text:
# careful exposition of transfinite recursion

Given a well ordered set W and a family of sets X(w) indexed by the elements w of W, transfinite recursion allows one often to define a function f on W that takes values f(w) in X(w). (I distinguish this from transfinite induction, which establishes a family of propositions.) The recursive definition involves providing a formula for f(w) in terms of the values of f at elements of W smaller than w, but there may also be an auxiliary condition on the family of previous values. For example, in the proof of Zorn's lemma by transfinite recursion from the well ordering theorem of Zermelo, one needs to know that the previous values form a chain: the next value is then a strict upper bound for that chain.

Is there a good reference in the published literature that gives a careful abstract criterion for specifying what sort of auxiliary conditions "work", together with a proof?

(I'm not asking for an exposition here, just for references to the literature. The reason I ask is that I'm in the process of formalizing the method of transfinite recursion, and I wonder whether I'm following the best approach, whether this has been done before, and whether a careful expository paper would be worth disseminating.)

• Is the "auxiliary condition" known as "the invariant" in computer-sciency circles? – Andrej Bauer Apr 12 '17 at 15:34
• Yes, it's just like that. – Dan Grayson Apr 12 '17 at 20:19

These auxiliary conditions are never crucial to the argument: we can always define our recursive procedure to "trivialize" if they fail, and then separately prove that they don't.

Let's look at the Zorn example you give. At an abstract level, what we have is:

• A well-ordering $(W, \prec)$, and

• A map $F$ from chains in $P$ to chains in $P$ (where $P$ is the poset we're looking at).

We want to define $I(w)$ for all $w\in W$, where $I$ is the "iterate"of $F$, but on the face of it we need to know that we never "stop being a chain" - that is, $I(w)$ needs to be a chain for us to define $I(w+1)=F(I(w))$.

We get around this by working with a modified version of $F$: for a subset $A$ of $P$, $G(A)$ is defined as follows:

• If $A$ is a chain, then $G(A)=F(A)$.

• Otherwise, $G(A)=A$.

Then we can use transfinite recursion as usual to define an iterate $J$ of $G$, without a problem. We then prove by transfinite induction that $J(w)$ is a chain for each $w$, so in fact $J$ is an iterate of $F$ as hoped.

So there's no real need to use these "auxiliary conditions."

• Right, thank you, but my interest is in locating references for the possibility of treating the auxiliary conditions simultaneously, rather than postponing them. – Dan Grayson Apr 13 '17 at 13:32


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0
Technical Briefs

# Geometrical Effects on the Temperature Distribution in a Half-Space Due to a Moving Heat Source

[+] Author and Article Information
Mohsen Akbari1

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canadamohsen_akbari@sfu.ca

David Sinton

Department of Mechanical Engineering, University of Victoria, Victoria, BC, V8W 2Y2, Canada

Majid Bahrami

Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canada

1

Corresponding author.

J. Heat Transfer 133(6), 064502 (Mar 02, 2011) (10 pages) doi:10.1115/1.4003155 History: Received February 26, 2010; Revised November 24, 2010; Published March 02, 2011; Online March 02, 2011

## Abstract

Fundamental problem of heat transfer within a half-space due to a moving heat source of hyperelliptical geometry is studied in this work. The considered hyperelliptical geometry family covers a wide range of heat source shapes, including star-shaped, rhombic, elliptical, rectangular with round corners, rectangular, circular, and square. The effects of the heat source speed, aspect ratio, corners, and orientation are investigated using the general solution of a moving point source on a half-space and superposition. Selecting the square root of the heat source area as the characteristics length scale, it is shown that the maximum temperature within the half-space is a function of the heat source speed (Peclet number) and its aspect ratio. It is observed that the details of the exact heat source shape have negligible effect on the maximum temperature within the half-space. New general compact relationships are introduced that can predict the maximum temperature within the half-space with reasonable accuracy. The validity of the suggested relationships is examined by available experimental and numerical data for the grinding process, for medium Peclet numbers. For ultrafast heat sources, an independent experimental study is performed using a commercial $CO2$ laser system. The measured depth of the engraved grooves is successfully predicted by the proposed relationships.

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## Figures

Figure 1

Schematic of a symmetrical moving plane heat source with arbitrary shape

Figure 2

Hyperellipse as a general symmetric geometry covers an array of source geometries: (a) star shape (n<1), (b) rhombic (n=1), (c) elliptical (n=2), (d) rectangular with round corners (n=4), and (e) rectangular (n→∞)

Figure 3

Schematic diagram of the laser beam, the engraved groove, and cross-sectional image of the wooden substrate (red oak) following laser exposure at the typical relative beam speed of U∗=U/Umax=0.6 and relative power of P∗=P/Pmax.=0.4. Image is taken by an inverted microscope (Unitron, Commack, NY) with a 10× magnification.

Figure 4

Effect of heat source shape on the quasi-steady maximum temperature for two typical aspect ratios, 0.1 and 0.5, and Peclet number of Pe=10

Figure 5

Effect of the aspect ratio on the maximum temperature of a plane moving heat source at various source speeds (Peclet number)

Figure 6

Maximum temperature as a function of Peclet number for aspect ratio of εm=1, a typical value. Note that two asymptotes for stationary, Pe→0, and fast moving heat source, Pe→∞, can be recognized in the present plot.

Figure 7

Variation in θmax∗/θmax,0∗ as a function of dimensionless depth for elliptical (n→2) and rectangular (n→∞) heat sources with Pe=10 and various aspect ratios

Figure 8

Maximum dimensionless temperature in a half-space. Rectangular heat source with Pe=2.86 and aspect ratio of εm=4.39; experimental data from Ref. 25; see Table 4 for the experiment parameters.

Figure 9

Effect of laser beam speed on the depth of engraved channels using single pass ablation. Square (◻) and delta (△) symbols are the present experimental measurements for percentage powers of 20% and 40%, respectively. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.

Figure 10

Effect of laser power on the depth of engraved channels using single pass ablation at maximum beam speed. Square (◻) symbols are the present experimental measurements maximum beam speed. Two limits of the reported ignition temperature are shown as the dashed line for 500°C and solid line for 420°C.

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G03 Chapter Contents
G03 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentG03BAF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

G03BAF computes orthogonal rotations for a matrix of loadings using a generalized orthomax criterion.

## 2  Specification

 SUBROUTINE G03BAF ( STAND, G, NVAR, K, FL, LDFL, FLR, R, LDR, ACC, MAXIT, ITER, WK, IFAIL)
 INTEGER NVAR, K, LDFL, LDR, MAXIT, ITER, IFAIL REAL (KIND=nag_wp) G, FL(LDFL,K), FLR(LDFL,K), R(LDR,K), ACC, WK(2*NVAR+K*K+5*(K-1)) CHARACTER(1) STAND

## 3  Description

Let $\Lambda$ be the $p$ by $k$ matrix of loadings from a variable-directed multivariate method, e.g., canonical variate analysis or factor analysis. This matrix represents the relationship between the original $p$ variables and the $k$ orthogonal linear combinations of these variables, the canonical variates or factors. The latter are only unique up to a rotation in the $k$-dimensional space they define. A rotation can then be found that simplifies the structure of the matrix of loadings, and hence the relationship between the original and the derived variables. That is, the elements, ${\lambda }_{ij}^{*}$, of the rotated matrix, ${\Lambda }^{*}$, are either relatively large or small. The rotations may be found by minimizing the criterion:
 $V=∑j=1k∑i=1p λij* 4-γp∑j=1k ∑i=1p λij* 2 2$
where the constant $\gamma$ gives a family of rotations with $\gamma =1$ giving varimax rotations and $\gamma =0$ giving quartimax rotations.
It is generally advised that factor loadings should be standardized, so that the sum of squared elements for each row is one, before computing the rotations.
The matrix of rotations, $R$, such that ${\Lambda }^{*}=\Lambda R$, is computed using first an algorithm based on that described by Cooley and Lohnes (1971), which involves the pairwise rotation of the factors. Then a final refinement is made using a method similar to that described by Lawley and Maxwell (1971), but instead of the eigenvalue decomposition, the algorithm has been adapted to incorporate a singular value decomposition.

## 4  References

Cooley W C and Lohnes P R (1971) Multivariate Data Analysis Wiley
Lawley D N and Maxwell A E (1971) Factor Analysis as a Statistical Method (2nd Edition) Butterworths

## 5  Parameters

1:     STAND – CHARACTER(1)Input
On entry: indicates if the matrix of loadings is to be row standardized before rotation.
${\mathbf{STAND}}=\text{'S'}$
${\mathbf{STAND}}=\text{'U'}$
Constraint: ${\mathbf{STAND}}=\text{'S'}$ or $\text{'U'}$.
2:     G – REAL (KIND=nag_wp)Input
On entry: $\gamma$, the criterion constant with $\gamma =1.0$ giving varimax rotations and $\gamma =0.0$ giving quartimax rotations.
Constraint: ${\mathbf{G}}\ge 0.0$.
3:     NVAR – INTEGERInput
On entry: $p$, the number of original variables.
Constraint: ${\mathbf{NVAR}}\ge {\mathbf{K}}$.
4:     K – INTEGERInput
On entry: $k$, the number of derived variates or factors.
Constraint: ${\mathbf{K}}\ge 2$.
5:     FL(LDFL,K) – REAL (KIND=nag_wp) arrayInput/Output
On entry: $\Lambda$, the matrix of loadings. ${\mathbf{FL}}\left(\mathit{i},\mathit{j}\right)$ must contain the loading for the $\mathit{i}$th variable on the $\mathit{j}$th factor, for $\mathit{i}=1,2,\dots ,p$ and $\mathit{j}=1,2,\dots ,k$.
On exit: if ${\mathbf{STAND}}=\text{'S'}$, the elements of FL are standardized so that the sum of squared elements for each row is $1.0$ and then after the computation of the rotations are rescaled; this may lead to slight differences between the input and output values of FL.
If ${\mathbf{STAND}}=\text{'U'}$, FL will be unchanged on exit.
6:     LDFL – INTEGERInput
On entry: the first dimension of the arrays FL and FLR as declared in the (sub)program from which G03BAF is called.
Constraint: ${\mathbf{LDFL}}\ge {\mathbf{NVAR}}$.
7:     FLR(LDFL,K) – REAL (KIND=nag_wp) arrayOutput
On exit: the rotated matrix of loadings, ${\Lambda }^{*}$. ${\mathbf{FLR}}\left(\mathit{i},\mathit{j}\right)$ will contain the rotated loading for the $\mathit{i}$th variable on the $\mathit{j}$th factor, for $\mathit{i}=1,2,\dots ,p$ and $\mathit{j}=1,2,\dots ,k$.
8:     R(LDR,K) – REAL (KIND=nag_wp) arrayOutput
On exit: the matrix of rotations, $R$.
9:     LDR – INTEGERInput
On entry: the first dimension of the array R as declared in the (sub)program from which G03BAF is called.
Constraint: ${\mathbf{LDR}}\ge {\mathbf{K}}$.
10:   ACC – REAL (KIND=nag_wp)Input
On entry: indicates the accuracy required. The iterative procedure of Cooley and Lohnes (1971) will be stopped and the final refinement computed when the change in $V$ is less than ${\mathbf{ACC}}×\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1.0,V\right)$. If ACC is greater than or equal to $0.0$ but less than machine precision or if ACC is greater than $1.0$, then machine precision will be used instead.
Suggested value: $0.00001$.
Constraint: ${\mathbf{ACC}}\ge 0.0$.
11:   MAXIT – INTEGERInput
On entry: the maximum number of iterations.
Constraint: ${\mathbf{MAXIT}}\ge 1$.
12:   ITER – INTEGEROutput
On exit: the number of iterations performed.
13:   WK($2×{\mathbf{NVAR}}+{\mathbf{K}}×{\mathbf{K}}+5×\left({\mathbf{K}}-1\right)$) – REAL (KIND=nag_wp) arrayWorkspace
14:   IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.
On exit: ${\mathbf{IFAIL}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6  Error Indicators and Warnings

If on entry ${\mathbf{IFAIL}}={\mathbf{0}}$ or $-{\mathbf{1}}$, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
${\mathbf{IFAIL}}=1$
 On entry, ${\mathbf{K}}<2$, or ${\mathbf{NVAR}}<{\mathbf{K}}$, or ${\mathbf{G}}<0.0$, or ${\mathbf{LDFL}}<{\mathbf{NVAR}}$, or ${\mathbf{LDR}}<{\mathbf{K}}$, or ${\mathbf{ACC}}<0.0$, or ${\mathbf{MAXIT}}\le 0$, or ${\mathbf{STAND}}\ne \text{'S'}$ or $\text{'U'}$.
${\mathbf{IFAIL}}=2$
The singular value decomposition has failed to converge. This is an unlikely error exit.
${\mathbf{IFAIL}}=3$
The algorithm to find $R$ has failed to reach the required accuracy in the given number of iterations. You should try increasing ACC or increasing MAXIT. The returned solution should be a reasonable approximation.

## 7  Accuracy

The accuracy is determined by the value of ACC.

If the results of a principal component analysis as carried out by G03AAF are to be rotated, the loadings as returned in the array P by G03AAF can be supplied via the parameter FL to G03BAF. The resulting rotation matrix can then be used to rotate the principal component scores as returned in the array V by G03AAF. The routine F06YAF (DGEMM) may be used for this matrix multiplication.

## 9  Example

This example is taken from page 75 of Lawley and Maxwell (1971). The results from a factor analysis of ten variables using three factors are input and rotated using varimax rotations without standardizing rows.

### 9.1  Program Text

Program Text (g03bafe.f90)

### 9.2  Program Data

Program Data (g03bafe.d)

### 9.3  Program Results

Program Results (g03bafe.r)


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Question: Explain natural sampling and flat top sampling. What is aliasing error? How it can be overcome?
0

Mumbai University > Electronics > Sem 4 > Priniciples of Communication Engineering

mumbai university pce • 1.8k views
 modified 8 months ago  • written 9 months ago by
0

NATURAL SAMPLING:

• Natural sampling is performed by multiplying w(t) by a train of pulses:

$$W_s(t) = w(t) s(t)$$

where

$$s(t) = \sum_{k=-\infty}^\infty P \left( \frac{t-kT_s}{\tau} \right)$$

• Natural sampling takes a slice of the waveform and the top of the slice preserves the shape of the waveform.
• PAM using natural sampling is as shown below:

FLAT TOP SAMPLING:

• In flat top sampling, the top of the samples remains constant and equal to the instantaneous value of the modulating signal at the start of the sampling.
• Thus the amplitude of the pulse after sampling is kept constant and the top of the sampled pulse do not follow the contour of the modulating signal unlike Natural sampling.
• The duration of each sample is τ and the sampling rate is fs=1/Ts
• Therefore, Ts=1/fs
• Sample and hold circuit is used for the generation of the sampled signal to attain flat top sampling.

Shannon's Sampling theorem:

• Sampling theorem states that in any pulse modulation system if the sampling rate of the samples exceeds twice the maximum signal frequency, then this ensures the reconstruction of the original signal in the receiver with minimum distortion.
• Sampling theorem can be expressed as given below: fs≥2fm Where, fs is the sampling frequency and fm is the maximum modulating signal frequency
• Sampling is a process of translating continuous analog signal into discrete analog signal, where the sampled signal is the discrete time representation of the original analog signal.

Aliasing:

• Aliasing is an effect that causes different signals to become indistinguishable from each other during sampling.

• Signal loss may occur due to aliasing effect.

Now, we may state the sampling theorem for strictly band limited signals of finite energy into two equivalent parts:

• A band limited signal of finite energy, which only has frequency components less than W Hertz, is completely described by specifying the values of the signal at instants of time separated by 1/2W seconds

• A band limited signal of finite energy which only has frequency components less than W Hertz , may be completely recovered from a knowledge of its sample taken at the rate of 2W samples per second.

The sampling rate of 2W samples per second for a signal bandwidth of W Hertz is called the Nyquist rate, its reciprocal 1/2W measured in seconds is called the Nyquist interval.

Fig: a) spectrum of a strictly band limited signal g(t)

b) spectrum of a sampled version of g(t) for $T_s$ = $\frac{1}{2W}$

NOTE : The concept of under sampling and over sampling is explained below.

• When sampling frequency $f_r =2W$ then this type of sampling is called correct sampling and here there is no aliasing effect seen in this mechanism i.e when $f_s = 2W$.

• When $f_s \lt 2W$ then it is under sampling and there will be aliasing effect induced here.

• When $f_s \gt 2W$ then it is over sampling and there will no aliasing effect.

The effect of aliasing can be reduced by :

• Pre-alias filter must be used to limit band of frequency of the required signal fm Hz.

• Sampling frequency fs must be selected such that sampling frequency is greater than twice the maximum modulating signal frequency.


text:
The Kepler Follow-Up Observation Program. II. Stellar Parameters from Medium- and High-Resolution Spectroscopy.

@article{Furlan2018TheKF,
title={The Kepler Follow-Up Observation Program. II. Stellar Parameters from Medium- and High-Resolution Spectroscopy.},
author={E. Furlan and D. Ciardi and W. Cochran and M. Everett and D. Latham and G. W. Marcy and L. Buchhave and M. Endl and H. Isaacson and E. Petigura and T. Gautier and D. Huber and A. Bieryla and W. Borucki and E. Brugamyer and C. Caldwell and A. Cochran and A. Howard and S. Howell and M. Johnson and P. MacQueen and S. Quinn and P. Robertson and S. Mathur and N. Batalha},
journal={arXiv: Solar and Stellar Astrophysics},
year={2018}
}
• E. Furlan, +22 authors N. Batalha
• Published 2018
• Physics
• arXiv: Solar and Stellar Astrophysics
• We present results from spectroscopic follow-up observations of stars identified in the Kepler field and carried out by teams of the Kepler Follow-Up Observation Program. Two samples of stars were observed over six years (2009-2015): 614 standard stars (divided into "platinum" and "gold" categories) selected based on their asteroseismic detections and 2667 host stars of Kepler Objects of Interest (KOIs), most of them planet candidates. Four data analysis pipelines were used to derive stellar… CONTINUE READING
12 Citations

References

SHOWING 1-10 OF 73 REFERENCES


text:
Show that $\gamma$ is a straight line [closed]

Let $\gamma : I \rightarrow \mathbb{R}^3$ be a parametretrized smooth curve with unit speed. Assume there exist a fixed vector $q$ such that $\gamma ''(s)=q, \ \forall s \in I$. Show that $\gamma$ is a straight line

How would one approach this?

I've thougt that since $\gamma$ have unit speed, then $||\gamma'(t)||=1,\ \forall t$ and then the arc length between any $t_1,t_2\in I$ would be $\int_{t_1}^{t_2} 1 \ dt=t_2-t_1$. But could I conclude it's a straight line from this, since the distance between two points, is just found by subtracting the to points with eachother

closed as off-topic by T. Bongers, Shailesh, Leucippus, Daniel W. Farlow, user91500Jun 22 '16 at 4:50

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – T. Bongers, Shailesh, Leucippus, Daniel W. Farlow, user91500
If this question can be reworded to fit the rules in the help center, please edit the question.

$\gamma''(s) = q$ gives $\gamma'(s) = qs + p$. Geometrically, $\gamma'$ is a straight line and every point on this straight line is at the same distance $1$ from the origin, so $\gamma'$ must be reduced to a point, hence $q = 0$ and $\gamma' = p$, with $\|p \|= 1$. This gives $\gamma = ps + c$. Another approach is to plug in several values of $s$ in the equation $\|qs + p\| = 1$, to get $q = 0$.
• Is it because $\gamma$ have unit speed, that every point on $\gamma'$ have distance 1 from origin? – jta Jun 21 '16 at 21:51
• @Jta yes, because a point on the image of $\gamma'$ takes the form $\gamma'(s)$, and $\|\gamma'(s)\| = 1$ – user258700 Jun 21 '16 at 21:52
• Thanks! But I don't see why it has to have unit speed? Wouldnt it work as long $||\gamma'(t)||=c,\ \forall t$ for some constant $c$? – jta Jun 21 '16 at 22:10
• @Jta of course it would, by the same reasoning. The reason why the question supposes that $\gamma$ is unit speed is that, in general, one is only interested in unit-speed curves because any (regular) curve with constant speed can be made into a unit-speed curve. – user258700 Jun 21 '16 at 22:17


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# Initial Length

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Initial Length Formulas

 $$\large{ l_i = \frac{ l_f }{ \overrightarrow{\alpha_l} \; \left( T_f \;- \; T_i \right) \;+\; 1 } }$$ (linear thermal expansion coefficient) $$\large{ l_i = \frac{ \Delta l }{ \epsilon } }$$ (strain)

### Where:

 Units English Metric $$\large{ l_i }$$ = initial length $$\large{ft}$$ $$\large{m}$$ $$\large{ l_f }$$ = final length $$\large{ft}$$ $$\large{m}$$ $$\large{ \Delta l }$$ = length differential $$\large{ft}$$ $$\large{m}$$ $$\large{ \overrightarrow{\alpha_l} }$$   (Greek symbol alpha) = linear thermal expansion coefficient $$\large{ \frac{1}{F} }$$ $$\large{ \frac{1}{C} }$$ $$\large{ \epsilon }$$  (Greek symbol epsilon) = strain $$\large{ \frac{in}{in} }$$ $$\large{\frac{mm}{mm}}$$ $$\large{ T_f }$$ = final temperature $$\large{F}$$ $$\large{C}$$ $$\large{ T_i }$$ = initial temperature $$\large{F}$$ $$\large{C}$$

Tags: Length Equations


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# AAPG Bulletin

Abstract

AAPG Bulletin, V. 87, No. 7 (July 2003),

P. 1123-1144.

## Release faults, associated structures, and their control on petroleum trends in the Recncavo rift, northeast Brazil

### Nivaldo Destro,1 Peter Szatmari,2 Fernando F. Alkmim,3 Luciano P. Magnavita4

1Petrobras Research Center, Ilha do Fundo, Quadra 7, 20179-900, Rio de Janeiro, Brazil; nivaldo@cenpes.petrobras.com.br
2Petrobras Research Center, Ilha do Fundo, Quadra 7, 20179-900, Rio de Janeiro, Brazil
3Department of Geology, Federal University of Ouro Preto, Morro do Cruzeiro, 35400-000, Ouro Preto, Minas Gerais, Brazil
4Petrobras Exploration and Production Department, Antnio Carlos Magalhes Avenue, 1113, 41856-900, Salvador, Bahia, Brazil

## AUTHORS

Nivaldo Destro received his degree in geology and an M.Sc. degree in structural geology from the Escola de Minas of the Federal University of Ouro Preto, where he is also conducting a Ph.D. project. He joined Petrobras in 1986 as an exploration geologist. Currently, he is a structural geologist at Petrobras Research Center in Rio de Janeiro, Brazil. His work has concentrated on the sealing properties of faults.

Peter Szatmari received his diploma in geology from the Eotvos University in Budapest, Hungary and his Ph.D. from the University of Edinburgh, United Kingdom. After a few years as a visiting fellow at Princeton University, United States and working as a consultant, he joined Petrobras Research Center in 1980, teaching and organizing research groups in tectonics. His main interests are the role of Fischer-Tropsch synthesis in petroleum origin and salt tectonics.

Fernando F. Alkmim received his degree in geology from the Escola de Minas of the Federal University of Ouro Preto (1978) and his Dr.rer.nat. degree in geology from the Technical University of Clausthal, Germany (1985). Alkmim is currently a professor at the Federal University of Ouro Preto, teaching field geology and tectonics. His research focuses on fault dynamics and Precambrian geology.

Luciano Magnavita received a degree in geology from the University of Braslia, Brazil, in 1976. He joined Petrobras in 1978, where he worked in the exploration department in Salvador. He obtained a Ph.D. in geology in 1992 from Oxford University, England. Since then, he has been working with several Brazilian basins. His main interests are tectonics and sedimentation in extensional basins, salt tectonics, and sealing processes associated with faulting.

## ACKNOWLEDGMENTS

This paper is a result of a Ph.D. project by N. Destro for Ouro Preto Federal University, Brazil. We thank Maria Alice N. F. de Arago for the helpful contribution in the identification of release faults in the Recncavo rift. Andr A. Bender made thoughtful review and suggestions on an earlier version of this manuscript. Walter B. Maciel and Carlos Eduardo B. de Salles Abreu are thanked for their thoughtful comments on the influence of release faults in the formation of turbidity systems. John H. Shaw, John Lorenz, and an anonymous referee are thanked for their thorough, helpful, and constructive reviews. We thank Petrobras for provision of financial support and permission to publish. F. F. Alkmim received support from CNPq (Brazilian Council for the Scientific and Technological Development) grant #300833/99-7.

## ABSTRACT

Release faults are rift cross faults, which develop to accommodate the variable displacements of the hanging-wall block along the strike of normal faults. Release faults are nearly perpendicular or obliquely oriented to the strike of the normal fault they are related to. They have maximum throws adjacent to the parent normal fault and die out in the hanging wall away from it. They form to release the bending stresses in the hanging wall and do not reflect the orientation of the regional stress field in a basin. Commonly, they show normal-oblique displacements and are preferentially located along the strike ramps. Release faults may also act at the scale of an entire basin, reaching displacements of thousands of meters. Joints, shale, and salt diapirs may develop in association with release faults. Because all these structures represent domains of stress release, they may work as conduits for oil migration and oil traps in extensional basins. This is the case of the Recncavo basin in northeastern Brazil, a Cretaceous failed rift, connected to the eastern Brazilian continental margin basins. In the Recncavo basin, two large-scale release faults, with displacements in the order of 3 km, developed in the hanging wall of the rift border faults and control the location of the main oil fields.

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Diference between Vrms & ac value of a signal

1. Jan 26, 2008

sphyics

What is Vrms value. How can i measure it practically with whatever instruments (read voltmeter, oscilloscope). is it some mathematical stuff or we can measure it directly as voltage is measured.

so please tell me the difference between rms value and ac value of a signal, is rms value releated to some heating effect.....

Last edited: Jan 26, 2008
2. Jan 26, 2008

dlgoff

For a sinusoidal wave, you can measure peak voltage, peak-to-peak voltage, average voltage over a half-cycle, or effective (Root Mean Square) voltage. RMS voltage of an ac source is usually what you will measure with your hand-held multimeter.

3. Jan 28, 2008

Ouabache

You could also use your oscilloscope, read the peak voltage and multiply by 0.707 (or more specifically, by $\sqrt {2}/2$). If you take a look at this page it may clarify the meaning for you.

4. Jan 28, 2008

sphyics

thanks dlgoff, Ouabache for the valuable informations.


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# Do ℕ, \mathbb{N}, \BbbN, \symbb{N} effectively differ, and is there a “canonical” specification of the naturals?

Continuing https://math.meta.stackexchange.com/a/22167/, as far as I understand, all the four of ℕ, \mathbb{N}, \BbbN, \symbb{N} work now, and \BbbN is advised against. Is there any reasonably default context (e.g., a self-constructed context that would redefine these macros and symbols wouldn't count) in which some of ℕ, \mathbb{N}, \BbbN, \symbb{N} produce different results than some others when using amssymb+unicode-math+{xe|lua}latex? Compiling the example

\documentclass{book}
\usepackage{fontspec}
\usepackage{amssymb}
\usepackage{unicode-math}
\usepackage{microtype}
\setmainfont{TeX Gyre Termes}
\setsansfont{TeX Gyre Heros}[Scale=0.88]
\setmonofont{TeX Gyre Cursor}
\setmathfont{TeX Gyre Termes Math}
\setmathfont{Asana Math}[
range={\setminus},
]
\setmathfont{XITSMath-Regular}[
Extension=.otf,
range={"2A3E},
BoldFont=XITSMath-Bold,
]
\begin{document}
$$ℕ \mathbb{N} \BbbN \symbb{N}$$
\end{document}

with xelatex, e.g., I get visibly indistinguishable letters

ℕℕℕℕ

I cannot distinguish them either when I put them as subscripts or superscripts.

Moreover, is there a consensus in the {xe|lua}[La]TeX world to name any of these ways as the standard way to denote the set of natural numbers?

(Of course, I leave aside the question whether the zero should belong to this set or not; it could flame up a war here and is up to the author anyway.)

## tl;dr

It's completely the same.

## Why do those four inputs produce the same output?

In unicode-math-table.tex we find

\UnicodeMathSymbol{"02115}{\BbbN}{\mathalpha}{/bbb n, open face n}

Every Unicode code point relevant for math has a name, so that unicode-math can do, in this case, the equivalent of

\Umathchardefℕ = "7 "0 "02115

(the second number could change in case range=bb is used to select a different font for these characters).

If you add \show\mathbb to your sample TeX file (after \begin{document}), you'll get

> \mathbb=\long macro:
->\symbb .

1. typing ℕ or \BbbN is the same
2. typing \mathbb{N} or \symbb{N} is the same

It only remains to discover what's the relationship between the two cases above. Simple: \symbb{N} does \BbbN. Not really by chaining N to Bbb, but something like that (it's more complicated because one can use range=bb to use a different font for blackboard bold letters).

Now we know that typing

$ℕ \BbbN \mathbb{N} \symbb{N}$

is exactly the same. The alias name \mathbb for \symbb is for backwards compatibility with older code.

Some explanation is in order. unicode-math used to have just \mathXX commands. However, it was realized that distinguishing between \mathXX and \symXX is necessary. The first form is about words used in math, the second form for single characters (and doesn't enforce ligatures if used for more characters in a row); these forms can point to different fonts. Typically, for instance, \mathbf will use the boldface text font, whereas \symbf{x} will use \mbfx, pointing to U+1D431 in the math font.

While the distinction is necessary for boldface, in the case of blackboard bold there is no usage of it as a text font, so no distinction is made between \mathbb and \symbb, by default. You (or a package) might redefine \mathbb to do something else (not that I recommend it).

## What's the preferred form?

I'd avoid \BbbN and probably prefer \symbb for newer documents, unless it's possible to directly type in ℕ.

• @user49915 Yes, indeed. Let me fix it: I copied the first match, but didn't notice the case. – egreg Apr 12 '19 at 13:26

The difference is mainly historical. \BbbN was created for the original amsfonts, pre-LaTeX; it should be considered obsolete now. (Oops! @egreg points out in a comment that \BbbN has been defined for unicode-math, so I was thinking of \Bbb{N}. That surely should be considered obsolete.) The original LaTeX equivalent is \mathbb{N}, and should still be reliable.

\symbb{N} was defined for fonts developed after the blackboard bold alphabet was added to Unicode.

The symbol itself (which I can't represent because it's not available on the aged laptop I'm using) depends on having a utf-8 capable input device, and is not available for pdflatex, which is still limited to 8-bit input.

All forms are equivalent, and the one you use depends on which flavor of LaTeX you're using. There may also be some restrictions associated with the publisher, if you're submitting your document for publication.

This may not give an unambiguous answer to your question, but it should give you some idea of how the development of the blackboard bold fonts and their support affects the decision of which should be used in what circumstances.

• \BbbN is a specific command in unicode-math. The command \Bbb (with an argument) is obsolete. – egreg Apr 12 '19 at 6:24

If you modify your file to have

\showoutput
$$ℕ \mathbb{N} \BbbN \symbb{N} \showlists$$

Then you get

\mathord
.\fam0 ℕ
\mathord
.\fam0 ℕ
\mathord
.\fam0 ℕ
\mathord
.\fam0 ℕ
### horizontal mode entered at line 20

Four identical N, same font and same math class (mathord).

I would say use ℕ if you like Unicode input and \symbb{N} if you prefer ASCII TeX command markup. So they are the preferred forms, but as they are all the same thing it doesn't matter much which you use.

Of course other font setups may make things differ. In general \symxx will give you characters from the same font using the math alphabet ranges, whereas \mathxx might do that or might (as in classic tex) use a different font.

• I'd use \mathbbm of the bbm package for all blackboard bold letters: clean, nice, slender. Blackboard bold is nowhere bold on the blackboard, this is why we simply double some of the lines. \mathbb N makes the slanted line bold. – Máté Wierdl Apr 16 '19 at 20:32
• @MátéWierdl bbm font is OK if it fits with the overall font design but if you use unicode-math \symbb then the blackboard bold N comes from the same font as the normal N and is chosen by the font designer to match. – David Carlisle Apr 16 '19 at 21:44
• I see, @DavidCarlisle. How do I access \symbb in pdflatex? – Máté Wierdl Apr 18 '19 at 1:23
• @MátéWierdl \symbb is unicode-math so just xetex or luatex, the whole point of \symxx` commands is that they access the math alphabets from the same font, position 8469 in the case of ℕ that can not mean anything in pdftex which has at most 256 characters per font, and most math fonts only have 128 characters – David Carlisle Apr 18 '19 at 7:26


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### Identifier Expected Error in JSP page

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Hello,I have a war file that when I deploy on one server works, however onanother server I am getting an Identifier Expected error on thisfunctionpublic List<String> func()The error is saying that it is expecting a variable instead of<String.  Is this an issue with Java 1.5 not being configured on thatmachine?Thanks for any help you can provide.  I am using GoDaddy as a providerand it works on their shared host but when I got a virtual dedicatedhost and deployed the war file this is what I'm getting.  I also gottheir service plan which prevents me from lookin at the server...  Ican't ssh in.Thank you for any help you can provide.-Jia
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On Thu, 28 Jun 2007 19:08:10 -0700, jiali2121@yahoo.com wrote, quotedor indirectly quoted someone who said :>I have a war file that when I deploy on one server works, however on>another server I am getting an Identifier Expected error on this>function>public List<String> func()See http://mindprod.com/applets/wassup.htmland http://mindprod.com/jgloss/properties.htmlto learn about system properties, in particular java.version.Then you can dump out what version you are running in a tiny test app.--Roedy Green Canadian Mind ProductsThe Java Glossaryhttp://mindprod.com
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# Spring 2017

Date: 14 February 2017, CB 3.7, 14:15

Kate Button & Michelle St Clair (Bath) (Joint seminar)

(Kate Button) Personalising psychological care

Abstract: Depression and anxiety are leading causes of disability in the UK. Improving access to psychological therapies (IAPT) aims to reduce this disability by making ‘talking therapies’ available through the NHS. IAPT has been a success, providing therapy to those who would have otherwise not had access, and half of patients referred make a full recovery. However, we can still do better. The aim of this research is to use routinely collected IAPT data to identify optimal care regimes for a given patient. By providing evidence to tailor psychological care to the individual, we aim to further improve recovery rates.

(Michelle St Clair) Statistics and Human Development: Characterising developmental trajectories and (causal) pathways through childhood, adolescence and adulthood

Abstract: I will be giving a short overview of my research with regard using large scale longitudinal projects and/or longitudinal cohort databases to evaluate developmental trajectories using complex multivariate person centred and variable centred statistical techniques. I will also evaluate some work that is looking at possible causal pathways or relationships between experiences in early life and outcomes in later life using longitudinal cohort data.

Date: 17 Feb 2017, 4W 1.7, 15:15 (Landscapes seminar)

Adrian Bowman (Glasgow)

Surfaces, shapes and anatomy

Abstract: Three-dimensional surface imaging, through laser-scanning or stereo-photogrammetry, provides high-resolution data defining the surface shape of objects. In an anatomical setting this can provide invaluable quantitative information, for example on the success of surgery. Two particular applications are in the success of facial surgery and in developmental issues with associated facial shapes. An initial challenge is to extract suitable information from these images, to characterise the surface shape in an informative manner. Landmarks are traditionally used to good effect but these clearly do not adequately represent the very much richer information present in each digitised images.
Curves with clear anatomical meaning provide a good compromise between informative representations of shape and simplicity of structure, as well as providing guiding information for full surface representations. Some of the issues involved in analysing data of this type will be discussed and illustrated. Modelling issues include the measurement of asymmetry and longitudinal patterns of growth.

Date: 14 March 2017, CB 3.7, 13:15

Kari Heine (Bath)

TBA

Date: 28 March 2017, CB 3.7, 13:15

Paul Northrop (UCL)

Extreme value threshold selection

Abstract: A common form of extreme value modelling involves modelling excesses of a threshold by a generalised Pareto (GP) distribution. The GP model arises by considering the possible limiting distributions of excesses as the threshold increased. Selecting too low a threshold leads to bias from model mis-specification; raising the threshold increases the variance of estimators: a bias-variance trade-off. Many existing threshold selection methods do not address this trade-off directly, but rather aim to select the lowest threshold above which the GP model is judged to hold approximately. We use Bayesian cross-validation to address the trade-off by comparing thresholds based on predictive ability at extreme levels. Extremal inferences can be sensitive to the choice of a single threshold. We use Bayesian model averaging to combine inferences from many thresholds, thereby reducing sensitivity to the choice of a single threshold. The methodology is illustrated using significant wave height datasets from the North Sea and from the Gulf of Mexico.

Date: 25 April 2017, CB 3.7, 13:15

Heather Battey (Imperial)

Exploring and exploiting new structured classes of covariance and inverse covariance matrices

Abstract: Estimation of covariance and inverse covariance (precision) matrices is an essential ingredient to virtually every modern statistical procedure. When the dimension, p, of the covariance matrix is large relative to the sample size, the the sample covariance matrix is inconsistent in non-trivial matrix norms, and its non-invertibilty renders many techniques in multivariate analysis impossible. Structural assumptions are necessary in order to restrain the estimation error, even if this comes at the expense of some approximation error if the structural assumptions fail to hold. I will introduce new structured model classes for estimation of large covariance and precision matrices. These model classes result from imposing sparsity in the domain of the matrix logarithm. After studying the structure induced in the original and inverse domains, I will then introduce estimators of both the covariance and precision matrix that exploit this structure. I derive the convergence rates of these estimators and show that they achieve a new minimax lower bound over classes of covariance and precision matrices whose matrix logarithm is sparse. The implication of this result is that the estimators are efficient and the minimax lower bound is sharp.

Date: 2 May 2017, CB 3.7, 13:15

Anthony Lee (Warwick)

TBA

Date: 9 May 2017, CB 3.7, 13:15

Tiago de Paula Peixoto (Bath)

TBA

Date: 16 May 2017, CB 3.7, 13:15

Stats PhD students (Bath)

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# Autumn 2016

Date: 11 October 2016, CB 5.8, 13:15

Daniel Falush (Bath)

The painting palettes of human ancestry

Abstract: Genomic technology is advancing at a remarkable pace and provide a great deal of information on our origins but requires new statistical technology to analyze. I will describe our chromosome painting approach to summarizing ancestry information (available from here). A Hidden Markov Model is used to fit each individual as a mosaic of the other individuals in the sample. A summary of this painting is used to subdivide the sample into populations with discrete ancestry profiles, using a merge-split sampler. I illustrate the application of this method to subdivide the British Isles into 17 regions with distinct ancestry profiles. Historical admixture events can be explored using mixture modelling. I show how Non Linear Least Squares and curve fitting can be used to estimate global admixture events in the last 3,000 years.

Date: 25 October 2016, CB 5.8, 13:15

Francisco Javier Rubio (LSHTM)

Tractable Bayesian variable selection: beyond normality

Abstract: Bayesian variable selection for continuous outcomes often assumes normality, and so do its theoretical studies. There are sound reasons behind this assumption, particularly for large $$p$$: ease of interpretation, analytical and computational convenience. More flexible frameworks exist, including semi- or non-parametric models, often at the cost of losing some computational or theoretical tractability. We propose a simple extension of the Normal model that allows for skewness and thicker-than-normal tails but preserves its tractability. We show that a classical strategy to induce asymmetric Normal and Laplace errors via two-piece distributions leads to easy interpretation and a log-concave likelihood that greatly facilitates optimization and integration. We also characterize asymptotically its maximum likelihood estimator and Bayes factor rates under model misspecification. Our work focuses on the likelihood and can thus be combined with any likelihood penalty or prior, but here we adopt non-local priors, a family that induces extra sparsity and which we characterize under misspecification for the first time. Under suitable conditions Bayes factor rates are of the same order as those that would be obtained under the correct model, but we point out a potential loss of sensitivity to detect truly active covariates. Our examples show how a novel approach to infer the error distribution leads to substantial gains in sensitivity, thus warranting the effort to go beyond normality, whereas for near-normal data one can get substantial speedups relative to assuming unnecessarily flexible models.

The methodology is available as part of R package mombf.

Joint work with David Rossell.

Date: 1 November 2016, CB 5.8, 13:15

Keming Yu (Brunel)

Data Adaptive Tail-index Regression

Abstract: Tail-index is an important measure to gauge the heavy-tailed behavior of a distribution. The problem of estimation of a Tail-index from various types of data has become rather important. Tail-index regression is introduced when covariate information is available. Inference of Tail-index regression may face two challenges: small sample bias with the analysis of small to moderate size data and the problem of storage and computational efficiency with dealing with massive data. In this paper we derive new statistical inference for Tail-index regression based on Pareto-type of distributions and Burr-XII distributions.

Date: 15 November 2016, CB 5.8, 13:15

Theresa Smith (Bath)

Age-period-cohort models for cancer incidence

Abstract: Age-period-cohort models have been used to examine and forecast cancer incidence and mortality for over three decades. However, the fitting and interpretation of these models requires great care because of the well-known identifiability problem that exists; given any two of age, period, and cohort, the third is determined.

In this talk I introduce APC models and the identifiability problem. I examine proposed ‘’solutions’’ to this problem and approaches based on an identifiable parameterization. I conclude with an analyis of cancer incidence data from Washington State and a discussion of future research directions.

Date: 21 November 2016, CB 3.16, 13:15 (Note different time and venue)

Adam Johansen (Warwick)

Search and Jump Algorithm for Markov Chain Monte Carlo Sampling

Abstract: We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associated marginal likelihood L is central to likelihood-based inference for unknown statistical parameters. We define a class of “twisted” models: each member is specified by a sequence of positive functions psi and has an associated psi-auxiliary particle filter that provides unbiased estimates of L. We identify a sequence psi* that is optimal in the sense that the psi-auxiliary particle filter’s estimate of L has zero variance. In practical applications, psi is unknown so the psi-auxiliary particle filter cannot straightforwardly be implemented. We use an iterative scheme to approximate psi, and demonstrate empirically that the resulting iterated auxiliary particle filter significantly outperforms the bootstrap particle filter in challenging settings. Applications include parameter estimation using a particle Markov chain Monte Carlo algorithm and approximation of conditioned diffusion sample paths. [arxiv: 1511.06286]

Joint work with Pieralberto Guarniero and Anthony Lee

Date: 22 November 2016, CB 5.8, 13:15

Chris Jennison (Bath)

Search and Jump Algorithm for Markov Chain Monte Carlo Sampling

Abstract: MCMC sampling is now established as a fundamental tool in statistical inference but there are still problems to solve. MCMC samplers can mix slowly when the target distribution has multiple modes. A more insidious problem arises when sampling a distribution that is concentrated on a thin sub-region of a high-dimensional sample space. I shall present a new approach to mode-jumping and show how this can be used to sample from some challenging “thin” distributions.

Joint work with Adriana Ibrahim, University of Malasya.

Date: 6 December 2016, CB 5.8, 13:15

Sam Livingstone (Bristol)

Some recent advances in dynamics-based Markov chain Monte Carlo

Abstract: Markov chain Monte Carlo methods based on continuous-time dynamics such as Langevin diffusions and Hamiltonian flow are among the state of the art when performing inference for challenging models in many application areas. I will talk about some statistical models which Markov chains produced by these methods can explore well, and others for which they often struggle to do so. I’ll discuss some existing and new algorithms that use gradient information and/or exploit the geometry of the space through an appropriate Riemannian metric, and how these inputs can both positively and negatively affect exploration, using the notion of geometric ergodicity for Markov chains.

Date: 13 December 2016, CB 5.8, 13:15

Ilaria Prosdocimi (Bath)

A statistician’s wander into flood hydrology

Abstract: In the design and maintenance of structures such as dams or drainage networks, it is essential to be able to obtain reliable estimates of the magnitude and frequency of extreme events such as high river flow and rainfall totals. This talk will discuss methods to perform such estimation, focusing on similarities and differences of the different approaches developed by statisticians and civil engineers. Rather than presenting final results, the talk will focus on discussing the open challenges in the statistical methods for flood frequency estimation and will suggest possible future research avenues.

# Spring 2016

Date: 19 April 2016, CB 5.1, 14:15

Nick Whiteley (Bristol)

Variance estimation in the particle filter

Abstract: Particle filters provide sampling based approximations of marginal likelihoods and filtering expectations in hidden Markov models. However, estimating the Monte Carlo variance of these approximations, without generating multiple independent realizations of the approximations themselves, is not straightforward. We present an unbiased estimator of the variance of the marginal likelihood approximation, and consistent estimators of the asymptotic variance of the approximations of the marginal likelihood and filtering expectations. These estimators are byproducts of a single run of a particle filter and have no added computational complexity or storage requirements. With additional storage requirements, one can also consistently estimate higher-order terms in the non-asymptotic variance. This is information can be used to approximate the variance-optimal allocation of particle numbers.

Joint work with Anthony Lee, University of Warwick

Date: 26 April 2016, CB 5.1, 14:15

Statistical shape analysis in a Bayesian framework for shapes in two and three dimensions

Thomai Tsiftsi (Bath)

Abstract: Shape analysis is an integral part of object classification and has been used as a tool by many branches of science such as computer vision, pattern recognition and shape classification. In this talk I will present a novel shape classification method which is embedded in the Bayesian paradigm and utilises the efficacy of geometrical statistics as well as differential geometry. I will focus on the statistical classification of planar shapes by using techniques which replace some previous approximate results by analytic calculations in a closed form. This gives rise to a new Bayesian shape classification algorithm of which the efficiency was tested on available shape databases. Finally, I will conclude by demonstrating the extension of the proposed classification algorithm for shapes in three-dimensions.

Date: 3 May 2016, CB 5.1, 14:15

Hilbertian Fourth Order Blind Identification

Germain Van Bever (Open University)

Abstract: In the classical Independent Component (IC) model, the observations $$X_1,\cdots,X_n$$ are assumed to satisfy $$X_i=\Omega Z_i$$, $$i=1,\dots,n$$, where the $$Z_i$$’s are i.i.d random vectors with independent marginals and $$\Omega$$ is the mixing matrix. Independent component analysis (ICA) encompasses the set of all methods aiming at $$X=(X_1,\dots,X_n)$$, that is estimating a (non unique) unmixing matrix $$\Gamma$$ such that $$\Gamma X_i$$, $$i=1,\dots,n$$, has independent components. Cardoso (1989) introduced the celebrated Fourth Order Blind Identification (FOBI) procedure, in which an estimate of $$\Gamma$$ is provided, based on the regular covariance matrix and a scatter matrix based on fourth moments. Building on robustness considerations and generalizing FOBI, Invariant Coordinate Selection (ICS, 2009) was originally introduced as an exploratory tool generating an affine invariant coordinate system. The obtained coordinates, however, are proved to be independent in most IC models.

Nowadays, functional data (FD) are occurring more and more often in practice, and only little statistical techniques have been developed to analyze this type of data (see, for example Ramsay and Silverman 2006). Functional PCA is one such technique which only aims at dimension reduction with very little theoretical considerations. In this talk, we propose an extension of the FOBI methodology to the case of Hilbertian data, FD being the go-to example used throughout. When dealing with distributions on Hilbert spaces, two major problems arise: (i) the scatter operator is, in general, non-invertible and (ii) there may not exist two different affine equivariant scatter functionals. Projections on finite dimensional subspaces and Karhunen-Lo`eve expansions are used to overcome these issues and provide an alternative to FPCA. More importantly, we show that the proposed construction is Fisher consistent for the independent components of an appropriate Hilbertian IC model.

Affine invariance properties of the resulting FOBI components will be discussed and potential extension to a FICS procedure will be sketched. Simulated and real data are analyzed throughout the presentation to illustrate the properties and the potential benefits of the new tools.

This work is supported by the EPSRC grant EP/L010429/1.

References

• J.F. Cardoso (1989), Source Separation Using Higher Moments Proceedings of IEEE international conference on acoustics, speech and signal processing 2109-2112.

• D. Tyler, F. Critchley, L. Dumbgen and H. Oja (2009), Invariant Co-ordinate Selection J.R. Statist. Soc. B., 2009,71, 549-592.

• J. Ramsay and B.W. Silverman (2006) Functional Data Analysis 2nd edn. Springer, New York

# Autumn 2015

Date: 13 October 2015, 8W 2.13, 13:15

Evangelous Evangelou (Bath)

Writing and publishing your own R package: Some techniques and useful tools.

Abstract: Publishing an R package requires quality code but also adherence to CRAN policies. I will present some techniques for automating the process of creating and maintaining an R package the and some good practices from my experience as a package author.

Date: 20 October 2015, 8W 2.13, 13:15

Causal Models and How to Refute Them

Robin Evans (Oxford)

Abstract: Directed acyclic graph models (DAG models, also called Bayesian networks) are widely used in the context of causal inference, and they can be manipulated to represent the consequences of intervention in a causal system. However, DAGs cannot fully represent causal models with confounding; other classes of graphs, such as ancestral graphs and ADMGs, have been introduced to deal with this using additional kinds of edge, but we show that these are not sufficiently rich to capture the range of possible models. In fact, no mixed graph over the observed variables is rich enough, regardless of how many edges are used. Instead we introduce mDAGs, a class of hyper-graphs appropriate for representing causal models when some of the variables are unobserved. Results on the Markov equivalence of these models show that when interpreted causally, mDAGs are the minimal class of graphs which can be sensibly used. Understanding such equivalences is critical for the use of automatic causal structure learning methods, a topic in which there is considerable interest. We elucidate the state of the art as well as some open problems.

Date: 27 October 2015, 8W 2.13, 13:15

Jonty Rougier (Bristol)

Predicting large explosive eruptions for individual volcanoes

Abstract:Large explosive volcanic eruptions can be devastating, given that many volcanoes capable of such eruptions are close to cities. But data, on which predictions could be based, is very limited. Globally, such eruptions happen about once every two years, but the record is rapidly thinned going backwards in time, where the rate of under-recording depends not just on time, but also on location and magnitude. I describe our approach to assessing the under-recording rate, and to making predictions for sets of volcanoes with similar recorded histories, based on an exchangeable model of eruption rates. This is part of our larger project to provide a return period curve for each volcano. This is joint work with volcanologists Profs Steve Sparks and Kathy Cashman.

Date: 10 November 2015, 8W 2.13, 13:15

Haakon Bakka (NTNU)

A spatial random effect with one range for each region (the Difficult Terrain model component)

Abstract:Classical models in spatial statistics assume that the correlation between two points depends only on the distance between them (i.e. the models are stationary). In practice, however, the shortest distance may not be appropriate. Real life is not stationary! For example, when modelling fish near the shore, correlation should not take the shortest path going across land, but should travel along the shoreline. In ecology, animal movement depends on the terrain or the existence of animal corridors. We will show how this kind of information can be included in a spatial non-stationary model, by defining a different spatial range (distance) in each region.

We will answer the following questions:

• How to make a model with one range in each region?
• Is the algorithm fast enough for real data? (Hint: Yes!)
• How to avoid overfitting with flexible random effects?
• How to interpret the inference when you have flexible random effects?
• How do we model a point process with different cluster sizes in different regions, without changing the average number of points?

Date: 17 November 2015, 8W 2.13, 13:15

Daniel Williamson (Exeter)

Earth system models and probabilistic Bayesian calibration: a screw meets a hammer?

Abstract: The design and analysis of computer experiments, now called “Uncertainty Quantification” or “UQ” has been an active area of statistical research for 25 years. One of the most high profile methodologies, that of calibrating a complex computer code using the Bayesian solution to the inverse problem as described by Kennedy and O’Hagan’s seminal paper in 2001, has become something of a default approach to tackling applications in UQ and has over 1200 citations. However, is this always wise? Though the method is well tested and arguably appropriate for many types of model, particularly those for which large amounts of data are readily available and in which the limitations of the underlying mathematical expressions and solvers are well understood, many models, such as those found in climate simulation, go far beyond those successfully studied in terms of non-linearity, run time, output size and complexity of the underlying mathematics.

Have we really solved the calibration problem? To what extent is our “off the shelf approach” appropriate for the problems faced in fields such as Earth system modelling? In this talk we will discuss some of the known limitations of the Bayesian calibration framework (and some perhaps unknown) and we explore the extent to which the conditions in which calibration is known to fail are met in climate model problems. We will then present and argue for an alternative approach to the problem and apply it an ocean GCM known as NEMO.

Date: 24 November 2015, 8W 2.13, 14:15 (Note the kick-off time of 2:15)

Georg Lindgren (Lund)

Stochastic models for ocean waves - Gaussian fields made more realistic by Rice formula and some physics

Abstract: Gaussian fields were introduced in the early fifties as models for irregular ocean waves and they have been used in ocean engineering ever since. A simple modification leads to the more realistic stochastic Lagrange models, which account for horizontal and vertical movements of individual water particles, leading to realistic asymmetry of the generated waves.

Rice formula for the expected number of level crossings and its modern implementation to “level sets” makes it possible to derive exact statistical distributions for many important wave characteristics, like steepness and asymmetry. In the talk I will describe the stochastic Lagrange model and some of its statistical properties.

Date: 9 December 2015, CB 4.1, 13:15 (Note the different day (Wednesday) and venue)

John Copas (Warwick)

Title Model choice and goodness of fit

Abstract: How do we know whether a statistical model is sensible? The usual answer is to check that the model gives a reasonable fit to the data. The seminar will look at the variation between inferences based on different models, and show that this can be extremely large, even amongst models which seem to fit the data equally well. What does this tell us about most applications of statistics which completely ignore the problem of model uncertainty? What does it tell us about formal methods of model selection and model averaging which all, directly or indirectly, depend on model fit?


text:
## score counter and putting objects to collect

Questions about the LÖVE API, installing LÖVE and other support related questions go here.
Forum rules
Before you make a thread asking for help, read this.
Saltyham
Prole
Posts: 7
Joined: Wed Jul 10, 2013 6:23 pm

### score counter and putting objects to collect

Hello everyone I've just recently started using love2d and being a coding novice how would I put a score counter and what would be the quickest way to put down Items that disappear when the player touches them and add to the score counter any hints or tips would be nice
micha
Inner party member
Posts: 1083
Joined: Wed Sep 26, 2012 5:13 pm

### Re: score counter and putting objects to collect

Create a table. Let's say you call it "objectList". Then store all objects that are on screen in this table. Each object itself is a table again, holding data like the coordinates, height, width and the image. In the draw-part you loop over all entries to draw them. In the update-part you have to check for collision with the player. If so, remove the object from objectList.

For a score counter you could create a global variable called score and increase it, whenever a collision with one of the objects happens.

If I remember correctly, you can find some information on collecting items in this tutorial.
Saltyham
Prole
Posts: 7
Joined: Wed Jul 10, 2013 6:23 pm

### Re: Didn't help much :/

Still Having a hard time figuring this out, How would this code look, what would be in it.
seanmd
Prole
Posts: 35
Joined: Sat Jun 22, 2013 7:47 am

### Re: score counter and putting objects to collect

Is there a piece of your code where powerups are marked as collected or destroyed? In that chunk of code increment a score variable that you initialize to zero upon entering the game state. It all sort of depends on how your game is structured as to how you go about keeping track of things.

an overly simplified example:

Code: Select all

local levelScore = 0

function game:enter()
...
levelScore = 0
...
end

local function collect(collectible)
...
levelScore = levelScore + collectible.value
...
end

Saltyham
Prole
Posts: 7
Joined: Wed Jul 10, 2013 6:23 pm

### Re: score counter and putting objects to collect

Thanks, but the issue I'm worried about at the moment is making the objects disappear when the player is over them. If you have any code for that I would be most grateful.
davisdude
Party member
Posts: 1154
Joined: Sun Apr 28, 2013 3:29 am
Location: North Carolina

### Re: score counter and putting objects to collect

It would be easier if you posted a .love. Then we could truly help you.
GitHub | MLib - Math and shape intersections library | Walt - Animation library | Brady - Camera library with parallax scrolling | Vim-love-docs - Help files and syntax coloring for Vim
Saltyham
Prole
Posts: 7
Joined: Wed Jul 10, 2013 6:23 pm

### Re: score counter and putting objects to collect

Its a bit bad but here ya go.
Attachments
The adventure of based god.love
My.Love
(1.67 MiB) Downloaded 125 times
davisdude
Party member
Posts: 1154
Joined: Sun Apr 28, 2013 3:29 am
Location: North Carolina

### Re: score counter and putting objects to collect

Your game is not really all that bad (albeit a bit strange)

I chose to make little fruits to eat for your 'based god'
I made it so that about half of you had to be over it in order to be able to eat it.

Notes:
The Title (The adventures of lil B) becomes red when you scroll over 'quit'.
You registered the image 'baseland' twice.
Player movement is rather sluggish.

I fixed some other things too, but you're probably really only interested in the 'fruits.lua' bit.

If you have any questions about the code, feel free to ask!
I mostly did performance related things, although it still loads extremely slowly for me...

The score counter will be homework...
Attachments
the adventure of based god.love
(1.67 MiB) Downloaded 131 times
GitHub | MLib - Math and shape intersections library | Walt - Animation library | Brady - Camera library with parallax scrolling | Vim-love-docs - Help files and syntax coloring for Vim
Saltyham
Prole
Posts: 7
Joined: Wed Jul 10, 2013 6:23 pm

### Re: score counter and putting objects to collect

Thank you very much for the help, I'm gonna reverse engineer the hell out of additions you put in. also instead of making the fruits disappear could i change them into another graphic, also is there a way to get a sound effect for the picking up of the fruits?
Plu
Inner party member
Posts: 722
Joined: Fri Mar 15, 2013 9:36 pm

### Re: score counter and putting objects to collect

Certainly. Probably the best way is, on pickup, replace the fruit with a new entity with a different image, but the same location. This will also prevent old code from trying to pick the new image up as well (because the code should only respond to collisions with specific objects)

You can play sound using

Code: Select all

soundFile = love.audio.newSource( 'filename.wav' )

to load the sound (give it a filename to the sound and call it ONCE during loading) and you can play the sound fragment by calling

Code: Select all

love.audio.play( soundFile )

### Who is online

Users browsing this forum: Bing [Bot], Google [Bot] and 6 guests


text:
# Graceful graphs all of whose vertices are labelled with primes or squares

Do graceful graphs exist with more than any arbitrarily large number of vertices, all of which are labelled with a prime or non-negative square number.

Recall that a graceful graph is a graph with m edges whose vertices can be labelled with some subset of the integers between 0 and m inclusive, no two vertices sharing a label, and each of its edges uniquely identified by the absolute difference between its end points (so that this magnitude lies between 1 and m inclusive).

There is evidence (https://math.stackexchange.com/questions/3253495/integers-as-differences-of-squares-and-primes/3253666#3253666) that the answer to this is no, but a proof is lacking.

This graphs shows the number of numbers between $$1$$ and $$n$$ that are left out.