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Wednesday, 24 May 2017, 3:29 AM
Site: Learning Management System
Course: 601393 - Human Computer Interaction Course File (603393CF-11)
Glossary: hci g
J

#### joint action

Both people involved in a joint action intend to do their part and believe that the joint action includes their and the other person’s part. (See the text for a more formal and comprehensive definition.)

#### juxtaposability

A level of visibility (in the cognitive-dimensions framework) at which any required subset of components can be viewed simultaneously. It is an essential requirement for certain cognitive strategies, such as design by modification of existing material, or for checking consistency of form across instances of similar components. See also visibility.

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Conference Photo

# Introduction

The workshop is intended to discuss ongoing and future work studying the central molecular zone of our galaxy, with a particular emphasis on the relationship between the molecular gas and star formation.

The conference web page is http://eso.org/~aginsbur/ESO-CMZ-2015.html and abstracts are listed at http://eso.org/~aginsbur/abstracts.html.

This document is intended to include notes from the workshop and a starting point for future work, especially observing proposals and perhaps even papers.

# The “Dense” ISM

Discussions on what would normally be considered high-density gas ($$n\sim10^4$$ cm$$^{-3}$$) but in the CMZ is “typical”.

What are the true gas densities and what is the density distribution? Which clouds are bound? Are they supported by turbulence, magnetic fields, thermal pressure, shear, or are they freely collapsing?

What are the magnetic fields and temperatures of these clouds?

What is the geometry of the molecular gas in the CMZ - is there really a ring? Are the clouds on elliptical orbits? Which orbits?

Do cosmic rays, turbulence, x-rays, photons at other wavelengths, or other mechanisms heat the cloud interiors? Exteriors?

What do we still need to understand from the kinematics? Are positions every uniquely associated with a given kinematic signature? How can we describe the turbulence?

What explains the “cloud collision” kinematics often seen toward CMZ clouds (Tanaka et al., 2015; Tanaka et al., 2014; Oka et al., 2012)?

Comparison of H2CO and NH3 temperatures and morphology – large and small scales

## Global properties?

Total molecular mass? $$4\times10^7$$ M$$_\odot$$ out to $$r<200$$ pc?

Slightly less than 5% of the total molecular gas reservoir of $$\sim8.4\times10^8$$ in the Galaxy is concentrated in the center of the Galaxy, in a region with a diameter of $$\sim$$ 600 parsecs (Dahmen et al., 1998; Nakanishi et al., 2006). The total mass of molecular gas in the CMZ is believed to be 3$$^{+2}_{-1}\times10^7$$ (Dahmen et al., 1998), with 10% of this gas concentrated in one giant molecular cloud complex, Sgr B2 (Gordon et al., 1993), located $$\sim$$ 100 parsecs in projection to the east of the dynamical center of the Galaxy.

# Cores in the CMZ

Protostellar cores are, by definition, the precursors to stars. What do they look like in the CMZ? Are there good chemical tracers for cores in the CMZ? Are dust-based masses accurate?

Why don’t we observe cores in The Brick? Are they absent, or invisible? Do we see cores in other clouds? How do cores in the CMZ compare with cores in the Galactic plane?

# Comparison to the Galactic Disk

How does star formation differ in our Galactic center from the rest of the Galaxy?

Longmore et al. (2013): Lower SFR/dense gas

How do the isotope ratios in the center of the Milky Way compare to the disk? $$^{13}$$C/$$^{12}$$C appears lower, at least, (e.g., Riquelme et al., 2010), as do more recent estimates of the $$^{15}$$N/$$^{14}$$N ratio (Adande et al., 2011).

# Comparison to other Galaxies

What are the most similar galactic centers to our own? What can we learn from comparing these galaxies to ours?

How does our galactic center compare with other galaxies? Its pressure and sensitivity are similar to high-z star-forming galaxies (Kruijssen et al., 2013).

1. M83: similar mass galaxy, more active CMZ, face on

How do isotope ratios in the Galactic center compare to those in the (centers of) other galaxies, and what role does opacity play in measurements in both of these regions?

With ALMA it will be easily possible for galaxies at  3 Mpc to observe their centers at parsec-scale resolution, or the resolution of existing (and planned) single-dish millimeter surveys. In our Galactic center, what can then be done is to probe inside any particularly representative or “proxy” clouds at resolutions orders of magnitude more compact than can be achieved in the more distant and extreme nuclei.

# Molecular gas around a black hole

How is molecular gas affected by the presence of Sgr A*? Do we see its effects anywhere beyond the circumnuclear disk? (yes) SiO has been suggested to be correlated with the Fe 6.4 KeV line in the central 200 pc (Martin-Pintado et al., 2000), with the G0.11-0.11 cloud (Handa et al., 2006) being a notable example of very high SiO abundances being associated with time-variable X-ray emission (Ponti et al., 2010).

# Summary of existing and ongoing surveys

Sorted from low to high frequency. Probably should be a table.

Uniform-coverage Surveys:

Pointed & Targeted Surveys (typically toward high column-density gas):

• 230 GHz SMA Legacy Survey of the CMZ (Battersby, Keto)

• NH3 (1,1)-(5,5) and H2O masers, GCMS (Kauffmann et al.)

• NH3 (1,1)-(7,7), HC3N, and CH3OH masers (Mills et al.)

• 220 + 290 GHz APEX observations of five/seven CMZ clouds (Immer, Kauffmann, Pillai)

Missing: 50-80 GHz, 115-210 GHz

Options for filling in these frequency ranges:

• GBT 4mm receiver : 67-93 GHz

• ALMA Band 4: 125-163 GHz

• APEX Band 5 (SEPIA): 158-211 GHz

Figure showing coverage for a selection of existing and in-progress surveys (Figure needs inclusion of APEX-H2CO, SWAG and SMA surveys to be up to date; such inner 2 degree surveys should probably by done with a zoomed-in secondary figure)

Rough map of existing and proposed-for ALMA observations in the inner R < 200 pc, with arcsecond (subarcsecond to 1.5 arcsecond) resolution.

Non-exhaustive map of existing and proposed-for high-frequency VLA observations at  2-3$$''$$ resolution

# Proposals: Ideas and plans

(remember that this is public)

Large surveys of the CMZ: More needed? How should we prioritize?

1. LASMA band 7 APEX survey?

2. JCMT-HARPS CO 3-2 survey?

3. Multi-J 13CO surveys?

Followup to APEX 1.4mm survey? Bigger, deeper, complementary transitions?

Followup to SMACMZ survey? More area? Higher frequency? Multiple frequencies? ALMA, SMA?

Low frequencies: VLA large survey? Extension of Law et al. (2008)a continuum survey?

1. (deep) S band, to include CH and recombination lines?

2. X band, to include HC3N 1-0?

# Preparing for Cycle 4

What line surveys (single dish and other) exist?

Cover a large area with a single band (3?) or a targeted cloud sample at multiple bands for, e.g., excitation?

ALMA configuration options:

• No special modes (OTF)

• Vanilla setup: band 3, 4, 5, or 6 (or 7)

• At least 2 GHz continuum? Or just spectral line?

# SMA-CMZ

8 GHz now, 16 GHz future, but extra 8 GHz probably only good for continuum

Data to become public when they are reduced.

How can we identify star forming cores? Original idea: hot core tracers + outflows. Does that work? CH$$_3$$OH masers, but incomplete/maybe just shock tracers?

Evolutionary sequence in massive cores seen in dust ridge clouds. Steve: free-fall times come from single-dish, large scale. Diederik: position along ridge dominates spread in density. (Comment by Diederik: I have now checked this quantitatively and it turns out that the position is indeed somewhat more important, but not by much – from Table 2 in Kruijssen et al. (2015), the time-scale spread is from 0.30 Myr post-pericentre to 0.74 post-pericentre (a factor of 2.5), whereas the density spread is factor of 4 => factor of 2 in free-fall time.)

Lines mapped: H$$_2$$CO, C$$^{18}$$O, CH$$_3$$OH, $$^{13}$$CO, SiO.

Sgr B2: Dust is dominant at 1mm, but free-free is partially still present

Lots of interesting & impressive detections. PDFs - do they mean anything?

# Mixed temperature components

How much gas can be cold?

# Hi-Gal Compact Sources

Single-band extraction with subsequent band-merging

Inner region: 27% “protostellar” and 73% “prestellar” sources in $$|\ell|<5$$. Large dispersion in latitude for both populations.

Most higal “cores” are clouds in the CMZ

Qizhou: Correlation with 24sources? Yes, included. Do all 24 sources have 70 counterparts? Yes.

Dust temperature: CMZ vs Galactic disk - essentially the same in both. 16 vs 13 K for proto/pre-stellar. L/M is also nearly the same in and out of the CMZ... slightly less difference in the CMZ than outside.

# Milky Way simulation: Emsellem, Renaud, Bournaud, Teyssier

http://irfu.cea.fr/Pisp/florent.renaud/mw_large.php

See ref paper = (Renaud 2013) and (Emsellem 2014)

Relative Milky Way BH and nuclear cluster mass may be an order of magnitude less than in simulation, BH / CMZ (MW) $$\sim0.1$$ BH/CMZ(sim) but to be checked.

Clearly the mass ratio, extent, etc will decide on the fate, and cycle (if cycle there is).

# The IMF

The relevant papers, that expand the view of what such extreme conditions mean in galaxies beyond the CMZ are : http://adsabs.harvard.edu/abs/2011MNRAS.414.1705P

and for some of the consequences for the initial conditions of SF and the IMF:

Future Meetings?

Prior to Cycle 4 call: similar meeting? 20ish participants Where?

Lorentz Center? Sexten? Aspen?

IAU 322 Australia Reefish 25-29 July 2016?

Aspen center:

• Summer workshop deadline end of May. Summer 2016, 40 participants. 3 weeks

• Winter workshop deadline January. Winter 2016. 80 participants. 1 week

• Summer 2017.... deadline May 2016?

(Higher energy) CMZ-focused meetings:

• Ringberg June 5-11

• COSPAR July 30-August 4?

• Summer 2016 - ESO Galactic star formation meeting

# Key follow-up work

• Further proper motion studies. Interested: Everyone.

• Large spatial scale ($$b\pm1$$) CO mapping to test Diederik’s latest theory

• SEPIA line surveys - what is useful in Band 5?

• keep an eye on the CO J=3-2 mapping projects (ongoing) - they may lead to followup with LASMA higher-J high-density tracers? (characterize density, temperature more accurately)

### References

1. G. Dahmen, S. Huttemeister, T. L. Wilson, R. Mauersberger. Molecular gas in the Galactic center region. II. Gas mass and N_, = H_2/I_^(12)CO conversion based on a C^(18)O(J = 1 - 0) survey. 331, 959-976 (1998).

2. M. A. Gordon, U. Berkermann, P. G. Mezger, R. Zylka, C. G. T. Haslam, E. Kreysa, A. Sievers, R. Lemke. Anatomy of the Sagittarius complex. 3: Morphology and characteristics of the SGR B2 giant molecular giant molecular cloud. 280, 208-220 (1993).

3. P. A. Jones, M. G. Burton, M. R. Cunningham, N. F. H. Tothill, A. J. Walsh. Spectral imaging of the central molecular zone in multiple 7-mm molecular lines. 433, 221-234 (2013). Link

4. P. A. Jones, M. G. Burton, M. R. Cunningham, M. A. Requena-Torres, K. M. Menten, P. Schilke, A. Belloche, S. Leurini, J. Martín-Pintado, J. Ott, A. J. Walsh. Spectral imaging of the Central Molecular Zone in multiple 3-mm molecular lines. 419, 2961-2986 (2012).

5. J. M. D. Kruijssen, S. N. Longmore. Comparing molecular gas across cosmic time-scales: the Milky Way as both a typical spiral galaxy and a high-redshift galaxy analogue. 435, 2598-2603 (2013).

6. J. M. D. Kruijssen, J. E. Dale, S. N. Longmore. The dynamical evolution of molecular clouds near the Galactic Centre - I. Orbital structure and evolutionary timeline. 447, 1059-1079 (2015).

7. C. J. Law, F. Yusef-Zadeh, W. D. Cotton. A Wide-Area VLA Continuum Survey near the Galactic Center at 6 and 20 cm Wavelengths. 177, 515-545 (2008).

8. C. J. Law, F. Yusef-Zadeh, W. D. Cotton, R. J. Maddalena. Green Bank Telescope Multiwavelength Survey of the Galactic Center Region. 177, 255-274 (2008).

9. S. N. Longmore, J. Bally, L. Testi, C. R. Purcell, A. J. Walsh, E. Bressert, M. Pestalozzi, S. Molinari, J. Ott, L. Cortese, C. Battersby, N. Murray, E. Lee, J. M. D. Kruijssen, E. Schisano, D. Elia. Variations in the Galactic star formation rate and density thresholds for star formation. 429, 987-1000 (2013).

10. H. Nakanishi, Y. Sofue. Three-Dimensional Distribution of the ISM in the Milky Way Galaxy: II. The Molecular Gas Disk. 58, 847-860 (2006).

11. T. Oka, Y. Onodera, M. Nagai, K. Tanaka, S. Matsumura, K. Kamegai. ASTE CO J = 3-2 Survey of the Galactic Center. 201, 14 (2012).

12. G. Ponti, R. Terrier, A. Goldwurm, G. Belanger, G. Trap. Discovery of a Superluminal Fe K Echo at the Galactic Center: The Glorious Past of Sgr A* Preserved by Molecular Clouds. 714, 732-747 (2010). Link

13. D. Riquelme, M. A. Amo-Baladron, J. Martin-Pintado, R. Mauersberger, S. Martin, L. Bronfman. Tracing gas accretion in the Galactic center using isotopic ratios. ArXiv e-prints (2010).

14. K. Tanaka, M. Nagai, K. Kamegai, T. Oka. CO-0.30-0.07: A Peculiar Molecular Clump with an Extremely Broad Velocity Width. ArXiv e-prints (2015).

15. Kunihiko Tanaka, Tomoharu Oka, Shinji Matsumura, Makoto Nagai, Kazuhisa Kamegai. High Velocity Compact Clouds in the Sagittarius C Region. (2014).

16. A. J. Walsh, S. L. Breen, T. Britton, K. J. Brooks, M. G. Burton, M. R. Cunningham, J. A. Green, L. Harvey-Smith, L. Hindson, M. G. Hoare, B. Indermuehle, P. A. Jones, N. Lo, S. N. Longmore, V. Lowe, C. J. Phillips, C. R. Purcell, M. A. Thompson, J. S. Urquhart, M. A. Voronkov, G. L. White, M. T. Whiting. The H$$_{2}$$O Southern Galactic Plane Survey (HOPS) - I. Techniques and H$$_{2}$$O maser data. 416, 1764-1821 (2011).

17. F. Yusef-Zadeh, M. Wardle, D. Lis, S. Viti, C. Brogan, E. Chambers, M. Pound, M. Rickert. 74 MHz Nonthermal Emission from Molecular Clouds: Evidence for a Cosmic Ray Dominated Region at the Galactic Center. Journal of Physical Chemistry A 117, 9404-9419 (2013).

18. F. Yusef-Zadeh, W. Cotton, S. Viti, M. Wardle, M. Royster. Widespread Methanol Emission from the Galactic Center. ArXiv e-prints (2013).

19. G R Adande, L M Ziurys. MILLIMETER-WAVE OBSERVATIONS OF CN AND HNC AND THEIR 15N ISOTOPOLOGUES: A NEW EVALUATION OF THE 14N/ 15N RATIO ACROSS THE GALAXY. The Astrophysical Journal 744, 194 (2011).

20. E. Emsellem, F. Renaud, F. Bournaud, B. Elmegreen, F. Combes, J. M. Gabor. The interplay between a galactic bar and a supermassive black hole: nuclear fuelling in a subparsec resolution galaxy simulation. Monthly Notices of the Royal Astronomical Society 446, 2468–2482 Oxford University Press (OUP), 2014. Link

21. Toshihiro Handa, M Sakano, Seiichiro Naito, M Hiramatsu, M Tsuboi. Thermal SiO and H13CO+ Line Observations of the Dense Molecular Cloud G0.11-0.11 in the Galactic Center Region. The Astrophysical Journal 636, 261 (2006).

22. J Martin-Pintado, P de Vicente, Nemesio J Rodríguez-Fernández, A Fuente, P Planesas. A correlation between the SiO and the Fe 6.4 keV line emission from the Galactic center. Astronomy and Astrophysics 356, L5 (2000).

23. F. Renaud, F. Bournaud, E. Emsellem, B. Elmegreen, R. Teyssier, J. Alves, D. Chapon, F. Combes, A. Dekel, J. Gabor, P. Hennebelle, K. Kraljic. A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds. Monthly Notices of the Royal Astronomical Society 436, 1836–1851 Oxford University Press (OUP), 2013. Link


text:
GrounderUK

Joined 24 January 2015

Hello. You can leave me a message on my talk page. If you have a comment about the contents of this, my user page, please feel free to make a careful change here, if that's easier for you. Please include a link to your talk page. If you expect a reply, please also leave a comment on my talk page. I am here to help (among other things).

My mother tongue is British English. I speak several European languages, so I might call myself un citoyen européen de l'anglophonie. My professional career has included writing and reviewing many hundreds of documents by or for people for whom English is a second or third language (for a few, perhaps a higher ordinal applies). I have been an en.wikipedia and en.wiktionary contributor on an occasional basis for many years.

Wikipedia:Babel
 en This user is a native speaker of the English language.

Keeping it simpler

Keeping it simple is hard. I just aim to make it simpler.

Word choice

Simpler words are usually more common than less simple alternatives, but not always. If the natural word to use is simple enough, using a more common word could be less simple. For example, walk is quite a common word (ranking around 2000) but go, on and foot are all more common. Should I write If you go on foot to work... or If you walk to work...? What about Take the dog for a go on foot!? Actually, the verb walk [215] is slightly more common than the noun foot [214] but the form of the verb walk [66] is less common than the singular of the noun foot [73]. And if we look at the string walk [×244], we see that foot [×176] is a little less common and {go} on foot [×0.27] is almost rare. (The braces { and } around go just indicate that all forms of the verb are counted, so it includes went on foot and going on foot, for example. The string walk does not include strings beginning walk; {walk} [×611] is just plain common: about the same as the word above [×609].)

Putting words together

A word is never going to make a good encyclopedia by itself. A list of words is hardly any better. A series of simple sentences might be good enough.

Putting sentences together

A simple series of simple sentences made up of simple words is not a simple encyclopedia. The sentences need to be organised. Sentences about the same thing belong in the same article. They may even belong in the same sentence. Putting two or more sentences into the same sentence is called conjunction. Simple conjunction uses words like and or but or punctuation like colons and semi-colons; the result is a less simple sentence. Less simple conjunction (of sentences) makes one sentence less important than another. This is called subordination. The result may be a main clause and a subordinate clause, which it is in this sentence...

Paragraphs, sub-sections and sections

The topic of an article will be the sub-topic of some other article, to which it should link (early on). The sub-topics of an article should be in the article itself, with a link to any article which has the sub-topic as its topic (typically a Main Article). Two uncommon words are proximate [×1] and ultimate [×60] [1]. If an article does not link to its proximate category by use of a Category page, there should be a phrase in the first sentence or two of the article's Lead Section. For example, "William Shakespeare was a person from Warwickshire in England who wrote plays and poems, mainly between 1590 and 1613." (there is no category for Warwickshire playwright/poets of the late 16th and early 17th century, perhaps because there would be only one notable person in that category).

Note

Numbers in brackets show how often a word has been used in texts contained in the British National Corpus. I use an × to show relative frequency. "[×60]" means that a word has been used sixty times more often than a word followed by "[×1]". For more common words, I may simply use a number [493]. This is the number of times the word occurs (on average) for each million words in an earlier version of the corpus which has a Creative Commons licence. The word number has a frequency of 493, according to my source.[2] Because the corpus contains about one hundred million words, this means that it occurs there about 49,300 times ${\displaystyle ({\tfrac {493}{1,000,000}}}$  × ${\displaystyle 100,000,000=49,300)}$ .

I have been using the cqpweb website to query the British National Corpus (XML Edition). Sadly, I cannot find any licensing or citation links there, but the creator does request a reference to his article in "published research" (so I hope my citation on this page will do for now).

BNC itself provides a bibliographic reference: "The British National Corpus, version 3 (BNC XML Edition). 2007. Distributed by Bodleian Libraries, University of Oxford, on behalf of the BNC Consortium. URL: http://www.natcorp.ox.ac.uk/". It is my belief, however, that its licensing relates to the text within the Corpus, not statistical analysis of those texts (or any subset of them). Put simply, I can tell you how often a word is used but I cannot quote an example from the Corpus [x7]. In case I am wrong: "Data cited herein have been extracted from the British National Corpus, distributed by the University of Oxford on behalf of the BNC Consortium. All rights in the texts cited are reserved." (You will note that no texts have, in fact, been cited.)

I am working on a spreadsheet version of Creative Commons frequency data [2] ("BNC1994") and I shall share a read-only link when it is finished. For now, you may find the draft web version v0.1 of some use. Please feel free to ask if you would like some help. Or leave comments on my talk page,

References

1. Hardie, A (2012). "CQPweb - combining power, flexibility and usability in a corpus analysis tool" (PDF). cqpweb.lancs.ac.uk/usr/index.php?ui=who_the_hell. International Journal of Corpus Linguistics 17 (3). pp. 380–409. Archived from the original (PDF) on 2020-06-16. Retrieved 2020-06-07.
2. "Companion Website for: Word Frequencies in Written and Spoken English: based on the British National Corpus". Archived from the original on 6 November 2019. Retrieved 2020-04-05.


text:
UGC NET Follow
March 12, 2021 8:48 am 30 pts
The variability in observed values of dependent variable y about the regression line is measured in terms of OVariance O Residuals O Observed value OEstimated Value
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• Rucha rajesh shingvekar
variance
• Rucha rajesh shingvekar
The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The ...
• Priya gulani
The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean. Variance tells you the degree of spread in your data set. The...


text:
### Top 4 Arxiv Papers Today in Rings And Algebras

##### #1. Tor-pairs: products and approximations
###### Manuel Cortés Izurdiaga
Recently the author has studied rings for which products of flat modules have finite flat dimension. In this paper we extend the theory to characterize when products of modules in $\mathcal T$ have finite $\mathcal T$-projective dimension, where $\mathcal T$ is the left hand class of a Tor-pair $(\mathcal T,\mathcal S)$, relating this property with the relative $\mathcal T$-Mittag-Leffler dimension of modules in $\mathcal S$. We apply these results to study the existence of approximations by modules in $\mathcal T$. In order to do this, we give short proofs of the well known results that a deconstructible class is precovering and that a deconstructible class closed under products is preenveloping.
more | pdf | html
None.
###### Tweets
mathRAb: Manuel Cortés Izurdiaga : Tor-pairs: products and approximations https://t.co/RB3jm1MzO0 https://t.co/8Hsg4Y14wV
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Sample Sizes : None.
Authors: 1
Total Words: 6816
Unqiue Words: 1262

##### #2. Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras
###### G. R. Biyogmam, J. M. Casas, N. Pacheco Rego
In this paper, we introduce the notion Lie-derivation. This concept generalizes derivations for non-Lie Leibniz algebras. We study these Lie-derivations in the case where their image is contained in the Lie-center, call them Lie-central derivations. We provide a characterization of Lie-stem Leibniz algebras by their Lie-central derivations, and prove several properties of the Lie algebra of Lie-central derivations for Lie-nilpotent Leibniz algebras of class 2. We also introduce ${\sf ID}_*-Lie$-derivations. A ${\sf ID}_*-Lie$-derivation of a Leibniz algebra G is a Lie-derivation of G in which the image is contained in the second term of the lower Lie-central series of G, and that vanishes on Lie-central elements. We provide an upperbound for the dimension of the Lie algebra $ID_*^{Lie}(G)$ of $ID_*Lie$-derivation of G, and prove that the sets $ID_*^{Lie}(G)$ and $ID_*^{Lie}(G)$ are isomorphic for any two Lie-isoclinic Leibniz algebras G and Q.
more | pdf | html
None.
###### Tweets
mathRAb: G. R. Biyogmam, J. M. Casas, N. Pacheco Rego : Lie-central derivations, Lie-centroids and Lie-stem Leibniz algebras https://t.co/zFIgbX4ZBg https://t.co/6HvlwFS9uk
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 3
Total Words: 9870
Unqiue Words: 1637

##### #3. Pointed Hopf actions on central simple division algebras
###### Pavel Etingof, Cris Negron
We examine actions of finite-dimensional pointed Hopf algebras on central simple division algebras in characteristic 0. (By a Hopf action we mean a Hopf module algebra structure.) In all examples considered, we show that the given Hopf algebra does admit a faithful action on a central simple division algebra, and we construct such a division algebra. This is in contrast to earlier work of Etingof and Walton, in which it was shown that most pointed Hopf algebras do not admit faithful actions on fields. We consider all bosonizations of Nichols algebras of finite Cartan type, small quantum groups, generalized Taft algebras with non-nilpotent skew primitive generators, and an example of non-Cartan type.
more | pdf | html
None.
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 2
Total Words: 11972
Unqiue Words: 2290

##### #4. On the Galois correspondence for Hopf Galois structures arising from finite radical algebras and Zappa-Szép products
###### Lindsay N. Childs
Let $L/K$ be a $G$-Galois extension of fields with an $H$-Hopf Galois structure of type $N$. We study the ratio $GC(G, N)$, which is the number of intermediate fields $E$ with $K \subseteq E \subseteq L$ that are in the image of the Galois correspondence for the $H$-Hopf Galois structure on $L/K$, divided by the number of intermediate fields. By Galois descent, $L \otimes_K H = LN$ where $N$ is a $G$-invariant regular subgroup of $\mathrm{Perm}(G)$, and then $GC(G, N)$ is the number of $G$-invariant subgroups of $N$, divided by the number of subgroups of $G$. We look at the Galois correspondence ratio for a Hopf Galois structure by translating the problem into counting certain subgroups of the corresponding skew brace. We look at skew braces arising from finite radical algebras $A$ and from Zappa-Sz\'ep products of finite groups, and in particular when $A^3 = 0$ or the Zappa-Sz\'ep product is a semidirect product, in which cases the corresponding skew brace is a bi-skew brace, that is, a set $G$ with two group operations $\circ$...
more | pdf | html
None.
None.
None.
###### Other stats
Sample Sizes : None.
Authors: 1
Total Words: 0
Unqiue Words: 0

Assert is a website where the best academic papers on arXiv (computer science, math, physics), bioRxiv (biology), BITSS (reproducibility), EarthArXiv (earth science), engrXiv (engineering), LawArXiv (law), PsyArXiv (psychology), SocArXiv (social science), and SportRxiv (sport research) bubble to the top each day.

Papers are scored (in real-time) based on how verifiable they are (as determined by their Github repos) and how interesting they are (based on Twitter).

To see top papers, follow us on twitter @assertpub_ (arXiv), @assert_pub (bioRxiv), and @assertpub_dev (everything else).

To see beautiful figures extracted from papers, follow us on Instagram.

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text:
# Is this a valid proof?

1. Oct 6, 2013

### kaos

Is this a valid proof? Also is this way of doing it valid?

Statement : There are infinitely many natural numbers n where the square root of n is rational.

Proof:
sqrt of n = x (where x is natural)
n= x squared

And n can be any natural number(x) squared ,and there are infinitely many natural numbers (x)
therefore there are infinitely many n which has a natural square root. Since natural numbers are rational , there are infinitely many natural numbers n where the square root of n is rational.

2. Oct 6, 2013

### Ray Vickson

Your argument seems fine. There is one small point, though, that you should consider: how do you know that different integers x yield different integers x^2? (You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)

3. Oct 6, 2013

### Abhilash H N

Try going like this...
There are two possibilities:
1.There are infinitely many natural numbers n where the square root of n is rational.
2.There are finite natural number whose roots are rational.
If things were go as 1. then the proof is complete. If things were to go as 2. then we have to prove it wrong..
If second condition is satisfied then we will come up with a maximum number nmax (say) whose root is rational. Prove that there exist another number greater than nmax whose root is rational.
So the 2. possibility is ruled out, hence we are left with only one possibility which is 1.
Regards

4. Oct 6, 2013

### kaos

Thanks for responding.

Isn't the square of an integer always different?(except 1 or 0 i guess)?

And I dont understand the "(You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)" part (specifically what are you referring to that is collapsing?).

5. Oct 6, 2013

### kaos

Yes i know of proof by contradiction, but i used a more straightforward method. Though im not entirely sure my proof works.

6. Oct 6, 2013

### Dick

It's perfectly valid. The set of all n^2 for n any natural number i.e. {1^2,2^2,3^2,...} has an infinite number (since there are no duplicates, that's what Ray was saying about 'collapsing') of elements all of which are all natural numbers. Their square roots are all natural numbers, i.e. {1,2,3....} hence rational. That's what you are saying, right? In fact, those are the ONLY natural numbers that have rational square roots, but you don't need to show that.

7. Oct 7, 2013

### HallsofIvy

Staff Emeritus
No, that is not true. (2)^2= (-2)^2. However, YOU are working with natural numbers, not integers (do you understand the difference?) so it is true. But the point is that, unless you are "given" that, you need to prove it. Suppose m and n are different natural numbers. Then $n- m\ne 0$ because they are different. Further $m+n\ne 0$ (why?). Therefore $m^2- n^2= (m- n)(m+ n)$ is not 0 so $m^2$ is not equal to $n^2$.

For example, when squaring, the set {-3, -2, 2, 3} "collapses" to the smaller set {4, 9}. The proof above shows that cannot happen for the natural numbers.

Last edited: Oct 7, 2013
8. Oct 7, 2013

### kaos

Ah right i confused naturals(whole numbers larger than zero) with integers (integers include less than zero whole number right). Thanks for the explanation.


text:
# 고로 슬래그와 플라이 애시를 혼입(混入)한 투수성(透水性) 폴리머 콘크리트의 특성(特性)에 관(關)한 실험적(實驗的) 연구(硏究)

• Sung, Chan Yong (Dept. of Agricultural Engineering, College of Agriculture, Chungnam National University) ;
• Kim, In Su (Graduate School, Chungnam National University) ;
• Jo, Il Ho (Graduate School, Chungnam National University) ;
• Youn, Joon No (Graduate School, Chungnam National University) ;
• Kim, Young Ik (Dept. of Agricultural Engineering, College of Agriculture, Chungnam National University) ;
• Seo, Dae Seuk (Graduate School, Chungnam National University)
• Published : 1999.12.30

#### Abstract

This study is performed to evaluate the properties of permeable polymer concrete with blast furnace slag and fly ash. The following conclusions are drawn: 1. The highest strength is achieved by 50% filled blast furnace slag powder and fly ash permeable polymer concrete, it is increased 36% by compressive strength and 217% by bending strength than that of the normal cement concrete, respectively. 2. The static modulus of elasticity is in the range of $100{\times}10^3{\sim}130{\times}10^3kgf/cm^2$, which is approximately 43~51% of that of the normal cement concrete. 3. The dynamic modulus of elasticity is in the range of $102{\times}10^3{\sim}130{\times}10^3kgf/cm^2$, which is approximately less compared to that of the normal cement concrete. The highest dynamic modulus is showed by 50% filled blast furnace slag powder and fly ash permeable polymer concrete. The dynamic modulus of elasticity are increased approximately 0~4% than that of the static modulus. 4. The water permeability is in the range of $4.612{\sim}5.913l/cm^2/h$, and it is largely dependent upon the mix design.


text:
# Is the boundary $\partial S$ analogous to a derivative?

Without prethought, I mentioned in class once that the reason the symbol $\partial$ is used to represent the boundary operator in topology is that its behavior is akin to a derivative. But after reflection and some research, I find little support for my unpremeditated claim. Just sticking to the topological boundary (as opposed to the boundary of a manifold or of a simplicial chain), $\partial^3 S = \partial^2 S$ for any set $S$. So there seems to be no possible analogy to Taylor series. Nor can I see an analogy with the fundamental theorem of calculus. The only tenuous sense in which I can see the boundary as a derivative is that $\partial S$ is a transition between $S$ and the "background" complement $\overline{S}$.

I've looked for the origin of the use of the symbol $\partial$ in topology without luck. I have only found references for its use in calculus. I've searched through History of Topology (Ioan Mackenzie James) online without success (but this may be my poor searching). Just visually scanning the 1935 Topologie von Alexandroff und Hopf, I do not see $\partial$ employed.

I have two questions:

Q1. Is there a sense in which the boundary operator $\partial$ is analogous to a derivative?

Q2. What is the historical origin for the use of the symbol $\partial$ in topology?

Thanks!

Addendum. Although Q2 has not been addressed, it seems appropriate to accept one among the wealth of insightful responses to Q1. Thanks to all!

-
Vague answer that needs to be explained in more detail: The boundary operator $\partial$ is analogous to the exterior derivative $d$ acting on differential forms. I think they can be viewed as adjoints of each other, which act on complexes (submanifolds versus differential forms) that are dual to each other (via integration). –  Deane Yang Nov 16 '10 at 16:36
As Deane says, it's Stoke's theorem: $$\int_M d\omega = \int_{\partial M} \omega$$ If you write integration as a pairing, then $$\langle d\omega, M\rangle = \langle \omega, \partial M\rangle$$ shows that $\partial$ is the adjoint of the de Rham $d$. –  José Figueroa-O'Farrill Nov 16 '10 at 16:49
I think the analogy between the boundary operator and differentiation is a lot stronger in the context of singular homology or cell complexes. In that setting you can map a cell to its boundary taken with orientation which ensures that the boundary of a boundary vanishes. And of course in this setting the boundary is really just the differential of the complex computing the homology of your space, which shows the connection to the classical "d", since you could also have computed the cohomology of the space using the de Rham complex where the differential is just the ordinary differential. –  Dan Petersen Nov 16 '10 at 16:54
Oops -- I should have written Stokes's Theorem. (For the Nth time, I wish I could edit comments.) –  José Figueroa-O'Farrill Nov 16 '10 at 17:04
@Willie: such as ... this one? Seriously, that's "Qn2" in the original post! –  Loop Space Nov 16 '10 at 18:40

The surface area $|\partial S|$ of a (bounded, smooth) body $S$ is the derivative of the volume $|S_r|$ of the $r$-neighbourhoods $S_r$ of $S$ at $r=0$:

$$|\partial S| = \frac{d}{dr} |S_r| |_{r=0}.$$

Thus, for instance, the boundary $\partial D_r$ of the disk $D_r$ of radius $r$ has circumference $\frac{d}{dr} (\pi r^2) = 2\pi r$.

More generally, one intuitively has the Newton quotient-like formula

$$\partial S = \lim_{h \to 0^+} \frac{S_h \backslash S}{h};$$

the right-hand side does not really make formal sense, but certainly one can view $S_h \backslash S$ as a $[0,h]$-bundle over $\partial S$ for $h$ sufficiently small (in particular, smaller than the radius of curvature of $S$).

In a similar spirit, one informally has the "chain rule"

$${\mathcal L}_X S "=" (X \cdot n) \partial S$$

for the "Lie derivative" of $S$ along a vector field $X$, where $n$ is the outward normal. (There may also be a divergence term, depending on whether one is viewing $S$ as a set, a measure, or a volume form.) Again, this does not really make formal sense, although Stokes' theorem already captures most of the above intuition rigorously (and, as noted in the comments, Stokes' theorem is probably the clearest way to link boundaries and derivatives together).

EDIT: A more rigorous way to link boundaries with derivatives proceeds via the theory of distributions. The weak derivative $\nabla 1_S$ of the indicator function of a smooth body $S$ is equal to $-n d\sigma$, where $n$ is the outward normal and $d\sigma$ is the surface measure on $\partial S$. (This is really just a fancy way of restating Stokes' theorem, after one unpacks all the definitions.) This can be used, for instance, to link the Sobolev inequality with the isoperimetric inequality.

In a similar spirit, $\frac{1_{S_h} - 1_S}{h}$ converges in the sense of distributions as $h \to 0$ to surface measure $d\sigma$ on $\partial S$, thus providing a rigorous version of the intuitive difference formula given previously.

-
I really like your definition of the boundary as the limit of a "difference quotient". This is a good example of what "morally correct" means to me. –  Deane Yang Nov 16 '10 at 21:10
I second Deane's comment. This erudite and enlightening response is more than my question deserves, and I am appreciative! In fact all the comments and answers are illuminating. Thanks! –  Joseph O'Rourke Nov 17 '10 at 0:21

A partial answer to Q1 -- apologies if this is obvious, but I don't see it written here yet, and this is the thing that made me sit up and take notice of the fact that there's some sort of connection between the boundary operator $\partial$ and differentiation. If $X$ and $Y$ are two topological spaces and $A \subset X$, $B\subset Y$ are closed, then they satisfy a product rule of sorts: $$\partial(A\times B) = ((\partial A)\times B) \cup (A \times (\partial B)).$$ This also works without the assumption that $A$ and $B$ are closed if you're willing to weaken the analogy a bit by replacing the right-hand side with $\partial(A\times B) = ((\partial A)\times \overline{B}) \cup (\overline{A} \times (\partial B))$.

-
Very nice observation!!! –  Joseph O'Rourke Nov 17 '10 at 21:44
For CAT(0) spaces, there is a compactification also denoted by $\partial$ and this rule only holds non-equivariantly in this context. This is a bit of a flaw of the analogy. –  HenrikRüping Nov 17 '10 at 22:22

I like Vaughn's answer, but it seems to me that another form of product rule holds. If $A$ and $B$ are reasonnable subsets of $\mathbb R^n$ (perhaps one needs only that they are the closure of their interior), then $$\partial(A\cap B)=(\partial A\cap B)\cup(A\cap\partial B).$$ Here, $\cap$ and $\cup$ are the boolean operators, which are the analogues of $\times$ and $+$.

-

I think that there are (at least) two occurences of boundary in your question. One is the notion of frontier in general topology (closure minus interior) the other in differential (or geometric) topology, namely the set of points where the space under consideration is like $\mathbb{R}_+\times\mathbb{R}^{n-1}$ rather than like $\mathbb{R}^n$. The second is the one related to derivative in de Rham's theory of currents. These are functionals (continuous in a suitable topology) on differential forms (maybe twisted) on a smooth manifold $M$. The boundary of a current $T$ is then defined by Stokes formula as the adjoint of exterior differential : $\partial T$ on $\alpha$ is $T$ on $d\alpha$. And that's it ! For example, a current might be integration on some submanifold with boundary inside $M$, and its $\partial$ is then integration on the boundary of the submanifold. De Rham himself wrote a book on the subject, but I suspect that the ideas have now evolved to much higher depths (so to speak), with all this higher categories stuff, which I'm not competent to discuss.

-

Another, not too mathematical, analogy comes from image processing. There you can consider an image $u$ as a real valued function on a rectangle, say. A basic method for edge detection is to calculate the absolute value of the gradient of $u$ and consider all points where this value is large enough as an edge point. If your image is a (smoothed) characteristic function, then this will give you an approximation to the boundary of the set by thresholding the absolute value of the gradient of the image.

Similarly, the morphological gradient also gives the boundary of an object. Here, you consider the object as the support of an indication function. For this function you calculate the so-called closing with some parameter $\epsilon>0$ (which is nothing else as the indicator function of the $\epsilon$-enlaged object). The morphological gradient is then the difference of this closing and the function itself and encodes the boundary of the object.

-

I am way out of my depth here, but the subdifferential of a convex function $f$ at a point $x$ is often denoted by $\partial f$ and consists of all the supporting hyperplanes for $f$. I'm not sure but I think this could be generalized to non-convex functions if you just look at planes that are tangential in local neighborhoods.

In either case, if you look at the boundary of a set as the intersection of all its tangent planes, you can see the connection between derivatives and the boundary pretty clearly.

-
–  Joseph O'Rourke Dec 28 '14 at 1:17


text:
## Monday, September 24, 2007 ... //

### Live from the United Nations

Most of the speakers had nothing to say so they were emitting the same verbal fog as nearly everyone else.

The only exception I noticed was the Czech President. Download his talk in the IVR format playable by RealPlayer 11. In the 6.99 MB file (9 minutes), Václav Klaus starts to talk in 30 seconds. See also the transcript.

I have watched about 20 speakers and it's just a complete catastrophe. If someone suggested that Czechia is going to leave the United Nations, I would almost definitely agree. It's an organization full of bureaucrats who look like concerned careerist members of Komsomol. All of them are ready to say an arbitrary amount of lies, none of them is willing to think with his or her brain, and their statements reflect neither science nor the opinions of the people of the Earth.

While the percentage of skeptics among scientists as well as the population is of order 10-50 percent, there is exactly one leader of a U.N. member country that has the courage to offer his skeptical viewpoint. I think that this proves that most politicans in the current world are spineless jerks.

It seems that Klaus is a brave man. After having heard dozens of these puppets saying that no one is allowed to disagree and everyone has to consider stupid girls from Greenpeace to be the main constituency of the international organization - and literally tons of similar ideological and alarmist garbage - it is non-trivial that he gave the talk that he has prepared.

The Cuban minister who speaks now is very characteristic, too. Climate change is caused by consumerist capitalist countries and Fidel Castro has discovered this fact. What he says is otherwise identical - this Cuban viewpoint is the pure essence of the global warming movement. I think that the Cuban minister's comment is fair: it really seems that nearly the whole world has bought the ideology of Fidel Castro. That unfortunately includes even China.

#### snail feedback (4) :

Theo Richel
theo@richel.org

reader Luboš Motl said...

Dear theo, I apologize, but as you can see by Larry's fast comments, fast comments work for most of us.

The IVR format is extremely annoying but it was the only way I could find to catch the video... Do you have the newest RealPlayer?

All the best
Lubos

Hi! I liked your site! It's very nice!
Crime scene cleanup


text:
#### Archived

This topic is now archived and is closed to further replies.

# Getting input from 0x60

This topic is 5649 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

How does I get input from 0x60 , i am trying to get multiple keys, i use MSVC++ 6.0 thnx and sorry about my english hehehe i am brazilian

##### Share on other sites
If I''m right, you want to access directly the "keyboard" port (It''s been long so maybe I''m wrong). This is both possible and impossible. It''s possible when you want to write a driver (but I won''t suggest that and as I''ve never written any, maybe it''s a wrong solution). And it''s impossible under standard windows environment. Use DirectInput instead (a part of DirectX)

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Well if you really want to and can read the port, you need a scancode lookup table. You basically use the scancode as an offset into this array of ASCII codes although it is a little more complicated than that. Check out http://www.nondot.org/sabre/os/articles/. It might be .com instead so check both.

##### Share on other sites
You can use GetAsyncKeyState to check for multiple keys being pressed. Check the MSB of the return-value, if it is set, the key is pressed. Example:

    #define IsKeyDown(key) (0x8000 & GetAsyncKeyState(key)) #define IsKeyUp(key) (!IsKeyDown(key)) //Use the macros as follows:if (IsKeyDown(VK_SPACE)){   // Space is currently pressed} if (IsKeyUp(VK_F1)){   // F1 is not pressed}

As someone mentioned above, you can also use DirectInput, though it's a bit more involved.

For further information about GetAsyncKeyState and the VK_-codes it accepts as argument check the MSDN.

[edited by - Dactylos on June 24, 2002 10:06:55 AM]

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Take care with Async though, as it won''t matter if your window has the focus or not, your program will still respond to the keypress (unless you idle the frame loop when you window isn''t the focus window).

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Thanx a lot guys , before i learn DirectX i'll try Dactylos axample thanx to everyone thx thx thx

Getkeystate is in windows.h ???

[/edit]

[edited by - Homer Simpson on June 24, 2002 11:01:04 AM]

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# What is the difference between control flow and control logic?

I'm trying to learn about declarative programming, and while reading the wiki it said the following:

In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow.

What exactly does this mean? I am struggling to find a definition that effectively differentiates the two terms, especially in the context of declarative programming. Is it just describing a type of abstraction?

P.S Would it help if i could tag this as declarative programming? I can't create the tag myself

• I added "logic programming", which I think is a reasonable near-synonym. Jan 12 '17 at 20:18

Control flow is oriented around the idea of imperative statements. What is the computer doing at this given time? What will it do next? What actions should it perform?

Declarative programming abstracts this away (or at least tries to). You're program is now not a set of instructions for the computer to follow, but a sort of specification for the problem. In order to be powerful enough to be Turing complete, these specifications are usually recursive.

The main difference is that a declarative program makes no promises about how it will be run. You state the logic, and the compiler/interpreter makes a program that fulfills that logic.

One of the most important aspects of a declarative description is that it's (relatively) standalone. A procedure in an imperative language says "do this thing to the current state". A declarative program says often will not depend on its context, or will make its context more explicit.

In practice, you can usually infer the control flow of a declarative program pretty easily, especially in strict languages like ML, F# or Elm. There's a pretty close correspondence between recursive declarations and loops, and between declarative functions and imperative procedures.

Things get fuzzier in a language like Haskell, where evaluation is lazy (you don't decide what gets run when). Or in Prolog, where there's an implicit backtracking search that the runtime does for you. You're not coding these things manually, you're simply specifying what the result should look like, not how you will get that result.

• ‘You’re not coding these things manually, you’re simply specifying what the result should look like, not how you will get that result.’ In other words, declarative programming is in the problem space (isn’t it design by contract?) while imperative programming is in the solution space. E.g. declarative statement: the square root of a non-negative real $x$ is the non-negative real $y$ such that $y^2 = x$; imperative statement: the square root of a non-negative real $x$ is approximated by applying Newton’s method with the function $y \mapsto y^2 - x$ defined on the non-negative reals. Jul 19 at 15:09
• Are SQL (e.g. INSERT INTO relation (x) VALUES (3);), HTTP (e.g. PUT /path HTTP/1.1 {"x": 3}), HTML (e.g. <!DOCTYPE html><html lang=""><title>x</title>), and CSS (e.g. h1 { font-size: 3rem; }) declarative programming or imperative programming? Jul 19 at 18:25
• @Maggyero I'd say that those are all declarative. But it's a spectrum: even in C you're not giving low-level commands to the CPU. In a sense when you say x = 3; in C, you're saying "generate the program such that after executing it, the value in memory denoted by x is 3. So in a sense all languages have declarative elements, at different levels of abstraction. Jul 19 at 18:38
• I would have thought that they are all imperative since their statements are commands (SELECT, INSERT, UPDATE, DELETE commands for SQL, GET, PUT, DELETE commands for HTTP, commands to create the DOM structure for HTML, commands to attach style to the DOM structure for CSS), not constraints (e.g. preconditions, postconditions, or invariants). Jul 19 at 20:11


text:
# any rational number is a sum of unit fractions

## Representation

Any rational number $\frac{a}{b}\in\mathbb{Q}$ between 0 and 1 can be represented as a sum of different unit fractions. This result was known to the Egyptians, whose way for representing rational numbers was as a sum of different unit fractions.

The following greedy algorithm can represent any $0\leq\frac{a}{b}<1$ as such a sum:

1. 1.

Let

 $n=\left\lceil\frac{b}{a}\right\rceil$

be the smallest natural number for which $\frac{1}{n}\leq\frac{a}{b}$. If $a=0$, terminate.

2. 2.

Output $\frac{1}{n}$ as the next term of the sum.

3. 3.

Continue from step 1, setting

 $\frac{a^{\prime}}{b^{\prime}}=\frac{a}{b}-\frac{1}{n}.$

## Proof of correctness

###### Proof.

The algorithm can never output the same unit fraction twice. Indeed, any $n$ selected in step 1 is at least 2, so $\frac{1}{n-1}<\frac{2}{n}$ – so the same $n$ cannot be selected twice by the algorithm, as then $n-1$ could have been selected instead of $n$.

It remains to prove that the algorithm terminates. We do this by induction on $a$.

For $a=0$:

The algorithm terminates immediately.

For $a>0$:

The $n$ selected in step 1 satisfies

 $b\leq an

So

 $\frac{a}{b}-\frac{1}{n}=\frac{an-b}{bn},$

and $0\leq an-b – by the induction hypothesis, the algorithm terminates for $\frac{a}{b}-\frac{1}{n}$.

## Problems

1. 1.

The greedy algorithm always works, but it tends to produce unnecessarily large denominators. For instance,

 $\frac{47}{60}=\frac{1}{3}+\frac{1}{4}+\frac{1}{5},$

but the greedy algorithm selects $\frac{1}{2}$, leading to the representation

 $\frac{47}{60}=\frac{1}{2}+\frac{1}{4}+\frac{1}{30}.$
2. 2.

The representation is never unique. For instance, for any $n$ we have the representations

 $\frac{1}{n}=\frac{1}{n+1}+\frac{1}{n\cdot(n+1)}$

So given any one representation of $\frac{a}{b}$ as a sum of different unit fractions we can take the largest denominator appearing $n$ and replace it with two (larger) denominators. Continuing the process indefinitely, we see infinitely many such representations, always.

Title any rational number is a sum of unit fractions AnyRationalNumberIsASumOfUnitFractions 2013-03-22 12:48:31 2013-03-22 12:48:31 Mathprof (13753) Mathprof (13753) 7 Mathprof (13753) Derivation msc 11A67 Egyptian algorithm


text:
Feature Selection in Linear Regression

I have a insurance dataset as given below. For which I need to build a model to calculate the charges.

   age     sex     bmi  children smoker     region      charges
0   19  female  27.900         0    yes  southwest  16884.92400
1   18    male  33.770         1     no  southeast   1725.55230
2   28    male  33.000         3     no  southeast   4449.46200
3   33    male  22.705         0     no  northwest  21984.47061
4   32    male  28.880         0     no  northwest   3866.85520

But I am not sure whether the column "region" can be dropped. Is there any test can be performed to consider only significant variables?

• Do one hot encoding of the column Apr 30 '18 at 13:19

First, transform your columns, then apply linear regression, but do you want to know about the influence of your features on your selected dependent variable?

Read this article, as it provides great insight at how interpret the coefficients given by the algorithm can be interpreted and further discussed or tweaked.

Why don't you consider Gradient Boosting Decision Trees (GBDT) for Regression which you will find many Python implementation for (XGboost, LightGBM and CatBoost).

• They have an intrinsic way to calculate feature importance (due to the way trees splits work .e.g Gini score and so on).
• They can deal with categorical variables that you have (sex, smoke, region)
• Also account for any possible correlations among your variables. Simple linear models fail to capture any correlations which could lead to overfitting.
• There are many ways to regularize GBDTs, which may come very handy!

With GBDTs you only have to be careful with continuous variable, in your case the bmi variable, not to be artificially overruling your trees (trees have hard time dealing very continuous data). You can easily overcome this challenge by rounding up/down or binning your continuous variable or other methods.

If you have strong reasons to stick to linear regressions, maybe you could use LASSO which is a regularized linear regression that harshly penalizes (=0) the less important variables. People actually use LASSO for feature selection as well.

The pacakge leaps in R has functions, like regsubsets, that do this. Essentially, what this functions do is they compare different models with criteria that you can choose and take the model that does the best according to the criterium chosen.

Please note that keeping the model with the highest $R^2$ is not a very good criterium, as models with more variables will always have higher $R^2$. The criteria that regsubsets can use are adjusted R^2 and Bayesian Information Criterion, among others.

• Thanks for the answer. I will try to implement with the given package. However is there a similar package in python too ? Apr 30 '18 at 10:49
• This question addresses it: stackoverflow.com/questions/37624920/… Apr 30 '18 at 10:51
• Apparently the best you can do is call R from Python. Sadly R has many statistical fancy things that python doesn't. Apr 30 '18 at 10:52
• Did I help answer your question? May 2 '18 at 12:53


text:
"Optional title"
entype, enid, cid${}_\tau$, cid${}_{vx}$, cid${}_{vy}$, cid${}_{vz}$, $t_{beg}$, $t_{end}$
##### Parameter definition
VariableDescription
entype Entity type
options: P, PS, FS
enid Entity identification number
cid${}_\tau$ ID of a CURVE or FUNCTION defining the shear traction
cid${}_{vx}$ ID of a CURVE or FUNCTION defining reference velocity in x-direction
cid${}_{vy}$ ID of a CURVE or FUNCTION defining reference velocity in y-direction
cid${}_{vz}$ ID of a CURVE or FUNCTION defining reference velocity in z-direction
$t_{beg}$ Start time
default: 0
$t_{end}$ End time
default: 1.0e10
##### Description

This command defines shear traction on a surface. It can be used to model drag forces and prescribed friction loads. The local direction of the traction $\hat{\mathbf t}$ is in that of the reference velocity ${\mathbf v}_{ref}$ vector minus the local velocity vector ${\mathbf v}({\mathbf x})$, projected onto the surface.

$\displaystyle{ \hat{\mathbf t} = \frac{({\mathbf I}-\hat{\mathbf n} \otimes \hat{\mathbf n})({\mathbf v}_{ref}-{\mathbf v})} {\Vert ({\mathbf I}-\hat{\mathbf n} \otimes \hat{\mathbf n})({\mathbf v}_{ref}-{\mathbf v}) \Vert}}$

Here $\hat{\mathbf n} = \hat{\mathbf n}({\mathbf x})$ is the local surface normal direction.

##### Example

The following commands apply shear traction on the part with ID 1. The traction is a linear function of the relative tangential velocity vtang. Note that vtang is a built in variable that can be accessed in FUNCTION. The reference velocity is ramping up from 0 to 100 in x-direction.

*PARAMETER
%C = 2.0