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# Highlights from EDRM Workshop 2019

The annual EDRM Workshop was held at Duke Law School starting on the evening of May 15th and ending at lunch time on the 17th.  It consisted of a mixture of panels, presentations, working group reports, and working sessions focused on various aspects of e-discovery.  I’ve provided some highlights below.  You can find my full set of photos here.

Herb Roitblat presented a paper on fear of missing out (FOMO).  If 80% recall is achieved, is it legitimate for the requesting party to be concerned about what may have been missed in the 20% of the responsive documents that weren’t produced, or are the facts in that 20% duplicative of the facts found in the 80% that was produced?

A panel discussed the issues faced by in-house counsel.  Employees want to use the latest tools, but then you have to worry about how to collect the data (e.g., Skype video recordings).  How to preserve an iPhone?  What if the phone gets lost or stolen?  When doing TAR, can the classifier/model be moved between cases/clients?  New vendors need to be able to explain how they are unique, they need to get established (nobody wants to be on the cutting edge, and it’s hard to get a pilot going), and they should realize that it can take a year to get approval.  There are security/privacy problems with how law firms handle email.  ROI tracking is important.  Analytics is used heavily in investigations, and often in litigation, but they currently only use TAR for prioritization and QC, not to cull the population before review.  Some law firms are adverse to putting data in the cloud, but cloud providers may have better security than law firms.

The GDPR team is working on educating U.S. judges about GDPR and developing a code of conduct.  The EDRM reference will be made easier to update.  The AI group is focused on AI in legal (e.g., estimating recidivism, billing, etc.), not implications of AI for the law.  The TAR group’s paper is out.  The Privilege Logs group wants to avoid duplicating Sedona’s effort (sidenote: lawyers need to learn that an email is not priv just because a lawyer was CC’ed on it).  The Stop Words team is trying to educate people about things such as regular expressions, and warned about cases where you want to search for a single letter or a term such as “AN” (for ammonium nitrate).  The Proportionality group talked about the possibility of having a standard set of documents that should be produced for certain types of cases and providing guidelines for making proportionality arguments to the court.

A panel of judges said that cybersecurity is currently a big issue.  Each court has it’s own approach to security.  Rule 16 conferences need to be taken seriously.  Judges don’t hire e-discovery vendors, so they don’t know costs.  How do you collect a proprietary database?  Lawyers can usually work it out without the judge.  There is good cooperation when the situations of the parties isn’t too asymmetric.  Attorneys need to be more specific in document requests and objections (no boilerplate).  Attorneys should know the case better than the judge, and educate the judge in a way that makes the judge look good.  Know the client’s IT systems and be aware of any data migration efforts.  Stay up on technology (e.g., Slack and text messages).  Have a 502(d) order (some people object because they fear the judge will assume priv review is not needed, but the judges didn’t believe that would happen).  Protect confidential information that is exchanged (what if there is a breach?).   When filing under seal, “attorney’s eyes only” should be used very sparingly, and “confidential” is over used.

# TAR vs. Keyword Search Challenge, Round 6 (Instant Feedback)

This was by far the most significant iteration of the ongoing exercise where I challenge an audience to produce a keyword search that works better than technology-assisted review (also known as predictive coding or supervised machine learning).  There were far more participants than previous rounds, and a structural change in the challenge allowed participants to get immediate feedback on the performance of their queries so they could iteratively improve them.  A total of 1,924 queries were submitted by 42 participants (an average of 45.8 queries per person) and higher recall levels were achieved than in any prior version of the challenge, but the audience still couldn’t beat TAR.

In previous versions of the experiment, the audience submitted search queries on paper or through a web form using their phones, and I evaluated a few of them live on stage to see whether the audience was able to achieve higher recall than TAR.  Because the number of live evaluations was so small, the audience had very little opportunity to use the results to improve their queries.  In the latest iteration, participants each had their own computer in the lab at the 2019 Ipro Tech Show, and the web form evaluated the query and gave the user feedback on the recall achieved immediately.  Furthermore, it displayed the relevance and important keywords for each of the top 100 documents matching the query, so participants could quickly discover useful new search terms to tweak their queries.  This gave participants a significant advantage over a normal e-discovery scenario, since they could try an unlimited number of queries without incurring any cost to make relevance determinations on the retrieved documents in order to decide which keywords would improve the queries.  The number of participants was significantly larger than any of the previous iterations, and they had a full 20 minutes to try as many queries as they wanted.  It was the best chance an audience has ever had of beating TAR.  They failed.

To do a fair comparison between TAR and the keyword search results, recall values were compared for equal amounts of document review effort.  In other words, for a specified amount of human labor, which approach gave the best production?  For the search queries, the top 3,000 documents matching the query were evaluated to determine the number that were relevant so recall could be computed (the full population was reviewed in advance, so the relevance of all documents was known). That was compared to the recall for a TAR 3.0 process where 200 cluster centers were reviewed for training and then the top-scoring 2,800 documents were reviewed.  If the system was allowed to continue learning while the top-scoring documents were reviewed, the result was called “TAR 3.0 CAL.”  If learning was terminated after review of the 200 cluster centers, the result was called “TAR 3.0 SAL.”  The process was repeated with review of 6,000 documents instead of 3,000 so you can see how much recall improves if you double the review effort.  Participants could choose to submit queries for any of three topics: biology, medical industry, or law.

The results below labeled “Avg Participant” are computed by finding the highest recall achieved by each participant and averaging those values together.  These are surely somewhat inflated values since one would probably not go through so many iterations of honing the queries in practice (especially since evaluating the efficacy of a query would normally involve considerable labor instead of being free and instantaneous), but I wanted to give the participants as much advantage as I could and including all of the queries instead of just the best ones would have biased the results to be too low due to people making mistakes or experimenting with bad queries just to explore the documents.  The results labeled “Best Participant” show the highest recall achieved by any participant (computed separately for Top 3,000 and Top 6,000, so they may be different queries).

 Biology Recall Top 3,000 Top 6,000 Avg Participant 54.5 69.5 Best Participant 66.0 83.2 TAR 3.0 SAL 72.5 91.0 TAR 3.0 CAL 75.5 93.0
 Medical Recall Top 3,000 Top 6,000 Avg Participant 38.5 51.8 Best Participant 46.8 64.0 TAR 3.0 SAL 67.3 83.7 TAR 3.0 CAL 80.7 88.5
 Law Recall Top 3,000 Top 6,000 Avg Participant 43.1 59.3 Best Participant 60.5 77.8 TAR 3.0 SAL 63.5 82.3 TAR 3.0 CAL 77.8 87.8

As you can see from the tables above, the best result for any participant never beat TAR (SAL or CAL) when there was an equal amount of document review performed.  Furthermore, the average participant result for Top 6,000 never beat the TAR results for Top 3,000, though the best participant result sometimes did, so TAR typically gives a better result even with half as much review effort expended.  The graphs below show the best results for each participant compared to TAR in blue.  The numbers in the legend are the ID numbers of the participants (the color for a particular participant is not consistent across topics).  Click the graph to see a larger version.

The large number of people attempting the biology topic was probably due to it being the default, and I illustrated how to use the software with that topic.

One might wonder whether the participants could have done better if they had more than 20 minutes to work on their queries.  The graphs below show the highest recall achieved by any participant as a function of time.  You can see that results improved rapidly during the first 10 minutes, but it became hard to make much additional progress beyond that point.  Also, over half of the audience continued to submit queries after the 20 minute contest, while I was giving the remainder of the presentation.  40% of the queries were submitted during the first 10 minutes, 40% were submitted during the second 10 minutes, and 20% were submitted while I was talking.  Since there were roughly the same number of queries submitted in the second 10 minutes as the first 10 minutes, but much less progress was made, I think it is safe to say that time was not a big factor in the results.

In summary, even with a large pool of participants, ample time, and the ability to hone search queries based on instant feedback, nobody was able to generate a better production than TAR when the same amount of review effort was expended.  It seems fair to say that keyword search often requires twice as much document review to achieve a production that is as good as what you would get TAR.

# Highlights from Ipro Tech Show 2019

Ipro renamed their conference from Ipro Innovations to the Ipro Tech Show this year.  As always, it was held at the Talking Stick Resort in Arizona and it was very well organized.  It started with a reception on April 29th that was followed by two days of talks.  There were also training days bookending the conference on April 29th and May 2nd.  After the keynote on Tuesday morning, there were five simultaneous tracks for the remainder of the conference, including a lot of hands-on work in computer labs.  I was only able to attend a few of the talks, but I’ve included my notes below. You can find my full set of photos here.  Videos and slides from the presentations are available here.

Dean Brown, who has been Ipro’s CEO for eight months, opened the conference with some information about himself and where the company is headed.  He mentioned that the largest case in a single Ipro database so far was 11 petabytes from 400 million documents.  Q1 2019 was the best quarter in the company’s history, and they had a 98% retention rate.  They’ve doubled spending on development and other departments.

Next, there was a panel where three industry experts discussed artificial intelligence.   AI can be used to analyze legal bills to determine which charges are reasonable.  Google uses AI to monitor and prohibit behaviors within the company, such as stopping your account from being used to do things when you are supposed to be away.  Only about 5% of the audience said they were using TAR.  It was hypothesized that this is due to FRCP 26(g)’s requirement to certify the production as complete and correct.  Many people use Slack instead of e-mail, and dealing with that is an issue for e-discovery.  CLOC was mentioned as an organization helping corporations get a handle on legal spending.

The keynote was given by Kevin Surace, and mostly focused on AI.  You need good data and have to be careful about spurious correlations in the data (he showed various examples that were similar to what you find here).  An AI can watch a video and supplement it with text explaining what the person in the video is doing.  One must be careful about fast changing patterns and black swan events where there is no data available to model.  Doctors are being replaced by software that is better informed about the most recent medical research.  AI can review an NDA faster and more accurately than an attorney.  There is now a news channel in China using an AI news anchor instead of a human to deliver the news.  With autonomous vehicles, transportation will become free (supported by ads in the vehicle).  AI will have an impact 100 times larger than the Internet.

I gave a talk titled “Technology: The Cutting Edge and Where We’re Headed” that focused on AI.  I started by showing the audience five pairs of images from WhichFaceIsReal.com and challenged them to determine which face was real and which was generated by an AI.  When I asked if anyone got all five right, I only saw one person raise their hand.  When I asked if anyone got all five wrong, I saw three hands go up.  Admittedly, I picked image pairs that I thought were particularly difficult, but the result is still a little scary.

I also gave a talk titled “TAR Versus Keyword Challenge” where I challenged the audience to construct a keyword search that worked better than technology-assisted review.  The format of this exercise was very different from previous iterations, making it easy for participants to test and hone their queries.  We had 1,924 queries submitted by 42 participants.  They achieved the highest recall levels seen so far, but still couldn’t beat TAR.  A detailed analysis is available here.

# Misleading Metrics and Irrelevant Research (Accuracy and F1)

If one algorithm achieved 98.2% accuracy while another had 98.6% for the same task, would you be surprised to find that the first algorithm required ten times as much document review to reach 75% recall compared to the second algorithm?  This article explains why some performance metrics don’t give an accurate view of performance for ediscovery purposes, and why that makes a lot of research utilizing such metrics irrelevant for ediscovery.

The key performance metrics for ediscovery are precision and recall.  Recall, R, is the percentage of all relevant documents that have been found.  High recall is critical to defensibility.  Precision, P, is the percentage of documents predicted to be relevant that actually are relevant.  High precision is desirable to avoid wasting time reviewing non-relevant documents (if documents will be reviewed to confirm relevance and check for privilege before production).  In other words, precision is related to cost.  Specifically, 1/P is the average number of documents you’ll have to review per relevant document found.  When using technology-assisted review (predictive coding), documents can be sorted by relevance score and you can choose any point in the sorted list and compute the recall and precision that would be achieved by treating documents above that point as being predicted to be relevant.  One can plot a precision-recall curve by doing precision and recall calculations at various points in the sorted document list.

The precision-recall curve to the right compares two different classification algorithms applied to the same task.  To do a sensible comparison, we should compare precision values at the same level of recall.  In other words, we should compare the cost of reaching equally good (same recall) productions.  Furthermore, the recall level where the algorithms are compared should be one that is sensible for for ediscovery — achieving high precision at a recall level a court wouldn’t accept isn’t very useful.  If we compare the two algorithms at R=75%, 1-NN has P=6.6% and 40-NN has P=70.4%.  In other words, if you sort by relevance score with the two algorithms and review documents from top down until 75% of the relevant documents are found, you would review 15.2 documents per relevant document found with 1-NN and 1.4 documents per relevant document found with 40-NN.  The 1-NN algorithm would require over ten times as much document review as 40-NN.  1-NN has been used in some popular TAR systems.  I explained why it performs so badly in a previous article.

There are many other performance metrics, but they can be written as a mixture of precision and recall (see Chapter 7 of the current draft of my book).  Anything that is a mixture of precision and recall should raise an eyebrow — how can you mix together two fundamentally different things (defensibility and cost) into a single number and get a useful result?  Such metrics imply a trade-off between defensibility and cost that is not based on reality.  Research papers that aren’t focused on ediscovery often use such performance measures and compare algorithms without worrying about whether they are achieving the same recall, or whether the recall is high enough to be considered sufficient for ediscovery.  Thus, many conclusions about algorithm effectiveness simply aren’t applicable for ediscovery because they aren’t based on relevant metrics.

One popular metric is accuracy, which is the percentage of predictions that are correct.  If a system predicts that none of the documents are relevant and prevalence is 10% (meaning 10% of the documents are relevant), it will have 90% accuracy because its predictions were correct for all of the non-relevant documents.  If prevalence is 1%, a system that predicts none of the documents are relevant achieves 99% accuracy.  Such incredibly high numbers for algorithms that fail to find anything!  When prevalence is low, as it often is in ediscovery, accuracy makes everything look like it performs well, including algorithms like 1-NN that can be a disaster at high recall.  The graph to the right shows the accuracy-recall curve that corresponds to the earlier precision-recall curve (prevalence is 2.633% in this case), showing that it is easy to achieve high accuracy with a poor algorithm by evaluating it at a low recall level that would not be acceptable for ediscovery.  The maximum accuracy achieved by 1-NN in this case was 98.2% and the max for 40-NN was 98.6%.  In case you are curious, the relationship between accuracy, precision, and recall is:
$ACC = 1 - \rho (1 - R) - \rho R (1 - P) / P$
where $\rho$ is the prevalence.

Another popular metric is the F1 score.  I’ve criticized its use in ediscovery before.  The relationship to precision and recall is:
$F_1 = 2 P R / (P + R)$
The F1 score lies between the precision and the recall, and is closer to the smaller of the two.  As far as F1 is concerned, 30% recall with 90% precision is just as good as 90% recall with 30% precision (both give F1 = 0.45) even though the former probably wouldn’t be accepted by a court and the latter would.   F1 cannot be large at small recall, unlike accuracy, but it can be moderately high at modest recall, making it possible to achieve a decent F1 score even if performance is disastrously bad at the high recall levels demanded by ediscovery.  The graph to the right shows that 1-NN manages to achieve a maximum F1 of 0.64, which seems pretty good compared to the 0.73 achieved by 40-NN, giving no hint that 1-NN requires ten times as much review to achieve 75% recall in this example.

Hopefully this article has convinced you that it is important for research papers to use the right metric, specifically precision (or review effort) at high recall, when making algorithm comparisons that are useful for ediscovery.

# TAR vs. Keyword Search Challenge, Round 5

The audience was challenged to construct a keyword search query that is more effective than technology-assisted review (TAR) at IG3 West 2018.  The procedure was the same as round 4, so I won’t repeat the details here.  The audience was small this time and we only got one query submission for each topic.  The submission for the law topic used AND to join the keywords together and matched no articles, so I changed the ANDs to ORs before evaluating it.  The results and queries are below.  TAR beat the keyword searches by a huge margin this time.

 Biology Recall Query Top 3,000 Top 6,000 Search 20.1% 20.1% TAR 3.0 SAL 72.5% 91.0% TAR 3.0 CAL 75.5% 93.0%
 Medical Recall Query Top 3,000 Top 6,000 Search 28.5% 38.1% TAR 3.0 SAL 67.3% 83.7% TAR 3.0 CAL 80.7% 88.5%
 Law Recall Query Top 3,000 Top 6,000 Search 5.5% 9.4% TAR 3.0 SAL 63.5% 82.3% TAR 3.0 CAL 77.8% 87.8%

biology query: (Evolution OR develop) AND (Darwin OR bird OR cell)
medical query: Human OR body OR medicine OR insurance OR license OR doctor OR patient
law query: securities OR conspiracy OR RICO OR insider

# Highlights from IG3 West 2018

The IG3 West conference was held by Ing3nious at the Paséa Hotel & Spa in Huntington Beach, California. This conference differed from other recent Ing3nious events in several ways.  It was two days of presentations instead of one.  There were three simultaneous panels instead of two.  Between panels there were sometimes three simultaneous vendor technology demos.  There was an exhibit hall with over forty vendor tables.  Due to the different format, I was only able to attend about a third of the presentations.  My notes are below.  You can find my full set of photos here.

Stop Chasing Horses, Start Building Fences: How Real-Time Technologies Change the Game of Compliance and Governance

AI and the Corporate Law Department of the Future
Gartner says AI is at the peak of inflated expectations and a trough of disillusionment will follow.  Expect to be able to buy autonomous vehicles by 2023.  The economic downturn of 2008 caused law firms to start using metrics.  Legal will take a long time to adopt AI — managing partners still have assistants print stuff out.  Embracing AI puts a firm ahead of its competitors.  Ethical obligations are also an impediment to adoption of technology, since lawyers are concerned about understanding the result.

Advanced TAR Considerations: A 500 Level Crash Course
Continuous Active Learning (CAL), also called TAR 2.0, can adapt to shifts in the concept of relevance that may occur during the review.  There doesn’t seem to be much difference in the efficiency of SVM vs logistic regression when they are applied to the same task.  There can be a big efficiency difference between different tasks.  TAR 1.0 requires a subject-matter expert for training, but senior attorneys are not always readily available.  With TAR 1.0 you may be concerned that you will be required to disclose the training set (including non-responsive documents), but with TAR 2.0 there is case law that supports that being unnecessary [I’ve seen the argument that the production itself is the training set, but that neglects the non-responsive documents that were reviewed (and used for training) but not produced.  On the other hand, if you are taking about disclosing just the seed set that was used to start the process, that can be a single document and it has very little impact on the result.].  Case law can be found at predictivecoding.com, which is updated at the end of each year.  TAR needs text, not image data.  Sometimes keywords are good enough.  When it comes to government investigations, many agencies (FTC, DOJ) use/accept TAR.  It really depends on the individual investigator, though, and you can’t fight their decision (the investigator is the judge).  Don’t use TAR for government investigations without disclosing that you are doing so.  TAR can have trouble if there are documents having high conceptual similarity where some are relevant and some aren’t.  Should you tell opposing counsel that you’re using TAR?  Usually, but it depends on the situation.  When the situation is symmetrical, both sides tend to be reasonable.  When it is asymmetrical, the side with very little data may try to make things expensive for the other side, so say something like “both sides may use advanced technology to produce documents” and don’t give more detail than that (e.g., how TAR will be trained, who will do the training, etc.) or you may invite problems.  Disclosing the use of TAR up front and getting agreement may avoid problems later.  Be careful about “untrainable documents” (documents containing too little text) — separate them out, and maybe use meta data or file type to help analyze them.  Elusion testing can be used to make sure too many relevant documents weren’t missed.  One panelist said 384 documents could be sampled from the elusion set, though that may sometimes not be enough.  [I have to eat some crow here.  I raised my hand and pointed out that the margin of error for the elusion has to be divided by the prevalence to get the margin of error for the recall, which is correct.  I went on to say that with a sample of 384 giving ±5% for the elusion you would have ±50% for the recall if prevalence was 10%, making the measurement worthless.  The mistake is that while a sample of 384 technically implies a worst case of ±5% for the margin of error for elusion, it’s not realistic for the margin of error to be that bad for elusion because ±5% would occur if elusion was near 50%, but elusion is typically very small (smaller than the prevalence), causing the margin of error for the elusion to be significantly less than ±5%.  The correct margin of error for the recall from an elusion sample of 384 documents would be ±13% if the prevalence is 10%, and ±40% if the prevalence is 1%.  So, if prevalence is around 10% an elusion sample of 384 isn’t completely worthless (though it is much worse than the ±5% we usually aim for), but if prevalence is much lower than that it would be].

40 Years in 30 Minutes: The Background to Some of the Interesting Issues we Face

Digging Into TAR
I moderated this panel, so I didn’t take notes.  We did the TAR vs. Keyword Search Challenge again.  The results are available here.

After the Incident: Investigating and Responding to a Data Breach

Employing Technology/Next-Gen Tools to Reduce eDiscovery Spend
Have a process, but also think about what you are doing and the specifics of the case.  Restrict the date range if possible.  Reuse the results when you have overlapping cases (e.g., privilege review).  Don’t just look at docs/hour when monitoring the review.  Look at accuracy and get feedback about what they are finding.  CAL tends to result in doing too much document review (want to stop at 75% recall but end up hitting 89%).  Using a tool to do redactions will give false positives, so you need manual QC of the result.  When replacing a patient ID with a consistent anonymized identifier, you can’t just transform the ID because that could be inverted, resulting in a HIPAA violation.

eDiscovery for the Rest of us
What are ediscovery considerations for relatively small data sets?  During meet and confer, try to cooperate.  Judges hate ediscovery disputes.  Let the paralegals hash out the details — attorneys don’t really care about the details as long as it works.  Remote collection can avoid travel costs and hourly fees while keeping strangers out of the client’s office.  The biggest thing they look for from vendors is cost.  Need a certain volume of data for TAR to be practical.  Email threading can be used at any size.

Does Compliance Stifle or Spark Innovation?
Startups tend to be full of people fleeing big corporations to get away from compliance requirements. If you do compliance well, that can be an advantage over competitors.  Look at it as protecting the longevity of the business (protecting reputation, etc.).  At the DoD, compliance stifles innovation, but it creates a barrier against bad guys.  They have thousands of attacks per day and are about 8 years behind normal innovation.  Gray crimes are a area for innovation — examples include manipulation (influencing elections) and tanking a stock IPO by faking a poisoning.  Hospitals and law firms tend to pay, so they are prime targets for ransomware.

Panels That I Couldn’t Attend:
California and EU Privacy Compliance
What it all Comes Down to – Enterprise Cybersecurity Governance
Selecting eDiscovery Platforms and Vendors
Defensible Disposition of Data
Biometrics and the Evolving Legal Landscape
Storytelling in the Age of eDiscovery
Technology Solution Update From Corporate, Law Firm and Service Provider Perspective
The Internet of Things and Everything as a Service – the Convergence of Security, Privacy and Product Liability
Similarities and Differences Between the GDPR and the New California Consumer Privacy Act – Similar Enough?
The Impact of the Internet of Things on eDiscovery
Escalating Cyber Risk From the IT Department to the Boardroom
So you Weren’t Quite Ready for GDPR?
Security vs. Compliance and Why Legal Frameworks Fall Short to Improve Information Security
How to Clean up Files for Governance and GDPR
Deception, Active Defense and Offensive Security…How to Fight Back Without Breaking the Law?
Information Governance – Separating the “Junk” from the “Jewels”
What are Big Law Firms Saying About Their LegalTech Adoption Opportunities and Challenges?
Cyber and Data Security for the GC: How to Stay out of Headlines and Crosshairs

# Podcast: Can You Do Good TAR with a Bad Algorithm?

Bill Dimm will be speaking with John Tredennick and Tom Gricks on the TAR Talk podcast about his recent article TAR, Proportionality, and Bad Algorithms (1-NN).  The podcast will be on Tuesday, November 20, 2018 (podcast description and registration page is here).  You can download the recording here:
RECORDED PODCAST

# TAR vs. Keyword Search Challenge, Round 4

This iteration of the challenge was performed during the Digging into TAR session at the 2018 Northeast eDiscovery & IG Retreat.  The structure was similar to round 3, but the audience was bigger.  As before, the goal was to see whether the audience could construct a keyword search query that performed better than technology-assisted review.

There are two sensible ways to compare performance.  Either see which approach reaches a fixed level of recall with the least review effort, or see which approach reaches the highest level of recall with a fixed amount of review effort.  Any approach comparing results having different recall and different review effort cannot give a definitive conclusion on which result is best without making arbitrary assumptions about a trade off between recall and effort (this is why performance measures, such as the F1 score, that mix recall and precision together are not sensible for ediscovery).

For the challenge we fixed the amount of review effort and measured the recall achieved, because that was an easier process to carry out under the circumstances.  Specifically, we took the top 3,000 documents matching the search query, reviewed them (this was instantaneous because the whole population was reviewed in advance), and measured the recall achieved.  That was compared to the recall for a TAR 3.0 process where 200 cluster centers were reviewed for training and then the top-scoring 2,800 documents were reviewed.  If the system was allowed to continue learning while the top-scoring documents were reviewed, the result was called “TAR 3.0 CAL.”  If learning was terminated after review of the 200 cluster centers, the result was called “TAR 3.0 SAL.”  The process was repeated with 6,000 documents instead of 3,000 so you can see how much recall improves if you double the review effort.

Individuals in the audience submitted queries through a web form using smart phones or laptops and I executed some (due to limited time) of the queries in front of the audience.  They could learn useful keywords from the documents matching the queries and tweak their queries and resubmit them.  Unlike a real ediscovery project, they had very limited time and no familiarity with the documents.  The audience could choose to work on any of three topics: biology, medical industry, or law.  In the results below, the queries are labeled with the submitters’ initials (some people gave only a first name, so there is only one initial) followed by a number if they submitted more than one query.  Two queries were omitted because they had less than 1% recall (the participants apparently misunderstood the task).  The queries that were evaluated in front of the audience were E-1, U, AC-1, and JM-1.  The discussion of the result follows the tables, graphs, and queries.

 Biology Recall Query Top 3,000 Top 6,000 E-1 32.0% 49.9% E-2 51.7% 60.4% E-3 48.4% 57.6% E-4 45.8% 60.7% E-5 43.3% 54.0% E-6 42.7% 57.2% TAR 3.0 SAL 72.5% 91.0% TAR 3.0 CAL 75.5% 93.0%
 Medical Recall Query Top 3,000 Top 6,000 U 17.1% 27.9% TAR 3.0 SAL 67.3% 83.7% TAR 3.0 CAL 80.7% 88.5%
 Law Recall Query Top 3,000 Top 6,000 AC-1 16.4% 33.2% AC-2 40.7% 54.4% JM-1 49.4% 69.3% JM-2 55.9% 76.4% K-1 43.5% 60.6% K-2 43.0% 62.6% C 32.9% 47.2% R 55.6% 76.6% TAR 3.0 SAL 63.5% 82.3% TAR 3.0 CAL 77.8% 87.8%

E-1) biology OR microbiology OR chemical OR pharmacodynamic OR pharmacokinetic
E-2) biology OR microbiology OR pharmacodynamic OR cellular OR enzyme OR activation OR nucleus OR protein OR interaction OR genomic OR dna OR hematological OR sequence
E-3) biology OR microbiology OR pharmacodynamic OR cellular OR enzyme OR activation OR nucleus OR protein OR interaction OR genomic OR dna OR hematological OR sequence OR pharmacokinetic OR processes OR lysis
E-4) biology OR microbiology OR pharmacodynamic OR cellular OR enzyme OR activation OR nucleus OR protein OR interaction OR genomic OR dna OR hematological OR sequence OR pharmacokinetic OR processes OR lysis OR study
E-5) biology OR microbiology OR pharmacodynamic OR cellular OR enzyme OR activation OR nucleus OR protein OR interaction OR genomic OR dna OR hematological OR sequence OR pharmacokinetic OR processes OR lysis OR study OR table
E-6) biology OR microbiology OR pharmacodynamic OR cellular OR enzyme OR activation OR nucleus OR protein OR interaction OR genomic OR dna OR hematological OR sequence OR pharmacokinetic OR processes OR lysis OR study OR table OR research
U) Transplant OR organ OR cancer OR hypothesis
AC-1) law
AC-2) legal OR attorney OR (defendant AND plaintiff) OR precedent OR verdict OR deliberate OR motion OR dismissed OR granted
JM-1) Law OR legal OR attorney OR lawyer OR litigation OR liability OR lawsuit OR judge
JM-2) Law OR legal OR attorney OR lawyer OR litigation OR liability OR lawsuit OR judge OR defendant OR plaintiff OR court OR plaintiffs OR attorneys OR lawyers OR defense
K-1) Law OR lawyer OR attorney OR advice OR litigation OR court OR investigation OR subpoena
K-2) Law OR lawyer OR attorney OR advice OR litigation OR court OR investigation OR subpoena OR justice
C) (law OR legal OR criminal OR civil OR litigation) AND NOT (politics OR proposed OR pending)
R) Court OR courtroom OR judge OR judicial OR judiciary OR law OR lawyer OR legal OR plaintiff OR plaintiffs OR defendant OR defendants OR subpoena OR sued OR suing OR sue OR lawsuit OR injunction OR justice

None of the keyword searches achieved higher recall than TAR when the amount of review effort was equal.  All six of the biology queries were submitted by one person.  The first query was evaluated in front of the audience, and his first revision to the query did help, but subsequent (blind) revisions of the query tended to hurt more than they helped.  For biology, review of 3,000 documents with TAR gave better recall than review of 6,000 documents with any of the queries.  There was only a single query submitted for the medical industry, and it underperformed TAR substantially.  Five people submitted a total of eight queries for the law category, and the audience had the best results for that topic, which isn’t surprising since an audience full of lawyers and litigation support people would be expected to be especially good at identifying keywords related to the law.  Even the best queries had lower recall with review of 6,000 documents than TAR 3.0 CAL achieved with review of only 3,000 documents, but a few of the queries did achieve higher recall than TAR 3.0 SAL when twice as much document review was performed with the search query compared to TAR 3.0 SAL.

# Highlights from the Northeast eDiscovery & IG Retreat 2018

The 2018 Northeast eDiscovery and Information Governance Retreat was held at the Salamander Resort & Spa in Middleburg, Virginia.  It was a full day of talks with a parallel set of talks on Cybersecurity, Privacy, and Data Protection in the adjacent room. Attendees could attend talks from either track. Below are my notes (certainly not exhaustive) from the eDiscovery and IG sessions. My full set of photos is available here.

Stratagies For Data Minimization Of Legacy Data
Backup and archiving should be viewed as separate functions.  When it comes to spoliation (FRCP Rule 37), reasonableness of the company’s data retention plan is key.  Over preservation is expensive.  There are not many cases on Rule 37 relating to backup tapes.  People are changing their behavior due to the changes in the FRCP, especially in heavily regulated industries such as healthcare and financial services.  Studies find that typically 70% of data has no business value and is not subject to legal hold or retention requirements for compliance.  When using machine learning, you can focus on finding what to keep or what to get rid of.  It is often best to start with unsupervised machine learning.  Be mindful of destructive malware.  To mitigate security risks, it is important to know where your data (including backup tapes) is.  If a backup tape goes missing, do you need to notify customers (privacy)?  To get started, create a matrix showing what you need to keep, keeping in mind legal holds and privacy (GDPR).  Old backup tapes are subject to GDPR.  Does the right to be forgotten apply to backup tapes?  There is currently no answer.  It would be hard to selectively delete data from the tapes, so maybe have a process that deletes during the restore.  There can be conflicts between U.S. ediscovery and GDPR, so you must decide which is the bigger risk.

Preparing A Coordinated Response To Government Inquiries And Investigations

Digging Into TAR
I moderated this panel, so I didn’t take notes. We challenged the audience to create a keyword search that would work better than technology-assisted review. Results are posted here.

Implementing Information Governance – Nightmare On Corporate America Street?

Technology Solution Update From Corporate, Law Firm And Service Provider Perspective
Artificial intelligence (AI) should not merely analyze; it should present a result in a way that is actionable.  It might tell you how much two people talk, their sentiment, and whether there are any spikes in communication volume.  AI can be used by law firms for budgeting by analyzing prior matters.  There are concerns about privacy with AI.  Many clients are moving to the cloud.  Many are using private clouds for collaboration, not necessarily for utilizing large computing power.  Office 365 is of interest to many companies.  There was extensive discussion about the ediscovery analytics capabilities being added from the Equivio acquisition, and a demo by Marcel Katz of Microsoft.  The predictive coding (TAR) capability uses simple active learning (SAL) rather than continuous active learning (CAL).  It is 20 times slower in the cloud than running Equivio on premises.  There is currently no review tool in Office 365, so you have to export the predictions out and do the review elsewhere.  Mobile devices create additional challenges for ediscovery.  The time when a text message is sent may not match the time when it is received if the receiving device is off when the message is sent.  Technology needs to be able to handle emojis.  There are many different apps with many different data storage formats.

The ‘Team Of Teams’ Approach To Enterprise Security And Threat Management
Fast response is critical when you are attacked.  Response must be automated because a human response is not fast enough.  It can take 200 days to detect an adversary on the network, so assume someone is already inside.  What are the critical assets, and what threats should you look for?  What value does the data have to the attacker?  What is the impact on the business?  What is the impact on the people?  Know what is normal for your systems.  Is a large data transfer at 2:00am normal?  Simulate a phishing attack and see if your employees fall for it.  In one case a CEO was known to be in China for a deal, so someone impersonating the CEO emailed the CFO to send $50 million for the deal. The money was never recovered. Have processes in place, like requiring a signature for amounts greater than$10,000.  If a company is doing a lot of acquisitions, it can be hard to know what is on their network.  How should small companies get started?  Change passwords, hire an external auditor, and make use of open source tools.

From Data To GRC Insight
Governance, risk management, and compliance (GRC) needs to become centralized and standardized.  Practicing incident response as a team results in better responses when real incidents happen.  Growing data means growing risk.  Beware of storage of social security numbers and credit card numbers.  Use encryption and limit access based on role.  Detect emailing of spreadsheets full of data.  Know what the cost of HIPAA violations is and assign the risk of non-compliance to an individual.  Learn about the NIST Cybersecurity Framework.  Avoid fines and reputational risk, and improve the organization.  Transfer the risk by having data hosted by a company that provides security.  Cloud and mobile can have big security issues.  The company can’t see traffic on mobile devices to monitor for phishing.

# TAR vs. Keyword Search Challenge, Round 3

This iteration of the challenge, held at the Education Hub at ILTACON 2018, was structured somewhat differently from round 1 and round 2 to give the audience a better chance of beating TAR.  Instead of submitting search queries on paper, participants submitted them through a web form using their phones, which allowed them to repeatedly tweak their queries and resubmit them.  I executed the queries in front of the participants, so they could see the exact recall achieved (since all documents were marked as relevant or non-relevant by a human reviewer in advance) almost instantaneously and they could utilize the performance information for their queries and the queries of other participants to guide improvements to their queries. This actually gave the participants an advantage over what they would experience in a real e-discovery project since performance measurements would normally require human evaluation of a random sample from the search output, which would make execution of several iterations of a query guided by performance evaluations very expensive in terms of review labor.  The audience got those performance evaluations for free even though the goal was to compare recall achieved for equal amounts of document review effort.  On the other hand, the audience did still have the disadvantages of having limited time and no familiarity with the documents.

As before, recall was evaluated for the top 3000 and top 6000 documents, which was enough to achieve high recall with TAR (even with the training documents included, so total review effort for TAR and the search queries was the same).  Audience members were free to work on any of the three topics that were used in previous versions of the challenge: law, medical industry, or biology.  Unfortunately, the audience was much smaller than previous versions of the challenge, and nobody chose to submit a query for the biology topic.

Previously, the TAR results were achieved by using the TAR 3.0 workflow to train with 200 cluster centers, documents were sorted based on the resulting relevance scores, and top-scoring documents were reviewed until the desired amount of review effort was expended without allowing predictions to be updated during that review (e.g., review of 200 training docs plus 2,800 top scoring docs to get the “Top 3,000” result).  I’ll call this TAR 3.0 SAL (SAL = Simple Active Learning, meaning the system is not allowed to learn during the review of top-scoring documents).  In practice you wouldn’t do that.  If you were reviewing top-scoring documents, you would allow the system to continue learning (CAL).  You would use SAL only if you were producing top-scoring documents without reviewing them since allowing learning to continue during the review would reduce the amount of review needed to achieve a desired level of recall.  I used TAR 3.0 SAL in previous iterations because I wanted to simulate the full review in front of the audience in a few seconds and TAR 3.0 CAL would have been slower.  This time, I did the TAR calculations in advance and present both the SAL and CAL results so you can see how much difference the additional learning from CAL made.

One other difference compared to previous versions of the challenge is how I’ve labeled the queries below.  This time, the number indicates which participant submitted the query and the letter indicates which one of his/her queries are being analyzed (if the person submitted more than one) rather than indicating a tweaking of the query that I added to try to improve the result.  In other words, all variations were tweaks done by the audience instead of by me.  Discussion of the results follows the tables, graphs, and queries below.

 Recall Medical Industry Top 3,000 Top 6,000 1a 3.0% 1b 17.4% TAR 3.0 SAL 67.3% 83.7% TAR 3.0 CAL 80.7% 88.5%

 Recall Law Top 3,000 Top 6,000 2 1.0% 3a 36.1% 42.3% 3b 45.3% 60.1% 3c 47.2% 62.6% 4 11.6% 13.8% TAR 3.0 SAL 63.5% 82.3% TAR 3.0 CAL 77.8% 87.8%

1a)  Hospital AND New AND therapies
1b)  Hospital AND New AND (physicians OR doctors)
2)   Copyright AND mickey AND mouse
3a)  Schedule OR Amendments OR Trial OR Jury OR Judge OR Circuit OR Courtroom OR Judgement
3b)  Amendments OR Trial OR Jury OR Judge OR Circuit OR Courtroom OR Judgement OR trial OR law OR Patent OR legal
3c)  Amendments OR Trial OR Jury OR Judge OR Circuit OR Courtroom OR Judgement OR trial OR law OR Patent OR legal OR Plaintiff OR Defendant
4)  Privacy OR (Personally AND Identifiable AND Information) OR PII OR (Protected AND Speech)

TAR won across the board, as in previous iterations of the challenge.  Only one person submitted queries for the medical industry topic.  His/her revised query did a better job of finding relevant documents, but still returned fewer than 3,000 documents and fared far worse than TAR — the query was just not broad enough to achieve high recall.  Three people submitted queries on the law topic.  One of those people revised the query a few times and got decent results (shown in green), but still fell far short of the TAR result, with review of 6,000 documents from the best query finding fewer relevant documents than review of half as many documents with TAR 3.0 SAL (TAR 3.0 CAL did even better).  It is unfortunate that the audience was so small, since a larger audience might have done better by learning from each other’s submissions.  Hopefully I’ll be able to do this with a bigger audience in the future.


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## Geometry: Common Core (15th Edition)

We use the equation for the volume of a pyramid to obtain: $Volume = \frac{1}{3}\times A_{base}\times height$ $Volume = \frac{1}{3}\times 10\times 10 \times 6$ $Volume = 200 cm^{3}$

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Tag Info

5

Amplitude coefficients are complex. The reflection and transmission coefficients must account for both amplitude change and phase change. In order to account for both of these, complex coefficients are required. These are the most general, and are needed for a complete description. In some special (and simple) cases, the phase shift is $0^\circ$ or ...

0

The moller operator take the wave function and send to $t=-\infty$ with the influence of potential $V$ and send back to $t=0$ without the influence of $V$. $$\Omega_+ = \lim_{t \rightarrow -\infty } e^{i H t } e^{- i H_0 t }$$ If we make this with a far away wave function $\psi$, this wave function don't feel the potential $V$ at time $t=0$. But we don't ...

0

The wave packet concept is also related to the inability of plane wave to describe the communication of information. The plane wave wave occupies the whole space, whereas the wave packet is localised at some position with certain distribution. This is intimately related to the group velocity and phase velocity that are also used in classical optics. To ...

3

The time evolution of wave function is dictated by the Schrödinger equation, as you surely well know. Let's take the simple free particle in $\mathbb{R}^d$ (with mass $1/2$ and $\hbar=1$): $$i\partial_t \psi(t,x)=-\Delta_x \psi(t,x)\; ;$$ where $\Delta$ is the Laplacian operator (i.e. $\partial_x^2$). Mathematically, this is a linear PDE (partial ...

1

The most common colour for the sky on Earth is a white sky. Clouds cover around 70% of the Earth, and the nature by which they are scattering shortwave radiation makes them appear white or grey. This is because photons coming from the Sun are likely to be scattered multiple times, and because the dependence on wavelength is not strongly increasing or ...

2

This is an extremely hard question to answer definitely; its answer is heavily dependent on three things (1) the makeup of the atmosphere in question (2) the density of the atmosphere in question and (3) the surface temperature, and therefore the spectrum of output light, of the star in question. If the atmopsphere's gasses are themselves are coloured (e.g. ...

0

Hmm... Mars has a red sky. But that's cause of the iron content in the soil absorbs other parts of the visible spectrum and reflects back the red part, so the sky looks reddish. I do not think a blackish sky was too far-fetched cause carbon tends to be black, smoke is blackish grey. Perceived color depends on different elements absorbing different portions ...

1

We know/assume that the mass of the particle is constant. Elastic scattering means no change in kinetic energy (in the center-of-mass frame). Since the mass of the particle is constant, this means there is no change in the speed (not velocity; speed) of the particle during an elastic collision. Torque is $\vec{\tau} = \vec{r} \times \vec{F}$. For a ...

1

Probably too late now, but I have to answer this. There is indeed a way to predict the direction of a scattered Lyman $\alpha$ photon. The answer depends on whether the scattering takes place in the core or the wings of the line. In the core (i.e. closer to the line center than about 3 Doppler widths), we can use the dipole approximation, so the phase ...

0

Certainly late for your homework problem, but figure below shows the schematic of elastic scattering. The scattering angle is $\Theta$. The momentum transfer vector is $\Delta \bf{p}$. Since your question starts with potential, we shall obtain the force first: \begin{align} F(r) &= \frac{dV}{dr} \\ &= -\frac{\alpha}{r^2} \end{align} At any time, ...

Top 50 recent answers are included


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# stability … boring old and simple stability

[xxx@yyy~]$uptime 15:07:51 up 505 days, 47 min, 14 users, load average: 0.39, 0.35, 0.19 [xxx@yyy~]$ uname -s
Linux

43.6 mega-seconds. For the pair of 1.6 GHz CPUs that are in here, this is a combined 1.4 x 10^17 clock cycles. Or for the chemists among us … this is 0.23 micro-mole of clock cycles. You would need 4.3 million of these machines to provide one mole (6.022 x 10^23) cycles per year.


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# Rational rank of l-group

Is it possible to have a finitely generated lattice - ordered group has rational rank bigger than the number of generators of the group?

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Is the group abelian? Otherwise I don´t know the definition of rational rank. –  Giovanni De Gaetano Feb 7 '12 at 9:27

This answer suppose, given the tag, that we are dealing with an Abelian ordered group $G$. (Actually the fact that $G$ is ordered does not come into play once supposed the abelianity)
Then we can suppose, without loss of generality, $G$ to be torsion free. Indeed if $T(G)$ is the torsion group of $G$ then $r(G)=r(G/T(G))$. So we can suppose $G=G/T(G)$ which has equal rank and maybe a smaller set of generators.
But then $G$ is abelian, finitely generated and torsion free, so it is an abelian free group with $n$ generators and it has rank $n$.


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# Digraph intermediate connectivity

What's the name for a digraph such that for each pair of vertices $u,v$, there is either a path from $u$ to $v$ or a path from $v$ to $u$? I'd call it just connected, since this is an intermediate property between weak and strong connectivity, and is in fact equivalent to the existence of a path containing all vertices. However, I'm not an expert of the subject, and I was unable to find any reference about this, so far.

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Just `connected' is fine. For example, Wikipedia and Tutte agree. However, since "the number of systems of terminology presently used in graph theory is equal, to a close approximation, to the number of graph theorists," (R.P. Stanley, 1986) you might want to include the definition anyway.

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Thank you! I had not seen the definition on Wikipedia. It was added by an anonymous user on last Oct 13, apparently. I had asked the same question in the talk page, but nobody answered me there. The reference from Tutte is completely satisfactory for me. – Ale De Luca Jul 5 '10 at 18:13

Another term that has been used is "unilateral" or "unilaterally connected". I don't have a particularly strong opinion in favor of this terminology, but I am slightly opposed to just calling it "connected". (I usually assume "connected" means "weakly connected" for digraphs.) However, I must admit a reference by Tutte is good.

Some references for "unilateral":

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thank you very much! – Ale De Luca Jul 7 '10 at 17:16

Such digraph is called traceable. For example, it is defined as such in the paper http://www.ams.org/bull/1976-82-01/S0002-9904-1976-13955-9/S0002-9904-1976-13955-9.pdf

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Thank you very much for your answer. It seems, however, that the definition of traceable graph in such paper requires the existence of a Hamiltonian path. This is not equivalent to what I am asking; I am not interested whether the path visits each vertex exactly once, as long as it does visit all of them. For example, the digraph $\{(a,b),(b,a),(a,c),(c,a),(a,d)\}$ is "connected" as I'm meaning, but it is not traceable as the shortest path visiting all vertices is $bacad$ (or $cabad$), thus visiting $a$ twice. The same graph is also not strongly connected, as no edge starts from $d$. – Ale De Luca Jul 5 '10 at 0:29

Such a graph is called a semiconnected graph. You can find references to it in Cormen and Diestel's book on graph theory http://diestel-graph-theory.com/

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Thanks… but again, it doesn't quite seem to be the same thing. In Diestel's book I could only find a definition for semiconnectedness of submultigraphs of infinite graphs. It is not obvious to me how would this apply to digraphs in general. – Ale De Luca Jul 5 '10 at 18:10


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## Normal elements of degree one in Ore extensions.(English)Zbl 1010.16024

An element $$c$$ of a ring $$R$$ is ‘normal’ if $$Rc=cR$$. This note concerns normal elements $$c$$ of the form $$dx+e$$ (with $$d,e\in A$$) of Ore extensions $$R=A[x;\sigma,\delta]$$, where $$A$$ is a domain. In particular it is proved that $$d$$ is normal in $$A$$ and that if $$e$$ is regular modulo $$Ad$$ then $$R/Rc$$ is a domain. The author indicates how this can be applied to show that $${\mathcal O}/{\mathcal O}\Delta$$ is a domain, when $$\mathcal O$$ is the coordinate ring of $$n\times n$$ quantum matrices over a field $$F$$ and $$\Delta$$ is the quantum determinant. A similar conclusion can be deduced for the analogous factor of the multiparameter ring of quantum matrices. The lemma has found recent application in work of K. R. Goodearl and T. H. Lenagan [Duke Math. J. 103, No. 1, 165-190 (2000; Zbl 0958.16025)].

### MSC:

 16S36 Ordinary and skew polynomial rings and semigroup rings 17B37 Quantum groups (quantized enveloping algebras) and related deformations

### Keywords:

Ore extensions; normal elements; quantum matrices; domains

Zbl 0958.16025
Full Text:


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##### Exercise 1

Since (as calculated in the example)

$e^{-0.000121 \times 5730} \approx \dfrac{1}{2},$

we may rewrite the equation $$m = 100 \, e^{-0.000121 \, t}$$ as

\begin{align*} m &= 100 \, e^{-0.000121 \, t} \\ &= 100 \, \Bigl( e^{-0.000121 \times 5730} \Bigr)^{\tfrac{t}{5730}} \\ &\approx 100 \, \Bigl( \dfrac{1}{2} \Bigr)^{\tfrac{t}{5730}}. \end{align*}

From this equation we can see that, when $$t$$ increases by 5730, the exponent $$\dfrac{t}{5730}$$ increases by 1 and so $$m$$ is multiplied by $$\dfrac{1}{2}$$.

##### Exercise 2

Since the population is given by $$x(t) = 1000 \, e^{0.1 \, t}$$, the population is double its initial value when

$2000 = 1000 \, e^{0.1 \, t} \quad \implies \quad t = \dfrac{\log_e 2}{0.1} \approx 6.93 \text{ years.}$
##### Exercise 3

If the growth rate is $$k$$, then the population $$P$$ will be given by $$P(t) = C e^{kt}$$ after $$t$$ years. The population will double over a time period of length $$T$$ if

\begin{align*} P(t + T) = 2P(t) \quad &\iff \quad C e^{k(t + T)} = 2Ce^{kt} \\ &\iff \quad e^{kT} = 2 \\ &\iff \quad T = \dfrac{1}{k} \log_e 2. \end{align*}
##### Exercise 4
1. Let $$P$$ be the number of pheasants $$t$$ years after introduction. With continuous growth rate $$k=1$$, we have $$P(t) = C e^{t}$$ for a constant $$C$$. Since $$P(0) = 8$$, we have $$C=8$$ and so $$P(t) = 8 e^t$$. After 60 years, the pheasant population is $$P(60) = 8 e^{60} \approx 9.14 \times 10^{26}$$.
2. At 1.5 kg per pheasant, we have $$9.14 \times 10^{26} \times 1.5 \approx 1.37 \times 10^{27}$$ kg of pheasants. This is much greater than the mass of the earth.
3. A continuous growth rate as rapid as 100% cannot persist for long. The pheasants will rapidly run out of food, land and other resources. The population's growth will slow down as these limits are reached. A more realistic model is discussed in the section Links forward (Logistic growth).
##### Exercise 5

Let $$P(t)$$ denote the population after $$t$$ years.

1. In this case we effectively have a constant continuous growth rate of $$k=0.1$$, starting from a population of 1700. We obtain $$P(t) = 1700 \, e^{0.1 \, t}$$. After seven years, the number of birds is $$P(7) = 1700 \, e^{0.7} \approx 3420$$ (to three significant figures).
2. This is the situation in the example, which gives 3030 birds after seven years.
3. This is effectively the situation in the earlier example, but with an extra 700 birds added at the end. Thus, to three significant figures, there are $$2010 + 700 = 2710$$ birds after seven years.

We see that the earlier the birds migrate, the larger the final population. The earlier they arrive, the more time they have to reproduce.

##### Exercise 6
1. With the patch on, we have $$\dfrac{dA}{dt} = 1 - 0.12 A$$, which has general solution $A(t) = C e^{-0.12 \, t} + \dfrac{1}{0.12}.$ Since $$A(0) = 0$$, we obtain $$C = - \dfrac{1}{0.12}$$. Thus \begin{align*} A(t) &= - \dfrac{1}{0.12} e^{-0.12 \, t} + \dfrac{1}{0.12}\\ &= \dfrac{1}{0.12} \bigl( 1 - e^{-0.12 \, t} \bigr), \end{align*} so \begin{align*} A(16) &= \dfrac{1}{0.12} \bigl(1 - e^{-0.12 \times 16} \bigr) \\ &\approx 7.11\ \mu\text{g/L (to three significant figures)}. \end{align*}
2. With the patch off, $$\dfrac{dA}{dt} = -0.12 A$$, which has general solution $$A(t) = C e^{-0.12 \, t}$$. Since $$A(16) \approx 7.11$$, we obtain $$C \approx 48.5$$, so \begin{align*} A(24) &\approx 48.5 \, e^{-0.12 \times 24} \\ &\approx 2.72\ \mu\text{g/L (to three significant figures)}. \end{align*}
##### Exercise 7
1. The population reaches 2 million when $2\,000\,000 = 500\,000 \, e^{0.01 \, t} + 500\,000.$ Rearranging this gives $e^{0.01 \, t} = 3 \quad \iff \quad t = 100 \, \log_e 3.$ So $$t \approx 109.86$$ hours (to two decimal places).
2. If there were no extraction, then we would have the differential equation $\dfrac{dp}{dt} = 0.015 \, p - 0.005 \, p = 0.01 \, p.$ Thus the growth rate is $$k=0.01$$ and hence the doubling time is \begin{align*} T &= \dfrac{1}{k} \log_e 2 \\ &= 100 \, \log_e 2 \\ &\approx 69.31 \text{ hours (to two decimal places).} \end{align*}
##### Exercise 8
1. $$M(t) = 100 \, (1+r)^t$$
2. The amount in the account doubles when $$(1+r)^t = 2$$. Taking the natural logarithm of both sides gives $$t \, \log_e (1+r) = \log_e 2$$, so

$t = \dfrac{ \log_e 2}{ \log_e (1+r) }.$
3. Rewriting $$(1+r)^t$$ as $$e^{t \, \log_e (1+r)}$$ gives $$M = 100 \, e^{t \, \log_e (1+r)}$$. Therefore \begin{align*} \dfrac{dM}{dt} &= 100 \, \log_e (1+r) \, e^{t \, \log_e (1+r)} \\ &= M \, \log_e (1+r), \end{align*} and hence the continuous growth rate is $$\log_e (1+r)$$.
##### Exercise 9

The discrete growth rate $$r$$ and the continuous growth rate $$k$$ are related by $$k = \log_e (1 + r)$$. So $$k = 1$$ gives $$1 = \log_e (1+r)$$, and therefore

$r = e - 1 \approx 1.72 \ \ \text{(to two decimal places)}.$

This discrete growth rate of 1.72 per year is analogous to an interest rate of 172% per annum; the number of pheasants was multiplied by 2.72 each year.

##### Exercise 10

From

$\dfrac{dx}{dt} = kx \Bigl( 1 - \dfrac{x}{R} \Bigr) = \dfrac{kx(R-x)}{R},$

we obtain

$\dfrac{dt}{dx} = \dfrac{R}{kx(R-x)}.$

Writing this expression in terms of partial fractions we obtain

$\dfrac{dt}{dx} = \dfrac{1}{kx} + \dfrac{1}{k(R-x)}.$

Integrating gives

\begin{align*} t &= \dfrac{1}{k} \log_e x - \dfrac{1}{k} \log_e (R-x) + c \\ &= \dfrac{1}{k} \log_e \Bigl(\dfrac{x}{R-x}\Bigr) + c, \end{align*}

where $$c$$ is a constant of integration. Rearranging, we obtain

$x = \dfrac{R}{e^{-k(t-c)} + 1},$

as desired.

##### Exercise 11

The equilibrium value of $$n$$ is given by $$-\dfrac{m}{k}$$, which is assumed to be the existing number of HIV viruses before the experiment.

##### Exercise 12

After administering the agent so that $$m=0$$, the number of viruses $$n$$ obeys the differential equation $$\dfrac{dn}{dt} = kn$$, giving exponential decay. The half-life $$T$$ is given by $$T = - \dfrac{1}{k} \log_e 2$$. Since $$T=0.24$$ days, we have

$0.24 = - \dfrac{1}{k} \log_e 2 \quad \iff \quad k = - \dfrac{1}{0.24} \log_e 2 \approx -2.88811.$
##### Exercise 13
1. Since $$-\dfrac{m}{k} \approx 100\,000$$ and $$k \approx -2.88811$$, we have $m \approx 100\,000 \times 2.88811 = 288\,811.$ That is, approximately $$288\ 811$$ viruses are produced per day per millilitre of extracellular fluid.
2. Multiplying $$m$$ by the $$15\ 000$$ millilitres of extracellular fluid gives a production rate of $$4.3 \times 10^9$$ viruses per day. That's a lot!
##### Exercise 14

Let $$T$$ be the temperature of the coffee (in $$^\circ$$C) after $$t$$ minutes. By Newton's law we have

$\dfrac{dT}{dt} = -k(T - 20) = -kT + 20k,$

so the general solution is $$T(t) = C e^{-kt} + 20$$, where $$C$$ is a constant. We have $$T(0) = 100$$, so $$100 = C + 20$$, and therefore $$C=80$$. From $$T(2) = 80$$, we have $$80 = 80 \, e^{-2k} + 20$$, and hence $$k = - \dfrac{1}{2} \, \log_e \dfrac{3}{4}$$. Thus

$T(t) = 80 \, e^{ \dfrac{1}{2} (\log_e \dfrac{3}{4}) \, t} + 20 = 80 \, \Bigl( \dfrac{3}{4} \Bigr)^{\tfrac{t}{2}} + 20.$

After five minutes, the temperature is

$T = 80 \, \Bigl( \dfrac{3}{4} \Bigr)^{\tfrac{5}{2}} + 20 \approx 58.97\ ^\circ\text{C}.$

The temperature is 40 $$^\circ$$C when

\begin{align*} 40 &= 80 \, \Bigl( \dfrac{3}{4} \Bigr)^{\tfrac{t}{2}} + 20 \\ \Bigl( \dfrac{3}{4} \Bigr)^{\tfrac{t}{2}} &= \dfrac{1}{4} \\ \dfrac{t}{2} \, \log_e \dfrac{3}{4} &= \log_e \dfrac{1}{4} \\ t &= \dfrac{2 \, \log_e \dfrac{1}{4}}{ \log_e \dfrac{3}{4}} \approx 9.64 \text{ minutes.} \end{align*}
##### Exercise 15

Let $$T$$ be the temperature of the metal (in $$^\circ$$C) after $$t$$ minutes. From Newton's law of cooling we have

$\dfrac{dT}{dt} = -k(T-20) = -kT + 20 k,$

which has general solution $$T(t) = Ce^{-kt} + 20$$. From $$T(6) = 80$$ and $$T(8) = 50$$ we obtain

$C e^{-6k} + 20 = 80 \qquad \text{and} \qquad C e^{-8k} + 20 = 50,$

giving $$Ce^{-6k} = 60$$ and $$Ce^{-8k} = 30$$. Dividing these two equations gives $$e^{2k} = 2$$, so that $$k = \dfrac{1}{2} \log_e 2$$. From $$Ce^{-6k} = 60$$ we then have

$60 = C e^{- \dfrac{6}{2} \log_e 2} = C \times 2^{-3} = \dfrac{C}{8},$

so that $$C = 480$$. We have thus found the temperature $$T(t)$$ to be

\begin{align*} T(t) &= 480 \, e^{- \dfrac{1}{2} (\log_e 2) \, t} + 20 \\ &= 480 \, \Bigl(\dfrac{1}{\sqrt 2}\Bigr)^t + 20, \end{align*}

and so the initial temperature was $$T(0) = 500$$ $$^\circ$$C.

Next page - References


text: (a) The applied voltage sweep. Finally, the unit of current is the ampere, which is defined as one coulomb of charge passing a given point in one second. In these devices photonic energy from sunlight is absorbed by electrons and converted into electrical energy. Nicholas Hylton of Imperial College London in the UK says: ‘What they have demonstrated is a new method of converting light into electrical energy. study 9. Generators can be powered by steam turbines heated by coal, natural gas, oil or a nuclear reactor. However, protons are mostly immobilized inside atomic nuclei, so the job of carrying charge from one place to another is handled by electrons. Lucky for us, one ampere is defined as one coulomb per second, so technically they're the same thing. Try refreshing the page, or contact customer support. In a direct current, abbreviated DC, the electrons move in one direction. When you hear the word 'current,' what does it make you think of? A generator produces a direct current through the conversion of mechanical energy into electrical energy. The NCVT3P automatically detects and indicates voltage (12-Volt to 1000-Volt AC) allowing broad application. Question #1 A copper wire has a diameter of 1.652 mm. A photoresistor is an input transducer that converts light energy into a change in resistance, resulting in a change in the current flowing in the circuit. At first the S.S. Columbia's electrical sockets were connected to the newly installed electric dynamo by a pair of cloth braided copper wire to a threaded hollow brass tubular brack… So now you’re ready to make sure the final piece of the power path—back to the … DC has important applications in energy storage and for powering many of our electronics. flashcard set{{course.flashcardSetCoun > 1 ? Diploma in Electrical Engineering (light current) or Clinical Engineering and/or knowledge on Healthcare sector with 3-5 years of experience in repair and… The high voltage is then stepped down as it is distributed through a network of substations until it gets to the transformer near your house, where it is finally stepped down to 110 V. (In the United States, wall sockets and lights run on 110 V at 60 Hz. A current could then be created by touching the amber to a body with less charge or to ground. This brings us to an important point. 1. the light produced by a current of electricity which in passing through a resisting medium heats it to incandescence or burns it. To learn more, visit our Earning Credit Page. Sometimes, over the course of installation, a wire might be jostled or damaged in such a way as to compromise its ability to transmit electricity to your new light. Visit PayScale to research electrical engineer salaries by city, experience, skill, employer and more. Don't they store electrical energy?' UW personnel need to be aware of the hazards electricity poses, such as shock, fire and explosion, and either eliminate or control those hazards. What magnitude current flows when the drift velocity is 0.700 mm/s? Millwright, Instrument Technician, Maintenance Technician and more on Indeed.com It can light your home, wash and dry your cloths, and even raise your garage door at the flip of the switch. We can think of the flow of electrons in a wire as the flow of water in a pipe, according to Michael Dubson, a professor of physics at the University of Colorado Bolder. Select a subject to preview related courses: So, why do we need DC at all? 8. Generators have rotating coils of wire that pass through magnetic fields as they turn. Anyone can earn As we mentioned earlier, batteries only create DC, and in turn, can only be charged with DC. Current is a quantity, meaning it is the same number regardless of the direction of the flow, without a positive or negative number. Batteries create a direct current because the electrons flow from the positive to the negative side. Determine whether the following statements are true or false. In 1.0 s, 3.8 x 10^16 electrons and 1.2 x 10^16 singly charges positive ions move in opposite directions through a sur, A copper wire has a circular cross section with a radius of 3.25 mm. This type of current is created by generators in a power plant because it works best for long distance power transmission. An electric light is a device that produces light by the flow of electric current.It is the most common form of artificial lighting and is essential to modern society, providing interior lighting for buildings and exterior light for evening and nighttime activities. Did you know… We have over 220 college If, Thus, the power consumed in an electrical circuit is said to one watt if one ampere current flows through the circuit when a potential difference of 1 volt is applied across it.The bigger unit of electrical power is the kilowatt (kW), it is usually used in the power system. If the wire carries a current of 3.10 A, find the drift speed of the electrons in the wire. Alternating current is produced by electric generators that operate on Faraday’s Law of Induction, by which a changing magnetic field can induce an electric current in a conductor. Units and Notation for Electrical Current . The marbles represent the electrons and the tube represents the wire. The Physics Classroom: Current Electricity, Most accurate map of our galaxy pinpoints 1.8 billion cosmic objects, Voyager mission finds a new type of electron burst at the edge of our solar system, Sprawling 8-mile-long 'canvas' of ice age beasts discovered hidden in Amazon rainforest, Lost islands beneath the North Sea survived a mega-tsunami 8,000 years ago, Black holes may not exist, but fuzzballs might, wild theory suggests. To do this, you need to make pigtails in the wires to split the electrical path. The phrase "current through a toaster" surely refers to the flow of electrons through the heating element and not the flow of slices of bread through the slots. To do this, print or copy this page on a blank paper and underline or round the answer. However, because the polarity of AC changes 60 times per second, the two sides of alternating current are designated as hot and ground. Conductors contain many free electrons that normally move around from atom to atom in random directions. An electric light is a device that produces visible light from electric current. Lamps usually have a base made of ceramic, metal, glass, or plastic, which secures the lamp in t… As the coils rotate, they open and close with respect to the magnetic field and produce an electric current that reverses direction every half turn. 01 March 2016, Electric current is electric charge in motion. Testing With a Multimeter. Christianlly has taught college physics and facilitated laboratory courses. The generators used in power plants to produce electricity for your home are designed to produce alternating current. Jim Lucas - Live Science Contributor In long-distance power transmission lines, the wires carry the hot side, and the ground side travels through the Earth to complete the circuit.Â, Since power equals voltage times amperage, you can send more power down the line at the same amperage by using higher voltage. When the connections are made properly, the circuit will “close” and current will flow through the circuit and light the lam… | 25 Create an account to start this course today. Highly sensitive ammeters can measure currents as small as 10.0 fA. © copyright 2003-2020 Study.com. Minimum Qualifications: N4 Applicable National N3 Certificate with four subjects or a Senior Certificate in an applicable technical discipline. In the past several decades, DC has become more important due to the widespread use of electronics. Stay up to date on the coronavirus outbreak by signing up to our newsletter today. As with all quantities defined as a … courses that prepare you to earn Sciences, Culinary Arts and Personal The solution to this problem was to reduce the voltage right outside the home before sending it inside. The wire is 3.8 m long and carries a current of 3.3 A. The electric field direction within a circuit is by definition the direction that positive test charges are pushed. While electrical energy is transferred through the conductor at nearly the speed of light, the individual electrons move at a much slower pace. Â© It bounces around nearly at random and only makes progress at a few millimeters per second. A wire carries a current of 4 A. The light is, in fact, an electrical signal. What Is the Rest Cure in The Yellow Wallpaper? It can take the form of a sudden discharge of static electricity, such as a lightning bolt or a spark between your finger and a ground light switch plate. There are two different types of current in widespread use today. The standard rate at which alternating current reverses direction is at 60 Hz. A simple electrical circuit consists of a power source, two conducting wires (one end of each being attached to each terminal of the cell), and a small lamp to which the free ends of the wires leading from the cell are attached. His "voltaic pile" consisted of a stack of alternating zinc and copper plates separated by layers of cloth soaked in salt water and produced a steady source of direct current (DC). Earn Transferable Credit & Get your Degree, Electrical Resistance: Definition, Unit & Variables, Electric Circuit Fundamentals: Components & Types, What Is Electricity? He has a master's degree in Physics and is pursuing his doctorate study. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons It is measured as the net rate of flow of electric charge past a region. It is interesting to note that the current is carried by only one wire and not two. Lamps are commonly called light bulbs; for example, the incandescent light bulb. AC is used primarily for long-distance power transmission, largely because of its ability to easily transform into other voltages. However, in circuit analysis, the direction of current is relevant. Probably the most common place to see something rated in amps is in the circuit breaker box in your house. Even household current (120 volts) can stop your heart. The adjective "electric" is implied by the context of the situation being described. 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He and others improved and refined his invention over the next few decades. More specifically, the electric current is the rate of charge flow past a given point in an electric circuit. Electrical light synonyms, Electrical light pronunciation, Electrical light translation, English dictionary definition of Electrical light. first two years of college and save thousands off your degree. I have both a black and a white unconnected wires, yet they both have 110 current … But while electrons are the charge carriers in metal wires, the charge carriers in other circuits can be positive charges, negative charges or both. The ET45-Voltage Tester is a simple, easy to use tester to check, verify or troubleshoot common residential electrical wiring in electrical outlets, light fixtures, doorbells and more. Shock. When we talk about electricity, the charged particles we're referring to are almost always electrons. Enrolling in a course lets you earn progress by passing quizzes and exams. The density of free electrons is 8.5\times 10^{28} m^{-3}\\ a) Find the magnitude of t, Working Scholars® Bringing Tuition-Free College to the Community, Summarize how electrons move in a current, Differentiate between alternating and direct current. However, when we apply a voltage to the conductor, all of the free electrons will move in the same direction, creating a current. The reason for this is that the diameter of the wires determines the amount of current, or amperage, they can carry without overheating and losing energy, but the voltage is limited only by how well the lines are insulated from the ground. Electrical transmission towers support wires that carry electricity from power plants to homes. The current goes through a complete forward-and-reverse cycle 60 times each second, or 60 hertz (Hz) (50 Hz in some countries). | {{course.flashcardSetCount}} - Definition & Formula, Potential Difference: Definition, Formula & Examples, Electric Potential Energy: Definition & Formula, Progressive Resistance Exercise: Definition & Types, Effects of Electric Currents on the Human Body, What is Capacitance? An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. The charge can be negatively charged electrons or positive charge carriers including protons, positive ions or holes. Electric current ran through platinum filament, heated it and filament started emitting light. This ocean going vessel installation employed use of a first form "1880 Wire Terminal Base" wood socket and carbon filament incandescent bulb. We get water out the other end almost instantaneously because the incoming water pushes the water that's already in the pipe toward the end. Find the expression for the steady state curre. Current is the flow of charged particles through a conducting medium, such as a wire. In fact, if you were to walk leisurely alongside a current carrying wire, you would be traveling more than 100 times faster than the electrons! That's a good association, because that's precisely the reason electrical current was given its name. In Europe, nearly everything runs on 230 V at 50 Hz. All switches do the same thing: Connect wires to allow electric current to flow or disconnect wires to stop electric current from flowing. The motion of these electrons is random, so there is no flow in any given direction. More commonly, though, when we speak of electric current, we mean the more controlled form of electricity from generators, batteries, solar cells or fuel cells.Â, Most electric charge is carried by the electrons and protons within an atom. False, because the correct statement is, The speed of electrons as they drift through a conducting wire is surprisingly slow. Circuits: A circuit is a path over which electric current can flow from and to an electric source. Free electrons are the electrons that are not attached to the nucleus of an atom and are free to move when external energy is applied. 4. Visit the CLEP Natural Sciences: Study Guide & Test Prep page to learn more. Well, first and foremost, it's important to realize that we currently don't have any way to store electrical energy. Not sure what college you want to attend yet? In technical usage, a replaceable component that produces light from electricity is called a lamp. The particles that carry charge through wires in a circuit are mobile electrons. But, isn't it a lot easier to say amps? The two sides of direct current are designated as positive and negative. Current is measured by the amount of electrical charge that moves past a given point, such as the circuit breaker, in the time period of one second. Platinum was used as a material because of its high melting point. In semiconductors they can be electrons or holes. However, the transmission speed of the signal, when electrons start being pushed out the other end of the wire after we flip the switch, is nearly the speed of light, which is about 300 million meters per second (186,000 miles per second). You can test out of the Electrical Question #2: My electrical wiring project involves a Fluorescent Light in the Basement. The voltage right outside the home before sending it inside to the … electrical Apprenticeship jobs now available energy. 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# Right Triangle problem

• December 15th 2012, 06:27 PM
mathematics123
Right Triangle problem
Hi, I've been working on this problem for a while now and can't seem to figure it out. I know the right answer but I'm having problems getting to it on my own.

Here's the problem: "Find the length of the shorter leg of a right triangle if the longer leg is 3cm more than the shorter leg and the hypotenuse is 6cm more than the shorter leg."

Here is the what I have so far, I know the answer is 9cm but I cannot figure out how they got to that.

Shorter leg = x, longer leg = x+3, hypotenuse = x+6. Using a2 + b2 = c2 I get x2 + (x+3)2 = (x+6)2

x2 + x2 + 9 = x2 + 36

2x2 + 9 = x2 + 36
-9 - 9
2x2 = x2 + 27
-x2 -x2

x2 = 27 ??????
• December 15th 2012, 06:46 PM
jakncoke
Re: Right Triangle problem
You are correct until the $x^2 + (x+3)^2 = (x+6)^2$ I think maybe you distributed wrong. $(x+6)^2 \not = x^2 + 6^2$

Here, $(x + 6)^2 = (x+6) * (x+6) = x*x + x*6 + 6*x + 6*6 = x^2 + 12x + 36$
$(x+3)^2 = (x+3)*(x+3) = x*x + x*3 + 3*x + 3*3 = x^2 + 6x + 9$
• December 15th 2012, 07:08 PM
mathematics123
Re: Right Triangle problem
Thank you very much!! I knew that too, I can't believe I did that.