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# Lattices and codes with long shadows

 Title: Lattices and codes with long shadows Author: Elkies, Noam Citation: Elkies, Noam D. 1995. Lattices and codes with long shadows. Mathematical Research Letters 2(5): 643-651. Full Text & Related Files: Elkies - Lattices and codes.pdf (138.3Kb; PDF) Abstract: In an earlier paper we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that 2|(v,w-v) for all v in L; it is known that the characteristic vectors all have norm congruent to n mod 8 and comprise a coset of 2L in L.] Here we use modular forms and the classification of unimodular lattices of rank <24 to find all L whose minimal characteristic vectors have norm n-8. Along the way we also obtain congruences and a lower bound on the kissing number of unimodular lattices with minimal norm 2. We then state and prove analogues of these results for self-dual codes, and relate them directly to the lattice problems via "Construction A". Other Sources: http://www.mrlonline.org/mrl/1995-002-005/index.html http://arxiv.org/abs/math/9906086 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:2961697 Downloads of this work:

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## C Aptitude Questions And Answers With Explanation dracula genealogique

. (65 Questions with Explanation) L.C.M and H.C . To whom this Quantitative Aptitude Test Problems With Answers pdf free download Question and Answers section is .

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C Aptitude Questions and Answers . Answer: 5 4 3 2 1 Explanation: .

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Triangle and its properties - Grade 7 (Question: 1621349452)

If two angles in a triangle add up to $103^0$, then find the value of the third angle.


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My Math Forum Area of a Sector of a Circle

 Algebra Pre-Algebra and Basic Algebra Math Forum

 May 18th, 2009, 12:06 PM #1 Newbie   Joined: May 2009 From: Las Vegas Posts: 21 Thanks: 0 Area of a Sector of a Circle From my textbook: $\frac{\theta}{\theta_1}=\frac{A}{A_1}$ (This I understand) Suppose that $\theta_1= 2\pi$ Then $A_1$= area of the circle = $\pi r^2$ (I don't understand this. How is the area of a sector the same as the area of the circle?)
 May 18th, 2009, 12:32 PM #2 Senior Member   Joined: Mar 2009 Posts: 318 Thanks: 0 The area of the circle is the area of the sector whose angle is "the whole way 'round".
May 18th, 2009, 12:41 PM   #3
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 Originally Posted by stapel The area of the circle is the area of the sector whose angle is "the whole way 'round".
Well that makes sense. I was looking at a picture in the text next to the example; the picture that had, so far, gone with the example. It showed a circle with about a 20 degree angle and I thought they were referring to that illustration.

Thanks for putting up with my "denseness"

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# Now I do all of my own adjustments and I have no plans to change that unless I run into something that's beyond me. Even if that scenario occurs, I still plan to try to learn as much as I can so that hopefully I will be able to take care of any future issues that are related. Mark did a great job for me but I feel that I do a better job adjusting my instruments to my needs.

Sound also factors into this, though I'd argue equipment is less critical than playing technique. But a muffled high-impedance humbucker makes it much harder to bring out the right notes than a twangy Tele singlecoil. And in particular, distortion can quickly make an utter mess out of an only slightly muddy clean signal. So, keep the gain down when playing more chordal stuff, and treble up especially when doing delicate arpeggios etc..
Some great IR's by Redwirez are available for free at their website as some kind of 25th anniversary thing, and if you use windows you can use VSThost as your "DAW" although all it does is host plugins. It's great because it loads so much quicker than a full DAW and doesn't have all the tricky options that just distract you from playing guitar. Like a real amp, it's plug-n-play (after setting it up, of course--- you'll want to set the sample rate to 192khz so that you can get ~8000 samples a sec with oversampling at 4x on each plugin). It can record, too, so it's a really easy, simple solution. Of course, you'll need a real DAW to mix and master.
The American Deluxe Telecaster (introduced in 1998; upgraded in 2004, 2008, and 2010) features a pair of Samarium Cobalt Noiseless pickups and the S-1 switching system. Models made prior to 2004 featured two Fender Vintage Noiseless Tele single-coils, Fender/Fishman Powerbridge piezo system and 4-bolt neck fixing. Other refinements include a bound contoured alder or ash body and an abalone dot-inlaid maple neck with rosewood or maple fingerboard, 22 medium-jumbo frets, rolled fingerboard edges, and highly detailed nut and fret work. The HH model sported an ebony fingerboard, quilted or flamed maple top and a pair of Enforcer humbuckers with S-1 switching (discontinued as of 2008). As of March 23, 2010, Fender updated the American Deluxe Telecaster with a compound radius maple neck, N3 Noiseless Tele pickups and a reconfigured S-1 switching system for wider sonic possibilities. The new model now sports staggered, locking tuning machines, which provide better break angle over the nut for increased sustain and improved tuning stability.
Let's look at how the professionals go about combining the close and ambient techniques we've looked at so far, in order to create specific custom setups for different recordings. Joe Barresi, for example, relies heavily on the trusty SM57 and MD421 combination, but he'll choose from a variety of other mics to give character to particular sounds. "The two microphones I use most for recording electric guitars are the Shure SM57 and the Sennheiser MD421, often both, close up, placed at the edge of the speaker, where the speaker centre meets the cone, or, if I'm looking for a more bright sound, dead centre. When I want more low end, I may have an AKG C414 on there, and when I'm after a little more personality, a Neumann U87, backed up a foot, or a ribbon mic, like the Royer 122, or an RCA BK5 or 77."
Orville Gibson founded the company in Michigan and stayed a family business until the early 50's. Ted Mcarty ran the company from 1951 or so, and is the "father" of most successful Gibson electric guitars, the Les Paul, the SG, Explorer, Flying V, ES-335 and so on.. In the late 60's Gibson was bought by the Norlin Corp, who mainly were known for making refrigerators. Most feel Gibson adopted a quanity over quality approach to guitar making during this period and 1970's to 1980's Gibson electrics are considered less desireable by most guitar collectors, and considered outright junk by many others.. Cosmetic changes to Gibson models during that period apparently reflect the poor taste of the buying public during that era... and while a 1974 Gibson SG may look ugly compared to the classic 1961 or 1968 models, please remember this was the era of ployester liesure suits and Chrysler Cordobas.. In 1986 Gibson was bought by a group who understood guitar making, and is a privately held company to this day. Gibson quality has appeared to improve steadily from 1987 to present day, but it seems to be unanimous that todays models do not approach the craftsmanship of the late 1950's when Gibson apparently peaked.

## In 1883, a german immigrant named Frederic Gretsch started a small instrument manufacturing company in Brooklyn, New York. On a trip to visit home in 1895, he died unexpectedly, leaving the company in the hands of his 15-year-old son, Fred. The company flourished for generations, especially due to the popularity of their hollow body guitars with rockabilly, blues, and jazz musicians. In 1967, however, the brand began to falter after the Gretsch family sold to then music industry giant Baldwin. In 1985, Fred W. Gretsch bought the company back from Baldwin and began restoring it to its former glory – coinciding with the rise of one of their most prolific artists, Brian Setzer of the Stray Cats. Today, their guitars, like the USA Custom Shop White Falcon pictured above, are used by a wide array of musicians from all walks of life, including Billy F. Gibbons of ZZ Top, Tim Armstrong of Rancid, Band of Skulls, and Portugal. the Man.

Anyway, as the Strat-style guitars have three pickups, the selector switch works like this: all the way to the left (relative to the Jimi pic) would limit the guitar’s output to the sound of the neck pickup. One position to the right will blend the neck pickup with the middle pickup. Put the switch in the middle, and you’ll get just the sound of the middle pickup, as you may have guessed. The next position will blend the middle and bridge pickups, and all the way to the right, it’s all bridge pickup.
Solder the electronics. The pickups you purchased should come with a schematic that shows exactly how to connect these to the controls and to the input for the guitar cord. Follow this schematic, using an ordinary electronics soldering iron to complete the job. Wrap any wiring connections with electrical tape, unless the manufacturer’s instructions suggest another method.

I have a Vox Shadow that's sunburst, white pick guard that surrounds 3 solid chrome face pickups and the middle pick up has "VOX" engraved in it. 3 seperate volume controls and a master volume control. Tuning keys are all chrome, and the green decal on the face of the headstock reads Shadow, JMI Dartford, Kent. Neck is attached withthe help of a chrome plate, on the back side of the 'plank' body is an access plate for the jack that states made in England. Guitar also has the original roller/tremelo tail piece with palm lever. The numbers of 64728 are stamped on the back side of the headstock just below the tuning keys. Finish is beginning to crack a bit but it's all original, right down to the volume pots that have to be cleaned from time to time. It must be a rather unknown line that Vox had as I can't find out much on it either. Had this guitar for many years. Was handed to me in pieces in an old 'cardboard' case, (that has since gone away) put it back together and added it to my "music room".

Even cheaper (abour $40) is the Behringer Guitar Link (review: Behringer Guitar Link UCG102 USB Interface Review). One nice thing is the long cord.. you can sit a ways away from your PC without needing an extender, and like the line 6, it’s also got a headphone output. They offer some guitar effects software as well, via download, and a basic DAW program. Worth checking out, as this does check every basic box for forty bucks. I have not used this, but I have used other Behringer audio interfaces. Cheap, basic, but they do include ASIO drivers (read ahead). ###### Playing power chords right up at the ‘dusty' end (past the 8th fret) gets difficult, because the frets are so close together. In the next stage we'll learn how to play power chords with a fifth-string root too, which solves that problem. However, it's important not to rush ahead, so make sure you put your effort just into the sixth-string root chords for now. Searching 'guitar' on YouTube, Google, etc can be overwhelming. Ten billion results come up. I wish we could just be nice to kids with questions. I noticed this answer mentioned "pickups" several times. Kid probably has no idea what a pickup is. My brother showed me the switches, pickups, and explained them to me in five minutes, in person on a real guitar. It was like being taught magic. It comes with a single coil pickup in the neck position and a humbucker at the bridge - switching between the two pickups gives you both a strat like sound and an LP like tone. The pickup selector is 3-way so you can play with both pickups at the same time. It sports a shorter 24.75" scale length and smaller 12" radius on the rosewood topped mahogany bolt-on neck with a 1.6875" nut width making it very playable and accessible to guitarists of all levels of experience. Many customer reviews suggest the Empire HG feels and plays like a more expensive guitar. The simplest way to explain modulation effects is that they make a copy of the original signal, modify the copy in some way, and then mix the original and the copy back together. The result is sort of like a pitch-shift taken to the next level, where instead of simply adding new notes or varying the fundamental, they can create entirely new sounds altogether. Here are the usual suspects of modulation effects: I signed up for the Free GuitarTricks Trial and the first lesson that I checked out was titled something like “Blues Style Level 2 – How B.B. King Starts The Blues”. You wouldn’t believe it. Shortly after starting this lesson I felt that my playing sounded the way it should be sounding. It sounded kind of the same as how B.B. King sounded. I was over the moon. This was simply an amazing experience and I never looked back. Today I am almost sure that I would probably be a Rock Star today if Guitar Tricks would have been around 20 years earlier ;-). Maybe it's time for you to start to think about what is comfortable for you to play. 10-46 is probably the most standard size used by players. Although, I'd put money on the fact that your Mockingbird came with 9s. Mine did, and they were the first things to go (very fast, but too floppy). While there is some merit to staying with 9-42 for familiarity's sake, making the move to a 10-46 set should be pretty easy to do while you're still learning.  I'm no musician, know very little about guitars, but I think I stumbled on to a great deal. The predicament we faced last Christmas was that my two nieces, ages just 7 and 5, both fell in love with a toy "music" setup consisting of a plastic "guitar" and a fake microphone. I won't say the famous girl-toy-brand name it was marketed under but it was pretty much a collection of junk. The "guitar" had a few buttons on it to make noise... it would have been broken and tossed away inside of a week. And here in Costa Rica - a price of 34,000 colones or roughly$70!
Guitar scales free movie. Guitar Scales This lesson covers the basic ways to play chromatic scales on the guitar. Guitar scale reference - Here is a listing of some basic fingerings for many games. GUITAR SCALES guitar chords guitar scales chord progressions Search our collection of guitar scales, with charts and music playback jam contacts chord name reverse scales metronome forums tuner. Guitar Scales: Lookup guitar scales on

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I have a Fender Chinese made Telecaster from the Modern Player Series. The finish is spectacular, and while it sometimes feels like they just used a lot of gloss to cover it, it plays and sounds well. I have played it through many amps and it does the job of both a Telecaster and a Strat style. With a humbucking pickup, a lipstick and a strat pickup, this is a satisfying guitar and moddable for people looking for something they can work on without fear of screwing up and wasting a thousand dollars.
Several producers like to create larger-than-life recorded sounds by splitting the guitarist's instrument signal to several different amps, which are then recorded simultaneously. Joe Barresi is a devotee of this tactic, and uses a dedicated guitar splitter box, such as the Little Labs PCP Instrument Distro or Systematic Systems Guitar Splitter, for the purpose. "In choosing the amplifiers and speakers, it's important to remember that larger speakers give a more compact, tighter sound. A tiny amp turned all the way up will give a more blown-out sound."

The custom pickup for the AZ was developed in collaboration with Seymour Duncan. The pickups feature a moderate output through Alnico-5 magnets to keep the clarity of the fundamental tone when using a distortion sound, and to deliver a clear pick attack. From treble to bass, and from high-E string to low-E string, the overall tonal balance is evenly adjusted, and works well with various effect pedals.
This list kind of blows. There are no greatest guitarists. And I hate how people think guitar is sickly limited to rock guys who in the whole scheme of things are pretty amateur. How about Eric clapton? Heck if Charlie Christian or django rhinehardt had never started playing solos guitar would still be a strict rhythm instrument playing crotchets to emphasise the beat. He had 2 fingers and did more for the guitar than anyone on this list? Especially Tom Morello? How about pat methany, wes Montgomery, pat martino, tal farlow, JOHN MCLAUGHLIN, george benson? Listen to any of those guys and it will completely redefine your thoughts on the guitar. It can so easily be intelligent and soulful simultaneously…
There are two main types of amplifier: valve and solid state. Solid state guitar amplifiers tend to be cheaper and lighter, but they don't offer as good a sound as valve amplifiers. Valve ones, on the other hand, have working parts, so they're a little more maintenance heavy. Most serious musicians go for valve amplifiers due to the superior sound and lower wattage requirements.
Bottom Line: The Zoom G3X is everything a guitar multi-effects pedal should be, and then some. As strange as it sounds, as we researched what owners of this pedal are saying about it, it was difficult to find any outright negative comments (any negative feedback tends to be centered around the notion that digital multi-fx don’t sound as good as individual pedals, which is a hotly debated topic). You have to consider how amazingly low the G3X price tag is versus how many features it packs in. It’s not the best in the world at any one thing - the looper isn’t as good as a TC Electronic Ditto, and the delays might not match up to a Strymon - but it does a lot of things quite well, and the user interface is such a pleasure to use. The Zoom G3X will be your best friend if:
I’m not a Fender amp guy at all. I know, a lot of people swear by them, and they do sound great, and are a standard in the indie world. They tend to have less options and features that a beginner might want to play around with, and to get those options you end up spending more money than you might be comfortable with. You also don’t get much horsepower for the cash compared to some of the other lower priced options. To me, a cheap Fender sounds like…a cheap Fender. Blues guys sure do love those Mustangs though.

Now we’ve moved away from the three ‘main’ shapes of steel-strung acoustics, we start looking at the off-shoots and variants which exist to give players even more options and opportunity to find the guitar which is exactly right for them. First among them is probably still well-known and identifiable in itself; the round-shoulder dreadnought. Again, these are largely Gibson-led creations, and include among their ranks the famous J-45 style famously employed by the Beatles and Noel Gallagher.
Onboard effects had already appeared on various guitars, especially Höfner and Vox models, but these were not truly “active” in the modern sense. Alembic, with support from the Grateful Dead, was exploring active pickup systems, but these were still basically custom-made instruments. Both had a master volume and tone control with three-way select and a “band rejection filter tone switch,” also called a midrange bypass filter. Ovation was among the first to offer linear potentiometers to correlate movement with effect. Controls inside were mounted on a circuitboard with individual trim pots that can be adjusted to control the volume of each pickup.
If you can afford to go to a store and drop $3000 on the latest, greatest Les Paul Gibson or vintage Fender Stratocaster, this is a very different question. But let’s assume your budget isn’t quite that big. Many affordable guitars are very similar, but come in a variety of packages that include lots of extras and even an amplifier. In case you are looking to buy the amp separately, here is an amazing list of 10 Best and Affordable Guitar Amps for Beginners: 2016 and while you are it, check out: Top 5 Guitar Plug-Ins You Need to Know: AmpliTube, Guitar Rig & Others. Basic Guitar chords and signatures. Find and save list of chords. Basic guitar chords A sheet of the most used rock chords. Suitable for beginners. Empty chord sheet All about how to play guitar chords and guitar chord charts. Once you finished the free online guitar lessons you know all there is to know about guitar. Music guitar tabs archive with over guitar chords for guitar, keyboard, banjo and viola, tabs for guitar, bass, drums, guitar note The first part of this book shows why Guthrie is such a great player, and dives into his mindset when it comes to teaching and playing. I really believe you should go buy this book, so I don't want to give too much away, but he covers great topics like how to avoid guitar injuries, setting goals for yourself, thoughts on technique, tone and gear, and general tips on how to practice. Ukuleles were in highest production from 1916 to the 1930's, though still manufactured in quantity until 1965. Production quantities during some periods were as great as Martin guitars. Martin ukes are considered to be the best for craftsmenship and sound. The Koa wood models are more collectible than mahagony models. The fancier style 5 models are worth more than plainer styles 0 to 3. All sizes are collectible. ok thank you so much! Unfortunately, it’s not as loud as the other single coils of my strat. I tried splitting to the other coil but doesn’t split. I followed the wiring diagram bit by bit. =( Thank you so much for responding right away. I’m a session musician here in our country and this is actually my first time to mod my guitar. Thank you so much! I became more and more frustrated with as my playing did not mach my ambitions at all. I tried to listen to records to figure out what was being played. I tried to come up with the proper techniques on how to play the riffs that I could hear. I tried to make my guitar and my playing sound the way it should. But, even after long hours, it always felt like I did not quite get there. What I really wanted, was to be a Rock Star!The written music available in the music stores was expensive and incomplete. There was nobody around who could make me understand what a power chord was, how to mute individual strings while letting others ring. I was locked in my open chord basic folk guitar strumming background. I knew that I needed a totally new approach to become the lead, riff and chops playing blues pop and rock guitar player I wanted to be. And there was no way that I could see how to simply snap out of my predicament……. Two new 325s were created for Lennon and were shipped to him while The Beatles were in Miami Beach, Florida, on the same 1964 visit to the US: a one-off custom 12-string 325 model and an updated six-string model with modified electronics and vibrato. He used this newer 6-string model on The Beatles’ sequentially “second” appearance on The Ed Sullivan Show.[7] ##### On PremierGuitar.com, "Sponsored Content" refers to articles, videos, or audio recordings that are produced or curated by an advertiser but that Premier Guitar is happy to share alongside our own editorial content due to the Sponsored Content’s educational, musical, or entertainment value. Sponsored Content is clearly labeled everywhere it appears, and Premier Guitar's editorial department has no involvement in its creation. Absolutely love this guitar!! One great instrument for a great price. Ordering was easy and delivered before projected date. I am no professional by any means, but as I've progressed, I wanted a guitar I could grow with and play for years to come. This is it!! I've played a lot of acoustics ranging from Gibson to Taylor but absolutely love this Martin. The action is like butter and coming from the Martin collection, the sound and tone is at a minimum of FANTASTIC!! If you are looking for an outstanding piece of musical magic to add to your collection, or something to purchase to have for a lifetime without spending your life savings to obtain it, this is the one you are looking for. Reverbs and delays can sound particularly unruly when run into an amp set dirty. If you use natural amp distortion but still like using pedals, you can run some effects into the front of your amp, and run time-based effects into an effects loop (most modern amps with channel switching will have an effects loop). Some modern programmable pedals, such as the TC Nova System or Eventide Time Factor delay, allow you to switch between -10 and +4 operation, so you can use them in front of your amp at the instrument level or at line level in an amp effects loop. This is really handy, allowing you to create and store presets tailored for using the pedal either in front of the amp or in the loop. Of course you can also use studio-type rack effects in amp effects loops. Units such as the Fractal Audio Axe FX and TC Electronic G-Major work great in this configuration, allowing you to store many presets and get pristine time-based effects, whether you are using clean sounds or dirty sounds. Other unique features of this wonderful guitar are the 70’s styled headstock logo which effectively rounds out the look of this American instrument very nicely. Weighing just 7.2 pounds, the guitar is of pure single coil bliss! It sounds great as all Teles do and it plays like a dream. For every guitar lover, this is a true workhorse instrument to get. Some of the best pedals in this segment, like the TC Electronic Sentry, will allow you to set both the volume threshold where the noise gate kicks in, and the type of interference you want to filter out. The important thing to remember about noise gate pedals is that they only eliminate hissing when you don’t play. As soon as you do, the pedal disengages and the noise comes back. With that said, noise gate pedals are essential for a good tone.  A tung oil-finished rock maple neck, and a slightly more curved fretboard radius of 13.75 inches are the other small modifications to the ‘speed’ features on the MD200. However, it has a thinner bolt-on neck as compared to the MD400’s wider mahogany set neck. That said, both neck profiles remain a shallow “C” shape, and the guitars’ dramatically beveled cutaways give you ample room to reach the high notes. On the forum there are thousands of people at all stages of playing that can offer advice on new beginner guitars. I have to admit that I play pretty much only top-end gear and don't know the latest on all the new budget guitars, but on the community forum there are people learning that can all give you advice based on personal experience, and there's no substitute for that! Time to turn our attention back to the guitars themselves. The following are some of the better low-cost electric guitars available on the market today; refer to an anatomy of electric guitars to see definitions of guitar pieces and places. When you're deciding, go to a store and try them out for heft, comfort, stability, sound quality, and appearance. Shop around, comparing, for instance, online prices against local store prices. This is an investment, so choose wisely. A classic Western guitar from the Far East, this Vintage Global guitar was made in Japan sometime in the 1960s and imported for Sears and Montgomery Ward department stores. It's got a swell pick guard with a honeysuckle blossom and a hummingbird and an ominously undecorated fretboard that has absolutely no dots or markings whatsoever. Other features of the Vintage Global guitar include a snazzy sunburst finish, classic imitation wood inlay decorative sound hole decal, and cheap white plastic tuning knobs. This classical acoustic guitar has absolutely nothing in the way of "warm tones" or any other term typically used to describe finely crafted stringed instruments. Instead, it has a distinctive sharp and rumbly quality that is great for recording or live applications where a "lo-fi" sound is desired. This Global guitar has decent action and is easy to play. Speaking from experience, it really cuts through the other tracks in recording and adds a humble trashy sound while staying in tune and functioning like a normal, decent quality guitar. The Vintage Global guitar showed signs of moderate use and had a number of nicks and scratches around the edges. The hummingbird pick guard had some scratches / wear in the black glossy surface near the very top corner, but otherwise was in excellent condition. The neck was straight and the guitar had no cracks or other serious bodily damage. Body measures 17 /2 inches x 14 inches x 3 1/2 inches. Neck measures 16 1/4 inches in length from nut to end (minus headstock) and is 2 3/8 inches at widest point. This Global Hummingbird Guitar sold and is probably making beautiful music on the other side of the country, but lots or really cool-looking vintage Global guitars can be found on eBay. Guitar Tricks is a step-by-step learning system that’s designed to make learning guitar easy. The Guitar Fundamentals level 1 training curriculum has been totally reworked, improved and only recently re-released. Nothing else is as beginner-friendly as Guitar Tricks. In addition to working your way through the fundamental lessons of the Core Learning system you can explore great songs arranged with beginners in mind. Chorus and flanging are created in fairly similar ways, the main difference being that chorus doesn't use feedback from the input to the output and generally employs slightly longer delay times. Phasing is similar to both chorus and flanging, but uses much shorter delay times. Feedback may be added to strengthen the swept filter effect it creates. Phasing is far more subtle than flanging and is often used on guitar parts. With chorus, phasing and flanging, the delay time, modulation speed and modulation depth affect the character of the effect very significantly. A generic modulated delay plug-in allows you to create all these effects by simply altering the delay time, feedback, modulation rate and modulation depth parameters. Most of the time, low modulation depths tend to work well for faster LFO speeds (often also referred to as the rate), while deeper modulation works better at slower modulation rates. Stimson’s basic pickup design was used on most of National Dobro’s subsequent electrics, however, by around 1935 or so, when Supro arrived on the scene, the pickup had been modified to have a single coil wrapped around the two bar poles. Nevertheless, virtually all of National Dobro/Valco pickups were evolutionary descendents of this Stimson pickup. How are we supposed to choose an Ibanez model? Well, here’s what we went with. Made out of mahogany with a vintage look to appease the masses, the Ibanez Roadcore RC365H offers a retro feel with a modern sound. The f-hole on the lower part of the guitar creates a deep and rich resonant sound, while the neck contains an RC bolt that adds both warmth and depth to the notes. Due to the stringing throughout the body and an improved bridge, tuning becomes easier while switching through progressions, while the rosewood fingerboard presents both style and comfortability. The highly touted feature on this guitar is the custom designed Core-Tone pickup, reducing additional hum and reverberation for clarity in tone. With various tones provided by a three-way selector, this electric guitar offers high-quality features while maintaining a classic rock-and-roll vibe.  The SS-4L was almost identical in electronics and other appointments to the SD, with the main differences being in body shape, vibrato and pickups. The body was more like a Strat, except the entire lower horn was lopped off and slanted toward the lower bout. Very, very… well, this is one of those ideas that’s so ugly it becomes beautiful! This had a new, very nifty vibrato system, one of the coolest the Japanese ever produced. This consisted of a plate or platform resting on springs, sitting above the top of the guitar. This then had a metal block with several holes along the treble side, into which the arm was inserted and secured with a thumbwheel screw. The SS-4L had two-tone metal-covered pickups with six poles along the rear edge, two half-slots exposing a gold insert in the center and six holes showing the insert along the front edge. These “two-tones” would become a mainstay of many early ’60s Teiscos. These guys are the best in town! I had my Gretsch 6120 Upgraded with a new Pickup. They were quick and at a reasonable price. They do amazing work. They also have a great selection of guitars and Amps for sale. I highly recommend stopping by. If your looking for a new guitar for yourself or your kids they will help you find the perfect guitar for your price range. I highly recommend stopping by. They also do amp repair! Stop by and see for yourself. Similar to Jackson guitars, B.C Rich is famous for their sharp jagged edges and heavy metal sounds. The influence of their hard rock and heavy metal sound spans decades. Bands such as Motley Crue and Slayer are just a few of the bands that made B.C Rich guitars such a huge staple in the world of heavy metal. When you see the shape of B.C Rich guitars, there is no doubt as to what kind of music is going to come from them. B.C Rich offers a decent selection of guitars ranging from beginner up to pro-level instruments. They even have models that don’t have that signature “heavy metal” jagged style. Most B.C Rich guitars have a mahogany body and at least some of the components are made from rosewood. Obviously, the quality depends on the price, but even their highest priced models could still use a few upgrades to really bring up the sound quality. Designed to restore Fender’s reputation after a group of employees led by William C. Schultz took over ownership from CBS in the early 1980s. The pickups used in early models were dual humbucking Red Lace Sensors in the bridge position and a single Blue Lace Sensor in the neck position. Later models (post 1995 or so) used three Gold Lace Sensors or a Red/Silver/Blue set in a Strat-like configuration, as well as low-friction roller nuts, locking synchronized vibrato bridge and tuners, and a bound contoured alder body with ash veneers. These instruments were discontinued in 1998 with the advent of the American Deluxe series. In 2011 Fender released the Modern Player Telecaster Plus as a part of the Modern Player series. The guitar has a humbucker in the bridge, a Strat pickup in the middle, and a Tele pickup in the neck positions. The first thing is to adjust height. If you have the first type, you will need a flathead screwdriver. The two posts holding the bridge have flat slotted heads showing at either end. You can turn these clockwise to lower the strings or counter-clockwise to raise them. Find the string height that suits you. For an electric guitar, it will be about 1/4" off of the neck or lower. Get the strings as low as you can for comfort, but be careful that your frets don't start buzzing or that the strings are not coming into contact with pickups or any other parts. If this happens, your strings are too low. If the bridge is the second type, you will need a very narrow Allen wrench to adjust the saddles; you will find the Allen heads on either side of the saddle top. Of course, the big news was the introduction of the Spectrum 5. This had a slim, highly contoured body with a pointed upper horn pointing up and a hooked lower horn. The body featured a German carve relief along the edge. The head was the new hooked kind from ’64-65, while inlays were triangular “picks,” sort of like Kays of the time. Pickguards were two-part plastic covering the entire area under the strings, with volume and tone controls and stereo and mono jacks. The “vegematic” push-buttons came in five groovy colors. #### Replace components. From plugging in and unplugging my guitar so much, the stock input jack lost its grab. So I had an extra Radioshack one lying around, and I soldered it in. Now all my cords are held tight. I also had a problem(common with Teles as I understand it) with my input jack "cup" coming out with wires and all. Once you take a look at how it's held in there, it's an easy fix. Frets are the metal strips (usually nickel alloy or stainless steel) embedded along the fingerboard and placed at points that divide the length of string mathematically. The strings' vibrating length is determined when the strings are pressed down behind the frets. Each fret produces a different pitch and each pitch spaced a half-step apart on the 12 tone scale. The ratio of the widths of two consecutive frets is the twelfth root of two ( {\displaystyle {\sqrt[{12}]{2}}} ), whose numeric value is about 1.059463. The twelfth fret divides the string in two exact halves and the 24th fret (if present) divides the string in half yet again. Every twelve frets represents one octave. This arrangement of frets results in equal tempered tuning. The original Fender Mustang is something of a cult classic. It was loved by alternative bands and players - including Kurt Cobain - in the '90s for its short scale, affordability and potential for modding. The Bullet Mustang is the most affordable version of the model yet. In keeping with Squier’s other entry-level models, it features a basswood body, which gives it an incredibly lithe, lightweight feel. This, combined with its 24-inch scale length, makes it a great choice for beginners. The two humbuckers are the most obvious departure from the original, providing angular grit in the bridge position and a pleasing, earthy warmth in the neck. The bolt-on maple neck and six saddle hardtail bridge feel reassuringly rigid, while the tuners did a sterling job in our tests of holding their pitch without too much hassle. The volume and tone knobs, often a clear indicator of quality control in budget guitars, are installed firmly enough with no evident wobble, while the pickup selector switch is angled so it won’t get knocked if your playing becomes too... ahem... enthusiastic. Meanwhile, the 12-inch radius, rosewood ’board is pancake flat and makes string bends simple for even the most sausage-fingered player. The C profile neck is also extremely comfortable to hold, while the satin finish makes fretboard-spanning licks a doddle.$149/£120 is practically peanuts to spend on a new guitar. For Squier to cram in the features it has, with the overall levels of build quality on display, is seriously impressive.
Half a step down from standard tuning. Used by bands/artists such as: Jimi Hendrix, Coheed and Cambria, Black Sabbath, Motörhead, Cannibal Corpse (Chris Barnes era), Nirvana, AFI, Rise Against, Failure, Weezer, Green Day, Kiss, The Hellacopters, Backyard Babies, Guns N' Roses, Neil Young, Van Halen, Brand New, Blind Guardian, Metallica (on the "Load", "Reload" and "Garage Inc." albums, "The God That Failed" and in live performances of standard tuned songs since 1995), AC/DC (some songs and in live performances of standard tuned songs since 2008), Slayer, Alcest, Rage Against The Machine, Stevie Ray Vaughan, Yngwie Malmsteen, Alice in Chains, The Smashing Pumpkins, The Killers, Relient K, Suede, RED on "Not Alone", Beach House, Third Day (on "I Can Feel It"), Die Ärzte (since "Geräusch") Skillet (on "A Little More"), and Vertical Horizon, Tyler Bryant & the Shakedown.
Volume pots are wired as simple voltage dividers. Higher settings have higher resistance to ground and lower series resistance, so more signal passes through. When maxed, volume pot has zero series resistance and full pot resistance to ground. Signal takes the path of least resistance and most of it will go though. However, some signal, mostly treble will be lost. With low pot values (250K) it will be more noticeable than with higher (500K and 1M) pots. That’s why typical pot values for brighter single coil pickups is 250K and for warmer humbuckers 500K or sometimes even 1M.
Nor were Decca guitars made for or marketed to children. They were made at the same factory that made Teisco, Teisco del Rey, Kingston, Heit, Kawai and other brands of guitars. Some of these are quite decent beginner's instruments, and some are just flat out interesting/weird. No, they're not the same quality of a Gibson, Fender or Burns guitar from the same period, but they also cost a fraction of one of those guitars. And coincidentally, Fender guitars nowadays are largely made in Indonesia, China and Korea, places that *wish* they could make things as well as they can in Japan, so chew on that before you slag on Japanese-made guitars.
If you are looking for a simple and old school way to spice up your guitar sound, tremolo is a great option. Tremolo lowers the amplitude of your signal at a regular rate. It's like having a machine move your volume knob back and forth rhythmically, and it's one of the first effects that were built into early amplifiers. While simple in concept , tremolo adds a great movement to you tone, in either a subtle or intense way. The choice is yours. On low settings, a pleasant motion effect can add some ear candy to your tone. Set on high, a “stutter” or “chop” effect can add emphasis to a song or riff. Some pedals will even split the repeats in stereo, which adds a genuine vortex to your tone.
@BLAKTORX - Charvel is a great brand for metal and shred that is really starting to regain some prominence in the music world. I really like the Pro Mod Series. Music Man, too, makes some good gear, but I tried to keep my list to 10. The Ibanez GIO series guitars are good for beginners. Seems like you're into metal. In that price range you might also check out the Jackson JS Series.
That would work, of course, but the result would be very different. You’d have minimum cut in the center position, with treble cuts of differing size in either direction, depending on the caps’ values. I’m not sure that would be particularly useful — the activity would be the same in either direction up to the point where the value of the greater cap kicks in. (I suppose one advantage would be that you could leap quickly to two “preset” values by turning the pot to minimum or maximum, as if you’d installed to caps on a DPDT switch, as seen here.) Or course, you’d have to worry about centering the pot, unless you could can find a part with a center detente. The resonant peaks, and therefore the overall tone, differ from standard. HOW exactly they differ is one of the things that I’m going to explore. 🙂
The Yamaha LL16 gives you high-end features for a lot less money, starting off with its solid Engelmann spruce top and solid rosewood back and sides. This all solid body results in richer and more detailed acoustic tone, something that you will have to pay top dollars for from other acoustic brands. It also sports a slightly smaller body that gives it an elegant appeal, adding to its already favorable affordable price and top-tier specs.
These electric guitar tone tips from Guitar Control are money saving and time saving tips you can use to create great guitar tone without investing in anything other than the guitar you already own. Your volume control, your tone control, and your switches are a wealth of guitar sounds. Also, the way you play your guitar -- the dynamics. All of these elements can be used separately or together to build guitar tones into any of the solos you play. This is an awesome lesson for beginners because you can put these tricks to work immediately to get the results you’re looking for, and if you’re short on cash, these guitar tone tips will allow you to express yourself with tone without having to spend money.

Although they just released the Gibson 2016 line, Gibson's first production electric guitar, marketed in 1936, was the ES-150 model (“ES” for “Electric Spanish” and “150” reflecting the \$150 price of the instrument). The ES-150 guitar featured a single-coil, hexagonally shaped pickup, which was designed by Walt Fuller. It became known as the “Charlie Christian” pickup, named for the great jazz guitarist who was among the first to perform with the ES-150 guitar. The ES-150 achieved some popularity, but suffered from unequal loudness across the six strings.


text:
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

The tolower() function returns an error where it can’t map to the Unicode character set of the input data – a common occurrence when analysing social media data with emoticons.

Emoticons are those symbols that are commonly used on mobile phones but aren’t always recognised on all platforms.

For example, when converting tweets to @delta (Delta Airlines), I got the following error:

Error in tolower(text) :
invalid input '@ActualALove: First time I've seen a foot-rest in first class! Oh @Delta, how I love thee \ud83d\ude0a✈\ud83d\udc78 http://t.co/noKI9CiM' in 'utf8towcs'

When I looked up the actual tweet, it looked liked this.

The two unicode characters that weren’t recognised were \ud83d\ude0a (SMILING FACE WITH SMILING EYES) and \ud83d\udc78 (PRINCESS).

Gaston Sanchez has posted a solution to this problem in his blog Data Analysis Visually Enforced. I’ve used the code and it works well. When I have time, I’ll extend it to replace the offending characters instead of returning NA for the entire string.


text:
# OptimizerMonitor#

class composer.callbacks.OptimizerMonitor(log_optimizer_metrics=True)[source]#

Computes and logs the L2 norm of gradients as well as any optimizer-specific metrics implemented in the optimizer’s report_per_parameter_metrics method.

L2 norms are calculated after the reduction of gradients across GPUs. This function iterates over the parameters of the model and may cause a reduction in throughput while training large models. In order to ensure the correctness of the norm, this function should be called after gradient unscaling in cases where gradients are scaled.

Example

>>> from composer import Trainer
>>> from composer.callbacks import OptimizerMonitor
>>> # constructing trainer object with this callback
>>> trainer = Trainer(
...     model=model,
...     optimizers=optimizer,
...     max_duration="1ep",
...     callbacks=[OptimizerMonitor()],
... )

The metrics are logged by the Logger to the following keys as described below. grad_l2_norm and layer_grad_l2_norm are logged in addition to metrics logged by the optimizer’s report_per_parameter_metrics method. For convenience we have listed the metrics logged by DecoupledAdamW below.

Key

Logged data

l2_norm/grad/global

L2 norm of the gradients of all parameters in the model on the Event.AFTER_TRAIN_BATCH event.

l2_norm/grad/LAYER_NAME

Layer-wise L2 norms

l2_norm/moment/LAYER_NAME

Layer-wise L2 norms of Adam first moment after

calling optimizer step.

l2_norm_ratio/moment_grad/LAYER_NAME

Layer-wise ratio of the gradient norm to the moment norm after calling optimizer step.

cosine/moment_grad/LAYER_NAME

Layer-wise cosine angle between gradient and moment after calling optimizer step.

l2_norm/param/LAYER_NAME

Layer-wise L2 norms of parameter weights

l2_norm/second_moment_sqrt/LAYER_NAME

Layer-wise L2 norms of the square root

of the Adam second moment is.

l2_norm/update/LAYER_NAME

Layer-wise L2 norms of the step

cosine/update_grad/LAYER_NAME

Layer-wise cosine between the gradient and the step

l2_norm_ratio/update_param/LAYER_NAME

Layer-wise ratio between step size and parameter norm


text:
# Pyramid (geometry)

Known as: Snub tetrahedral pyramid, Oblique pyramid, Decagonal pyramid
In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle… (More)
Wikipedia

## Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
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• 2004
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We analyze the ultimate ownership and control of 3,740 corporations in five Western European countries. We document that families… (More)
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• 1998
In this paper, we propose the Pyramid-Technique, a new indexing method for high-dimensional data spaces. The Pyramid-Technique is… (More)
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We present data on ownership structures of large corporations in 27 wealthy economies, making an effort to identify the ultimate… (More)
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• 1997
We investigate a novel multicast technique, called Skyscraper Broadcasting (SB), for video-on-demand applications. We discuss the… (More)
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• Multimedia Systems
• 1996
Pyramid broadcasting is a new way of giving video-on-demand service on a metropolitan scale. We multiplex the most frequently… (More)
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text:
# Math-Linux.com

Knowledge base dedicated to Linux and applied mathematics.

Home > Latex > How to make a presentation with Latex - Introduction to Beamer

## How to make a presentation with Latex - Introduction to Beamer

We shall see in this article how to make a presentation with LaTeX, using the powerful class Beamer. If you want to make an outstanding "stressfree" presentation and bring your ideas or your work under a whole new light, let’s get started!!!

### Installing the Beamer class

You will first need to install the package Beamer.
Under Debian or Ubuntu, you can type the following command:

# apt-get install latex-beamer

Once the latex-class Beamer is installed, you are definitely ready to stat your first presentation!!!

### Basic presentation with Beamer

\documentclass{beamer}
\usepackage[latin1]{inputenc}
\usetheme{Warsaw}
\title[Make a LaTeX presentation using Beamer]{Introduction  to Beamer\\How to make a presentation with LaTeX?}
\institute{Math-linux.com}
\date{Jule 13, 2007}
\begin{document}

\begin{frame}
\titlepage
\end{frame}

\begin{frame}{Introduction}
This is a short introduction to Beamer class.
\end{frame}

\end{document}

A few explanations:

\documentclass{beamer}

means that our document is a Beamer presentation

\usepackage[latin1]{inputenc}

this package enables us to use special letters (with accents, cedillas, etc). You can discard this command when the presentation is in English.

\usetheme{Warsaw}

This is our outer theme (color and background). As you can imagine, there are tons of themes. You can refer to Beamer documentation for more details.

\title[Making a LaTeX presentation with Beamer]{Introduction to Beamer\\How to make a LaTeX presentation?}

this defines the title of the presentation. As you can see, there are two titles:
the first one, between brackets. [Making a LaTeX presentation with Beamer] is a substitute title which appears at the bottom of the page. This is useful especially if the original title is long. Since this is anoption only, if it is not mentioned, then the original title is the one shown in the bottom of the page.
the second one, between braces, is the principal title of the presentation.
The command

\author{Nadir Soualem -- Astozzia}

defines Nadir Soualem and Astozzia (us!) as the authors of the presentation.

\institute{Math-linux.com}

defines where the presentation was held. Finally, we use

\date{July 13, 2007}

as the date.

To define the document, we use the markers

\begin{document}
...
\end{document}

To define a slide of the presentation, we use the markers

\begin{frame}
...
\end{frame}

To define a page title (frame), we mention it as follows

\begin{frame}{Introduction}

Introduction will be the title of the page.
To define the first page, which contains details such as the title, the author, the date, etc - we use a frame in which we include the \titlepage command

\begin{frame}
\titlepage
\end{frame}

To define a frame containing the layout of the presentation, we proceed as follows:

\AtBeginSubsection[]
{
\begin{frame}<beamer>
\frametitle{Layout}
\tableofcontents[currentsection,currentsubsection]
\end{frame}
}

The layout is therefore mentioned at every section and subsection.
You should insert \section and \subsection throughout the presentation and out of the frames:

\section{Name_of_the_section}
\begin{frame}
...
\end{frame}
...
\section{Name_of_the_section}
\subsection{Name_of_the_subsection}
\begin{frame}
...
\end{frame}

### Animations — Overlays

A good presentation is one that is dynamic and attracts the audience’s interest. Generally, we resort to a dynamic type of presentations. Alternatively stated, when we speak, we simultaneously show significant points of the talk, or hide others, or keep just the important ones.
We shall see in this section how animations function in Beamer.

### Item-by-item list view: the \pause command

In order to view several items of a list on the same slide, we type the following commands inside a frame:

\begin{itemize}
\pause \item Beamer is a wonderful class
\pause \item One can make animations
\pause \item One uses the\textbf{pause} command, for example
\pause \item in order to bring in important ideas
\end{itemize}

We will thus see the items of our list, one by one.

### Item-by-item list view: the \item<n-> command

An alternative way to visualize the elements of a list item by item is to use the \item<n-> command, where n is a natural number referring to the slide, beginning from which the item appears.

\begin{itemize}
\item<2-> appears from slide 2 on
\item<3-> appears from slide 3 on
\item<4-> appears from slide 4 on
\item<5-> appears from slide 5 on
\end{itemize}

### List item interval and isolated items: the \item<n-m> and \item<p> commands

An example is worth a long speech:

\begin{itemize}
\item<2-> appears from slide 2 on
\item<2-4> appears from slide 2 to slide 4
\item<4> appears on slide 4
\item<3-> appears from slide 3 on
\end{itemize}

\item<n-m> means that the list item will appear on slides numbered n to m, whereas \item<p> means that the item will appear on slide p.

### Item-by-item long list view: the [<+->] command

Sometimes the lists you want to display are long and it is not practical to use the
\item<n-> command. An alternative solution is the use of the [<+->] command

\begin{itemize}[<+->]
\item L
\item A
\item T
\item E
\item X
\end{itemize}

Up to now, we have dealt with lists. We shall now see how to use text and slides.

### Displaying and hiding text in slides: the \uncover<n->, \uncover<n-m> and \uncover<p> commands

\uncover<n-> will display the text from slide n on;
\uncover<n-m> means the text element will appear from slide n to m. Finally, \uncover<p> means that the text will appear on slide p.
Here is a case in point of a frame containing the \uncover command.

\begin{frame}

\uncover<2->
{appear from slide 2 on\\}
\uncover<3-4>
{appears from 3 to slide 4\\}
\uncover<4>{appears on slide 4\\}
\uncover<3->{appears from slide 3 on\\}

\end{frame}

Be careful not to forget the braces after the \uncover command. The syntax is as follows:

\uncover<n>{...}
\uncover<n-m>{...}
\uncover<p>{...}

### Displaying and hiding text in slides: the \only<n->, \only<n-m> and \only<p> commands

\only works like\uncover with the exception that the \only command is not as "cumbersome" on slides. Here is an example:

\begin{frame}

\only<2->
{appear from slide 2 on\\}
\only<3-4>
{appears from 3 to slide 4\}
\only<4>{appear on slide 4\\}
\only<3->{appear from slide 2 on\\}

\end{frame}

Here is an other example to better grasp the difference between \only and \uncover

\begin{frame}

\begin{itemize}
\item Language used by Beamer: L\uncover<2->{A}TEX
\item Language used by Beamer: L\only<2->{A}TEX
\end{itemize}

\end{frame}

### Hide text in slides: the \invisible<n> commands

\invisible<n> makes text invisible on slide n

\begin{frame}

\invisible<2>{This text will be invisible on slide 2, but not on others slides}\\
This text is always visible\\
\uncover<1->{Beamer} \uncover<2->{is}  \uncover<3->{super} \uncover<4->{powerful}

\end{frame}

### Another alternative: the \alt<n>{...}{...} commands

As an alternative, one can use the \alt{...}{...} command on a slide. The first argument is the value on slide n. The second is for values other than n. Here is an example:

\alt<3>{I am on slide 3\\}{I am not on slide 3\\}
\only<2->
{appears from slide 2 on\\}
\only<3-4>
{appears from slide 3 to slide 4\\}
\only<4>{appears on slide 4\\}
\only<3->{appears from slide 3 on\\}

### Highlighting text in red: the \alert<n>{...} command

To highlight text in red on slide n, we use the \alert<n>{...} command.

\alert<1>{This text} \alert<2>{is} \alert<3>{red}

### Successively highlighting list items in red: the <+-| alert@+> command

\begin{itemize}
\item <+-| alert@+> Robert De Niro
\item <+-| alert@+> Brian De Palma
\end{itemize}

### Using colors in a text on a slide: the \color<n->{...}{...}, \color<n-m>{...}{...} and\color<p>{...}{...} commands

The first argument is the red, green, yellow, blue, etc ... The second is the text to be colored

Some colors ...\\
\color<2>{green}{Green color\\}
Great !!!

To define internal links, we should add the following package in the preamble

\usepackage{hyperref}

Then, we should define a label pointing on the frame:

\begin{frame}[label=MY_LABEL]
The link will point to this frame
\end{frame}

you define MY_LABEL as you please !
Finally, on the frame where the link is to be created, we proceed as follows:

\hyperlink{MY_LABEL}{\beamergotobutton{Refer to this page}}

There we are! We can see a button Refer to this page pointing to the frame labeled MY_LABEL.

Thus, the first argument of \hyperlink{...}{\beamergotobutton{...}} is the name of the label to be pointed at and \beamergotobutton{...} has the name of the button as an argument.

### Defining blocks inside frames

For important stuff, we define blocks as follows:

\begin{block}{Block title}
This is a block in blue
\end{block}

This is a block in red

\begin{exampleblock}{Example-block title}
This is a block in green
\end{exampleblock}

As clear as onion soup !!!

### Dynamic display of tables: the \pause and \onslide<n-> commands

First off, we should add the package colortbl to the preamble

\usepackage{colortbl}

To display rows dynamically, we shall use the \pause command as follows:

\begin{tabular}{lcccc}
Class & A & B & C & D \\\hline
X     & 1 & 2 & 3 & 4 \pause\\
Y     & 3 & 4 & 5 & 6 \pause\\
Z     &5&6&7&8
\end{tabular}

To display columns dynamically, we shall use the \onslide<n-> command as follows:

\begin{tabular}{lc<{\onslide<2->}c<{\onslide<3->}c<{\onslide<4->}c<{\onslide}c}
Class & A & B & C & D \\
X     & 1 & 2 & 3 & 4 \\
Y     & 3 & 4 & 5 & 6 \\
Z     &5&6&7&8
\end{tabular}

### Writing on several columns: the \begin{columns}...\end{columns} commands

For two columns, we proceed as follows:

\begin{columns}
\begin{column}[l]{5cm}
First column
\end{column}
\begin{column}[r]{5cm}
Second column
\end{column}
\end{columns}

l,r,c refers to the position: left, right, center.
The syntax is as follows:

\begin{columns}
\begin{column}[position]{column width}
...
\end{column}
\begin{column}[position]{column width}
...
\end{column}
\end{columns}

### Inserting a figure in a Beamer presentation

To insert an image or a figure, we proceed as in LaTeX by using the \includegraphics command. Here is an example:

\begin{figure}
\includegraphics[options]{path_to_image}
\end{figure}

In Beamer, we should distinguish between two types of figures:
PS type: .eps, .ps and pspicture type (LaTeX)
General type: .pdf, .png, .jpg, .jpeg
You will need to compile a Beamer-class file.

### Compiling a Beamer presentation

I assume that the your file is called file.tex.. There are ways to compile, depending on the type of figure you inserted. For PS-type figures, we shall use the following commands

$latex file.tex$ latex file.tex
$dvips file.dvi$ ps2pdf file.ps

We shall obtain the file file.pdf.

For general-type figures, we shall use the command

$latex2pdf file.tex$ latex2pdf file.tex

We shall also obtain the file file.pdf.

### Conclusion

It goes without saying that explaining all the possibilities that Beamer offers is way too long. This is why I am referring to this exhaustive documentation documentation.

Have fun !!!


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Select Page

# Standard error using the Fisher Information Matrix

### Purpose

The variance of the maximum likelihood estimate (MLE) $\hat{\theta}$, and thus confidence intervals, can be derived from the observed Fisher information matrix (FIM), itself derived from the observed likelihood (i.e., the pdf of observations y):

$I_{y}(\hat{\theta})\triangleq -\frac{\partial^2}{\partial\theta^2}\log({\cal L}_y(\hat{\theta}))$

There are two different algorithms: by linearization or by stochastic approximation. When “linearization” is used, the structural model is linearized, and the full statistical model is approximated by a Gaussian model. When “stochastic approximation” is used, the exact model is used, and the Fisher information matrix (F.I.M) is approximated stochastically. The final estimations are displayed in the command window (Matlab or DOS) together with the population parameters:

• the estimated fixed effects, their standard-errors, the absolute and relative p-values obtained from the Wald test (only for the coefficients of the covariates),
• the estimated variances (or standard deviations) and their standard-errors,
• the estimated residual error parameters and their standard-errors,
• the estimated correlation matrix of the random effects if the covariance matrix is not diagonal,
• the correlation matrix of the fixed effect estimates, with the smallest and largest eigenvalues,
• the correlation matrix of the variance components estimates, with the smallest and largest eigenvalues,

All that information is appended to the file pop_parameters.txt. The following file presents an example on the theophylline_project.

******************************************************************
*      theophylline_project.mlxtran
*      November 26, 2015 at 16:17:01
*      Monolix version: 4.4.0
******************************************************************

Estimation of the population parameters

parameter     s.e. (lin)   r.s.e.(%)   p-value
ka_pop          :     1.57         0.31          20
V_pop           :    0.454        0.019           4
beta_V_t_WEIGHT :   -0.471          0.3          63        0.11
Cl_pop          :   0.0399       0.0034           9

omega_ka        :    0.641         0.14          22
omega_V         :    0.113        0.035          31
omega_Cl        :    0.272        0.066          24

a               :    0.735        0.056           8

______________________________________________
correlation matrix of the estimates(linearization)

ka_pop               1
V_pop             0.15       1
beta_V_t_WEIGHT      0    0.09       1
Cl_pop           -0.06   -0.15    0.01       1

Eigenvalues (min, max, max/min): 0.79  1.3  1.6

omega_ka      1
omega_V   -0.02       1
omega_Cl      0   -0.01       1
a         -0.02   -0.11   -0.05       1

Eigenvalues (min, max, max/min): 0.87  1.1  1.3

Numerical covariates
t_WEIGHT = log(WEIGHT/70)

Notice that the chosen method is displayed in the file.

### Best practices: when to use “linearization” and when to use “stochastic approximation”

Firstly, it is only possible to use the linearization algorithm for the continuous data. In that case, this method is generally much faster than stochastic approximation and also gives good estimates of the FIM. The FIM by model linearization will generally be able to identify the main features of the model. More precise– and time-consuming – estimation procedures such as stochastic approximation and importance sampling will have very limited impact in terms of decisions for these most obvious features. Precise results are required for the final runs where it becomes more important to rigorously defend decisions made to choose the final model and provide precise estimates and diagnostic plots. In the theophylline example, the evaluation of the FIM is presented with the CPU time.

Method s.e. $(ka_{pop}, V_{pop}, \beta_{V,t_{WEIGHT}}, Cl_{pop})$ s.e. $(\omega_{ka}, \omega_{V}, \omega_{Cl})$ e.v. correlation matrix of the estimates CPU time [s]
Linearization (0.31, 0.019, .3, .0035) (0.14, 0.035, .066) (0.8, 1.3, 1.6, 0.87, 1.1, 1.3) .1
Stochastic Approximation (0.31, 0.019, .3, .0035) (0.15, 0.035, .068) (0.8, 1.2, 1.5, 0.79, 1.2, 1.5) 3.4

One can see that it the stochastic approximation is much more costly in computation time but the result is more precise.


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The Postgraduate Forum provides a friendly environment for pure maths PhD students and postdocs to present their research, or any other maths that interests them. The talks are intended to be accessible to all PhD students in pure maths, and we also welcome everyone else interested in coming along! Contacts: Frankie Higgs and Tiziano Gaudio

### 2018-19

term 2
Jan 14 14:00 PSC LT
Meu Celorrio Ramirez
Jan 21 14:00 Fylde B35
Matt Booth (University of Edinburgh)
Jan 28 14:00 PSC LT
Luke Hamblin (University of Glasgow)
Feb 04 14:00 Fylde B35
Sean Dewar
Feb 11 14:00 PSC LT
Frankie Higgs
Feb 18 14:00 Fylde B35
Feb 25 14:00 Fylde LT2
Mar 04 14:00 Fylde LT2
George Liddle
Mar 11 14:00 Fylde B35
Serte Donderwinkel (University of Oxford)
Mar 18 14:00 PSC LT

### Abstracts

Jan 14 14:00 PSC LT
Meu Celorrio Ramirez Evolution algebras

Evolution algebras were introduced in 2006 in order to study non-Mendelian genetics. A pioneer in this research was Tian who in 2008 showed connections between the evolution algebras and several different fields.

We will see the genetical motivation of these algebras, as well as defining them algebraically. During the talk, we will see also the connection of the evolution algebras and the graph theory, and we will establish some basic definitions that will allow us to work out if an evolution algebra is decomposable or not. Time permitting, we will speak about the classification for these algebras when their dimension is 2 and 3.

Jan 21 14:00 Fylde B35
Matt Booth (University of Edinburgh) Deformation theory

Deformation theory can be thought of as the study of infinitesimal thickenings of geometric or algebraic objects. Equivalently, it is the study of infinitesimal neighbourhoods in moduli spaces. In this talk, I'll provide an introduction to some deformation-theoretic concepts. I'll explain Deligne's philosophy that in characteristic zero, deformation problems are "controlled" by differential graded Lie algebras (dglas). I'll talk about derived deformation theory, and how it clarifies some concepts within the classical theory, in particular the proofs of Lurie and Pridham that dglas are equivalent to derived moduli problems via Koszul duality. Time permitting, I'll talk about an application of noncommutative deformation theory to birational geometry in the form of the Donovan-Wemyss contraction algebra, and I will mention how derived noncommutative deformations also fit into the picture.

Jan 28 14:00 PSC LT
Luke Hamblin (University of Glasgow) Tilings and their dynamical systems

A tiling is a decomposition of Euclidean space into pieces that fit together without gaps or overlaps. The most basic examples consist of periodic structures such as a tiling by unit cubes, which can be used to model the structure of a crystal of table salt. More interesting examples can be obtained by requiring that our tiles are unable to tessellate the space in a periodic manner. Physical realizations of these aperiodic tilings are called quasicrystals and were first observed in a man-made material in 1984, with the first naturally occurring specimen discovered in 2009. In this talk I will provide an introduction to tiling theory and explain some ways that we can associate dynamical systems to a tiling.

Feb 04 14:00 Fylde B35
Sean Dewar Matroids and rigidity

We will cover the basics of finite and infinite matroids and give examples.

Feb 11 14:00 PSC LT
Frankie Higgs Settlement processes on graphs

On an infinite, connected, locally finite graph, we can define "internal diffusion-limited aggregation" (IDLA), in which a large number of explorers starting from the same point perform random walks until they all find a free spot to settle. For the integer lattice, the scaling limit of the explored region is known to be a Euclidean ball, and we will see some variations of the model for which this is either known and conjectured to hold.

We will also look at some of the more interesting properties enjoyed by IDLA and other settlement processes, and the link between IDLA and chip-firing games.

Feb 18 14:00 Fylde B35
Nora Seeliger A few examples of $$p$$-good and $$p$$-bad classifying spaces

For every prime $$p$$ the $$p$$-completion functor of Bousfield and Kan relates a space to its nilpotent completion. A space is $$p$$-good if the induced map is a homology isomorphism. We give examples of spaces which are good and bad at different primes in the sense of Bousfield and Kan in any arbitrary combination. Moreover we investigate which impact the existence of a Sylow $$p$$-subgroup has on the homotopy type on the classifying space and under which conditions the homotopy type of wedges of classifying spaces is good or bad for a solid ring $$R$$. We give results relating to various other $$R$$-homological structures and a collection of examples.

Feb 25 14:00 Fylde LT2
Konrad Krolicki Weighted graphs and cocycles

The classical definition of an amenable group relies on the notion of an invariant mean, which turns out to be equivalent to the Følner condition. This condition depends on a Cayley graph of the group and so we can talk about amenable graphs. In the talk I will discuss graphs with an additional notion of weight function $$w$$ on their vertices and give motivation for considering such structures.

Mar 04 14:00 Fylde LT2
George Liddle Phase transitions in planar random growth

Random growth occurs in many real world settings, for example, we see it exhibited in the growth of tumours, bacterial growth and lightning patterns. As such we would like to be able to model such processes to determine their behaviour in their scaling limits. Well studied models to describe these different processes include the Eden model and DLA. In a 1998 paper Hastings and Levitov introduced a one parameter family of conformal maps $$\mathrm{HL}(\alpha)$$ which can be used to model all such Laplacian growth processes and allows us to vary between the previous models by varying alpha. We will consider a regularised version of this model and show that at certain values of $$\alpha$$ a phase transition on the scaling limits occurs.

Mar 11 14:00 Fylde B35
Serte Donderwinkel (University of Oxford) The ant in the labyrinth

The Random Walk in a Random Environment (RWRE) is a generalization of the well-known random walk. In the RWRE, the transition probabilities itself are random. A natural application of this is the propagation of heat, or the diffusion of matter through an irregular environment. As we all know, the independent increments of the Simple Random Walk (SRW) make it an easy class of processes to study. However, since the walker of an RWRE gets more information about its environment as time progresses, this process is no longer Markovian. This makes it a lot more challenging to obtain results on the limiting behaviour of the walk, and indeed many basic questions in dimension $$d\geq 2$$ remain open. I will first give an introduction of the field of RWRE, and will introduce trapping effects. Informally, this is the occurrence of pockets in the random environment where the walk spends a long time with relatively high probability.

These trapping effects will be further explored in a specific model of a RWRE, namely of a biased random walk on the 2-dimensional lattice after performing supercritical percolation. In this model, a walker with a small bias in the positive $$x$$-direction will have a positive velocity. However, as the bias increases, the velocity vanishes. This is due to the walker spending a superlinear amount of time in dead ends in the cluster. These results were obtained by Berger, Gantert and Peres in 2003 and by Snitzman in 2003. I will give an overview of the main ideas in their proofs.

Mar 18 14:00 PSC LT
Zac Hall Profinite groups and a Burnside ring

Constructing a profinite group through inverse limits of finite groups, we can characterise a topology of subgroups of this topological group.

Using this we establish notions of $$G$$-spaces and what it means to be essentially finite or almost finite. In particular, we consider Hall's $$p$$-construction and its ideals and the infinite pro-$$p$$ partition group.