Tools of trade
A report on the evaluation of the program was recently published by the Australian Government Department of Education, Employment and Workplace Relations. A copy of the report can be downloaded from here. The copy was obtained from http://www.deewr.gov.au/Skills/Resources/Publications/Pages/RegionalSkills.aspx on 21 December 2011 at 02:31 hrs.
Australian Doctor recently published a discussion article on the use of multidose vials for influenza vaccine. The discussion follows on from the publication in the Medical Journal of Australia of an article by Angela O’Brien-Malone and me regarding some of the medico-legal aspects of the use of the vials. The Australian Doctor article is particularly interesting because it presents a several competing points of view, with some practitioners arguing for the use of the vials, and others against.
A PDF copy of the article is available here.
Consider the following problem. You have made a connection to a machine to which you want to transfer some data. You know that if you are silent for some finite, but unknown time, then the machine will hang-up on you. To keep the line open, you need to ‘ping’, or speak to, the machine at the other end. How often do you need to speak?
An alternative way of thinking about the problem is in terms of the lease time for an IP address that has been assigned by a DHCP server. Unless you have been assigned a permanent IP address by your internet service provider (ISP), then it is possible that each time you connect to the network, the DHCP server will assign you a new IP address. Typically, however, short disconnections from the network followed by reconnection will not result in a change of the IP address. In particular, if you reconnect to the network within the so-called ‘lease time’ of the IP address, then the address will be unchanged. If you reconnect after the expiry of the lease then the IP address that you are assigned from the pool of available addresses is likely to be (but is not guaranteed to be) different from the previously assigned address. How do you discover the lease time that the DHCP server uses? It’s a question that clearly interests a great many users although their question is usually phrased as ‘How do I change my IP address?’, or ‘How do I force my ISP to give me a new IP address?’
Phrased that way, the answer is, of course, that you can’t force the ISP. What you can do is to disconnect from your ISP for a duration that exceeds the the DHCP lease time of the IP address. But that begs the original question.
I have not seen any literature related to the problem and I was surprised to learn, from my own analysis, just how time-expensive it is to pinpoint the lease time with any accuracy. I considered the following two, mutually exclusive possibilities: (a) I have a certain (as in sure) upper-bound for the lease-time, or (b) I have no idea of the lease time. If one were only reasonably sure, for example, that the lease-time is a couple of hours but were nonetheless absolutely certain that it could not exceed a year, then the situation would still meet the criterion for Scenario-a. I also make an important assumption that might, in fact, not be strictly true of the DHCP protocol. Specifically, I assume that by reconnecting to your ISP, the timer for the line will be reset so that the amount of lease-time that has expired on reconnection is zero.
The strategy that I examined relating to each of the two possibile scenarios was essentially one of binary search. However, it is a kind of binary search quite unlike those that are normally described for solving problems such as finding an entry in a database. What I used was an appropach that seems intuitively obvious although I have no proof of its optimality.
Imagine that you know for certain that the lease time is less than a week. You might then try disconnecting from your ISP for half a week and, if your IP number remains unchanged, try disconnecting for three-quarters of week. If that then proves to be successful in changing the IP address, you might try disconnecting for 5/8 of a week, and so forth. The difference between this strategy and a normal binary search on a random-access machine is that ‘time’ does not have a random-access feature! Even worse, it does not have a rewind feature as a tape drive would. To improve on your upper-bound for the lease time of three-quarters of a week, you cannot simply rewind by 1/8 of a week to test the effectiveness of a 5/8-week disconnection. Instead you have to restart from time zero.
For any given lease time that is less than the lease-time’s upper-bound, there is a specific total time—the discovery time— that it will take you to discover that that time is indeed the lease time. For example, assume that you know that 1024 time-units provides an upper bound on the lease time; that is, you know that the actual lease time is strictly less than 1024 time-units. Imagine also that the actual (but unknown) lease time is 73 time-units; in other words, 73 is the number that you are wanting to discover. The discovery process would proceed as an iteration of: (a) connection, (b) waiting, (c) checking whether a new IP number has been assigned, (d) increasing or decreasing the waiting time appropriately, and (e) disconnection. The waiting time (discovery) sequence would be: 512 units (half the upper bound), 256, 128, 64, 64 + 32 = 96, 64 + 16 = 80, 64 + 8 = 72, 64 + 8 + 4 = 76, 64 + 8 + 2 = 73, 64 + 8 + 1 = 73. The total time spent on the discovery process would then be 1431 time units … far greater than I would have guessed prior to doing the analysis.
I determined what the total discovery time would be for each (integer) lease time between 1 time-unit and 1023 time-units on the assumption that (Scenario 1) I knew that 1024 was an upper bound for the lease time, or (Scenario 2) I had no information regarding an upper bound.
The red line in the graph above shows the relationship between lease-time and discovery-time for Scenario 1. There are several things to note. First, the discovery time increases monotonically, though not strictly monotonically, with lease-time. For example, it takes as long (1577 time units) to pin-point a lease-time of 103 units as a lease-time of 104 units. Second, one can see that the red line does not intersect the origin, indicating that there is some fixed (time) cost for the discovery process, even if the lease-time proves to be very short. In fact, using the strategy that I’ve described it will cost 1023 time units to discover that the lease time is 1 time unit when the only available prior information is that the lease-time upper bound is 1024 and, in general, costs 2n–1 time-units to discover that the lease time is of duration 1 when the only known upper bound is 2n.
The violet line in the graph above shows the relationship between lease-time and discovery-time when there the upper-bound on the lease-time is unknown. The strategy that is assumed here is to begin with a disconnection of 1 time-unit and if that is unsuccessful in producing a change in IP address, disconnecting for 2 time-units, and then 4 time-units, and so forth, until a new IP address is obtained. Once that has been achieved, one has succeeded in obtaining a previously unknown upper-bound on the lease-time and one proceeds with a binary search following the strategy described for the scenario where the upper bound is known. As one can see from the graph, the times are short at the low end, but grow fast. In fact, the time-complexity for the case where there is no known upper-bound is O(n log n), as shown by the plot of the function n log2n (blue curve).
DHCP, lease time, binary search, IP address
Mark R. Diamond
Multiply together all the digits of a positive integer, n. Using the result, repeat the digit-multiplication process to obtain a new result. Continue until a single digit result is obtained. The number of steps, p, that it takes for n to be changed to the single digit end-point, is called the multiplicative persistence of n. (Sloane, 1973).
It is widely believed that there is no integer in base-10 that has a multiplicative persistence greater than 11. On several websites there is appears an assertion to the effect that any number with multiplicative persistence greater than 11 must have more than 3000 decimal digits—see, for example, this page at the University of Waterloo. However, I have been completely unable to trace the origin of the assertion. The Mathworld entry on multiplicative persistence refers to the work of Phil Carmody in 2001, and, more modestly, states that the lower bound on a number with persistence greater than 11 is 10233. That provides the background to what follows here.
I used Mathematica to extend the range of known results by testing the multiplicative persistence of all those numbers that can be represented as strings of up to one thousand 2s, one thousand 3s, and one thousand 7s, or as strings of up to one thousand 3s, one thousand 5s, and one thousand 7s. To see why these numbers are of particular interest, see the main paper.
My main result is the null result. None of the integers that I tested, other than those already known, had a multiplicative persistence greater than or equal to 11. Of course, if there is already a genuine basis for the assertion regarding a lower bound of 103000 on a persistence 12, then I have unnecessarily wasted a few hours of computer time!
Almost all of the 1,000,000,000 numbers that I tested (products of powers of 2, 3, and 7, and products of powers of 3, 5, and 7) had a persistence of 2. Put another way, most numbers represented by strings of up to one thousand 2s, one thousand 3s, and one thousand 7s, or by strings of up to one thousand 3s, one thousand 5s, and one thousand 7s, have persistence 3.
An ASCII file of the complete results (omitting those power products with persistence 2) can be downloaded from here. The file is surprisingly small. The rows represent numbers of the form 2j × 3k × 7l and of the form 3j × 5k × 7l. The exponent of 2 is in columns 1–4, column 5 is blank, the exponent of 3 is in columns 6–9, column 10 is blank, the exponent of 5 is in columns 11–14, column 15 is blank, the exponent of 7 is in columns 16–19, column 20 is blank, and the multiplicative persistence of the number formed as the product of the powers of 2, 3, 5 and 7 is shown in columns 21–24. You can also download a Mathematica notebook that produces the results.
[1] Sloane, N J. A. (1973). The persistence of a number. Journal of Recreational Mathematics 6, 97–98.
[2] Diamond, M. R., & Reidpath, D. D. (1998). A Counterexample to Conjectures by Sloane and Erdos Concerning the Persistence of Numbers, Journal of Recreational Mathematics 29, 89–92.
Contributors: Mark R. Diamond
In 2005, in a posting on Reality War Games, I suggested the possibility that a well equipped military might create an on-line game that recruited gamers from around the world to participate in the simulation of a planned, real-life, military offensive. Something of much the same kind has just been announced in a paper (doi:10.1038/nsmb.2119) published in the journal, Nature Structural and Molecular Biology.
Online players of the protein folding game Foldit were awarded points for producing progressively more accurate models of the protein known as M-PMV retroviral protease. Players scored points according to the energy state of the protein fold that they produced. The lower the energy state of the folded protein, the higher a player’s score. The Foldit players were able to generate models of sufficient quality that it was then possible to build on those models to determine the actual structure of the protein. So, the idea no longer seems so remote that the next massively parallel multi-player online game that you join will actually be a rehersal for World War III.
Khatib, F., Dimaio, F., Foldit Contenders Group, Foldit Void Crushers Group, Cooper, S., Kazmierczyk, M., Gilski, M., Krzywda, S., Zabranska, H., Pichova, I., Thompson, J., Popović, Z., Jaskolski, M., & Baker, D. (2011). Crystal structure of a monomeric retroviral protease solved by protein folding game players. Nature Structural and Molecular Biology, doi: 10.1038/nsmb.2119
Contributors: Mark R. Diamond
Falls in the elderly are a significant cause of mobidity.
Fortunately, researchers at the University of New South Wales have developed a device which might help to identify those at greatest risk of falling. The latest incarnation of the device [1], for which I have coined the name, ‘dodderimeter’, measures acceleration along each of the x, y and z space axes and then uses a combination of frequency-domain and time-domain analyses of the signals to predict the likelihood of a fall. It might even become as ubiquitous as the Holter monitor.
[1] Liu, Y., Redmond, S., Wang, N., Blumenkron, F., Narayanan, M., Lovell, N. (2011). Spectral Analysis of Accelerometry Signals from a Directed-Routine for Falls-Risk Estimation. IEEE Transactions on Biomedical Engineering, 99, 1. doi: 10.1109/TBME.2011.2151193. [PubMed]
Nelson Mandela, who is widely regarded as showing the virtue of forgiveness. Picture: wikipedia.org
Searching the web for information on the scale turns up thousands of entries, very few of which are related in any serious way to the scientific investigation of the scale. One of the few is the doctoral dissertation of Dennis P. O’Neil, PhD who did his doctoral research at the Department of Psychology and Neuroscience at Duke University. His dissertation reproduces the entire VIA Strengths scale. Working from that, together with the information published by the International Personality Item Pool and the descriptions in the book by Christopher Petersen and Martin Seligman [1], it is possible to determine the structure, and hence the scoring key.
The scale is conceptually divided into blocks of 24 questions. Each block has one question relating to each of the 24 character strengths and virtues. Importantly, it turns out that the order, within each block, in which the questions relate to a strength or virtue, is identical across blocks. The full scoring key is described in detail in a new publication [2] in the December 2010 issue of Psychological Reports written by Angela O’Brien-Malone, Rosalind Woodworth and me. The article is available at the D.O.I. link given in the reference.
Two versions of a spreadsheet for questionnaire scoring are available for download. A version in Open Document Spreadsheet format can be obtained here; and a version suitable for Microsoft Excel can be found here. I shall update and improve the spreadsheets as time permits.
[1] Petersen, C., & Seligman, M. (2004). Character Strengths and Virtues: A Handbook and Classification. Oxford: Oxford University Press.
[2] Diamond, M., O’Brien-Malone, A., & Woodworth, R. J. (2010). Scoring the VIA Survey of Character. Psychological Reports, 107(4), 833-836. DOI: 10.2466/02.07.09.PR0.107.6.833-836
A very (very) long arm.
The Board’s demand is almost certainly ultra vires, founded on a misunderstanding of the limited powers granted to the Board by the Health Practitioner Regulation National Law. In a paper that Angela O’Brien-Malone circulated on 3 December 2010 to university psychology departments around Australia, we argued that, were the Board able to effect its claim, it would subvert the explicit object and purpose of the Health Practitioner Regulation National Law, have a seriously adverse effect on the discipline of psychology in Australia, and and have a substantive negative effect on the national supply of health practitioners. Our paper, entitled Beyond Its Power and Against the National Interest, can be downloaded here.
Contributors: Mark R. Diamond
Doorway to the Senate Chamber at Parliament House, Canberra. Image: Wikipedia
The scope of the Committee’s enquiry is broad and they were willing to accept submissions on any matter related to the original discussion paper. Angela O’Brien-Malone and I made a submission to the Committee emphasising the important roles that evidence and evaluation play in open and transparent government. A copy of our submission is available here.
Contributors: Mark Diamond, Angela O’Brien-Malone
Does the janitor have access to your confidential computer files? Clip art licensed from DiscoverySchool.com
Our colleague, whom we will call Alice, is the recipient of a large grant to fund a research project examining psychological and genetic variables in a large population sample. As part of the research, data are collated from a range of genetic and psychological tests as well as on past sexual behaviour and current antibody status to several diseases.
Alice would like to store her data on a computer. Indeed, given the vast amount of information being collected, and the analyses that will ultimately be done, it is difficult to imagine that the data would be stored in any other way.
Alice has guaranteed to the granting body, to her volunteer subjects and to the university that the data will be held securely, in confidence, and that only those people who need to have access to the data will be able to access it. Such a guarantee is also implicit in various Australian laws. But Alice has a problem — geek power. Alice’s computer was purchased, using her grant funds, by her university’s IT department because the university requires that all IT purchases be made this way. The IT department has installed a popular operating system on the computer. The particular operating system allows one or more users of the computer to be given special privileges which will allow those users to change the usage rights (“permissions”) of other users, and to access and change any files stored on the computer. Users with such status are sometimes referred to as “administrators”, “super-users”, and “root password holders”. Readers should note that most Unix®, Linux®, and Windows XP® systems, as well as others, fit this description.
Alice’s now has a problem. The university IT department will neither (a) disclose to Alice the administrator password for her own machine, (b) surrender their own Administrator privileges on Alice’s machine, nor (c) give her the privileges associated with being an Administrator. The results of this denial are manifold, but all derive from the fact that Alice cannot be sure of the integrity, confidentiality or security of any of her data.
One method of securing data is to render it indecipherable to an unauthorized person by using suitable cryptographic software but Alice cannot install such software on her machine, because only an Administrator can install new software so that it functions correctly. Furthermore, even were Alice able to install the software, she would have no way of preventing or discovering whether the software had subsequently been subverted in a way that destroyed the security it purported to give. The covert alteration of software is hardly a far-fetched idea — many of the recent computer viruses that have plagued users do precisely this.
Lest anyone suggest that the situation Alice faces is that same as that faced by an office that gives access to a janitor, we should point out that this is not so. A paper based office can lock files in a drawer, a filing cabinet, or safe if need be. The janitor who cleans and tidies a bank does not have automatic access to the vault; and it is not the janitor who decides where the bank manager can and cannot go. Geek power is the exact reverse of janitorial power, though we would argue that they should be the same.
IT departments do not exist because they are a desirable feature of a research institution in and of themselves. Rather, they are a service department, and however sophisticated the service that they provide might become, they would have no raison d’etre but for the utility of that service to the productive components of the university.
Contributors: Daniel D. Reidpath, Mark R. Diamond