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  • Parsing SQLIO Output to Excel Charts using Regex in PowerShell

    - by Jonathan Kehayias
    Today Joe Webb ( Blog | Twitter ) blogged about The Power of Regex in Powershell, and in his post he shows how to parse the SQL Server Error Log for events of interest.  At the end of his blog post Joe asked about other places where Regular Expressions have been useful in PowerShell so I thought I’d blog my script for parsing SQLIO output using Regex in PowerShell, to populate an Excel worksheet and build charts based on the results automatically. If you’ve never used SQLIO, Brent Ozar ( Blog...(read more)

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  • Why I don’t need to go on the SQLCruise

    - by Jonathan Kehayias
    Brent Ozar ( Blog | Twitter ) and Tim Mitchell ( Blog | Twitter ) are putting on a new type of event in the month of August after SQL Saturday #40 in South Florida July, 31st , properly named SQLCruise .  The concept is great, at least in my opinion, you pay for a cruise, get to have a break, and at the same time attend a mini-conference on SQL Server with training provided by two great speakers.  The cost is relatively affordable, so what could possibly make it better?  How about...(read more)

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  • Why I don’t need to go on the SQLCruise

    - by Jonathan Kehayias
    Brent Ozar ( Blog | Twitter ) and Tim Ford ( Blog | Twitter ) are putting on a new type of event in the month of August after SQL Saturday #40 in South Florida July, 31st , properly named SQLCruise . The concept is great, at least in my opinion, you pay for a cruise, get to have a break, and at the same time attend a mini-conference on SQL Server with training provided by two great speakers. The cost is relatively affordable, so what could possibly make it better? How about a sponsor offering up...(read more)

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  • Chicago SQL Saturday

    - by Johnm
    This past Saturday, April 17, 2010, I journeyed North to the great city of Chicago for some SQL Server fun, learning and fellowship. The Chicago edition of this grassroots phenomenon was the 31st scheduled SQL Saturday since the program's birth in late 2007. The Chicago SQL Saturday consisted of four tracks with eight sessions each and was a very energetic and fast paced day for the 300+/- SQL Server enthusiasts in attendance. The speaker line up included national notables such as Kevin Kline, Brent Ozar, and Brad McGehee. My hometown of Indianapolis was well represented in the speaker line up with Arie Jones, Aaron King and Derek Comingore. The day began with a very humorous keynote by Kevin Kline and Brent Ozar who emphasized the importance of community events such as SQL Saturday and the monthly user group meetings. They also brilliantly included the impact that getting involved in the SQL community through social media can have on your professional career. My approach to the day was to try to experience as much of the event as I could, so there were very few sessions that I attended for their full duration. I leaped from session to session like a bumble bee, gleaning bits of nectar from each session. Amid these leaps I took the opportunity to briefly chat with some of the in-the-queue speakers as well as other attendees that wondered the hallways. I especially enjoyed a great discussion with Devin Knight about his plans regarding the upcoming Jacksonville SQL Saturday as well as an interesting SQL interpretation of the Iron Chef, which I think would catch on like wild-fire. There were two sessions that stood out as exceptional. So much so that I could not pull myself away: Kevin Kline presented on "SQL Server Internals and Architecture". This session could have been classified as one that is intended for the beginner. Kevin even personally warned me of such as I entered the room. I am a believer in revisiting the basics regardless of the level of your mastery, so I entered into this session in that spirit. It was a very clear and precise presentation. Masterfully illustrated and demonstrated. Brad McGehee presented on "How and When to Use Indexed Views". This was a topic that I was recently exploring and was considering to for use in an integration project. Brad effectively communicated the complexity of this feature and what is involved to gain their full benefit. It was clear at the conclusion of this session that it was not the right feature for my specific needs. Overall, the event was a great success. The use of volunteers, from an attendee's perspective was masterful. The only recommendation that I would have for the next Chicago SQL Saturday would be to include more time in between sessions to permit some level of networking among the attendees, one-on-one questions for speakers and visits to the sponsor booths. Congratulations to Wendy Pastrick, Ted Krueger, and Aaron Lowe for their efforts and a very successful SQL Saturday!

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  • SQLPeople Interviews - Crys Manson, Jeremiah Peschka, and Tim Mitchell

    - by andyleonard
    Introduction Late last year I announced an exciting new endeavor called SQLPeople . At the end of 2010 I announced the 2010 SQLPeople Person of the Year . Check out these interviews from your favorite SQLPeople ! Interviews To Date Tim Mitchell Jeremiah Peschka Crys Manson Ben McEwan Thomas LaRock Lori Edwards Brent Ozar Michael Coles Rob Farley Jamie Thomson Conclusion I plan to post two or three interviews each week for the forseeable future. SQLPeople is just one of the cool new things I get to...(read more)

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  • SQLAuthority Book Review – Professional SQL Server 2008 Internals and Troubleshooting

    - by pinaldave
    Professional SQL Server 2008 Internals and Troubleshooting by Christian Bolton, Justin Langford, Brent Ozar, James Rowland-Jones, Steven Wort Link to Amazon (Worldwide) Link to Flipkart (India) Brief Review: Having a book on internal and associating that with real life is “almost” an impossible task. The reason for using the word “almost” is because this book has accomplished this [...]

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  • SQLAuthority Book Review Professional SQL Server 2008 Internals and Troubleshooting

    Professional SQL Server 2008 Internals and Troubleshooting by Christian Bolton, Justin Langford, Brent Ozar, James Rowland-Jones, Steven WortLink to Amazon (Worldwide)Link to Flipkart (India)Brief Review: Having a book on internal and associating that with real life is almost an impossible task. The reason for using the word almost is because this book has accomplished this [...]...Did you know that DotNetSlackers also publishes .net articles written by top known .net Authors? We already have over 80 articles in several categories including Silverlight. Take a look: here.

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  • On the Fourth Day of the SQL Series...

    - by andyleonard
    Introduction Brent Ozar ( Blog | @BrentO ) has done it again - started something. This time it's The Twelve Days of SQL Series . I was passed the baton from David Stein ( Blog | @made2mentor ) who covered Day 3 with a tribute to his favorite post . And Now, My Selection: I liked Rafael Salas' ( Blog | @RafSalas ) post entitled Denali CTP 1: SSIS Parameters – Bring Them On! Rafael is a friend and fellow SSIS guy. In this post he does a good job pointing out the differences between SSIS Parameters...(read more)

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  • SQLPeople Interviews - Steve Fibich and Cindy Gross

    - by andyleonard
    Introduction Late last year I announced an exciting new endeavor called SQLPeople . At the end of 2010 I announced the 2010 SQLPeople Person of the Year . Check out these new interviews from some cool SQLPeople ! Interviews To Date Cindy Gross Steve Fibich Tim Mitchell Jeremiah Peschka Crys Manson Ben McEwan Thomas LaRock Lori Edwards Brent Ozar Michael Coles Rob Farley Jamie Thomson Conclusion I plan to post two or three interviews each week for the forseeable future. SQLPeople is just one of the...(read more)

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  • Reminder: Totally Awesome and Totally Free Training SQL Server Training

    - by KKline
    One of the things that I enjoy about working for Quest Software is that we give back copiously to the community. From activities and offerings like SQLServerPedia , to our free posters mailed anywhere in North America (and don't forget the free hi-res PDFs for the rest of the world ), Don't forget that free DVDs of our virtual conferences featuring me, along with Buck Woody ( blog | twitter ) and Brent Ozar ( blog | twitter ) will be mailed anywhere in North America free of charge, now available...(read more)

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  • Fixing SSMS Tabs

    - by Tara Kizer
    It never occurred to me that the way SSMS handles tabs could be changed, and it’s just that the default settings suck.  In this blog post, Brent Ozar shows us how to fix SSMS so that the tabs are actually usable and not annoying anymore. I can’t love his post enough.  It has really helped me become more efficient.  I’m always flipping between tabs and can’t quickly find the one I need at some critical time, but now I can easily find it!

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  • Getting baseline and performance stats - the easy way.

    - by fatherjack
    OK, pretty much any DBA worth their salt has read Brent Ozar's (Blog | Twitter) blog about getting a baseline of your server's performance counters and then getting the same counters at regular intervals afterwards so that you can track performance trends and evidence how you are making your servers faster or cope with extra load without costing your boss any money for hardware upgrades. No? well, go read it now. I can wait a while as there is a great video there too...http://www.brentozar.com/archive/2006/12/dba-101-using-perfmon-for-sql-performance-tuning/,...(read more)

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  • How are people using virtualisation with SQL Server? Part 3

    - by GavinPayneUK
    Monitoring After CPU, memory and storage, monitoring is the fourth thing which changes massively according to Brent Ozar’s list when you move to virtualisation. Some of the performance counters we used to organise our lives around become meaningless and the performance of the host server is often over-looked when looking for problems. What’s encouraging here is that the majority of people are already looking beyond the performance of virtual server and at the performance of the host server. This...(read more)

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  • SQL Cruise Alaska 2011

    - by Grant Fritchey
    I had the extreme good fortune to get sent on the last SQL Cruise to Alaska. I love my job. In case you don't what this is, SQL Cruise is a trip on a cruise ship during which you get to attend classes while on the boat, learning all about SQL Server and related topics as well as network with the instructors and the other Cruisers. Frankly, it's amazing. Classes ran from Monday, 5/30, to Saturday, 6/4. The networking was constant, between classes, at night on cruise ship, out on excursions in Alaskan rainforests and while snorkeling in ocean waters. Here's a run down of the experience from my point of view. Because I couldn't travel out 2 days early, I missed the BBQ that occurred the day before the cruise when many of the Cruisers received their swag bags. Some of that swag came from Red Gate. I researched what was useful on a cruise like this and purchased small flashlights and binoculars for all the Cruisers. The flashlights were because, depending on your cabin, ships can be very dark. The binoculars were so that the cruisers could watch all the beautiful landscape as it flowed by. I would have liked to have been there when the bags were opened, but I heard from several people that they appreciated the gifts. Cruisers "In" the hot tub. Pictured: Marjory Woody, Michele Grondin, Kyle Brandt, Grant Fritchey, John Halunen Sunday I went to board the ship with my wife. We had a bit of an adventure because I messed up our documents. It all worked out and we got on board to meet up at the back of the boat at one of the outdoor bars with the other Cruisers, thanks to tweets letting everyone know where to go. That was the end of electronic coordination on the trip (connectivity in Alaska was horrible for everyone except AT&T). The Cruisers were a great bunch of people and it was a real honor to meet them and get to spend time with them. After everyone settled into their cabins, our very first activity was a contest, sponsored by Red Gate. The Cruisers, in an effort to get to know each other and the ship, were required to go all over taking various photographs, some of them hilarious. The winning team of three would all win prizes. Some of the significant others helped out and I tagged along with a team that tied for first but lost the coin toss. The winning team consisted of Christina Leo (blog|twitter), Ryan Malcom (twitter), Neil Hambly (blog|twitter). They then had to do math and identify the cabin with the lowest prime number, oh, and get a picture of it and be the first to get back up to the bar where we were waiting. Christina came in first and very happily carried home an Ipad2. Ryan won a 1TB portable hard drive and Neil won a wireless mouse (picture below, note my special SQL Server Central Friday Shirt. Thanks Steve (blog|twitter)). Winners: Christina Leo, Neil Hambly, Ryan Malcolm. Just Lucky: Grant Fritchey Monday morning classes started. Buck Woody (blog|twitter) was a special guest speaker on this cruise. His theme was "Three C's on the High Seas: Career, Communication and Cloud." The first session was all on Career. I'm not going to type out all my notes from the session, but let's just say, if you get the chance to hear Buck talk about how to manage your career, I suggest you attend. I have a ton of blog posts that I'll be putting together over the next several months (yes, months) both here and over on ScaryDBA. I also have a bunch of work I'm going to be doing to get my career performance bumped up a notch or two (and let's face it, that won't be easy). Later on Monday, Tim Ford (blog|twitter) did a session on DMOs. Specifically the session was on Tim's Period Table of DMOs that he has put together, and how to use some of the more interesting DMOs in your day to day job. It was a great session, packed with good information. Next, Brent Ozar (blog|twitter) did a session on how to monitor and guide SAN configuration for the DBA that doesn't have access to the SAN. That was some seriously useful information. Tuesday morning we only had a single class. Kendra Little (blog|twitter) taught us all about "No Lock for Yes Fun".  It was all about the different transaction isolation levels and how they work. There is so often confusion in this area and Kendra does a great job in clarifying the information. Also, she tosses in her excellent drawings to liven up the presentation. Then it was excursion time in Juneau. My wife and I, along with several other Cruisers, took a hike up around the Mendenhall Glacier. It was absolutely beautiful weather and walking through the Alaskan rain forest was a treat. Our guide, Jason, was a great guy and it was a good day of hiking. Wednesday was an all day excursion in Skagway. My wife and I took the "Ghost and Good Time Girls" walking tour that ended up at a bar that used to be a brothel, the Red Onion. It was a great history of the town. We went back out and hit a few museums and exhibits. We also hiked up the side of the mountain to see the Dewey Lake and some great views of the town. Finally we hiked out to the far side of town to see the Gold Rush cemetery. Hiking done we went back to the boat and had a quiet dinner on our own. Thursday we cruised through Glacier Bay and saw at least four different glaciers including sitting next to the Marjory Glacier for  about an hour. It was amazing. Then it got better. We went into class with Buck again, this time to talk about Communication. Again, I've got pages of notes that I'm going to be referring back to for some time to come. This was an excellent opportunity to learn. Snorkelers: Nicole Bertrand, Aaron Bertrand, Grant Fritchey, Neil Hambly, Christina Leo, John Robel, Yanni Robel, Tim Ford Friday we pulled into Ketchikan. A bunch of us went snorkeling. Yes, snorkeling. Yes, in Alaska. Yes, snorkeling in the ocean in Alaska. It was fantastic. They had us put on 7mm thick wet suits (an adventure all by itself) so it was basically warm the entire time we were in the water (except for the occasional squirt of cold water down my back). Before we got in the water a bald eagle flew up and landed about 15 feet in front of us, which was just an incredible event. Then our guide pointed out about 14 other eagles in the area, hanging out in the trees. Wow! The water was pretty clear and there was a ton of things to see. That was absolutely a blast. Back on the boat I presented a session called Execution Plans: The Deep Dive (note the nautical theme). It seemed to go over well and I had several good questions come out of the session that will lead to new blog posts. After I presented, it was Aaron Bertrand's (blog|twitter) turn. He did a session on "What's New in Denali" that provided a lot of great information. He was able to incorporate new things straight out of Tech-Ed, so this was expanded beyond his usual presentation. The man really knows what he's talking about and communicates it well. Saturday we were travelling so there was time for a bunch of classes. Jeremiah Peschka (blog|twitter) did a great overview of some of the NoSQL databases and what they should be used for. The session was called "The Database is Dead" but it was really about how there are specific uses for these databases that SQL Server doesn't fill, but also that these databases can't replace SQL Server in other areas. Again, good material. Brent Ozar presented again with a session on Defensive Indexing. It was an overview of how indexes work and a deep dive into how to apply them appropriately in your databases to better support access. A good session, as you would expect. Then we pulled into Victoria, BC, in Canada and had a nice dinner with several of the Cruisers, including Denny Cherry (blog|twitter). After that it was back to Seattle on Sunday. By the way, the Science Fiction Museum in Seattle isn't a Science Fiction Museum any more. I was very disappointed to discover this. Overall, it was a great experience. I'm extremely appreciative of Red Gate for sending me and for Tim, Brent, Kendra and Jeremiah for having me. The other Cruisers were all amazing people and it was an honor & privilege to meet them and spend time with them. While this was a seriously fun time, it was also a very serious training opportunity with solid information coming from seasoned industry pros.

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  • Top 10 Linked Blogs of 2010

    - by Bill Graziano
    Each week I send out a SQL Server newsletter and include links to interesting blog posts.  I’ve linked to over 500 blog posts so far in 2010.  Late last year I started storing those links in a database so I could do a little reporting.  I tend to link to posts related to the OLTP engine.  I also try to link to the individual blogger in the group blogs.  Unfortunately that wasn’t possible for the SQLCAT and CSS blogs.  I also have a real weakness for posts related to PASS. These are the top 10 blogs that I linked to during the year ordered by the number of posts I linked to. Paul Randal – Paul writes extensively on the internals of the relational engine.  Lots of great posts around transactions, transaction log, disaster recovery, corruption, indexes and DBCC.  I also linked to many of his SQL Server myths posts. Glenn Berry – Glenn writes very interesting posts on how hardware affects SQL Server.  I especially like his posts on the various CPU platforms.  These aren’t necessarily topics that I’m searching for but I really enjoy reading them. The SQLCAT Team – This Microsoft team focuses on the largest and most interesting SQL Server installations.  The regularly publish white papers and best practices. SQL Server CSS Team – These are the top engineers from the Microsoft Customer Service and Support group.  These are the folks you finally talk to after your case has been escalated about 20 times.  They write about the interesting problems they find. Brent Ozar – The posts I linked to mostly focused on the relational engine: CPU, NUMA, SSD drives, performance monitoring, etc.  But Brent writes about a real variety of topics including blogging, social networking, speaking, the MCM, SQL Azure and anything else that seems to strike his fancy.  His posts are always well written and though provoking. Jeremiah Peschka – A number of Jeremiah’s posts weren’t about SQL Server.  He’s very active in the “NoSQL” area and I linked to a number of those posts.  I think it’s important for people to know what other technologies are out there. Brad McGehee – Brad writes about being a DBA including maintenance plans, DBA checklists, compression and audit. Thomas LaRock – I linked to a variety of posts from PBM to networking to 24 Hours of PASS to TDE.  Just a real variety of topics.  Tom always writes with an interesting style usually mixing in a movie theme and/or bacon. Aaron Bertrand – Many of my links this year were Denali features.  He also had a great series on bad habits to kick. Michael J. Swart – This last one surprised me.  There are some well known SQL Server bloggers below Michael on this list.  I linked to posts on indexes, hierarchies, transactions and I/O performance and a variety of other engine related posts.  All are interesting and well thought out.  Many of his non-SQL posts are also very good.  He seems to have an interest in puzzles and other brain teasers.  Michael, I won’t be surprised again!

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  • PASS Summit 2011 &ndash; Part II

    - by Tara Kizer
    I arrived in Seattle last Monday afternoon to attend PASS Summit 2011.  I had really wanted to attend Gail Shaw’s (blog|twitter) and Grant Fritchey’s (blog|twitter) pre-conference seminar “All About Execution Plans” on Monday, but that would have meant flying out on Sunday which I couldn’t do.  On Tuesday, I attended Allan Hirt’s (blog|twitter) pre-conference seminar entitled “A Deep Dive into AlwaysOn: Failover Clustering and Availability Groups”.  Allan is a great speaker, and his seminar was packed with demos and information about AlwaysOn in SQL Server 2012.  Unfortunately, I have lost my notes from this seminar and the presentation materials are only available on the pre-con DVD.  Hmpf! On Wednesday, I attended Gail Shaw’s “Bad Plan! Sit!”, Andrew Kelly’s (blog|twitter) “SQL 2008 Query Statistics”, Dan Jones’ (blog|twitter) “Improving your PowerShell Productivity”, and Brent Ozar’s (blog|twitter) “BLITZ! The SQL – More One Hour SQL Server Takeovers”.  In Gail’s session, she went over how to fix bad plans and bad query patterns.  Update your stale statistics! How to fix bad plans Use local variables – optimizer can’t sniff it, so it’ll optimize for “average” value Use RECOMPILE (at the query or stored procedure level) – CPU hit OPTIMIZE FOR hint – most common value you’ll pass How to fix bad query patterns Don’t use them – ha! Catch-all queries Use dynamic SQL OPTION (RECOMPILE) Multiple execution paths Split into multiple stored procedures OPTION (RECOMPILE) Modifying parameter values Use local variables Split into outer and inner procedure OPTION (RECOMPILE) She also went into “last resort” and “very last resort” options, but those are risky unless you know what you are doing.  For the average Joe, she wouldn’t recommend these.  Examples are query hints and plan guides. While I enjoyed Andrew’s session, I didn’t take any notes as it was familiar material.  Andrew is a great speaker though, and I’d highly recommend attending his sessions in the future. Next up was Dan’s PowerShell session.  I need to look into profiles, manifests, function modules, and function import scripts more as I just didn’t quite grasp these concepts.  I am attending a PowerShell training class at the end of November, so maybe that’ll help clear it up.  I really enjoyed the Excel integration demo.  It was very cool watching PowerShell build the spreadsheet in real-time.  I must look into this more!  On a side note, I am jealous of Dan’s hair.  Fabulous hair! Brent’s session showed us how to quickly gather information about a server that you will be taking over database administration duties for.  He wrote a script to do a fast health check and then later wrapped it into a stored procedure, sp_Blitz.  I can’t wait to use this at my work even on systems where I’ve been the primary DBA for years, maybe there’s something I’ve overlooked.  We are using EPM to help standardize our environment and uncover problems, but sp_Blitz will definitely still help us out.  He even provides a cloud-based update feature, sp_BlitzUpdate, for sp_Blitz so you don’t have to constantly update it when he makes a change.  I think I’ll utilize his update code for some other challenges that we face at my work.

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  • How to bring Paging File usage metric to zero?

    - by AngryHacker
    I am trying to tune a SQL Server. Per Brent Ozar's Performance Tuning Video, he says the PerfMon's Paging File:%Usage should be zero or ridiculously close to it. The average metric on my box is around 1.341% The box has 18 GB of RAM, the SQL Server is off, the Commit Charge Total is 1GB and yet the PerfMon metric is not 0. The Performance of the Task Manager states that PF Usage is 1.23GB. What should I do to better tune the box?

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • Going to the Score Cards - Exceptional DBA Awards 2011

    - by Rodney
    This year marks my 4th year as a judge for the Exceptional DBA Awards, founded by Red Gate in 2008 to "recognize the essential but often overlooked contributions of DBAs, the unsung heroes of the IT community." As a professional DBA myself I have been honored to participate as a judge. It is not an easy job because there is a voluminous amount of nominees from all over the world. Each judge has to read through every word of the nominee's answers, deciding what makes each person special and stand out amongst their peers. What drives them? What single element of their submission will shine above all others? It is my hope that what I am about to divulge to you as a judge will prompt you to think about yourself or someone you know and decide that you may be the exceptional DBA who can take home the gold at this year's award ceremony in Seattle. We are more than a few weeks into the nomination process and there are quite a number of submissions already. I can not tell you how many as that would not be fair. I can say it is not 1 million or more. I can also say that it is not 100,000. But that is all I can say about that. However, I can tell you that it is enough this year that we are breaking records on the number of people who have been influenced, inspired or intrigued by the awards in the past. I remember them all like it were yesterday. fuzzy thought cloud here. It was a rainy day in Seattle (all memories for each award ceremony will start thusly) and I was in the hotel going over my notes on what I wanted to say about the winner of the 2008 Red Gate Exceptional DBA Award. The notes were on index cards that I had either bought or stolen from my wife, I do not recall, but I was nervous which was unlike me. This was, after all, a big night for the winner. Of course, we, the judges and the SQL community, had already decided the winner and now all that remained was to present the award. The room was packed. It was Casino night, sponsored by sqlservercentral.com. Money (fake), drinks (not fake) and camaraderie flowed through the room. Dan McClain won the award that year. He worked for Anheuser-Busch at the time. I promise that did not influence my decision. We presented Dan with the award. He was very proud of this achievement, rightfully so, as was the SQL community for him. I spoke with Dan throughout the conference and realized how huge this award was for him, not just personally but professionally. It was a rainy day in Seattle in 2009 and I was nervous. I was asked to speak to a group of people again as a judge for the Exceptional DBA Awards. This year, Josef Richberg would be the recipient of the award, but he would not be able to attend. We all prayed for him as he fought through an illness and congratulated him for his accomplishments as a DBA for his company. He got better and sallied forth and continued to give back to the SQL community that he saw as one big family. In 2010, and I am getting ahead of myself, he was asked to be a judge himself for the very award he had just received the year before. It was a sunny day in Seattle and I missed it, because it was in July and I was not there. It was a rainy day in Seattle and it is 2010 and Tracy Hamlin enters a submission that blows this judge away. She is managing a 50 Terabyte distributed database ("50 Gigabytes! Are you kidding me!!!", Rodney jokes.)  and loves her daily job as a DBA working with developers, mentoring them and teaching them best practices with kindness and patience. She is a people person who just happens to have 10+ years experience with RDBMS'. She wins the award and goes on to be recognized as famous at PASS. It will be a rainy day in Seattle this year when I sit amongst my old constituent judges and friends, Brad McGehee, http://www.simple-talk.com/books/sql-books/how-to-become-an-exceptional-dba,-2nd-edition/, Steve Jones, whom we all know and love at http://www.sqlservercentral.com and a young upstart to the SQL Community, this cat named Brent Ozar to announce the 2011 winner. I personally have not heard of Brent but I am told I have interviewed him for a DBA position several years ago and turned him down, http://www.brentozar.com/archive/2011/05/exceptional-dba-contest/ . I hope that did not jeopardize his future in the SQL world. I am a big hearted oaf and would feel horrible. Hopefully I will meet him at PASS and we can work this all out and I can help him get a DBA job. The rain has stopped and a new year is upon us. The stakes are high...the competition is fierce...the rewards are incredible. The entry form awaits you. http://www.exceptionaldba.com/ I very much look forward to meeting you and presenting the award to you in front of hundreds of your envious but proud peers as the new Exceptional DBA for 2011 at the PASS Summit. Here is what you could win: The Exceptional DBA of the Year receives full conference registration for the 2011 PSS Summit in Seattle, where the awards ceremony will take place, four nights' hotel accommodation, and $300 towards travel expenses. They will also be featured on Simple-Talk. Are you ready? Are you nervous?

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  • Sessions I Submitted to the PASS Summit 2010

    - by andyleonard
    Introduction I'm borrowing an idea and blog post title from Brent Ozar ( Blog - @BrentO ). I am honored the PASS Summit 2010 (Seattle, 8 - 11 Nov 2010) would consider allowing me to present. It's a truly awesome event. If you have an opportunity to attend and read this blog, please find me and introduce yourself. If you've built a cool solution to a business or technical problem; or written a script - or a bunch of scripts - to automate part of your daily / weekly / monthly routine; or have some...(read more)

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  • Welcome to Jackstown

    - by fatherjack
    I live in a small town, the population count isn't that great but let me introduce you to some of the population. We'll start with Martin the Doc, he fixes up anything that gets poorly, so much so that he could be classed as the doctor, the vet and even the garage mechanic. He's got a reputation that he can fix anything and that hasn't been proved wrong yet. He's great friends with Brian (who gets called "Brains") the teacher who seems to have a sound understanding of any topic you care to pass his way. If he isn't sure he tells you and then goes to find out and comes back with a full answer real quick. Its good to have that sort of research capability close at hand. Brains is also great at encouraging anyone who needs a bit of support to get them up to speed and working on their jobs. Steve sees Brains regularly, that's because he is the librarian, he keeps all sorts of reading material and nowadays there's even video to watch about any topic you like. Steve keeps scouring all sorts of places to get the content that's needed and he keeps it in good order so that what ever is needed can be found quickly. He also has to make sure that old stuff gets marked as probably out of date so that anyone reading it wont get mislead. Over the road from him is Greg, he's the town crier. We don't have a newspaper here so Greg keeps us all informed of what's going on "out of town" - what new stuff we might make use of and what wont work in a small place like this. If we are interested he goes ahead and gets people in to demonstrate their products  and tell us about the details. Greg is pretty good at getting us discounts too. Now Greg's brother Ian works for the mayors office in the "waste management department" nowadays its all about the recycling but he still has to make sure that the stuff that cant be used any more gets disposed of properly. It depends on the type of waste he's dealing with that decides how it need to be treated and he has to know a lot about the different methods and when to use which ones. There are two people that keep the peace in town, Brent is the detective, investigating wrong doings and applying justice where necessary and Bart is the diplomat who smooths things over when any people have a dispute or disagreement. Brent is meticulous in his investigations and fair in the way he handles any situation he finds. Discretion is his byword. There's a rumour that Bart used to work for the United Nations but what ever his history there is no denying his ability to get apparently irreconcilable parties working together to their combined benefit. Someone who works closely with Bart is Brad, he is the translator in town. He has several languages that he can converse in but he can also explain things from someone's point of view or  and make it understandable to someone else. To keep things on the straight and narrow from a legal perspective is Ben the solicitor, making sure we all abide by the rules.Two people who make for an interesting evening's conversation if you get them together are Aaron and Grant, Aaron is the local planning inspector and Grant is an inventor of some reputation. Anything being constructed around here needs Aarons agreement. He's quite flexible in his rules though; if you can justify what you want to do with solid logic but he wont stand for any development going on without his inclusion. That gets a demolition notice and there's no argument. Grant as I mentioned is the inventor in town, if something can be improved or created then Grant is your man. He mainly works on his own but isnt averse to getting specific advice and assistance from specialist from out of town if they can help him finish his creations.There aren't too many people left for you to meet in the town, there's Rob, he's an ex professional sportsman. He played Hockey, Football, Cricket, you name it. He was in his element as goal keeper / wicket keeper and that shows in his personal life. He just goes about his business and people often don't even know that he's helped them. Really low profile, doesn't get any glory but saves people from lots of problems, even disasters on occasion. There goes Neil, he's a bit of an odd person, some people say he's gifted with special clairvoyant powers, personally I think he's got his ear to the ground and knows where to find out the important news as soon as its made public. Anyone getting a visit from Neil is best off to follow his advice though, he's usually spot on and you wont be caught by surprise if you follow his recommendations – wherever it comes from.Poor old Andrew is the last person to introduce you to. Andrew doesn't show himself too often but when he does it seems that people find a reason to blame him for their problems, whether he had anything to do with their predicament or not. In all honesty, without fail, and to his great credit, he takes it in good grace and never retaliates or gets annoyed when he's out and about.  It pays off too as its very often the case that those who were blaming him recently suddenly find they need his help and they readily forget the issues pretty rapidly.And then there's me, what do I do in town? Well, I'm just a DBA with a lot of hats. (Jackstown Pop. 1)

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  • Pain of the Week/Expert's Perspective: Performance Tuning for Backups and Restores

    - by KKline
    First off - the Pain of the Week webcast series has been renamed. It's now known as The Expert's Perspective . Please join us for future webcasts and, if you're interested in speaking, drop me a note to see if we can get you on the roster! The bigger your databases get, the longer backups take. That doesn't really seem like a huge problem — until disaster strikes and you need to restore your databases as fast as possible. Join my buddy Brent Ozar ( blog | twitter ), a Microsoft Certified Master of...(read more)

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  • Typesetting LaTeX fraction terms to be larger in an equation

    - by gotgenes
    I have the following formula in LaTeX, based on Fisher's Exact Test. (NOTE: requires the use of the amsmath package for \binom.) \begin{equation} P(i,j) = \sum_{x=|N(V_i) \cap V_j|}^{\min\{|V_j|, |N(V_i)|} \frac{ \binom{|V_j|}{x} \binom{|V - V_j|}{|N(V_i)| - x}} {\binom{|V|}{|N(V_i)|}} \end{equation} This renders the fraction portion with very small, difficult to read text: I would like my text more readable, as in the following example: What trickery can I use to get LaTeX to render my equation similarly?

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