text:
Overview¶

This section provides an overview of how pydrobert-speech is organized so that you can get your feature representation just right.

The input to pydrobert-speech are (acoustic) signals. The output are features. We call the operator that transforms the signal to some feature representation a computer. Operators that act on the signal and produce a signal, like random dithering, are preprocessors, and operators that act on features and produce features, like unit normalization, are postprocessors. The latter two operators exist in the submodules pydrobert.speech.pre and pydrobert.speech.post and follow the usage pattern

>>> y = Op().apply(x)

A computer, which can be found in pydrobert.speech.compute, will require more complicated initialization. The standard feature representation, which is a 2D time-log-frequency matrix of energy, derives from compute.LinearFilterBankFrameComputer. It calculates coefficients over uniform time slices (frames) using a bank of filters. Children of LinearFilterBankFrameComputer all have similar representations and all use linear banks of filters, but can be computed in different ways. The classic method of computation is the compute.ShortTimeFourierTransformFrameComputer.

Banks of filters are derived from pydrobert.speech.filters.LinearFilterBank. Children of the parent class, such as filters.ComplexGammatoneFilterBank, will decide on the shape of the filters.

LinearFilterBankFrameComputer instances compute coefficients at uniform intervals in time. However, the distribution over frequencies is decided by the distribution of filter frequency responses from the filter bank, which, in turn, depends on a scaling function. Scaling functions can be found in pydrobert.speech.scales, such as scales.MelScaling. Scaling functions transform the frequency domain into some other real domain. In that domain, filter frequency bandwidths are distributed uniformly which, when translated back to the frequency domain, could be quite non-uniform.

In sum, you build a computer by first choosing a scale from pydrobert.speech.scales. You then pass that as an argument to a filter bank that you’ve chosen from pydrobert.speech.filters. Finally, you past that as an argument to your computer of choice. For example:

>>> from pydrobert.speech import *
>>> scale = scales.MelScaling()
>>> bank = filters.ComplexGammatoneFilterBank(scale)
>>> computer = compute.ShortTimeFourierTransformFrameComputer(bank)
>>> # preprocess the signal
>>> feats = computer.compute_full(signal)
>>> # postprocess the signal

This is a bit different from the syntax described in the README. There, we use aliases. Aliases are a simple mechanism for unpacking hierarchies of parameters, such as the hierarchy between these computers, filter banks, and scales. We can streamline the above initialization as

>>> computer = compute.ShortTimeFourierTransformFrameComputer(
...     {"name": "tonebank", "scaling_function": "mel"})

or even

>>> computer = compute.FrameComputer.from_alias("stft",
...     {"name": "tonebank", "scaling_function": "mel"})

The dictionaries are merely keyword argument dictionaries with the special key "name" or "alias" referring to an alias of the subclass you wish to initialize (unless you just pass a string, at which point it’s considered the alias with no arguments). Aliases are listed in each subclass’ alias class member. Besides for brevity, aliases provide a principled way of storing hierarchies on disk via JSON. Thus, it’s possible to access most of pydrobert-speech’s flexibility from the provided command-line hooks.

Finally, there are some visualization functions in the pydrobert.speech.vis module (requires matplotlib), some extensions to pydrobert-kaldi data iterators in pydrobert.speech.corpus, and command line implementations in pydrobert.speech.command_line.


text:
# Can you recommend an efficient encoding algorithm for sound with long periods of silence?

As a side personal project, I'm coding an Android application that I plan to use to record the sounds of our first baby. I'm kind of new to the world of Android development and sound processing, so please bear with me if this question is naive :)

What I'm trying to do is to constantly save the sounds in our baby room, splitting the recordings in 2-hour intervals. I plan to keep this data for future analysis (e.g. plotting crying times, which I'll correlate with other events, and maybe cry identification).

So far the application is working fine. However, I wonder if there is an efficient codec I can use considering that 90% of the time there will be silence. I've tried modifying the PCM raw data before enters the codec setting to zero any values below a specific threshold, but this did not reduce the file size substantially. This was a wild guess, just in case this would "help" the codec (I've tried AAC/HE and MP3, not yet AMR).

Can you please point me in the right direction?...

I don't mind using a solution that requires post processing of the files. For example, I've looked into http://sox.sourceforge.net, but that strips silence periods reducing the recording length (I want to keep the timestamps and length untouched).

Note: using SoX to split the file in parts using a naming scheme that allows me to reconstitute original times it's an option... but I could not come with that script, yet).

Bonus question: will AMR-NB be enough to encode a baby cry, if I want to run some processing later? (for example this or this) or... should I stick to AMR-WB?

Thank you,

Update July 22nd:

Thanks everyone for the responses so far. The idea of using just WAV injecting zeros, and later using bzip2, etc. to compress the repetitive data is really good (thanks @MBaz).

@Fat32: I've erased the files, but I recall sizes around ~20Mb/hr, with no substantial change after replacing low PCM values (approximately 50% of the stream) with zeros.

Another update: AMR-WB is giving me better results than AAC/HE, ~6 Mb/hr. So I'll probably stick to it, however I'm not sure how the low bitrate + sampling rate will affect things if later I decide to run some infant identification analysis later (i.e. if the loss of information will remove data points crucial for the neural net).

• Traditional entropy encoders such as gzip and bzip2 are very good at compressing repetitive data. Have you tried gzipping the raw PCM? One great benefit would be that you'd have lossless compression. If there is low-level random noise in the PCM, you may try thresholding the data before compression.
– MBaz
Jul 20, 2017 at 14:32
• This is a very good and creative idea, thanks! Jul 22, 2017 at 0:47

Thresholding should reduce the file size to the limits of the encoder being used. AAC/H.264 are using the state of the art general purpose audio compression codecs (which could only be beaten by application specific optimized codecs, such as speech vocoders etc).

May be your files are already minimal? Put some numerical data such as the sampling rate, average bits per sample, recording duration and file sizes...

If I were so inclined to do what you want to do( I have 3 children, youngest is 25 , so I'm not so inclined) , I would use a motion detector to trigger recording for the first few months. Crying is usually accompanied with vigorous hand and arm motion.

There are a number of wifi video cameras with integrated motion detectors and microphones, as well as web based api's.

The most typical situation for a young couple is to be extremely sleep deprived for the first few months. You might want to take a minimal effort approach.

You might try using some sort of activity detector algorithm, and just not feed the codec any data (not even zeros) when no activity was detected. For the time stamps, you might prepend recorded activity with an FSK time mark and/or voice synthesized time announcement, and feed that to the codec in front of the captured audio samples.

You should get rather good results with using both a) a hard noise gate (so that the material compresses perfectly when you are having silence) b) a variable bit rate recording: MP3 as well as OGG/Vorbis encoders can readily provide those.

When you are planning on eventually analyzing breathing patterns, of course the noise gate will either not be effective or ruin your data.

But option b) should also help a bit when used alone.

format: plain


text:
Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Gaussian limits for vector-valued multiple stochastic integrals

Auteur(s):

Code(s) de Classification MSC:

• 60F05 Central limit and other weak theorems
• 60H05 Stochastic integrals

Résumé: We establish necessary and sufficient conditions for a sequence of $d$% -dimensional vectors of multiple stochastic integrals $\mathbf{F}% _{d}^{k}=\left( F_{1}^{k},...,F_{d}^{k}\right)$, $k\geq 1$, to converge in distribution to a $d$-dimensional Gaussian vector $\mathbf{N}_{d}=\left( N_{1},...,N_{d}\right)$. In particular, we show that if the covariance structure of $\mathbf{F}_{d}^{k}$ converges to that of $\mathbf{N}_{d}$, then componentwise convergence implies joint convergence. These results extend to the multidimensional case the main theorem of Nualart and Peccati (2003).

Mots Clés: Multiple stochastic integrals ; Limit theorems ; Weak convergence ; Brownian motion.

Date: 2003-11-04

Prépublication numéro: PMA-861


text:
# Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond

 Title: Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond Author: Stanwix, Paul L.; Pham, Linh My; Maze, Jeronimo R.; Le Sage, David Anthony; Yeung, Tsun Kwan; Cappellaro, Paola; Hemmer, Philip R.; Yacoby, Amir; Lukin, Mikhail D.; Walsworth, Ronald L. Note: Order does not necessarily reflect citation order of authors. Citation: Stanwix, Paul L., Linh M. Pham, Jeronimo R. Maze, David Le Sage, Tsun K. Yeung, Paola Cappellaro, Philip R. Hemmer, Amir Yacoby, Mikhail D. Lukin and Ronald L. Walsworth. 2010. Coherence of nitrogen-vacancy electronic spin ensembles in diamond. Physical Review B 82(20): 201201. Full Text & Related Files: Stanwix_CoherenceNitrogen.pdf (447Kb; PDF) Abstract: We present an experimental and theoretical study of electronic spin decoherence in ensembles of nitrogen-vacancy (NV) color centers in bulk high-purity diamond at room temperature. Under appropriate conditions, we find ensemble NV spin coherence times ($$T_2$$) comparable to that of single NV with $$T_2>600 \mu s$$ for a sample with natural abundance of $$^{13}$$C and paramagnetic impurity density ∼1015 cm$$^{−3}$$. We also observe a sharp decrease in the coherence time with misalignment of the static magnetic field relative to the NV electronic spin axis, consistent with theoretical modeling of NV coupling to a $$^{13}$$C nuclear-spin bath. The long coherence times and increased signal-to-noise provided by room-temperature NV ensembles will aid many applications of NV centers in precision magnetometry and quantum information. Published Version: doi:10.1103/PhysRevB.82.201201 Other Sources: http://walsworth.physics.harvard.edu/oldsite/pdf/e201201.pdf http://walsworth.physics.harvard.edu/publications/2010_Stanwix_PRB.pdf Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8951177

### This item appears in the following Collection(s)

• FAS Scholarly Articles [6466]
Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University


text:
# void qsort

void qsort(void *__base, size_t __nmemb, size_t __size, __compar_fn_t __compar)

The qsort() function is a modified partition-exchange sort, or quicksort.

The qsort() function sorts an array of nmemb objects, the initial member of which is pointed to by base. The size of each object is specified by size. The contents of the array base are sorted in ascending order according to a comparison function pointed to by compar, which requires two arguments pointing to the objects being compared.

The comparison function must return an integer less than, equal to, or greater than zero if the first argument is considered to be respectively less than, equal to, or greater than the second.


text:
# Inferring the conditional mean - Mathematics > Probability

Abstract: Consider a stationary real-valued time series $\{X n\} {n=0}^{\infty}$ with apriori unknown distribution. The goal is to estimate the conditionalexpectation $EX {n+1}|X 0, ., X n$ based on the observations $X 0, .,X n$ in a pointwise consistent way. It is well known that this is not possibleat all values of $n$. We will estimate it along stopping times.

Author: Gusztav Morvai, Benjamin Weiss

Source: https://arxiv.org/


text:
# Windows – Which special variables are available when writing a shell command for a context menu

command linewindowswindows 7windows-registry

When extending the Windows' shell context menu (e.g. for adding an 'Open command here' prompt on directories), a 'command' key needs to be created in the registry.

The value of this 'command' key apparently can be any valid command line.

I want to know which 'special variables' are available for use inside this command line.

For example, I use following command for opening a cmd window from within a directory's context menu (*):

cmd.exe /e:on /f:on /s /k pushd "%V"

I cannot find any reference to what %V actually means or what the full list of such variables is.

(*)
Following registry keys are created for this:

[HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Directory\shell\cmdshell]
@=Open Command Prompt Here"

HKEY_LOCAL_MACHINE\SOFTWARE\Classes\Directory\shell\cmdshell\command]
@="cmd.exe /e:on /f:on /s /k pushd \"%V\""

A comment by Chris Guzak on the Extending Shortcut Menus MSDN article lists the various "command line variables" that are available:

%* – Replace with all parameters.

%~ – Replace with all parameters starting with and following the second parameter.

%0 or %1 – The first file parameter. For example "C:\Users\Eric\Desktop\New Text Document.txt". Generally this should be in quotes and the applications command line parsing should accept quotes to disambiguate files with spaces in the name and different command line parameters (this is a security best practice and I believe mentioned in MSDN).

%<n> (where <n> is 2-9) – Replace with the nth parameter.

%s – Show command.

%h – Hotkey value.

%i – IDList stored in a shared memory handle is passed here.

%l – Long file name form of the first parameter. Note that Win32/64 applications will be passed the long file name, whereas Win16 applications get the short file name. Specifying %l is preferred as it avoids the need to probe for the application type.

%d – Desktop absolute parsing name of the first parameter (for items that don't have file system paths).

%v – For verbs that are none implies all. If there is no parameter passed this is the working directory.

%w – The working directory.

So %L or %l should be preferred.


text:
Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down on April 23, and its replacement, statalist.org is already up and running.

# Re: Re: st: Comparing coefficients across sub-samples

 From Christopher Baum To "" Subject Re: Re: st: Comparing coefficients across sub-samples Date Fri, 3 Aug 2012 12:17:30 +0000

<>
On Aug 3, 2012, at 2:33 AM, James wrote:

> However, my data set has large N (1167) and small T (1 to 20). Is there anyway I can reshape my data and still use -sureg-?

No. By design -sureg- cannot be used when T < N. A fixed effect or dynamic panel data model is appropriate in this setting,
as they assume T fixed as N->\infty.

Kit

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/


text:
# gluonts.dataset.multivariate_grouper module¶

class gluonts.dataset.multivariate_grouper.MultivariateGrouper(max_target_dim: Optional[int] = None, num_test_dates: Optional[int] = None, train_fill_rule: Callable = <function mean>, test_fill_rule: Callable = <function MultivariateGrouper.<lambda>>)[source]

Bases: object

The MultivariateGrouper takes a univariate dataset and groups it into a single multivariate time series. Therefore, this class allows the user to convert a univariate dataset into a multivariate dataset without making a separate copy of the dataset.

The Multivariate Grouper has two different modes:

Training: For training data, the univariate time series get aligned to the earliest time stamp in the dataset. Time series will be left and right padded to produce an array of shape (dim, num_time_steps)

Test: The test dataset might have multiple start dates (usually because

the test dataset mimics a rolling evaluation scenario). In this case, the univariate dataset will be split into n multivariate time series, where n is the number of evaluation dates. Again, the time series will be grouped but only left padded. Note that the padded value will influence the prediction if the context length is longer than the length of the time series.

Rules for padding for training and test datasets can be specified by the user.

Parameters
• max_target_dim – Set maximum dimensionality (for faster testing or when hitting constraints of multivariate model). Takes the last max_target_dim time series and groups them to multivariate time series.

• num_test_dates – Number of test dates in the test set. This can be more than one if the test set contains more than one forecast start date (often the case in a rolling evaluation scenario). Must be set to convert test data.

• train_fill_rule – Implements the rule that fills missing data after alignment of the time series for the training dataset.

• test_fill_rule – Implements the rule that fills missing data after alignment of the time series for the test dataset.

static to_ts(data: Dict[str, Any]) → pandas.core.series.Series[source]


text:
# First fundamental form in the Gibbons-Hawking-York boundary term

Let me expose my problem, I am trying to perform the explicit variation of the Gibbons-Hawking-York boundary term, $$S_{GH}=\int_{\partial M} d^{n-1}x\sqrt{\left|h\right|}K$$ The problem I have is that in the calculation of $\delta\sqrt{\left|h\right|}$, it seems like I should carry the calculation as if $h$ was the first fundamental form $$h_{\mu\nu}=g_{\mu\nu} - \sigma n_{\mu} n_{\nu}$$ inasmuch as I obtain the good result doing so. First, I use the identity $$\delta\sqrt{\left|h\right|} = -\frac12 \sqrt{\left|h\right|} h_{\mu\nu} \delta h^{\mu\nu}$$ then I express $\delta h$ in fuction of $\delta g$ $$\delta h^{\mu\nu} = \delta g^{\mu\nu} -\sigma \delta n^\mu n^\nu -\sigma n^\mu\delta n^\nu$$ and using the fact that $h_{\mu\nu} n^\mu = 0$, we obtain

$$\delta\sqrt{\left|h\right|} = -\frac12 \sqrt{\left|h\right|} h_{\mu\nu} \delta g^{\mu\nu}.$$

My problem is that $h$ is not the first fundamental form in the first expression, but the induced metric. The determinant of the first fundamental form is 0 in gaussian normal coordinates, so it seems like I am skipping a step in this derivation, but I just cannot find what (I never had a course in differential geometry, so my understanding of the difference between the first fundamental form and the induced metric is really poor).

I got the answer reading a book from E. Poisson, what I was doing was indeed wrong, you have to start with the induced metric given by $$h_{ab}= g_{\mu\nu}e^{\mu}_a e^{\nu}_b$$ where $$e^{\mu}_a=\frac{\partial x^{\mu}}{\partial y^a}$$ are the tangent vectors to curves of the hypersurface. Then, you just replace $g$ by $h$ in the usual relation $$\delta\sqrt{\left|h\right|} = -\frac12 \sqrt{\left|h\right|} h_{ab} \delta h^{ab}.$$ Using the Kronecker invariance, one finds
$$\delta\sqrt{\left|h\right|} = \frac12 \sqrt{\left|h\right|} h^{ab} \delta h_{ab}.$$
Then using the fact that $$\delta h_{ab} =\delta g_{\mu\nu}e^\mu_a e^\nu_b$$ since the tangent vectors are invariant, we finally get $$\delta\sqrt{\left|h\right|} = \frac12 \sqrt{\left|h\right|} h^{\mu\nu} \delta g_{\mu\nu}$$ where we have used the definition of the PROJECTOR $$h^{\mu\nu} = h^{ab}e^\mu_a e^\nu_b.$$ And this is where the problem was coming, $h^{\mu\nu}$ is NOT the induced metric, but a projector associated to that induced metric.
and your coordinates $h_{\mu \nu}=g_{\mu \nu}-\sigma n_{\mu}n_{\nu}$ arent gaussian coordinates in general.
gaussian are for example flrw metrics like $ds^2=-dt^2+h_{ij}(t)dx^idx^j$ with spacelike $i,j$ where there is no mixed time/space basis term in the second part of the line element, only a scalefactor dependent on $t$


text:
# The galois group of x^4 + 1 over Q

1. May 19, 2009

### Daveyboy

This thing splits if we adjoin e^ipi/4.
Let $$\zeta$$=e^ipi/4 =$$\frac{\sqrt{2}}{2}$$+$$\frac{i\sqrt{2}}{2}$$
so x4+1=

(x-$$\zeta$$)(x-$$\zeta$$2)(x-$$\zeta$$3)(x-$$\zeta$$4).

Then I want to permute these roots so the Galois group is just S4.

But, Q($$\zeta$$)=Q(i,$$\sqrt{2}$$) and [Q(i,$$\sqrt{2}$$):Q]=4 (degree)

I have the theorem that Galois group $$\leq$$ degree of splitting field over base field.

Since |S4|=24 something is wrong, but what I can not find what is wrong with the logic.

2. May 20, 2009

### matt grime

What's wrong is that you've forgotten the definition of a Galois group - it is the group of field automorphisms, not just the arbitrary permutation of roots.


text:
# Lesson 10

What Are Percentages?

### Problem 1

What percentage of a dollar is the value of each coin combination?

1. 4 dimes
2. 1 nickel and 3 pennies
3. 5 quarters and 1 dime

### Solution

For access, consult one of our IM Certified Partners.

### Problem 2

1. List three different combinations of coins, each with a value of 30% of a dollar.

2. List two different combinations of coins, each with a value of 140% of a dollar.

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

The United States government used to make coins of many different values. For each coin, state its worth as a percentage of $1. $$\frac12$$ cent 3 cents 20 cents$$$2 \frac12$$

### Solution

For access, consult one of our IM Certified Partners.

### Problem 5

Elena bought 8 tokens for $4.40. At this rate: 1. How many tokens could she buy with$6.05?
2. How much do 19 tokens cost?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 9.)

### Problem 6

A snail travels 10 cm in 4 minutes. At this rate:

1. How long will it take the snail to travel 24 cm?
2. How far does the snail travel in 6 minutes?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 8.)

### Problem 7

1. 3 tacos cost \\$18. Complete the table to show the cost of 4, 5, and 6 tacos at the same rate.

number of tacos cost in dollars rate in dollars per taco
3 18
4
5
6
2. If you buy $$t$$ tacos for $$c$$ dollars, what is the unit rate?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 3, Lesson 7.)


text:
Normalize a Gaussian Integer - Maple Help

# Online Help

###### All Products    Maple    MapleSim

Home : Support : Online Help : Mathematics : Group Theory : Numbers : Integer Functions : Gaussian Integers : GaussInt/GInormal

GaussInt[GInormal] - Normalize a Gaussian Integer

 Calling Sequence GInormal(z)

Parameters

 z - Gaussian integer

Description

 • GInormal returns the first quadrant associate of the input Gaussian integer z
 • If z is in the jth quadrant $1\le j\le 4$, ${I}^{5-j}z$ is the first quadrant associate of z

Examples

 > $\mathrm{with}\left(\mathrm{GaussInt}\right):$
 > $\mathrm{GInormal}\left(3-2I\right)$
 ${2}{+}{3}{}{I}$ (1)
 > $\mathrm{GIunitnormal}\left(3-2I\right)$
 $\left[{-}{I}{,}{2}{+}{3}{}{I}{,}{I}\right]$ (2)
 See Also

## Was this information helpful?

 Please add your Comment (Optional) E-mail Address (Optional) What is ? This question helps us to combat spam


text:
Hyperbolica, game dedicated to Non-Euclidean geometry just released on Steam for pi day!
store.steampowered.com/app/125

I'm in Matt Parker's π day video as part of the team failing to reproduce local hero William Shanks's by-hand approximation of π: youtube.com/watch?v=dtiLxLrzjO

Just curious, how many digits of π do you have memorized?

Honestly I haven't really bothered going beyond 9 significant digits (3.14159265) since I doubt any manual estimate calculations I have to do involving π would need further precision, plus I know this truncation is rounded off properly (the next truncation that's also rounded off is 3.141592653589793, an extra 7 digits to tackle)

Chanced upon this #piano album full of pieces inspired by π, released for #PiDay2022:

ecstaticquiet1.bandcamp.com/al

Ukranian conflict

Among some of the volunteers recently reported to be killed in is Yulia Zdanovska, silver medalist for 2017 European Girls’ Olympiad

khpg.org/en/1608810174

44 3/6

⬛🟩⬛⬛⬛🟪🟪⬛
🟪🟩🟩🟪🟩⬛⬛🟩
🟩🟩🟩🟩🟩🟩🟩🟩

34 3/6: quite a lucky starting guess

🟩🟩🟩🟩⬛⬛🟪🟪
🟪🟪🟩🟩⬛🟩⬛⬛
🟩🟩🟩🟩🟩🟩🟩🟩

33 3/6

⬛🟪⬛⬛🟪🟪🟪🟪
🟩🟪🟪⬛🟪🟪🟩🟪
🟩🟩🟩🟩🟩🟩🟩🟩

So I know people have talked about optimal first guesses in , but are there optimal first guesses for ?

Maybe someone can generate all the 8-token equations that comply with Nerdle's rules and perform some info theory analysis on them

Random idea for a game (partially inspired by ):

Give the player a limited number of guesses to figure out a mystery finite set of integers $$S=\{n_1,\ldots,n_k\}$$, given $$k = |S|$$ and hint indicators for each guess $$S_j$$:

- for each $$n_i\in S$$, whether $$n_i \in S_j$$;
- if all $$n_i \in S_j$$, whether $$S=S_j$$ or $$S\subsetneq S_j$$

Prior non-final guesses could be infinite sets to whittle down the possibilities, e.g. $$\{3n:n\in\mathbb{Z}\}$$

2022 = 2 ⋅ 3 ⋅ 337

From Quanta Magazine: a look at some of 2021's breakthroughs in +

quantamagazine.org/the-year-in

Found this YouTuber's personal take on -induced anxiety - well maybe more focused on (mental) arithmetic - and its roots in stress from early experiences in school:

Jordan Ellenberg reacts to some famous scenes depicting on-screen, both great and not-so-great:

(Bonus: he actually consulted for + showed up in one of the movies featured)

Article on Nature outlining a framework for mathematicians to use to discover insights. with case studies in knot theory + representation theory:

nature.com/articles/s41586-021

Yet another discussion on the origin of (discovered or invented?), this time involving William Shatner + Stanford U's Keith Devlin:

Celebrating 10 years of by examining the number 10 (and talking about friendly numbers) 🎂🎉

The recording of "The Great Big and Gameshow", hosted by Dr Tom Crawford on 13 October at IF Oxford, is out on YouTube:

"Irish Dara Ó Briain has received an award for his contribution to raising public awareness of .

This is an award that is presented each year during Maths Week – the annual all-island festival of maths and numeracy, which is currently running with events across the country and online."

siliconrepublic.com/innovation

Just thought of signal boosting the Azimuth Project: azimuthproject.org/azimuth/sho

Show older

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!


text:
Viser treff 1-20 av 25

• #### ATLAS search for new phenomena in dijet mass and angular distributions using pp collisions at $\sqrt{s}$=7 TeV

(Peer reviewed; Journal article, 2013-01)
Mass and angular distributions of dijets produced in LHC proton-proton collisions at a centre-of-mass energy $\sqrt{s}$=7 TeV have been studied with the ATLAS detector using the full 2011 data set with an integrated ...
• #### Flavour tagged time dependent angular analysis of the $B_s^{0} \rightarrow J/\psi \phi$ decay and extraction of $\Delta\Gamma_s$ and the weak phase $\phi_s$ in ATLAS

(Peer reviewed; Journal article, 2014-09)
A measurement of the $B_s ^{0}\rightarrow J/\psi \phi$ decay parameters, updated to include flavour tagging is reported using $4.9 fb^{-1}$ of integrated luminosity collected by the ATLAS detector from $\sqrt{s}= ... • #### Jet energy measurement and its systematic uncertainty in proton–proton collisions at √s=7TeV with the ATLAS detector  (Peer reviewed; Journal article, 2015-01-15) The jet energy scale (JES) and its systematic uncertainty are determined for jets measured with the ATLAS detector using proton–proton collision data with a centre-of-mass energy of s√=7 TeV corresponding to an integrated ... • #### Measurement of isolated-photon pair production in pp collisions at root s=7 TeV with the ATLAS detector  (Peer reviewed; Journal article, 2013-01-11) The ATLAS experiment at the LHC has measured the production cross section of events with two isolated photons in the final state, in proton-proton collisions at s√=7TeV. The full data set collected in 2011, corresponding ... • #### Measurement of the azimuthal anisotropy for charged particle production in \(\sqrt{s_{NN}}$ = 2.76 TeV lead-lead collisions with the ATLAS detector

(Peer reviewed; Journal article, 2012-07-24)
Differential measurements of charged particle azimuthal anisotropy are presented for lead-lead collisions at $\sqrt{s_{NN}}$ = 2.76 TeV with the ATLAS detector at the LHC, based on an integrated luminosity of approximately ...
• #### Measurement of the b-hadron production cross section using decays to D*+ μ − X final states in pp collisions at √s = 7 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2012-11-21)
The b-hadron production cross section is measured with the ATLAS detector in pp collisions at √s = 7 TeV, using 3.3 pb−1 of integrated luminosity, collected during the 2010 LHC run. The b-hadrons are selected by partially ...
• #### Measurement of the cross-section of high transverse momentum vector bosons reconstructed as single jets and studies of jet substructure in $pp$ collisions at ${\sqrt{s}}$ = 7 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2014-11)
This paper presents a measurement of the cross-section for high transverse momentum $W$ and $Z$ bosons produced in $pp$ collisions and decaying to all-hadronic final states. The data used in the analysis were recorded ...
• #### Measurement of the electroweak production of dijets in association with a Z-boson and distributions sensitive to vector boson fusion in proton-proton collisions at √s= 8 TeV using the ATLAS detector

(Peer reviewed; Journal article, 2014-04-07)
Measurements of fiducial cross sections for the electroweak production of two jets in association with a Z-boson are presented. The measurements are performed using 20.3 fb−1 of proton-proton collision data collected at a ...
• #### Measurement of the inclusive isolated prompt photons cross section in pp collisions at √s =7TeV with the ATLAS detector using 4.6fb-1

(Peer reviewed; Journal article, 2014-03)
A measurement of the cross section for the production of isolated prompt photons in pp collisions at a center-of-mass energy √s=7  TeV is presented. The results are based on an integrated luminosity of 4.6  fb−1 collected ...
• #### Measurement of the production cross section of prompt J/ψ mesons in association with a W± boson in pp collisions at √s = 7 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2014-04)
The process pp → W ± J/ψ provides a powerful probe of the production mechanism of charmonium in hadronic collisions, and is also sensitive to multiple parton interactions in the colliding protons. Using the 2011 ATLAS ...
• #### Measurement of the top quark pair production charge asymmetry in proton-proton collisions at √s = 7 TeV using the ATLAS detector

(Peer reviewed; Journal article, 2014-02)
This paper presents a measurement of the top quark pair ( tt¯ ) production charge asymmetry A C using 4.7 fb−1 of proton-proton collisions at a centre-of-mass energy s√ = 7 TeV collected by the ATLAS detector at the LHC. ...
• #### Measurement of the underlying event in jet events from 7 TeV proton–proton collisions with the ATLAS detector

(Peer reviewed; Journal article, 2014-08)
Distributions sensitive to the underlying event in QCD jet events have been measured with the ATLAS detector at the LHC, based on 37 pb‾¹ of proton–proton collision data collected at a centre-of-mass energy of 7 TeV. ...
• #### Measurements of top quark pair relative differential cross-sections with ATLAS in pp collisions at root s=7 TeV

(Peer reviewed; Journal article, 2013-01-15)
Measurements are presented of differential cross-sections for top quark pair production in pp collisions at s√=7 TeV relative to the total inclusive top quark pair production cross-section. A data sample of 2.05 fb−1 ...
• #### Muon reconstruction efficiency and momentum resolution of the ATLAS experiment in proton–proton collisions at √s=7 TeV in 2010

(Peer reviewed; Journal article, 2014-09)
This paper presents a study of the performance of the muon reconstruction in the analysis of proton–proton collisions at √s = 7TeV at the LHC, recorded by the ATLAS detector in 2010. This performance is described in terms ...
• #### Search for a Multi-Higgs Boson Cascade in $W^+W^− b\bar{b}$ events with the ATLAS detector in pp collisions at √s = 8 TeV

(Peer reviewed; Journal article, 2014-02-19)
A search is presented for new particles in an extension to the Standard Model that includes a heavy Higgs boson $H^0$ , an intermediate charged Higgs boson (H±), and a light Higgs boson $h^0$ . The analysis searches ...
• #### Search for dark matter in events with a hadronically decaying W or Z boson and missing transverse momentum in pp collisions at √s = 8 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2014-01-29)
A search is presented for dark matter pair production in association with a W or Z boson in pp collisions representing 20.3  fb−1 of integrated luminosity at s√=8  TeV using data recorded with the ATLAS detector at the ...
• #### Search for dark matter in events with a Z boson and missing transverse momentum in pp collisions at √s = 8TeV with the ATLAS detector

(Peer reviewed; Journal article, 2014-07-10)
A search is presented for production of dark-matter particles recoiling against a leptonically decaying Z boson in 20.3  fb⎻¹ of pp collisions at s√=8  TeV with the ATLAS detector at the Large Hadron Collider. Events with ...
• #### Search for direct chargino production in anomaly-mediated supersymmetry breaking models based on a disappearing-track signature in pp collisions at $\sqrt{s}$=7 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2013-01)
A search for direct chargino production in anomaly-mediated supersymmetry breaking scenarios is performed in pp collisions at $\sqrt{s}$ = 7 TeV using 4.7 fb$^{-1}$ of data collected with the ATLAS experiment at the ...
• #### Search for direct top squark pair production in events with a Z boson, b-jets and missing transverse momentum in √s = 8 TeV pp collisions with the ATLAS detector

(Peer reviewed; Journal article, 2014-06)
A search is presented for direct top squark pair production using events with at least two leptons including a same-flavour opposite-sign pair with invariant mass consistent with the Z boson mass, jets tagged as originating ...
• #### Search for high-mass dilepton resonances in $pp$ collisions at $\sqrt {s}$ = 8 TeV with the ATLAS detector

(Peer reviewed; Journal article, 2014-09)
The ATLAS detector at the Large Hadron Collider is used to search for high-mass resonances decaying to dielectron or dimuon final states. Results are presented from an analysis of proton--proton $pp$ collisions at a ...


text:
# Given a number $N$ and a prime $P$, how many numbers $\leq N$ are divisable by P but not by any smaller primes?

The following Math Exchange question deals with a similar problem:

Not divisible by $2,3$ or $5$ but divisible by $7$

However, the answers given become infeasible quite quickly because the amount of permutations increases too rapidly as P grows.

• It doesn't become infeasible sooo quickly, because the products of primes in the inclusion-exclusion grow pretty fast. What sort of $N$ and $P$ are you interested in? – Daniel Fischer Jun 29 '15 at 8:51
• I'm working with N in the range of 10^9 and P in the range of 10^4, for example. – Nicolás Siplis Jun 29 '15 at 8:54
• Then you have around $1000$ primes less than $P$ to consider, and the products of such primes you need to consider do not exceed about $10^5$. That's products of at most six primes. With a good dynamic programming approach to break out as soon as you can, that is feasible. At least unless you have very tight time constraints. If you don't need an exact count and an approximation suffices, Mertens' third theorem becomes relevant. – Daniel Fischer Jun 29 '15 at 9:05
• I considered applying Merten's third theorem but I figured inclusion-exclusion would yield a better answer. – Nicolás Siplis Jun 29 '15 at 9:07
• Wait. The quotient $N/P$ is only about $10^5$, when $P$ is near the upper end. That calls for sieving. Take the DP approach when $P$ is smaller. – Daniel Fischer Jun 29 '15 at 9:08


text:
We Do Space Research.

# Learning Materials

• 一文看懂AutoEncoder模型演进图谱
• “深度推荐系统”
• AutoEncoder; Denoising AutoEncoder; Sparse AutoEncoder; CNN/LSTM AutoEncoder;
• 生成模型引入AutoEncoder --> Variational AutoEncoder (VAE是一个里程碑式的研究成果，倒不是因为他是一个效果多幺好的生成模型，主要是提供了一个结合概率图的思路来增强模型的鲁棒性。后续有很多基于VAE的扩展，包括infoVAE、betaVAE和factorVAE等。)
• 自动编码器：各种各样的自动编码器
• https://blog.keras.io/building-autoencoders-in-keras.html
• 通常情况下，使用自编码器做数据压缩，性能并不怎么样。
• 自编码器在实际应用中用的很少，2012年人们发现在卷积神经网络中使用自编码器做逐层预训练可以训练深度网络
• 到了2015年底，通过使用残差学习（ResNet）我们基本上可以训练任意深度的神经网络。（查这个用ResNet的训练方法）
• 自编码器并不是一个真正的无监督学习的算法，而是一个自监督的算法
• 如果你的输入是序列而不是2D的图像，那么你可能想要使用针对序列的模型构造自编码器，如LSTM。要构造基于LSTM的自编码器，首先我们需要一个LSTM的编码器来将输入序列变为一个向量，然后将这个向量重复N此，然后用LSTM的解码器将这个N步的时间序列变为目标序列。

• 自监督学习是监督学习的一个实例，其标签产生自输入数据。要获得一个自监督的模型，你需要想出一个靠谱的目标跟一个损失函数，问题来了，仅仅把目标设定为重构输入可能不是正确的选项（为什么？）

• 基本上，要求模型在像素级上精确重构输入不是机器学习的兴趣所在，学习到高级的抽象特征才是。
• 事实上，当你的主要任务是分类、定位之类的任务时，那些对这类任务而言的最好的特征基本上都是重构输入时的最差的那种特征。
• MATLAB: Train Stacked Autoencoders for Image Classification
• This example showed how to train a stacked neural network to classify digits in images using autoencoders.

Mark E Pittelkau, “Survey of Calibration Algorithms for Spacecraft Attitude Sensors and Gyros”, Advances in the Astronautical Sciences, vol. 129, 2007, pp. 1–55.

# 1. Introduction

The purpose of this paper is to present an overview of the various calibration algorithms, to examine their merits, and to show where and how they have been applied.

This survey extends back to 1969, although there were some relatively minor developments before that time.

This survey focuses mainly on methods rather than applications.

A critical review of the literature is provided, including strengths and weaknesses of algorithms and an assessment of results and conclusions in the literature.

In this post I summarize everything about GP. An individual post will be organized when I felt that I got enough materials, insights, and thoughts.

At the end, I attach all other individual posts about GP or having mentioned GP.

Jonathan Ko, “Gaussian Process for Dynamic Systems”, PhD Thesis, University of Washington, 2011.

Bayes filter equation in Eq. 4.1 (p.34) has a typo (should be $\propto$, not $=$)

$p(x_t|z_{1:t},u_{1:t-1}) \propto p(z_t|x_t) \int \textcolor{red}{p(x_t|x_{t-1},u_{t-1})} \textcolor{green}{p(x_{t-1}|z_{1:t-1},u_{1:t-2})} dx_{t-1}$

• $\textcolor{red}{Red}$ part is dynamics model, describing how the state $x$ evolves in time based on the control input $u$ (p.34)
• $\textcolor{green}{Green}$ part is observation model, describing the likelihood of making an observation $z$ given the state $x$
• GP-BayesFilter improves these two parts.

The dynamics model maps the state and control $(x_t,u_t)$ to the state transition $\Delta x_t = x_{t+1} - x_t$. So, the training data is

$D_p = <(X,U),X'>$

The observation model maps from the state $x_t$ to the observation $z_t$. So, the training data is

$D_o = $

The resulting GP dynamics and observation models are (p.44)

$p(x_t|x_{t-1},u_{t-1}) \approx \mathcal{N}(\text{GP}_\mu([x_{t-1},u_{t-1}],D_p), \text{GP}_\Sigma([x_{t-1},u_{t-1}],D_p))$

and

$p(z_t|x_t) \approx \mathcal{N}(\text{GP}_\mu(x_t,D_o), \text{GP}_\Sigma(x_t,D_o))$

Bruce P. Gibbs, Least-squares estimation, kalman filtering, and modeling: a practical handbook, Hoboken, N.J: Wiley, 2011.

Rasmussen, Carl Edward, and Christopher K. I. Williams. 2006. Gaussian Processes for Machine Learning. Adaptive Computation and Machine Learning. Cambridge, Mass: MIT Press. http://www.gaussianprocess.org/gpml/chapters/.

# 笔记

Sec 2讲了做regression的几乎所有基础理论。

Sec 3讲做classification，没有看。

Sec 4讲不同covairance的性质，未看，待看。

Bayesian inference