text:
# Extending Partial Representations of Circle Graphs

Steven Chaplick, Radoslav Fulek, Pavel Klavík

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

## Abstract

The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle graphs, where the input consists of a graph g and a partial representation $$\mathcal{r'}$$ giving some pre-drawn chords that represent an induced subgraph of g. The question is whether one can extend $$\mathcal{r'}$$ to a representation $$\mathcal{r}$$ of the entire g, i.e., whether one can draw the remaining chords into a partially pre-drawn representation.our main result is a polynomial-time algorithm for partial representation extension of circle graphs. To show this, we describe the structure of all representation a circle graph based on split decomposition. This can be of an independent interest.keywordsintersection graphinterval graphchordal graphprime graphcircle graphthese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Original language English Graph Drawing. GD 2013 S. Wismath, A. Wolff Springer, Cham 131-142 https://doi.org/10.1007/978-3-319-03841-4_12 Published - 2013 Yes

### Publication series

Series Lecture Notes in Computer Science 8242 0302-9743
• ### Extending partial representations of circle graphs

Chaplick, S., Fulek, R. & Klavík, P., Aug 2019, 91, 4, p. 365-394 30 p.

format: plain


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# TOST for equivalence test

Let's say that we are measuring the tracking position error of two controllers and we want to know if both controllers are similar (we already perform a "differences" test but we are requested to perform an equivalence test).

For example, if the mean $\mu$ (in meters) of one controller (12 samples) is 0.00344 (standard deviation $\sigma=0.0006481424$), the other (12 samples) is 0.00331 ($\sigma=0.000498$).

If $\varepsilon$ is the magnitude of region similarity. How do we define this $\varepsilon$?

I could consider $\varepsilon$ as $N \cdot \sigma$ as the region of similarity so, for example if $N=3$ then $\varepsilon=3\cdot(0.00064)=0.0019$ (using the data of the first controller).

Or, I could use something like $\varepsilon=\mu \cdot 0.05$, this takes 5% of the mean (of the first controller) which gives $\varepsilon = 0.0172$.

The question is, should we use the data for controller 1 or 2---as in the previous options---to define this parameter; or should do we consider other kind of difference measure between them in order to determine the epsilon parameter?.

Finally, why not use the epsilon as a 0.9 which may indicate that the 90% of the 'data (or the area of the distribution)' should be similiar?

I appreciate any advice in order to determine the epsilon.

Please see e.g. the function here:
https://github.com/cran/equivalence/blob/master/R/rtost.R

http://www.inside-r.org/packages/cran/equivalence/docs/rtost

Thanks

• This is a little hard to follow. You have a real statistical question here, so it is on topic, but note that asking about how to use R can be off topic. You may want to edit this to make your statistical question clearer & more accessible to people who don't use R. – gung - Reinstate Monica May 3 '16 at 20:22
• You might find the write up on the tost tag (especially the final paragraphs) a useful answer to your question. – Alexis May 11 '17 at 23:01

The null hypothesis is $H_0 : |\mu_1 - \mu_2| > \varepsilon$ (where $\mu_1$ and $\mu_2$ are means for controller 1 and 2). Thus $\varepsilon$ is the minimum value by which we will define how similar is the response (tracking error) of the controller.
Thus, I think that due to the equipment and the resolution of the mechanical device, $\varepsilon$=1mm is a good choice. But this value is defined subjectively, by experience or taken into account any advice on the particular field of interest.


text:
## Boundedness of Cesàro and Riesz means in variable dyadic Hardy spaces.(English)Zbl 1418.42037

Summary: We consider two types of maximal operators. We prove that, under some conditions, each maximal operator is bounded from the classical dyadic martingale Hardy space $$H_p$$ to the classical Lebesgue space $$L_p$$ and from the variable dyadic martingale Hardy space $$H_{p(\cdot)}$$ to the variable Lebesgue space $$L_{p(\cdot)}$$. Using this, we can prove the boundedness of the Cesàro and Riesz maximal operator from $$H_{p(\cdot)}$$ to $$L_{p(\cdot)}$$ and from the variable Hardy-Lorentz space $$H_{p(\cdot),q}$$ to the variable Lorentz space $$L_{p(\cdot),q}$$. As a consequence, we can prove theorems about almost everywhere and norm convergence.

### MSC:

 42B30 $$H^p$$-spaces 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 60G42 Martingales with discrete parameter 60G46 Martingales and classical analysis 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text:

### References:

 [1] H. Aoyama, Lebesgue spaces with variable exponent on a probability space, Hiroshima Math. J. 39 (2009), no. 2, 207-216. · Zbl 1190.46026 [2] D. L. Burkholder, Martingale transforms, Ann. Math. Statist. 37 (1966), 1494-1504. · Zbl 0306.60030 [3] D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. · Zbl 0301.60035 [4] D. L. Burkholder and R. F. Gundy, Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math. 124 (1970), 249-304. · Zbl 0223.60021 [5] L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157. · Zbl 0144.06402 [6] D. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis, Appl. Numer. Harmon. Anal., Birkhäuser/Springer, Heidelberg, 2013. · Zbl 1268.46002 [7] D. Cruz-Uribe, A. Fiorenza, J. M. Martell, and C. Pérez, The boundedness of classical operators on variable $$L^{p}$$ spaces, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 1, 239-264. · Zbl 1100.42012 [8] D. Cruz-Uribe, A. Fiorenza, and C. J. Neugebauer, The maximal function on variable $$L^{p}$$ spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), no. 1, 223-238. · Zbl 1037.42023 [9] D. Cruz-Uribe and L. D. Yang, Variable Hardy spaces, Indiana Univ. Math. J. 63 (2014), no. 2, 447-493. · Zbl 1311.42053 [10] L. Diening, Maximal function on generalized Lebesgue spaces $$L^{p(\cdot)}$$, Math. Inequal. Appl. 7 (2004) no. 2, 245-253. · Zbl 1071.42014 [11] L. Diening, P. Harjulehto, P. Hästö, and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents, Lecture Notes in Math. 2017, Springer, Heidelberg, 2011. · Zbl 1222.46002 [12] N. Fujii, A maximal inequality for $${H}^{1}$$-functions on a generalized Walsh-Paley group, Proc. Amer. Math. Soc. 77 (1979), no. 1, 111-116. · Zbl 0415.43014 [13] G. Gát, On $$(C,1)$$ summability of integrable functions with respect to the Walsh-Kaczmarz system, Studia Math. 130 (1998), no. 2, 135-148. · Zbl 0905.42016 [14] G. Gát, Pointwise convergence of the Fejér means of functions on unbounded Vilenkin groups, J. Approx. Theory 101 (1999), no. 1, 1-36. [15] G. Gát, Almost everywhere convergence of sequences of Cesàro and Riesz means of integrable functions with respect to the multidimensional Walsh system, Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 2, 311-322. · Zbl 1284.42084 [16] G. Gát and U. Goginava, A weak type inequality for the maximal operator of $$(C,\alpha)$$-means of Fourier series with respect to the Walsh-Kaczmarz system, Acta Math. Hungar. 125 (2009), nos. 1-2, 65-83. [17] U. Goginava, On some $$(H_{p,q},L_{p,q})$$-type maximal inequalities with respect to the Walsh-Paley system, Georgian Math. J. 7 (2000), no. 3, 475-488. · Zbl 0979.42014 [18] U. Goginava, Almost everywhere summability of multiple Walsh-Fourier series, J. Math. Anal. Appl. 287 (2003), no. 1, 90-100. · Zbl 1050.42018 [19] U. Goginava, Maximal operators of $$(C,\alpha)$$-means of cubic partial sums of d-dimensional Walsh-Fourier series, Anal. Math. 33 (2007), no. 4, 263-286. [20] B. Golubov, A. Efimov, and V. Skvortsov, Walsh Series and Transforms, Math. Appl. (Soviet Ser.) 64, Kluwer Academic, Dordrecht, 1991. [21] C. Herz, $$H_{p}$$-spaces of martingales, \(0
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
## anonymous one year ago please help asap.. water is being drained from a container which has the shape of an inverted right circular cone. the container has a radius of 6.00 inches at the top and a height of 10.0 inches. at the instant when the water in the container is 9.00 inches deep, the surface level is falling at a rate 1.2 inches per second. find the rate at which water is being drained from the container.

1. DanJS

use similar triangles to put the volume formula for the cone into a function of just height

2. DanJS

differentiate, and solve for dV/dt

3. anonymous

I have no idea what im doing on this problem or what goes where?

4. triciaal

|dw:1438102666151:dw|

5. DanJS

|dw:1438103043478:dw|

6. dan815

Do you know the formula for the volume of a cone as a function of its height V=f(h)

7. DanJS

solve for r, and put that into the volume formula so it is just in terms of h.

8. DanJS

Givens - h=9, dh/dt = 1.2

9. triciaal

and I saw this |dw:1438103242401:dw|

10. DanJS

$V = \frac{ 1 }{ 3 }\pi*r^2*h$ from similar triangles... $r = \frac{ 3 }{ 5 }h$ $V(h) = \frac{ 1 }{ 3 }\pi*(\frac{ 3 }{ 5 }h)^2*h$

11. DanJS

simplify that, then differentiate both sides w.r.t time, you are given dh/dt

12. DanJS

when h = 9

13. DanJS

$V = \frac{ 3 }{ 25 }\pi*h^3$

14. DanJS

chain rule $\frac{ dV }{ dt }=[\frac{ 3 }{ 25 }\pi]*3h^2*\frac{ dh }{ dt }$

15. DanJS

you are given h and dh/dt, find dV/dt


text:
# Yanxi Zhang

Ontology type: schema:Person

NAME

Yanxi

SURNAME

Zhang

### Publications in SciGraph latest 50 shown

• 2018-06-02 Studies of the resonance structure in D0→K∓π±π±π∓ decays in EUROPEAN PHYSICAL JOURNAL C
• 2018-03-29 A measurement of the CP asymmetry difference between Λc+ → pK−K+ and pπ−π+ decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-03-23 First measurement of the CP-violating phase ϕsdd¯ in Bs0 → (K+π−)(K−π+) decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-03-13 Search for the lepton-flavour violating decays B( s)0 → e±μ∓ in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-03-12 Measurement of CP asymmetry in Bs0 → Ds∓K± decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-03-08 Measurements of the branching fractions of Λc+ → pπ−π+, Λc+ → pK−K+, and Λc+ → pπ−K+ in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-02-16 Measurement of branching fractions of charmless four-body Λb0 and Ξb0 decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-01-29 Search for excited Bc+ states in JOURNAL OF HIGH ENERGY PHYSICS
• 2018-01-26 First observation of B+ → Ds+K+K− decays and a search for B+ → Ds+ϕ decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-12-20 Measurement of the Y(nS) polarizations in pp collisions at s=7 and 8 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-12-06 Measurement of the B± production cross-section in pp collisions at s=7 and 13 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-11-29 Updated search for long-lived particles decaying to jet pairs in EUROPEAN PHYSICAL JOURNAL C
• 2017-11-27 Measurement of CP violation in B0 → J/ψKS0 and B0 → ψ(2S)KS0 decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-11-23 Measurement of CP observables in B± → DK*± decays using two- and four-body D final states in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-11-08 Study of bb¯ correlations in high energy proton-proton collisions in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-11-08 Updated branching fraction measurements of B( s)0 → KS0h+h′ − decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-10-13 Improved limit on the branching fraction of the rare decay KS0→μ+μ- in EUROPEAN PHYSICAL JOURNAL C
• 2017-10-12 Study of prompt D0 meson production in pPb collisions at sNN=5 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-08-09 Resonances and CP violation in Bs0 and B¯s0→J/ψK+K− decays in the mass region above the ϕ(1020) in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-07-05 Observation of the decay Bs0 → ηcϕ and evidence for Bs0 → ηcπ+π− in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-06-21 Observation of the decay Λb0 → pK−μ+μ− and a search for CP violation in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-05-11 Erratum to: Measurement of forward J/ψ production cross-sections in pp collisions at s=13 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2017-04-12 New algorithms for identifying the flavour of B0 mesons using pions and protons in EUROPEAN PHYSICAL JOURNAL C
• 2016-09-02 Erratum to: Measurements of prompt charm production cross-sections in pp collisions at s=13 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-08-24 Measurement of the CKM angle γ using B0 → DK*0 with D → KS0π+π− decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-07-21 A precise measurement of the B0 meson oscillation frequency in EUROPEAN PHYSICAL JOURNAL C
• 2016-07-11 Production of associated Y and open charm hadrons in pp collisions at s=7 and 8 TeV via double parton scattering in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-06-21 Model-independent measurement of the CKM angle γ using B0 → DK∗0 decays with D → KS0π+π− and KS0K+K− in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-05-27 Measurement of the properties of the Ξb∗ 0 baryon in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-05-23 Observation of Λb0 → ψ(2S)pK− and Λb0 → J/ψπ+π−pK− decays and a measurement of the Λb0 baryon mass in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-05-13 Observations of Λb0 → ΛK+π− and Λb0 → ΛK+K− decays and searches for other Λb0 and Ξb0 decays to Λh+h′− final states in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-04-06 Model-independent measurement of mixing parameters in D0 → KS0π+π− decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-03-22 Measurements of prompt charm production cross-sections in pp collisions at s=13 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-03-18 Study of ψ(2S) production and cold nuclear matter effects in pPb collisions at sNN=5 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-03-07 Observation of the Bs0 → J/ψϕϕ decay in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-02-19 Study of DsJ(*) + mesons decaying to D∗ +KS0 and D*0K+ final states in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-02-16 Angular analysis of the B0 → K*0μ+μ− decay using 3 fb−1 of integrated luminosity in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-01-26 Measurement of forward W and Z boson production in pp collisions at s=8 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2016-01-04 First observation of the decay Bs0 → KS0K∗(892)0 at LHCb in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-12-15 Search for long-lived heavy charged particles using a ring imaging Cherenkov technique at LHCb in EUROPEAN PHYSICAL JOURNAL C
• 2015-11-27 Measurement of the forward-backward asymmetry in Z/γ∗ → μ+μ− decays and determination of the effective weak mixing angle in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-11-16 Forward production of Υ mesons in pp collisions at s=7 and 8 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-11-12 Measurement of CP violation parameters and polarisation fractions in Bs0→J/ψK¯∗0 decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-10-26 Measurement of forward J/ψ production cross-sections in pp collisions at s=13 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-10-08 Measurement of the Bs0 → ϕϕ branching fraction and search for the decay B0 → ϕϕ in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-10-08 Measurement of the time-integrated CP asymmetry in D0 → KS0KS0 decays in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-10-06 First measurement of the differential branching fraction and CP asymmetry of the B± → π±μ+μ− decay in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-09-25 Angular analysis and differential branching fraction of the decay Bs0 → ϕμ+μ− in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-09-14 Measurement of the exclusive Υ production cross-section in pp collisions at s=7 TeV and 8 TeV in JOURNAL OF HIGH ENERGY PHYSICS
• 2015-09-01 Search for the Λb0 → Λη ′ and Λb0 → Λη decays with the LHCb detector in JOURNAL OF HIGH ENERGY PHYSICS

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text:
# Prove that the number of bits in a positive $m$-bit integer $n$ is $n-\sum_{k=1}^{m-1} \lfloor n/2^k \rfloor$

The number of bits in a positive $m$-bit integer $n$ is $n-\sum_{k=1}^{m-1} \lfloor n/2^k \rfloor$.

The proof is just outlined, and I thought that it would be interesting to see what proofs could be found.

The source also states that the sum of the digits of a positive $m$-digit integer $n$ is $n-9\sum_{k=1}^{m-1} \lfloor n/10^k \rfloor$.

You can also write this as $$n - \sum_{k=1}^{\infty} \lfloor n/2^{k} \rfloor$$ because the terms for $k\ge m$ will be zero.

Now, we know that $$\sum_{k=1}^{\infty} n/2^k = n$$

How much of this do we lose by the floor operation?

Well, each set bit in $n$ will appear once in $\sum_{k=1}^\infty n/2^k$ at each position to the right of the binary point. Therefore, for each set bit, the sum of exact fractions will exceed the sum of floors by $0.111\ldots_2 = 1$.

Thus, when we subtract the sum of floors from $n$, we get the number of bits that have contributed to a deficit in the sum-of-floors.

Alternatively, we can see by induction that $$n - \sum_{k=1}^m \lfloor n/2^k\rfloor = \lfloor n/2^m \rfloor + \text{number of ones in the m lowest bits of n}$$

Whenever we subtract half of the $\lfloor n/2^m\rfloor$ that's left, the remainder will be another half of it, plus one if the bit we just shifted out past the binary point was a one.


text:
The Community for Technology Leaders

# Building a General Purpose Pedagogical Agent in a Web-Based Multimedia Clinical Simulation System for Medical Education

Yuh-Ming Cheng
Lih-Shyang Chen
Hui-Chung Huang
Sheng-Feng Weng
Yong-Guo Chen
Chyi-Her Lin

Pages: pp. 216-225

Abstract—In medical education, pedagogical agents are widely used by computer learning systems to simulate tutors and/or mimic tutoring interactions, as well as offering just-in-time and adaptive feedback. Although the theoretical aspect of the pedagogical agents has been well-documented in literature, relatively fewer efforts have been made on how a pedagogical agent should be implemented in a real multimedia computerized simulation learning environment. In this paper, we propose a general purpose pedagogical agent architecture and implement it in the multimedia medical simulation Web-based learning system called Health Information Network Teaching System (HINTS) to further facilitate students' learning and thereby make the HINTS a more helpful educational tool. Our focus is the design of the general purpose pedagogical architecture and its implementation in a multimedia computerized simulation learning environment. A preliminary students' performance evaluation result is also reported. We analyzed how to evaluate the students' performance and how the hints were given by the pedagogical agent. The system has been installed in the National Cheng Kung University Medical Center, Tainan, Taiwan for trial purposes. Some experiments have been conducted and the results have shown that the pedagogical agent indeed help the students in their learning process.

Index terms—e-Learning for medical education, pedagogical agent, computer-assisted learning, virtual peers, human-computer interaction, learning companions.

## Introduction

The problem-based learning (PBL) model [ 1], [ 2], [ 3] has its roots in the apprenticeship or learning-by-doing method. It emphasizes a "real-world" approach to learning: a student-centered process that is both constructive and collaborative and has been widely used in medical education [ 4], [ 5]. In practice, instructors must not only be experts in their specific knowledge domain, but also be specially trained as guides to entertain, motivate, and provide hints to their students. Therefore, although PBL is a very effective learning method in some cases, it is usually a very labor-intensive and time-consuming process for the instructors. Since the World Wide Web and multimedia technology have attracted a great deal of attention as a vehicle for delivering e-Learning, some medical schools and centers have incorporated multimedia computerized PBL into their clinical training curriculum to make PBL clinical education more efficient [ 7], [ 8]. The theoretical aspect of the multimedia computerized PBL has been studied extensively in [ 9], [ 10] which described it as online authentic learning. Therefore, we will not repeat the details of the theoretical foundation and concepts. However, current multimedia computerized PBL systems still have some drawbacks that may impair the efficiency of the students' learning. For instance, they do not really emulate the traditional PBL clinical education where the teachers can not only entertain, motivate, and provide hints for the students but also diagnose the students' misconceptions and resolve them. Therefore, although multimedia computerized PBL clinical education is more efficient than traditional methods in terms of the labor involved, it may be less effective. However, an agent-assisted, computer-based architecture may be employed as a promising medium for implementing a multimedia computerized PBL environment [ 11], [ 12], [ 13].

We have implemented an interactive multimedia computerized PBL clinical education system called Health Information Network Teaching System (HINTS) [ 14]. In the HINTS system, students: 1) are puzzled and challenged by the patient's problems; 2) try to interactively get more information needed from the system, such as questioning the patients and ordering various laboratory tests, as well as getting the associated multimedia information from the system, such as Computed Tomography (CT) images and the sound of the patient's heart beats; and 3) work on their ways in an attempt to diagnose and cure the patient's problem. In other words, the HINTS can simulate the step-by-step scenario of a real clinical case in a clinical setting without using 3D virtual reality techniques—the 3D visual effects. The details will be described later on. In other words, the HINTS simulates the clinical setting and enables students to work on the virtual patient to practice their diagnostic thinking processes and skills.

Although the theoretical aspect of the pedagogical agents has been well-documented in literature [ 15], [ 16], [ 17], [ 18], less efforts have been made on how a pedagogical agent should be implemented in a real computerized simulation learning environment. We propose and implement here a general purpose pedagogical agent architecture that inhabits the HINTS to further facilitate the students' learning and make the HINTS more effective and efficient for learning. In the domain of learning, "effectiveness" describes the learning outcomes (better grades) whereas "efficiency" is always associated with time (studying faster) [ 6]. Although our focus is the design of the pedagogical architecture and its implementation, a preliminary students' performance evaluation result is reported. The result shows that the agent can make the learning more efficient. However, a more in-depth evaluation of the effectiveness of the system is still needed in the future. We will follow the same definitions in this paper. In Section 2, we present how the HINTS really works in practice and briefly describes the theoretical backgrounds of the pedagogical agent adopted by HINTS. In Section 3, since the pedagogical agent has to evaluate the student's performance in order to decide how to provide timely hints to the students, we will discuss how the student performance is evaluated in the HINTS. We will also describe how the pedagogical agent works from the students' point of view to facilitate their learning. In Section 4, the architecture of the pedagogical agent and some implementation issues are discussed. In Section 5, we will report the results of our experiments with the system. Finally, we will offer our conclusions in the Section 6.

## Background

### 2.1 Description of HINTS

For explanation purposes, we will briefly give an example of how the HINTS works first. The main window of HINTS is shown in Fig. 1. The left panel of the window is the display of the teaching cases organized as a tree structure. The right panel of the window is the display of the sections of a given teaching case. The student is supposed to select a case first, then select one of the sections for browsing the selected case. The contents of the corresponding section will be displayed at the center portion of the window. The HINTS is basically a PBL system in which the student is challenged by the initial status of a patient and works his/her way toward a correct final diagnosis (by browsing through several sections) followed by the patient management until the patient is completely cured. In other words, HINTS is a simulation system that allows the users to diagnose and cure the virtual patient in the system. In the HINTS, the student is first challenged by the patient's chief complaints and reads the patient's basic information section where the patient's height, weight, age, and so on are described. Then, in the present illness section, the system will present to the student many questions to ask the patient. The student is supposed to select which questions are critical to ask in order to reach a correct diagnosis for this particular case and the corresponding answer to the selected question will be shown by the system. In the Physical Examination (PE) section, the system presents a patient's figure as shown in Fig. 2a. The student is supposed to first select one of the PE types: inspection, palpation, and auscultation followed by clicking on the part of the human body where the selected PE should be carried out. The system will respond with the associated multimedia information, such as the heart beat sound for the auscultation of a certain point on the patient's chest, and the picture of the skin for the inspection of a certain part of the patient's body. In the laboratory section, the student is supposed to enter a hypothesis—a disease name followed by clicking on various test items as shown in Fig. 2b to test against the hypothesis. The system will display the associated test results, such as CT images or ultrasound images. The same process can be repeated over and over again. In the course of this diagnosis procedure, the student can go back and forth among these sections until he or she gets enough information and feels comfortable to give a correct final diagnosis followed by the patient management section.

Figure    Fig. 1. The layout of the main HINTS windows.

Figure    Fig. 2. The presentation of the Physical examination and Laboratory test. (a) The section on Physical examination. (b) The section on Laboratory tests.

The HINTS is a multimedia simulation system that allows students to deal with the virtual patient in the system to emulate the situation when dealing with a real clinical case. However, whenever the students have difficulty dealing with the patient's problem, they are unable to get any guidance, encouragement, or other reference information from the system. In other words, the students are completely on their own when browsing a teaching case in HINTS.

### 2.2 The Theory the Pedagogical Agent Relies on and Related Literature Survey

From a theoretical point of view, between the potential competence level and the actual competence level a student has, there exists a zone of proximal development proposed by L.S. Vygotsky [ 19] to characterize scaffolding. This zone can be regarded as an area where scaffolds are needed to promote learning [ 20]. Scaffolds to be provided include vertical and horizontal levels as a temporary support in the zone of proximal development [ 21], [ 22]. Depending on the learning performance, the instructor gradually gives more control of the learning activities to the student. Scaffolding also encourages the use of language or discourse to promote reflection and higher order thinking [ 4]. We make use of an animated pedagogical agent [ 23], [ 24] to implement the scaffolding support in the HINTS learning environment.

There exists a wide spectrum of pedagogical agents according to their complexity and sophistication [ 25], [ 26]. For instance, there is "Adele" [ 10], [ 27], which makes use of rules to highlight specific aspects of a clinical case, suggests correct procedures for the students, provides hints and rationales for particular actions, refers to relevant background material, and provides a contextual assessment. Although Adele and similar systems make use of advanced artificial intelligence technology and are very sophisticated [ 28], [ 29], they are very "domain and application" specific. In other words, they may not be directly applicable to any other systems without modification. Their development also involves enormous input from the domain experts and the programmers. At the other extreme of the spectrum of pedagogical agents, a pedagogical agent may be much less sophisticated but more general and easier to develop. This paper is intended to develop such a general purpose pedagogical agent—applicable to any multimedia simulation learning environment—that will not only assist students to learn, but also can be easily implemented.

Although the theoretical aspect of the pedagogical agents has been well-documented in literature, relatively fewer efforts have been made on how a pedagogical agent should be implemented in a real multimedia computerized PBL simulation learning environment. This paper is an attempt to develop a pedagogical agent to deal with more general problems that students in a PBL simulation learning environment may encounter. We will focus on the implementation issues rather than the theoretical aspect of the pedagogical agent. The pedagogical agent has a life-like persona [ 30]—the Merlin developed by Microsoft [ 31] (Microsoft Corporation, 1998 as part of the MS Agent package)—that is able to interact with students on an ongoing basis. The Merlin can speak, via a text-to-speech engine or recorded audio. The Merlin enables the students to feel that HINTS is easy to work with and increases student motivation and attention. Since the Merlin is used as the representative of this computer-assisted system for instructions we proposed here, we use "the pedagogical agent" to refer to our system instead of "a computer-assisted system for instructions" or "a multimedia hint system."

Furthermore, since our medical center is committed to globalizing our education system, another reason to use the Merlin as the representative of the system is to have the Merlin to show up and speak to the learners in English using the Microsoft's text-to-speech mechanism such that the learners can have more listening comprehension practices as a by-product of our system. In other words, using the Merlin is not a "must" for our system; perhaps a pure text-based dialog system without Merlin works just as fine, or even better, in other environments.

### 2.3 The Basic System Architecture Block Diagram

Our HINTS PBL teaching case system is essentially a multimedia Computer-Aided Instruction (CAI) system. Generally speaking, a CAI system is composed of three major models: a knowledge model, a student model, and a tutor model [ 32]. We further describe the details of these models here as follows.

1. Knowledge model: This is a database that contains knowledge on specific topics which an expert in that particular domain would reasonably be expected to possess. In our system, the knowledge model contains data related to many different clinical cases which are to be learned.
2. Student model: This model provides a mechanism for assessing the state of the student's current knowledge of the information held within the knowledge base.
3. Tutor model: This model tries to play the role of a human tutor and is responsible for managing the overall learning environment.

The pedagogical agent is put into the picture of the CAI system as shown in Fig. 3, in addition to these three models for facilitating the learning environment. We will further elaborate the system architecture in Section 4.

Figure    Fig. 3. The pedagogical agent in the CAI system.

## The Functionality of the Pedagogical Agent

Since the agent should be able to provide appropriate hints to the students at the appropriate time, it must analyze the student's performance when practicing a teaching case, build a database of past activities, and provide students with hints to answer the questions. As described previously, rather than giving students implicit hints that may require specific domain knowledge channeled through AI technology, the system provides students with explicit hints to enable them to answer the questions directly. Although these kinds of hints are less attractive and less inspiring from the student's point of view, they are easier to implement and apply to all sorts of teaching cases since specific domain knowledge is not required.

### 3.1 The Performance Evaluation

Since the pedagogical agent has to evaluate the student's performance in order to decide what to do, the way the student performance is evaluated in the HINTS system is discussed here.

A student's overall performance in a teaching case is the weighted sum of the performances of all the sections in the case. In general, each section has many items for the students to select and there are some "suggested items" that are specified by the domain expert and are supposed to be selected by the students. The reason the term "suggested items" is used as opposed to the "correct items" is that for a given case in a clinical setting, there are usually several different approaches for a clinician to diagnose a patient's disease and it is virtually impossible to clearly define what is correct and what is not correct. However, for the sake of the argument, one can think of the suggested items as the correct items that the experts suggest the students to select. In the HINTS, there are two statistics derived from the students' answers that are significant and should be shown to the instructors for their reference: one is the "suggested hit rate"; the other is the "selected hit rate," and are defined as follows: 1) The "suggested hit rate" is the percentage of suggested items selected by the student. This indicates whether the student has indeed learned what he/she is supposed to. In other words, it reveals how "effectively" all the items are selected by the student. For instance, in the laboratory test section, there are more than 4,000 items the student can select for the diagnosis. There may be only 10 suggested items. If five items in these 10 suggested items are selected by the student, the student's suggested hit rate is 50 percent. 2) The "selected hit rate" is the percentage of suggested items out of all the items selected by the student. This reveals how "efficiently" the items are selected by the student. For instance, suppose that there are only 10 suggested items in the laboratory test section of a teaching case and all of them are selected by a student. The student's suggested hit rate is 100 percent. However, in total, the student selected 100 laboratory items (which included the 10 suggested items) in the course of diagnosis. His/Her selected hit rate is only 10 percent. Although the student eventually got the right diagnosis, this may imply that he/she does not efficiently make use of his/her knowledge. In other words, the student, in fact, did not do a good job in this case although he/she did get whatever needs to be selected and the correct final diagnosis of the case. Therefore, his/her performance should not be the same as one who selected only 15 items and also got all the 10 suggested items. Generally speaking, both suggested and selected hit rates are useful indications as to whether the students have really mastered what they are supposed to learn. Therefore, in our implementation, these two factors constitute the overall performance of each section with the default weights 0.6 and 0.4 for the suggested and selected hit rates, respectively, for the laboratory section, and 0.8 and 0.2 for the interrogation inquiry and physical examination sections. This is because for the interrogation inquiry and physical examination sections, the extra questions asked of the patient and physical examinations do not really cost anything other than the physician's time while the extra laboratory examinations do cost money or even the patient's health. Therefore, the "selected hit rate" should be less important and be counted for less.

### 3.2 Horizontal Scaffolding

As stated previously, the scaffolds to be provided include vertical and horizontal levels. Since a teaching case in the HINTS is partitioned into several sections, the horizontal scaffold can be built up on a section-to-section basis. In other words, in each section, the system tries to build up the scaffold for each section independent of other sections (without considering how the scaffolds in other sections are done). As opposed to the horizontal scaffolding, the vertical scaffolding, which will be discussed in the next section in detail, considers how to build up the scaffolds to support students' learning over several sections.

Whenever the student finishes up a section, the agent will check the student's answers against the correct ones. Whatever is missed by the student will be used as hints for the student. Since each section in the HINTS is a multiple-selection type of question, it is very easy for the system to provide these hints to the student.

However, in practice, students may want to try out the teaching case on their own to some extent (without any hints). For instance, the student may say: "Please leave me alone unless my performance is less than 60 percent (in terms of the performance described previously)." In other words, the system should enable the students to set the level for horizontal scaffolding hints so that he/she can adjust it based on his/her own subjective confidence instead of the objective observation of his/her performance by the system. This arrangement will make the system more adaptive to each individual and become more interesting and challenging for students to use [ 33], [ 34].

Therefore, at the beginning of a teaching case, the hints level is set to a certain level such as 60 percent. Since the student's performance is evaluated in such a manner as described above, roughly speaking this means that if the student does not select 40 percent of the correct answers, the remaining 60 percent of the correct answers may be revealed to the student at the end of each section. If the hints level is set to zero, the agent will never show up. If the hints level is set to 100 percent, the agent will always show up and provide hints. The agent will tell the student what percentage of the correct answers have been selected by the student—say "30 percent"—and ask the student whether or not they wish to see the hints. There are two possible results:

1. The student may be surprised at the 30 percent of his/her correct answers in this example, realizing that he/she is not doing a good job in the current section, and would like to go back to this section to re-examine the questions more carefully without further hints. In this case, the student would select "No" and go back to the section to reselect more items. In our experiments, surprisingly, the students thought that it was a very useful aid for them to practice the case. It is particularly useful for a novice since it gives the student a rough feeling about how well he/she is doing. When the student finishes up the second trial for the section, the system will re-evaluate his/her performance again and the same process will repeat itself.

At this point, the student is strongly encouraged to read the answers one at a time so that he/she has a chance to think about what the answers imply. Hopefully, after a few answers are shown, the student can realize what is going on, then shut down the agent, and go back to the section to continue to work on the case on his/her own.

Figure    Fig. 4. The pedagogical agent interacts with the student for the hints. (a) Ask the student whether he/she would like to get some hints. (b) Reveal hints. (c) The resources of the item are displayed after the hyperlink "View" is clicked in (b). (d) The rationale of the item is displayed after the hyperlink "The rationale of this item provided by the author" in (c) is clicked.

### 3.3 Vertical Scaffolding

As for the vertical scaffolding, it is used to help the student in terms of his/her overall performance instead of that of each individual section (done by the horizontal scaffolding). In the context of the multimedia computerized PBL, if the student does not really catch onto the important point at the beginning of a case study, he/she may go astray and go toward a completely wrong direction. In such a situation, the teaching case may become a "big jungle," and the student is simply making random guesses and struggling to get out of it instead of learning anything meaningful, and getting very frustrated in the process.

In order to analyze this situation, we first define two different learning models in the context of PBL learning models: straight model and regression model. In the straight model, the system will allow the student to work his/her way toward a solution to the problem regardless of whether he/she is on the right track or not. This model is, in general, reasonable for a short exercise. However, it may not be suitable for a long learning task. For instance, if the student gives a wrong diagnosis, the rest of the patient management procedure might be detoured to a completely different clinical pathway which may be perfectly correct for the given diagnosis (which is wrong). In general, in the lengthy problem solving process of a PBL environment, a small error upfront may affect all subsequent results and result in a large problem at the end. In this case, it is difficult to evaluate how much knowledge the student does correctly understand. One way to fix this problem is to use the "regression" model.

In the regression model (within the context of the medical teaching case system), the whole diagnosis and treatment procedure of a teaching case that the system emulates is divided into several stages. The system will establish a checkpoint at the end of each stage. At each checkpoint, irrespective of whether the student is on the right track or not, the agent will always appear and ask the student whether or not he/she would like to see the summary of the current status of the case at that point in time. The summary outlines the situation and the status of the correct clinical pathway at that particular point in time. If the student selects "Yes," the system will show him/her the summary. In other words, the student will be informed of what he/she should know about the case at this particular point in time and, in effect, "restart" the case from this correct point on. This arrangement enables the system to correct the student's thinking process at the end of each stage of the clinical pathway. Therefore, this mode is more suitable for a novice.

In our implementation, we use the regression model since each case study in our system is a lengthy problem-based learning process. The regression model will make the learning more effective and prevent the students from getting frustrated. Every teaching case in the system was divided into three stages, each of which consists of several sections of the case. They are: 1) the present illness stage includes basic patient information, chief complaints, and present illness sections. At the end of this stage, once the student has completed his/her patient interview, he/she is supposed to fully understand what the patient's current conditions are in order to make the rest of the learning procedure more meaningful. The HINTS system will summarize what the present illness is so that the student can conduct further examinations based on the patient's current situation. Otherwise, if the student does not fully understand the present illness, he/she may consider the case in a completely different direction and continue on the wrong track. 2) The diagnosis stage includes past history, family history, physical examination, laboratory test, and diagnosis sections. At the end of this stage, the student is supposed to have reached a correct diagnosis in order to make patient management in the following section more meaningful. Therefore, if the student does not get a correct diagnosis, the system will either provide him/her with the correct diagnosis or ask him/her to try again until he/she gets the correct one. This arrangement will make the next stage—the patient management, more meaningful in case that the student did not get the correct one. 3) The patient management stage. At the end of this stage, the system will give the student a summary of how he/she performed in each individual section as well as his/her overall performance, costs incurred to date, how much time was spent, and so on.

However, as the student becomes more sophisticated in the clinical pathway and can answer at least half of the questions correctly, the summary will make the case less challenging and less interesting. Therefore, the pedagogical strategy is to start with the regression model containing many stages, then progressively reduce the number of stages in the regression model, and eventually switch to the straight model.

Furthermore, at each checkpoint, the agent can also evaluate how well the student has done in the associated stage by taking the average of the overall performance of all the sections in the stage. If the student's performance is outside the range of the scaffold level of $+/{-}15$ percentage points, the agent will suggest to the student that he/she should lower/raise the scaffold level to match his/her own performance.

## The Architecture and the Pedagogy Strategy of the HINTS System

As stated in the background section, the basic architecture block diagram and the pedagogy strategy of the agent are shown in Fig. 5. The horizontal and vertical scaffolding engines described in the previous section and the horizontal scaffolding database form the pedagogy strategy of the agent in the system. The agent architecture is carefully designed in such a way that it is independent of the HINTS so that HINTS can run with or without the agent. This is an important feature, as it also allows HINTS to be used for testing purposes (without the pedagogical agent). In other words, the agent is simply an additional educational companion that may or may not show up when HINTS is used.

Figure    Fig. 5. The HINTS architecture.

The system works in the following fashion:

1. The instructor module arranges the teaching cases to be learned.
2. The student can set the hints level or simply ignore it (in this case, the default value is used).
3. Based on the teaching case selected by the student, the instructor module references the student profile database and the knowledge model database, then uses a rule-based engine to present the teaching case to the student in the PBL fashion described earlier.
4. The student's answers are stored in a log database.
5. At the end of each section, the agent evaluates the student's answers against the suggested items in the knowledge model, compares the evaluation result with the hints level, and offers hints to the student accordingly through the horizontal scaffolding engine, storing them in the student learning database for future usage.
6. The horizontal scaffolding engine also records the results in the horizontal scaffolding database.
7. At each checkpoint, the vertical scaffolding engine references the horizontal scaffolding database and the knowledge model, and provides the vertical scaffolding to the student. Although the architecture of the agent is not simple, there is no huge amount of computation involved. As a result, the students do not really feel any delay while interacting with the system with the existence of the pedagogical agent.

## Initial Field Tests

HINTS has been up and running in the medical center of National Cheng Kung University for three years. Currently, there are 50 teaching cases in the system for the clinical practice training of the medical school students. The system was implemented on Microsoft Internet Information Server version 6.0 (IIS), and SQL database technologies. Students can simply use the World Wide Web (WWW) browser to login to the HINTS and browse the teaching cases at the computer center in the medical school or at home, if a wide-bandwidth Internet connection is available. Before the pedagogical agent was installed in the system, more than 200 medical school students from the fifth to seventh grades (equivalent to first to third grade students in a medical school in the American medical education system) have had experience in using the system.

Since the main purpose of this study is to investigate how a pedagogical agent should be implemented in a real computerized simulation learning environment, such as the HINTS, we need to find out whether the designed pedagogical agent is really effective especially for the training of the thinking process. Therefore, we hypothesize that the pedagogical agent can improve the efficiency of the students' learning. The following is the description of our field test method and its results.

### 5.1 Participants of the Experiments

The participants of the experiments were 80 students from the fifth and sixth grades in our medical school. These students have been using the HINTS for many times over several months and have had no problems in using the HINTS [ 35]. They were randomly partitioned into the control group A and the experimental group B with 40 students in each group. In the HINTS system, the system administrator could turn on or off the pedagogical agent. Group A used the system without the agent while group B used it with the agent. The students in both groups did not know that only half of the students would receive additional hints.

### 5.2 Experimental Design

There are six teaching cases used in the experiments: two simple ones, two mediocre ones, and two difficult ones. The students browsed through these cases sequentially. We measured how many times the students had tried before they got at least 60 percent of the correct answers. The focus of this experiment is to see whether the hints provided by the pedagogical agent can improve the efficiency of the students' learning. Since this experiment includes only two groups: the control group and experimental group, we made use of the t-test for the computation of the result of the experiment that is shown in Section 5.4.1.

Furthermore, right after the students of group B finished their browsing of the six teaching cases, some survey data were collected by asking them to fill in an online questionnaire. The questions in the questionnaire are designed simply to see whether our design and implementation of the pedagogical agent is effective or not. In order to obtain a reliable survey result, expert validity was adopted in this study. The questions in the questionnaire were reviewed, revised, and eventually approved by six experts including three medical education experts, one statistics expert, and two information science experts.

### 5.3 Procedures

In order to ensure the correctness of the evaluation of the agent system, we have the following procedure. Prior to the evaluation, we demonstrated the HINTS operation including the mechanism of the agent to all the students and made sure the students could use HINTS without difficulty. At the beginning (the first classroom lecture for a case), the instructor gave the students some background knowledge about the particular case in the classroom. Then, the students browsed through the case including reading through the basic information and chief complaint sections in HINTS, specifying which part of the patient's body should be examined, what questions should be asked, and what laboratory tests should be ordered to get more information and insight into the patient's status from HINTS, and finally gave their final diagnoses for the exercise. All the students' answers were logged by the system for further analysis. Furthermore, as described before, some survey data were collected by asking them to fill in an online questionnaire right after the students of the groups finished browsing the six teaching cases.

In the second classroom lecture, the instructor and students discussed the results computed by HINTS and their experience with the teaching case.

### 5.4 Results

#### 5.4.1 Analysis of the t-Test

As described before, we measured how many times the students had tried before they got at least the 60 percent of the correct answers. The 60 percent score in group B does not include those answers provided by the agent. By using an Independent Samples t-test procedure, where ${\rm P}<0.05$ is considered to be significant, the average, standard deviation, and P-value are computed by the software package SPSS 12.0 and are listed in Table 1. In Table 1, it can be found that there are significant differences between groups A and B in all the cases $({\rm P}<0.05)$ . Apparently, the pedagogical agent plays an important role in their learning activities.

Table 1. The Results of the t-Test

#### 5.4.2 Analysis of Questionnaire

Table 2 uses a five-point Likert Scale and summarizes the students' responses to a series of questions posed by the current researchers. The students have also made a variety of comments after using the various teaching cases in the system. The principal results of this study may be summarized as follows (some of the results are provided by the instructors):

Table 2. Summary of Results from the Student Responses to a Series of Questions

1. As expected, the students all felt that the teaching cases with the pedagogical agent were much more helpful than those without the agent, especially for their thinking process. The results of the t-test also demonstrated the significance of the pedagogical agent.
2. All the students agreed that the system significantly improves their skills in dealing with actual clinical cases as shown in Table 2. The standard deviation values are very small. This implies that there is a consensus regarding the students' responses to the agent. We have also interviewed the students who have experiences with the HINTS with and without the pedagogical agent. They expressed that without the agent, when they do not have any idea on how to work on a case and they do not get any hints from the system, they simply do not know what to do other than making random guesses. In other words, they are completely on their own. With the agent, they can get some hints from the system. Furthermore, they can control how many hints they want to get from the agent. For instance, for any given clinical case, there are more than 2,600 possible laboratory test items for them to select. When they call on the agent, the agent can tell them which items should be selected little by little under their control. The hints do provide some clues and thinking directions for them to think about the case. Of course, sometimes with the hints, they are still confused. In any case, they are certainly better off with the agent.
3. The instructors feel that although the agent does not handle the students' problems intelligently in the sense that it cannot answer individual or specific problems, it does save the instructors a lot of time in working with the students throughout the teaching cases. They believe that the agent can serve students as a teaching assistant in their learning process.
4. From the system logs of the students' learning, the average times the students in groups A and B spent on a case are 51 and 37 minutes, respectively. In the student interviews, the students had expressed that they would like to be able to spend about 40 minutes on average on a case. Apparently, the agent indeed can make the learning more efficient and enable students to finish a case within 40 minutes.

## Conclusions

In this paper, we describe how our multimedia pedagogical agent was designed and implemented in the simulation of the medical teaching case learning environment, such as HINTS. Although our focus is the design of the pedagogical architecture and its implementation, a preliminary students' performance evaluation result is reported. A more in-depth evaluation of the effectiveness of the system is still needed in the future. The system has been deployed and tested by the students. Based on our experiences, our conclusions are:

1. Although the agent does not really intelligently detect a student's misconceptions or provide them with customized hints, it can at least save the human instructors some time and trouble going through a teaching case with the students and providing constant guidance to the students.
2. Although a human instructor can certainly do a better job than the agent in terms of tutoring, the presence of a human instructor may put the students under some pressure. Using the agent, the students feel they can work through the teaching cases in a more relaxed and stress-free environment. In particular, the agent is indeed extremely useful for novices. This is because although they have enough basic medical knowledge for the clinical cases, they do not have enough experience in applying their knowledge to the cases. The agent is able to provide them with useful hints.
3. The teaching case needs to be developed by the domain experts without the development of the pedagogical agent in mind. However, the agent inhabiting the system can be easily developed without the "explicit involvement" of a domain expert since the agent simply reveals the items which need to be selected with their rationale and related resources little by little under the students' control. Of course, the hints information is originally provided by the domain experts as the answers to the problems under study instead of the hints to the students. In other words, the hints are provided by the domain experts implicitly and the system makes use of the agent mechanism to provide the hints information at the right time to the students when they need the hints.
4. Despite the preliminary success of the agent development, ultimately there is still a need to make the agent more intelligent in order to cope with the various and inevitable problems that students encounter during their learning process.
5. As discussed in Section 5.2, the pedagogical agent should not provide too many hints to the students without costing the students anything. Otherwise, the students will take the hints for granted without really thinking about how to solve the problems on their own and always try to rely on the hints instead of working with the system on their own.
6. Although the theoretical aspect of the pedagogical agents has been well-documented in literature, less efforts have been made on how a pedagogical agent should be implemented in a real computerized simulation learning environment. Here, we propose and implement a pedagogical agent architecture that inhabits the HINTS to further facilitate the students' learning and make the HINTS more efficient for learning. Our focus is the design of the pedagogical architecture and its implementation. A more in-depth evaluation of the effectiveness of the system is still needed in the future.

## Acknowledgments

The authors wish to thank the medical students of National Cheng Kung University for participating in the evaluation process and providing feedback of the HINTS. This project was supported by a grant from the National Science Council, Executive Yuan ROC (96-2516-S-366-001).

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• 14. Y.-M. Cheng, L.-S. Chen, C.-H. Lin, and J.-H. Chen, "A Multimedia Teaching Case Learning System for Medical Education," Proc. World Conf. Educational Multimedia, Hypermedia and Telecomm. (ED-MEDIA '03), pp. 369-372, 2003.
• 15. C.-Y. Choua, T.-W. Chan, and C.-J. Lin, "Redefining the Learning Companion: The Past, Present, and Future of Educational Agents," Computers & Education, vol. 40, pp. 255-269, 2003.
• 16. J.C. Lester, S.G. Towns, and P.J. FitzGerald, "Achieving Affective Impact: Visual Emotive Communication in LifeLike Pedagogical Agents," Int'l J. Artificial Intelligence in Education, vol. 10, pp. 278-291, 1999.
• 17. M.F. Canut, G. Gouarderes, and E. Sanchis, "The Systemion: A New Agent Model to Design Intelligent Tutoring System," Proc. Ninth Int'l Conf. Artificial Intelligence in Education (AI-ED '99), pp. 54-63, 1999.
• 18. Y. Kim, and A. Baylor, "A Social-Cognitive Framework for Pedagogical Agents as Learning Companions," Educational Technology Research & Development, vol. 54, no. 6, pp. 569-596, 2006.
• 19. L.S. Vygotsky, Mind in Society: The Development of Higher Psychological Processes. Harvard Univ. Press, 1978.
• 20. T. Sharpe, "Unpacking' Scaffolding: Identifying Discourse and Multimodal Strategies that Support Learning," Language and Education, vol. 20, no. 3, pp. 211-231, 2006.
• 21. A.H. Dyson, "Weaving Possibilities: Rethinking Metaphors for Early Literacy Development," The Reading Teacher, vol. 44, pp. 202-213, 1990.
• 22. A.S. Palincsar, "The Role of Dialogue in Providing Scaffolded Instruction," Educational Psychologist, vol. 21, nos. 1/2, pp. 73-98, 1986.
• 23. J.W. Lewis, and S. Erin, "Animated Pedagogical Agents: An Opportunity to Be Grasped?" J. Educational Multimedia and Hypermedia, vol. 11, no. 3, pp. 267-286, 2002.
• 24. H. Lieberman, and T. Selker, "Agents for the User Interface," Handbook of Agent Technology, J. Bradshaw, ed., MIT Press, 2003.
• 25. M. Ueno, "Animated Pedagogical Agent Based on Decision Tree for e-Learning," Proc. Fifth IEEE Int'l Conf. Advanced Learning Technologies, pp. 188-192, 2005.
• 26. J. Holmes, "Designing Agents to Support Learning by Explaining," Computers & Education, vol. 48, pp. 523-547, 2007.
• 27. W.L. Johnson, "Pedagogical Agent Research at CARTE," AI Magazine, vol. 22, no. 4, pp. 85-94, 2001.
• 28. R. Crowley, and O. Medvedeva, "An Intelligent Tutoring System for Visual Classification Problem Solving," Artificial Intelligence in Medicine, vol. 36, pp. 85-117, 2006.
• 29. R. Crowley, E. Legowski, O. Medvedeva, E. Tseytlin, E. Roh, and D. Jukic, "An ITS for Medical Classification Problem-Solving: Effects of Tutoring and Representations," Proc. 12th Int'l Conf. Artificial Intelligence in Education (AIED '05), C.-K. Looi, G. McCalla, B. Bredeweg, and J. Breuker, eds., pp. 192-199, IOS Press, 2005.
• 30. E. André, T. Rist, and J. Müller, "WebPersona: A Life-Like Presentation Agent for the World-Wide Web," Knowledge-Based Systems, vol. 11, pp. 25-36, 1998.
• 31. Microsoft Corporation, Microsoft Agent Software Development Kit with Cdrom. Microsoft Press, 1998.
• 32. W.J. Clancey, Knowledge-Based Tutoring: The GUIDON Program. The MIT Press, 1987.
• 33. P. Brusilovsky, and E. Millán, User Models for Adaptive Hypermedia and Adaptive Educational Systems. Springer, 2007.
• 34. P. Brusilovsky, and C. Peylo, "Adaptive and Intelligent Web-Based Educational Systems," Int'l J. Artificial Intelligence in Education, vol. 13, pp. 156-169, 2003.
• 35. L.-S. Chen, Y.-M. Cheng, S.-F. Wen, Y.-G. Chen, and C.-H. Lin, "Applications of a Time Sequence Mechanism in the Simulation Cases of a Web-Based Medical PBL System," J. Educational Technology & Soc., vol. 12, no. 1, pp. 149-161, 2009.

## About the Authors

Yuh-Ming Cheng received the PhD degree in electrical engineering from the National Cheng Kung University, Taiwan. Since February 2005, he has been an associate professor in computer science and information engineering at Shu Te University, Taiwan. His research interests include software engineering, multimedia Web application system, e-Learning, game-based learning, and sensor network applications. He is a reviewer for international journals such as the Journal of Educational Technology & Society and Computers & Education.
Lih-Shyang Chen received the PhD degree in computer science from the University of Pennsylvania in 1987. Since August 1990, he has been with the Department of Electrical Engineering at National Cheng Kung University, where he is currently a professor. His research interests include computer graphics, image processing, pattern recognition, network systems, multimedia Web application systems, and e-Learning systems.
Hui-Chung Huang is a student at the Institute of Computer and Communication Engineering, National Cheng Kung University, Taiwan. His main research focuses on the multimedia system and Web application.
Sheng-Feng Weng received the master's degree from the National Cheng Kung University, Taiwan. He is currently a doctoral student in the Department of Electrical Engineering, National Cheng Kung University, Taiwan. His main research focuses on the multimedia system, Web application, and medical education system.
Yong-Guo Chen received the MD degree in medicine from China Medical University, Taiwan, and the second degree in medical information science from Taipei Medical University. Since August 1994, he has been on deputation to the hospital for his resident physician practice. He is currently a doctoral student in the Department of Electrical Engineering, National Cheng Kung University, Taiwan. His main research focuses on medical informatics, medical multimedia, collaboration learning in medical education, electronic medical record, and medical AI.
Chyi-Her Lin is a professor of pediatrics and dean for medical education, College of Medicine, National Cheng Kung University. His research interests include medical education and neonatology.


text:
# Chapter 3:   All the command line options

## 3.1   -c: perform simple validity check

The -c option does a simple validity check of the dvi file: (a) the first two bytes should be 247 2, (b) there should be at least four 233's at the end of the file immediately preceded by a 2.

This is not much of a check: it will certainly not catch dvi files whose middle bytes have become corrupted, but it will at least catch files that are clearly not dvi files (such as text files).

Note that the -c option is implicit in almost every other option, so its main use is to detect files that are probably not dvi files.

See section 15 of dvitype.web for more information.

Example of use:
dvii -c test.dvi

dvi file 'test.dvi' passed validation check (level 0).

## 3.2   -C: perform more rigorous (and slower) validity check

(Note: this is a capital 'C'.) This command causes dvii to traverse the entire dvi file parsing each opcode. If the dvi file is corrupted, this command will detect it.

However, you pay for this: -C is much slower than -c.

dvii -C test

dvi file 'test.dvi' passed validation check (level 1).

## 3.3   -d: dump opcodes

(This option is available in version 0.42 and later.) This option (which implies the -C option) displays all the opcodes. Here is a sample:
dvii -d test

o:247
o:139
o:141
o:159
o:142
...
o:248
dvi file 'test.dvi' passed validation check (level 1).

where ... are many opcodes. The script details.pl uses this mode to create an opcode summary of the file; see section C.3 for more information on details.pl.

## 3.4   -f: display fonts

If you want to list all the fonts used in a dvi file, use the -f option. Note that different sizes of the same font will list separately.

dvii -f test

f:[50/cmr10/1200]::4bf16079
f:[23/cmbx10/1000]::1af22256
f:[0/cmr10/1000]::4bf16079

The file test.dvi calls 3 fonts: font number 50 is cmr10 at size 1200, font number 23 is cmr10 at size 1000, and font number 0 is cmbx10 at size 1000. (For more information on fonts, see chapter 5.)

## 3.5   -F: display fonts on each page

This option (which implies the -p and -f options) lists the fonts used on each page.

dvii -F test

f:[50/cmr10/1200]::4bf16079
f:[23/cmbx10/1000]::1af22256
f:[0/cmr10/1000]::4bf16079
p:[1/1]
start of font list
Font [0/cmr10/1000]
end of font list
p:[2/2]
start of font list
Font [0/cmr10/1000]
end of font list
p:[3/3]
start of font list
Font [0/cmr10/1000]
Font [23/cmbx10/1000]
end of font list
p:[4/4]
start of font list
Font [0/cmr10/1000]
end of font list
p:[5/-1]
start of font list
Font [0/cmr10/1000]
Font [50/cmr10/1200]
end of font list
p:[6/-3]
start of font list
Font [0/cmr10/1000]
end of font list

## 3.6   -g: suppress control characters when showing special text

The -g option can be used when displaying \special information. If a \special contains text with unprintable characters, it may corrupt some computer screens. So, instead of trying to print these unpleasant characters, dvii will instead print a .'.

Here is what the \special text looks like without the -g option:
dvii -s test.dvi

s:[2/2]:: A short special
s:[3/3]:: abcdefghijklmnopqrstuvwxyzABCDE...
s:[4/4]:: PSfile 1.eps
s:[4/4]:: PSfile 2.eps
s:[4/4]:: PSfile 3.EPS
s:[4/4]:: PSfile dog1.gif
s:[4/4]:: PSfile cat.eps
s:[6/-2]:: Some control characters: []

(Note: there are four control characters between the square brackets; because TeX does not like these particular characters, you cannot see them here.)

Now with the -g option:
dvii -s -g test.dvi

s:[2/2]:: A short special
s:[3/3]:: abcdefghijklmnopqrstuvwxyzABCDE...
s:[4/4]:: PSfile 1.eps
s:[4/4]:: PSfile 2.eps
s:[4/4]:: PSfile 3.EPS
s:[4/4]:: PSfile dog1.gif
s:[4/4]:: PSfile cat.eps
s:[6/-2]:: Some control characters: [....]

## 3.7   -h: show main help screen

This option shows the main help screen which begins
dvii -h

This is dvii 0.?? (DVI file information) by Adam Lewenberg
Send bug reports to adam@macrotex.net

dvii -h             (Print help screen)
dvii dvifile        (Print dvi information)
dvii [many possible options] dvifile
-------------------------------------------
-H : show complete list of options
-h : show this help screen
-u : display dvi summary
...

etc.

## 3.8   -H: show options help screen

This option displays all the command line options:
dvii -H

All the command line options:
-c : perform simple validity check
-C : perform more rigorous (and slower) validity check
-f : display fonts
...

etc.

## 3.9   -m#: add message digest information when displaying pages

(See Chapter 7 on message digests.) Display a 16-byte message digest for each page.
dvii -m test

[message digest: simple sum]
p:[1/1]::D8C977816A091771A3A631E7592DAE6D
p:[3/3]::1139D12267E3D60267CC788905909170
p:[4/4]::68E5A2E9D7320743CB85769CAAE9B023
p:[5/-1]::DE72BC3345FFDF7E779C8C667DCE3F97

## 3.10   -M#: add message digest information but ignore certain opcodes

(See Chapter 7 on message digests.) Display a 16-byte message digest for each page, but ignore certain dvii opcodes.

Depending upon the value of #, certain of the dvi information will be ignored when computing the message digest.

• -M0 Do not ignore any of the opcodes; equivalent to -m.
• -M1 Ignore all font assignments and font definitions.
• -M2 Ignore all NOPS (no ops).
• -M4 Ignore all \special's.
• -M8 Ignore all pushes and pops.
These options can be combined by adding; for example, to ignore fonts and \special's, use -M5. A rationale as to why you might want to ignore certain dvii page information when computing a message digest follows.

If you use page message digests to detect when a page has changed, you may get false alarms when the only thing that changes in the dvi file is the order of font definitions: the page looks the same but will have a different message digest because the message digest has changed.

For example, consider the two files
% File A                      % File B
\font\a=cmr10 at 11pt         \font\b=cmr10 at 12pt
\font\b=cmr10 at 12pt         \font\a=cmr10 at 11pt
\a A                          \a A
\b A                          \b A
\end                          \end

These two files generate identical looking output but different dvi code because the font numbering is different. If you use dvii -m you will see different fingerprints:
[message digest: simple sum]
A: p:[1/1]::6676847979940C046D093C93789A1812
B: p:[1/1]::6676837979940B056D093C94789A1812
^

But, if you use dvii -M1 you get
[message digest: simple sum (ignore font)]
A: p:[1/1]::B42E10A601774236B86D11CE2F8C25E4
B: p:[1/1]::B42E10A601774236B86D11CE2F8C25E4

By examining the fonts with the -f option you can see where the two dvi files differ:

dvii -f filea                       dvii -f fileb
f:[51/cmr10/1200]::4bf16079         f:[51/cmr10/1100]::4bf16079
f:[50/cmr10/1100]::4bf16079         f:[50/cmr10/1200]::4bf16079
f:[0/cmr10/1000]::4bf16079          f:[0/cmr10/1000]::4bf16079

The font cmr10 at 1200 is font 51 in filea, whereas it is font 50 in fileb.

## 3.11   -n#: display # bytes of special text

Normally, dvii -s test will display a maximum of 128 bytes of the \special text. For example, let filec.tex be the file
\special{0123456789abcdefghijklmnopqrstuvwxyzABCDE...}
\bye

(Note that the '...' indicates more special text which we omit due to space limitations in this manual.)

dvii -s filec
s:[1/1]:: 0123456789abcdefghijklmnopqrstuvwxyzABCDE...

However, you can tell dvii how many bytes to display by using the -n option:
dvii -s -n20 filec
s:[1/1]:: 0123456789abcdefghij

Finally, if you want to display all the \special text, use -n-1:
dvii -s -n-1 test
s:[1/1]:: 0123456789abcdefghijklmnopqrstuvwxyzABCDE...

Here, the output of dvii -s -n-1 test looks like dvii -s test only because we do not have enough page to show the entire \special text, but believe me, dvii -s -n-1 test will display all the \special text.

## 3.12   -p: display page information

To display a list of physical page/TeX page pairs, use the -p option:
dvii -p test

p:[1/1]
p:[2/2]
p:[3/3]
p:[4/4]
p:[5/-1]
p:[6/-3]

The first number indicates the physical page and the second number indicates the TeX page. For example, the sixth physical page has TeX page -3.

For more information on the difference between physical pages and TeX pages, see section 4.1.

## 3.13   -P: suppress the display of physical pages

(This option is available in version 0.43 and later.) This option only makes sense when you are listing page information, e.g., when using the -p or the -M option. Here is what you get with dvii -p test:
dvii -p test

p:[1/1]
p:[2/2]
p:[3/3]
p:[4/4]
p:[5/-1]
p:[6/-3]

and here is what you get when you add the -P option:
dvii -p -P test

p:[XX/1]
p:[XX/2]
p:[XX/3]
p:[XX/4]
p:[XX/-1]
p:[XX/-3]

So, why might you want to do something so silly? This is most useful when using the message digest feature to detect page changes (see Chapter 7). Imagine that you have message digest information for your entire 1000-page book. Later, you compile only one chapter. If you create a message digest of the chapter, the physical pages will no longer agree with the message digest for the entire book. So, suppressing the physical pages is the only way you can reliably tell if there has been a change.

## 3.14   -s: display specials

The -s lists each \special in the file and the page on which it appears. For example:
dvii -s test

s:[2/2]:: A short special
s:[3/3]:: abcdefghijklmnopqrstuvwxyzABCDE...
s:[4/4]:: PSfile 1.eps
s:[4/4]:: PSfile 2.eps
s:[4/4]:: PSfile 3.EPS
s:[4/4]:: PSfile dog1.gif
s:[4/4]:: PSfile cat.eps
s:[6/-3]:: Some control characters: []

Thus, there is a \special on (physical) page 2 consisting of the text A short special'.

The \special text on page 6/-3 contains some control characters which do not show up on the printed page because they do not correspond to any printable characters. (Actually, the text is [^A^B^C^D].)

## 3.15   -S: count number of specials

Normally, the summary that the -u option generates includes the number of pages and the number of fonts, but not the number of specials. If you want a count of the number of specials, use -S; note that -S implies -u
dvii -S test

File size: 1500 bytes (1 K)
Comment string:  TeX output 2001.01.25:0933
Page count: 6
Number of fonts: 3
Number of specials: 8

## 3.16   -T: give timing information

To see how long dvii took to run, use the -T option:
dvii -T -C test

dvi file 'test.dvi' passed validation check (level 1).
User time: 0.0 seconds
Real time: 0.0 seconds

The User time' is the time external to the computer to run; that is, if you started a stopwatch before executing the command and then stopped it after the command finished, the elapsed time corresponds to the User time'.

On the other hand, most modern operating systems are capable of running many programs at once, switching from one to the other. So, while it may appear to you that a command takes 5 minutes to run, the computer itself may have only spent 1 minute of the 5 minutes on your program, spending the other 4 minutes on other tasks. Hence, 1 minute would be Real time'.

If the file is small enough (as it is in the cast of test.dvi above), you may see both times listed as 0.0 seconds.

## 3.17   -u: display summary

To display a summary of a dvi file, use the -u option:
dvii -u test.dvi
File size: 1500 bytes (1 K)
Comment string:  TeX output 1999.12.05:1951
Page count: 6
Number of fonts: 3

The summary tells us: the dvi test.dvi file is 1500 bytes long (roughly 1 kilobyte), was compiled on December 5, 1999 at 7:51 AM, has 6 pages, and contains 3 fonts.

See also the -S` option.


text:
# 2005-2006 seminars

 Tuesday, July 11, 2006 The learnability of Quantum States Scott Aaronson (University of Waterloo) Tuesday, May 23, 2006 On Margulis' Normal Subgroup Theorem Tim Steger (IAS) Tuesday, May 16, 2006 Randomness Reduction in Some Results of Asympotic Geometric Analysis Shiri Artstein (IAS) Monday, May 15, 2006 New Connections Between Derandomization, Worst-Case Complexity and Average-Case Complexity Danny Gutfreund (Harvard University) Tuesday, May 9, 2006 On the Minimal Density of Triangles in Graphs (continued) Alexander Razborov (IAS) Monday, May 8, 2006 Universal Graphs Michael Capalbo (DIMACS) Tuesday, May 2, 2006 Almost Normal Subgroups of Lattices George Willis (University of Newcastle) Tuesday, May 2, 2006 On the Minimal Density of Triangles in Graphs Alexander Razborov (IAS) Monday, May 1, 2006 Many Hamiltonian Cycles Jeff Kahn (Rutgers University) Tuesday, April 25, 2006 Relative Property T in Lie Groups and their Lattices Yves de Cornulier (École Normale Supérieure) Tuesday, April 25, 2006 Click here for details about DIMACS Workshop No Seminar Due to DIMACS Workshop Monday, April 24, 2006 Click here for details about DIMACS Workshop No Seminar Due to DIMACS Workshop Tuesday, April 18, 2006 Actions of Product Groups on Manifolds Alex Furman (University of Illinois at Chicago) Tuesday, April 18, 2006 Black Boxes, Inc. Avi Wigderson (IAS) Monday, April 17, 2006 Simultaneous Optimization and Fairness Ashish Goel (Stanford University) Tuesday, April 11, 2006 New Techniques in Online Game Playing Elad Hazan (Princeton University) Monday, April 10, 2006 Computational Hardness From Gaussian Isoperimetry: On Hardness of Graph Coloring, the Shape of Double Bubbles and Related Problems Elchanan Mossel (University of California, Berkeley) Tuesday, April 4, 2006 Isospectrality and Commensurability Alan Reid (University of Texas, Austin) Tuesday, April 4, 2006 Periodic Orbits and Extractors Elon Lindenstrauss (Princeton University) Monday, April 3, 2006 The Arrangement Method for Linear Programming Vladlen Koltun (Stanford University) Tuesday, March 28, 2006 The Grothendieck Constant of an Expander Noga Alon (Tel Aviv University and IAS) Monday, March 27, 2006 The Cover Time of Random Walks on Random Graphs Alan Frieze (Carnegie Mellon University) Tuesday, March 21, 2006 Cartesian Products as Profinite Completions and Representation Growth of Groups Martin Kassabov (Cornell University) Tuesday, March 21, 2006 Linear Representations of the Automorphism Group of a Free Group Fritz Grunewald (IAS) Tuesday, March 21, 2006 Kazhdan's Property (T) for Linear Groups Over General Rings Yehuda Shalom (IAS) Tuesday, March 21, 2006 Golod-Shafarevich Groups with Property (T) and Kac-Moody Groups Mikhail Ershov (IAS) Monday, March 20, 2006 Relaxed Two-Coloring of Cubic Graphs Tibor Szabo (ETH) Thursday, March 16, 2006 Time-Space Trade-Offs for Predecessor Search Mikkel Thorup (AT & T) Tuesday, March 14, 2006 Group Theoretic Algorithms For Fast matrix Multiplication Balazs Szedgedy (IAS) Monday, March 13, 2006 On the (Im)possibility of Basing One-Way Functions on NP-Hardness Adi Akavia (MIT) Tuesday, March 7, 2006 Asymptotics and Spectra of Cayley and Schreier Graphs of Branch Groups Zoran Sunik (Texas A & M) Tuesday, March 7, 2006 Strong Approximation in Random Towers of Graphs Yair Glasner (IAS) Monday, March 6, 2006 COMPUTER SCIENCE/DISCRETE MATH I No seminar, due to talk of Christos Papadimitriou at Princeton University Tuesday, February 28, 2006 A Canonical Form for Automorphisms of Totally Disconnected Locally Compact Groups George Willis (University of Newcastle, NSW) Tuesday, February 28, 2006 Independent Transversals in Locally Sparse Graphs Po-Shen Loh (Princeton University) Monday, February 27, 2006 Hamilton Cycles in Expanding and Highly Connected Graphs Michael Krivelevich (Tel Aviv University) Thursday, February 23, 2006 The Jones Polynomial and Quantum Computation Dorit Aharonov (Hebrew University) Tuesday, February 21, 2006 Lattices of Minimum Covolume in Classical Chevalley Groups over $\mathbb F_q((t))$ Alireza Salehi-Golsefidy (Yale University) Tuesday, February 21, 2006 Irrational Quadratic Forms II Gregory Margulis (IAS and Yale University) Monday, February 20, 2006 The Grothendieck Inequality Revisited Ron Blei (University of Connecticut) Tuesday, February 14, 2006 Generalized Harmonic Maps Superridity and Uniformly Convex Metric Spaces Tsachik Gelander (Yale University) Tuesday, February 14, 2006 Quantum Computing and Finite Permutation Groups Aner Shalev (Hebrew University) Monday, February 13, 2006 Cohomology in Grothendieck Topologies and Lower Bounds in Boolean Complexity Joel Friedman (University of British Columbia) Friday, February 10, 2006 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS CONFERENCE Various Thursday, February 9, 2006 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS CONFERENCE Various Wednesday, February 8, 2006 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS CONFERENCE Various Tuesday, February 7, 2006 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS CONFERENCE Various Monday, February 6, 2006 COMPUTER SCIENCE/DISCRETE MATH 1 Monday, February 6, 2006 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS CONFERENCE Various Tuesday, January 31, 2006 Paley Graphs and the Combinatorial Topology of the Bruhat Decomposition Ron Livnè (IAS) Tuesday, January 31, 2006 Cryptography and the P vs NP Question Andrej Bogdanov (IAS) Monday, January 30, 2006 From Trees to General Graphs: Counting Independent Sets up to the Tree Threshold Dror Weitz (DIMACS) Tuesday, January 24, 2006 The Classification of Finite Simple Groups: Aspects of the Second Generation Proof Inna Korchagina (University of Birmingham) Tuesday, January 24, 2006 Random Discrete Matrices: A Survey Van Vu (IAS) Monday, January 23, 2006 Dispersion of Mass and the Complexity of Randomized Algorithms Santosh Vempala (MIT) Tuesday, January 17, 2006 Linear Representations and Arithmeticity of Lattices in Products of Trees Shahar Mozes (IAS) Tuesday, January 17, 2006 Szemeredi's Regularity Lemma and Compactness Balazs Szegedy (IAS) Monday, January 16, 2006 Internal Conflict in a Computational System Adi Livnat (Princeton University) Tuesday, December 20, 2005 Normal Subgroups of the Multiplicative Group of a Finite Dimensional Division Algebra, and Valuations Andrei S. Rapinchuk (IAS) Tuesday, December 20, 2005 Ramanujan Complexes of any Affine Type Donald Cartwright (University of Sydney) Tuesday, December 13, 2005 Hanoi Tower Groups, their Spectra and Growth of Diameters of Schreier Graphs Rostislav Grigorchuk (Texas A & M) Tuesday, December 13, 2005 Dependent Random Choice and Extremal Problems Benny Sudakov (Princeton University and IAS) Monday, December 12, 2005 From Combinatorial Patterns to Strongly Correlated Networks States in Population Neural Code Elad Schneidman (Princeton University) Tuesday, December 6, 2005 Around Property (T) Andrzej Zuk (IAS) Tuesday, December 6, 2005 Coding Theory: Survey of Recent Progress and Open Questions Madhu Sudan (MIT) Monday, December 5, 2005 Rational Secure Computation and Ideal Mechanism Design Silvio Micali (MIT) Wednesday, November 30, 2005 Uniform Kazhdan Groups Denis Osin (City College, New York) Tuesday, November 29, 2005 Szemeredi's Regularity Lemma in Analysis Balazs Szegedy (IAS) Monday, November 28, 2005 Almost Orthogonal Linear Codes are Locally Testable Tali Kaufman (MIT) Tuesday, November 22, 2005 The Comparison Between Kac-Moody and Arithmetic Groups Bertrand Remy (Lyon) Tuesday, November 22, 2005 Euclidean Embeddings of Finite Metric Spaces: Distortion and Expansion James Lee (IAS) Monday, November 21, 2005 NO SEMINAR Friday, November 18, 2005 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS WORKSHOP various speakers Thursday, November 17, 2005 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS WORKSHOP various speakers Wednesday, November 16, 2005 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS WORKSHOP various speakers Tuesday, November 15, 2005 NO SEMINAR Tuesday, November 15, 2005 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS WORKSHOP various speakers Monday, November 14, 2005 NO SEMINAR Monday, November 14, 2005 LIE GROUPS, REPRESENTATIONS AND DISCRETE MATHEMATICS WORKSHOP various speakers Tuesday, November 8, 2005 Spectra of Laplacians of Buildings Tim Steger (IAS) Tuesday, November 8, 2005 Expander Graphs on the Symmetric Groups, Part II Eyal Rozenman (IAS) Monday, November 7, 2005 Near-Optimal Algorithms for Unique Games Yuri Makarychev (Princeton University) Tuesday, November 1, 2005 Buildings and the Spectra of their Laplacians Tim Steger (IAS) Tuesday, November 1, 2005 Expander Graphs on the Symmetric Groups Eyal Rozenman (IAS) Monday, October 31, 2005 Quantum Information and the PCP Theorem Ran Raz (Weizmann Institute of Science, Israel) Friday, October 28, 2005 Hyperbolic Polynomials and Van der Waerden/Schrijver-Valiant like Conjectures Leonid Gurvits (Los Alamos National Laboratory) Tuesday, October 25, 2005 NO SEMINAR Monday, October 24, 2005 No Seminar Due to FOCS Friday, October 21, 2005 Combinatorics of Simplicial Complexes Gil Kalai (Hebrew University and Yale University) Tuesday, October 18, 2005 NO SEMINAR Monday, October 17, 2005 Embeddings of Earthmover Metrics Assaf Naor (Microsoft Research) Tuesday, October 11, 2005 From Ramanujan Graphs to Ramanujan Complexes Alex Lubotzky (IAS) Tuesday, October 11, 2005 Why and Which Expanders? 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# Energy of central potential in QM

A hydrogen atom (Coulomb potential) has energy that only depends on $n$ (if we ignore other effects like spin-orbit coupling). In general (not necessarily Coulomb, can be any V), does $E$ depend on both $\ell$ and $n$ (since the radial equation has both $n$ and $\ell$)? What about $m$? Since $m$ doesn't appear in the radial equation, does it mean that energy does not depend on $m$?

• At higher order the energy does depend on m and manifests itself as fine-structure (the spin-orbit coupling term anyway), and at even higher order in the hyperfine structure. – J. O'Brien Antognini Jun 1 '16 at 18:11
• – Qmechanic Jun 1 '16 at 18:35
• But there is m because we use perturbation theory to 'add' those higher order effects, right? I wanna ask given a potential $V(r,\phi,\theta)$ in general, what does the energy depend by just solving the Schrodinger Equation (and ignore other higher effects that may appear in reality)? – Physicist Jun 1 '16 at 18:53

The wave function of the hydrogen atom $\psi(r,\theta,\phi)$ is a product of the radial part, the angular part and azimuthal term $$\psi_{n,\ell,m}(r,\theta,\phi) = R(r)\Theta(\theta)\Phi(\phi).$$ The radial part $R(r)$ obeys Laguerre polynomials or, $$R_{n\ell}(r) = Ae^{-\rho/2}\rho^\ell L^{2\ell+1}_{n-\ell-1},~ \rho = \frac{2r}{na_0},$$ and $A$ is a complicated constant, The angular part $\Theta(\theta)$ is given by spherical harmonics $Y^\ell_m(\theta,\phi)$ and the azimuthal is $\Phi(\phi) = e^{im\phi}$, where $m$ is the projection of the angular momentum on the $z$ axis.

The energy levels of the bound-states of a hydrogen atom only depend on the radial quantum number n .

This is a special property of a (1/r) type of interaction potential .

For a general central potential, V (r ) the quantized energy levels of a bound-state can depend on both n and l values.

The property that the energy levels of a hydrogen atom only depend on n , and not on l and m, points to the feature that the energy spectrum of a hydrogen atom is highly degenerate.

By degeneracy of a state we mean that there are many different states of the system which possess the same energy eigen value.

For a given value of l , there are (2l+1) different allowed values of m (i.e.,-l , -l+1 , ...0 1 ,2, (l-1) ,+l ).

Likewise, for a given value of n, there are n different allowed values of l (i.e. 0 , 1, 2, ,(n-1)).

Now, all states possessing the same value of n have the same energy (i.e., they are degenerate )

The total number of degenerate states for a given value of n comes out to be n^2.

The above degeneracy gets lifted if the interaction potential has such terms which can give rise to splitting of the degenerate states.

A common example is placing the atom in a magnetic field which splits the different m -states. or spin-orbit interaction term in the potential .


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