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User:Jeff Hasse/Missing Person Case Study -- Brandon Swanson

Event Timeline
Tuesday, May 13, 2008

Brandon started his evening at a house in Lynd, MN rented by several friends. He had just finished a year-long technical school program in wind energy. It was the night before graduation and he was at a small gathering of five people described as a “get together of a few friends.” He consumed an unknown amount of alcohol. One eyewitness stated that the gathering was “low key” and Brandon was not overly intoxicated.

Between 10:30 and 11:00 pm, he left the gathering alone and drove to another friend’s house in Canby to say goodbye to a classmate. It was reported that he had an additional shot of whiskey at this party. He was there only for a short time and left some time after midnight for his home in Marshall.

Wednesday, May 14, 2008

The two-lane Highway 68 is a direct route southeast from Canby to Marshall. Brandon had driven it many times. Yet he doesn’t appear to have taken Highway 68 to get home. It appears that he was driving on gravels roads northeast of the highway to get home. We believe he was on the gravel roads to avoid detection by law enforcement and a DUI charge. These gravel roads do not parallel the highway, they are at about a 45 degree angle to the highway (running east-west and north-south), so he would have had to make multiple turns in a stair-step fashion to follow the highway’s relative path.

We know that he eventually ended up driving west down a minimum maintenance road for a mile. This is actually a field road between two large crop fields. He was attempting to turn south back on to a gravel road when he missed the field approach and went into the ditch at low speeds. The ditch bank was shallow but steep there and the frame of the car became hung up, so he was not able to back out or go forward. This occurred at approximately 1:15 a.m. There was no damage to the car and no evidence of injury inside the vehicle.

Brandon attempted to contact two or three of his friends by cell phone but was unable to reach them, so he called his parents for assistance at 1:54 a.m. Brandon says he is in a ditch between Marshall and Lynd and directs his parents there. There were several calls placed between Brandon and his parents between 1:54 and 2:17 a.m. During one call, he states he is on the left side of the road just off Highway 23 (suggesting from the position his car was found that he was oriented towards the south and was confusing Highway 68 for Highway 23). During this time, Brandon’s parents searched for him by car but were unable to find him.

There has been considerable speculation as to why Brandon was so disoriented as to his location. We believe that it is relatively easy to explain. His disorientation was likely due to a combination of five factors: 1) fatigue, 2) at least mild intoxication (Remember, his blood alcohol was still rising after he left Canby from that shot of whiskey.), 3) unfamiliar roads (While he had driven Hwy 68 many times, he probably had little reason to drive the gravel roads.), 4) the fact that all the intersections look relatively alike (mostly tilled fields with very few landmarks), and 5) possibly simple distraction. These all could have contributed to him not knowing exactly where he was.

How he came to the conclusion that he was near Lynd is a little more difficult to explain. While we will never know for sure, we believe that when he realized he had travelled down a minimum maintenance road, he conducted what is known as a transderivational search. He searched his memory for other minimum maintenance roads that he knew and came up with the gravel road which lies along a golf course between Marshall and Lynd with which he was apparently familiar.

At 2:17a.m., Brandon’s mother calls him. Brandon is clearly becoming impatient and tells her that he is going to walk to Lynd. He directs his parents to meet him at the Lyndwood Tavern in Lynd.

At 2:23 a.m., Brandon and his father begin a 47-minute cell phone call. During this call, Brandon indicates that he was walking along a gravel road away from Marshall towards Lynd. At some point, he leaves the road and travels cross-country, stating that he is going to “cut across because it will be quicker than following the road.” He further stated that he had encountered two fence lines and noted that there was water nearby. Shortly after, Brandon exclaims; “Oh s***.” His father believes he hears Brandon’s foot slipping and the phone goes dead. This was at 3:10 a.m. No further contact was made, even after repeated attempts.

Weather in the early morning hours of May 14th was mostly clear with a light wind (for the area) of 6-9 mph. The temperature at the time of his disappearance was 46° F and dropped to a low of 39° F. The moon was at its third quarter, due west of Brandon’s position, and setting at the time the phone went dead.

Brandon’s parents continue to look for him throughout the night. At 6:30 a.m., they contact the Lyon County Sheriff’s Office and report him missing.

Reflex Tasking Phase of the Search
Wednesday, May 14, 2008

We do not have any direct documentation regarding the early hours of the search. The following is based on reports from Brandon’s family and media reports.

We can presume that, after taking the initial information, an ATL (attempt to locate) was issued for Brandon and his car. It is our understanding that the Sheriff’s Office put in a request to Brandon’s cell carrier for data. We also understand that no information was immediately available because no one was at the carrier’s offices yet that morning. Shortly after the office opened, they found that Brandon's cell had been connected to the cell tower located just south of Minneota. I presume that they immediately refocused their search efforts in that area. At approximately 12:30 p.m., a Lyon County Sheriff Deputy found Brandon’s car located 1.5 miles north of MN Highway 68 on the border of Lyon and Lincoln Counties. The UTM coordinate of the vehicle’s location is 14T, 730613mE, 4945208mN (WGS84).

Regarding information that can be gleaned from a cell-phone call after the fact: While this is somewhat beyond my expertise, this is what I understand. Contrary to popular belief, cell phone carriers do not constantly keep track of the exact GPS location of every phone in the system (Big Brother isn't really watching...); only what tower each phone is connected to. This is for several reasons. Not all phones are GPS capable. While phone systems can roughly triangulate a call’s origin, this requires the phone to be picked up by multiple towers (and many calls are only carried by one tower). And keeping records of this data would require massive data storage capacity which increases cost to the carriers. In order for a law enforcement agency to track the phone, the phone has to be queried by the carrier. This requires some paperwork and approvals. We don’t know if this was attempted in this case, but it likely would not have been any help, since by this time, the phone was most probably already inoperable.

In the various missing person websites, many inferences have been made regarding the fact that Brandon's cell phone rang for a time before it went straight to voice mail. Unfortunately, little can be accurately inferred from this. According to one of our team members who is an executive at a regional telephone company, the ring that you hear when you call someone has little to do with what is happening at the other end (the recipient's phone). It is an artificial sound that is being generated at a switch in some building, not by the recipient's phone. It is a holdover from the old analog phone days. The way a phone handles voice-mail when it is turned off or disabled is entirely dependent on how this function is programmed at the phone carrier's computer systems. Therefore, there is a great deal of variability regarding how it works between carriers, calling plans, and even models of phones. While there are many possibilities regarding what happened at the end of Brandon's phone call to his father (the phone may have been lost, shorted out in water, battery dead, working but Brandon wasn't able to use it, etc.), the only thing that can be accurately inferred is that Brandon wasn't able to reestablish contact with his father after that point.

Some more information regarding cell phone tower networks:

The paradigm is the assumption that, when you make a call on your cell phone, it automatically routes to the nearest cell tower, and that by capturing those records police can determine where you made a call—and thus where you were—at a particular time. That, is not how the system works.

When you hit “send” on your cell phone, a complicated series of events takes place that is governed by algorithms and proprietary software, not just by the location of the cell tower. First, your cell phone sends out a radio-frequency signal to the towers within a radius of up to roughly twenty miles—or fewer, in urban areas—depending on the topography and atmospheric conditions. A regional switching center detects the signal and determines whether to accept the call. There are hundreds of such regional centers across the country.

The switching center determines the destination of your call and connects to the land lines that will take it to cell towers near the destination. Almost simultaneously, the software “decides” which of half a dozen towers in your area you’ll connect with. The selection is determined by load-management software that incorporates dozens of factors, including signal strength, atmospheric conditions, and maintenance schedules. The system is so fluid that you could sit at your desk, make five successive cell calls and connect to five different towers. During a conversation, your signal could be switched from one tower to the next; you’ll also be “handed off” to another tower if you travel outside your coverage area while you’re speaking. Designed for business and not tracking, call-detail records provide the kind of information that helps cell companies manage their networks, not track phones.

We (the civilian SAR resources involved in the case) know little about the first day’s search efforts. One media account mentioned that, besides using local officers for the initial search efforts, they requested the help of a canine from nearby Chippewa County. I don’t know what this dog found. However, I suspect that this dog is a police canine and attempted to run a non-scent-specific track (as opposed to a scent-specific trailing dog). This would have been at least 10 hours after the cell-phone contact was lost, which is a stretch for a tracking dog (which generally follows fear scent and the track made by crushed vegetation).

We also know that the car was towed away the first day of the search. In an unfortunate coincidence, the roads were graded the morning of the 14th, destroying any footprints.

Thursday, May 15, 2008

By 11:00 a.m., members of the Codington County Search Dive & Rescue team arrived at the request of the Lyon County Sheriff. This was a very good call.

While initial attempts at obtaining a direction of travel using trailing dogs failed, once they switched to another scent article, one of the dogs was able to pick up a trail. From Brandon’s vehicle, it traveled ½ mile south then turned west onto 390th St. where it continued for a mile. There, the trail turned north onto Co. Rd. 16. The trail continued north for ½ mile then turned west onto the driveway of an abandoned farm. It continued west for approximately ¼ of a mile and then left the driveway and roughly followed the course of the Yellow Medicine River heading northwest. At one point the bloodhound jumped into the Yellow Medicine River and then exited it. The handler interpreted this behavior as possibly indicating that Brandon might have fallen into the river at that point. However, the trail continued past this point to a drainage, where it continued north towards the gravel road forming the boundary between Lincoln and Yellow Medicine Counties. The dog was unable to trail any further.

This trail is consistent with Brandon’s 47-minute cell phone conversation with his father. We know he travelled along gravel roads for most of the conversation. He then left the road and travelled cross-country at the driveway. He mentioned two fencelines, which are in the area. The terrain near the river is wooded, uneven, and has many animal den holes. In addition, Brandon was congenitally blind in his left eye, making his depth perception poor (especially in the dark). And the moon was setting during the conversation, leaving him with only starlight to navigate by. Finally, the average person walks between 1 and 3 miles per hour. That puts Brandon between ¾-mile and 2.5-miles away from his car when the phone went dead. The trail to the point in the river where the dog jumped in is within that range.

We believe that it is most likely that Brandon tripped, stumbled, or slipped on one of the many hazards in the area. He likely dropped his phone and it was rendered inoperable somehow (shorted out in water, hit something hard and broke, battery popped out, or he simply couldn't find it again).

In addition to the bloodhounds, two area search dogs worked the area near the car and around the Yellow Medicine River. There were also an unknown number of emergent volunteers searching the area around the vehicle and a team from the Department of Natural Resources that floated the river in a boat.

Based on the bloodhound trail, a presumption was made that Brandon fell into the water and drowned. Much of the search effort from this point on is directed towards this scenario. While this was a reasonable scenario to explore, other scenarios exist, such as Brandon stumbled, lost or broke his phone, and continued walking. In fact, the bloodhound evidence is more suggestive of the second scenario. While the dog did at one point jump into the Yellow Medicine River, it came out again and continued with good purpose of movement, suggesting the trail continued. The dog was able to follow the trail until just shy of another gravel road. When a dog stops trailing, this doesn’t necessarily mean the trail "ends;" it may simply mean that the dog is at the end of its "nose time." This was over a three-mile trail, which is a relatively long trail.

The Search Planning Process
Every Search Manager must deal with two fundamental questions during a missing person search: Where do we search? and How do we search? This section describes the ways the planning team decided where to search in the Brandon Swanson case. These are standard practices taught by both the so-called Land SAR community (e.g., NASAR) and the so-called Mathematical model (e.g., the Air Force’s Inland SAR Planning Course).

There are four standard methods used to determine the overall search area and initial search priorities:

1) Theoretical Maximum Distance Traveled
 * This is simply the rate of travel multiplied by the time traveled. Since the average person walks between 1 and 3 mph, and Brandon walked between 47 and 53 minutes, this gave us the 0.75 to 2.5-mile initial planning ring.  (On the master map, the minimum distance is designated with diamonds and the maximum distance by triangles.)

2) Statistical
 * Retrospective studies based on the International Search and Rescue Incident Database found that, in these circumstances (abandoned vehicles), subjects were found 5.6 miles from the Last Known Position 95% of the time, yielding a total search area of 98.5 square miles. The median distance is 1.3 miles (5.3 square mile search area).

3) Subjective Considerations
 * This includes evaluating attractants, navigation aids, and navigation barriers that might influence where Brandon would go. This yielded a number of "investigative clues" that helped us set initial search priorities.
 * The following subjective considerations were evaluated in this case:
 * Attractants (principally lights from the surrounding area):
 * The most visible man-made light in the area was the prominent glow from the east-southeast in the direction of Minneota (although it is likely that this was a glow of lights from Marshall).
 * There was a scattering of individual lights in all directions. None stood out.
 * Navigation Aids:
 * County roads (For the majority of the 47 minute conversation, Brandon traveled along one of the gravel roads.)
 * The glow of lights in the distance. (Brandon believed he was oriented to his location.)
 * Navigation Barriers:
 * Yellow Medicine River to the south (although multiple bridges cross the river)
 * Mud Creek to the north (although multiple bridges cross the creek)
 * Highway 68 SSE

4) Deductive Reasoning
 * We came up with and evaluated a number of scenarios that might explain the circumstances of his disappearance.
 * Known: On May 15, 2008, Brandon left a gathering in Canby to drive home Marshall when he drove west down a field road, attempted to turn south onto a gravel road, and became stuck.  He believed he was somewhere between Marshall and Lynd.  Between 2:15 and 2:25 am, he left his car and began walking.  He was attempting to meet his parents at the Lyndwood Tavern.  At the end of a 47-minute cell phone conversation, Brandon uttered an expletive and the phone went dead.
 * Due to the nature of this case, planners evaluated two separate sets of scenarios: What direction Brandon might have headed during the cell phone conversation and what happened after the cell phone went dead.

 * A. Initial Direction of Travel Scenarios (During the cell-phone conversation):
 * 1. Brandon traveled easterly.
 * 1.1 Due east across field road (395th St), 110th Ave around Congers Marsh, east on Lyon-Yellow Medicine Rd.
 * 1.2 South on Lyon-Lincoln County Rd., east on 390th St (towards Taunton).
 * 2. Brandon traveled south.
 * 3. Brandon traveled westerly (towards Porter).
 * If Brandon intended to go west from his LKP, he only had two choices if he wanted to walk along a road. 1) To go south along the road he was on and turn west at the nearest intersection or 2) Go north and turn west.  Either way, he would likely turn west at the nearest opportunity.
 * 3.1 South on Lyon-Lincoln County Rd, west on 390th St. Then either south on 270th St to Highway 68 or north on 270th St.
 * 3.2 North on Lyon-Lincoln County Rd, west on 400th St.
 * 3.3 North on Lyon-Lincoln County Rd, west on 170th Ave (or 180th, 190th, etc.)
 * 4. Brandon traveled northerly (on Lyon-Lincoln County Rd).
 * 5. Brandon traveled northeasterly.

 * B. Scenarios After Phone Went Dead:
 * 1. Brandon was killed at the point the phone went dead (or became immobilized by injury and later perished in the same area).
 * Notes: Brandon was traveling cross-country at the time.  During the 47-minute conversation, Brandon likely traveled between ¾ to 2.5 miles.
 * 1.1 Brandon drowned in one of the many waterways in the area.
 * 1.2 Brandon stumbled, injured himself (thereby becoming immobilized), and later succumbed to the cold weather.
 * 2. Brandon slipped and his phone was somehow rendered inoperable, but he was able to continue walking.
 * 2.1 Brandon became wet from falling, wet grass, and/or sweating from the exertion of walking and became hypothermic over time, eventually succumbing to it.
 * 2.2 Brandon eventually fell into some sort of well, cistern, or tank and perished there.
 * 3. Brandon was picked up by someone and taken outside of the search area.
 * 3.1 Brandon was later harmed by whoever picked him up.
 * 3.2 Brandon obtained a ride from someone who was able to transport him to safety and Brandon is alive and well and living elsewhere.

Planning Scenarios Discussion

 * This is the process we used to evaluate the various scenarios regarding what happened to Brandon before and after the cell phone went dead. Feel free to add to the arguments.

Initial Direction of Travel Scenarios (During the cell-phone conversation):

 * 1. Brandon traveled due east across the field road (395th St) to 110th Ave around Congers Marsh, then east on Lyon-Yellow Medicine Rd.
 * Arguments for: Brandon may have been backtracking his route.  (It is unknown in what direction he thought the Lyndwood Tavern laid.)
 * Arguments against: Brandon thought he was between Marshall and Lynd.  There is no evidence that he was backtracking towards Marshall.

 * 2. Brandon traveled east by first going south on Lyon-Lincoln County Rd., then east on 390th St.
 * Arguments for:
 * Taunton was the closest town to the LKP.
 * During the cell phone call, he stayed on the Minneota Tower.
 * Arguments against:
 * Taunton was nearly invisible (no glow of lights).

 * 3. Brandon traveled south on the Lyon-Lincoln Road.
 * Arguments for: None known
 * Arguments against: He would have reached the highway within the 47-minute conversation.  If so, he would likely have mentioned it to his parents.  No mention was made.

 * 4. Brandon traveled westerly by first going south on Lyon-Lincoln County Rd, west on 390th St., then either south on 270th St to Highway 68 or north on 270th St.
 * If Brandon intended to go west from his LKP, he only had two choices if he wanted to walk along a road. 1) To go south along the road he was on and turn west at the nearest intersection or 2) Go north and turn west.  Either way, he would likely turn west at the nearest opportunity.
 * Arguments for:
 * Brandon’s vehicle was heading west when it went into the ditch. Accordingly, he likely thought his destination was to the west or northwest.
 * The brightest glow in the sky was Minneota, which was east-southeast of Brandon’s LKP. He would likely have thought that this was Marshall and headed away from it towards where he thought Lynd was located.
 * At one point in the conversation, when asked on which side of the road his car was located, he replied; “On the left side.” This indicates that he was facing south at that time, which may suggest an intended direction of travel.
 * Later, he mentioned that he could clearly see the moon (suggesting that it was within his field of vision). At the time he was walking, the moon was due west of his position near or at the horizon.  While certainly a “soft” clue, this suggests that he may have been heading westerly at the time he made the statement.
 * Brandon stated that he believed he was on the road between Savannah Hills Golf Course and Lynd. He also believed that he is just off Highway 23.  If one compares the relative positions of Marshall, the Lyndwood Tavern, and Highway 23 with the positions of Minneota and Highway 68, a westerly direction of travel makes sense.
 * The trail established by trailing dog on Day 2 of the search.
 * Arguments against:
 * Porter is farther away than Taunton, (but Brandon probably didn’t know that).

 * 5. Brandon traveled westerly by first going north on Lyon-Lincoln County Rd, then west on 400th St.
 * Arguments for:
 * Brandon’s vehicle was heading west when it went into the ditch. Accordingly, he likely thought his destination was to the west.
 * The brightest glow in the sky was Minneota, which was east-south-east of Brandon’s LKP. He would likely have thought that this was Marshall and headed away from it towards where he thought Lynd was located.
 * Later, he mentioned that he could clearly see the moon (suggesting that it was within his field of vision). At the time he was walking, the moon was due west of his position near or at the horizon.  While certainly a “soft” clue, this suggests that he may have been heading westerly at the time he made the statement.
 * Brandon stated that he believed he was on the road between Savannah Hills Golf Course and Lynd. He also believed that he is just off Highway 23.  If one compares the relative positions of Marshall, the Lyndwood Tavern, and Highway 23 with the positions of Minneota and Highway 68, a westerly direction of travel makes sense.
 * Arguments against:
 * At one point in the conversation, when asked on which side of the road his car was located, he replied; “On the left side.” This indicates that he was facing south at that time, which may suggest an intended direction of travel (towards the south).
 * Porter is farther away than Taunton, (but Brandon probably didn’t know that).

 * 6. Brandon traveled westerly by first going north on Lyon-Lincoln County Rd, then west on 170th Ave (or 180th, 190th, etc.).
 * Arguments for: He may have decided to turn west at any intersection.
 * Arguments against: If he wanted to head west, it is more likely that he turned west at the nearest opportunity.  The phone conversation suggests that he was single-minded in his determination to go to the tavern.

 * 7. Brandon traveled north on the Lyon-Lincoln County Rd.
 * Arguments for:
 * There was a direct line of travel north.
 * It is unknown in what direction he thought the Lyndwood Tavern laid.
 * Arguments against:
 * At some point in the conversation, he left the road and went cross-country, so it is clear that Brandon believed that the tavern was not in a direct path along the road.

 * 8. Brandon traveled northeasterly.
 * Arguments for: None known
 * Arguments against: None known

Scenarios After Phone Went Dead:
 * 1. Brandon was killed at the point the phone went dead (or became immobilized by injury and later perished in the same area).
 * Notes: Brandon was traveling cross-country at the time.  During the 47-minute conversation, Brandon likely traveled between ¾ to 2.5 miles.

 * 1.1 Brandon drowned in one of the many waterways in the area.
 * Possible waterways include:
 * The Yellow Medicine River to the south and west.
 * The Mud Creek to the north.
 * Any of the many drainage ditches in the area.
 * Arguments for:
 * During the phone conversation, Brandon noted hearing moving water nearby.
 * Drowning would certainly account for Brandon’s disappearance.
 * Water searches are difficult to search to a 100% POD, therefore it is possible that he is still missing in the ¾ - 2.5 mile radius from the LKP.
 * Arguments against:
 * While it is clear that Brandon’s phone was rendered inoperable when he uttered the expletive, it is dangerous to assume that Brandon was unable to continue walking after that point.
 * The area within the ¾ - 2.5 mile radius from the LKP has been searched extensively without success (especially the Yellow Medicine River), suggesting that Brandon is located elsewhere.

 * 1.2 Brandon stumbled, injured himself (thereby becoming immobilized), and later succumbed to the cold weather.
 * Arguments for:
 * During the night in question, it is nearly certain that an immobile subject would have become hypothermic (especially with the light clothing that Brandon was wearing).
 * Arguments against:
 * A subject located on the ground within the ¾ - 2.5-mile radius from the LKP would likely have been found by now.

 * 2. Brandon slipped and his phone was somehow rendered inoperable, but he was able to continue walking.
 * 2.1 Brandon became wet from falling, wet grass, and/or sweating from the exertion of walking and became hypothermic over time, eventually succumbing to it.
 * Arguments for:
 * One cannot assume that Brandon stopped moving at the point the cell phone went dead. Cell phones are relatively fragile devices.
 * The area within the ¾ - 2.5 mile radius from the LKP has been searched extensively without success, suggesting that Brandon is located elsewhere. Per Robert Koester in Lost Person Behavior, “Hill, in an examination of suspended searches, found that in almost every case the search planners failed to search outside the median.”  In this case, the median distance is 1.3 miles (which has been searched extensively).  Statistically, there is a 50% chance that Brandon will be located beyond this distance.
 * Arguments against: None known

 * 2.2 Brandon eventually fell into some sort of well, cistern, or tank and perished there.
 * Arguments for:
 * This scenario would certainly account for why no one has spotted his body.
 * Arguments against:
 * Modern well casings for residential use are generally 4-6” in diameter. Small enough for a puppy to fall into, but not a human.  Municipal and commercial casing are often in the range of 16-20” in diameter, which is large enough to fall into.  However, there are none in the area that aren’t enclosed in buildings.  The only well that is large enough for an adult male to fall into that would have been accessible to Brandon is a hand-dug brick or timber lined well.  Any in the area would be over 100 years old and most likely be collapsed.  An intact pioneer well is an exceptionally rare thing in this area (if they are in the area at all).  The likelihood that he found the one intact pioneer well in the entire region is extremely low.
 * For many years, Minnesota law has required that old wells and cisterns be filled in and/or capped.
 * A more likely possibility is falling into a cistern. Many, if not most, old farms in the area had one.  Windmills would pump water into a cistern where it is more readily accessible.  They are often covered with a wooden covering which can rot away.  While all the teams have been looking for them, none have been found.
 * There just aren’t a lot of abandoned farms within the search area. We have found at least three old farmsteads on the map that have been completely wiped off the land.  The farmland in this area is so valuable that every footing, cistern, and piece of concrete has been removed.
 * All of the search teams that I have worked with on this search are aware of old cisterns and the like. The three or four abandoned farms we have found have been searched thoroughly.

 * 3. Brandon was picked up by someone and taken outside of the search area.
 * 3.1 Brandon was later harmed by whoever picked him up.
 * Arguments for: None known
 * Arguments against: The likelihood of meeting a predator in this rural area on a weeknight is quite remote.

 * 3.2 Brandon obtained a ride from someone who was able to transport him to safety and Brandon is alive and well and living elsewhere.
 * Arguments for: None known.
 * Arguments against:
 * Brandon did not have any means of supporting himself. 3.3 Brandon dropped his phone into water so he could no longer contact anyone, and continued walking. He was exposed to the cold and fatigue and lay down on a field, the next morning a farmer plowed over him. Keeping it quiet from anyone else he had to hide the body evidence, even though it was an accident. Brandon's scent was found on a piece of farm equipment and the farmer was reluctant to let investigators search. A possible way he got rid of all evidence was feeding Brandon to the animals.

Other possible scenarios

 * 1) Brandon was disoriented because he was taken against his will, blindfolded, and driven to the ditch location by an unknown operator.
 * 2) Unknown operator leaves Brandon in the car at the ditch and while unknown is gone Brandon escapes.
 * 3) Unknown operator catches up with Brandon in the woods, incapacitates him, and is driven away in another vehicle.
 * 4) This explains the disorientation and why a body has never been found in this search area.


text:
Search and rescue/SAR mission 2008 02

Situation

Brandon Swanson, age 19, disappeared on Wednesday, May 14, 2008, in Minnesota. At about 3:10 AM he was walking cross country in the dark while talking on his cell phone to his father, when he said "oh s***" and the phone call ended.

Brandon had been driving home to Marshall from a party at a friend's home in Canby, when he became disoriented. Canby is about 30 miles northwest of Marshall. Although Highway 68 goes from Canby directly to Marshall, Brandon drove on gravel and dirt back roads. These back roads are used mainly by local farmers to access agricultural fields ''Incorrect. They are used by locals everyday for everyday activities.'': most intersections lack signage [is this true? No] and the roads have few other distinguishing features. At one intersection Brandon drove the car into a shallow ditch, high-centering it. He used his cell phone to call home and ask his parents to come get him. He said he was near Lynd. Lynd is about 6 miles southwest of Marshall on Highway 23. Brandon's parents went to get him but did not find him or his car. At 2:23 AM Brandon's father called him and they discussed what to do. The duration of this phone call was about 47 minutes. While they talked, Brandon set out walking to meet his parents in Lynd. He walked at first on gravel roads, then cross country, until the abrupt end of the call. Brandon's parents were unable to make further contact. They continued to search for him and called 911 at 6:30 AM.

Around 12:30 PM a Lyon County Sheriff Deputy found Brandon's car about 2 miles northwest of Taunton. Taunton is on Highway 68 about 17 miles northwest of Marshall. The car was high-centered in a ditch at the intersection of a dirt road and north-south Lyon Lincoln Road, 1.3 miles north of its intersection with Highway 68 and 0.5 miles south of the county line. The WGS84 UTM coordinate of this location is 14T, 730613mE, 4945208mN (see Google Map). No other physical evidence was found, neither objects nor Brandon's tracks. That morning, before the car was found, gravel roads in the vicinity were graded.

Brandon's father wrote from memory what Brandon had said about his location. Brandon said his car was stuck near a highway that he identified as Highway 23 between Marshall and Lynd, and that he was walking on a gravel road toward Lynd. He "encountered" a fence line twice and noted "water nearby".

Event Timeline
Tuesday, May 13, 2008

Brandon started his evening at a house in Lynd, MN rented by several friends. He had just finished a year-long technical school program in wind energy. It was the night before graduation and he was at a small gathering of five people described as a “get together of a few friends.” He consumed an unknown amount of alcohol. One eyewitness stated that the gathering was “low key” and Brandon was not overly intoxicated.

Between 10:30 and 11:00 pm, he left the gathering alone and drove to another friend’s house in Canby to say goodbye to a classmate. It was reported that he had an additional shot of whiskey at this party. He was there only for a short time and left some time after midnight for his home in Marshall.

Wednesday, May 14, 2008

The two-lane Highway 68 is a direct route southeast from Canby to Marshall. Brandon had driven it many times. Yet he doesn’t appear to have taken Highway 68 to get home. It appears that he was driving on gravels roads northeast of the highway to get home. We believe he was on the gravel roads to avoid detection by law enforcement and a DUI charge. These gravel roads do not parallel the highway, they are at about a 45 degree angle to the highway (running east-west and north-south), so he would have had to make multiple turns in a stair-step fashion to follow the highway’s relative path.

We know that he eventually ended up driving west down a minimum maintenance road for a mile. This is actually a field road between two large crop fields. He was attempting to turn south back on to a gravel road when he missed the field approach and went into the ditch at low speeds. The ditch bank was shallow but steep there and the frame of the car became hung up, so he was not able to back out or go forward. This occurred at approximately 1:15 a.m. There was no damage to the car and no evidence of injury inside the vehicle.

Brandon attempted to contact two or three of his friends by cell phone but was unable to reach them, so he called his parents for assistance at 1:54 a.m. Brandon said he was in a ditch between Marshall and Lynd and directed his parents there. There were several calls placed between Brandon and his parents between 1:54 and 2:17 a.m. During one call, he stated he was on the left side of the road just off Highway 23 (suggesting from the position his car was found that he was oriented towards the south and was confusing Highway 68 for Highway 23). During this time, Brandon’s parents searched for him by car but were unable to find him.

At 2:17a.m., Brandon’s mother called him. Brandon was clearly becoming impatient and he told her that he was going to walk to Lynd. He directed his parents to meet him at the Lyndwood Tavern in Lynd.

At 2:23 a.m., Brandon and his father begin a 47-minute cell phone call. During this call, Brandon indicates that he was walking along a gravel road away from Marshall towards Lynd. At some point, he leaves the road and travels cross-country, stating that he is going to “cut across because it will be quicker than following the road.” He further stated that he had encountered two fence lines and noted that there was water nearby. Shortly after, Brandon exclaims; “Oh s***.” His father believes he hears Brandon’s foot slipping and the phone goes dead. This was at 3:10 a.m. No further contact was made, even after repeated attempts.

Weather in the early morning hours of May 14th was mostly clear with a light wind for the area of 6-9 mph. The temperature at the time of his disappearance was 46° F and dropped to a low of 39° F. The moon was at its third quarter, due west of Brandon’s position, and setting at the time the phone went dead.

Brandon’s parents continue to look for him throughout the night. At 6:30 a.m., they contact the Lyon County Sheriff’s Office and report him missing.

Location
The search area is in southwestern Minnesota, near South Dakota. Lyon Lincoln Road, where the car was found, marks the boundary between Lyon and Lincoln counties, and their boundary with Yellow Medicine County is 0.5 miles to the north.

As in most of the United States, in Minnesota search and rescue is the responsibility of the county sheriff.

The area is rich farmland, and relatively flat and wet. Water (mainly small creeks and lakes) and fence lines are widespread. Both highways Which highways are you referring to? share a right of way with a railroad, ''Incorrect. While the topo for Highway 68 shows a RR track, it has been completely erased from the landscape.'' and are roughly paralleled on their north sides by creeks.

When he high-centered the car, Brandon was driving west on a dirt road dividing Section 6 in Eidsvold Township (see Public Land Survey System), and tried to turn south onto the gravel road on the west boundary line of the section / township / county. Evidently he knew (or thought) he was near a highway, but not which highway. ''Incorrect. He believed he "was just off Highway 23."'' Thus, it is not known which side of the highway he thought he was on, nor which way he intended to walk relative to the highway to reach his destination. Brandon thought he was walking to a populated place on the highway, and he was between two such places: Porter to the northwest and Taunton to the southeast. How did he decide which way to go? Could he see lights ahead of him? Which lights would he have seen?

A search dog used early in the search traveled northwest, toward Porter. This information led to much of the subsequent search being devoted to the northwest of the car. ''Incomplete. The bloodhound trail led to the search efforts at the YMR. Other developments not yet reported led to the search focusing to the northwest.''

Subject
Male age 19 (May 2008), height 5 feet 6 inches, weight 120–130 pounds (slender build), Caucasian, average complexion, hair short brown, no facial hair, eyes blue. Last seen wearing a white MN Twins baseball cap, glasses, sterling silver chain necklace, white T-shirt, blue striped polo shirt, black hooded zip front sweatshirt with emblem on back, baggy blue jeans (hip hop style), belt (probably), white tennis shoes. Carried a black cell phone (Motorola SLVR L7c), wallet, car keys.

Reflex Tasking Phase of the Search
Wednesday, May 14, 2008

We do not have any direct documentation regarding the early hours of the search. The following is based on reports from Brandon’s family and media reports.

We can presume that, after taking the initial information, an ATL (attempt to locate) was issued for Brandon and his car. It is our understanding that the Sheriff’s Office put in a request to Brandon’s cell carrier for data. We also understand that no information was immediately available because no one was at the carrier’s offices yet that morning. Shortly after the office opened, they found that Brandon's cell had been connected to the cell tower located just south of Minneota. I presume that they immediately refocused their search efforts in that area. At approximately 12:30 p.m., a Lyon County Sheriff Deputy found Brandon’s car located 1.5 miles north of MN Highway 68 on the border of Lyon and Lincoln Counties. The UTM coordinate of the vehicle’s location is 14T, 730613mE, 4945208mN (WGS84).

We (the civilian SAR resources involved in the case) know little about the first day’s search efforts. One media account mentioned that, besides using local officers for the initial search efforts, they requested the help of a canine from nearby Chippewa County. I don’t know what this dog found. However, I suspect that this dog is a police canine and attempted to run a non-scent-specific track (as opposed to a scent-specific trailing dog). This would have been at least 10 hours after the cell-phone contact was lost, which is a stretch for a tracking dog (which generally follows fear scent and the track made by crushed vegetation).

We also know that the car was towed away the first day of the search. In an unfortunate coincidence, the roads were graded the morning of the 14th, destroying any footprints.

Thursday, May 15, 2008

By 11:00 a.m., members of the Codington County Search Dive & Rescue team arrived at the request of the Lyon County Sheriff.

While initial attempts at obtaining a direction of travel using trailing dogs failed, once they switched to another scent article, one of the dogs was able to pick up a trail. From Brandon’s vehicle, it traveled ½ mile south then turned west onto 390th St. where it continued for a mile. There, the trail turned north onto Co. Rd. 16. The trail continued north for ½ mile then turned west onto the driveway of an abandoned farm. It continued west for approximately ¼ of a mile and then left the driveway and roughly followed the course of the Yellow Medicine River heading northwest. At one point the bloodhound jumped into the Yellow Medicine River and then exited it. The handler interpreted this behavior as possibly indicating that Brandon might have fallen into the river at that point. However, the trail continued past this point to a drainage, where it continued north towards the gravel road forming the boundary between Lincoln and Yellow Medicine Counties. The dog was unable to trail any further.

This trail is consistent with Brandon’s 47-minute cell phone conversation with his father. We know he travelled along gravel roads for most of the conversation. He then left the road and travelled cross-country at the driveway. He mentioned two fencelines, which are in the area. The terrain near the river is wooded, uneven, and has many animal den holes. In addition, Brandon was congenitally blind in his left eye, making his depth perception poor (especially in the dark). And the moon was setting during the conversation, leaving him with only starlight to navigate by. Finally, the average person walks between 1 and 3 miles per hour. That puts Brandon between ¾-mile and 2.5-miles away from his car when the phone went dead. The trail to the point in the river where the dog jumped in is within that range.

We believe that it is most likely that Brandon tripped, stumbled, or slipped on one of the many hazards in the area. He likely dropped his phone and it was rendered inoperable somehow (shorted out in water, hit something hard and broke, battery popped out, or he simply couldn't find it again).

In addition to the bloodhounds, two area search dogs worked the area near the car and around the Yellow Medicine River. There were also an unknown number of emergent volunteers searching the area around the vehicle and a team from the Department of Natural Resources that floated the river in a boat.

Based on the bloodhound trail, a presumption was made by the local commanders that Brandon fell into the water and drowned. Much of the search effort from this point on is directed towards this scenario. While this was a reasonable scenario to explore, other scenarios exist, such as Brandon stumbled, lost or broke his phone, and continued walking. In fact, the bloodhound evidence is more suggestive of the second scenario. While the dog did at one point jump into the Yellow Medicine River, it came out again and continued with good purpose of movement, suggesting the trail continued. The dog was able to follow the trail until just shy of another gravel road.

The Search Planning Process
Every Search Manager must deal with two fundamental questions during a missing person search: Where do we search? and How do we search? This section describes the ways the planning team decided where to search in the Brandon Swanson case. These are standard practices taught by both the so-called Land SAR community (e.g., NASAR) and the so-called Mathematical model (e.g., the Air Force’s Inland SAR Planning Course).

There are four standard methods used to determine the overall search area and initial search priorities:

1) Theoretical Maximum Distance Traveled
 * This is simply the rate of travel multiplied by the time traveled. Since the average person walks between 1 and 3 mph, and Brandon walked between 47 and 53 minutes, this gave us the 0.75 to 2.5-mile initial planning ring.  (On the master map, the minimum distance is designated with diamonds and the maximum distance by triangles.)

2) Statistical
 * Retrospective studies based on the International Search and Rescue Incident Database found that, in these circumstances (abandoned vehicles), subjects were found 5.6 miles from the Last Known Position 95% of the time, yielding a total search area of 98.5 square miles. The median distance is 1.3 miles (5.3 square mile search area).

3) Subjective Considerations
 * This includes evaluating attractants, navigation aids, and navigation barriers that might influence where Brandon would go. This yielded a number of "investigative clues" that helped us set initial search priorities.
 * The following subjective considerations were evaluated in this case:
 * Attractants (principally lights from the surrounding area):
 * The most visible man-made light in the area was the prominent glow from the east-southeast in the direction of Minneota (although it is likely that this was a glow of lights from Marshall).
 * There was a scattering of individual lights in all directions. None stood out.
 * Navigation Aids:
 * County roads (For the majority of the 47 minute conversation, Brandon traveled along one of the gravel roads.)
 * The glow of lights in the distance. (Brandon believed he was oriented to his location.)
 * Navigation Barriers:
 * Yellow Medicine River to the south (although multiple bridges cross the river)
 * Mud Creek to the north (although multiple bridges cross the creek)
 * Highway 68 SSE

4) Deductive Reasoning
 * We came up with and evaluated a number of scenarios that might explain the circumstances of his disappearance.
 * Known: On May 15, 2008, Brandon left a gathering in Canby to drive home Marshall when he drove west down a field road, attempted to turn south onto a gravel road, and became stuck.  He believed he was somewhere between Marshall and Lynd.  Between 2:15 and 2:25 am, he left his car and began walking.  He was attempting to meet his parents at the Lyndwood Tavern.  At the end of a 47-minute cell phone conversation, Brandon uttered an expletive and the phone went dead.
 * Due to the nature of this case, planners evaluated two separate sets of scenarios: What direction Brandon might have headed during the cell phone conversation and what happened after the cell phone went dead.

 * A. Initial Direction of Travel Scenarios (During the cell-phone conversation):
 * 1. Brandon traveled easterly.
 * 1.1 Due east across field road (395th St), 110th Ave around Congers Marsh, east on Lyon-Yellow Medicine Rd.
 * 1.2 South on Lyon-Lincoln County Rd., east on 390th St (towards Taunton).
 * 2. Brandon traveled south.
 * 3. Brandon traveled westerly (towards Porter).
 * If Brandon intended to go west from his LKP, he only had two choices if he wanted to walk along a road. 1) To go south along the road he was on and turn west at the nearest intersection or 2) Go north and turn west.  Either way, he would likely turn west at the nearest opportunity.
 * 3.1 South on Lyon-Lincoln County Rd, west on 390th St. Then either south on 270th St to Highway 68 or north on 270th St.
 * 3.2 North on Lyon-Lincoln County Rd, west on 400th St.
 * 3.3 North on Lyon-Lincoln County Rd, west on 170th Ave (or 180th, 190th, etc.)
 * 4. Brandon traveled northerly (on Lyon-Lincoln County Rd).
 * 5. Brandon traveled northeasterly.

 * B. Scenarios After Phone Went Dead:
 * 1. Brandon was killed at the point the phone went dead (or became immobilized by injury and later perished in the same area).
 * Notes: Brandon was traveling cross-country at the time.  During the 47-minute conversation, Brandon likely traveled between ¾ to 2.5 miles.
 * 1.1 Brandon drowned in one of the many waterways in the area.
 * 1.2 Brandon stumbled, injured himself (thereby becoming immobilized), and later succumbed to the cold weather.
 * 2. Brandon slipped and his phone was somehow rendered inoperable, but he was able to continue walking.
 * 2.1 Brandon became wet from falling, wet grass, and/or sweating from the exertion of walking and became hypothermic over time, eventually succumbing to it.
 * 2.2 Brandon eventually fell into some sort of well, cistern, or tank and perished there.
 * 3. Brandon was picked up by someone and taken outside of the search area.
 * 3.1 Brandon was later harmed by whoever picked him up.
 * 3.2 Brandon obtained a ride from someone who was able to transport him to safety and Brandon is alive and well and living elsewhere.

Scenarios
Scenarios here are limited to those within the scope of search and rescue. Scenarios such as running away from home and abduction by aliens are outside that scope. Brandon could be...

 * 1) in the Yellow Medicine River
 * 2) in water other than the Yellow Medicine River
 * 3) in an agricultural field
 * 4) in conservation land or woods
 * 5) in an abandoned well or cistern
 * 6) in a fence rowLaguyon 06:16, 4 February 2010 (UTC)

Yellow Medicine River
This scenario was the focus of much of the initial search. Conservative cumulative POD estimates effectively rule out approximately six miles of the river (PODcum >96%). An additional four miles of river was searched to PODcum of 46-52%

Water other than the Yellow Medicine River
There are many road ditches, field drainage ditches, creeks, and wetlands in the area. These were the focus of much of the HRD canine's search efforts for two reasons. 1) A body partially or fully submerged is difficult to find visually, but canines are quite effective. 2) Wet areas form good scent pools for the canines to detect, even if remains are not nearby.

With the amount of water in the area and the continued findings of the canines, this final location scenario remains a high probability.

Agricultural field
The fields within 2-3 miles of the LKP were searched early. Because the fields were not planted yet or newly planted with no growth, PODs were relatively high.

The canine teams initially avoided searching fields for several reasons: 1) The assumption that few fields had been planted when Brandon went missing, therefore the farmers would have found him while planting.  2) Farmers tend to be very sensitive about crop damage and we wanted to avoid that issue. 3) The constant wind blowing through the area allowed the dogs to effectively sample many of the fields from their edges.

Once we determined that the remains were likely within the Mud Creek drainage, and we found out that over 60% of the fields in the area had already been planted when Brandon went missing, we felt we could no longer ignore the fields. This occurred in the late spring of 2009. Since then, we have been systematically detail-searching each of the fields in the area, an exhausting process.

Recently, five different certified HRD dogs gave full trained final responses on a field cultivator sitting by the side of a field. This may or may not indicate that the body is scattered in a nearby field. This is one of the more puzzling findings.

Conservation land or woods
There is quite a bit of CRP (Conservation Reserve Program--a wetland preservation program)in the area. In addition, there are wooded areas and tall grass along most creeks and drainages in the search area. The wooded shelter-belts around every farm in the region are particularly dense. All of these are being systematically searched.

This remains a very high-probability scenario.

Abandoned well or similar
Old hand-dug water wells, cisterns, and similar underground structures with inadequate covers are potential traps for anyone walking over them.

This scenario has been considered but only minimally and extensively investigated. It is thought that all most former homesteads within current agricultural fields have been fully reclaimed. An old homestead that still stands about 1.3 miles west of the car was thoroughly searched.

Former homesteads can be identified by comparing old topographic maps with recent satellite imagery which has been done.

In addition to old homesteads, land used for rural schools should be identified. These schools had wells which may never have been sealed or have become open with time. The schools were placed so that walking distance was no more than two miles.Laguyon 18:41, 1 February 2010 (UTC)
 * Interestingly, none have been found. We are used to finding these elsewhere.  They often have coal chutes to dank basements that still operate and can trap children.  Tillable land is so valuable in the area that these all appear to have been reclaimed also.

Thanks to Baby Jessica and other high-profile cases, all the searchers (including the untrained emergent volunteers) are aware of abandoned wells and the like and actively searched for them.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Search and rescue/SAR mission 2008 02


text: User:Mscholz

title: User:Mscholz


text: User talk:Mscholz

title: User talk:Mscholz


text:
User:Egm6341.s2010.Team1.lei/HW1

For HW 1, I am responsible for 3 problems: 5-1(2),6-1(1)and 8-3(1).

The details of solutions of each problem is following:

=Problem 5-1b=

Find
Use the Intermediate Mean Value Theorem to show Eq. (5) [[media:Egm6341.s10.mtg2.pdf|Lec. 2-2]] and Eq. (1) [[media:Egm6341.s10.mtg2.pdf|Lec. 2-3]]

Given
Eq. (5)
 * $$R_{n+1}\left ( x \right )=\frac{1}{n!}\int_{x_{0}}^{x}\left ( x-t \right )^{n}f^{(n+1)}\left ( t \right )dt$$

Eq. (1)
 * $$R_{n+1}\left ( x \right )=\frac{(x-x_{0})^{n+1}}{(n+1)!}f^{(n+1)}\left ( \xi \right )$$

IMVT
 * $$\int_{a}^{b}w\left ( x \right )f\left ( x \right )dx=f\left ( \xi \right )\int_{a}^{b}w\left ( x \right )dx$$

Solution [[media:HW1_P5_1_2.jpg|P5-1b]]
Let $$w\left ( x \right )$$ be nonnegative in the integral on $$[a,b] \,$$ and let $$f\left ( x \right )$$ be continuous on $$[a,b] \,$$. Then,

 * $$\int_{a}^{b}w\left ( x \right )f\left ( x \right )dx=f\left ( \xi \right )\int_{a}^{b}w\left ( x \right )dx$$

for
 * $$\xi \in [a,b]$$

Using a Taylor series expansion,
 * $$f\left ( x \right )=P_{n}\left ( x \right )+R_{n+1}\left ( x \right )$$

where
 * $$R_{n+1}\left ( x \right )=\frac{1}{n!}\int_{x_{0}}^{x}\left ( x-1 \right )^{n}f^{(n+1)}\left ( t \right )dt$$
 * $$\Rightarrow \frac{1}{n!}f^{(n+1)}\left ( \xi \right )\int_{x_{0}}^{x}\left ( x-t \right )^{n}dt$$
 * $$\Rightarrow \frac{1}{n!}f^{(n+1)}\left ( \xi \right )\left ( \frac{-1}{n+1} \right )\left ( x-t \right )^{n+1}|_{x_{0}}^{x}$$
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow \frac{(x-x_{0})^{n+1}}{(n+1)!}f^{(n+1)}\left ( \xi \right ) $$ $$
 * $$\displaystyle
 * }
 * }

=Problem 6-1=

Find
Construct the Taylor series of $$f(x) \,$$ around $$x_0=\frac{\pi}{4}$$ for $$n=0,1,...,10 \,$$.

Plot these series for each $$n \,$$. Then estimate the maximum of $$R(x) \,$$ at $$x=\frac{\pi}{2}$$

Given

 * $$f\left ( x \right )=\sin x$$ for $$x\in [0,\pi ]$$

Solution [[media:HW1_P6_1_1.jpg|P6-1]]

 * $$f\left ( x \right )=\sin x=P_n(x)+R_{n+1}(x)$$
 * $$P_n(x)=f(x_0)+\frac{(x-x_0)}{1!}f^{(1)}(x_0)+\frac{(x-x_0)^2}{2!}f^{(2)}(x_0)+...+\frac{(x-x_0)^n}{n!}f^{(n)}(x_0)$$
 * $$R_{n+1}(x)=\frac{(x-x_0)^{n+1}}{(n+1)!}f^{(n_1)}(\xi)$$

For
 * $$f(x)=\sin x, f^{(1)}(x)=\cos x, f^{(2)}(x)=-\sin x, f^{(3)}(x)=-\cos x, f^{(4)}(x)=\sin x \,$$

When $$n=0 \,$$
 * $$\Rightarrow \sin x=P_0(x)+R_1(x)=\frac{\sqrt{2}}{2}+(x-\frac{\pi}{4})\cos \xi$$

When $$n=1 \,$$
 * $$\Rightarrow \sin x=P_1(x)+R_2(x)=\frac{\sqrt{2}}{2}\left [ 1+\left ( x-\frac{\pi}{4} \right ) \right ]-\frac{(x-\frac{\pi}{4})^2}{2!}\sin \xi$$

When $$n=2 \,$$
 * $$\Rightarrow \sin x=P_2(x)+R_3(x)=\frac{\sqrt{2}}{2}\left [ 1+\left ( x-\frac{\pi}{4} \right )-\frac{(x-\frac{\pi}{4})^2}{2!} \right ]-\frac{(x-\frac{\pi}{4})^3}{3!}\cos \xi$$

When $$n=3 \,$$
 * $$\Rightarrow \sin x=P_3(x)+R_4(x)=\frac{\sqrt{2}}{2}\left [ 1+\left ( x-\frac{\pi}{4} \right )-\frac{(x-\frac{\pi}{4})^2}{2!}-\frac{(x-\frac{\pi}{4})^3}{3!} \right ]+\frac{(x-\frac{\pi}{4})^4}{4!}\sin \xi$$

...

When $$n=10 \,$$
 * $$\Rightarrow \sin x=P_{10}(x)+R_{11}(x)=\frac{\sqrt{2}}{2}\left [ 1+\left ( x-\frac{\pi}{4} \right )-\frac{(x-\frac{\pi}{4})^2}{2!}-\frac{(x-\frac{\pi}{4})^3}{3!}...- \frac{(x-\frac{\pi}{4})^{10}}{10!}\right ]-\frac{(x-\frac{\pi}{4})^{11}}{11!}\cos \xi$$

Finally, the maximum can be computed with,
 * $$R_{n+1}(x)=\frac{(x-x_0)^{n+1}}{(n+1)!}f^{(n+1)}(\xi)$$ for $$\xi \in [0,\pi] \,$$
 * $$\left | R_{n+1}(x) \right |\leq \frac{(x-x_0)^{n+1}}{(n+1)!}\max \left \{ f^{(n+1)}(\xi) \right \} \leq \frac{(x-x_0)^{n+1}}{(n+1)!}=\frac{(\frac{\pi}{4})^{n+1}}{(n+1)!}\leq \frac{\pi}{4}$$

=Problem 8-3=

Find
Prove $$P_2(x_j)=f(x_j)\,$$

Given
$$P_2(x_j)=\sum _{i=0}^{2}l_i(x_j)f(x_i)$$

Solution [[media:HW1_P8_3_1.jpg|P8-3]]

 * $$P_2(x_j)=\sum _{i=0}^{2}l_i(x_j)f(x_i)=l_0(x_j)f(x_0)+l_1(x_j)f(x_1)+l_2(x_j)f(x_2)$$

Also,
 * $$l_1(x_j)=\delta _{ij}=\left\{\begin{matrix}

1(i=j)\\ 0(i\neq j) \end{matrix}\right.$$ And
 * $$l_0(x_0)=1\,$$
 * $$l_0(x_1)=l_0(x_2)=0\,$$

 * $$l_1(x_1)=1\,$$
 * $$l_1(x_0)=l_1(x_2)=0\,$$

 * $$l_2(x_2)=1\,$$
 * $$l_2(x_0)=l_2(x_1)=0\,$$

Therefore,
 * $$P_2(x_0)=l_0(x_0)f(x_0)+l_1(x_0)f(x_1)+l_2(x_0)f(x_2)=f(x_0)\,$$
 * $$P_2(x_1)=l_0(x_1)f(x_0)+l_1(x_1)f(x_1)+l_2(x_1)f(x_2)=f(x_1)\,$$
 * $$P_2(x_2)=l_0(x_2)f(x_0)+l_1(x_2)f(x_1)+l_2(x_2)f(x_2)=f(x_2)\,$$

...

 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow P_2(x_j)=\sum _{i=0}^{2}l_i(x_j)f(x_i)=f(x_j) $$ $$
 * $$\displaystyle
 * }
 * }

title: User:Egm6341.s2010.Team1.lei/HW1


text:
User:Egm6341.s2010.Team1.lei/HW2

For HW 2, I am responsible for 3 problems: 9-1(a),12-3(a)and 13-2(a).

=Problem 9-1(a)=

Find
Use Eq. (3) [[media:Egm6341.s10.mtg8.pdf|Lec. 8-3]] and Eq. (1) [[media:Egm6341.s10.mtg8.pdf|Lec. 8-3]] to find expression for $$C_0,C_1,C_2 \,$$ in terms of $$(x_i,f(x_i)), i=0,1,2 \,$$

Given
Eq. (3) [[media:Egm6341.s10.mtg8.pdf|Lec. 8-3]]
 * $$P_2(x)=\sum _{i=0}^{2}l_i(x)f(x_i)$$

Eq. (1) [[media:Egm6341.s10.mtg8.pdf|Lec. 8-3]]
 * $$f_{2}\left ( x \right )=p_{2}\left ( x \right )=C_2 x^2+C_1 x^1+C_0, C_0,C_1,C_2= 3 unknowns \,$$

Solution
From Eq. (2) [[media:Egm6341.s10.mtg7.pdf|Lec. 7-3]]
 * $$l_{i,n}\left ( x \right )=l_{i}\left ( x \right )=\prod_{j=0,j\neq i}^n\frac{x-x_j}{x_i-x_j}$$

Then
 * $$l_{0}\left ( x \right )=\frac{(x-x_1)(x-x_2)}{(x_0-x_1)(x_0-x_2)}$$
 * $$l_{1}\left ( x \right )=\frac{(x-x_0)(x-x_2)}{(x_1-x_0)(x_1-x_2)}$$
 * $$l_{2}\left ( x \right )=\frac{(x-x_0)(x-x_1)}{(x_2-x_0)(x_2-x_1)}$$

Also From Eq. (3) [[media:Egm6341.s10.mtg8.pdf|Lec. 8-3]]
 * $$P_2(x)=\sum _{i=0}^{2}l_i(x)f(x_i)$$

 * $$\Rightarrow P_2(x)=\sum _{i=0}^{2}l_i(x)f(x_i)=l_{0}\left ( x \right )f(x_0)+l_{1}\left ( x \right )f(x_1)+l_{2}\left ( x \right )f(x_2)=C_2 x^2+C_1 x^1+C_0 $$

 * $$\Rightarrow C_2=\frac{f(x_0)}{(x_0-x_1)(x_0-x_2)}+\frac{f(x_1)}{(x_1-x_0)(x_1-x_2)}+\frac{f(x_2)}{(x_2-x_0)(x_2-x_1)}$$
 * $$\Rightarrow C_1=\frac{-f(x_0)(x_1+x_2)}{(x_0-x_1)(x_0-x_2)}+\frac{-f(x_1)(x_0+x_2)}{(x_1-x_0)(x_1-x_2)}+\frac{-f(x_2)(x_0+x_1)}{(x_2-x_0)(x_2-x_1)}$$
 * $$\Rightarrow C_0=\frac{f(x_0)(x_1x_2)}{(x_0-x_1)(x_0-x_2)}+\frac{f(x_1)(x_0x_2)}{(x_1-x_0)(x_1-x_2)}+\frac{f(x_2)(x_0x_1)}{(x_2-x_0)(x_2-x_1)}$$

 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

C_2=\frac{f(x_0)}{(x_0-x_1)(x_0-x_2)}+\frac{f(x_1)}{(x_1-x_0)(x_1-x_2)}+\frac{f(x_2)}{(x_2-x_0)(x_2-x_1)}$$
 * $$ \displaystyle

C_1=\frac{-f(x_0)(x_1+x_2)}{(x_0-x_1)(x_0-x_2)}+\frac{-f(x_1)(x_0+x_2)}{(x_1-x_0)(x_1-x_2)}+\frac{-f(x_2)(x_0+x_1)}{(x_2-x_0)(x_2-x_1)}$$
 * $$ \displaystyle

C_0=\frac{f(x_0)(x_1x_2)}{(x_0-x_1)(x_0-x_2)}+\frac{f(x_1)(x_0x_2)}{(x_1-x_0)(x_1-x_2)}+\frac{f(x_2)(x_0x_1)}{(x_2-x_0)(x_2-x_1)}$$

$$
 * $$\displaystyle
 * }
 * }

=Problem 12-3(a)=

Find
Prove $$P_{n+1}^{(n+1)}\left ( x \right )={(n+1)}!$$

Given

 * $$q_{n+1}\left ( x \right ):=(x-x_{0})(x-x_{1})(x-x_{2})...(x-x_{n})$$

Solution

 * $$n=0 \,$$
 * $$q_{1}\left ( x \right ):=(x-x_{0})$$

 * $$q_{1}^{(1)}\left ( x \right )=1$$

 * $$n=1 \,$$
 * $$q_{2}\left ( x \right ):=(x-x_{0})(x-x_{1})$$

 * $$q_{2}^{(2)}\left ( x \right )=2\times 1=2!$$

 * $$n=2 \,$$
 * $$q_{3}\left ( x \right ):=(x-x_{0})(x-x_{1})(x-x_{2})$$

 * $$q_{3}^{(3)}\left ( x \right )=3\times 2\times 1=3!$$

 * $$n=3 \,$$
 * $$q_{4}\left ( x \right ):=(x-x_{0})(x-x_{1})(x-x_{2})(x-x_{3})$$

 * $$q_{4}^{(4)}\left ( x \right )=4\times 3\times 2\times 1=4!$$

...

 * $$n=n \,$$
 * $$q_{n+1}\left ( x \right ):=(x-x_{0})(x-x_{1})(x-x_{2})(x-x_{3}...(x-x_{n})$$

 * $$q_{n+1}^{(n+1)}\left ( x \right )=n\times (n-1)\times (n-2)...\times 1=(n+1)!$$

 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow P_{n+1}^{(n+1)}\left ( x \right )={(n+1)}!$$ $$
 * $$\displaystyle
 * }
 * }

=Problem 13-2(a)=

Find

 * $$\left | E_{1} \right |\leq \frac{(b-a)^{3}}{12}M_2=\frac{h^{3}}{12}M_2)$$

Given

 * $$n=1, \, q_{2}\left ( x \right )=(x-a)(x-b)$$
 * $$h:=b-a\,$$

Solution
Let:$$M_2:= max f^{(2)} (\xi), \xi \in [a,b]$$
 * $$\left | E_{1} \right |\leq \frac{M_2}{2!}\int_{a}^{b}\left |q_{2}\left ( x \right )\right |dx $$
 * $$=\frac{M_2}{2!}\int_{a}^{b}\underbrace{\left ( x-a \right )}_{\geq 0}\underbrace{\left ( b-x \right )}_{\geq 0}dx $$
 * $$=\frac{M_2}{2!}\int_{a}^{b}[(b+a)x-ab-x^2] dx$$
 * $$=\frac{M_2}{2!}[\frac{1}{2}(b+a)x^2-ab x-\frac{1}{3}x^3]|_{a}^{b}$$
 * $$=\frac{M_2}{2!}\times \frac{1}{6}(b^3-3ab^2+3a^2b-a^3) $$
 * $$=\frac{M_2}{2!}\times \frac{1}{6}(b^2-2ba+a^2)(b-a) $$
 * $$=\frac{M_2}{2!}\times \frac{1}{6}(b-a)^2(b-a) $$
 * $$=\frac{M_2}{2!}\times \frac{1}{6}(b-a)^3 $$
 * $$=\frac{M_2}{12}(b-a)^3 $$

and
 * $$h:=b-a\,$$
 * $$=\frac{M_2}{12}h^3 $$
 * {| style="width:100%" border="0" align="left"

 * style="width:50%; padding:10px; border:2px solid #8888aa" |
 * $$ \displaystyle
 * $$ \displaystyle

\Rightarrow \left | E_{1} \right |\leq \frac{(b-a)^{3}}{12}M_2=\frac{h^{3}}{12}M_2$$ $$
 * $$\displaystyle
 * }
 * }

title: User:Egm6341.s2010.Team1.lei/HW2


text:
User talk:Jeff Hasse/Missing Person Case Study -- Brandon Swanson

Brandon Swanson
Here is my start: SAR mission 2008 02. --Una Smith 18:33, 30 January 2010 (UTC)


text:
Cooking/Introduction/Buying bread

{| cellpadding="10" cellspacing="5" style="width: 900px; background-color: inherit; margin-left: auto; margin-right: auto"
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 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Module:I Basic
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 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Techniques:
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Skills:Purchasing
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 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Food knowledge:Bread
 * }

 * {| cellpadding="4" cellspacing="0" width="350px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Equipment & appliances:Knives Boards
 * }
 * }

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Objectives

 * 1) Purchase, prepare, display and taste a variety of breads.
 * 2) Build a vocabulary for describing the qualities of ingredients.
 * 3) Develop internet research skills.
 * 4) Acquire purchasing experience.
 * 5) Serve food.
 * 6) Obtain and react to consumer criticism.
 * }

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Assignment
Research, purchase, observe and prepare a number of types of commercially produced bread. Serve to other people and ask for their opinions.
 * }

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 * style="width: 40%; background-color: #FFE7CC; border: 4px solid #C47451; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Essential reading
Bread

List of breads

Cookbook:Bread

 * }

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 * style="width: 40%; background-color: #FFE7CC; border: 4px solid #C47451; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Vocabulary
Crust

Crumb = The interior of baked goods, not the crust; interior texture formed by air cell pockets trapped inside a webbing of starch and protein gelatinized by baking.

Texture

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Preparation skills
Download the worksheet for this activity and complete all the sections for preparing and serving bread.
 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Weights and measures:
Insert text here.

Methods and techniques
Insert text here.

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Equipment and appliances
Bread knives, bread plates, bread boards and bread baskets.

Knowledge of:
Search the internet for bread knives, bread plates, bread boards and bread baskets.

Download and complete the search worksheet and log.

Experience with:
Slice or serve each type of bread in an appropriate manner using any of the above equipment.

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Ingredients
Types of bread.

Sourdough

Knowledge of:
Search the internet for references to a variety of types of bread and how it is served and record your findings.

Download and complete the search worksheet and log.

Experience with:
Slice or serve each type of bread in an appropriate manner.

Taste and describe any breads that you use.
 * Look at the crust appearance, look at the crumb, smell the bread, taste a little and chew well. Swallow.
 * Complete a tasting sheet for different types of bread so you have a record for future use.

Name of bread tasted:

Appearance

Crust. How does the bread look on the outside?

Crumb texture and hole structure. How does the bread look on the inside?

Aroma

How does the bread smell?

Taste

How does the bread taste? What is your first impression? What does it taste like after you have swallowed?

Food combinations

With what foods does this bread taste good?

Comment:
Some words which can be used to describe bread:

Appearance - Shape:

Round, batard, oval, long, open cuts, pointy, plump, flat, skinny.

Appearance - Color:

Dark, golden brown, medium brown, deep brown, golden, light yellow, bubbly, shiny, glossy.

Aroma / Smell:

Wheaty, nutty, honey, sweet, herbaceous, fragrant, tangy, sharp, sour, mild, milky, buttery.

Taste & Flavor:

Buttery, sweet, sour, salty, tangy, salty, sharp, wheaty, bland, complex, one-dimensional.

Crumb and crust texture and colour:

Dense, dark, cream coloured, white, pale, large holes, chewy, small, cakey, airy, shiny, even texture crumb, gummy, small, holes, yellow.

Add your own words to the list.

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Health and safety
Use the internet to find out if there are any particular health risks or allergies associated with bread or its ingredients.

What are the ingredients of each type of bread that you will be using?

Try an internet search for each ingredient combined with "allergy". e.g.Yeast allergy gave these search results.

What action will you take to prevent harm to your consumers?

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Purchasing and budgeting
Visit your local supermarket or bakery and find out which breads they stock and their cost. Purchase bread for your assignment.

Complete a product comparison sheet for bread and decide which you would like to use and if it is within your budget.

If so, add the chosen items to your shopping list.

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Presentation

Search various sources for presentation ideas and record your findings on a search worksheet. Use the ideas gained to present your bread attractively.

Comment:

Google images has some pictures of "boiled eggs" as does Wikimedia Commons. You could upload your own pictures to Wikimedia Commons.

 * }

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 * style="width: 40%; background-color: #ECE5B6; border: 4px solid #ADA96E; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Recording and evaluation

Keep your completed worksheets in a file as a record of your completion of this Activity unit. You can also photograph your cooking as it progresses and when it is completed ready for serving. Invite your consumers to comment on any aspect of the food you have served and if possible make a note of their comments and whether you will make any changes to anything in the future.

 * }

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 * style="width: 40%; background-color: #b7ccd6; border: 4px solid #87AFC7; vertical-align: top; -moz-border-radius-topleft: 3px; -moz-border-radius-bottomleft: 3px; -moz-border-radius-topright: 3px; -moz-border-radius-bottomright: 3px"|

Further and background reading:
Insert text here.

More experience:
Insert text here.

Extension activities:
Insert text here.

See also:

 * }

title: Cooking/Introduction/Buying bread


text:
Information management notes

Introduction
This page serves as a place to collect thoughts (and resources) on the topic of managing information for the purposes of:

 * accessibility
 * reuse/repurposing
 * archiving
 * increasing user acceptance/adoption (data capture stage as well as data use)

The objective of collecting these thoughts is to organize a rationale for how to use the various available tools on a collaborative scientific project which is expected to generate information products of lasting value. In the near term, a specific project will be driving the development of this solution. However, it is hoped that the salient features of both the problem and the solution can be distilled into a more generalized understanding which will aid projects of this type.

Theme
For the purposes of this effort, modern information systems are defined as being comprised of both human and machine. Humans are involved at the start, and are ultimately the audience for any information. It is ultimately the human's job to understand the information asset in order to effectively discharge their roles as producers and consumers of information. Between the producers and consumers are the custodians, which are often machines.

In the above figure, the rectangles represent individuals involved with the understanding of the material. The circle represents the storage system, which is capable of storing, preserving, indexing and retrieving the material without attempting to understand it.

Information management, in the context of this producer-custodian-consumer model, involves defining the responsibilities and expectations of each role as well as how the roles interact.

Custodian Role

 * 1) Custodians of information do not need to understand the information in the item itself.
 * 2) Custodians must keep items safe from destruction and alteration
 * 3) Custodians must be able to accept new items and retrieve them later.
 * 4) Custodians must be able to index items, for example:
 * 5) * Traditional "card catalog" found in libraries:
 * 6) ** by subject
 * 7) ** by author
 * 8) ** by title
 * 9) * by "groups" of holdings
 * 10) * by characteristic properties

Producer Role

 * 1) Producers provide information resources to the custodian.
 * 2) Producers typically understand the information.
 * 3) Producers determine what constitutes a "group" of documents.
 * 4) Producers define what (if any) additional characteristic properties apply to the group.
 * 5) Producers determine values for each of the characteristic properties for each information resource provided to the custodian.

Author subrole

 * 1) The producer created the item submitted to the custodian
 * 2) Accepts queries about the contents of this item
 * 3) Producers respond to consumer requests for explanatory or additional information about an information resource.

Translator subrole

 * 1) Producer acquired the item from some other source and submitted it to the custodian
 * 2) Producer includes lineage information to indicate the origin of the document.

Consumer Role

 * 1) Consumers are qualified to learn the information in the resource.
 * 2) Consumers search for information resources and groups of information resources held by the custodian, using the defined properties.
 * 3) Consumers request information resource holdings from the Custodian.
 * 4) Consumers probably want to subset the information holdings in unanticipated ways.
 * 5) Consumers direct requests for explanatory or additional information to the producers.

Collections of holdings

 * 1) May be ad-hoc or systematized.
 * 2) Ways to define membership in a collection:
 * 3) Declarative (by explicitly claiming membership)
 * 4) Implicit/type (by possessing properties characteristic of all members in the collection)
 * 5) Implicit/instance (by possessing property values characteristic of all members in the collection)
 * 6) Systematized collection schemes may include the notion of superior and subordinate grouping levels, as in a hierarchy.
 * 7) Implicit schemes, depend on each item advertising its own intrinsic characteristics
 * 8) this is more extensible
 * 9) this is easier to validate
 * 10) Declarative schemes depend on each item asserting that they belong to a collection.
 * 11) this includes no information as to why the item is part of the group
 * 12) thus it is harder to later group items in unanticipated ways.

Hierarchical Classification

 * 1) Special case:
 * 2) * all leaves are the same distance from the root
 * 3) * all nodes which are the same distance from the root are the same "type"
 * 4) Two methods to implement hierarchical classification:
 * 5) * tree of nodes
 * 6) * common set of properties
 * 7) Differences in searching/forming groups:
 * 8) * locating subtrees
 * 9) * searching for a value (or combination of values) in the correct property(ies)
 * 10) Typically in a hierarchical classification tree, each level (in "distance from the root of the system") has a specific meaning, and would always map to the same property.  See the following. [[File:Biological_classification_L_Pengo.svg]]

If the above were:
 * 1) implemented as a "tree",
 * 2) * a set of categories would be created to reflect the accepted "Domains", "Kingdoms", "Phylums"
 * 3) * Each category/subgroup explicitly claims membership in the appropriate superior node.
 * 4) * Each resource explicitly claims membership in the appropriate category in the tree.
 * 5) * Resources which participate in this classification scheme are identified because they claim membership in something which can trace it's lineage back to the root node of the scheme...in this case, "life".
 * 6) implemented as a set of properties,
 * 7) * resources which participate in the classification scheme are identified by the presence of properties without regard for their value. The presence of subordinate properties is optional, but if one of the properties is set, all superior properties must also be set.
 * 8) * resources are located within the classification scheme by the values stored in the relevant properties.
 * 9) * the hierarchy can be derived by selecting all participants in the scheme and analyzing the property values.
 * 10) * An explicit category structure is not required.

Collection membership as a managed entity
Consistency is expected from members of the same collection. There are three levels of consistency:
 * 1) the manner or system in which properties get their values and/or membership is asserted
 * 2) the presence of properties
 * 3) the meaning of property values

Automated extraction of information related to characteristic properties is a requirement for large holdings of information resources, and this requires a consistent, deterministic expression. Relying on a human reader to interpret information on a case by case basis is simple to set up but requires a high level of tedious and error-prone effort to maintain. Additionally, the properties which are only accessible to a human reader are not available for searching and filtering.

The criteria for collection membership must be consistently applied to all members of the collection. If criteria are to change or the collections are to evolve, the collection system itself should be versioned, and each member must be updated such that it is consistent with the new definition.

Example: setting property values
Consider the "collection" of reports in the US Forest Service Fire Effects Information System (FEIS). In the article describing Abies fraseri, the states in which Abies fraseri exists are coded as follows: STATES :  NC TN  VA

In the same collection, the report describing the effects of fire on Anas acuta presents the states in which the bird lives as:

STATES :

In the first case, a whitespace separated list is used and in the second case, HTML table markup is used. Other inconsistencies include the designation of the name of the property to which values are being assigned: sometimes a boldface string is used, sometimes a third-level heading is used. The boldfaced string is especially problematic for automatic processing because it is not guaranteed that all bold text signifies a property name. It is only that the bold text is on its own line with a colon after it which causes the human reader to infer that a list of states follows. Likewise, the human will immediately recognize that the states form a "list" and the table markup is merely a device to make the list more compact. There is no significance to states being in the same row or the same column.

In the situation where a human consumer is intended to interpret and process the information, authors are free to use any expression which effectively communicates to the human. When the intent is to supply information to a computer, authors must effectively communicate meaning to the computer. Once the computer understands the content, it can present the information to the human in a variety of ways.

Example: Controlling property values
Ideally, there is a one-to-one relationship between a concept and the property value which represents that concept. This ensures that the Producers who supply property values are following the same rules used by the Consumers who construct searches. Falling short of this ideal leads to the situation where producers could tag an article with the string "CO2", and Consumers search for "carbon dioxide". The Custodian will not return the desired information resources because Producers and Consumers used alternate means of expressing the same thing.

To solve this problem in the field of chemistry, the International Union of Pure and Applied Chemistry (IUPAC) has made an attempt to standardize the means of referring to chemical substances and compounds. This standard method is called the International Chemical Identifier (InChI). The fixed length equivalent of this identifier, InChIKey, looks much like a random string of characters. Both identifiers may be automatically generated from a description of the molecular structure itself. In addition, there is a human readable standard name. One public database of many chemical compounds and substances is Pubchem.

For the purposes of having the Producers and Consumers follow the same rules, it is clear that an algorithm which deterministically generates a text representation of a chemical given the structural information is preferable to a human readable name. Human nomenclature tends to evolve over time, and alternate names are often widely recognized by practitioners. Successfully searching by a chemical name may depend on knowing the person who entered the information into the collection of holdings, or knowing when it was entered.

Identification of chemical substances to humans and the computer may require "related properties." These properties should be synchronized to all refer to the same item or concept. In this example:

Example: Explicitly defining allowed property values
For the case where the number of allowable property values is manageably small, it is possible to enumerate the identifiers. Enumeration effectively controls the representation of a unique concept to the computer, but it does not communicate the concept itself to the human. For instance, setting the "Instrument" property to the value "1" effectively distinguishes instrument number one from all the other instruments. However, it does nothing to communicate anything about that instrument: what does it measure; what is the make, model, serial number of the instrument, when was its most recent calibration?

For each property, it is important to define the list of permissible meanings and the list of permissible representations for those meanings. The representation must be machine readable and distinct from all other representations of the same type. The meaning may be automatically comprehensible (as in a table) or written for human consumption (as in prose).

Defining instances of a type for subsequent reference
There are times when it is insufficient to simply define an enumeration of values. At times it is necessary to provide a more complete description about what the enumeration refers to. This strategy collects the descriptive information into one place and allows other managed objects simply to refer to it. When the reference is used as the value of a property, specific meaning can be conveyed: i.e., an "instruments used" property could refer to another object within the system; an "analytes" property could contain a link to a substance description on pubchem. In both cases, the target of the reference explains the meaning of the property value.

When it is necessary to describe specific instances, it is probable that a common "type" has already been defined. Similar if not identical information will be provided about each instance of the type. In the case of an "Instrument", a good, common set of properties might be: "Manufacturer", "Model", "Serial Number", "Last calibration date". It could also be that each instrument has additional/unique information which can be filled out, or which is not machine-interpretable.

There are two options for defining instances of a common type:
 * 1) If the type is completely machine-comprehensible, the instances could be defined in a single table.
 * 2) For the case where a tabular structure does not have the required flexibility, each instance must be described separately.

Spectrum of Information Management Comprehension
An automated custodian becomes more capable when it understands more about the content it is managing. The degree of comprehension can be visualized as a spectrum from "black box" to "completely described"

 * 1) Black box: the system knows nothing about the contents of the item.  The item can be stored and retrieved, but nothing else can be done.  This is analogous to throwing all files in a single directory with cryptic names.  The only method of searching for content is to perform a full text search for likely keywords.
 * 2) Classified black box: the system knows very little about the contents of the item.  Predefined groups of items are explicitly constructed.  This is analogous to devising a directory structure or filing scheme, into which all items are filed.  Full text searches may be combined with group. It is not possible for the system to form new groups which have an unanticipated organizing principle.
 * 3) Tagged items: in addition to a predefined filing scheme, a free-text keywording system associates descriptive phrases with information resources.
 * 4) Property-value associations: a generalization of "tagging", each item can be associated with a set of properties; each of which has it's own set of values.  A property imposes an interpretation on it's value.  The text of the "Author" property is expected to be the name of an author.  Likewise, properties may have a "type": like a number or a date.  Properties help to make searches and filters much more precise and narrow down the results.  Properties serve as a summary of the salient characteristics of the managed item.  A well-designed set of properties makes it possible to quickly locate information resources which are relevant in a context not anticipated by the Producers.
 * 5) References to/associations of managed items: the system provides a way for one item to refer to another in a semantically meaningful way.  The reference may be bidirectional or unidirectional, and may have arbitrary multiplicities on each end.  Simple links are not considered to fall in this category.  Named links, where the name refers to a specific relationship such as "related resources", "children", or "instruments used", are what is described here.
 * 6) Types/interfaces/aspects: collections of property-value associations occur in combination to fully describe an aggregate concept.  Information resources would be considered to implement the "interface" or possess the "aspect" if they had values for all required properties belonging to the interface or aspect definition.  For instance, a temperature range would specify both a minimum and a maximum temperature; and an information resource would be considered to have the "temperature range" interface if it had both the required minimum and maximum temperature properties.  Types, interfaces, and aspects could all be used to limit the legitimate targets of references and associations.
 * 7) Database/Datastore: the information resource is completely described in a machine-comprehensible framework.  Typically, much work has been invested in defining a common data structure and importing data into that structure.  Searches and filters can be precise to the point of selecting a portion of data from a particular source.  The information itself is represented in a tabular, XML, object oriented, or similar machine-comprehensible model.

Three main theorems present themselves:
 * 1) The benefit of an information management system is directly proportional to the level of automated comprehension.
 * 2) The level of automated comprehension is directly proportional to the amount of effort invested in furnishing information to the machine.
 * 3) Benefit is largely realized by Consumers, but effort is largely expended by Producers.  Custodians need only supply an appropriate tool.

Spectrum of Information Management Accessibility
Mostly from Memory (computers), Computer storage and Memory hierarchy. This spectrum traces the proximity of information to the actor which operates on it. In general, latency increases and bandwidth decreases for items listed later.

Accessibility, in this case, is defined in terms of efficiently retrieving and operating on the data. In most cases, processes which are human-bound (e.g., spend the majority of the time waiting on human input, like word processing) will perform acceptably well with any form of online storage. Processes which are IO bound benefit primarily from increasing the bandwidth which can be sustained between the storage device and the processing unit.

 * 1) Internal
 * 2) CPU Register File
 * 3) Hierarchical CPU cache
 * 4) Main
 * 5) Main Memory (RAM)
 * 6) On-line mass storage (Secondary storage)
 * 7) Local Mass Storage device
 * 8) On site Networked Mass Storage device
 * 9) Remote networked mass storage device
 * 10) Tertiary (Tertiary storage)
 * 11) Tape library with robotic tape loader.
 * 12) Human-loaded tape drive
 * 13) Off-line bulk storage
 * 14) Removable media

Workflows
Using information is one of the primary reasons for gathering it in the first place.

 * 1) Completely human operated (computer comprehension not required)
 * 2) Machine-guided and tracked human processes (computer understands the process, but not the information)
 * 3) Human triggered automatic operation, machine tracked (Human understands the process, machine operates on information and logs activity)
 * 4) Fully automated process. (computer understands process and information.)

Presentation Breakdown
In this section, the plan for presenting the information on this page in an orderly way is outlined. More than one article is likely to be required.

 * 1) Article: Introduction
 * 2) Article: Spectrum of Information management
 * 3) Article: Roles and Interactions
 * 4) Article: Collections and classification
 * 5) Article: Defining instances of types
 * 6) Article: Worked example: SMURFS data mining
 * 7) Article: Worked example: SMURFS analysis
 * 8) Article: Summary

title: Information management notes