text:
# Chebyshev2D¶

class astropy.modeling.polynomial.Chebyshev2D(x_degree, y_degree, x_domain=None, x_window=None, y_domain=None, y_window=None, n_models=None, model_set_axis=None, name=None, meta=None, **params)[source]

Bivariate Chebyshev series..

It is defined as

$P_{nm}(x,y) = \sum_{n,m=0}^{n=d,m=d}C_{nm} T_n(x ) T_m(y)$

where T_n(x) and T_m(y) are Chebyshev polynomials of the first kind.

For explanation of x_domain, y_domain, x_window and y_window see Notes regarding usage of domain and window.

Parameters
x_degreeint

degree in x

y_degreeint

degree in y

x_domaintuple or None, optional

domain of the x independent variable

y_domaintuple or None, optional

domain of the y independent variable

x_windowtuple or None, optional

range of the x independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window

y_windowtuple or None, optional

range of the y independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window

**paramsdict

keyword: value pairs, representing parameter_name: value

Other Parameters
fixeda dict, optional

A dictionary {parameter_name: boolean} of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively the fixed property of a parameter may be used.

tieddict, optional

A dictionary {parameter_name: callable} of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively the tied property of a parameter may be used.

boundsdict, optional

A dictionary {parameter_name: value} of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, the min and max properties of a parameter may be used.

eqconslist, optional

A list of functions of length n such that eqcons[j](x0,*args) == 0.0 in a successfully optimized problem.

ineqconslist, optional

A list of functions of length n such that ieqcons[j](x0,*args) >= 0.0 is a successfully optimized problem.

Notes

This model does not support the use of units/quantities, because each term in the sum of Chebyshev polynomials is a polynomial in x and/or y - since the coefficients within each Chebyshev polynomial are fixed, we can’t use quantities for x and/or y since the units would not be compatible. For example, the third Chebyshev polynomial (T2) is 2x^2-1, but if x was specified with units, 2x^2 and -1 would have incompatible units.

Methods Summary

 fit_deriv(x, y, *params) Derivatives with respect to the coefficients.

Methods Documentation

fit_deriv(x, y, *params)[source]

Derivatives with respect to the coefficients.

This is an array with Chebyshev polynomials:

$T_{x_0}T_{y_0}, T_{x_1}T_{y_0}...T_{x_n}T_{y_0}...T_{x_n}T_{y_m}$
Parameters
xndarray

input

yndarray

input

*params

throw-away parameter list returned by non-linear fitters

Returns
resultndarray

The Vandermonde matrix


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Weighting and Aggregating Weather Data

In this post, we will learn how to aggregate fine-grained daily weather data to larger geographies, while weighting by population. We’ll do this for multiple days, and we’ll use parallel processing methods to speed things up, as it can take a long time. We’ll also create an animated graph with the resulting data.

In particular, we’ll aggregate PRISM data, which gives estimated temperature and precipitation (and other things) at a 4km resolution, to the state level. We will weight by population using data from the Census/SEDAC, which comes in approximately a 1km resolution. Much of the credit for what follows goes to Patrick Baylis and his post, from which I base a large portion of what will come. He does a great job of explaining a lot of the things I don’t and gives a good explanation for why one might want to weight weather data by population. Note that when using daily PRISM data, it’s probably good to be aware of something he mentions in another blog post - that the PRISM data may actually be measuring weather from the day before, so you should take this into account.

First, let’s load a bunch of packages:

library(gganimate)
library(prism)
library(tidyverse)
library(exactextractr)
library(raster)
library(future)
options(future.rng.onMisuse="ignore")
library(purrr)
library(furrr)
library(ggthemes)
library(lubridate)
library(beepr)

Next, we will download PRISM data using the prism package. To do so, we need to first set the directory we want to store the data in; you many need to manually create the folder. We then specify the variable we want (ppt, tmean, tmin, tmax, tdmean, vpdmin, or vpdmax) and the date range. We will choose the max temperature for the first ten days of March 2020. Note that these files can get pretty big pretty quickly, so we are only looking at a few days.

prism_set_dl_dir("data/prism/tmax")
get_prism_dailys(type = "tmax", minDate = "2020-03-01",
maxDate = "2020-03-10", keepZip=FALSE)

We’ll now create a list called file_list, which contains the list of files in the current prism_set_dl_dir directory. Each one corresponds to one day. We will 1) extract the date using regular expressions, 2) see if the data release is stable (TRUE) or not (recent data are not yet considered stable), and 3) determine which variable it is (tmean, tmax, etc.). In this example, 2) will all be true, and 3) will be tmax. Later, we will go through each line of file_list, using the file as input into a function. The function will load the corresponding data file and compute the aggregated value for each state.

file_list <- ls_prism_data(name=TRUE) %>%
rename(file = files) %>%
mutate(date=substr(file, nchar(file)-11, nchar(file)-4),
stable = str_detect(file, "stable"),
type=str_extract(file, "(?<=_)[a-z]*(?=_)"))

head(file_list)
##                                   file
## 1 PRISM_tmax_stable_4kmD2_20200301_bil
## 2 PRISM_tmax_stable_4kmD2_20200302_bil
## 3 PRISM_tmax_stable_4kmD2_20200303_bil
## 4 PRISM_tmax_stable_4kmD2_20200304_bil
## 5 PRISM_tmax_stable_4kmD2_20200305_bil
## 6 PRISM_tmax_stable_4kmD2_20200306_bil
##                                         product_name     date stable type
## 1 Mar 01 2020 - 4km resolution - Maximum temperature 20200301   TRUE tmax
## 2 Mar 02 2020 - 4km resolution - Maximum temperature 20200302   TRUE tmax
## 3 Mar 03 2020 - 4km resolution - Maximum temperature 20200303   TRUE tmax
## 4 Mar 04 2020 - 4km resolution - Maximum temperature 20200304   TRUE tmax
## 5 Mar 05 2020 - 4km resolution - Maximum temperature 20200305   TRUE tmax
## 6 Mar 06 2020 - 4km resolution - Maximum temperature 20200306   TRUE tmax

The next step is to get a shapefile for states. (We could also get counties, etc.)

states = tigris::states(cb = TRUE, resolution = "20m") %>%
filter(!NAME %in% c("Alaska", "Hawaii", "Puerto Rico"))

Download the population raster data, load it as a raster, and crop it based on the state shapefile. You can download it at SEDAC by selecting Census 2000 and Population Counts for Continental US.

population_raster = raster("data/census/population/usgrid_data_2000/geotiff/uspop00.tif")
population_crop = crop(population_raster, states)

Now we’ll create a function that aggregates the weather data. We will create both unweighted and weighted versions. Note that we get slightly different results if we don’t use weather_crop and population_crop and instead use weather_raster and population_raster. If anyone can shed light on why, I’d be interested in hearing.

daily_weather <- function(file, date, type, stable) {
#get the weather raster variable based on the file name
# note here that you may need to adjust your working directory so that it points
# to the correct place
weather_raster = raster(paste0("data/prism/tmax/", file, "/", file, ".bil"))
#crop the weather raster based on the states shapefile
weather_crop = crop(weather_raster, states)
#use resample to make the population_crop rectangle be the same as the
#weather_crop rectangle as they were initially not perfectly overlapping.
#we can't use exact_extract unless we do this step
population_rs = raster::resample(population_crop, weather_crop)
#we will work on the new variable called data
data <- states
#aggreagte to states without weighting by population (unweighted)
data[[paste0(type, "_u")]] <- exact_extract(weather_crop, data, fun = "mean")
#aggreagte to states while weighting by population (weighted)
data[[paste0(type, "_w")]] <- exact_extract(weather_crop, data, fun = "weighted_mean", weights=population_rs)
#create columns from the date and type variables
data$date <- date data[[paste0(type, "_stable")]] <- stable #select relevant columns from the data frame data <- data.frame(data) %>% arrange(NAME) %>% dplyr::select(c(6,13,14,11,12)) data } We will then apply the above daily_weather function to each row of file_list using pmap. Or, actually future_pmap, which is a parallel processing version of pmap. You can change the number of workers based on your computer’s setup. (If you just want to use pmap, get rid of the plan() function and swap pmap for future_pmap). The function produces a dataframe, which we store in the weather column of the file_list dataframe. Each element (row) of the weather column contains its own dataframe. This dataframe within a dataframe contains the aggregated weather for the day for each state. plan(multisession, workers = 7) file_list2 <- file_list %>% mutate(weather=future_pmap(across(c(file, date, type, stable)), ~ daily_weather(..1, ..2, ..3, ..4))) %>% as_tibble #this step can take some time, so you can get a notification when it is done beep() Next, we’ll create the weather dataframe, which binds together all of the dataframes from file_lists’s weather column. weather is at the day-state level. weather <- bind_rows(file_list2$weather)
head(weather)
##          NAME     date tmax_stable     tmax_u    tmax_w
## 1     Alabama 20200301        TRUE 16.8803024 16.193275
## 2     Arizona 20200301        TRUE 19.1284809 23.761177
## 3    Arkansas 20200301        TRUE 19.2444706 19.301489
## 4  California 20200301        TRUE 16.4584484 19.828274
## 5    Colorado 20200301        TRUE 11.7001238 13.523680
## 6 Connecticut 20200301        TRUE  0.6898845  1.343361

Merge in the geography information from states (this step is probably not necessary if you don’t want to plot).

weather2 <- left_join(weather, states %>% dplyr::select(NAME, geometry), by=c("NAME"))

Finally, we’ll do a bit of cleaning, etc., such as creating Fahrenheit versions of the variables and creating variables for year, month, and day.

weather2 <- weather2 %>% mutate(tmax_u_f = tmax_u*(9/5)+32,
tmax_w_f = tmax_w*(9/5)+32,
year=substr(date,1,4),
month=substr(date,5,6),
day=substr(date,7,8)) %>%
rename(state=NAME) %>%
dplyr::select(state, date, year, month, day, geometry, tmax_stable,
tmax_u, tmax_u_f, tmax_w, tmax_w_f)

If you wanted, you put some of the above code into additional function(s), which would make it easier to do this for multiple weather variables.

Lastly, we’ll plot the data using gganimate.

a <- ggplot() +
geom_sf(data = weather2, aes(geometry=geometry, fill = (tmax_w_f)), show.legend = TRUE) +
scale_fill_viridis_c("Daily Max °F", option="H", breaks=c(-10, 5, 20, 35, 50, 65, 80, 95, 110)) +
theme_void() +
theme(plot.subtitle = element_text(size=16, hjust = 0.5, vjust=-3)) +
theme(plot.caption = element_text(size=12)) +
labs(caption = "Data: PRISM, SEDAC. Data is modeled. @toddrjones.") +
theme(legend.position = c(0.25, -.001), legend.key.size = unit(1.5,"line"),
legend.direction = "horizontal",
legend.box = "horizontal") +
guides(fill = guide_colourbar(barwidth = 15, barheight = 1)) +
transition_time(as_date(date)) +
labs(subtitle = paste('Date: {frame_time}'))

anim_save("tmax_2020.gif", a, end_pause=8, width = 600, height = 300, duration=5, nframes=100)

format: plain


text:
# Why differential flatness is called “flat”?

A system is differentially flat if the state and control input can be written as functions of the flat outputs and their time derivatives.

In other words, if a system is differentially flat, we can represent the state of the system and control signal as: $$x = x(y, \dot y, \ddot y, ... , y^{(p)}$$ $$u = u(y, \dot y, \ddot y, ... , y^{(q)}$$

It's really a nice property of the system. But I don't quite get the name of this property. Why it is called differential "flatness". What does it have to do with "flat"?

• Not a complete answer, but (Fliess 1995) says: "the terminology flat is due to the fact that y plays a somehow analogous role to the flat coordinates in a differential geometric approach to the Frobenius theorem" (p. 3). Also, there is a geometric definition of "flat" which might be coming into play. – Parker Lusk Oct 3 '18 at 18:37


text:
Holomorphy of the Dirac resolvent with relatively form bounded potentials
Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 3, pp. 269-300.
@article{AIHPA_1993__59_3_269_0,
author = {White, Gregory B.},
title = {Holomorphy of the Dirac resolvent with relatively form bounded potentials},
journal = {Annales de l'I.H.P. Physique th\'eorique},
pages = {269--300},
publisher = {Gauthier-Villars},
volume = {59},
number = {3},
year = {1993},
zbl = {0791.47057},
mrnumber = {1276327},
language = {en},
url = {archive.numdam.org/item/AIHPA_1993__59_3_269_0/}
}
White, Gregory B. Holomorphy of the Dirac resolvent with relatively form bounded potentials. Annales de l'I.H.P. Physique théorique, Tome 59 (1993) no. 3, pp. 269-300. http://archive.numdam.org/item/AIHPA_1993__59_3_269_0/

[CC] R.J. Cirincione and P.R. Chernoff, Dirac and Klein-Gordon Equations: Convergence of Solutions in the Nonrelativistic Limit, Commun. Math. Phys., Vol. 79, 1981, pp. 33-46. | MR 609226 | Zbl 0471.35024

[De] P.A. Deift, Applications of a Commutation Formula, Duke Math. J., Vol. 45, 1978, pp. 267-310. | MR 495676 | Zbl 0392.47013

[DS] N. Dunford and J.T. Schwartz, Linear Operators, Part I, New York, Interscience, 1963. | MR 188745

[F] W.G. Faris, Self-Adjoint Operators, Lecture Notes in Mathematics, Vol. 433, Berlin, Heidelberg, New York, Springer-Verlag, 1975. | MR 467348 | Zbl 0317.47016

[FW] L.L. Foldy and S.A. Wouthuysen, On the Dirac Theory of Spin 1/2 Particles and its Non-Relativistic Limit, Phys. Rev., Vol. 78, 1950, pp. 29-36. | Zbl 0039.22605

[GGT] F. Gesztesy, H. Grosse and B. Thaller, A Rigorous Approach to Relativistic Corrections of Bound State Energies for Spin-1/2 Particles, Ann. I.H.P. (Phys. Théor.), Vol. 40, 1984, pp. 159-174. | Numdam | MR 747200 | Zbl 0534.46053

[GNP] D.R. Grigore, G. Nenciu and R. Purice, On the Nonrelativistic Limit of the Dirac Hamiltonian, Ann. I.H.P. (Phys. Théor.), Vol. 51, 1989, pp. 231-263. | Numdam | MR 1034588 | Zbl 0705.35115

[H] W. Hunziker, On the Nonrelativistic Limit of the Dirac Theory, Commun. Math. Phys., Vol. 40, 1975, pp. 215-222. | MR 363275

[K] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., New York, Berlin, Springer-Verlag, 1980.

[L] E. Lieb, The Stability of Matter: From Atoms to Stars, Bull. Am. Math. Soc., Vol, 22, No. 1, 1990, pp. 1-49. | MR 1014510 | Zbl 0698.35135

[M] A. Messiah, Quantum Mechanics, Vols. 1 & 2. Amsterdam: North Holland, 1970.

[N] G. Nenciu, Self-Adjointness and Invariance of the Essential Spectrum for Dirac Operators Defined as Quadratic Forms, Comm. Math. Phys., Vol. 48, 1976, pp. 235-247. | MR 421456 | Zbl 0349.47014

[RS] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. I, II, IV. New York, London, Academic Press 1972-1978. | MR 493419 | Zbl 0242.46001

[S] B. Simon, Quantum Mechanics for Hamiltonians Defined as Quadratic Forms: Princeton, New Jersey, Princeton University Press, 1971. | MR 455975 | Zbl 0232.47053

[T] E.C. Titchmarsh, On the Relation between the Eigenvalues in Relativistic and Nonrelativistic Quantum Mechanics, Proc. Roy. Soc., Vol. A 266, 1962, pp. 33-46. | MR 131598 | Zbl 0127.19004

[V1] K. Veselic, Perturbation of Pseudoresolvents and Analyticity in 1/c of Relativistic Quantum Mechanics, Commun. Math. Phys., Vol. 22, 1971, pp. 27-43. | MR 300579 | Zbl 0212.15701

[V2] K. Veselic, The Nonrelativistic Limit of the Dirac Equation and the Spectral Concentration, Glasnik Mat., Vol. 4, 1969, pp. 231-241. | MR 267294 | Zbl 0212.16402

[W] G.B. White, Splitting of the Dirac Operator in the Nonrelativistic Limit, Ann. I.H.P. (Phys. Théor.), Vol. 53, 1990, pp. 109-121. | EuDML 76491 | Numdam | MR 1077468 | Zbl 0712.35082


text:
# Continuous functions remaining constant

I solved a problem in analysis and i was thinking of generalizing this question which i couldn't succeed.

If $f:\mathbb{R} \to \mathbb{R}$ is a continuous function which satisfies $f(x)=f(2x+1)$, for all $x \in \mathbb{R}$ then prove that $f$ is constant. I was able to prove it considering $g(x)=f(x-1)$ and showing that $g(x) \to g(0)$.

Now my question is suppose $f: \mathbb{R} \to \mathbb{R}$ is a continuous function and satisfies $f(p(x))=f(x)$ for every polynomial $p(x) \in \mathbb{R}$, then what should be the condition on $p(x)$ such that $f$ remains constant.

-
There seems to be some kind of quantifier error in your question: if $f(p(x)) = f(x)$ for every polynomial $p(x) \in \mathbb{R}[x]$, then in particular it holds for $p(x) = 2x+1$ so by what you say above $f$ is constant. (Or, easier: for each $c \in \mathbb{R}$, take $p(x) = x+c$.) I think you mean to ask: for which polynomials $p \in \mathbb{R}[x]$ does $f = f \circ p$ imply that $f$ is constant. Is that correct? –  Pete L. Clark Jul 15 '10 at 12:26
@Pete: or easier, take $p(x) = c$. You can even drop the continuity assumption. :) –  Willie Wong Jul 15 '10 at 12:34
I'm also added the dynamical systems tag as I think that this question can be interpreted as something like ergodicity of the iterated map $p^n(x)$. But I am not sure. –  Willie Wong Jul 15 '10 at 12:52
This is related to the concept of "topological transitivity" in dynamical systems. A continuous transformation $T$ of a metric space $X$ is called topologically transitive if for every pair of nonempty open sets $U, V$, there exists $n$ such that $T^n(U) \cap V \neq \emptyset$. If $X$ is compact, then topological transitivity implies that any continuous real-valued $f$ such that $f = f \circ T$ must be constant. On the other hand, this statement about $T$-invariant continuous functions is strictly weaker than topological transitivity. I'm not quite sure how this works in the noncompact case. –  Ian Morris Jul 15 '10 at 13:22

I'll assume, per Pete's comment above, that you are looking for polynomials $p(x)$ with real coefficients such that $f(p(x)) = f(x)$ implies $f$ is constant.
It suffices (though I am not sure if this is necessary) then that $p(x)$ has a fixed point that is strictly unstable or strictly stable in the strict sense. In other words, there exists $x_0$ such that $p(x_0) = x_0$ and such that $|p(x - x_0)| > (1+\epsilon) |x-x_0|$ for some $\epsilon > 0$ or $|p(x - x_0)| < (1 - \epsilon)|x - x_0|$. Basically the exact same argument you used to show the property for $2x+1$ can be used for this case.
This was a putnam problem. If $f$ is continuous and satisfies $f(2x^{2}-1)=2xf(x)$ then $f \equiv 0$ on $[-1,1]$. See for this also $f$ remains a constant. –  S.C. Jul 16 '10 at 10:52


text:
# Easy Macro Recorder 4.1

## How to uninstall Easy Macro Recorder 4.1 from your system

This page is about Easy Macro Recorder 4.1 for Windows. Below you can find details on how to remove it from your computer. It was created for Windows by GoldSolution Software, Inc.. Take a look here where you can find out more on GoldSolution Software, Inc.. Detailed information about Easy Macro Recorder 4.1 can be seen at . The application is usually placed in the C:\Program Files (x86)\Easy Macro Recorder folder (same installation drive as Windows). Easy Macro Recorder 4.1's entire uninstall command line is C:\Program Files (x86)\Easy Macro Recorder\unins000.exe. The application's main executable file is called Macro Recorder.exe and its approximative size is 460.27 KB (471312 bytes).

The following executable files are contained in Easy Macro Recorder 4.1. They occupy 1.20 MB (1260078 bytes) on disk.

• Macro Recorder.exe (460.27 KB)
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2016-07-01 / Written by Dan Armano for Advanced Uninstaller PRO


text:
#### • Class 11 Physics Demo

Explore Related Concepts

# Grade 6 Mathematics Exam Papers

6th grade maths cover the latest syllabus which is being published by the board. Exercise materiel was designed for this book reflect the skills from curricular, grade level tests. Constructed response to the problem with examples are given for all exercise. Standardized test and assessment are carried out to rate the subject knowledge of the students, which is much longer than necessary .

In order to make understand both concept and procedure to solve the problem a lot of research is carried for lower classes from the department. The practice has always been an ingredient for students learning. Self study can be brought out by making use of worksheets,solving sample problem , solving exam papers, etc. The class covers the topic under addition, subtraction, fraction, multiplication, exponents,decimals, orders of operation, solving algebraic equation, measurements.

A set of 6th grade exam paper is given below for students reference.

1. write the three equivalent fraction

a)  $\frac{2}{3}$ b)  $\frac{2}{3}$ c)  $\frac{15}{24}$

2. Simplify

a)  subtract $\frac{12}{4}$ from $\frac{21}{5}$

b) Find 6  - $\frac{19}{4}$

3. what is the median of test result score

22,26,28,30,32,24

4. Arrange the decimal in ascending order

a) 78.19,63.56,56.12,80.35,96.56

b) 15.96,16.89,20.31,36.89,11.23

5. Simplify the exponents

a) 17x 215 b) 2x 6x3 c) 3x 65 d) 0x 83

6. Add the exponents    a) 6+ 35 b) 056 + 65

7. Convert the decimal into percentage

a)  0.96 b)  0.02 c)  1.12 d)  2.36

8. Find the third angle when two angles are given

a) 1150,150 b) 450,350    c) 850,620

9. Convert

a)  516 cm  into m b) 56 dan into dm c) 26 km into m   d) 562 g into mg

10. Solve for the variable

a)  5 - x = 10   b)  2x + 11 = 22   c)  8 + y = 16    d) 18 + 3x = -15

11. Find the value of

a) (-2.1) x (-2.1) x (-2.1) b) (-0.05) x (-0.05) c) $\frac{5}{4}$*$\frac{5}{4}$*$\frac{5}{4}$*$\frac{5}{4}$


text:
Kazuo Habiro

Holonomy in the Hopf Bundle over the symmetric space $$\mathbb{C}P^n$$

video: comming soon.
abstract:
The fundamental group of a basepointed topological space is one of the most fundamental concepts in algebraic topology. The fundamental group is important also in manifold topology, and in low dimensions it gives a very strong invariant.
In this talk, I plan to discuss the quantum fundamental group'' of a $$3$$-manifold, which is a refinement of the fundamental group, defined using isotopy classes of bottom tangles instead of homotopy classes of based loops. The set of bottom tangles in a $$3$$-manifold admits a very rich algebraic structure, and many constructions that work on fundamental groups work on quantum fundamental groups as well. For example, one can define the classifying space of the quantum fundamental group of a $$3$$-manifold, and the quantum representation variety'' associated to a co-ribbon Hopf algebra (such as the quantum group $$\mathrm{SL}_q(2)$$).


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Introduction: Simulation-based training may improve overall healthcare value by improving outcomes and minimizing complications. However, there is limited information regarding the cost-effectiveness of simulation curricula, particularly in musculoskeletal conditions. The purpose of this study was to estimate the cost effectiveness of simulation training aimed at reducing cast saw injury by orthopaedic surgery residents. Methods: Beginning in January 2013, third-year orthopaedic residents rotating at a tertiary care children’s hospital were enrolled in a simulation-based curriculum, involving instruction on distal radius fracture reduction, cast application, and cast removal using an oscillating cast saw. Each group of residents completed two sessions in the simulation lab as part of this curriculum. For patients treated for distal radius fractures by orthopaedic residents in the Emergency Department, the incidence of cast saw injuries was analyzed before and after implementation of the simulation curriculum. Actual and potential costs associated with cast saw injuries–including wound care, need for clinical visits, as well as potential medicolegal payments–were obtained. Prior studies suggest that potential medicolegal costs of complications relating to closed treatment of distal radius fractures approach $100,000. The costs of cast saw injury were compared to the cost of the simulation curriculum to calculate overall savings and return on investment. Results: In the 2.5 years prior to simulation, cast saw injuries occurred at a rate of approximately 5.5 per 100 casts cut by orthopaedic residents. For the 2.5-year period post-simulation, the cast saw injury rate decreased to approximately 0.7 per 100 casts cut (p=0.0948). Actual costs attributed to cast saw injuries per resident rotation were approximately$65.83 before simulation, and negligible after simulation. Potential costs from medicolegal payments before and after simulation were estimated at $160,000 and$60,000 per rotation, respectively. The total cost to implement the casting simulation-based workshop was $2,465.31 per resident rotation. Total potential savings for the 2.5-year period post-simulation was$488,002.60, representing a 40 to 1 theoretical return on investment. Conclusions: The simulation-based curriculum on distal radius fracture reduction, casting, and cast removal for orthopaedic surgical residents was effective in reducing cast saw injuries and yielded a 40 to 1 return on investment. These results support the further development and investment in simulation-based training as cost-effective means of improving patient safety and clinical outcomes. 1 Halanski M, Noonan KJ: Cast and Splint Immobilization: Complications. Journal of the American Academy of Orthopaedic Surgeons 2008:16:30-40.

Figure 1

Absolute of cast saw injuries per resident rotation before and after initiation of simulation-based training program in January of 2013 (indicated by vertical line). As residents rotated every 6 months, each year was divided into a first half (A) and second half (B). Mean number of cast saw injuries per 6-month resident rotation before and after simulation indicated by dashed line.

Figure 1

Absolute of cast saw injuries per resident rotation before and after initiation of simulation-based training program in January of 2013 (indicated by vertical line). As residents rotated every 6 months, each year was divided into a first half (A) and second half (B). Mean number of cast saw injuries per 6-month resident rotation before and after simulation indicated by dashed line.

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# Six sided dice problem

· by tuxdna · Read in about 1 min · (40 words) ·

Six sided dice problem

Summary:

$$n = \sum_{k=1}^{\infty}{k*P(rolls=k)}$$

Where:

$$P(rolls=k) = q^{(k-1)} * p$$

p is probability we get a 6 in k’th roll, and q^(k-1) is probability we do not get a 6 in all k-1 rolls.


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## markov model in data compression

On December 28th, 2020, posted in: Uncategorized by

The popular dynamic Markov compression algorithm (DMC) offers state-of-the-art compression performance and matchless conceptual simplicity. We adopt a low-rank model which is motivated by the state aggregation of controlled systems. We assessed its impact … From the primary data matrix (samp200.dat), construct a … In 1997 Booksten, Klein & Raita [2] showed that concordances can e ciently be compressed using Markov models (both hidden and regular). Firstly, a given JPEG image is extracted from blocked images to obtain amplitude and three angles ($$\psi$$, $$\phi$$, and $$\theta$$). Dynamic Markov compression (DMC) is a lossless data compression algorithm developed by Gordon Cormack and Nigel Horspool. data compression. If a page of the book isn't showing here, please add text {{BookCat}} to the end of the page concerned. Such models can be used to predict future message characters and can therefore be used as a basis for data compression. Such models can be used to predict future message char-acters and can therefore be used as a basis for data compression… In probability theory, a Markov model is a stochastic model used to model randomly changing systems. Probability Model Next if we discard the assumption of independence also, we come up with a better data compression scheme but we have to define the dependency of data sequence on each other. Objective: To determine whether tibial neurolysis performed as a surgical intervention for patients with diabetic neuropathy and superimposed tibial nerve compression in the prevention of the diabetic foot is cost-effective when compared with the current prevention programme. In contrast to N-gram Markov models, which attempt to estimate conditional distributions of the form P(σ|s), with s ∈ ΣN and σ ∈ Σ, VMM algorithms learn such con-ditional distributions where context lengths |s| vary in response to the available statistics in the training data. We study the state compression of finite-state Markov process from its empirical trajectories. This category contains pages that are part of the Data Compression book. Contents• Introduction – Introduction – Motivation• Markov Chain• Hidden Markov Models• Markov Random Field 28/03/2011 Markov models 2 3. In practice, however, the cost of DMC's simplicity and performance is often outrageous memory consumption. Data Compression Using Adaptive Coding and Partial String Matching JOHN G. CLEARY AND IAN H. WITTEN, MEMBER, IEEE Abstract-The recently developed technique of arithmetic coding, in conjunction with a Markov model of the source, is a powerful method of data compression in situations where a linear treatment is inap- propriate. Information systems. Model reduction is a central problem in analyzing complex systems and high-dimensional data. Models of computation. It assigns each sequence to a cluster by means of Euclidean distance. Login options . Probabilistic computation. DMC generates a finite context state model by adaptively generating a Finite State Machine (FSM) that captures symbol frequencies within the source message. Most commonly used compression methods are either dictionary-based or statistical. The crux of data compression is to process a string of bits in order, predicting each subsequent bit as accurately as possible. Data compression using dynamic Markov modelling. Less than 500 views • Posted On Sept. 30, 2020. Markov Models 1. DATA COMPRESSION USING DYNAMIC MARKOV MODELLING Gordon V. Cormack University of Waterloo and R. Nigel Horspool University of Victoria ABSTRACT A method to dynamically construct Markov models that describe the characteristics of binary messages is developed. Such models are used to study thermodynamics and statistical mechanics; bioinformatics, enzyme activity, and population dynamics; solar irradiance and wind power; price trends; speech recognition and generation; data compression and pattern recognition; reinforcement learning and gesture recognition. Prediction by Partial Matching. For Ex. Composite Source Model in Data Compression. learn probabilistic ﬁnite state automata, which can model sequential data of considerable complexity. Data structures. The accuracy of this prediction is reflected directly in compression effectiveness. A ... Hidden Markov models are powerful models with a rich mathematical structure. As expected, Markov models are particularly useful in text compression, where the probability of the next letter is heavily influenced by the preceding letters. An edition of Image Segmentation and Compression Using Hidden Markov Models (2000) Image Segmentation and Compression Using Hidden Markov Models by Jia Li. A similar assumption, that there is an underlying Markov model for the data, is made in the Ziv-Lempel13.14 and the Cleary-Witten1 techniques. ADD COMMENT 0. written 4.5 years ago by Sayali Bagwe • 5.8k: 1.Physical Models: If we know something about the physics of the data generation process, we can use that information to construct a model. Data compression techniques reduce the costs for information storage and transmission and are used in many applications, ranging from simple file size reduction to speech and video encoding. Mumbai University > EXTC > Sem 7 > Data Compression and Encryption. Data Compression Using Adaptive Coding and Partial String Matching Abstract: The recently developed technique of arithmetic coding, in conjunction with a Markov model of the source, is a powerful method of data compression in situations where a linear treatment is inappropriate. A general 2-part coding scheme for given model order but unknown parameters based on PHMM is presented. The hidden Markov model (HMM) is a doubly embedded stochastic process. Speciﬁcally, we employ the dynamic Markov compression (Cormack and Horspool, 1987) and prediction by partial matching (Cleary and Witten, 1984) algorithms. The ap- plications have often involved estimating the probabilities of hidden states in e.g. Discrete mathematics. Statistical methods combine entropy coding with modeling techniques. Zero Frequency Model in Markov Models in Text Compression. In fact, it is provable that Ziv-Lempel coding approaches the optimal compression factor for sufficiently long messages that are generated by a. Markov model. In this paper, we consider the use of adaptive data compression models for spam ﬁltering. Khalid Sayood, in Introduction to Data Compression (Fifth Edition), 2018. 0. Thus, QVZ has the option of clustering the data prior to compression. Dynamic Markov Compression (DMC), developed by Cormack and Horspool, is a method for performing statistical data compression of a binary source. You can view a list of all subpages under the book main page (not including the book main page itself), regardless of whether they're categorized, here. They coded con- Specifically, it uses the K-means algorithm (MacQueen etal., 1967), initialized using C quality value sequences chosen at random from the data. Adaptive coding allows the model to be constructed dy- namically … 3.3. The purpose of this paper is to show that neural networks may be promising tools for data compression without loss of … It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property).Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. Markov Models in Data Compression. We will briefly review Forward-Backward Gibbs sampling (FBG) for Bayesian Hidden Markov Models, and its acceleration through compression of the data into blocks. Title: DMC.fm Author: nigelh Created Date: 9/21/2004 8:45:23 PM To this end, the Markov modelling technique is combined with Guazzo's arithmetic coding scheme to produce a powerful method of data compression. Such models can be used to predict future message characters and can therefore be used as a basis for data compression. combination with a regular Markov Model and used the new model for compression of binary images. Data layout. Theory of computation. The challenge today is to find a research area in which Markov models play no role. While these permitted considerable reduction in storage, the short memory of Markov models may limit their compression efficiency. The models that incorporate relative compression, a special case of referential compression, are being steadily improved, namely those which are based on Markov models. recognition problems. The compression is based on having the model learn the image, then saving its resulting parameters. It uses predictive arithmetic coding similar to prediction by partial matching (PPM), except that the input is predicted one bit at a time (rather than one byte at a time). CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): The recently developed technique of arithmetic coding, in conjunction with a Markov model of the source, is a powerful method of data compression in situations where a linear treatment is inappropriate. By first considering the case of equal emission variances among all states, we show that optimal compression is equivalent to a concept called selective wavelet reconstruction , following a classic proof in wavelet theory. Markov Models in Text Compression. PATTERN RECOGNITION Markov models Vu PHAM phvu@fit.hcmus.edu.vn Department of Computer Science March 28th, 201128/03/2011 Markov models 1 2. Several known attempts at reducing DMC's unwieldy model growth have rendered DMC's compression performance uncompetitive. 0 Ratings 0 Want to read; 0 Currently reading; 0 Have read; This edition published in 2000 by Springer US in Boston, MA. Data management systems. Model Development Here, you will use the data from the 200 sample points on the PNW im-ages to calculate transition probabilities for a Markov model. Comments. Mathematics of computing. Due to the fact that exact substring matches in non-binary signal data are rare, using full resolution conditioning information generally tends to make Markov models learn slowly, yielding poor compression. The transi-tion probabilities will be based on landscape change from 1971 to 1984. Zero Frequency Model in Markov Models in Text Compression. Data Compression is the process of removing redundancy from data. A method to dynamically construct Markov models that describe the characteristics of binary messages is developed. One of the most popular ways of representing dependence in the data is through the use of Markov models, named after the Russian mathematician Andrei Andrevich Markov (1856-1922). To this end, the Markov modelling technique is combined with Guazzo coding to produce a powerful method of data compression. The Prediction by Partial Matching (PPM) is a sophisticated algorithm for data compression based on statistical models, and is among the most efficient techniques concerned to compression without loss of information .The PPM algorithm creates a tree (PPM tree) that represents a variable-order Markov Model, in which the last n characters represent … Introduction• Markov processes are first proposed by … In this paper, a feature based on the Markov model in quaternion discrete cosine transform (QDCT) domain is proposed for double JPEG compression detection. Data compression. Traditionally, Markov models have not been successfully used for compression of signal data other than binary image data. In this paper, we propose a new model, the substitutional tolerant Markov model (STMM), which can be used in cooperation with regular Markov models to improve compression efficiency. 1. Marks: 5 M. Year: Dec 2012. mumbai university data compression and encryption • 9.2k views. 5 M. 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# Freefall

• October 22nd 2007, 09:59 AM
vesperka
Freefall
Last physics problem for the day I promise :)

A stone falls from rest from the top of a cliff. A second stone is thrown downward from the same height 3.1s later with an initial speed of 60.76m/s. They hit the ground at the same time.

The acceleration of gravity is 9.8m/s/s.

a) How long does it take the first stone to hit the ground? Answer in units of s.

b) How high is the cliff? Answer in units of m.

Based on the information given it definitely seems possible to solve this problem, but I just can't seem to put the information together.
• October 22nd 2007, 10:15 AM
mathmonster
firstly form 2 separate equations s = ut + (a(t^2))/2, then equate them

ut + (a(t^2))/2 = ut + (a(t^2))/2

taking one t as t = -3.1 and the other as just t.
• October 22nd 2007, 10:19 AM
vesperka
Hmm, I just created two position functions for each rock. The first rock is simply 4.9x^2 and the second rock is (4.9x^2)+(60.76x). I'm trying to find when their distances are equal because they hit the ground at the same time, but my calculator is only giving me 0,0 for an intersection :p

Bleh, I'm not factoring time into my equation of the second rock, which is why they never have an equal distance :\

Using your help I got t = 1.55 seconds, I think it works :D I did it backwards though, making the first rock's equation t+3.1.
• October 22nd 2007, 10:20 AM
mathmonster
which will give a value for t, then to find height of the cliff plug t into the equation in my first post.
god i havent done that for 3 years, i used to love the mechanic part of maths until i got to university
• October 22nd 2007, 10:33 AM
topsquark
Quote:

Originally Posted by vesperka
Last physics problem for the day I promise :)

A stone falls from rest from the top of a cliff. A second stone is thrown downward from the same height 3.1s later with an initial speed of 60.76m/s. They hit the ground at the same time.

The acceleration of gravity is 9.8m/s/s.

a) How long does it take the first stone to hit the ground? Answer in units of s.

b) How high is the cliff? Answer in units of m.

Based on the information given it definitely seems possible to solve this problem, but I just can't seem to put the information together.

As always, set up your coordinate system. I have the origin at the base of the cliff and +y upward. I am defining the starting time t = 0 s when the second stone is thrown.

So for the first stone we have
$y_ 0 = h = ?$
$v_0 = 0~m/s$
$a = -9.8~m/s^2$

Giving a position equation of
$y = y_0 + v_0t + \frac{1}{2}at^2 = h - 4.9t^2$

For the second stone we have
$y_0 = h = ?$
$v_0 = -60.76~m/s$
$a = -9.8~m/s^2$

Giving position equation of
$y = y_0 + v_0(t + 3.1) + \frac{1}{2}a(t + 3.1)^2 = h - 60.76t - 4.9t^2$ (Recall that the second stone is thrown at 3.1 s.

They hit the ground at the same time, so at time t they both have a position y = 0. So
$h - 4.9(t + 3.1)^2 = h - 60.76t - 4.9t^2$

Giving t = 1.55 s.

So how tall is the cliff? Pick a stone:
$0 = h - 4.9(1.55 + 3.1)^2$

Giving h = 105.95 m.

-Dan
• October 22nd 2007, 04:51 PM
mathmonster
see i got the height of the cliff as 11.7m when i first did the calculation, but it seemed wrong so i plugged t into the equation for the stone with initial velocity 60.76m/s and got the height of the cliff as 106m, which makes more sense as the stone takes 1.55s to hit the floor and the initial vel. is 61m/s.
• October 22nd 2007, 08:07 PM
topsquark
Quote:

Originally Posted by mathmonster
see i got the height of the cliff as 11.7m when i first did the calculation, but it seemed wrong so i plugged t into the equation for the stone with initial velocity 60.76m/s and got the height of the cliff as 106m, which makes more sense as the stone takes 1.55s to hit the floor and the initial vel. is 61m/s.

I'm not doing so hot today, am I? (Puke)

I forgot to add the 3.1 s when using that equation. If you plug the 1.55 s into the "thrown rock" equation you get the correct height. If you plug 1.55 + 3.1 (s) into the "dropped rock" equation you also get the right answer.

I have corrected this in my original post. (And I also got the 105.95 m answer.)


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# How Safe Is The Constant Pressure Assumption For Enthalpy?

1. May 6, 2015

### DocZaius

I am curious about a statement that is usually tacked onto the end of a derivation showing enthalpy with constant pressure being equal to the heat into the system.

First Law of Thermodynamics
$\Delta U = Q - W_{by}$

Define Enthalpy and look at its change:
$H=U+PV \\ \Delta H = \Delta U + \Delta (PV)$

Plug in First Law:
$\Delta H = Q - W_{by} + \Delta (PV)$

Under constant pressure:
$\Delta H = Q - P\Delta V + P\Delta V \\ \Delta H = Q$

And here is the part that I've heard and read more than once (Khan uses it in his enthalpy video for example). It is said that considering enthalpy at a constant pressure is useful for us, since that is the condition under which most of our chemical experiments occur (e.g. those done inside test tubes, etc.). But I always wonder why we can say that. My intuition would be that when a chemical reaction occurs, particularly a violent one, the pressure conditions at the center of the reaction would not necessarily adhere to those of its environment. I understand that an open test tube would be connected to the atmospheric pressure of the room, but surely for a short period of time and under very local conditions (e.g. at the center of the reaction) there must be a significant pressure gradient around the reaction? I would think that force per area in surfaces considered around the reaction would be relatively high. And is it not during that short period of time and at that specific location that we are considering quantities such as enthalpy?

My intuition appears to be wrong in this case, since clearly people have been using enthalpy under constant pressure as a useful quantity for a long time. But I am curious why it is that before any equilibrium is reached, we can safely assume constant pressures in energetic chemical reactions.

Last edited: May 6, 2015
2. May 6, 2015

### dipole

You've not understood the basic assumption of all thermodynamics, which the consideration of systems under equilibrium. You need to go back to chapter 1 page 1 of your thermo book of choice and re-read this.

3. May 6, 2015

### DocZaius

Shouldn't it be called thermostatics then? :P Anyhow, fair enough but if one got from point A (pre-reaction) to point B (post-reaction) under conditions that are clearly not quasi-static, I don't understand why we get to usefully apply these quantities that were derived assuming constant equilibrium.

In other words, I'm OK with my book announcing that the basic assumption will be that all considered systems will be under equilibrium. But I don't understand why it proceeds to tackle systems that clearly don't stay under equilibrium.

P.S. And does that mean then that this enthalpy-at-constant-pressure quantity would then only be useful for slow reactions that approximate equilibrium as best as possible?

Last edited: May 6, 2015
4. May 7, 2015

### Staff: Mentor

Don't forget that the work done by the system on the surroundings for a closed system between two thermodynamic equilibrium states is always given by $W=\int P_{Int} dV$, where PInt is the pressure at the interface with the surroundings (atmospheric pressure in your example). (See my recent Physics Forums Insight article https://www.physicsforums.com/insights/understanding-entropy-2nd-law-thermodynamics/). This equation applies irrespective of whether the process is reversible or irreversible, and/or how non-uniform the conditions are within the reaction vessel. Only in the case of a reversible process is Pext = P, where P is the pressure that one would calculate from the equation of state for the gas.

However, for an irreversible process, if the final equilibrium state of a system has been attained via spontaneous reaction at constant interface pressure (PInt), the final equilibrium pressure of the system Pfinal will be equal to PInt (which is the same as in the initial equilibrium pressure of the system). So, $W=P_{final}ΔV=P_{Int}ΔV=PΔV$.

Chet


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## Does my model have numerical issues?

You can follow these steps to help determine whether a model is experiencing numerical issues:

1. Isolate the model for testing by exporting a model file and a parameter file. The easiest way to do this is to create a gurobi.env file in your working directory that contains the following line:
Record 1

Then, run your Gurobi program, which will produce gurobi.rec files. Afterwards, you can replay this recording file using gurobi_cl.
2. Using the Gurobi Interactive shell, run some simple Python code to read the model that the replay produces, and print the summary statistics:
m = read('gurobi.rew')
m.printStats()

The output will look like:
Statistics for model (null) :
Linear constraint matrix    : 25050 Constrs, 15820 Vars, 94874 NZs
Variable types              : 14836 Continuous, 984 Integer
Matrix coefficient range    : [ 0.00099, 6e+06 ]
Objective coefficient range : [ 0.2, 65 ]
Variable bound range        : [ 1, 5e+07 ]
RHS coefficient range       : [ 1, 5e+07 ]

The range of numerical coefficients is one indication of potential numerical issues. As a very rough guideline, the ratio of the largest to the smallest coefficient should be less than ; smaller is better.

In this example, the matrix range is

3. If possible, re-solve the model using the same parameters and review the logs. With the Python shell, use code like the following:
m.read('gurobi.prm')
m.optimize()

Here are some examples of warning messages that suggest numerical issues:
Warning: Model contains large matrix coefficient range
Consider reformulating model or setting NumericFocus parameter
to avoid numerical issues.
Warning: Markowitz tolerance tightened to 0.5
Numeric error
Numerical trouble encountered
Restart crossover...
Sub-optimal termination
Warning: ... variables dropped from basis
Warning: unscaled primal violation = ... and residual = ...
Warning: unscaled dual violation = ... and residual = ...

4. When the optimize function completes, print solution statistics. With the Python shell, use code like the following:
m.printQuality()

which provides a summary of solution quality:
Solution quality statistics for model Unnamed :
Maximum violation:
Bound       : 2.98023224e-08 (X234)
Constraint  : 9.30786133e-04 (C5)
Integrality : 0.00000000e+00

Violations that are larger than the tolerances are another indication of numerical issues. Also, for a pure LP (without integer variables), print the condition number via the following Python command:

m.KappaExact

The condition number measures the potential for error in linear calculations; a large condition number, such as , is another indication of possible numerical issues, see this section for more details.
5. If changing parameters (e.g., Method or Seed) leads to a different optimization status (e.g., Infeasible instead of optimal), or if the optimal objective values changes, this is usually a sign of numerical issues. To further assess this you can tighten tolerances (to the order of or even ), and see if the behavior of the solver becomes consistent again. Note that tightening tolerances usually comes at the price of more computing time, and should not be considered as a solution for numerical issues.


text:
# Template:EvoLudoLab:RSP

Along the bottom of the applet there are several buttons to control the execution and the speed of the simulations - for details see the EvoLudo GUI documentation. Of particular importance are the parameters button and the data views pop-up list along the top. The former opens a panel that allows to set and change various parameters concerning the game as well as the population structure, while the latter displays the simulation data in different ways.

 Color code: Rock Scissors Paper New rock New scissors New paper
 Payoff code: Low High

## {{{title}}}

{{{doc}}}

### Data views

Snapshot of the spatial arrangement of strategies.
Snapshot of the spatial arrangement of strategies in 3D.
Time evolution of the strategy frequencies.
Trajectories of strategy frequencies shown in the simplex $$S_3$$. Double clicks in the interior of $$S_3$$ set the initial frequencies of strategies.
Snapshot of the spatial distribution of payoffs.
Snapshot of the spatial distribution of payoffs in 3D.
Time evolution of average population payoff bounded by the minimum and maximum individual payoff.
Payoff distribution of each strategy in population.
Degree distribution in structured populations.
Displays messages, warnings and errors reported by the simulation engine plus information on the applet/application.

## Game parameters

The list below describes only the parameters related to the rock-scissors-paper game and the population dynamics. Follow the link for a complete list and descriptions of all other parameters such as spatial arrangements or update rules on the player and population level.

Payoffs
general $$3\times 3$$ payoff matrix for the three strategic types $$R, S, P$$. The rock-paper-scissors game requires cyclic dominance between the three types.
Init Rock, Scissors, Paper
initial frequencies of rock, paper, and scissors types. If they do not add up to 100%, the values will be scaled accordingly.


text:
# Non-relativistic spinors

Even in a non-relativistic theory Spinors can arise as irreducible representations of the rotation subgroup of the symmetries of the theory. Why do people then put so much emphasize on the role of Relativity and the Dirac's equation in the topic? Is it just for historical reasons?

-

The Dirac equation has three predictions which explain phenomena observed in the hydrogen atom energy levels.

1. The gyromagnetic ratio of 2
2. The spin orbit interation which includes the Thomas precession, please, see for example Gurtler and D. Hestenes
3. The Darwin term (please see again, the last reference).

Now, Bargmann already in 1962 discovered the ray representations of the Galilean group (equivalently, the true representations of a central extension of the Galilean group now known as the Bargmann group) and described its spinor representations.

The fact is that it is possible to formulate Galilean invariant wave equations which give the correct gyromagnetic ratio, spin orbit interation and the Darwin term. please see for example FUSHCHYCH, NIKITIN,SALOGUB , however, these equations contain arbitrary parameters which must be fitted to the experiment.

The subject of Galilean invariant wave equations is still under research, please see for example a recent article by : Niederl and Nikitin .

In my opinion, one of the reasons that there are no free parameters in the relativistic case, which makes the relativistic theory especially elegant (in addition to its full consistency with experiment), is that the Lorentz group is simple in contrast with the Galilean group.

I don't know if it is possible to formualte a Galelian invariant theory fully consistent with the experiment in the nonrelativistic regime developed from first principles (as in the case of the Dirac equation) and without ad-hoc terms, but I think it is possible, because the Galilean group can be obtained as an Inonu-Wigner contarction of the Lorentz group. I think that at least, this way, one can reduce the number of free parameters.

-
It's not a huge deal, but while I would agree that the g factor is a prediction of the Dirac equation, the Dirac equation isn't necessary in order to get it right. One can use the non-relativistic Schrodinger-Pauli equation. See pg78-79 in Sakuri's ' Advanced QM.' – DJBunk Jun 12 '12 at 18:29

From a practical standpoint it depends on your field and motivation whether relativity and the Dirac equation are necessary tools. If you are working with things like the Aharonov–Bohm effect or in fields like Quantum Chemistry then full-blown Quantum Field Theory is unnecessary and quantum mechanics will suffice. Single-particle wave functions (or linear combinations of them) will be all you need to do your calculations. If you really want to be more precise then you can add relativistic corrections to your Hamiltonian, but you still don't need the Dirac equation or full blown QFT yet. However, if you are a particle physicist and want to smash things together at large energies and see what comes out you are going to need more machinery. Because of relativity ($E = m c^2$, roughly) you are going to create new, heavier particles either as external states in the final product of the collision or you will see effects of intermediate states of these heavier particles. In short you need a multi-particle theory that takes relativity into account- QFT including the Dirac equation (well, Lagrangian actually) is indispensable in this case. For more information on the limitations of non-relativistic quantum mechanics and how QFT addresses these limitations for particle physics I would see the the end of a Quantum mechanics book (chapter 20 in Shankar for example) or the beginning of a QFT textbook (chapters 1 & 2 of Peskin).

-


text:
# Example: Analytic Frequencies: CN¶

Download CN_SecDeriv.run

#! /bin/sh

# Calculation of analytical second derivatives is requested by specifying:
#   AnalyticalFreq
#   End
# in the ADF input.

# A good quality is specified for the numerical Becke integration to be sure of
# reliable results. In general, it seems advisable to use high accuracy for
# heavy nuclei at the moment, whereas default integration accuracy is usually
# sufficient for light atoms. The precision of the fit may be improved with the
# ZlmFit block keyword.

title CN

atoms
N  -1.3  0.0   0.0
C   0.0  0.0   0.0
end

Basis
Type DZ
Core None
End

charge -1

XC
LDA Xonly
End

BeckeGrid
quality good
End

AnalyticalFreq
End

eor

mv TAPE21 CN.t21
rm -f logfile

# After SCF is completed, the energy second derivatives matrix is calculated and
# analysed, which yields in this case one frequency.


text:
# Can I compare goodness of fit using the Kolmogrov-Smirnov test, if the distributions have a different number of parameters?

It seems that lognormal and Burr distributions are the best to fit my data. Can I compare their goodness of fit using a Kolmogorov-Smirnov test? The lognormal has 2 parameters whereas Burr has 3. To compare the values of the KS test, must the distributions have the same number of parameters?

• I have tried to edit the question to correct a few minor grammatical things but mostly to make the title more closely reflect the intent of the question. If you don't like my changes, feel free to revert them. – Silverfish Jun 4 '16 at 3:34

• 1. If the test is being used (rather than merely comparing test statistics), the parameters are being estimated from the data, so this wouldn't be a Kolmogorov-Smirnov test, it would be a form of Lilliefors test - and no longer nonparametric. $\;$ 2. If we're just comparing KS-statistics, and if the three parameter Burr is flexible enough to approximate the lognormal fairly well, it will essentially always fit at least as well as the lognormal, since it will also be free to not approximate the lognormal ... ctd – Glen_b May 19 '16 at 22:31


text:
# norm¶

tenpy.linalg.np_conserved.norm(a, ord=None, convert_to_float=True)[source]

Norm of flattened data.

Equivalent to np.linalg.norm(a.to_ndarray().flatten(), ord).

In contrast to numpy, we don’t distinguish between matrices and vectors, but simply calculate the norm for the flat (block) data. The usual ord-norm is defined as $$(\sum_i |a_i|^{ord} )^{1/ord}$$.

ord

norm

None/’fro’

Frobenius norm (same as 2-norm)

np.inf

max(abs(x))

-np.inf

min(abs(x))

0

sum(a != 0) == np.count_nonzero(x)

other

ususal ord-norm

Parameters
• a (Array | np.ndarray) – The array of which the norm should be calculated.

• ord – The order of the norm. See table above.

• convert_to_float – Convert integer to float before calculating the norm, avoiding int overflow.

Returns

norm – The norm over the flat data of the array.

Return type

float