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  • Outlook unable to print email

    - by Jason Taylor
    I have an installation of Outlook 2003 that won't print emails as of this morning. It can print calendars, and every other program can print fine. Outlook won't print the emails to any printer, not even a PDF creator. As soon as you hit "Print" nothing happens, there's no notification that the print job was sent or anything. The print server never receives a request to print from the computer.

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  • Windows 7 boot problem on a Lenovo Thinkpad Z61m 9450HAG

    - by Matt Taylor
    I recently did a full upgrade of Windows 7 on my Thinkpad. Everything worked fine after up until the second reboot (the first reboot after some updates installed worked OK). At second reboot time the system would just black screen before the Windows logo appears. Disk/wireless/power/battery lights are all lit and the disk light is active (flickering). However, if I remove my battery and boot with just power it boots fine and quickly, and everything is OK. Any help on why this won't boot with battery plugged in is greatly appreciated. I need to take this battery out on the road/trains, etc. A little more detail on this story. The battery I had inserted when doing the (failed) boot was a long life battery. I have not tried inserting this battery when Windows is logged in. I have another (normal life) battery that I have charged up within Windows. It has just got to 100% and I am about to reboot with it in. I am using the Lenovo power manager to diagnose the battery - all seems OK. I will report back shortly as to the outcome. OK, so I chose the reboot option from within Windows, the machine seemed to shutdown okay, but then stalled. It didn't turn off completely and didn't reboot, but just sat, with the fan humming, somewhere in between! I had to hold the power button in for a few seconds until the fan stopped and then hit the power button again to boot the machine from fresh. One good thing, with this battery (the normal one) it booted into Windows 7 the first time with a battery! So, now I have rebooting issues. I have 3 errors in the event log: A timeout was reached (30000 milliseconds) while waiting for the lxdxCATSCustConnectService service to connect. The lxdxCATSCustConnectService service failed to start due to the following error: The service did not respond to the start or control request in a timely fashion. The following boot-start or system-start driver(s) failed to load: cdrom Any thoughts?

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  • Force running a program as non-administrator in Vista

    - by Peter Taylor
    I've just installed, on Vista 32-bit, a program which in my opinion shouldn't require administrator rights. It's not installed in a system directory, and its purpose shouldn't obviously require any special privileges. However, the .exe has a UAC shield on it, and it asks me to elevate privileges immediately upon execution. I'm prepared to risk it doing nasty things with the privileges of my user account, but not prepared to risk elevating it. Is there anything I can do short of setting up a virtual machine for it (or downloading the source and compiling it myself)? (FWIW, the program in question is Pencil - pencil.evolus.vn/en-US/Downloads/Application.aspx - but I'm more interested in general answers than app-specific ones).

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  • Windows Server 2012 Hyper-V very slow

    - by Matt Taylor
    I have been running several Hyper-V VMs on Windows Server 2008 R2 for the past couple of years and enjoying perfectly adequate performance for my testing/development/r&d environments. I'm a software developer so my hardware knowledge is basic however I built the rig using: •Gigabyte GA-X58A-UD3R Intel X58 (Socket 1366) DDR3 Motherboard •Intel Core i7 960 3.20GHz (Bloomfield) (Socket LGA1366) •24GB triple channel RAM The host OS is running on an OCZ SSD and all the VMs are running on a 2TB Marvell SATA3 RAID 0 array consisting of 2 Western Digital Caviar Black 7,200rpm drives. I have tested the speed of the 2TB drive and appear to be getting less than 3Mbs but it can adequately run a 4 VM farm including a DC, (SQL) database and IIS application servers. I recently upgraded the SSD on which the host runs to a 256GB OCZ Vertex 4 and took the opportunity to upgrade to Windows Server 2012 and installed the Hyper-V role. I tried importing one of my existing Windows Server 2008 R2 VMs (and converted it to .vhdx) plus I have tried creating a brand new Windows Server 2008 R2 VM but both are running extremely slowly and I can see nothing obvious using the host and guest Task Manager/Resource Monitor tools. In both cases the VM has 8GB RAM (fixed), 4 CPUs, fixed size HD (not expanding) and is using an external virtual network running on a separate NIC to the host. I have upgraded the BIOS to the latest available version and checked the virtualization settings. I have run out of "obvious" (to a developer) things to check/configure and my next option will be to re-install the host OS but before I do I would very much appreciate any advice from any experts out there. Thanks

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  • Broad Band LAN connection through existing 6 wire phone line ( no phone connected )

    - by Paul Taylor
    I have an (up to but never achieved ) 10 mb broadband signal coming into my house along the telephone line. The modem then connects the broadband signal via a LAN connection and Wi-Fi signal to my computers and iPad. My workshop desk is 54 yards (approx. 50m) downhill from the modem (part of a separate building) – too far to give a good direct signal. The inside corner of the workshop (by a window) receives a weak signal. I have a disconnected telephone cable consisting of 6 wires going from the house to the workshop. The telephone is no longer used in the workshop - we use our mobile number for business calls. A broad band signal using the cable would not have to share with a phone. What would be the most economic price/efficient way to get the broadband signal to the workshop? I am writing in hope that since the telephone didn't need the six wires, an Ethernet connection might be similar and not need all the eight wires for a LAN connection. In theory could use the telephone wire to pull an Ethernet cable trough the underground pipe but I doubt if the cable would survive the strain. The broad band connection in the workshop does not have to have network facility. My skill level is high enough to do house wiring, plumbing and gas fitting; so given any sound advice and a wiring diagram or instructions I can probably work out the rest myself.

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  • overusage of RAM in Hypervm VPS

    - by Mac Taylor
    hey guys I have a VPS running on hypervm in proceses list i have something like this > /usr/libexec/mysqld --basedir=/usr > --datadir=/var/lib/mysql --user=mysql --pid-file=/var/run/mysqld/ user : mysql which takes 150 mb RAM and then /usr/sbin/named -u named -t /var/named/chroot user : Named 50 mb RAM taken by this process how can i solve this overusage of RAM and reduce it . I have access to root and SSH

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  • Restarting rsyslog re-sends logs again

    - by Jay Taylor
    I am running Ubuntu 12.04.1 LTS on EC2. I have a bunch of application servers which are configured to forward their logs to a central server via rsyslog. Since putting in Nagios monitoring on the log files on the central server, I've been getting alerts indicating that particular application servers are failing to forward their logs to the centralized server. Logging into the machines and restarting the rsyslog service fixes the problem. However, rsyslog then re-transmits the logs again, resulting in duplicates on the collector. Why is it doing this?

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  • Is there a way to insert a formatted calculation into Excel 2010 without using an image?

    - by Ryan Taylor
    I am maintaining a list of database column names, notes, and their calculations in an Excel 2010 spreadsheet. The calculations are included so as to document how to derive the values for the various columns and not for calculations within the spreadsheet. I have been entering the calculations into the cells simply as unformatted text like so: 100 - ((FiscalYearRegionConsumption - BaselineRegionConsumption) / (GoalRegionConsumption - BaselineRegionConsumption)) * 100 However, for long and/or complex calculations this could become rather unreadable. To improve readability and comprehension I would like to "pretty" print the calculation in an Excel cell. This would result in formatting that would like like this: The only solution I have come up with is to: Write the calculation in another application such as Word Take a screenshot of said calculation Past the screenshot into Excel The primary concern with this approach is maintenance. Should the calculation change or need correction I have to update two different sources of information. Is there a better way included a formatted calculation into an Excel cell?

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  • H.264 Pricing confusion

    - by Jamie Taylor
    not sure if this is the right place but there seems to be other H.264 questions here, if not please point me to the right place! I am taking uploaded content and encoding it to H.264, I'm confused about the pricing though. Do I have to pay to host and stream this video on my server (in Ireland). I've tried looking around google but there doesn't seem to be a definitive answer. Some countries have exceptions, some pay $2500. What kind of information should I be looking at to understand the pricing model more? Thanks.

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  • Upgrading PS1 Light Gun [on hold]

    - by Nathan Taylor
    Is There any possible way to upgrade the retro G-con Light Gun for PS1 to allow it to interact with HD TV's? I am aware that they were Designed purely for Tube TV's but I would be happy to know of any hardware that would maybe convert the light to hit the Pixels on an LCD TV. If not is there any other Light gun that would work on PS1 games but has the newer light gun hardware that can interact with a higher Pixel LCD TV?

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  • Software to replicate one computers display onto many other displays

    - by Joe Taylor
    We have a classroom setup with one teachers pc at the front. I am looking for some software, preferably open source although this is not a deal breaker, to force all displays in the room to replicate the teachers display. Also if this software could be locked so the students could not exit this software while it was running. Does anyone know of any software that could perform this task? I have googled around for a solution but haven't found anything suitable as yet. It would be running on Windows 7 Flavours of the software I have found are: Lanschool and NetOp. Open source alternatives would be better.

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  • Windows7 home 64bit + Outlook 2010, multiple non-concurrent users

    - by Jim Taylor
    We have one windows computer shared by eight people. I have set up separate login accounts for each user. One account has administrative privileges, the others are standard users. We installed Outlook 2010 with the intention that each user could access their own email separately, without seeing the mail of other users. This has not worked as we intended. When the administrator logs in to each standard user account and starts the outlook mail setup, he is prompted for the administrative password, and then sets up the mail account. When accessing the outlook mail program after setup, each mail account shows as a separate tab in a communal inbox, rather than a separate mail box for each user. How would we accomplish the desired separation of Outlook mail accounts? Thanks for your advice Jim T.

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  • Autoscaling EC2 with NFS mounts

    - by Jamie Taylor
    I'm trying to set up a shared filesystem on EC2 and I've read tutorials such as this: http://blog.ronaldmccollam.com/2012/07/configuring-nfs-on-ubuntu-in-amazon-ec2.html In step 2 it talks about configuring the exports, for this I need an IP range but when I'm auto-scaling I can't predict what the IP will be before it scales. Is there any other way of doing this while still staying secure? Thanks Edit: Just tried s3fs, didn't seem to work properly

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  • Log all files saved on XP system.

    - by Jason Taylor
    I have a user that frequently saves items (or even forgets to save) to places that he forgets. Usually a simple search finds them, but not always. Is there any way to log/track the most recently saved files? It would be great to be the last "saved" files as the recent documents feature is unreliable if he constantly opens documents in his search for the file he just saved. Alternatively, any ideas on how to control this situation?

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  • Localhost has just stopped working (using xampp)

    - by Joe Taylor
    I installed Xampp to use for local development of a Drupal site. Its been working fine out of the box until now. The main Xampp localhost welcome menu loads, however my subdirectory (localhost/drupal) doesn't. It just spins in the browser for ages and nothing happens. Just a blank screen. I've tried the edit people suggest in the hosts file but that hasn't work and I'm getting no errors so not sure what to do. Anyone have any ideas what might be wrong? PS I'm running Windows 7 edit: Log files: Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 123731968 bytes) in C:\xampp\apps\drupal\htdocs\sites\all\themes\directory\node--job.tpl.php on line 41 Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 123731968 bytes) in C:\xampp\apps\drupal\htdocs\sites\all\themes\directory\node--job.tpl.php on line 41 [Tue Nov 05 20:52:07.242454 2013] [ssl:warn] [pid 8432:tid 260] AH01909: RSA certificate configured for www.example.com:443 does NOT include an ID which matches the server name [Tue Nov 05 20:52:07.331459 2013] [core:warn] [pid 8432:tid 260] AH00098: pid file C:/xampp/apache/logs/httpd.pid overwritten -- Unclean shutdown of previous Apache run? [Tue Nov 05 20:52:07.820487 2013] [ssl:warn] [pid 8432:tid 260] AH01909: RSA certificate configured for www.example.com:443 does NOT include an ID which matches the server name [Tue Nov 05 20:52:07.898492 2013] [mpm_winnt:notice] [pid 8432:tid 260] AH00455: Apache/2.4.4 (Win32) OpenSSL/0.9.8y PHP/5.4.16 configured -- resuming normal operations [Tue Nov 05 20:52:07.898492 2013] [mpm_winnt:notice] [pid 8432:tid 260] AH00456: Server built: Feb 23 2013 13:07:34 [Tue Nov 05 20:52:07.898492 2013] [core:notice] [pid 8432:tid 260] AH00094: Command line: 'c:\xampp\apache\bin\httpd.exe -d C:/xampp/apache' [Tue Nov 05 20:52:07.905492 2013] [mpm_winnt:notice] [pid 8432:tid 260] AH00418: Parent: Created child process 7588 [Tue Nov 05 20:52:08.882548 2013] [ssl:warn] [pid 7588:tid 272] AH01909: RSA certificate configured for www.example.com:443 does NOT include an ID which matches the server name [Tue Nov 05 20:52:09.467582 2013] [ssl:warn] [pid 7588:tid 272] AH01909: RSA certificate configured for www.example.com:443 does NOT include an ID which matches the server name [Tue Nov 05 20:52:09.534585 2013] [mpm_winnt:notice] [pid 7588:tid 272] AH00354: Child: Starting 150 worker threads. Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 123731968 bytes) in C:\xampp\apps\drupal\htdocs\sites\all\themes\directory\node--job.tpl.php on line 41 Fatal error: Allowed memory size of 134217728 bytes exhausted (tried to allocate 123731968 bytes) in C:\xampp\apps\drupal\htdocs\sites\all\themes\directory\node--job.tpl.php on line 41

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  • Ubuntu 10.10 and Windows 7 (TrueCrypt) Multi-boot Problems

    - by Samuel Taylor
    I have now been searching days for a solution but have found nothing. I have Ubuntu 10.10 and Windows 7 with TrueCrypt as a multi-boot. It was working fine for a few weeks until I needed to reinstall Ubuntu. If I have the boot flag on the partition where Windows 7 is install (This is where the boot flags was when working before.), it boots fine in to Windows 7 but when pressing Esc it can't find grub2. If I have the boot flag on the partition where Ubuntu is install, it boots fine in to Ubuntu (by pressing Esc or typing the password) but unable to access Windows. I have tried reinstalling TrueCrypt Boot loader and repairing the header but it have no affect. My Partitions: sda1 - Windows 7 Recovery (GRUB2) sda2 - Windows 7 (TrueCrypt Boot Loader) sda3 - Ubuntu 10.10 (/) sda4 - Extended sda5 - Swap sda6 - Ubuntu (/home) Does anyone have any ideas? Thanks Sam

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  • Magical moving desktop icons

    - by Nathan Taylor
    I have encountered a very strange behavior in Windows 7 that I cannot seem to identify and I have never seen or heard of on any system configuration. Whenever I move my mouse to the left-most edge of my primary display (centered in 3-display setup), my desktop icons magically move away from the cursor (up or down and to the right). It only happens when my desktop has focus and the mouse is positioned on the left, top or bottom edge of the main display. Moving the mouse all the way to the right edge of my right secondary display causes the mouse icons to snap back into their correct position. Ridiculous video of the issue My setup is 3 displays on two display adapters. The main display is running at 2560x1600, connected to the machine via a USB-powered DVI-D to DisplayPort adapter and is driven by an NVIDIA NVS 3100M video card. The secondary displays are running at 1440x900 and 1200x1920 and are driven by integrated Intel HD Graphics (mobile). It seems like some kind of panning behavior, but it's obviously not working as expected. I have updated all of my drivers, but no change. It's probably worth noting that the desktop icons are set to auto-arrange.

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  • VM's, virtual networks and my home network.

    - by Jason Taylor
    I want to create a small lab of VM's to test out networking with. I have two PC's running VMWare and I need the VM's on these two PC's to be connected to their own LAN. I am planning on bridging the VM's into my home network. My home network and PC's are in the 192.168.0.0 range, but I want my VM's to be in 10.1.0.0. If I do it this way (Bridging the VM's on both hosts into the network) will the VM's be able to communicate? Will my home router freak out seeing two different subnets? Is there another, easier way to connect the virtual lan's on two vmware workstations together?

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  • How could all of my hard drives fail at once?

    - by Taylor
    I have an Ubuntu 13.04 server. Today I found the box had crashed. I restarted it, and now every single hard drive's partition table is missing. (1 SSD for /boot, /, and 3 2TB drives for RAID). I have the SSD connected to a laptop VIA USB-SATA cable, and sure enough, the partition table is missing. This tells me that the Motherboard / SATA controller / software actually broke the drives, not that they just can't be read correctly. Something similar happened to only the SSD a few months ago, and I was forced to just re-partition it. How the heck could his have happened? Bad Motherboard or SATA controller?

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  • Customising Windows 8 Start Screen Tiles

    - by Joe Taylor
    We are looking for an effective way to manage the start screen in Windows 8. So far using WSIM we can add certain start tiles by using the OOBE System - shell setup - SquareTiles and WideTiles properties. However this only seems to work for square tiles and not wide tiles, if anyone has any insight on this it would eb appreciated. However the main question is has anyone managed to modify this screen using a GPO, we can add application shortcuts to the Start menu list on the All Apps page using a create shortcut to all users start menu policy. However as we occasionally deploy apps throughout the year in line with the courses requirements we would want to be able to put a shortcut on the home screen. Is it possible?

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  • How does KMS (Windows Server 2008 R2) differentiate clients?

    - by Joe Taylor
    I have recently installed a KMS Server in our domain and deployed 75 new Windows 7 machines using an image I made using Acronis True Image. There are 2 variations of this image rolled out currently. When I go to activate the machines it returns that the KMS count is not sufficient. On the server with a slmgr /dlv it shows: Key Management Service is enabled on this machine. Current count: 2 Listening on Port: 1688 DNS publishing enabled KMS Priority: Normal KMS cumulative requests received from clients: 366 Failed requests received: 2 Requests with License status unlicensed: 0 Requests with License status licensed: 0 Requests with License status Initial Grace period: 1 Requests with License statusLicense expired or hardware out of tolerance: 0 Requests with License status Non genuine grace period: 0 Requests with License status Notification: 363 Is it to do with the fact that I've used the same image for all the PC's? If so how do I get round this. Would changing the SID help? OK knowing I've been thick whats the best way to rectify the situation. Can I sysprep the machines to OOBE on each individual machine? Or would NewSID work?

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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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  • Google I/O 2011: Querying Freebase: Get More From MQL

    Google I/O 2011: Querying Freebase: Get More From MQL Jamie Taylor Freebase's query language, MQL, lets you access data about more than 20 million curated entities and the connections between them. Level up your Freebase query skills with advanced syntax, optimisation tricks, schema introsopection, metaschema, and more. From: GoogleDevelopers Views: 2007 15 ratings Time: 46:49 More in Science & Technology

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