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# Treatment in Borderline Class III Malocclusion: Orthodontic Camouflage (Extraction) Versus Orthognathic Surgery

A-Bakr M. Rabie1, *, Ricky W.K. Wong2, G.U. Min3
1 Discipline of Orthodontics, Faculty of Dentistry, The University of Hong Kong, 2/F Prince Philip Dental Hospital, 34 Hospital Road, Sai Ying Pun, HKSAR, China
2 Discipline of Orthodontics, Faculty of Dentistry, The University of Hong Kong, 2/F Prince Philip Dental Hospital, 34 Hospital Road, Sai Ying Pun, HKSAR, China
3 Department of Stomatology, the Second People Hospital, Shenzhen, China

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open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this the Discipline of Orthodontics, Faculty of Dentistry, The University of Hong Kong, 2/F Prince Philip Dental Hospital, 34 Hospital Road, Sai Ying Pun, HKSAR, China Tel: 00-852-28590260 Fax: 00-852-25593803 E-mail: rabie@hkusua.hku.hk

## Abstract

### Aims:

To investigate the differences in morphological characteristics of borderline class III patients who had undergone camouflage orthodontic treatment or orthognathic surgery, and to compare the treatment effects between these two modalities.

### Materials and Methods:

Cephalograms of 25 patients (13 orthodontic, 12 surgical) with class III malocclusion were analyzed. All had a pretreatment ANB angle greater than -5º.

### Results:

Using discriminant analysis, only Holdaway angle was selected to differentiate patients in the pretreatment stage. Seventy-two per cent patients were correctly classified. In the orthodontic group, reverse overjet was corrected by retraction of the lower incisors and downward and backward rotation of the mandible. The surgical group was corrected by setback of the lower anterior dentoalveolus and uprighting of the lower incisors. No difference was found in posttreatment soft tissue measurements between the two groups.

### Conclusions:

Twelve degree for the Holdaway angle can be a guideline in determining the treatment modalities for borderline class III patients, but the preferences of operators and patients are also important. (2) Both therapeutic options should highlight changes in the lower dentoalveolus and lower incisors. (3) Both treatment modalities can achieve satisfactory improvements to the people.

Key Words: Class III malocclusion, camouflage, orthognathic surgery.

## INTRODUCTION

Class III malocclusion is far more prevalent in Asian countries than in the West. (Graber Mosby 2005) [1]. The incidence of anterior crossbite is 2.3-13 per cent among Japanese, 9.4-19 per cent among Koreans and 12.8 per cent among Chinese (Fu ZHKQYXZZ 2002) [2] (and 14.5 per cent in southern Chinese) (Chan AJODO 1974) [3]. Accordingly, class III malocclusions account for a large proportion of orthodontic patients in these countries—for example, 33 per cent of orthodontic patients in Japan and 20 per cent in China. (Fu ZHKQYXZZ 2002) [2] In contrast, the prevalence of class III malocclusion in the United States is only about 1.0 per cent of the total population, and only 5 per cent of orthodontic patients. (Graber Mosby 2005) [1].

There are three main treatment options for skeletal class III malocclusion: growth modification, dentoalveolar compensation (orthodontic camouflage), and orthognathic surgery. Growth modification should be commenced before the pubertal growth spurt, after this spurt, only the latter two options are possible. In such cases, however, how should clinicians determine whether or not patients are suitable for surgery?

Kerr et al(Kerr BJO 1992) [4] tried to establish some cephalometric yardsticks in adult patients with class III malocclusion to find objective criteria for treatment options. These researchers suggested that surgery should be performed for patients with an ANB angle of less than -4°, a maxillary/mandibular (M/M) ratio of 0.84, an inclination of the lower incisors to the mandibular of 83°, and a Holdaway angle of 3.5°. In 2002, a formula was developed to determine whether patients with class III malocclusion underwent either orthodontic treatment or orthognathic surgery, on the basis on the four variables: Wits appraisal, length of the anterior cranial base, M/M ratio, and lower gonial angle. (Stellzig-Eisenhauer AJODO 2002) [5]. However, these two studies did not provide methods to specifically distinguish between patients with borderline surgical-orthodontic class III malocclusion. Furthermore, Cassidy et al(Cassidy AJODO 1993) [6] investigated borderline class II division 1 malocclusions and found that characteristics on which the orthodontic or surgical decision had been based were similar for 27 adult orthodontic and 26 adult surgical patients. The treatment choices largely depended on the clinicians preferences.

Therefore, it is essential to evaluate borderline class III patients very carefully. The objectives of this study were to investigate the different morphological characteristics of borderline surgical-orthodontic class III patients and to compare treatment outcomes between the 2 patient groups. Data from this study will help clinicians in treatment planning.

## MATERIAL AND METHODS

### Orthodontic Group Samples

In this retrospective study, we investigated the treatment records from patients who attended the postgraduate clinic of the Discipline of Paediatric Dentistry and Orthodontics, Faculty of Dentistry, The University of Hong Kong, between 2003 and 2006. All anterior crossbite patients who had been treated by orthodontic means alone were included for selection. The selection criteria were as follows:

1. Southern Chinese
2. Orthodontic treatment performed
3. No obvious transversal discrepancy, non-cleft
4. ANB< 1° or Wits appraisal < -7.5 mm, as checked from pretreatment cephalometric records. These limits of the ANB angle and Wits appraisal for skeletal class III malocclusion were derived from cephalometric norms of southern Chinese. (Cooke EJO 1988) [7].

Twenty patients (13 extraction, 7 non-extraction) satisfied the inclusion criteria, but because the mechanisms of extraction and non-extraction treatment were different, and the sample for non-extraction was small, the non-extraction cases were excluded. Therefore, 13 patients (8 males and 5 females; mean age, 16.2±4.9 years) who underwent extraction were selected as the orthodontic group (Fig. 1). The details of the extraction protocols are shown in Table 1. Since all of the pretreatment ANB angles of these patients were greater -5°, this angle was used as the criterion for the surgical sample.

 Fig. (1). Extra-oral, intra-oral and cephalograms of one orthodontic sample before and after treatment

 Fig. (2). Extra-oral, intra-oral and cephalograms of one surgical sample before and after treatment

 Fig. (3). Landmarks used in this study: 1, soft-tissue nasion; 2, labrale superius; 3, labrale inferius; 4, soft-tissue pogonion; 5, sella; 6, nasion; 7, orbitale; 8, posterior nasal spine; 9, anterior nasal spine; 10, point A; 11, upper incisor apex; 12, incision superius; 13, upper first premolar tip; 14, upper molar mesial cusp tip; 15, lower molar mesial cusp tip; 16, lower first premolar tip, 17, incision inferius 18, lower incisor apex; 19, point B; 20, pogonion; 21, gnathion; 22, menton 23, lower gonion; 24, gonion; 25, posterior gonion; 26, arti-culare; 27, basion; 28, porion; 29, sphenoethmoidal point; 30, ptery-gomaxillare.

 Fig. (4). Superimposition of averaged pretreatment tracings of orthodontic and surgical groups along S-N at sella. Orthodontic group (dashed line); Surgical group (solid line).

 Fig. (5). Superimposition of averaged pretreatment and posttreatment tracings within orthodontic group along S-N at sella. Pretreatment (black line); Posttreatment (red line).

 Fig. (6). Lower incisor position change. Mandibular tracings super-imposed on anterior contour, internal cortical surface of the sym-physis and mandibular canal. Pretreatment (black line), posttreat-ment (red line) m   The mesiobuccal cusp tip of the mandibular permanent first molar it   The incisal tip of the most prominent mandibular central incisor ii   The incisal apex of the most prominent mandibular central incisor OL   Occlusal line, a line through m and the buccal cusp tip of the mandibular first premolar OLP   Occlusal line perpendiculare, a line perpendicular to OL through the most anterior point of the bony chin symphysis

 Fig. (7). Superimposition of averaged pretreatment and posttreatment tracings within surgical group along S-N at sella. Pretreatment (black line); Posttreatment (red line).

 Fig. (8). Superimposition of averaged posttreatment tracings of orthodontic and surgical groups along S-N at sella. Orthodontic group (dashed line); Surgical group (solid line)

Table 1.

Details of Extraction Protocols in the Orthodontic Group

Extracted Teeth Total (n=13)
14, 24, 34, 44 8
15, 25, 34, 44 2
13, 23, 34, 44 1
14, 25, 34, 44 1
34, 44 1
Table 2.

Comparison of the Pretreatment Values for the between Orthodontic and Surgical Groups

Pre-Treatment Orthodontic Group Pre-Treatment Surgical Group Mann-Whitney U Test
Mean SD Mean SD Sig.
Cranial base
PoOr-NBa(°) 27.45 1.82 28.86 3.91 NS
NSAr(°) 123.64 5.45 123.37 6.04 NS
BaSN(°) 131.47 4.39 131.49 5.00 NS
Maxillary
SNA(°) 79.89 2.67 80.96 5.08 NS
PP-SN(°) 8.76 2.18 9.98 3.50 NS
Mandibular
SNB(°) 81.35 2.81 83.08 6.60 NS
ML-SN(°) 33.84 5.23 35.65 6.32 NS
NPog-SN(°) 81.89 2.55 83.43 6.09 NS
Go-Me:S-N 111.38 8.22 118.99 9.10 *
Maxillary/Mandibular
ANB(°) -1.46 2.06 -2.12 2.51 NS
Wits(mm) -8.46 2.73 -10.86 5.61 NS
PP-ML(°) 25.08 5.56 25.67 6.97 NS
M/M ratio 0.85 0.07 0.83 0.10 NS
NAPog(°) -3.71 5.09 -3.61 7.07 NS
Vertical
ArGoMe(°) 121.23 4.28 123.71 9.62 NS
Goupper(°) 45.65 3.43 45.23 4.41 NS
Golower(°) 75.58 4.77 78.49 7.01 NS
Facial Prop 55.43 2.71 56.28 2.49 NS
Y-axis(°) 61.43 4.08 60.06 3.44 NS
Dentoaleolar
U1-SN(°) 111.76 6.02 108.74 11.07 NS
L1-ML(°) 93.74 7.30 86.91 10.97 NS
U1-L1(°) 120.65 7.89 128.71 10.95 *
Soft tissure
Holdaway angle 14.57 4.07 10.14 4.26 *
Z angle 66.77 7.85 73.99 10.64 NS

NS, not significant; * P<0.05; ** P<0.01; *** P<0.001.

Table 3.

Classification Results of Stepwise Discriminant Analysis

Original Group Membership Predicted Group Membership
Orthodontic Group Surgery Group
Orthodontic group 76.9% (n=10) 23.1% (n=3)
Surgery group 33.3% (n=4) 66.7% (n=8)
Table 4.

Comparison of the Pretreatment and Posttreatment Values within the Orthodontic Group

Pre-Treatment Orthodontic Group Post-Treatment Orthodontic Group Wilcoxon Signed Rank Test
Mean SD Mean SD Sig.
Cranial base
PoOr-NBa(°) 27.45 1.82 28.17 2.07 *
NSAr(°) 123.64 5.45 123.67 5.61 NS
BaSN(°) 131.47 4.39 132.41 5.20 NS
Maxillary
SNA(°) 79.89 2.67 79.11 3.49 NS
PP-SN(°) 8.76 2.18 9.00 2.97 NS
Mandibular
SNB(°) 81.35 2.81 80.79 2.84 NS
ML-SN(°) 33.84 5.23 33.65 6.16 NS
NPog-SN(°) 81.89 2.55 81.82 3.03 NS
Go-Me:S-N 111.38 8.22 114.43 7.07 **
Maxillary/Mandibular
ANB(°) -1.46 2.06 -1.68 1.54 NS
Wits(mm) -8.46 2.73 -7.23 3.22 NS
PP-ML(°) 25.08 5.56 24.65 6.31 NS
M/M ratio 0.85 0.07 0.85 0.05 NS
NAPog(°) -3.71 5.09 -5.33 5.04 NS
Vertical
ArGoMe(°) 121.23 4.28 119.44 3.87 **
Goupper(°) 45.65 3.43 43.69 3.71 **
Golower(°) 75.58 4.77 75.74 5.16 NS
Facial Prop 55.43 2.71 56.13 2.62 *
Y-axis(°) 61.43 4.08 61.03 3.91 NS
Dentoalveolar
U1-SN(°) 111.76 6.02 110.21 4.88 NS
L1-ML(°) 93.74 7.30 86.65 6.59 **
U1-L1(°) 120.65 7.89 129.48 5.61 **
Soft tissure
Holdaway angle 14.57 4.07 13.46 4.87 NS
Z angle 66.77 7.85 74.94 9.29 **

NS, not significant; * P<0.05; ** P<0.01; *** P<0.001.

Table 5.

The Values of the Retraction of the Lower Incisors in the Orthodontic Group (n=13)

Mean SD
Incisal tip (mm) 4.88 2.77
Incisal apex (mm) 1.92 1.78
Table 6.

Comparison of the Pretreatment and Posttreatment Values within the Surgical Group

Pre-Treatment Surgical Group Post-Treatment Surgical Group Wilcoxon Signed Rank Test
Mean SD Mean SD Sig.
Cranial base
PoOr-NBa(°) 28.86 3.91 28.49 3.40 NS
NSAr(°) 123.37 6.04 123.72 5.00 NS
BaSN(°) 131.49 5.00 132.53 5.84 NS
Maxillary
SNA(°) 80.96 5.08 80.91 4.63 NS
PP-SN(°) 9.98 3.50 9.53 3.68 NS
Mandibular
SNB(°) 83.08 6.60 79.62 5.12 **
ML-SN(°) 35.65 6.32 37.01 5.31 NS
NPog-SN(°) 83.43 6.09 81.38 4.86 *
Go-Me:S-N 118.99 9.10 117.02 7.71 NS
Maxillary/Mandibular
ANB(°) -2.12 2.51 1.30 2.36 **
Wits(mm) -10.86 5.61 -4.85 3.60 **
PP-ML(°) 25.67 6.97 27.48 5.94 NS
M/M ratio 0.83 0.10 0.93 0.12 **
NAPog(°) -3.61 7.07 -0.97 4.49 NS
Vertical
ArGoMe(°) 123.71 9.62 124.19 9.64 NS
Goupper(°) 45.23 4.41 45.56 4.92 NS
Golower(°) 78.49 7.01 78.64 6.34 NS
Facial Prop 56.28 2.49 56.58 2.87 NS
Y-axis(°) 60.06 3.44 61.05 4.04 NS
Dentoaleolar
U1-SN(°) 108.74 11.07 107.28 8.23 NS
L1-ML(°) 86.91 10.97 94.02 7.96 **
U1-L1(°) 128.71 10.95 121.70 7.17 NS
Soft tissure
Holdaway angle 10.14 4.26 14.72 2.90 **
Z angle 73.99 10.64 75.71 4.85 NS

NS, not significant; * P<0.05; ** P< 0.01; *** P<0.001.

Table 7.

Comparison of the Posttreatment Values between the Orthodontic and Surgical Groups

Post-Treatment Orthodontic Group Post-Treatment Surgical Group Mann-Whitney U Test
Mean SD Mean SD Sig.
Cranial base
PoOr-NBa(°) 125.90 129.50 28.49 3.40 NS
NSAr(°) 48.63 42.34 123.72 5.00 NS
BaSN(°) 132.41 5.20 132.53 5.84 NS
Maxillary
SNA(°) 79.11 3.49 80.91 4.63 NS
PP-SN(°) 9.00 2.97 9.53 3.68 NS
Mandibular
SNB(°) 80.79 2.84 79.62 5.12 NS
ML-SN(°) 33.65 6.16 37.01 5.31 NS
NPog-SN(°) 81.82 3.03 81.38 4.86 NS
Go-Me:S-N 114.43 7.07 117.02 7.71 NS
Maxillary/Mandibular
ANB(°) -1.68 1.54 1.30 2.36 **
Wits(mm) -7.23 3.22 -4.85 3.60 NS
PP-ML(°) 24.65 6.31 27.48 5.94 NS
M/M ratio 0.85 0.05 0.93 0.12 *
NAPog(°) -5.33 5.04 -0.97 4.49 **
Vertical
ArGoMe(°) 119.44 3.87 124.19 9.64 NS
Goupper(°) 43.69 3.71 45.56 4.92 NS
Golower(°) 75.74 5.16 78.64 6.34 NS
Facial Prop 56.13 2.62 56.58 2.87 NS
Y-axis(°) 61.03 3.91 61.05 4.04 NS
Dentoaleolar
U1-SN(°) 110.21 4.88 107.28 8.23 NS
L1-ML(°) 86.65 6.59 94.02 7.96 *
U1-L1(°) 129.48 5.61 121.70 7.17 **
Soft tissure
Holdaway angle 13.46 4.87 14.72 2.90 NS
Z angle 74.94 9.29 75.71 4.85 NS

NS, not significant; * P<0.05; ** P< 0.01; *** P<0.001.

### Surgical Group Samples

Patients with anterior crossbite who attended the postgraduate clinic of the Discipline of Oral and Maxillofacial Surgery, Faculty of Dentistry, The University of Hong Kong, between 2002 and 2006 for surgical treatment were included for selection. The reason for including one more year than the orthodontic group was to obtain a comparable sample size. The selection criteria were the same as those of the orthodontic group except for an ANB angle of greater than -5º. Twelve patients (2 males and 10 females; mean age, 19.4±4.9 years) were included in the surgical sample (Fig. 2). In them, nine patients had undergone bimaxillary surgery, two patients had undergone mandibular surgery only, and the rest one had undergone maxillary surgery only.

### Cephalometric Analyses

All lateral cephalograms that had been obtained before and after treatment were scanned (Epson Expression 1649-XL; Seiko Epson Corp., Japan), traced, and digitized by one investigator. A commercial cephalometric program (Winceph 7.0; Rise Corp., Japan) was used to study the cephalometric landmarks shown in Fig. (3). Twenty-four angular, one linear, and three proportional measures were used in this study, most of which were the same as those used in two previous studies, (Kerr BJO 1992) [4] (Stellzig-Eisenhauer AJODO 2002) [5] except for measurements of the NPog-SN angle, Go-Me/S-N ratio, and Z angle.

Because there is an obvious sexual dimorphism among class III patients (Ngan IJAOOS 1997) [8] (Baccetti AO 2005) [9] and this study combined males and females, only angles, proportional measurements, and Wits appraisal were measured in this investigation. All these variables have previously been proven to be independent of sex.

### Method Error

Cephalograms from 10 randomly chosen patients were retraced and redigitized on two different occasions separated by a 2-week interval. The method error was calculated using Dahlberg’s formula (Houston AJODO 1983) [10]:

$\mathrm{ME}=\sqrt{{d}^{2}/2n}$

where d is the difference between 2 registrations of a pair, and n is the number of double registrations. The random errors ranged from 0.46° to 1.79° for angular variables, from 0.02 to 1.68 for ratio variables, and 1.66 mm for Wits appraisal measurements.

### Statistical Analyses

Mann-Whitney U test was applied to compare variables between the orthodontic and surgical groups. Wilcoxon signed rank test was used to compare pretreatment and posttreatment variables for each group. Stepwise discriminant analysis was applied to identify the possible variables that best separated the pretreatment groups. The data were analyzed by using SPSS for Windows, version 13.0 (SPSS Inc., Chicago, Ill). Cutoffs for statistical significance were taken as P<0.05,<0.01, and <0.001.

## RESULTS

### Comparison of Pretreatment Values between Orthodontic and Surgical Group

Table 2 shows that significant differences (P<0.05) were found in three measurements: the Go-Me/S-N ratio, U1-L1 angle, and Holdaway angle. Stepwise discriminant analysis identified only one variable that distinguished between patients suitable for orthodontics from those suitable for surgery. That factor was the Holdaway angle (F likelihood to remove = .014). On the basis of the unstandardized discriminant function coefficients of the selected variable, along with a calculated constant, the following equation for individual scores was developed:

Individual score = -2.989+0.24×(Holdaway angle)

The critical score was 12°, which was the mean centroid of the two groups. This implies that a new borderline class III malocclusion patient with a Holdaway angle greater than 12° would be treated successfully by orthodontics alone. On the contrary, a new patient with a Holdaway angle of less than 12° should be treated by combined surgical-orthodontic treatment. In this way, 72 per cent of the patients were correctly classified. Three patients of the orthodontic group and four of the surgical group had been misclassified (Table 3).

### Comparison of Pretreatment and Posttreatment Values within Orthodontic Group

Significant increases were found in measurements for the PoOr-NBa angle (P<0.05), Go-Me/S-N ratio (P<0.01), lower facial height proportion (P<0.05), interincisal angle (P<0.01), and Z angle (P<0.01). The decreases in the gonion angle (P<0.01), upper gonion angle (P<0.01), and L1-ML angle (P<0.01) were also statistically significant (Table 4). After tracings were superimposed along the anterior cranial base at the nasion, the posttreatment tracing showed a more prognathic mandible, increased lower facial height, retracted lower incisors, and retruded lower lip than the pretreatment tracing.

To assess the movement pattern of the lower incisors, an analysis based on sagittal-occlusion analysis (Pancherz AJODO 1985) [11] and a ‘Pitchfork diagram’ (Johnston BJO 1996) [12] was conducted (Fig. 6). Table 5 shows that lower incisors were retracted 4.9 mm in the incisal tip and 1.9 mm in the incisal apex.

### Comparison of Pretreatment and Posttreatment Values within Surgical Group

After surgical treatment, samples in this group showed significant differences in the following measures: decreased SNB angle (P<0.01), NPog-SN angle (P<0.05); increased L1-ML angle, and Holdaway angle (P<0.01); highly increased ANB angle (P<0.01); and Wits appraisal and M/M ratio (P<0.01) (Table 6).

Fig. (7) shows the changes after surgery, mainly the setback of the mandibular dentoalveolus and chin, and the uprighting and retraction of the lower lip.

### Comparison of Posttreatment Values between Orthodontic Group and Surgical Group

The posttreatment comparison of the two groups and superimposition of averaged tracings are shown in Table 7 and Fig. (8), respectively. Significant differences were found in the ANB angle (P<0.01), M/M ratio (P<0.05), NAPog angle (P<0.01), L1-ML angle (P<0.05), and U1-L1 angle (P<0.01). Apart from the changes with respect to the hard tissues mentioned above, there were no significant differences in the two soft tissue measurements. Hence, both lateral profile improvements were esthetically harmonic, although the lower lip was more distally positioned bodily in the surgical group than in the orthodontic group.

## DISCUSSION

Class III malocclusion is among the most difficult de-formities to be corrected, especially using orthodontic means alone. This study focused on successfully treated borderline class III patients to provide some treatment guidelines that can help in treatment decisions for this malocclusion.

Borderline surgical/orthodontic cases refer to patients with mild to moderate skeletal problems that can be treated by either orthodontic or surgical means. Cassidy (Cassidy AJODO 1993) [6]defined “borderline cases” as those patients who were similar with respect to the characteristics on which the orthodontic/surgical decision appeared to have been based. In this study, the common characteristic of both groups was the same ANB angle range (above -5º).

Although many studies (Jacobson AO 1988) [13] suggested combining the ANB angle and Wits appraisal to evaluate the sagittal discrepancy, the ANB angle is still a simpler and more commonly used variable. In this study, the values of Wits appraisal showed no significant difference between the two groups before treatment. This finding indicated that the sagittal discrepancy was actually in the same range in the two groups.

All of the pretreatment cephalograms used in this study were taken in the CO position, regardless of whether or not the patients had mandibular anterior displacement. Gravely (Gravely BJO 1984) [14] found that a conventional cephalograph taken in the CO position could reasonably reflect the skeletal pattern in most cases. He doubted whether a second cephalograph taken with the incisors held edge to edge provided sufficient additional information.

Even though all the patients were in the same range of sagittal discrepancy, several significant differences could still be found between orthodontic and surgical patients before treatment. A lower Holdaway angle, higher Go-Me:S-N ratio, and increased U1-L1 angle indicated a more prognathic mandible, greater compensation of incisors, and a more concave profile in the surgical group. Discriminant analysis showed that for the measurement of the profile, the Holdaway angle, was the most crucial variable to classify patients. The threshold value was 12º, which meant that if one patient had a Holdaway angle of greater than 12º, he or she would most likely to be successfully treated by orthodontics. This value was much higher than the 3.5º suggested by Kerr. (Kerr BJO 1992) [4] The variable racial composition of the sample probably contributed to this difference.

The proportion of correctly classified patients was 72 per cent—less than the 92 per cent found in Stellzig-Eisenharer’s study. (Stellzig-Eisenhauer AJODO 2002) [5] A possible reason for the lower proportion is that morphology may not be the only factor that determines the treatment decision, especilally in borderline cases. The preference of patients and operators also could affect the final option chosen. Proffit (Proffit IJAOOS 1990) [15] found that psychologic rather than morphologic characteristics probably were the major influence on whether or not an individual decided to accept surgery. Bell (Bell AJODO 1985) [16] also pointed out that the decision of surgery was mainly related to the self-perception of patients. In addition, the preference of operators was also important. Cassidy (Cassidy AJODO 1993) [6] found that in borderline class II patients, the final treatment choice was highly depended on which clinician the patient happened to contact. Bell (Bell AJODO 1985) [16] opined that surgeons and orthodontists may differ in recommendations for surgical correction. Consequently, a Holdaway angle of 12º can be only a rough guideline to help in treatment planning. Nevertheless, the preference of patients should also be considered.

It is commonly believed that successful camouflage treatment for class III malocclusion can be achieved by proclination of maxillary incisors, retrusion of mandibular incisors, and downward and backward rotation of mandible. In this study, as all of the patients were extraction cases the upper incisors showed mild retroclination rather than proclination. This finding was similar to that reported by Battagel. (Battagel EJO 1991) [17] Thus, the retraction of the lower incisors and rotation of the mandible were crucial for crossbite correction. In a detailed analysis of the mode of movement of the lower incisors, the crown tips and root apices of the lower incisors were retracted by 4.9 mm and 1.9 mm, respectively, and this retraction was combined with tipping and bodily movement. The bodily movement of the roots was important in preventing over retroclination of the lower incisors. In order to do that, lingual root torque should be applied to the lower incisors during treatment.

After distalization of the lower incisors, the facial convexity was increased accordingly, which contributed to the significant change in Z angle. Unlike the Holdaway angle, the Z angle (Merrifield AJODO 1966) [18] uses the more protruded lip (upper or lower) rather than the upper lip to establish the profile line, whereas in class III malocclusion, lower lip is always more protruded than upper lip, this is why in this study the change of Z angle showed a statistically significant difference, whereas the Holdaway angle did not.

Surgical correction of class III malocclusion can be achieved by mandibular setback, maxillary advancement, or a combination of both procedures. In this study, 8 of 12 patient underwent bimaxillary surgery. The main skeletal changes after surgery were setback of the mandibular dentoalveolus and the uprighting of the lower incisors, whereas the skeletal base of both jaws did not show any significant changes. The setback of the dental alveolus in the mandibular anterior region contributed to the decreased ANB angle, increased Wits appraisal, and M/M ratio. Although the mandibular length did not show any obvious decrease, the chin point seemed to follow the setback of the apical base of the incisors, as manifested by the decreased NPog-SN angle. Possible reasons accounting for this finding include distal displacement of the mandible and remodeling of the chin point after anterior subapical osteotomy. The improvement in the Holdaway angle demonstrates the consequent adaptation of the soft tissue. The unchanged Z angle, however, may be explained by the decompensation of the lower incisors, which contributes to the stable position of the lower lip related to the chin point.

Because the profile rather than occlusion may be the main focus of concern for class III patients, (Bailey IJAOOS 2001) [19] improvement in the profile should play a major role in the evaluation of treatment outcomes. In this study, both patient groups showed obvious improvements in their profile. Although the lack of significant difference in Holdaway angle and Z angle between the two groups does not mean that orthodontic treatment can achieve the same degree of improvement as the surgical approach, orthodontics can still change the profile to achieve an acceptable esthetic effect. The most pronounced characteristic of soft tissue change in this study was limited to the lower lip rather than both lips, regardless of treatment group. This finding was different from that of previous studies, in which a change in both lips was described. (Lew IJAOOS 1990) [20] The sampling technique of the borderline and extraction cases may account for this difference.

## CONCLUSIONS

In conclusion, the present study indicates that (1) the Holdaway angle can be a reliable guide in determining the treatment modality for patients who represent borderline class III surgical cases; (2) the treatment effect of both treatment options should emphasize a change in the lower jaw and lower incisors; and (3) among correctly chosen patients, both treatment modalities can acquire a satisfactory profile improvement.

## REFERENCES

 [1] Graber TM, Vanarsdall RL, Vig KWL. Current Principles and Techniques In: Orthodontics . 4. St Louis: Mosby 2005; p. 565. [2] Fu M, Zhang D, Wang B, Deng Y, Wang F, Ye X. The prevalence of malocclusion in China--an investigation of 25392 children Zhonghua Kou Qiang Yi Xue Za Zhi 2002; 37: 371-3. [3] Chan GK. Class 3 malocclusion in Chinese (Cantonese) etiology and treatment Am J Orthod Dentofacial Orthop 1974; 65: 152-7. [4] Kerr WJ, Miller S, Dawber JE. Class III malocclusion surgery or orthodontics? Br J Orthod 1992; 19: 21-4. [5] Stellzig-Eisenhauer A, Lux CJ, Schuster G. Treatment decision in adult patients with Class III malocclusion orthodontic therapy or orthognathic surgery? Am J Orthod Dentofacial Orthop 2002; 122: 27-37. [6] Cassidy DW Jr, Herbosa EG, Rotskoff KS, Johnston LE Jr. A comparison of surgery and orthodontics in "borderline" adults with Class II, division 1 malocclusions Am J Orthod Dentofacial Orthop 1993; 104: 455-70. [7] Cooke MS, Wei SH. Cephalometric standards for the southern Chinese Eur J Orthod 1988; 10: 264-72. [8] Ngan P, Hagg U, Yiu C, Merwin D, Wei SH. Cephalometric comparisons of Chinese and Caucasian surgical Class III patients Int J Adult Orthodon Orthognath Surg 1997; 12: 177-88. [9] Baccetti T, Reyes BC, McNamara JA Jr. Gender differences in Class III malocclusion Angle Orthod 2005; 75: 510-20. [10] Houston WJ. The analysis of errors in orthodontic measurements Am J Orthod Dentofacial Orthop 1983; 83: 382-90. [11] Pancherz H, Hagg U. Dentofacial orthopedics in relation to somatic maturation.An analysis of 70 consecutive cases treated with the Herbst appliance Am J Orthod Dentofacial Orthop 1985; 88: 273-87. [12] Johnston LE Jr. Balancing the books on orthodontic treatment an integrated analysis of change Br J Orthod 1996; 23: 93-102. [13] Jacobson A. Update on the Wits appraisal Angle Orthod 1988; 58: 205-19. [14] Gravely JF. A study of the mandibular closure path in Angle Class III relationship Br J Orthod 1984; 11: 85-91. [15] Proffit WR, Philips C, Dann Ct. Who seeks surgical-orthodontic treatment? Int J Adult Orthodon Orthognath Surg 1990; 5: 153-60. [16] Bell R, Kiyak HA, Joondeph DR, MchNeill RW, Wallen TR. Perceptions of facial profile and their influence on the decision to undergo orthognathic surgery Am J Orthod Dentofacial Orthop 1985; 88: 323-32. [17] Battagel JM, Orton HS. Class III malocclusion a comparison of extraction and non-extraction techniques Eur J Orthod 1991; 13: 212-22. [18] Merrifield LL. The profile line as an aid in critically evaluating facial esthetics Am J Orthod Dentofacial Orthop 1966; 52: 804-22. [19] Bailey LJ, Haltiwanger LH, Blakey GH, Proffit WR. Who seeks surgical-orthodontic treatment a current review Int J Adult Orthodon Orthognath Surg 2001; 16: 280-92. [20] Lew KK. Soft tissue profile changes following orthodontic treatment of Chinese adults with Class III malocclusion Int J Adult Orthodon Orthognath Surg 1990; 5: 59-65.


text:
Thread: Maximum area of an area within y=x^2

1. Maximum area of an area within y=x^2

I've got this problem that I'm trying to solve, I've been twisting my brain for several hours now.

An area 'A' is limited by the curve y=x^2, the x-axel and the line x=2

In this area is a rectangle with the area R, as seen in the figure.

Calculate the maximum relation between R and A in exact form.

If someone could take a look at this and help me, I would appreciate it very very much!

2. if you make the left hand bottom corner of the rectangle point a then it follows that

$A = L\times W$

subing in some values gives

$A = f(a)\times (2-a)$

$A = a^2\times (2-a)$

$A = 2a^2-a^3$

for a maximum you must find where $\frac{dA}{da}=0$

$\frac{dA}{da}=4a-3a^2$

$0=4a-3a^2$

$0=a(4-3a)$

$a=0,\frac{4}{3}$

probably should discard zero as a solution at this point as it implies zero area.

now $f\left(\frac{4}{3}\right)= \frac{9}{16}$

Maximum area should be simple to find from here using

$A = L\times W$

$A = f(a)\times (2-a)$

format: plain


text:
01-396 J. Asch, R.D. Benguria, P. \v{S}\v{t}ov\'\i\v{c}ek
Asymptotic properties of the differential equation $h^3(h''+h')=1$ (217K, postscript) Oct 24, 01
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We derive the form of the asymptotic series, as $t\to +\infty$, for a general solution $h(t)$ of the non-linear differential equation $h(t)^{3}(h''(t)+h'(t))=1$.

Files: 01-396.src( 01-396.keywords , absMP.ps )


text:
# Largest symmetric matrix given rank

Let $\mathscr{M}[n,d]$ be collection of $n\times n$ symmetric matrices with real entries from $\{0,1\}$ such that every row/column is distinct with sum of every row/column being $d$.

What is minimum real rank of matrices in $\mathscr{M}[n,d]$?

Given real rank $r$, then $\mathscr{N}[r,d]$ be collection of symmetric rank $r$ square matrices with real entries from $\{0,1\}$ such that every row/column is distinct with sum of every row/column being $d$.

What is largest size of matrix in $\mathscr{N}[r,d]$?

Is there an algebraic or geometric way to describe these sets?

If you further assume that the diagonal of your matrices are all zeros, it's natural to view your matrices as adjacency matrices of graphs. With this identification, your sum condition means the graph is $d$-regular, and the distinct-row condition means the graph is reduced (see for example this paper).
In fact, that same paper considers a function $m(r)$, defined to be the number of vertices in the largest reduced graph of rank $r$. Note that upper bounds on $m(r)$ provide upper bounds for your second question. Kotlov and Lovasz's result in the beginning of section 4 gives that $m(r)=O(2^{r/2})$, and this is tight by Proposition 5.


text:
Abstract/Details

## ATOMIC DIFFUSION AT POLYCRYSTALLINE-SILICON/GALLIUM-ARSENIDE INTERFACES

KAVANAGH, KAREN LYNNE.
Cornell University ProQuest Dissertations Publishing,  1987. 8715603.

### Abstract (summary)

A study of the metallurgical and electrical stability of thin film polycrystalline-silicon/gallium arsenide (poly-Si/GaAs) interfaces by Rutherford backscattering, secondary ion mass spectroscopy and transmission electron microscopy is described. Considerable interdiffusion occurs at heavily As or P-doped poly-Si/GaAs (5-30 at%) interfaces whereas interdiffusion is negligible at GaAs interfaces with undoped poly-Si or As and B-doped poly-Si with dopant concentrations of less than 1 at%. Interfacial reaction is not detected after heat treatments to 1050$\sp\circ$C. The out-diffusion of Ga and As into heavily-doped poly-Si occurs via grain boundaries and the Si diffusion in the GaAs is characterized by steep slopes at the diffusion front which do not fit to simple solutions of the diffusion equation. It is proposed that the Si diffusion is enhanced by the diffusion of vacancies from the interface created by the disproportionation of the substrate. The diffusion profiles can be simulated with a position-dependent Si diffusion coefficient determined from the local vacancy concentration. Excellent fits to the data are obtained if it is further assumed that the vacancy diffusion is concentration-dependent and dominated by divacancy diffusion. This model was shown to apply equally well to the diffusion of P and In in GaAs also studied from poly-Si and to the diffusion of Ge, Sn and Si at SiO$\sb 2$/Ge/GaAs interfaces where the disproportionation of the substrate occurs by out-diffusion into the SiO$\sb 2$. Based on the divacancy diffusion model the enhancement in the diffusivity of Si, Ge, Sn, P and In in GaAs encapsulated with poly-Si or SiO$\sb 2$ may be as high as 10$\sp 4$ above the equilibrium diffusion coefficients.

The electrical stability of poly-Si/GaAs was correlated to interdiffusion. At interfaces where Si diffusion was detected the contacts were ohmic (contact resistivity 1.4 $\times$ 10$\sp{-4}$ $\Omega$-cm$\sp 2$ or poorly rectifying. At poly-Si:B(0.5 at%)/GaAs interfaces where no out-diffusion of Ga and As was detected a rectifying contact (barrier height of 0.83 eV) was obtained after heat treatments to 950$\sp\circ$C for 10 sec.

### Indexing (details)

Subject
Materials science
Classification
0794: Materials science
Identifier / keyword
Applied sciences
Title
ATOMIC DIFFUSION AT POLYCRYSTALLINE-SILICON/GALLIUM-ARSENIDE INTERFACES
Author
KAVANAGH, KAREN LYNNE
Number of pages
180
Degree date
1987
School code
0058
Source
DAI-B 48/05, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-206-18733-5
University/institution
Cornell University
University location
United States -- New York
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8715603
ProQuest document ID
303472828


text:
### A Central Limit Framework for Ring-LWE Decryption

Sean Murphy and Rachel Player

##### Abstract

The main contribution of this paper is to develop a statistical framework, based on a Central Limit argument, for analysing the noise in ciphertexts in homomorphic encryption schemes that are based on Ring-LWE. Such an approach is very general: apart from finite variance, no assumption on the distribution of the noise is required (in particular, the noise need not be subgaussian). We demonstrate that such a Central Limit approach can be used to obtain a high-quality approximation of the distribution of the noise in an appropriate decoding basis, even in dimension as small as n = 100. We apply our framework and results to a homomorphic Ring-LWE cryptosystem of Lyubashevsky, Peikert and Regev (Eurocrypt 2013, full version) in order to illustrate the benefit of this approach. We show that a Central Limit approach leads to tighter bounds for the probability of decryption failure than have been obtained in prior work.

##### Metadata
Available format(s)
Publication info
Preprint. MINOR revision.
Keywords
Ring-LWECentral Limit Theorem&#948-subgaussiandecryption failure probabilityhomomorphic encryption
Contact author(s)
s murphy @ rhul ac uk
History
2020-07-21: last of 4 revisions
2019-05-08: received
See all versions
Short URL
https://ia.cr/2019/452
License

CC BY

BibTeX

@misc{cryptoeprint:2019/452,
author = {Sean Murphy and Rachel Player},
title = {A Central Limit Framework for Ring-LWE Decryption},
howpublished = {Cryptology ePrint Archive, Paper 2019/452},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/452}},
url = {https://eprint.iacr.org/2019/452}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
# Determine which function is a better fit.

Andrew wants to estimate his gas mileage, or miles traveled per gallon of gas used. He records the number of gallons of gas he purchased and the total miles he traveled with that gas.

Create a scatter plot showing the relationship between gallons of gas and miles driven.

Which function is a better estimate for the function that relates gallons to miles: $y = 10x$ or $y = 22x$?

How is the equation of the function related to his gas mileage?

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

1. Plot each point on the coordinate plane.
2. Graph the function $y = 10x$ on the coordinate plane.
3. Graph the function $y = 22x$ on the same coordinate plane.
4. Look at the graph of the data and the functions.
5. Interpret the equation in the context of the problem, using the units of the x- and y-axes.

Created with GeoGebraShared by Walch Education, Mathguru
View as Java Applet
View as HTML5 Applet


text:
# Proving density of $H^2(\mathbb{R})$ in $L^2(\mathbb{R})$ .

I am trying to use the version of the Lumer-Phillips, which is stated as the following

Let $A$ be a linear operator defined on a dense linear subspace $D(A)$ of the reflexive Banach space $X$. Then $A$ generates a contraction semigroup if and only if $A$ is closed and both $A$ and its adjoint operator $A^∗$ are dissipative.

My operator $\mathcal{L}: D(\mathcal{L}) \subseteq X \longrightarrow X$ is defined by $$D(\mathcal{L})=H^2(\mathbb{R})$$ $$X = L^2 (\mathbb{R})$$ $$\mathcal{L} = - \nu \partial_x -\frac{\mu_2}{2} x^2 + \gamma \partial_xx .$$

My question is how do I show that $D(\mathcal{L})$ is dense in $X$? (Is it dense?) I do not know where to start!

Furthermore, I was wondering how one went about defining the spaces if the operator was to act on a complex variable? (So it made up part of the complex Ginzburg Landau equation).

Kindest regards,

Catherine

• Do you know that $C^\infty_0(\mathbb R)$ is dense in $L^2(\mathbb R)$? – Umberto P. Feb 2 '18 at 15:10
• Just to get the meaning of notation right, is these the space of infinitely-differentiable functions with compact support? – Catherine Drysdale Feb 2 '18 at 15:27

Indeed, smooth (i.e. $C^\infty$ functions) with compact support are dense in $L^2(\mathbb R)$, and this is a subspace of $H^2(\mathbb R)$.
• @CatherineDrysdale You will need to consider complex-valued Sobolev spaces, but this is an easy generalization of the real case: viewing $\mathbb C \cong \mathbb R^2,$ any complex valued function $u$ can be viewed as a pair $(u_1,u_2)$ of real-valued functions. Under this identification one can check $H^k(\Omega,\mathbb C) \simeq H^k(\Omega) \oplus H^k(\Omega)$ and all the properties remain (including density). – ktoi Feb 2 '18 at 18:07


text:
## Sunday, 30 April 2017

### Converting Unix Timestamp into SQL Server DateTime

It is well known that developing and integrating applications based on different technologies may end up being a huge challenge, especially when it comes to dealing with data stored in diverse data type formats as it is Timestamp in Unix and DateTime in SQL Server. This post intents to show you a method in SQL Server to convert Unix Timestamp into Datetime. Here it is:

CREATE FUNCTION [dbo].[UNIX_TIMESTAMP_TO_DATETIME] (
@timestamp integer
)
RETURNS datetime
AS
BEGIN
DECLARE @return datetime
SET @timestamp = @timestamp - 18000
SELECT @return = DATEADD(second, @timestamp,{d '1970-01-01'});

RETURN @return
END

The function takes as a parameter a Unix Timestamp value so that it is converted into Datetime, and it will then give you the equivalent value in SQL Server Datetime format.  I know it might not be the be-all and end-all, nevertheless, I am pretty sure it will be use for many people. I hope you make the most out of it. That’s all for now. Let me know any remarks you may have. Thanks for reading. Stay tuned.

## Wednesday, 12 April 2017

### Checking Disk Space usage and Database Files usage per partition disk

When it comes to monitoring and managing disk space we may have some graphic tools to help us complete these tasks rapidly, nevertheless, not everybody can afford to pay the tools, and most of them do not give some details we may need on the spur of the moment. For example, we may have the need to check how much disk space is occupied by database files exclusively so that a wise decision can be made to ensure we are using disk space properly of a database server. We may need to see a report something like this.

In the report we can appreciate that all partition disks are displayed, each of them has information related to the space used in total (db_file_size_on_disk_db) by all database files (data & log) and it also includes the equivalent in percentage (db_file_size_on_disk_pct). Thus, we will be able to know whether or not the disk space is being using properly. Furthermore, disk space capacity and disk space available in gigabytes and percentage can also seen (disk_capacity_gb, disk_space_available_gb, disk_space_available_pct).

Now it is high time to show the code to get that report containing that information:

CREATE PROC [dbo].[sp_DBA_mon_db_files_size_on_disk] (@volume_mount_point char(1)=NULL)
/*WITH ENCRYPTION*/
AS
begin
if (@volume_mount_point is not null )
begin
SELECT    vs.volume_mount_point,
vs.logical_volume_name,

DB_NAME(f.database_id) database_name,  f.type_desc,
vs.total_bytes/1024/1024/1024.0 AS [disk_capacity_gb],
cast( f.[size] / 128 /1024.0 as decimal(10,2)) AS [db_file_size_on_disk_gb],
cast( ( f.[size]*100/ 128 /1024.0 ) /   (vs.total_bytes/1024/1024/1024.0 )  as DECIMAL(10,2) ) AS [db_file_size_on_disk_pct],
cast(vs.available_bytes/1024/1024/1024.0 as DECIMAL(10,2)) AS [disk_space_available_gb],
cast ( ( vs.available_bytes *100.0  / vs.total_bytes) as DECIMAL(10,2) )  AS [disk_space_available_pct],
f.physical_name,
vs.file_system_type
FROM  sys.master_files AS f
CROSS APPLY   sys.dm_os_volume_stats(f.database_id, f.file_id) AS vs
WHERE   f.database_id < 32767 and  vs.volume_mount_point=@volume_mount_point + ':\'
order  by f.[size]  desc
end
else
begin
SELECT vs.volume_mount_point,
vs.logical_volume_name,
vs.total_bytes/1024/1024/1024.0 AS [disk_capacity_gb],
cast(SUM( f.[size] / 128 /1024.0) as decimal(10,2)) AS [db_file_size_on_disk_gb],
cast( (SUM( f.[size]/ 128 /1024.0) *100) /   (vs.total_bytes/1024/1024/1024.0 )  as DECIMAL(10,2) ) AS [db_file_size_on_disk_pct],
cast(vs.available_bytes/1024/1024/1024.0  as DECIMAL(10,2)) AS [disk_space_available_gb],
cast ( ( vs.available_bytes *100.0  / vs.total_bytes) as DECIMAL(10,2) )  AS [disk_space_available_pct],
vs.file_system_type
FROM  sys.master_files AS f
CROSS APPLY   sys.dm_os_volume_stats(f.database_id, f.file_id) AS vs
WHERE   f.database_id < 32767
group by  vs.volume_mount_point,vs.total_bytes ,   vs.logical_volume_name,  vs.total_bytes ,vs.file_system_type  ,  vs.available_bytes

end
end

The report could receive the letter of the partition disk as a parameter, and also it can be omitted. As you can see in the definition of the stored procedure, the default value for @volume_mount_point is NULL which means, according to the logic of it, that general information will be displayed, that is the report in the graphic, otherwise, giving the letter of a partition will allow you to get detail information for every database file located in that disk partition. That's is all for now. I hope it is useful and practical for you.  Let me know any remarks you may have. Thanks for reading. Stay tuned.

## Wednesday, 5 April 2017

### Looking into Modern_Spanish and Latin1_General

The collations Modern_Spanish and Latin1_General are both Windows collations and support the same character set (Code Page 1252), but there are some differences between both collations related to the treatment of some characters in terms of sorting/doing comparisons. Some of the differences are noticeable especially when Accent-Insensitive is used, in Modern_Spanish n and ñ are considered different characters whereas in Latin1_General they are considered a character and an accented version of the same character.

Today I am going to show off an example to make it clear so that you can take it on board to pre-empt unforeseen results or conflict of collations. This example is based on Modern_Spanish_CI_AI and Latin1_General_CI_AI.

create table TempTable (
Text_in_Latin1  varchar(100) collate Latin1_General_CI_AI,
Text_in_Modern varchar(100) collate Modern_Spanish_CI_AI
)
go
insert into TempTable values ('Español', 'Español')
insert into TempTable values ('Espanol', 'Espanol')
insert into TempTable values ('Espanól', 'Espanól')
go
select Text_in_Latin1 from TempTable where Text_in_Latin1='Espanol'
go
select Text_in_Modern from TempTable where Text_in_Modern='Espanol'
go
drop table TempTable

Text_in_Latin1
--------------------------------------
Español
Espanol
Espanól

Text_in_Modern
--------------------------------------
Espanol
Espanól

As you can see, the first result demonstrates that Español, Espanol and Espanól are treated as the same word when we use Accent-Insensitive whereas in the second one Español and Espanol are treated as different words. It is worth noting that you only must change the collation if you really understand the behaviour change. For example, one might think that Latin1_General_CI_AS (Windows Collation) and SQL_Latin1_General_CP1_CI_AS (SQL Collation) are the same, but they are not the same, there is a slight difference in the short behaviour between both for specific special characters like '-'. Here another example about it.

create table TempTable (
Text_in_Latin1  varchar(100) collate Latin1_General_CI_AS,
Text_in_SQL_Latin1 varchar(100) collate SQL_Latin1_General_CP1_CI_AS
)
go
insert into TempTable values ('es-pe', 'es-pe')
insert into TempTable values ('espe', 'espe')
go
select Text_in_Latin1 from TempTable order by Text_in_Latin1
go
select Text_in_SQL_Latin1 from TempTable order by Text_in_SQL_Latin1
go
drop table TempTable

Text_in_Latin1
---------------------------------------
espe
es-pe

Text_in_SQL_Latin1
---------------------------------------
es-pe
espe

To be honest, I personally like having the same collation for all databases, but it has to be done carefully and, more importantly, if you really want that change. That is all for now, let me know any remarks you may have.
HELLO, I'M PERCY REYES! — a book lover, healthy lifestyle lover... I've been working as a senior SQL Server Database Administrator (DBA) for over 20 years; I'm a three-time awarded Microsoft Data Platform MVP. I'm currently doing a PhD in Computer Science (cryptography) at Loughborough University, England — working on cryptographic Boolean functions, algorithmic cryptanalysis, number theory, and other algebraic aspects of cryptography. READ MORE


text:
Uses supsmu for non-seasonal series and a periodic stl decomposition with seasonal series to identify outliers and estimate their replacements.

tsoutliers(x, iterate = 2, lambda = NULL)

## Arguments

x time series the number of iteration only for non-seasonal series Box-Cox transformation parameter. If lambda="auto", then a transformation is automatically selected using BoxCox.lambda. The transformation is ignored if NULL. Otherwise, data transformed before model is estimated.

## Value

index

Indicating the index of outlier(s)

replacement

Suggested numeric values to replace identified outliers

na.interp, tsclean

tsoutliers(gold)#> $index #> [1] 770 #> #>$replacements


text:
# Drawing Awesome Spiral Shapes using Python Turtle Module

## Introduction

The Logo programming language is frequently linked to turtle graphics. In the late 1960s, Seymour Papert added turtle graphics support to Logo to support his version of the turtle robot, which is a simple robot controlled from the user’s workstation and designed to carry out the drawing functions assigned to it using a small retractable pen set into or attached to the robot’s body.

The standard library of the Python programming language now contains a Turtle graphics module. Turtle in Python, like its Logo ancestor, allows programmers to manipulate one or more turtles in a two-dimensional space.

## Overview of the syntax

A location, an orientation (or direction), and a pen are the three qualities of the turtle. Color, width, and on/off state are all properties of the pen (also called down and up).

“Move ahead 10 spaces” and “turn left 90 degrees” are orders that the turtle responds to based on its current location. The turtle’s pen can also be managed by enabling it, changing its color, and adjusting its breadth. By visualizing what they would do if they were the turtle, a pupil may comprehend (and forecast and reason about) the turtle’s motion. This is referred to as “body syntonic” reasoning by Seymour Papert.

Basic syntax:

import turtle // start of the program
//body
//of the main
//code
turtle.done() //end of the program

Inorder to understand the codes to draw various shapes given below, Getting Started with Powerful yet Easy Python Graphics Module, Turtle.

## Methods

A Python method is a label that can be applied to an object and is a piece of code that may be run on that object.

The most frequently, used turtle methods are:

## Drawing Spiral Shape

Drawing Spiral Shape using python turtle module is like learning anything else really. You learn the basic concept and then you can do the same with any other shape. Let me explain!!

In each cycle, the length of the side is reduced by a set number, resulting in spiral figures. Given below are the steps through which you can make a spiral out of any shape.

• Choose a figure’s side length and assign it to a variable side. The side of a figure, for example, is 20 units.
side = 20
• Run a for loop for a long time, and use the forward() and right() functions of the turtle module in that loop. The side variable should be passed to the forward() function, and the value of a figure’s exterior angle should be passed to the right() function. After that, reduce the side’s length by a certain amount.
for i in range(20):
t.forward(side)
t.right(exteriorAngle)
side = side - 2

## Spiral Square

For obtaining a spiral square,

• Import turtle.
• Set tom as our turtle object.
• Set the speed to 2.
• Set side as 200.
• Run a loop like mentioned above.
• turtle.done().
import turtle

tom = turtle.Turtle()
tom.speed(2)
side = 200
for i in range(100):
tom.forward(side)
tom.right(90) #Exterior angle of a square is 90 degree
side = side - 2

turtle.done()

### Output

The output for the spiral square is as follows. You can see, multiple squares overlapping over each other to form a Spiral Square.

## Spiral Star

For obtaining a spiral star,

• Import turtle.
• Set tom as our turtle object.
• Set the speed to 2.
• Set side as 2.
• Run a loop like mentioned above.
• turtle.done().
import turtle

tom = turtle.Turtle()
tom.speed(200)
side = 2
for i in range(100):
tom.forward(side)
tom.right(144) #Exterior angle of a star 144 is degree
side = side - 2

turtle.done()

### Output

The output for the spiral star is as follows. You can see, multiple stars overlapping over each other to form a Spiral Star.

## Spiral Triangle

For obtaining a spiral triangle,

• Import turtle.
• Set tom as our turtle object.
• Set the speed to 2.
• Set side as 2.
• Run a loop like mentioned above.
• turtle.done().
import turtle

tom = turtle.Turtle()
tom.speed(2)
side = 2
for i in range(70):
tom.forward(side)
tom.right(120) #Exterior angle of a triangle 120 is degree
side = side - 3

turtle.done()

### Output

The output for the spiral triangle is as follows. You can see, multiple triangles overlapping over each other to form a Spiral Triangle.

## Spiral Pentagon

For obtaining a spiral pentagon,

• Import turtle.
• Set tom as our turtle object.
• Set the speed to 2.
• Set side as 2.
• Run a loop like mentioned above.
• turtle.done().
import turtle

tom = turtle.Turtle()
tom.speed(2)
side = 2
for i in range(104):
tom.forward(side)
tom.right(72) #Exterior angle of a pentagon 72 is degree
side = side - 2

turtle.done()

### Output

The output for the spiral pentagon is as follows. You can see, multiple pentagons overlapping over each other to form a Spiral Pentagon.

## Spiral Polygon

Any two-dimensional geometry made up of straight lines is called a polygon. Polygons include triangles, quadrilaterals, pentagons, and hexagons, among others. The name of the shape indicates how many sides it has. A triangle, for example, has three sides, while a quadrilateral has four.

For obtaining a spiral star,

• Import turtle.
• Set tom as our turtle object.
• Set the speed to 2.
• Set side as a user input variable.
• Set length as a user input variable.
• Calculate the exterior angle as 360/side.
• Run a loop like mentioned above.
• turtle.done().
import turtle

tom = turtle.Turtle()
tom.speed(2)

side = int(input('Enter the number of sides of a polygon: '))
length = int(input('Enter the length of a side of a polygon: '))
exteriorAngle = 360/side

for i in range(200):
tom.forward(length)
tom.right(exteriorAngle)
length = length - 0.5

turtle.done()

### Output

The output for the spiral polygon is as follows. You can see, multiple polygons overlapping over each other to form a Spiral Polygon. As multiple shapes are polygons, the user can define the sides and length of each side of the polygon. For this instance we take 10 sides each of length 100.

The output is as follows for the above input:

SHARE Drawing Awesome Spiral Shapes using Python Turtle Module


text:
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# IMD school reputation

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IMD school reputation [#permalink]  22 Feb 2010, 20:03
I have not been much interested in European schools until I received an email from IMD and visited its website.

I have wanted to go to either Duke or Georgetown in the States but as I looked at the world MBA ranking, IMD was way higher ranked than both schools.

My quesiton is if there any disadvantes for me if I can go to IMD and graduate with MBA degree and get back to the States to get a job?

Is this school attractive to US employers? Most of people who graduated from IMD got jobs in U.K or any European countries.

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Re: IMD school reputation [#permalink]  22 Feb 2010, 22:16
bgrocker79 wrote:
I have not been much interested in European schools until I received an email from IMD and visited its website.

I have wanted to go to either Duke or Georgetown in the States but as I looked at the world MBA ranking, IMD was way higher ranked than both schools.

My quesiton is if there any disadvantes for me if I can go to IMD and graduate with MBA degree and get back to the States to get a job?

Is this school attractive to US employers? Most of people who graduated from IMD got jobs in U.K or any European countries.

IMD is solid gold especially if you're interested in moving into industry (less into finance and consulting - if I'm not wrong). It may not be so recognized in the States, but it's up there in Europe. i would go to IMD if I could get accepted, without a doubt.
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Re: IMD school reputation [#permalink]  23 Feb 2010, 03:22
ranks-and-clusterings-of-various-international-b-schools-78320.html

The above thread has some reputation / cluster related information ?
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Re: IMD school reputation [#permalink]  23 Feb 2010, 06:22

I will see if I like it or not. They are coming to DC area this Thursday so I will go see them. Thanks again for your post.

p.s> I like Finance and Consulting indusry. As you said, they are not strong at those industries, then I might not consider that school.
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Re: IMD school reputation [#permalink]  15 Mar 2010, 13:10
Also consider that they don't have internships or exchange programs, so there are slim chances to be involved in a project in US during the school (except maybe a visit to tech entrepreneurs in Silicon Valley).
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Re: IMD school reputation [#permalink]  15 Mar 2010, 13:29
IMD positions itself as a full time MBA program when in my opinion, it is an Executive MBA program. IMD stresses "leadership" and the ages of the students appears older than the other schools with more work experience. My experience is that they are disorganized and have a haughty attitude. So I didn't apply and happily applied to INSEAD.
In my opinion a much better school. Never mind the fact that Switzerland is undergoing a tremendous upheaval right now regarding immigration. The recent minaret ban is emblematic of the kind of xenophobia stirring in Switzerland and that will translate into a difficulty finding employment. My best friend was the head of recruiting for a Forbes 100 multinational. When I asked him what he thought about IMD he said "who's that?"
I think the school is also very overpriced and living expenses in Lausanne are outrageous. IF you can even find an apartment. A friend of mine is looking for 5 months still because they don't rent to foreigners. Google will tell you all you need to know. . . Just my opinions and experiences!
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Re: IMD school reputation [#permalink]  16 Mar 2010, 02:06
Head of recruiting for a Forbes 100 saying "Who's that?" in reference to IMD. Is that not a little overkill. Isn't the school consistenly ranked among the top 5 outside US?
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Re: IMD school reputation [#permalink]  16 Mar 2010, 05:13
tarun wrote:
Head of recruiting for a Forbes 100 saying "Who's that?" in reference to IMD. Is that not a little overkill. Isn't the school consistenly ranked among the top 5 outside US?

People might not know that school especially US recruiters. But, I agree with you. It is overkill. This school has ranked top 5. If they are "great" recruiters, they should know.
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Re: IMD school reputation [#permalink]  16 Mar 2010, 12:10
bgrocker79 wrote:
tarun wrote:
Head of recruiting for a Forbes 100 saying "Who's that?" in reference to IMD. Is that not a little overkill. Isn't the school consistenly ranked among the top 5 outside US?

People might not know that school especially US recruiters. But, I agree with you. It is overkill. This school has ranked top 5. If they are "great" recruiters, they should know.

Fully agree with you. It tells more about the person who said that than about the school
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Re: IMD school reputation [#permalink]  16 Mar 2010, 15:18
No need to dispute what I am saying. Just ask around. Also search Google and the forums about employment in Switzerland. Recently they reduced the amount of visas they are giving to foreigners for work in order to help the native Swiss. I would rather go to a school that is recognized around the world rather than regionally when spending that kind of money. Just my opinion. Also research how many people are interviewed versus how many are accepted. IMD is one of the few schools that doesn't interview outside of their school. INSEAD and others will have alumni interview you in YOUR region. IMD has no problem to bring you there for an interview so long as it's on your dime. Right?

Evgeny, Israel. : Do a Google search for the climate in Switzerland in regards to immigrants. Tell me what you find. THEN tell me you still want to go there.
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Re: IMD school reputation [#permalink]  16 Mar 2010, 21:00
Bergeron wrote:
No need to dispute what I am saying. Just ask around. Also search Google and the forums about employment in Switzerland. Recently they reduced the amount of visas they are giving to foreigners for work in order to help the native Swiss. I would rather go to a school that is recognized around the world rather than regionally when spending that kind of money. Just my opinion. Also research how many people are interviewed versus how many are accepted. IMD is one of the few schools that doesn't interview outside of their school. INSEAD and others will have alumni interview you in YOUR region. IMD has no problem to bring you there for an interview so long as it's on your dime. Right?

Evgeny, Israel. : Do a Google search for the climate in Switzerland in regards to immigrants. Tell me what you find. THEN tell me you still want to go there.

Bergeron, it really hard to say anything about your opinion because it is SO disconnected from the reality....
1. IMD doesn't offer employment only in Switzerland, but in all over Europe (and US if you REALLY want it).
2. IMD is as recognized around the globe as INSEAD (who's brand it not too much known, compared to HBS, MIT, Oxford, Standford, Yale.....)
3. The acceptance rate after the interview in IMD is about the same as in other schools (~50%)
4. They don't interview out of campus because they don't interview at all. They invite you for a one FULL day session with several "tests" and not only an 30 minutes interview (like other schools). I think it shows how much do they invest in selecting a team. BTW, if you consider a cost per hour of a ad-com member, you will see that IMD invests ALLOT of money in these sessions (about 7 people from the ad-com and the faculty)
5. If you are willing to invest ~$150K in an MBA, spending ~$1K more wont hurt you.
6. The climate regarding the immigrants isn't good in any country and maybe even worth in Switzerland, but who cares? You come there for 1 year, you're life is around IMD (as you don't have time for anything else) and than you leave to any other place you whish......

I'm not trying to say that IMD is the best school, but it's for sure as good as the other top 5 schools, and in specific things it's the 1st one...
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Re: IMD school reputation [#permalink]  16 Mar 2010, 21:12
Bergeron, it really hard to say anything about your opinion because it is SO disconnected from the reality....
1. IMD doesn't offer employment only in Switzerland, but in all over Europe (and US if you REALLY want it).
2. IMD is as recognized around the globe as INSEAD (who's brand it not too much known, compared to HBS, MIT, Oxford, Standford, Yale.....)
3. The acceptance rate after the interview in IMD is about the same as in other schools (~50%)
4. They don't interview out of campus because they don't interview at all. They invite you for a one FULL day session with several "tests" and not only an 30 minutes interview (like other schools). I think it shows how much do they invest in selecting a team. BTW, if you consider a cost per hour of a ad-com member, you will see that IMD invests ALLOT of money in these sessions (about 7 people from the ad-com and the faculty)
5. If you are willing to invest ~$150K in an MBA, spending ~$1K more wont hurt you.
6. The climate regarding the immigrants isn't good in any country and maybe even worth in Switzerland, but who cares? You come there for 1 year, you're life is around IMD (as you don't have time for anything else) and than you leave to any other place you whish......

I'm not trying to say that IMD is the best school, but it's for sure as good as the other top 5 schools, and in specific things it's the 1st one...[/quote]

I just want to mention one thing. They do have an interview out of campus. I think it was held in some Asian country. It was exactly same format- doing research about it confirmed it happened. Regarding reputation, it is top 5 schools which can be compared with MIT, HBS..
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Re: IMD school reputation [#permalink]  16 Mar 2010, 21:39
You are right indeed. They interview also in Asia and South America
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Re: IMD school reputation [#permalink]  17 Mar 2010, 07:27
I appreciate that the IMD shills have corrected me thanks to their "research" I have corrected the errant sentence to reflect this oversight. One can also now fly to Asia or South America. I wonder if the cost of hotels and flight would be a tax deduction?

IMD positions itself as a full time MBA program when in my opinion, it is an Executive MBA program. IMD stresses "leadership" and the ages of the students appears older than the other schools with more work experience. My experience is that they are disorganized and have a haughty attitude. So I didn't apply and happily applied to INSEAD.
In my opinion a much better school. Never mind the fact that Switzerland is undergoing a tremendous upheaval right now regarding immigration. The recent minaret ban is emblematic of the kind of xenophobia stirring in Switzerland and that will translate into a difficulty finding employment. My best friend was the head of recruiting for a Forbes 100 multinational for 12 years. When I asked him what he thought about IMD he said "who's that?"

Just my opinions and experiences!

Also search Google and the forums about employment in Switzerland. Recently they reduced the amount of visas they are giving to foreigners for work in order to help the native Swiss. I would rather go to a school that is recognized around the world rather than regionally when spending that kind of money. Just my opinion. Also research how many people are interviewed versus how many are accepted. IMD invites everyone to them for interviews. Others will have alumni interview you in YOUR region. IMD has no problem to bring you there for an interview so long as it's on your dime. Right?

Do a Google search for the climate in Switzerland in regards to immigrants. Tell me what you find. THEN tell me you still want to go there?
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Re: IMD school reputation [#permalink]  17 Mar 2010, 10:19
[quote="Bergeron"]I appreciate that the IMD shills have corrected me thanks to their "research" I have corrected the errant sentence to reflect this oversight. One can also now fly to Asia or South America. I wonder if the cost of hotels and flight would be a tax deduction?

quote]

But, take a look at the population. Many of them from Asia and Europe. Do you think which one will be better to fly to Swiss or to fly a certain Asian Country in order to save money? If they really want that school, they have to see it no matter how much they will spend. Also post graduation-as far as I know IMD salary is very high Thus eventually it will offset quicker than other schools. Regarding seeking a job is very challenging everywhere and through my experience, getting a job in U.S. is one of the most difficult thing because of immigration law well and I could say most expensive too.
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Re: IMD school reputation [#permalink]  17 Mar 2010, 12:09
bgrocker79 wrote:
Also post graduation-as far as I know IMD salary is very high Thus eventually it will offset quicker than other schools.

Really???

IMD is ranked in the bottom HALF for "salary percentage increase" according to the Financial Times Global ranking from 2010. They are the ONLY school in the top 25 that has a percentage less than 100%! They list 86% to be exact. Unless you work for the school let's stick to the info from the FT rankings or another reliable source.
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Re: IMD school reputation [#permalink]  17 Mar 2010, 12:57
Bergeron wrote:
bgrocker79 wrote:
Also post graduation-as far as I know IMD salary is very high Thus eventually it will offset quicker than other schools.

Really???

IMD is ranked in the bottom HALF for "salary percentage increase" according to the Financial Times Global ranking from 2010. They are the ONLY school in the top 25 that has a percentage less than 100%! They list 86% to be exact. Unless you work for the school let's stick to the info from the FT rankings or another reliable source.

hmmm.... can it be because people that go to IMD ALREADY EARN GREAT SALARY!?!?!!?!?
God, Bergeron, if you have no chance getting in, that doesnt mean the school is bad...
And, BTW, they are ranked number 1 in Economist
Can you please elaborate on "My experience is that they are disorganized"? I work with several IMD alumni and had a chance to visit the school and met several of the ad-com, faculty and program members, and the LAST thing I can say about it (or heard about it) is that they are "disorganized".
The only thing I COULD agree with you is that the program is somewhat similar to EMBA. But I dont as this program DOESNT takes executives and give them new tools, but they take low-mid range managers and educate+train them on BA
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Re: IMD school reputation [#permalink]  17 Mar 2010, 14:05
Quote:
Really???

IMD is ranked in the bottom HALF for "salary percentage increase" according to the Financial Times Global ranking from 2010. They are the ONLY school in the top 25 that has a percentage less than 100%! They list 86% to be exact. Unless you work for the school let's stick to the info from the FT rankings or another reliable source

In 2009, it looks better but yes in 2010 it doesn't look that good. But maybe you might want to check this out.

p.s)I clicked this link but didn't work but you can try to make a chart for money value. IMD is the first one out of 9 ultra elite schools( HBS,LBS, UPenn, Chicago, Columbia, INSEAD,IMD, MIT,Standford)

Also, the school's reputation can be very subjective just like some says Mc donald coffes is the best while some says starbucks is the best. Whenever candidates visit to schools, they might look different things. That's why even many different source made different rankings. But somehow I agree with you becase there are also standardized measurement such as number of dotors in that program or how diverse the MBA program is, and so on. I respect your experience but you don't need to say that IMD is bad. Rather you could say it wasn't my type of school.
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Re: IMD school reputation [#permalink]  17 Mar 2010, 14:19
knfevg wrote:
hmmm.... can it be because people that go to IMD ALREADY EARN GREAT SALARY!?!?!!?!?
God, Bergeron, if you have no chance getting in, that doesnt mean the school is bad...
And, BTW, they are ranked number 1 in Economist
Can you please elaborate on "My experience is that they are disorganized"? I work with several IMD alumni and had a chance to visit the school and met several of the ad-com, faculty and program members, and the LAST thing I can say about it (or heard about it) is that they are "disorganized".
The only thing I COULD agree with you is that the program is somewhat similar to EMBA. But I dont as this program DOESNT takes executives and give them new tools, but they take low-mid range managers and educate+train them on BA

I agree that IMD students earn higher pre-MBA salaries, as they tend to be more experienced. But as post-MBA wages are not greater than the ones for other MBA programs and the tuition fees and living expenditures are among the highest for the European programs, IMD's ROI is one of the lowest, thus IMD might not be the smartest choice, from a financially point of view.
And as this topic already caused bitter pro' & cons' stances, this might be an indicator that IMD reputation is still ... debatable.
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Re: IMD school reputation [#permalink]  17 Mar 2010, 21:46
a11c99 wrote:
knfevg wrote:
hmmm.... can it be because people that go to IMD ALREADY EARN GREAT SALARY!?!?!!?!?
God, Bergeron, if you have no chance getting in, that doesnt mean the school is bad...
And, BTW, they are ranked number 1 in Economist
Can you please elaborate on "My experience is that they are disorganized"? I work with several IMD alumni and had a chance to visit the school and met several of the ad-com, faculty and program members, and the LAST thing I can say about it (or heard about it) is that they are "disorganized".
The only thing I COULD agree with you is that the program is somewhat similar to EMBA. But I dont as this program DOESNT takes executives and give them new tools, but they take low-mid range managers and educate+train them on BA

I agree that IMD students earn higher pre-MBA salaries, as they tend to be more experienced. But as post-MBA wages are not greater than the ones for other MBA programs and the tuition fees and living expenditures are among the highest for the European programs, IMD's ROI is one of the lowest, thus IMD might not be the smartest choice, from a financially point of view.
And as this topic already caused bitter pro' & cons' stances, this might be an indicator that IMD reputation is still ... debatable.

Any school is debatable... Let's say INSEAD - ranked high but the the reputation of it is droping and they are beeing "acused" for being a "MBA machine".
BTW, the proportion of faculty member to the amount of students is on of the best in IMD (1/3)
Re: IMD school reputation   [#permalink] 17 Mar 2010, 21:46

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# Computing a bootstrap confidence interval for the prediction error with the percentile and the BCa method

I have two related questions regarding the computation of a non-parametric bootstrap confidence interval for the prediction error.

Setting: I have a sample S from a data population P and a learner L, and I want to compute a 95% confidence interval for the 0.632 bootstrap estimator $\hat{\theta}_{.632bs}$ of the prediction error $\theta$ of the classifier C learned by learner L on sample S.

Q1 My first question is whether the following procedure, to compute the confidence interval with the percentile method, is correct. Specifically, the sampling of a test set $S_{test}$ in step 2 to evaluate my classifier on. I have read that, for every observation, you have to keep track of predictions from bootstrap samples not containing that observation. This seems to come down to the same thing according to me? I compute the confidence interval with the percentile method as follows:

1. I compute the resubstitution error $\theta_{resub}$ of the classifier C learned by L on S
2. I compute N (e.g. = 1000) bootstrap estimates $\hat{\theta}_i^*$ of the prediction error on S as follows:

For i = 1 : 1000 do:

• Sample from S with replacement until I have a new sample $S_{train}$ the same size as S
• From all the instances that were not sampled in step 1, I sample again with replacement until I have a sample $S_{test}$ with the same size as S
• I learn a classifier on $S_{train}$ and evaluate it on $S_{test}$. The classifier performance on $S_{test}$ is my bootstrap estimate $\hat{\theta}_i^*$.
3. For each sample i of the N bootstrap samples I compute the estimate $\hat{\theta}^*_{i,.632bs}$ as $\hat{\theta}^*_{i,.632bs} = 0.368 \cdot \theta_{resub} + 0.632 \cdot \hat{\theta}_i^*$

4. I sort the 1000 bootstrap estimates
5. I select the 25th bootstrap estimate as the lower bound of the confidence interval and the 975th estimate as the upper bound of the confidence interval.

Q2 My second question is how to compute the confidence interval for the 0.632 bootstrap estimator for the prediction error with the bias corrected accelerated (BCa) method. Namely, I find that I have a problem here: I need an estimate of a term $b$ for the bias correction, and for term $a$, the acceleration term (http://www.tau.ac.il/~saharon/Boot/10.1.1.133.8405.pdf p1153-1154).

• To compute $b$, I need an estimate of the prediction error $\hat{\theta}$ from the complete sample S. I am not sure how to do this. I see several possibilities: The average of $\hat{\theta}^*_{i,.632bs}$ over all $i$, the resubstitution error, a hold-out error, perform cross-validation on S...?
• I have the same problem for computing $a$. Here, I need jackknife estimates that use all of the data from S except one instance $x_i$ ($S \setminus x_i$). What exactly do I compute here? Is this computation the same as computing the leave-one-out cross-validation estimator for the prediction error?

I have tried finding the answers in the literature, but I have difficulty understanding the papers I found, so I hope somebody can help me here. Thank you!

• Did you ever manage to solve this problem? I'm having the same issue right now. Mar 20, 2015 at 22:56
• The 0.632 and 0.632+ bootstrap estimators are needed only for discontinuous accuracy scoring rules. When you use continuous measures or AUROC the ordinary simple Efron-Gong optimism bootstrap is just fine. And I recommend against using discontinuous scoring rules that are optimized when the model is incorrect. Feb 7 at 13:25
• For bootstrapping or jackkinfing your estimate, you need an additional outer loop. Is this what you have tried? Feb 8 at 9:52