {
        public int Id
        {
            get;
            set;
        }
        // use this to check if it is match odds market or some other.
        public string MarketName
        {
            get;
            set;
        }

        public string Title
        {
            get;
            set;
        }

        public string Type
        {
            get;
            set;
        }

        public string Status
        {
            get;
            set;
        }

        public DateTime EventDate
        {
            get;
            set;
        }

        public int RunnerCount
        {
            get;
            set;
        }
    }
}

redpajama_set_name: RedPajamaGithub


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Hi all, Desperate for some advise, my dd is in y6 Elmhurst associate with Miss Howarth's and was asked last week to make a shopping list for this weeks class but as she was not on last years course she no idea what it is she should be doing? Is it a list of technique she would like to have, corrections she would like to fix, ingredients for a lasagne? Help please if anybody knows she's a little stressed to say the least! ????
Hello everyone, my dd had her first year 6 lesson at Elmhurst associates today and absolutely loved it. We couldn't be more pleased or proud of her ???? So excited to watch at the end of term ????
Well done to auntienora, and MAK that's an amazing achievement so well done ???????????? the wait continues for us! ????
Hugs to your daughter, I'll probably see you there with my DD! ????
Congratulations Twinklesmum, what a fabulous position to be in ????
Oooo good luck for the ballet exam ???? ????
Any more news anywhere? I feel like I'm possibly the only one still permanently refreshing this feed and my email account! ???? Please RBS put me out of my misery! ????????


text:
Bills vs. Panthers Postgame Barometer
Let's go position by position and see whose stock is rising, whose stock is falling, and what questions still remain.
— Stock Rising —
A clean performance from Josh Allen against a Panther's defense that sat Luke Kuechly. The Bills took advantage, working the middle of the field. Allen made mostly accurate passes to Beasley over the middle all throughout the first quarter and hit Tommy Sweeney deep in the seam to put the Bills on the goal line. He also had a nice touch pass to Sweeney in stride over a defenders shoulder. The 2nd year signal caller sprinkled in some polish to his already well-progressing game. (9/11, 102 yards, 81.8%, 0TDs, 0 INTS)
Matt Barkley
Barkley continues to show poise and anticipation as the backup signal-caller. If your number two can carve up a preseason defense, that is a good sign that he could give you a chance if your starter went down. He had the gorgeous bucket throw to Singletary as well as the TD to Duke Williams. Barkley's only mistake of the night was a miss to a wide-open Singletary in the flat when pressure got to him.
Devin Singletary
Singletary got very little work and made the most of it. He continued to show smarts in the run game getting the most out of every carry. His presence was felt in the passing game most. He caught three passes for 25 yards including a beautiful over the shoulder catch where he had to adjust to the football. He would have had more if Barkley gave him a catchable ball in the flat when he was pressured. Singletary contributed a nice blitz pickup as well. To me, he looks like the best running back on the team.
TJ Yeldon
Yeldon had a good game both on the ground and through the air. He is an NFL running back. If he doesn't make the roster, he will find himself on another roster in 2019 without question. He showed patience in the run game carrying the ball 7 times for 26 yards and smarts in the passing game, even if it was only one catch for 10 yards.
Beasley was on fire early catching the ball 5 times for 44 yards early. He was making a fool of linebackers when they were lined up with him in the slot. If Allen can keep his accuracy up, Beasley is going to feast underneath one week and when the defender's transition to him, a player like John Brown could feast down the field.
Duke Williams
Duke Williams had himself a night. He made a nice catch on a slant, but his biggest play was his acrobatic "go up and get it" touchdown grab in the second quarter from Matt Barkley. Those are the kinds of plays that will get him on this roster because not a single other receiver on this roster is even remotely capable of doing it. McDermott made it a point to see exactly what Williams was made of tonight.
Tommy Sweeney
Tommy Sweeney made up for a lackluster debut with two beautiful catches in the first quarter. He caught an over the shoulder throw from Josh Allen on the first drive and caught a bullet down the seam on the second drive to put the Bills on the goal line. He is a 53-man roster lock, and may actually start the year as the number one tight end.
Johnson continued to show pop coming away with a strip-sack in the game. He is a 53-man roster lock at this point and a guy who, if developed correctly, could be in contention to start in 2020. What a job by Brandon Beane in that 7th round.
Harrison Phillips
Phillips rebounded from being forced to play late into last week's game with a great performance this week. With a year under his belt, he looks stronger and was able to work his way using a stunt to get a sack on quarterback Tyler Henieke. Harrison's brother Jordan was great as well.
Deon Lacy
It may be too little too late, but Deon Lacey was all over the field. He made numerous plays from the linebacker position chasing people down on the edge.
Levi Wallace & Kevin Johnson
Johnson had the pick-six and was impressive with the second unit. However, just because his night was flashier doesn't mean he made any strides in winning the starting job. Levi Wallace had a great night as well including some acrobatic pass break-ups on jump balls. It is nice to finally have some depth at the position.
— Stock Falling —
Tyree Jackson
Tyree Jackson is learning quickly that the NFL is not the MAC. He is making poor decisions with the football and is slow to process. After said interception, Brian Daboll appeared to blow up at the young signal-caller on the sidelines. It is time the Bills consider bringing in a fourth quarterback or a quarterback to flat out replace Jackson. He is too many years of development away, and, at this point, his poor play would not bode well for a scout team role or help in evaluating the skill position players on the roster.
Senorise Perry
He may be known for his special team's prowess and not his running abilities, but Perry fumbled on his first carry and wasn't seen on the field again. Message sent.
David Sills
Sills may not even be the best candidate for the practice squad at this point. He is invisible in both practices and in games. He had plenty of run this week and the receivers around him were making plays, and he wasn't.
Cody Ford
Cody Ford was absolutely run by Bruce Irvin on practically every play. He isn't a tackle and that is okay. Let's hope Nsekhe gets back on the field soon, and Ford can move back to his natural position.
Run Blocking
Not counting quarterback scrambles, the Bills only ran the ball 22 times for 66 yards. That is only a three yards per carry average. While it is only preseason and teams aren't scheming their best run plays, it is still concerning the guys up front cannot get enough push for a better yards per carry average.
Run Defense
The Bills were gashed on pitches to the outside. While things tightened up past midfield and they kept the Panther's out of the endzone early, it is still concerning. That cannot happen in the regular season. Let's hope it was a product of the vanilla scheme.
Punters
Neither punter did anything to help themselves last night. It is looking more and more likely that the Bills will once again have to look outside of the organization for a punter before week one.
— Remaining Questions —
Does Shady still have it?
McCoy was targeted a lot early in both the passing and running game, but despite a touchdown, his stat line wasn't memorable. Is there really a big difference between McCoy and a guy like Singletary at this point in their careers?
Where was Robert Foster?
Robert Foster played early, but not often. Is Foster's roster spot secured as John Brown's primary backup? Are they trying to hide him in hopes of stashing him on the practice squad? Is his job in jeopardy? Is he trade bait?
Speaking of invisible… did Camp Phillips even play?
Are the Bills trying to hide him for the practice squad? Will it be "his turn" next week and someone else sits?
Do the Bills keep seven wide receivers?
Beasley, Brown, Jones, and Roberts are locked into spots. Foster is more than likely there as well. That leaves one spot for the emerging Isaiah McKenzie, Duke Williams, Ray-Ray McCloud, and even possibly Cam Phillips. It is not inconceivable they keep seven, one smaller guy, and Duke.
Do the Bills keep five defensive ends?
Lawson has proven he is stout against the run with a little pass-rush pop. Despite a special teams penalty, Love has been stout against the run and a coaches' favorite. With the emergence of Daryl Johnson, do the Bills keep five defensive ends? McDermott did it a lot in Carolina.
Defensive Players Stashed
I didn't see a lot of Maurice Alexander and Corey Thompson. Thompson is safe but is Alexander too?
Steven Hauschka
Is it time to start worrying about Haushka after that 48-yard miss? By all accounts he has been stellar in practice, but even if it is nerves, you don't like to see that from a kicker.
Related Topics:Buffalo Bills
The Bills Guys: Respect The Progress
An Early Look at the 2020 NFL Draft Class: Running Backs


Home News WWE Who Will Face WWE US Champion Kevin Owens At Battleground?
Who Will Face WWE US Champion Kevin Owens At Battleground?
AJ Styles won the Independence Day Battle Royal on tonight's WWE SmackDown from Phoenix to become the new #1 contender to WWE United States Champion Kevin Owens. Styles vs. Owens will take place at Battleground later this month in Philadelphia. Other battle royal participants were Sami Zayn, Konnor, Viktor, Sin Cara, Epico, Luke Harper, Dolph Ziggler, Tye Dillinger, Erick Rowan, Jason Jordan, Mojo Rawley, Zack Ryder, Tyler Breeze and Fandango.


In my last post, I shared the new Key Stage 3 assessment framework which I have created to enable us to assess students' progress without the use of levels. This framework is, of course, generic and abstract, merely setting out a very broad outline of what progress might look like in students' historical knowledge, skills and understanding. In this is follow-up post, I'm going to share how I intend to apply this framework to assessing specific pieces of students' work in class.
From time to time, students will be set a summative task which will allow us to assess their progress at the end of a specific unit of work. Before students complete these summative tasks, they will receive a tailored mark sheet which applies the new framework to the specific task in hand. You can see an example mark sheet below, for a task which students will carry out after they have completed their unit of work on invasion and migration to Britain pre-1066.
As you can see, the four broad attainment descriptors of the framework have been applied very directly to the content and demands of the task set. Along with this, the mark sheet also provides scope for students to self assess and peer assess before receiving teacher feedback.


text:
Q: Printing space and new lines within a loop issue The code i wrote works however during the second loop and onward the newlines and the 'totalmin' string isn't printed. can someone please tell me how to fix this? the loop is correct because the printed values (without the spaces) are correct
im using mars 4.4 and also used the code in 4.3 but the output was the same
Code:
#a1 is the minvalue base address for the minterms
#a2 holds value 1
#a3 holds minvalue[i]
#t0 is the counter
#t1 is the counter*4
#t2 holds the value of bit0[i]
#t3 holds the value of bit1[i]
#t4 holds the value of bit2[i]
#t5 holds the value of bit3[i]
#t6 holds the value of the compliment of bit0[i]....second use uses t6 as the product of bit0^bit1'
#t7 holds the value of bit2^bit3.... second use uses t7 as the product of (bit2^bit3)xor(bit1^bit0')
#t9 holds the min number
#s0 is the minvalue base address+(counter*4)
#s1 is the bit0 base address
#s2 is the bit1 base address
#s3 is the bit2 base address
#s4 is the bit3 base address
#s5 is the bit0 base address+(counter*4)
#s6 is the bit1 base address+(counter*4)
#s7 is the bit2 base address+(counter*4)
#t8 is the bit3 base address+(counter*4)
.data
bit0: .word 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1 #array which holds values of bit zero
bit1: .word 0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1 #array which holds values of bit one
bit2: .word 0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1 #array which holds values of bit two
bit3: .word 0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1 #array which holds values of bit three

minvalue: .word 0   #array which holds the min term for each value

space: .asciiz "   "                #creates a space when printing
newline: .asciiz "\n"               #creates a new line when printing
totalmin: .asciiz "the number of Minterms in F is:  "

.text
la $a1, minvalue        #base address for minterms
la $s1, bit0            #base address for bit0
la $s2, bit1            #base address for bit1
la $s3, bit2            #base address for bit2
la $s4, bit3            #base address for bit3

li $t0, 0           #t0 is the counter which is set to 0
li $a2, 1           #a2 holds value 1
li $t9, 0           #min number is set to 0

loop:
sll $t1, $t0, 2         #multiplies the current value of t0 by 4 or t1=i*4
add $s0, $a1, $t1       #adds the minvalue base address by 4 each loop or s0=   minvbase+(i*4)
add $s5, $s1, $t1       #adds the bit0 base address by 4 each loop or s5= bit0base+(i*4)
add $s6, $s2, $t1       #adds the bit1 base address by 4 each loop or s6= bit1base+(i*4)
add $s7, $s3, $t1       #adds the bit2 base address by 4 each loop or s7= bit2base+(i*4)
add $t8, $s4, $t1       #adds the bit3 base address by 4 each loop or t8=bit3base+(i*4)

lw $t2, 0($s5)          #t2 holds the value of bit0[i]
lw $t3, 0($s6)          #t3 holds the value of bit1[i]
lw $t4, 0($s7)          #t4 holds the value of bit2[i]
lw $t5, 0($t8)          #t5 holds the value of bit3[i]

not $t6, $t2            #t6 holds the value of the compliment of bit0[i]
and $t6, $t6, $t3       #t6 holds the value of bit1^bit0'
and $t7, $t4, $t5       #t7 holds the value of bit2^bit3
xor $t7, $t7, $t6       #t7 holds the value of (bit2^bit3)xor(bit1^bit0')

sw $zero, 0($s0)        #minterm[i] is intially set to zero
bne $t7, 0, minterm1        #if t7 is 1 then jump to minterm1

print:
lw $a3, 0($s0)          #a3 holds the value of minvalue[i]

li $v0, 1
move $a0, $t5
syscall

li $v0, 1
move $a0, $t4
syscall

li $v0, 1
move $a0, $t3
syscall

li $v0, 1
move $a0, $t2
syscall

li $v0, 4
la $a0, space
syscall

li $v0, 1
move $a0, $a3
syscall

li $v0, 4
la $a0, newline
syscall

addi $t0, $t0, 1        #increment counter or i++
bge $t0, 16, exit       #if t0 >= 16 jump to exit
j loop              #else jump to loop

minterm1:
sw $a2, 0($s0)          #rewrites the minterm[i] from zero to 1
addi $t9, $t9, 1        #min number= min number+1
j print

exit:
li $v0, 4
la $a0, totalmin
syscall

li $v0, 1
move $a0, $t9
syscall

li $v0, 10
syscall

output:
!http://puu.sh/7N1hx.png

A: minvalue: .word 0   #array which holds the min term for each value

The array you've declared only has space for a single 32-bit word, so your loop ends up overwriting other data located after minvalue.
If you meant for minvalue to hold 16 words you should use something like:
minvalue: .space 16*4


This royal wedding was special for many reasons. It was an improbable match from the beginning, but when Los Angeles actress Meghan Markle met Harry Prince of Wales something clicked and they soon were making vows that together they would change the world. Their marriage on Saturday, May 19 will certainly change the image of the royal family of the House of Windsor, breaking from long held traditions and moving in a direction that few could have imagined just a decade ago.
The union of Meghan Markle, an American biracial actress and Henry Charles Albert David, more commonly known as Prince Harry, who is the younger son of Charles, Prince of Wales, and Diana, Princess of Wales, sixth in the line of succession to the British throne, stirred up emotions with an enormous viewing audience around the world. In London, an estimated 100,000 celebrants lined the streets, including the tree-lined road known as the Long Walk, to watch the Duke and Duchess of Sussex pass by. Once inside St. George's Chapel at Windsor Castle, the break from longstanding British tradition became evident, with an inclusion of several African-American influences. As part of the ceremonies, Karen Gibson and The Kingdom Choir performed the beloved classic "Stand By Me," by Ben E. King. Following that performance, the Most Reverend Michael Curry, the first African American to preside in the Episcopal Church, delivered a rousing sermon to an audience that included Oprah, the Clooneys, the Beckhams, Serena Williams and Elton John.
Also of note is Markle's active southern California-based lifestyle, which included time spent at the beach, yoga and healthy eating. It's a lifestyle that has been well publicized in the media, but is refreshingly new to many places in the world, including Great Britain.
It's this emphasis that is also the focus of Adrienne Papp's web domain, Youthful & Ageless where health, wellness and anti-aging products and services are promoted on an ongoing basis to a worldwide audience. This newly-developed site brings together people and companies who are health conscious, mindful and have workable solutions to critical human issues, such as curing deadly diseases, mental health issues and undernourishment, just to mention a few.
Another company Papp is involved with operates a farm in Africa that produces organic watermelons, making this quintessential summertime fruit a year- round hydration drink and giving jobs to thousands in Africa while also supplying 200 gallons of clean water to individuals in developing nations. Their super drinks are high in anti-oxidants, minerals and electrolytes, as are the organic maple drinks that Papp is also handling. Pizoot, a healthy peanut-based snack invented by scientist Dr. Alfred P. Pizoot is another of the entrepreneurial companies coming on board with Youthful and Ageless.
Papp has also established a business relationship with rancher-lifestyle enthusiast Dr. Malcolm Lesavoy, a compassionate and prominent plastic surgeon with a practice in Beverly Hills California who travels the world to do reconstructive surgery on severely disfigured patients.
In addition to working with these companies and professionals, Papp is pleased to announce that Kimber Eastwood, daughter of the actor/director, Clint Eastwood, has been appointed as a member of the board for Youthful Ageless™ and will be working with the many anti-aging companies that have found a place on the site.


Welcome to the Chiropractic Business Network of SmartGuy.com. We are a group of Chiropractors worldwide. Feel free to interact with other professionals from across the world. You can find professionals, find deals on services, find professionals who might barter, or simple post questions, comments, or suggestions. Chiropractors specialize in a form of alternative medicine that deals with the diagnosis and treatment of mechanical disorders of the musculoskeletal system, especially in the spine. Proponents claim that such disorders affect general health via the nervous system.


text:
Foundations of Vision
Brian A. Wandell
Chapter 3: The Photoreceptor Mosaic
Home » Chapter 3: The Photoreceptor Mosaic
The Photoreceptor Mosaic
Units of Visual Angle
The Cone Mosaic
Behavioral Measurements
Biological Measurements
Why are the Cones Widely Spaced?
Visual Interferometry
Sampling and Aliasing
The and Cone Mosaic
Summary and Discussion
In Chapter 2 we reviewed Campbell and Gubisch's (1967) measurements of the optical linespread function. Their data are presented in Figure 2.12, as smooth curves, but the actual measurements must have taken place at a series of finely spaced intervals called sample points. In designing their experiment, Campbell and Gubisch must have considered carefully how to space their sample points because they wanted to space their measurement samples only finely enough to capture the intensity variations in the measurement plane. Had they positioned their samples too widely, then they would have missed significant variations in the data. On the other hand, spacing the sample positions too closely would have made the measurement process wasteful of time and resources.
Just as Campbell and Gubisch sampled their linespread measurements, so too the retinal image is sampled by the nervous system. Since only those portions of the retinal image that stimulate the visual photoreceptors can influence vision, the sample positions are determined by the positions of the photoreceptors. If the photoreceptors are spaced too widely, the image encoding will miss significant variation present in the retinal image. On the other hand, if the photoreceptors are spaced very close to one another compared to the spatial variation that is possible given the inevitable optical blurring, then the image encoding will be redundant, using more neurons than necessary to do the job. In this chapter we will consider how the spatial arrangement of the photoreceptors, called the photoreceptor mosaic, limits our ability to infer the spatial pattern of light intensity present in the retinal image.
We will consider separately the photoreceptor mosaics of each of the different types of photoreceptors. There are two fundamentally different types of photoreceptors in our eye, the rods and the cones. There are approximately 5 million cones and 100 million rods in each eye. The positions of these two types of photoreceptors differ in many ways across the retina. Figure 3.1 shows how the relative densities of cone photoreceptors and rod photoreceptors vary across the retina.
Figure 3.1: The distribution of rod and cone photorceptors across the human retina. (a) The density of the receptors is shown in degrees of visual angle relative to the position of the fovea for the left eye. (b) The cone receptors are concentrated in the fovea. The rod photoreceptors are absent from the fovea and reach their highest density 10 to 20 degrees peripheral to the fovea. No photoreceptors are present in the blindspot.
The rods initiate vision under low illumination levels, called scotopic light levels, while the cones initiate vision under higher, photopic light levels. The range of intensities in which both rods and cones can initiate vision is called mesopic intensity levels. At most wavelengths of light, the cones are less sensitive to light than the rods. This sensitivity difference, coupled with the fact that there are no rods in the fovea, explains why we can not see very dim sources, such as weak starlight, when we fixate our fovea directly on them. These sources are too dim to be visible through the all cone fovea. The dim source only becomes visible when it is placed in the periphery and be detected by the rods. Rods are very sensitive light detectors: they generate a detectable photocurrent response when they absorb a single photon of light (Hecht et al., 1942; Schwartz, 1978; Baylor et al. 1987).
The region of highest visual acuity in the human retina is the fovea. As Figure 3.1 shows, the fovea contains no rods, but it does contain the highest concentration of cones. There are approximately 50,000 cones in the human fovea. Since there are no photoreceptors at the optic disk, where the ganglion cell axons exit the retina, there is a blindspot in that region of the retina (see Chapter 5).
Figure 3.2: Mammalian rod and cone photoreceptors contain the light absorbing pigment that initiates vision. Light enters the photoreceptors through the inner segment and is funneled to the outer segment that contains the photopigment. (After Baylor, 1987)
Figure 3.2 shows schematics of a mammalian rod and a cone photoreceptor. Light imaged by the cornea and lens is shown entering the receptors through the inner segments. The light passes into the outer segment which contain light absorbing photopigments. As light passes from the inner to the outer segment of the photoreceptor, it will either be absorbed by one of the photopigment molecules in the outer segment or it will simply continue through the photoreceptor and exit out the other side. Some light imaged by the optics will pass between the photoreceptors. Overall, less than ten percent of the light entering the eye is absorbed by the photoreceptor photopigments (Baylor, 1987).
The rod photoreceptors contain a photopigment called rhodopsin. The rods are small, there are many of them, and they sample the retinal image very finely. Yet, visual acuity under scotopic viewing conditions is very poor compared to visual acuity under photopic conditions. The reason for this is that the signals from many rods converge onto a single neuron within the retina, so that there is a many-to-one relationship between rod receptors and neurons in the optic nerve fibers. The density of rods and the convergence of their signals onto single neurons improves the sensitivity of rod-initiated vision. Hence, rod-initiated vision does not resolve fine spatial detail.
The foveal cone signals do not converge onto single neurons. Instead, several neurons encode the signal from each cone, so that there is a one-to-many relationship between the foveal cones and optic tract neurons. The dense representation of the foveal cones suggests that the spatial sampling of the cones must be an important aspect of the visual encoding.
There are three types of cone photoreceptors within the human retina. Each cone can be classified based on the wavelength sensitivity of the photopigment in its outer segment. Estimates of the spectral sensitivity of the three types of cone photoreceptors are shown in Figure 3.3. These curves are measured from the cornea, so they include light loss due to the cornea, lens and inert materials of the eye. In the next chapter we will study how color vision depends upon the differences in wavelength selectivity of the three types of cones. Throughout this book I will refer to the three types of photoreceptors as the L, M and S cones.
(The letters refer to Long-wavelength, Middle-wavelength and Short-wavelength peak sensitivity.)
Figure 3.3: Spectral sensitivities of the L, M and S cones in the human eye. The measurements are based on a light source at the cornea, so that the wavelength loss due to the cornea, lens and other inert pigments of the eye play a role in determining the sensitivity. (Source: Stockman and Macleod, 1993).
Figure 3.4: Photoreceptor Sampling: The spatial mosaic of the human cones. A cross-section of the human retina at the level of the inner segments. Cones in the fovea (a) are smaller than cones in the periphery (b). As the separation between cones grows, the rod receptors fill in the spaces. (c) The cone density varies with distance from the fovea. Cone density is plotted as a function of eccentricity for seven human retinae (After Curcio et al, 1990).
Because light is absorbed after passing through the inner segment, the position of the inner segment determines the spatial sampling position of the photoreceptor. Figure 3.4 shows cross-sections of the human cone photoreceptors at the level of the inner segment in the human fovea (part a) and just outside the fovea (part b). In the fovea, cross-section shows that the inner segments are very tightly packed and form a regular sampling array. A cross-section just outside the fovea shows that the rod photoreceptors fill the spaces between the cones and disrupt the regular packing arrangement. The scale bar represents ; the cone photoreceptor inner segments in the fovea are approximately wide with a minimum center to center spacing of about . Figure 3.4c shows plots of the cone densities from several different human retinae as a function of the distance from the foveal center. The cone density varies across individuals.
Figure 3.5: Calculating Viewing Angle: By trigonometry, the tangent of the viewing angle, \phi, is equal to the ratio of height to distance in the right triangle shown. Therefore, \phi is the inverse tangent of that ratio (Equation e2:viewingAngle).
We can convert these cone sizes and separations into degrees of visual angle as follows. The distance from the effective center of of the eye's optics to the retina is (17 mm). We compute the visual angle spanned by one cone, , from the trigonometric relationship in Figure 3.5: the tangent of an angle in a right triangle is equal to the ratio of the lengths of the sides opposite and adjacent to the angle. This leads to the following equation:
The width of a cone in degrees of visual angle, , is approximately degrees, or roughly one-half minute of visual angle. In the center of the eye, then, where the photoreceptors are packed densely, the cone photoreceptors are tightly packed and their centers are separated by one-half minute of visual angle.
The S Cone Mosaic
Just as the rods and cones have different spatial sampling distributions, so too the three types of cone photoreceptors have different spatial sampling distributions. The sampling distribution of the short-wavelength cones was the first to be measured empirically, and it has been measured both with behavioral and physiological methods. The behavioral experiments were carried out as part of D. Williams dissertation at the University of California in San Diego. Williams, Hayhoe and MacLeod (1981) took advantage of several features of the short-wavelength photoreceptors. As background to their work, we first describe several features of the photoreceptors.
The photopigment in the short-wavelength photoreceptors is significantly different from the photopigment in the other two types of photoreceptors. Notice that the wavelength sensitivity of the L and M photopigments are very nearly the same (Figure 3.3). The sensitivity of the S photopigment is significantly higher in the short-wavelength part of the spectrum than the sensitivity of the other two photopigments. As a result, if we present the visual system with a very weak light, containing energy only in the short-wavelength portion of the spectrum, the S cones will absorb relatively more quanta than the other two classes. Indeed, the discrepancy in the absorptions is so large that it is reasonable to suppose that when short-wavelength light is barely visible, at detection threshold, perception is initiated uniquely from a signal that originates in the short-wavelength receptors.
We can give the short-wavelength receptors an even greater sensitivity advantage by presenting a blue test target on a steady yellow background. As we will discuss in later chapters, steady backgrounds suppress visual sensitivity. By using a yellow background, we can suppress the sensitivity of the and cones and the rods and yet spare the sensitivity of the cones. This improves the relative sensitivity advantage of the short-wavelength receptors in detecting the short-wavelength test light. it is reasonable to suppose that when short-wavelength light is barely visible, at detection threshold, perception is initiated uniquely from a signal that originates in the short-wavelength receptors.
During the experiment, the subjects visually fixated on a small mark. They were then presented with short-wavelength test lights that were likely to be seen with a signal initiated by the cones. After the eye was perfectly fixated, the subject pressed a button and initiated a stimulus presentation. The test stimulus was a tiny point of light, presented very briefly (10 ms). The test light was presented at different points in the visualfield. If light from the short-wavelength test fell upon a region that contained cones, sensitivity should be relatively high. On the other hand, if that region of the retina contained no cones, sensitivity should be rather low. Hence, from the spatial pattern of visual sensitivity, Williams, Hayhoe and Macleod inferred the spacing of the cones.
Figure 3.6: Short-wavelength Cone Mosaic: Psychophysical estimate of the spatial mosaic of the S cones. The height of the surface represents the observer's threshold sensitivity to a short wavelength test light presented on a yellow background. The test was presented at a series of locations spanning a grid around the fovea (black dot). The peaks in sensitivity probably correspond to the positions of the S cones. (From Williams, Hayhoe, and Macleod, 1981).
The sensitivity measurements are shown in Figure 3.6. First, notice that in the very center of the visual field, in the central fovea, there is a large valley of low sensitivity. In this region, there appear to be no short-wavelength cones at all. Second, beginning about half a degree from the center of the visual field there are small, punctate spatial regions of high sensitivity. We interpret these results by assuming that these peaks correspond to the positions of this observer's cones. The gaps in between, where the observer has rather low sensitivity are likely to be patches of and cones. Around the central fovea, the typical separation between the inferred cones is about 8 to 12 minutes of visual angle. Thus, there are five to seven cones per degree of visual angle.
There have been several biological measurements of the short-wavelength cone mosaic, and we can compare these with the behavioral measurements. Marc and Sperling (1977) used a stain that is taken up by cones when they are active. They applied this stain to a baboon retina and then stimulated the retina with short-wavelength light in the hopes of staining only the short-wavelength receptors. They found that only a few cones were stained when the stimulus was a short-wavelength light. The typical separation between the stained cones was about 6 minutes of arc. This value is smaller than the separation that Williams' et al. observed and may be a species-related difference.
F. DeMonasterio, S. Schein, and E. McCrane (1981) discovered that when the dye procion yellow is applied to the retina, the dye is absorbed in the outer segments of all the photoreceptors, but it stains only a small subset of the photoreceptors completely. Figure 3.7 shows a group of stained photoreceptors in cross-section.
The indirect arguments identifying these special cones as cones are rather compelling. But, a more certain procedure was developed by C. Curcio and her colleagues. They used a biological marker, developed based on knowledge of the genetic code for the cone photopigment, to label selectively the cones in the human retina (Curcio, et al. 1991). Their measurements agree well quantitatively with Williams' psychophysical measurements, namely that the average spacing between the cones is 10 minutes of visual angle. Curcio and her colleagues could also confirm some early anatomical observations that the size and shape of the cones differ slightly from the and cones. The cones have a wider inner segment, and they appear to be inserted within an orderly sampling arrangement of their own between the sampling mosaics of the other two cone types (Ahnelt, Kolb and Pflug, 1987).
Why are the S cones widely spaced?
The spacing between the cones is much larger than the spacing between the and cones. Why should this be? The large spacing between the cones is consistent with the strong blurring of the short-wavelength component of the image due to the axial chromatic aberration of the lens. Recall that axial chromatic aberration of the lens blurs the short-wavelength portion of the retinal image, the part cones are particularly sensitive to, more than the middle- and long-wavelength portion of the image (Figure 2.12). In fact, under normal viewing conditions the retinal image of a fine line at 450 nm falls to one half its peak intensity nearly 10 minutes of visual angle away from the location of its peak intensity. At that wavelength, the retinal image only contains significant contrast at spatial frequency components below 3 cycles per degree of visual angle. The optical defocus force the wavelength components of the retinal image the cones encode to vary smoothly across space. Consequently, the cones can sample the image only six times per degree and still recover the spatial variation passed by the cornea and lens.
Figure 3.7: Short-Wavelength Cone Mosaic: Procion Yellow Stains. Biological estimate of the spatial mosaic of the \Blue cones in the macaque retina. A small fraction of the cones absorb the procion yellow stain; these are shown as the dark spots in this image. These cones, thought to be the\Blue cones, are shown in a cross-section through the inner segment layer of the retina. (From DeMonasterio, Schein and McCrane, 1985) % Use figure in Rodieck's review of the primate retina % from DeMonasterio, McCrane, Newlander, Schein Density profile of % blue-sensitive cones along the horizontal meridian of macaque % retina. IOVS v. 26 p. 289-302, 1985 in Rodieck The Primate Retina % 1988 Comparative Primate Biology, V. 4, Neurosciences, p. 203-278 % fig 12. p. 218. In fact, I think one of these might be that one scanned.
Interestingly, the spatial defocus of the short-wavelength component of the image also implies that signals initiated by the cones will vary slowly over time. In natural scenes, temporal variation occurs mainly because of movement of the observer or an object. When a sharp boundary moves across a cone position, the light intensity changes rapidly at that point. But, if the boundary is blurred, changing gradually over space, then the light intensity changes more slowly. Since the short-wavelength signal is blurred by the optics, and temporal variation is mainly due to motion of objects, the cones will generally be coding slower temporal variations than the and cones.
At the very earliest stages of vision, we see that the properties of different components of the visual pathway fit smoothly together. The optics set an important limit on visual acuity, and the cone sampling mosaic can be understood as a consequence of the optical limitations. As we shall see, the and cone mosaic densities also make sense in terms of the optical quality of the eye.
This explanation of the cone mosaic flows from our assumption that visual acuity is the main factor governing the photoreceptor mosaic. For the visual streams initiated by the cones, this is a reasonable assumption. There are other important factors, however, that can play a role in the design of a visual pathway. For example, acuity is not the dominant factor in the visual stream initiated by rod vision. In principle the resolution available in the rod encoding is comparable to the acuity available in the cone responses; but, visual acuity using rod-initiated signals is very poor compared to acuity using cone-initiated signals. Hence, we shouldn't think of the rod sampling mosaic in terms of visual acuity. Instead, the high density of the rods and their convergence onto individual neurons suggests that we think of the imperative of rod-initiated vision in terms of improving the signal-to-noise under low light levels. In the rod-initiated signals, the visual system trades visual acuity for an increase in the signal-to-noise ratio. In the earliest stages of the visual pathways, then, we can see structure, function and design criteria coming together.
When we ask why the visual system has a particular property, we need to relate observations from the different disciplines that make up vision science. Questions about anatomy require us to think about the behavior the anatomical structure serves. Similarly, behavior must be explained in terms of algorithms and the anatomical and physiological responses of the visual pathway. By considering the visual pathways from multiple points of view, we piece together a complete picture of how system functions.
In behavioral experiments, we measure threshold repeatedly through individual and using small points of light as we did the cones. The pointspread function distributes light over a region containing about twenty cones, so that the visibility of even a small point of light may involve any of the cones from a large pool (see Figures 2.11 and 2.12). We can, however, use a method introduced by Y. LeGrand in 1935 to defeat the optical blurring. The technique is called visual interferometry, and it is based upon the principle of diffraction.
Figure 3.8: Young's double-slit experiment uses a pair of coherent light sources to create an interference pattern of light. The intensity of the resulting image is nearly sinusoidal, and its spatial frequency depends upon the spacing between the two slits.
Thomas Young (1802), the brilliant scientist, physician, and classicist demonstrated to the Royal Society that when two beams of coherent light generate an image on a surface such as the retinal surface, the resulting image is an interference pattern. His experiment is often called the double-slit or double-pinhole experiment. Using an ordinary light source, Young passed the light through a small pinhole first and then through a pair of slits, as illustrated in Figure 3.8. In the experiment, the first pinhole serves as the source of light; the double pinholes then pass the light from the common original source. Because they share this common source, light emitted from the double pinholes are in a coherent phase relationship and their wavefronts interfere with one another. This interference results in an image that varies nearly sinusoidally in intensity.
Figure 3.9: A visual interferometer creates an interference pattern as in Young's double-slit experiment. In the device shown here the original beam is split into two paths shown as the solid and dashed lines. (a) When the glass cube is at right angles to the light path, the two beams traverse an equal path and are imaged at the same point after exiting the interferometer. (b) When the glass is rotated, the two beams traverse slightly different paths causing the images of the two coherent beams to be displaced and thus create an interference pattern. (After Macleod, Williams and Makous, 1992).
We can also achieve this narrow pinhole effect by using a laser as the original source. The key elements of a visual interferometer used by MacLeod et al. (1992) are shown in Figure3.9. Light from a laser enters the beamsplitter and is divided into one part that continues along a straight path (solid line) and a second path that is reflected along a path to the right (dashed line). These two beams, originating from a common source, will be the pair of sources to create the interference pattern on the retina.
Light from each beam is reflected from a mirror towards a glass cube. By varying the orientation of the glass cube, the experimenter can vary the path of the two beams. When the glass cube is at right angles to the light path, as is shown in part (a), the beams continue in a straight path along opposite directions and emerge from the beamsplitter at the same position. When the glass cube is rotated, as is shown in part (b), the refraction due to the glass cube symmetrically changes the beam paths; they emerge from the beamsplitter at slightly different locations and act as a pair of point sources. This configuration creates two coherent beams that act like the two slits in Thomas Young's experiment, creating an interference pattern. The amount of rotation of the glass cube controls the separation between the two beams.
Each beam passes through only a very small section of the cornea and lens. The usual optical blurring mechanisms do not interfere with the image formation, since the lens does not serve to converge the light (see the section on lenses in Chapter 2). Instead, the pattern that is formed depends upon the diffraction due to the restricted spatial region of the light source.
Figure 3.10: Sinusoidal Interference Pattern. An interference pattern. The image was created using a double-slit apparatus. The intensity of the pattern is nearly sinusoidal. (From Jenkins and White, 1976.)
We can use diffraction to create retinal images with much higher spatial frequencies than are possible through ordinary optical imaging by the cornea and lens. Figure 3.10 is an image of a diffraction pattern created by a pair of two slits. The intensity of the pattern is nearly a sinusoidal function of retinal position. The spatial frequency of the retinal image can be controlled by varying the separation between the focal points; the smaller the separation between the slit, the lower the spatial frequency in the interference pattern. Thus, by rotating the glass cube in the interferometer and changing the separation of the two beams we can control the spatial frequency of the retinal image.
Visual interferometry permits us to image fine spatial patterns at much higher contrast than when we image these patterns using ordinary optical methods. For example, Figure 2.14 shows that a cycles per degree sinusoid cannot exceed 10 percent contrast when imaged through the optics. Using a visual interferometer, we can present patterns at frequencies considerably higher than cycles per degree at 100 percent contrast.
But a challenge remains: the interferometric patterns are not fine lines or points, but rather extended patterns (cosinusoids). Therefore, we cannot use the same logic as Williams et al. and map the receptors by carefully positioning the stimulus. We need to think a little bit more about how to use the cosinusoidal interferometric patterns to infer the structure of the cone mosaic.
Figure 3.11: Aliasing of signals results when sampled values are the same but in-between values are not. (a,b) The continuous sinusoids on the left have the same values at the sample positions indicated by the black squares. The values of the two functions at the sample positions are shown by the height of the stylized arrows on the right. (c) Undersampling may cause us to confuse various functions, not just sinusoids. The two curves at the bottom have the same values at the sampled points, differing only in between the sample positions.
In this section we consider how the cone mosaic encodes the high spatial frequency patterns created by visual interferometers. The appearance of these high frequency patterns will permit us to deduce the spatial arrangement of the combined and cone mosaics. The key concepts that we must understand to deduce the spatial arrangement of the mosaic are sampling and aliasing. These ideas are illustrated in Figure 3.11.
The most basic observation concerning sampling and aliasing is this: we can measure only that portion of the input signal that falls over the sample positions. Figure 3.11 shows one-dimensional examples of aliasing and sampling. Parts (a) and (b) contain two different cosinusoidal signals (left) and the locations of the sample points. The values of these two cosinusoids at the sample points are shown by the height of the arrows on the right. Although the two continuous cosinusoids are quite different, they have the same values at the sample positions. Hence, if cones are only present at the sample positions, the cone responses will not distinguish between these two inputs. We say that these two continuous signals are an aliased pair. Aliased pairs of signals are indistinguishable after sampling. Hence, sampling degrades our ability to discriminate between sinusoidal signals.
Figure ?? shows that sampling degrades our ability to discriminate between signals in general, not just between sinusoids. Whenever two signals agree at the sample points, their sampled representations agree. The basic phenomenon of aliasing is this: Signals that only differ between the sample points are indistinguishable after sampling.
Figure 3.12: Square-wave aliasing. The squarewave on top is seen accurately through the grid. The squarewave on the bottom is at a higher spatial frequency than the grid sampling. When seen through the grid, the pattern appears at a lower spatial frequency and rotated.
The exercises at the end of this chapter include some computer programs that can help you make sampling demonstrations like the one in Figure 3.12. If you print out squarewave patterns and various sampling arrays, using the programs provided, you can print various patterns onto overhead transparencies and explore the effects of sampling. Figure 3.12 shows an example of two squarewave patterns seen through a sampling grid. After sampling, the high frequency pattern appears to be a rotated, low frequency signal.
Sampling is a Linear Operation
The sampling transformation takes the retinal image as input and generates a portion of the retinal image as output. Sampling is a linear operation as the following thought experiment reveals. Suppose we measure the sample values at the cone positions when we present image ; call the intensities at the sample positions . Now, measure the intensities at the sample positions for a second image, ; call the sample intensities . If we add together the two images, the new image, , contains the sum of the intensities in the original images. The values picked out by sampling will be the sum of the two sample vectors, .
Since sampling is a linear transformation, we can express it as a matrix multiplication. In our simple description, each position in the retinal image either falls within a cone inner segment or not. The sampling matrix consists of rows representing the sampled values. Each row is all zero except at the entry corresponding to that row's sampling position, where the value is .
Aliasing of harmonic functions
For uniform sampling arrays we have already observed that some pairs of sinusoidal stimuli are aliases of one another (part (a) of Figure 3.11). We can analyze precisely which pairs of sinusoids form alias pairs using a little bit of algebra. Suppose that the continuous input signal is . When we sample the stimulus at regular intervals, the output values will be the value of the cosinusoid at those regularly spaced sample points. Suppose that within a single unit of distance there are sample points, so that our measurements of the stimulus takes place every units. Then the sampled values will be . A second cosinusoid, at frequency will be an alias if its sample values are equal, that is, if .
With a little trigonometry, we can prove that the sample values for any pair of cosinusoids with frequencies and will be equal. That is,
(To prove this we must use the cosine addition law to expand the right sides of the following equation. The steps in the verification are left as exercise ?? at the end of the chapter.) \comment{ Make sure this is in the problem section at the end of the chapter }
The frequency is called the Nyquist frequency of the uniform sampling array; sometimes it is referred to as the folding frequency. Cosinusoidal stimuli whose frequencies differ by equal amounts above and below the Nyquist frequency of a uniform sampling array will have identical sample responses.
Experimental Implications
The aliasing calculations suggest an experimental method to measure the spacing of the cones in the eye. If the cone spacing is uniform, then pairs of stimuli separated by equal amounts above and below the Nyquist frequency should appear indistinguishable. Specifically, a signal that is above the Nyquist frequency will appear the same as the signal that is an equal amount below the Nyquist frequency. Thus, as subjects view interferometric patterns of increasing frequency, as we cross the Nyquist frequency the perceived spatial frequency should begin to decrease even though the physical spatial frequency of the diffraction pattern increases.
Yellott (1982) examined the aliasing prediction in a nice graphical way. He made a sampling grid from Polyak's (1957) anatomical estimate of the cone positions. He simply poked small holes in the paper at the cone positions in one of Polyak's anatomical drawings. We can place any image we like, for example patterns of light and dark bars, behind the grid. The bits of the image that we see are only those that would be seen by the visual system. Any pair of images that differ only in the regions between the holes will be an aliased pair. Yellott introduced the method and proper analysis, but he used Polyak's (1957) data on the outer segment positions rather than on the positions of the inner segments (Miller and Bernard, 1983).
This experiment is relatively straightforward for the cones. Since these cones are separated by about minutes of visual angle, there are about six cones per degree of visual angle. Hence, their Nyquist frequency is cycles per degree of visual angle (cpd). It is possible to correct for chromatic aberration and to present spatial patterns at these low frequencies through the lens. Such experiments confirm the basic predictions that we will see aliased patterns (Williams and Collier, 1983).
The L and M Cone Mosaic
Experiments using a visual interferometer to image a high frequency pattern at high contrast on the retina are a powerful way to analyze the sampling mosaic of and cones. But, even before this was technical feat was possible, Helmholtz' (1896) noticed that extremely fine patterns, looked at without any special apparatus, can appear wavy. He attributed this observation to sampling by the cone mosaic. His perception of a fine pattern and his graphical explanation of the waviness in terms of sampling by the cone mosaic are shown in part (a) of Figure 3.13 (boxed drawings).
Figure 1.13: Drawings of perceived aliasing patterns by several different observers. Helmholtz' observed aliasing of fine patterns which he drew in part H1. He offered an explanation of his observations, in terms of cone sampling, in H2. Byram's (1944) drawings of three interference patterns at 40, 85 and 150 cpd are labeled B1, B2, and B3. Drawings W1,W2 and W3 are by subjects in Williams' laboratory who drew their impression of aliasing of an 80 cpd and two patterns at 110 cpd
G. Byram was the first to describe the appearance of high frequency interference gratings (Byram, 1944). His drawings of the appearance of these patterns are shown in part (b) of the figure. The image on the left shows the appearance of a low frequency pattern diffraction pattern. The apparent spatial frequency of this stimulus is faithful to the stimulus. Byram noted that as the spatial frequency increases towards 60 cpd, the pattern still appears to be a set of fine lines, but they are difficult to see (middle drawing). When the pattern significantly exceeds the Nyquist frequency, it becomes visible again but looks like the low-frequency pattern drawn on the right. Further, he reports that the pattern shimmers and is unstable, probably due to the motion of the pattern with respect to the cone mosaic (Helmholtz, Byram and Williams, 1944).
Over the last 10 years D. Williams' group has replicated and extended these measurements using an improved visual interferometer. Their fundamental observations are consistent with both Helmholtz and Byram's reports, but greatly extend and quantify the earlier measurements. The two illustrations on the left of part (c) of Figure 3.13 show Williams' drawing of 80 cpd and 110 cpd sinusoidal gratings created on the retina using a visual interferometer. The third figure shows an artist's drawing of a 110 cpd grating. The drawing on the left covers a large portion of the visual field, and the appearance of the patterns varies across the visual field. For example, at 80 cpd the observer sees high contrast stripes at some positions, while the field appears uniform in other parts of the field. The appearance varies, but the stimulus itself is quite uniform. The variation in appearance is due to changes in the sampling density of the cone mosaic. Cone sampling density is lower in the periphery than in the central visual field, so aliasing begins at lower spatial frequencies in the periphery than in the central visual field. If we present a stimulus at a high enough spatial frequency we observe aliasing in the central and peripheral visual field, as the drawings of the 110 cpd patterns in Figure 3.13 show.
There are two extensions of these ideas on aliasing you should consider. First, the cone packing in the fovea occurs in two dimensions, of course, so that we must ask what the appearance of the aliasing will be at different orientations of the sinusoidal stimuli. As the images in Figure 3.12 show, the orientation of the low frequency alias does not correspond with the orientation of the input. By trying the demonstration yourself and rotating the sampling grid, you will see that the direction of motion of the alias does not correspond with the motion of the input stimulus 1. These kinds of aliasing confusions have also been reported using visual interferometry (Coletta and Williams, 1987).
1 Use the Postscript program in the appendix section to print out a grid and a fine pattern and try this experiment.
Second, our analysis of foveal sampling has been based on some rather strict assumptions concerning the cone mosaic. We have assumed that the cones are all of the same type, that their spacing is perfectly uniform, and that they have very narrow sampling apertures. The general model presented in this chapter can be adapted if any one of these assumptions fails to hold true. As an exercise for yourself, a new analysis with altered assumptions might change the properties of the sampling matrix.
Visual Interferometry: Measurements of Human Optics
There is one last idea you should take away from this chapter: Using interferometry, we can estimate the quality of the optics of the eye.
Suppose we ask an observer to set the contrast of a sinusoidal grating, imaged using normal incoherent light. The observer's sensitivity to the target will depend on the contrast reduction at the optics and the observer's neural sensitivity to the target. Now, suppose that we create the same sinusoidal pattern using an interferometer. The interferometric stimulus bypasses the contrast reduction due to the optics. In this second experiment, then, the observer's sensitivity is limited only by the observer's neural sensitivity. Hence, the sensitivity difference between these two experiments is an estimate of the loss due to the optics.
The visual interferometric method of measuring the quality of the optics has been used on several occasions. While the interferometric estimates are similar to estimates using reflections from the eye, they do differ somewhat. The difference is shown in Figure 2.14, which includes the Westheimer's estimate of the modulation transfer function, created by fitting data from reflections, along with data and a modulation transfer function obtained from interferometric measurements. The current consensus is that the optical modulation transfer function is somewhat closer to the visual interferometric measurements than the reflection measurements. The reasons for the differences are discussed in several papers (e.g. Campbell and Green, 1965; Williams 1985; Williams et al., 1995).
The cones are present at a much lower sampling density, and they are absent in the very center of the fovea. Because they are sparse, we can measure the cone positions behaviorally using small points of light. The behavioral estimates of the cones are also consistent with anatomical estimates of the cone spacing.
The wide spacing of the cones can be understood in terms of the chromatic aberration of the eye. The eye is ordinarily in focus for the middle-wavelength part of the visual spectrum, and there is very little contrast beyond 2-3 cycles per degree in the short-wavelength part of the spectrum. The sparse cone spacing is matched to the poor quality of the retinal image in the short-wavelength portion of the spectrum.
The and cones are tightly packed in the central fovea, forming a triangular grid that efficiently samples the retinal image. Ordinarily, optical defocus protects us from aliasing in the fovea. Once aliasing between two signals occurs, the confusion cannot be undone. The two signals have created precisely the same spatial pattern of photopigment absorptions; hence, no subsequent processing, through cone to cone interactions or later neural interpolation, can undo the confusion. The optical defocus prevents high spatial frequencies that might alias from being imaged on the retina.
By creating stimuli with a visual interferometer, we bypass the optical defocus and image patterns at very high spatial frequencies on the cone mosaic. From the aliasing properties of these patterns, we can deduce some of the properties of the and cone mosaics. The aliasing demonstrations show that the foveal sampling grid is regular and contains approximately 120 cones per degree of visual angle. These measurements, in the living human eye, are consistent with the anatomical images obtained of the human eye reported by Curcio and her colleagues (Curcio, et al., 1991).
The precise arrangement of and cones within the human retina is unknown, though data on this point should arrive shortly (e.g., Bowmaker and Mollon, 1993). Current behavioral estimates of the relative number of and cones suggest that there are about twice as many cones as cones (Cicerone and Nerger, 1989).
The cone sampling grid becomes more coarse and irregular outside the fovea where rods and other cells enter the spaces between the cones. In these portions of the retina, high frequency patterns presented through interferometry no longer appear as regular low frequency frequency patterns. Rather, because of the disarray in the cone spacing, the high frequency patterns appear to be mottled noise. In the periphery, the cone spacing falls off rapidly enough so that it should be possible to observe aliasing without the use of an interferometer (Yellott, 1982).
In analyzing photoreceptor sampling, we have ignored eye movements. In principle, the variation in receptor intensities during these small eye movements can provide information to permit us to discriminate between the alias pairs. (You can check this effect by studying the images you observe when you experiment with the sampling grids.) The effects of eye movements are often minimized in experiments by flashing the targets briefly. But, even when one examines the interferometric pattern for substantial amounts of time, the aliasing persists. The information available from small eye movements could be very useful; but, the analysis assuming a static eye offers a good account of current empirical measurements, This suggests that the nervous system does not integrate information across minute eye movements to improve visual resolution (Packer and Williams, 1992).
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Chapter 1: Preface
Part 1: Image Encoding
Introduction to Image Encoding
Chapter 2: Image Formation
Chapter 4: Wavelength Encoding
Part 2: Image Representation
Introduction to Image Representation
Chapter 5: The Retinal Representation
Chapter 6: The Cortical Representation
Chapter 7: Pattern Sensitivity
Chapter 8: Multiresolution Image Representations
Part 3: Image Interpretation
Introduction to Image Interpretation
Chapter 9: Color
Chapter 10: Motion and Depth
Chapter 11: Seeing
Part 4: Appendix
Introduction to Appendix
Part 5: Teaching Resources
Example Programs
⇧ | Chapter 1: Preface | Chapter 2: Image Formation | Chapter 3: The Photoreceptor Mosaic | Chapter 4: Wavelength Encoding | Chapter 5: The Retinal Representation | Chapter 6: The Cortical Representation | Chapter 7: Pattern Sensitivity | Chapter 8: Multiresolution Image Representations | Chapter 9: Color | Chapter 10: Motion and Depth | Chapter 11: Seeing | Appendix | PART 1: Image Encoding | PART 2: Image Representation | PART 3: Image Interpretation | PART 4: Appendix | Example Programs | Online Teaching Resources |
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