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# The new color of Blockquotes bothers my eyes

The new color of blockquotes (transparent gray) bothers my eyes? See the example:

This is some text to illustrate how blockquotes look like.

Is that my problem or all?

• I agree. It is a bit annoying. – Asaf Karagila Aug 27 '20 at 19:31
• See related answer on the Meta question announcing the changes: meta.stackexchange.com/a/353557/279167 – Matt Samuel Aug 27 '20 at 21:29
• See this post, where the contrast between black text and grey text is more evident. I don't like this a bit. – amWhy Aug 27 '20 at 22:59
• @user400188: from their post it appears that they have done a major change in text formatting (aligning with CommonMark is one goal here) and they may not revert it. However if there is huge uproar over the grey colour used in quotes they may change the color to something else. I would prefer it black. – Paramanand Singh Aug 29 '20 at 3:54
• If so, they may lose many users!! – C.F.G Aug 29 '20 at 3:56
• @OmarS: see their announcement post. Some of the answers there give links to some scripts which disable the changes. I haven't tried them. In the long run I think users will have to get used to the changes as there is no other alternative to stackexchange right now. – Paramanand Singh Aug 29 '20 at 16:06
• off topic: why my post received 2 down-vote? (of course it is not important on meta, and of course the reputation isn't so important in life.) – C.F.G Aug 30 '20 at 11:04
• @C.F.G first there is no reputatjon on meta, second the post was tag feature-request at some point in which case dv means that somebody is against the requested feature, which in this case would mean they are in favor of the new look. – quid Aug 30 '20 at 11:31
• @C.F.G it is not that they downvote "just for that." The intent is that if somebody proposes a change the voting on the proposal is to be taken as a poll on the proposal (not as an evaluation of the post). I changed the tag as there is not clear proposal here. – quid Aug 30 '20 at 11:40
• @user400188 it is not that dramatic but to the extent it is a problem that's on the users that misused blockquotes for this. There were repeatedly warnings that blockquotes should not be used for emphasis, precisely because we do not know how it will look like down the road. math.meta.stackexchange.com/questions/25939 and math.meta.stackexchange.com/questions/23015 – quid Aug 30 '20 at 11:46
• I do not understand the question. There are best practices how to do such things; I assume those that did it know more about this than most that comment here, in any case more than I. In any case for users that have specific needs there are plenty of ways to control things locally as long as the formatting directives are used consistently. Let's hope the change will curb the rampant misuse of the feature. – quid Aug 30 '20 at 11:56
• @quid I don't think you can blame users for this mistake. The majority of people who use the site do not scour the meta for rules that where not mentioned on the official pages. If they are new and see other people using block quotes like this, then they will likely do the same thing. At the time of writing, those repeated warnings have only been read by at most 1229 people. – user400188 Aug 30 '20 at 12:24
• @user400188 it does not have much to do with being a "rule." You do have a point regarding most users going by imitation. However if you check the meta threads there was a lot of active resistance and the one meta post might have been seen more had it not been so ruthlessly downvoted into oblivion. – quid Aug 30 '20 at 12:36
• When I first saw the use of this block quote my impression was that it was designed to add a hell lot of emphasis to entire paragraphs. It wasn't at all clear that it was meant to quote something verbatim. Thus the visual look did not really match its intended purpose. Removing yellow background is a step ahead to align implementation with purpose of block quote. But changing color of the font adds a new purpose (which is actually not at all related to original purpose) of de-emphasizing the quoted text. – Paramanand Singh Aug 31 '20 at 15:55
• One can use a trick >$\color{black}{\text{some example}}$ to get ride of gray color of new blockquotes. Now it is emphasizing again!! – C.F.G Aug 31 '20 at 16:01


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# wave separation

Say there is a wave of sines and cosines. (<- one can think of Fourier theory.)

A) There is a wave that has the same frequency all the time. However, amplitude (- shape) of each period differs. Is it possible to separate this wave into combinations of waves that have the same amplitude for each wave?

B) Say there is a added combination of two waves that are same in frequency but different in amplitude. The amplitude of each wave is equal all the time. Can the signal be decomposed into two signals that were combined?

Thanks.

In the wikipedia article it's shown the simplest case, $y(t)=[1 + M \cdot \cos(\omega_m t + \phi)]\cdot \sin(\omega_c t)$ Here we have a sinuosid of "central frequency" $\omega_c$ and its amplitude varies by a sinusoid of frequency $\omega_m$ ("modulation frequency"). It's easy to show (oops) that this signal can be expressed as the sum of three sinusoids of frequencies $\omega_c$, $\omega_c+\omega_m$ and $\omega_c -\omega_m$.
For A, what you probably mean by the same frequency all the time is that the wave passes through zeros (maybe also maxima) at the right time spacing. It would be something like $f(t)=a_n\cos t$ where $a_n$ is the amplitude for period $n$. This is a well defined function (given the list of $a_n$) but it has energy at frequencies other than $\frac 1{2\pi}$ as you can see from an FFT. In particular, the derivative is not continuous when you change between the $a$'s

format: plain


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# Question about 3 momentum

1. Apr 5, 2008

### Davio

Hey guys, what exactly is a 3 momentum? I can't any references to it anywhere on the net, which actually tells me what is it, I know a energy 4 momentum is, px , py, pz e/c, but thats not much help!

2. Apr 5, 2008

### Hootenanny

Staff Emeritus
Three momentum is simply a vector containing all three momenta,

$$\boldmath P \unboldmath = \left(\begin{array}{c}p_x \\ p_y \\ p_z\end{array}\right)$$

Last edited: Apr 5, 2008
3. Apr 5, 2008

### robphy

3-momentum is the "spatial-part" of the 4-momentum.

Here is one place to consult:
http://www2.maths.ox.ac.uk/~nwoodh/sr/ [Broken]

Last edited by a moderator: May 3, 2017
4. Apr 5, 2008

### yuiop

In a 3D reference frame a line of arbitary length and direction from the origin of the frame can be described in terms of x,y and z component. Using pythagorous theorem we can find the length of that arbitary line from $$L =\sqrt{x^2+y^2+z^2}$$ You could call that length the 3 length sometimes abreviated to ||L||. When we include an additional dimension of time to the 3 spatial dimensions then we have the 4 length $$\sqrt{x^2+y^2+z^2-(ct)^2}$$

or $$\sqrt{||L||^2-(ct)^2}$$

Similarly 3 velocity ||v|| = $$\sqrt{v_x^2+v_y^2+v_z^2}$$

and 3 momentum ||p|| = $$\sqrt{p_x^2+p_y^2+p_z^2}$$

(Edited to fix the typo pointed out by ehj)

Last edited: Apr 5, 2008
5. Apr 5, 2008

### ehj

Shouldn't it be?
$$\sqrt{||L||^2-(ct)^2}$$

6. Apr 5, 2008

### yuiop

Yes, sorry about the typo. :(

7. Apr 5, 2008

### robphy

I should clarify that, given a 4-momentum vector,
the 3-momentum is essentially the "spatial-part" according to a given observer.
That is, the 3-momentum is [obtained from] the vector-component of the 4-momentum that
is [Minkowski-]perpendicular to an observer's 4-velocity.
From a given 4-momentum vector, different observers will determine different 3-momentum vectors.

Given a 4-momentum $$\tilde p$$ and an observer's 4-velocity $$\tilde u$$ (with $$\tilde u \cdot \tilde u=1$$ in the $$+---$$ convention),
Write out this identity [a decomposition of $$\tilde p$$ into a part parallel to $$\tilde u$$, and the rest perpendicular to $$\tilde u$$]:
$$\tilde p = (\tilde p \cdot \tilde u)\tilde u + (\tilde p - (\tilde p \cdot \tilde u)\tilde u)$$.

The 4-vector $$(\tilde p - (\tilde p \cdot \tilde u)\tilde u)$$ is "purely spatial" according to the $$\tilde u$$ observer [check it by dotting with u], and can be thought of as a three-component vector in $$\tilde u$$'s "space" by projection. That projected vector is the 3-momentum of the object according to $$\tilde u$$.

(Note, however, that the 4-vector $$(\tilde p - (\tilde p \cdot \tilde u)\tilde u)$$ is generally NOT "purely spatial" according to another observer $$\tilde w$$. To $$\tilde w$$, that 4-vector has both nonzero spatial- and temporal-parts.)

Last edited by a moderator: May 3, 2017
8. Apr 6, 2008

### Davio

Hey guys, feel a bit silly, of course its just the partial part! Whilst we're on that topic though, why is it -(ct)^2 and not positive? Is it because CT=Distance, L^2+D^2 =p^2 ? Surely not though because, L ^2 = x^2 +y^2 +z^2

9. Apr 6, 2008

### Staff: Mentor

With the "-" sign in that position, the "magnitude" of a 4-vector is invariant between different inertial reference frames. With a "+" sign instead, the "magnitude" is not invariant.

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# Multi-Source Time Series Data Prediction

I was wondering if anyone has experience with time series prediction for data from multiple sources. So for instance, time series $a,b,..,z$ each have their own shape, some may be correlated with others. The ultimate goal is to have a model trained such that the value at time $t+1$ for any given data source can be predicted.

I personally have two solutions that in theory could work, but was wondering if anyone knew of other frequently used methods.

2. Use feature engineering to model properties of each time series source as features along with usual features and use these with LSTM

• What are time series "from multiple sources"? What is the "own shape" of a time series? – tagoma Jul 17 '17 at 11:16
• so for instance, I have timeseries representing sales of multiple groups of supermarket product. A single sequence represents the sales of Product group X over a 5 year window. The sales curve of each individual product group id different, yet, there may be correlations between the sales of multiple groups. I tried lumping all of these together and using a few feature that would capture the statistical characteristics of that feature for both a long and short window, but the results were not great. Running predictions for each individual sequence seems to work fine (as expected) – Nmaple Jul 19 '17 at 15:46

I'm only aware (and using) a RNN which gets multiple time-series in it's first layer and then mixes those in the following layers. Let me know if you have a question on this approach.

• Thank you. Could you please read my comment above and see if you were also successful in using multiple time-series with different sources (in my case product types) in the same model? if so, did you have to do any form of feature engineering to take into account the characteristics of each individual sequence or did you apply another method? – Nmaple Jul 19 '17 at 15:48
• I have not done exactly that but there should be no general problem. I wouldn't do feature engineering. In general feature engineering is not needed for deep learning, sure there might be situations when it helps. – Tobi Jul 21 '17 at 11:45

You can certainly use an LSTM for this approach, as well as VAR, or potentially a more 'traditional' model (random forest). I have implemented multivariate LSTM for t+x prediction in Keras. Feature engineering may definitely help improve results.

I have also used VAR and was surprised at the effectiveness of this when compared against the LSTM. There are packages in Python and R for VAR.

Alternatively, if your features are effectively describing a pattern that is not necessarily dependent on the time component, a more traditional method such as random forest could be used. Probably not as effective as VAR or LSTM, but it's fast.

• thanks. were you able to use multi-source data (described in the above comment) in your example? I am able to predict t+1 for a single source timeseries. I am reluctant to call it uni-variate as it has multiple features but corresponds to a specific product group. In my case, the input for a single source prediction to keras looks like (100,5,20) – Nmaple Jul 19 '17 at 15:58

The answer is Data Fusion or Feature Fusion.

I am implementing one using neural networks to classify Human Activity using multiple kinds of sensors: accelerometer, binary sensors, ecc..

We train a neural network with multiple input layers: one for each data source.

The forward pass keeps these separate until deeper in the network, at which point we concatenate the feature representations and then proceed with a single, merged processing pipeline in the network which ends at a single classification layer.

We can think of it as each independent pipeline learn a feature representation of its data source that can then be usefully combined with the other representations to perform classification.

This maintains independence of each network branch (e.g. you could have an LSTM processing sequential data, whose latent state vector then is concatenated with a FC feature from a CNN processing pressure plate measurements as images, and so on).


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ISC Biotechnology 2016 Class-12 Previous Year Question Paper Solved for practice. Step by step Solutions with Questions of Part-1 and Part-2 (Section A , Section-B). By the practice of Biotechnology 2016 Class-12 Solved Previous Year Question Paper you can get the idea of solving.

Try Also other year except ISC Biotechnology 2016 Class-12 Solved Question Paper of Previous  Year for more practice. Because only ISC Biotechnology 2016 Class-12 is not enough for complete preparation of next council exam. Visit official website CISCE for detail information about ISC Class-12 Biotechnology.

## ISC Biotechnology 2016 Class-12 Previous Year Question Paper Solved

Part-I

Part-II

Maximum Marks: 80
Time allowed: Three hours

• Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.
• Answer Question 1 (Compulsory) from Part I and five questions from Part II, choosing two questions from Section A, two questions from Section B and one question from either Section A or Section B.
• The intended marks for questions or parts of questions are given in brackets [ ].
• Transactions should be recorded in the answer book.
• All calculations should be shown clearly.
• All working, including rough work, should be done on the same page as, and adjacent to the rest of the answer.

Part -1 (20 Marks)

### ISC Biotechnology 2016 Class-12 Previous Year Question Paper Solved

Question 1.
(a) Mention any one significant difference between each of the following : [5]
(i) Ligases and Helicases
(ii) Introns and Exons
(iii) Gel electrophoresis and Gel permeation
(iv) Sucrose and Starch
(v) Plasmids and Phages

(b) Answer the following questions : [5]
(i) Why is the nutrient medium autoclaved before using it for cell culture?
(ii) Name the enzyme that can synthesize DNA at a high temperature.
(iii) Why are restriction enzymes also called as molecular scissors ?
(iv) Name the nitrogenous bases present in RNA.
(v) Why is Agrobacterium tumifaciens called as the natural genetic engineer of plants ?

(c) Write the full form of each of the following :
(i) YAC
(ii) NCBI
(iii) RAM
(iv) SNP
(v) EMBL

(d) Explain briefly : [5]
(i) Somatic hybridization
(ii) Promoter gene
(iii) Site directed mutagenesis
(iv) DNA probes
(v) Primer
(a)

(i) Ligases are the enzymes which help in linking up of okazaki (DNA) segments produced on the parent strand with 5′-3′ direction. Hclicases help in unwinding the DNA helix, using ATP hydrolysis as a source of energy.

(ii) Introns are the intervening sequences which do not appear in the mature or processed RNA.
Exons are the coding sequences or expressed sequences that form functional and processed RNA.

(iii) Gel Electrophoresis is a technique by which negatively charged DNA fragments are separated by forcing them to move towards the anode under an electric field through a medium/matrix.

Gel permeation or filtration involves that molecules of different sizes can be separated from each other on the basis of their ability to enter the pores within the beaded gel, followed by passing down a column containing the gel. The technique is used in protein purification.

(iv) Sucrose is a disaccharide formed of glucose and fructose molecules while starch is a polysaccharide molecules formed of large number of glucose molecules arranged in the form of chains.

(v) Plasmids are the extra-chromosomal, self replicating, circular, double stranded DNA molecules present in bacteria.
Phages are the viruses which infect bacteria/cell. lyse it, integrate its DNA into it and replicate with the host chromosome.

(b)

(i) The nutrient medium is autoclaved to make it sterilise i.e., free from microbes.

(ii) DNA polymerase isolated from a bacterium Thermus aquations.

(iii) Restriction enzymes are called ‘molecular scissors’ because they make cuts at specific positions/recognition sites within both strands of DNA.

(v) Agrobacterium tumefaciens is able to deliver a piece of DNA known as ‘T-DNA’ to transform normal plant cells into tumour cells. By manipulating its Ti plasmid, it has now been modified into a useful cloning vector for delivering gene of our interest into a variety of plants.

(c)

(i) YAC = Yeast Artificial Chromosome.

(ii) NCBf = National Centre for Bioinformatics Information.

(iii) RAM = Random Access Memory.

(iv) SNP = Short Nucleotide Polymorphism.

(v) EMBL = European Molecular Biology Laboratory.

(d)

(i) Somatic hybrids are the hybrid plants produced through the fusion of protoplasts from two different varieties of plants each haring a desirable character. The hybrid protoplasts can be further grown to form a new plant.

(ii) Promoter gene a gene haring a regulatory sequence of DNA that initiates the expression of a gene.

(iii) Site directed mutagenesis involves induction of specified or desired changes in the base sequence at specified sites of genes, most successfully achieved by overlap extension PCR.
Or
The process of nucleotide changes in the cloned genes by specific in mutagenesis.

(iv) DNA probes are short 15-30 bases long, labelled oligonucleotides (RNA – DNA) used to detect complementary nucleotide sequences after hybridization and the auto radiograms gives many bands of different sizes.

(v) Primer is a short oligonucleotide that hybridizes with the template strand and gives a 3′- OH end at which a DNA polymerase start synthesis of DNA chain.

Part – II (50 Marks)

### ISC Biotechnology 2016 Class-12 Previous Year Question Paper Solved

Question 2.
(a) With reference to amino acids, explain :
(i) Any one physical and any one chemical property of amino acids.
(ii) Essential and non-essential amino acids.
(b) Briefly outline the various steps involved in the gene cloning technique
(c) List any four characteristics of genetic code.
(a) They are the building blocks of molecular proteins.
(i) Amino acids are the organic acids (with carboxylic group-COOH) having amino group (-NH2) generally attached to a-carbon or carbon next to the carboxylic group. Amino acids condenses to produce peptide (-NHCO-) bond.

(ii) Essential amino acids are essential for our body but they are not synthesised inside our body e.g., valine, isoleucine, lysine etc. They are supplemented through diet. Non-essential amino acids are those which are synthesised through transformation and transamination inside our body e.g., serine, alanine etc.

(b) The various steps involved in gene cloning technique are :

• Identification and isolation of desired DNA. .
• Amplification of gene of interest using PCR.
• Fragmentation/cutting of desired DNA and vector DNA by restriction enzymes.
• Ligation/joining of desired DNA fragment into vector using ligase enzyme.
• Transferring the recombinant DNA into host cell/organism by transformation, transfection, electroporation, microinjection (vectorless transfer), particle bombardment gun (Biolistics) (Vectorless transfer) or by Agrobacterium/retrovirus mediated gene transfer..
• Culturing the host cell for obtaining the foreign gene product/recombinant protein.
• Extraction of desired products or downstream processing.

(c) The characteristics of genetic codes are :

• Codes are universal.
• Codes are unambiguous and specific.
• Code is degenerate i.e., some amino acids are coded by more than one codon.
• Codons are read in a continuous fashion i.e., there are no commas or punctuation’s.

Question 3.  (ISC Biotechnology 2016 Class-12)
(a) Describe the three dimensional structure of DNA as proposed by Watson, Crick and Wilkins. Name a biochemical technique that was used by them to confirm the structure of DNA. [4]
(b) Explain the role of the following enzymes during the process of protein synthesis : [4]
(i) RNA polymerases and amino acyl tRNA synthetase.
(ii) Start codons and end codons.
(c) Why are auxins and cytokinins used in plant tissue culture ? [2]
(a) Watson, Crick and Wilkins described the structure of DNA but also indicated how it could be replicated and transfer from one organism to its off spring.
Salient features of double helix structure of DNA include :

• Double helix made of two polynucleotide chains.
• Sugar and phosphate form backbone and N-base project inside.
• The two chains are antiparallel with one chain has the polarity of 5′ → 3′, the other has 3’→ 5.
• Presence of double hydrogen bonds between A=T, and triple bond to between G = C The . purine always comes opposite to pyrimidines to create uniform distance.
• Two chains are coiled in a right handed fashion.
• Pitch (one turn) of helix is 3.4 nm (= 34 A) contains 10 bp with 0.34 nm (3.4 A) gap between adjacent bps. (1 nm = 10-9 m)
• Two chains of DNA are 20 A far apart, due to the pairing of purines with pyrimidines. This distance remains constant.
• The plane of one base pair stacks over the other in double helix to confer stability

Rosalind Franklin confirmed this structure of DNA through X-Ray crystallography.

(b)

(i) RNA polymerizes get associated transiently with initiation sigma factor (σ). They do not require a primer and can initiate the synthesis of a new chain on the template strand. It binds to the promoter site to start synthesis. The first nucleotide is labelled as + 1 and is called the transcription start site. It polymerizes ribonucleotides in 5′ → 3′ direction over 3′ → 5′ template DNA.

In prokaryotes, a single RNA polymerase transcribes all m-RNA, r-RNA and t-RNA. However, in case of Eukaryotas there are three different polymerizes i.e., RP+1 for r-RNA, RP-II for m-RNA and RP-III for t-RNA.
Amino acyl t-RNA syntheses couple each amino acid to its appropriate set of t-RNA molecules. There are 20 synthesizes for each of the 20 natural amino acids.

(ii) In prokaryotes, AUG acts as a start/initiation codon as well as codes for methionine. GUG acts as start codon for valine in Eukaryotes. UAA, UAQ UGA function as stop codons and do not code for any amino acid.

(c) Role of auxin :

• It helps in the formation of callus and in the development of xylem along with the promotion of cambial activity.
• It is used for the elongation and enlargement of plant cell and it inhibits the promotion of growths of apical and lateral buds.

Role of cytokinin:

• It stimulates the cell division process.
• It helps in the morphogenesis of plant cell, along with auxins.

Question 4.  (ISC Biotechnology 2016 Class-12)
(a) Explain how DNA technology has been used to create the following : [4]
(i) Dolly
(ii) Hepatitis B vaccine
(b) Write short notes on : [4]
(i) Batch culture and continuous culture.
(ii) Salinity resistance in crops.
(c) Name any two chemicals used to prepare the gel for gel electrophoresis. [2]
(a)

(i) Dolly – The first cloned animal :
Using nuclear transfer technique, the world’s first mammalian clone – Dolly, was born in February 1996. In 1995, Ian Wilmut and his research group (Scotland) took out udder from a six year old sheep A called clone mother, and put in a special solution. Nucleus of udder cell was taken out and put in a solution. At the same time an unfertilized egg was taken out from another sheep B called egg mother. Nucleus of the egg was removed and nucleated egg was put in a culture medium. The nucleus of udder cell and nucleated egg cell were put together followed by mild electric shock. Consequently nucleus was taken up by the nucleated cell. This cell was incubated onto growth medium then transferred into a surrogate mother. A little lamb Dolly was born in February, 1996.

(ii) It is true that proteins (vaccines) stimulate immune system and cause to secrete specific antibodies. Such specific amino acid sequences in the protein that stimulate immune response are called epitopes. Based on selected epitopes recombinant vaccines may be produced on commercial level which can prove more effective and safer than the conventional vaccines.

Working on these lines, a recombinant Hepatitis B vaccine was produced by cloning the synthetic gene (for the surface antigen of the virus) in yeast cells. This gene expressed well in yeast cells and produced 22 nm particles of hepatitis B virus (HBV) surface antigen (as produced in patients) infected with hepatitis B virus. The recombinant vaccine has high immunogenecity. This product has been marketed as a vaccine for protection against HBV infection.

(b) Tissues and cells cultured in a liquid medium produce a suspension of single cells and cells clumps of few to many cells, are called suspension culture. Suspension cultures are of two types:

(i) Batch culture: In a batch culture, the same medium and all the cells produced are retained in the culture vessel e.g., culture flasks (100-250 ml), fermenters (variable size) etc. The cell number of biomass, of a batch culture exhibits a typical sigmoid curve represented by lag phase (cell number or biomass remain unchanged), log phase (rapid increase in cell number) and finally stationary phase (cell member does not change). The lag-phase lasts about 3-4 cell generation. The stationary phase is forced on the culture.

• due to depletion of nutrients
• and due to accumulation of wastes.

They are maintained by subculturing. They are unsuitable for studies on cell growth and metabolism because of constant change in cell density and nutritional status.

Continuous culture: Here the cell population is maintained in a steady state by regularly replacing a portion of used or spend medium. Such culture systems are either

• closed or
• open system.

In closed system, cells are separated from the used medium, taken out for replacement and added back to the culture so that biomass keeps on increasing. In contrast, both cells and used medium are taken out from open continuous system and replaced by equal volumes of fresh medium.

(ii) A plant which bears a foreign gene for desired function of other organism is called transgenic crop. Using biotechnological approaches stress/salinity tolerant plants can be produced. They secrete stress-related osmolytes such as sugars (fructans and trehalose) sugar alcohols (mannitol) amino acids (betaine, glycine and proline) and other proteins. For example, betaine is highly effective osmolyte that accumulates in some plants during, water stress or high salinity: Betaine is synthesised both in bacteria and plants. A transgenic tobacco was prepared by transferring E.coli bet A. gene through Ti-plasmid. The transgenic tobacco was 80% salt tolerant (i.e. 300 mM) than the normal tobacco.

(c) (i) Agarose gels
(ii) Polyacrylamide gels.

Question 5.  (ISC Biotechnology 2016 Class-12)
(a) Give the step wise procedure of the Southern Blotting technique. Mention any two differences
between Southern Blotting technique and Northern Blotting technique. [4]
(b) Explain the principle and any two applications of each of the following biochemical techniques:
(i) Ion Exchange Chromatography
(ii) Colorimetry [4]
(c) What is the cause of inborn metabolic disorders? Give any two examples of these disorders. [2]
(a) Southern Blotting (Hybridization) Technique : In 1975, Edward M. Southern developed the technique of DNA separation and its hybridization. Therefore, in his honor this technique is known as ‘Southern blotting or Southern hybridization technique’. A specific DNA fragment can be separated and identified in a heterologous population of DNA molecules on the basis of binding of DNA probe with its complementary DNA strand.

The genomic DNA is isolated from the clone and digested with restriction enzymes. The DNA fragments are separated by agarose gel electrophoresis. Different DNA bands are formed on agarose gel which represents DNA fragments of varying sizes. These fragments are transferred from gel to nylon or nitrocellulose membrane. The process of DNA transfer is called ‘blotting’.

A nitrocellulose membrane is put over the gel. Many layers of filter paper are placed over nitrocellulose membrane. This assembly is put in a container having NaOH solution. NaOH denatures DNA and results in formation of single stranded DNA. DNA fragments are transferred from gel to membrane by capillary action.

The DNA fragments are fixed to membrane by using UV radiation or baking at 80°C. The pattern of DNA bands on membrane corresponds to the position of DNA on gel. The membrane is put in solution containing radio labelled DNA probe and incubated for some time. DNA probe hybridizes complementary DNA fragments fixed on membrane. It is gently washed at 12°C and dried. The membrane is exposed through a photographic film. DNA bands formed on photographic film corresponds to the original position of DNA fragments present on agarose gel.

Southern Blotting technique involves separation and identification of a specific DNA fragment. In Northern Blotting technique the RNA is analysed rather than DNA. During southern blotting NaOH denatures DNA to form single stranded DNA which are transferred from gel to nitro cellulose membrane. In northern blotting total RNA molecules are extracted and then mRNA molecules are isolated by using oligo (dT) cellulose Chromatography. RNA samples separated are transferred to a nylon membrane.

(b)

(i) Ion Exchange Chromatography Principle: It is based on reversible exchange of ions in solution with ions electrostatically bound to some sort of insoluble support medium. Separation is obtained since different molecules have different degree of interaction with ion exchanger due to difference in their charges, charge densities and distribution of charge on their surface.

Applications:

• A technique for separating two proteins differing by only one charged amino acid.
• It is capable of separating species with very minor differences in their properties.

The ion-exchange may be

• Anion exchanger or
• Cation exchanger.

(ii) Colorimetry:
Principle : It is based on the use of interaction of light energy with coloured solutions of certain molecules as when light passes through a coloured solution, some wavelengths are absorbed more than others. The amount of light absorbed is proportional to the intensity of colour and hence to the concentration of the compound.

Applications:

• Quantitative estimation i.e. concentration in solution.
• Detect and identification of biomolecules

(c) Inborn metabolic disorders are due to change in the gene, for the particular character. Some autosomal genes become recessive and are transmitted to the progeny.
Examples:

1. Albinism
2. Cystic fibrosis
3. Phenylketonuria
4. Sickle-cell anaemia
5. Alkaptonuria

Alkaptonuria: This was one of the first metabolic diseases described by Garrod in 1908. It is an inherited metabolic disorder produced due to deficiency of an oxidase enzyme requiredfor breakdown ofhomogentisic acid (also called alcapton, hence, alkaptonuria is also written as alcaptonuria). Lack of the enzyme is due to the absence of the normal form of gene that controls the synthesis of the enzyme. Hence, homogentisic acid then accumulates in the tissues and is also excreted in the urine. The most commonly affected tissues are cartilages, capsules of joints, ligaments and tendons. The urine of these patients if allowed to stand for some hours in air, turns black due to oxidation of homogentisic acid.

Albinism: It is caused by the absence of the enzyme tyrosinase which is essential for the synthesis of the pigment from dihydroxyphenylalanine. The gene for albinism (a) does not produce the enzyme tyrosinase but its normal allele (A) does. Thus, only homozygous individual (aa) is affected by this disease. Albinos (individuals with albinism) lack dark pigment melanin in the skin, hair and iris. Although albinos have poor vision yet they lead normal life.

Question 6.  (ISC Biotechnology 2016 Class-12)
(a) Discuss the significance of each of the following techniques used in cell culture technology: [4]
(i) Androgenesis and gynogenesis
(ii) In-vitro pollination
(b) Enumerate any two post transcriptional changes in the mRNA to produce a completely mature mRNA. [4]
(c) State any four achievements of the Human Genome Project. [2]
(a) (i) Androgenesis involves production of haploid plants by development of an egg cell
containing male nucleus. The female nucleus is eliminated before fertilization. Gynogenesis includes production of haploid plants by the development of an unfertilized egg cells because of delayed pollination (through use of abortive pollen pre-exposed to ionizing radiations or using an alien pollen). It is found in inter-specific crosses of potato.

(ii) In vitro pollination : A laboratory procedure, in which pollination and fertilisation occur under in vitro condition, offer an opportunity for producing hybrid embryoids among plants that cannot be crossed by conventional method of plant breeding. To overcome interspecific and intergeneric incompatibility cases, the style or part of it can be excised and pollen grains are either placed on the cut surface of ovary or transferred through a hole in the wall of ovary. This technique is called intra-ovarian pollination. It is applied successfully in Papaver somniferum, Argemone mexicana etc. It also involves direct pollination of cultured ovules or excised ovules together with placenta.

(b) Post-transcriptional changes : Modification at 5′ end of primary RNA (Heterogenous RNA or hnRNA) transcript is called capping. During capping, an extra guanosine residue in first added to the terminal nucleoside triphosphate of the primary RNA transcript. Guanosine residue is further modified by addition of methyl groups. Capping prevents the 5′ end of TORNA from being digested by exonucleases. It aids in the transport of m-RNA out of the nucleus and plays an important role in the m-RNA translation.

Addition of a string of adenosine residues, forming a poly (A) tail at 3′ end of the TO-RNA.

The process of removal of those parts of primary transcript, corresponding to introns and joining together of exons, is known as splicing.

(c) Achievement of Human Genome Project:

• Human genome is largely consisting of – 3 × 109 base pairs a lot of repeated sequences.
• 3 billion base pairs were translated into biologically meaningful information by using computers and it led to a new field of bioinformatics.
• Human genome sequencing will enable a new approach to biological research.
• Understanding of function of biological systems increases in public and private sectors due to knowledge from DNA sequences.
• More than 1200 genes are associated with common human disorders such as Cardio- . Vascular diseases, diabetes, (endocrine disease), Alzheimer disease (neurological disorder).
• Efforts for health care are being made to design drugs, genetically modified diets, nutraceuticals etc.

Question 7.  (ISC Biotechnology 2016 Class-12)
(a) Explain the method used for the construction of a genomic DNA library. Also state how a genomic DNA library differs from a cDNA library. [4]
(b) Discuss any four vector-less methods of transfer of foreign DNA into the host cells. [4]
(c) Define glycosidic bond and peptide bond. [2]
(a) DNA Library: DNA library is a collection of DNA fragments of one organism, each carries by a plasmid or virus and cloned in an appropriate host. A DNA probe is used to locate specific DNA sequence in the library. A collection representing the entire genome is called genomic (DNA) library. An assortment of DNA copies of messenger RNA produced by a cell is known as a complimentary DNA (cDNA) library.

Construction of Genomic Library: The process of subdividing genomic DNA into clonable elements and inserting them into host cells is called creating a library.

A complete library, by definition, contains the entire genomic DNA of the source organism and is called as genomic library. A genomic library’ is a set of cloned fragments of genomic DNA.

The process of creating a genomic library includes four steps:

1. In the first step the high molecular weight genomic DNA is separated and subjected to restriction enzy me digestion by using two compatible restriction enzy mes.
2. In the second step, the fragments are then fractionated or separated by using agarose gel electrophoresis to obtain fragments of required size.
3. These fragments are then subjected to alkaline phosphatase treatment to remove the phosphate. In the third step, the dephosphorylated insert is ligated into vector which could be a plasmid, phage or cosmid, depending upon the interest of the researcher.
4. In the last step, the recombinant vector is introduced into the host by electroporation and amplified in host.

In principle, all the DNA from the source organism is inserted into the host, but this is not fully possible as some DNA sequences escape the cloning procedure. Genomic library is a source of genes and DNA sequences. A genomic library is a set of cloned fragments of genomic DNA. Prior information about the genome is not required for library construction for most organisms. In principle, the genomic DNA, after the isolation, is subjected to RE enzyme for digestion to generate inserts.

cDNA libraries V/s Genomic libraries:

• Genomic library is a mixture of fragments of genomic DNA while cDNA obtained from ZM-RNA may cloned to give rise to a cDNA library. Genomic library contains DNA fragments that represent genes as well as those that are not genes. In contrast cDNA library contains only those genes that are expressed in the concerned tissue/organism. In both cases, a mixture of fragments is used for cloning to establish the library.
• Use of cDNA is absolutely essential when the expression of an eukaryotic gene is required in a prokaryote.
• Eukaryotic cDNAs are free from intron sequences.
• As a result of the above, they are smaller in size than the corresponding genes, i.e.. the genes that encoded them.
• A comparison of the cDNA sequence with the corresponding genome sequence permits the delineation of intron/exon boundaries.
• The contents of cDNA libraries from a single organism will vary widely depending on the developmental stage and the cell type used for preparation of the library. In contrast the genomic libraries w ill remain essentially the same irrespective of the developmental stage and the cell type used.
• A cDNA library will be enriched for abundant mRNAs. but may contain only a few or no clones representing rare mRNAs.

(b) Transfection: Transfection is the transfer of foreign DNA into cultured host cells mediated through chemicals. The charged chemical substances such as cationic liposomes, calcium phosphate of DEAE dextran are taken and mixed with DNA molecules. The recipient host cells are overtaxed by this mixture. Consequently the foreign DNA is taken up by the host cells.

Electroporation (Electric Field-mediated Membrane Permeation): In electroporation an electric current at high voltage (about 350 V) is applied in a solution containing foreign DNA and fragile host cells. This creates transient microscopic pores in cell membrane of naked protoplasts. Consequently foreign DNA enters into the protoplast through these pores. The transformed protoplasts are cultured in vitro which regenerate respective cell walls.

Microinjection : In this technique foreign DNA is directly and forcibly injected into the nucleus of animal and plant cells through a glass micropipette containing very fine tip of about 0.5 mm diameter. It resembles with injection needle. In 1982, for the first time Rubin and Spradling introduced Drosophila gene into P-element and microinjected into embryo.

Particle Bombardment Gun (Biolistics): This technique was developed by Stanford in 1987. In this method macroscopic gold or tungsten particles are coated with desired DNA. A plastic micro-carrier containing DNA coated gold/tungsten particles is placed near rupture disc. The particles are bombarded onto target cells by the bombardment apparatus. Consequently foreign DNA is forcibly delivered into the host cells

(c) Glycosidic bond (- O -) is the bond formed between the OH group attached to an anomeric carbon atom of a monosaccharide can easily dehydrate with an -OH group attached to another monosaccharide leading to the formation of a disaccharide.

Peptide bond (-NHCO-) is the bond formed between the carboxylic group (COOH) of one amino acid w ith the amino group (NH2) of another amino acid, with elimination of w ater to form a dipeptide.

Question 8.  (ISC Biotechnology 2016 Class-12)
(a) Explain the secondary and the quaternary structure of proteins. Mention any two important functions of proteins. [4]
(b) Discuss the method used for DN A sequencing by A utomated DNA sequencing technique. [4]
(c) Give any one example each of in-situ and ex-situ conservation. [2]
(a) Secondary Structure (2° structure) of Proteins: It is development of new steric relationships amongst the amino acids for protecting their peptide bonds through formation of intrapolypeptide and interpolypeptide hydrogen bonds. Secondary’ structure is of three types – α-helix β-pleated and collagen helix. The prefixes α and β signify the first and second types of secondary structure discovered by Pauling and Corey (1951).

(i) α-Helix: The polypeptide chain is spirally coiled, generally in a clockwise or right-handed

fashion (Fig.). There are 3.6 amino acid residues per turn of the spiral. The spiral is stabilized by straight hydrogen bonds between imide group (-NH-) of one amino acid and carbonyl group (—CO—) of fourth amino acid residue. In this way all the imide and carbonyl groups become hydrogen bonded. R-groups occur towards the outer side of a-helix. a-helix is the final structure in certain fibrous proteins, e.g., keratin (hair, nail, horn), epidermis (skin).

β-Pleated Sheets : Two or more polypeptide chains come together and form a sheet. Condensation is little. How ever, tw isting does occur. The same polypeptide may fold over itself to form two strands for p-pleating. Adjacent polypeptide chains may occur in parallel (e.g., p-keratin) or anti-parallel (e.g., silk fibrin). Straight hydrogen bonds occur between imide (-NH-) group of one polypeptide and carbonyl (-CO-) group of adjacent polypeptide. Cross-linkages help in stabilization of β-pleated sheets.

Collagen Helix (Fig.) : Collagen has a large amount of glycine (25%) and proline (and hydroxyproline, 25%). It cannot form a-helix due to them. Three of its polypeptide each having about 1000 amino acid residues, come together with each forming an extended left-handed helix. They run parallel, form a right-handed super-helix that is stabilised by hydrogen bonds amongst the three. The triple helix of collagen is often called tropo- collagen. Its one end is stabilised by -S-S- linkages amongst the three chains. Collagen occurs in those tissues where extensibility is limited, e.g., connective tissue, tendons, bones.

Quaternary Structure (4° Structure) of proteins : It is the last or fourth level of protein organisation found in only oligomeric proteins or multimers. The multimeric proteins are formed of two to several polypeptides. The monomers or polypeptide subunits are also called protomers. Protomers may be similar, e.g., two similar polypeptides in enzyme phosphorylase a. It is known as homogeneous quaternary structure. An oligomeric protein having dissimilar subunits shows heterogeneous quaternary structure, e.g., tetrameric haemoglobin with two a (141 amino acids each) and two β (146 amino acids each) polypeptide chains.

Functions of proteins:

• Major group of proteins are enzymes-biocatalyst.
• Myoglobin, a protein found in muscle store oxygen.
• Haemoglobin in RBC’s transports gases in and out of lungs.
• Proteins as structural element; as hairkeratins and bio-membranes.

(b) Automatic DNA Sequencing : In this new method a different fluorescent dye is tagged to the ddNTPs. Using this technique a DNA sequence containing thousands of nucleotides can be determined in a few hours. Each dideoxynucleotide is linked with a fluorescent dye that imparts different colours to all the fragments terminating in that nucleotide. All four labelled ddNTPs are added to a single capillary tube. It is a refinement of gel electrophoresis which separates fastly. DNA fragments of different colours are separated by their respective size in a single electrophoretic gel. A current is applied to the gel. The negatively charged DNA strands migrate through the pores of gel towards the positive end.

The small sized DNA fragments migrate faster and vica versa. All fragments of a given length migrate in a single peak. The DNA fragments are illuminated with a laser beam. Then the fluorescent dyes are excited and emit light of specific wavelengths which is recorded by a special ‘recorder’. The DNA sequences are read by determining the sequence of the colours emitted from specific peaks as they pass the detector. This information is fed directly to a computer which determines the sequence. A tracing electrogram of emitted light of the four dyes is generated by the computer (Fig.). Colour of each dye represents the different nucleotides. Computer converts the data of emitted light in the nucleotide sequences.

(c) In situ conservation refers to ‘on-site’ conservation of plants and animals as such. It is a process of protecting plants or animals in its natural habitat by protecting or cleaning up the habitat, or by defending the species from the predators, e.g., National Park, Sanctuaries and Biosphere Reserve.

Ex situ conservation is ‘off-site conservation’ by protecting an endangered species of plant or animal by removing part of population from a threatened habitat and placing it in a new location such as wild area, zoos or botanical gardens, in vitro gene bank, germplasm-banks, in vivo gene bank.

Question 9.  (ISC Biotechnology 2016 Class-12)
(a) What is meant by the term genomics ? Mention the difference between structural genomics and functional genomics. [4]
(b) How do the following databases contribute towards managing biological data : [4]
(i) GDB and MGD
(ii) PDB and PIR
(c) Name any two organisms whose genomes have been completely sequenced. [2]
(a) Genomics is a scientific discipline of mapping, sequencing and analysing the genome-the complete set of chromosomal and extra-chromosomal genes of an organism. Structural genomics deals with DNA sequencing, sequence assembly, construction of genetic, physical or sequence maps of high resolution of the organism.

Functional Genomics deals with reconstructing genome sequences and to find out the functions they do. It provides novel information about the genome. It helps in understanding of genes and functions of proteins and protein interactions.

(b)

(i) GDB (Genome Database): It is the official central repository for genome mapping data created by Human Genome Project. Its central node is located at the hospital for sick children. GDB holds a vast quantity of data submitted by hundreds of investigators. The GDB has many useful genome resource web-links on its resource page.

MGD (Mouse Genome Database) is the primary public mouse genomic catalogue resource. The MGD includes information on mouse genetic markers and nomenclature, molecular segments, phenotypes, comparative mapping data, graphical display of linkage, cytogenetic and physical maps.

(ii) PDB (Protein Data Bank) : This database has the sequence of those proteins, nucleic acid, whose 3-D structures are known by crystallography or NMR spectroscopy.
Source : NCBI-USA; EBI, UK.

PIR (Protein Information Resource): It is an integrated public bioinformatics resource to support genomic, proteomic and system biology, research and scientific studies.

(c) Organisms with completely sequenced genome : Phage λ , HIV, E.coli, Heliobacterpylori, Saccharomyces cerevisiae (yeast), Drosophila melanogaster (fruitfly). (any one organism)

-: End of ISC Biotechnology 2016 Class-12 Paper :-

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Zbl 0856.35002
Bertozzi, Andrea L.
Symmetric singularity formation in lubrication-type equations for interface motion.
(English)
[J] SIAM J. Appl. Math. 56, No.3, 681-714 (1996). ISSN 0036-1399; ISSN 1095-712X/e

Fourth-order degenerate diffusion equations arise in a lubrication approximation' of a thin film or neck driven by surface tension. Numerical studies of the lubrication equation (LE) $h_t+ (h^n h_{xxx})_x= 0$ with various boundary conditions indicate that singularity formation in which $h(x(t), t)\to 0$ occurs for small enough $n$ with anomalous' or `second type' scaling inconsistent with usual dimensional analysis.\par This paper considers locally symmetric or even singularities in the (LE) and in the modified lubrication equation (MLE) $h_t+ h^n h_{xxxx}= 0$. Both equations have the property that entropy bounds forbid finite time singularities when $n$ is sufficiently large. Power series expansions for local symmetric similarity solutions are proposed for equation (LE) with $n< 1$ and (MLE) for all $n\in \bbfR$. In the latter case, special boundary conditions that force singularity formation are required to produce singularities when $n$ is large. Matching conditions at higher order terms in the expansion suggests a simple functional form for the time dependence of the solution.\par Computer simulations presented here resolve the self similarity in the onset of the singularity of approximately 30 decades in $\min_x(h(x, t))$. Measurements of the similarity shape and time dependences show excellent agreement with the theoretical prediction.\par One striking feature of the solution to (MLE) is a transition from a finite time singularity to an infinite time singularity $n= 3/2$. Also both equations (LE) and (MLE) exhibit symmetric singularities for $n< 0$ with derivatives of order $k$ vanishing at the singular point for all $2< k< 4- 2n$. They also exhibit a blow up in derivatives of order greater than $4- 2n$.
[A.Bertozzi (Durham/NC)]
MSC 2000:
*35A20 Analytic methods (PDE)
35C20 Asymptotic expansions of solutions of PDE
35K55 Nonlinear parabolic equations
76B45 Capillarity
76M20 Finite difference methods

Keywords: second type self-similarity; lubrication approximation; fourth-order degenerate diffusion equations; modified lubrication equation

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# Decision-making in tree limb growth?

Sorry if this is a naive question, but it occurred to me as I was walking across campus today; How does a tree decide which limb is allocated the most resources, and thus grows the largest? My first thought is the first branch to deviate from the base receives the most energy investment, and so on, but I don't have the time (or will) to actually test that. Does it have more to do with efficacy of the limb for photosynthesis? Or is it largely due to chance/unknown variables? Thanks in advance, I feel this is something I learned back in botany and just forgot completely.


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2 edition of Variable selection in nonlinear systems modelling found in the catalog.

Variable selection in nonlinear systems modelling

K. Z. Mao

# Variable selection in nonlinear systems modelling

## by K. Z. Mao

Published by University of Sheffield, Dept. of Automatic Control and Systems Engineering in Sheffield .
Written in English

Edition Notes

 ID Numbers Statement K.Z. Mao and S.A. Billings. Series Research report / University of Sheffield. Department of Automatic Control and Systems Engineering -- no.658, Research report (University of Sheffield. Department of Automatic Control and Systems Engineering) -- no.658. Contributions Billings, S. A. Open Library OL16574290M

In machine learning and statistics, feature selection, also known as variable selection, attribute selection or variable subset selection, is the process of selecting a subset of relevant features (variables, predictors) for use in model construction. Feature selection techniques are used for several reasons: simplification of models to make them easier to interpret by researchers/users. theories, i.e. the theory of nonlinear dynamical systems and hysteresis, statistical decision the-ory, and approximation theory, in view of their applicability for grey-box modelling. These theories show us directly the way onto a new model class and its identiﬁcation algorithm.

Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an Pages: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio–Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio–temporal domains. This book is written with an emphasis on making the algorithms accessible so that they.

Over the past decades, Gets has evolved to become a theoretically well-founded methodology, and recently has also been supported by computer algorithms that make automatized variable selection possible. In this chapter, we review the main concepts and theory needed to use Gets, manually, or with the aid of an computer algorithm such as Autometrics. High-Performance Variable Selection for Generalized Linear Models: PROC HPGENSELECT Overview The HPGENSELECT procedure, available in SAS/STAT (which runs on Base SAS ), performs model selection for generalized linear models (GLMs). It ﬁts models for standard distributions in the exponential.

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### Variable selection in nonlinear systems modelling by K. Z. Mao Download PDF EPUB FB2

A new algorithm which preselects variables in non-linear system models is introduced by converting the problem into a variable selection procedure for a set of linearised models. Because on this result an algorithm which consists of a cluster analysis linearisation sub-region division procedure, a linear subset selection routine using an all Cited by: Variable Selection in Nonlinear Systems Modelling 11ings K.Z.M 0 Department of Automat'c Control and Systems Engineering University of Sheffield Sheffield 3JD, UK Abstract A new aloorithm which preselects variables in nonlinear svstem models is in- troduced bv convertinõ the problem into a variable selection procedure for a set.

Variable selection in linear models is essential for improved inference and interpretation, an activity which has become even more critical Variable selection in nonlinear systems modelling book high dimensional data. Term and Variable Selection for Nonlinear System Identification H.L.

Wei, S.A. Billings and J. Liu Department of Automatic Control and Systems Engineering, University of Sheffield Mappin Street, Sheffield, Sl 3D, UK The purpose of vanable selection is to pre-select a subset consisting of the significant vu-iables or to. For Gaussian responses, the common linear methods include stochastic search variable selection [George and McCulloch, ], selection-based priors [Kuo.

An integral part of engineering design is the development of models that describe physical behavior or phenomena in mathematical terms. As engineering systems have become more complex, classic linear methods of modeling and analysis have proved inadequate, creating a need for nonlinear models to solve design by: 9.

The goal of this paper is to present an approach to modelling that is applicable indifferently to linear and nonlinear systems. It is shown that finding the best model is equivalent to solving a min-max problem, and that the gradient of the objective function can be computed through formulae very similar to those appearing in classical optimal.

Abstract. This paper provides an overview of problems in multivariate modeling of epidemiologic data, and examines some proposed solutions. Special attention is given to the task of model selection, which involves selection of the model form, selection of the variables to enter the model, and selection of the form of these variables in the by: Nonlinear Systems is divided into three volumes.

The first deals with modeling and estimation, the second with stability and stabilization and the third with control. This three-volume set provides the most comprehensive and detailed reference available on nonlinear : Hardcover.

Cite this paper as: Kredler C., Fahrmeier L. () Variable Selection in Generalized Linear Models. In: Caussinus H., Ettinger P., Tomassone R. (eds) COMPSTAT 5th Symposium held at Toulouse Cited by: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains.

This book is written with an emphasis on making the algorithms accessible so that they can be applied and.

Contrary to phenomenological modelling, nonlinear modelling can be utilized in processes and systems where the theory is deficient or there is a lack of fundamental understanding on the root causes of most crucial factors on system.

Phenomenological modelling describes a system in terms of laws of nature. Abstract. In neural modeling of non-linear dynamic systems, the neural inputs can include any system variable with time delays.

To obtain the optimal subset of inputs regarding a performance measure is a combinational problem, and the selection process can be very by: 2. Nonlinear input variable selection (IVS) has been a topic of increasing interest in data-driven modeling applications.

Many recent nonlinear methods (e.g. Partial Mutual Information Selection (PMIS)) have been shown to outperform linear methods (e.g.

Pearson’s Partial Linear Correlation Input Selection (PCIS)) when specifying inputs for data. Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains.

This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in. In ordinary regression that's how you get the right $\sigma^2$. If you do variable selection you must do simultaneous penalization unless perhaps the alpha for keeping variables is or greater.

$\endgroup$ – Frank Harrell Jun 24 '11 at Robust variable selection for nonlinear models with diverging number of parameters Zhike Lva;, Huiming Zhua, Keming Yub aCollege of Business Administration, Hunan University, Changsha,PR China bDepartment of Mathematical Sciences, Brunel University, London UB8 3PH, UK Abstract We focus on the problem of simultaneous variable selection and estimation for File Size: KB.

Frequency Response of Nonlinear Systems 11 Continuous-Time, Severely Nonlinear, and Time-Varying Models and Systems 12 Spatio-temporal Systems 13 Using Nonlinear System Identification in Practice and Case Study Examples 13 References 14 2 Models for Linear and Nonlinear Systems 17 Introduction 17 Linear Models   We conducted simulation runs for each of the 6 conditions in which we varied the sample size (n = 60, and ).

The summary measure of the algorithm performance was the percent of times each variable selection procedure retained only X 1, X 2, and X 3 in the final model. (For PS selection, confounding was set to 20% and non Cited by: Contact D.

Hill Jr. Library. 2 Broughton Drive Campus Box Raleigh, NC () James B. Hunt Jr. Library. Partners WayCited by: 3. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion.

Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection Cited by: High Order Neuro-Fuzzy Dynamic Regulation of General Nonlinear Multi-Variable Systems: /ch The direct adaptive dynamic regulation of unknown nonlinear multi variable systems is investigated in this chapter in order to address the problem ofAuthor: Dimitris C.

Theodoridis, Yiannis S. Boutalis, Manolis A. Christodoulou.electromechanical systems due to its simple structure, ease of implementing variable speed control and low cost. In high accuracy servo control system, high control performance of DC motor is needed. DC motors have traditionally been modelled as IInd order linear system, which ignores the dead nonlinear zone of the Size: KB.


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# American Institute of Mathematical Sciences

April  2018, 38(4): 2079-2092. doi: 10.3934/dcds.2018085

## Minimization of the lowest eigenvalue for a vibrating beam

 1 LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China 2 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China 3 LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, China

* Corresponding author: Zhikun She; Email: zhikun.she@buaa.edu.cn

Received  May 2017 Published  January 2018

Fund Project: The third author is supported by the National Natural Science Foundation of China (Grant No. 11671378) and the Fund of UCAS. The fourth author is supported by the National Natural Science Foundation of China (Grants No. 11371047 and No. 11422111)

In this paper we solve the minimization problem of the lowest eigenvalue for a vibrating beam. Firstly, based on the variational method, we establish the basic theory of the lowest eigenvalue for the fourth order measure differential equation (MDE). Secondly, we build the relationship between the minimization problem of the lowest eigenvalue for the ODE and the one for the MDE. Finally, with the help of this built relationship, we find the explicit optimal bound of the lowest eigenvalue for a vibrating beam.

Citation: Quanyi Liang, Kairong Liu, Gang Meng, Zhikun She. Minimization of the lowest eigenvalue for a vibrating beam. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 2079-2092. doi: 10.3934/dcds.2018085
##### References:

show all references

##### References:
Function $\mathbf{L}(r)$ of $r$
 [1] Monika Laskawy. Optimality conditions of the first eigenvalue of a fourth order Steklov problem. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1843-1859. doi: 10.3934/cpaa.2017089 [2] Gang Meng. The optimal upper bound for the first eigenvalue of the fourth order equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6369-6382. doi: 10.3934/dcds.2017276 [3] Craig Cowan, Pierpaolo Esposito, Nassif Ghoussoub. Regularity of extremal solutions in fourth order nonlinear eigenvalue problems on general domains. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1033-1050. doi: 10.3934/dcds.2010.28.1033 [4] Haitao Che, Haibin Chen, Yiju Wang. On the M-eigenvalue estimation of fourth-order partially symmetric tensors. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2018153 [5] Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp well-posedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2018, 17 (2) : 487-504. doi: 10.3934/cpaa.2018027 [6] Jun-ichi Segata. Initial value problem for the fourth order nonlinear Schrödinger type equation on torus and orbital stability of standing waves. Communications on Pure & Applied Analysis, 2015, 14 (3) : 843-859. doi: 10.3934/cpaa.2015.14.843 [7] Zongming Guo, Long Wei. A fourth order elliptic equation with a singular nonlinearity. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2493-2508. doi: 10.3934/cpaa.2014.13.2493 [8] Changchun Liu. A fourth order nonlinear degenerate parabolic equation. Communications on Pure & Applied Analysis, 2008, 7 (3) : 617-630. doi: 10.3934/cpaa.2008.7.617 [9] Zongming Guo, Long Wei. A perturbed fourth order elliptic equation with negative exponent. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4187-4205. doi: 10.3934/dcdsb.2018132 [10] Tokushi Sato, Tatsuya Watanabe. Singular positive solutions for a fourth order elliptic problem in $R$. Communications on Pure & Applied Analysis, 2011, 10 (1) : 245-268. doi: 10.3934/cpaa.2011.10.245 [11] Baishun Lai, Qing Luo. Regularity of the extremal solution for a fourth-order elliptic problem with singular nonlinearity. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 227-241. doi: 10.3934/dcds.2011.30.227 [12] John R. Graef, Lingju Kong, Min Wang. Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Conference Publications, 2013, 2013 (special) : 291-299. doi: 10.3934/proc.2013.2013.291 [13] Feliz Minhós, T. Gyulov, A. I. Santos. Existence and location result for a fourth order boundary value problem. Conference Publications, 2005, 2005 (Special) : 662-671. doi: 10.3934/proc.2005.2005.662 [14] John R. Graef, Johnny Henderson, Bo Yang. Positive solutions to a fourth order three point boundary value problem. Conference Publications, 2009, 2009 (Special) : 269-275. doi: 10.3934/proc.2009.2009.269 [15] To Fu Ma. Positive solutions for a nonlocal fourth order equation of Kirchhoff type. Conference Publications, 2007, 2007 (Special) : 694-703. doi: 10.3934/proc.2007.2007.694 [16] José A. Carrillo, Ansgar Jüngel, Shaoqiang Tang. Positive entropic schemes for a nonlinear fourth-order parabolic equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (1) : 1-20. doi: 10.3934/dcdsb.2003.3.1 [17] Chunhua Jin, Jingxue Yin, Zejia Wang. Positive periodic solutions to a nonlinear fourth-order differential equation. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1225-1235. doi: 10.3934/cpaa.2008.7.1225 [18] Chuang Zheng. Inverse problems for the fourth order Schrödinger equation on a finite domain. Mathematical Control & Related Fields, 2015, 5 (1) : 177-189. doi: 10.3934/mcrf.2015.5.177 [19] M. Ben Ayed, K. El Mehdi, M. Hammami. Nonexistence of bounded energy solutions for a fourth order equation on thin annuli. Communications on Pure & Applied Analysis, 2004, 3 (4) : 557-580. doi: 10.3934/cpaa.2004.3.557 [20] Zhilin Yang, Jingxian Sun. Positive solutions of a fourth-order boundary value problem involving derivatives of all orders. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1615-1628. doi: 10.3934/cpaa.2012.11.1615

2018 Impact Factor: 1.143


text:
# Archive for the 'privacy' Category

## Your digital footprint: friendly reminder

Posted by Plamen Miltenoff on 31st August 2014

## Pro Domo Sua: Are We Puppets in a Wired World? Surveillance and privacy revisited…

Posted by Plamen Miltenoff on 23rd October 2013

http://www.nybooks.com/articles/archives/2013/nov/07/are-we-puppets-wired-world/

# Are We Puppets in a Wired World?

But while we were having fun, we happily and willingly helped to create the greatest surveillance system ever imagined, a web whose strings give governments and businesses countless threads to pull, which makes us…puppets. The free flow of information over the Internet (except in places where that flow is blocked), which serves us well, may serve others better. Whether this distinction turns out to matter may be the one piece of information the Internet cannot deliver.

by Evgeny Morozov

by John Naughton

#### Big Data: A Revolution That Will Transform How We Live, Work, and Think

by Viktor Mayer-Schönberger and Kenneth Cukier

#### Privacy and Big Data: The Players, Regulators and Stakeholders

by Terence Craig and Mary E. Ludloff
O’Reilly Media, 108 pp., \$19.99 (paper)

## ECAR STUDY OF UNDERGRADUATE STUDENTS AND INFORMATION TECHNOLOGY, 2013

Posted by Plamen Miltenoff on 8th October 2013

## Key Findings

See the 2013 report for a full list of key messages, findings, and supporting data.

• Students recognize the value of technology but still need guidance when it comes to better using it for academics.
• Students prefer blended learning environments while beginning to experiment with MOOCs.
• Students are ready to use their mobile devices more for academics, and they look to institutions and instructors for opportunities and encouragement to do so.
• Students value their privacy, and using technology to connect with them has its limits.
p. 10 students are generally confident in their prepraredness to use technology for course work, but those who are interested in more tech training favor “in calss” guidance over separate training options.

Educause’s ECAR Study, 2013


text:
# Hii they asked this again but in cm

###### Question:

hii they asked this again but in cm

### Your claim can be supported best when you present ...... The three main parts of an argumentative essay are the introduction, body paragraphs, and.......

Your claim can be supported best when you present ...... The three main parts of an argumentative essay are the introduction, body paragraphs, and..........

### How do I solve this? The options are 4, 6 , 14, or 8.

How do I solve this? The options are 4, 6 , 14, or 8....

### GRZ Inc. purchased a customized delivery truck in January 2018 for $70,000. They plan to use this truck for 7 years, and the company estimates the truck's salvage value will be$14,000 at the end of its useful life. (The company uses the straight-line method when recording depreciation.) In 2018, GRZ Inc.'s net income was $575,000, and their tax rate was 35%. What is the value of the depreciation tax shield?A)$2,800 B)$19,600 C)$3,500 D)$24,500 E)$201,250

GRZ Inc. purchased a customized delivery truck in January 2018 for $70,000. They plan to use this truck for 7 years, and the company estimates the truck's salvage value will be$14,000 at the end of its useful life. (The company uses the straight-line method when recording depreciation.) In 2018, GR...

### Beginning in the 1830s, what commodity did british merchants use to increase access to chinese markets?

Beginning in the 1830s, what commodity did british merchants use to increase access to chinese markets?...

### Good movies what are good action films? men who can defend themselves

Good movies what are good action films? men who can defend themselves...

### Suppose that the global crude oil price has risen due to refinery breakdowns caused by middle-east politics and warfare. Crude oil is an input in the gasoline production. At the same time, the demand for driving and, therefore, the demand for gasoline has also risen in the United States. You can accurately predict that the domestic price of gasoline is:_______

Suppose that the global crude oil price has risen due to refinery breakdowns caused by middle-east politics and warfare. Crude oil is an input in the gasoline production. At the same time, the demand for driving and, therefore, the demand for gasoline has also risen in the United States. You can acc...

### A rectangular flower garden measures 9 ft. by Il ft. About how long is a diagonal path through the garden?

A rectangular flower garden measures 9 ft. by Il ft. About how long is a diagonal path through the garden?...

### Find the length of EF

Find the length of EF...

### 33 pints=how many gallons?

33 pints=how many gallons?...

### The purpose of the Soviet blockade of berlin (1948-1949) was to

the purpose of the Soviet blockade of berlin (1948-1949) was to...

### Why does the house impose severe limits on floor debates??

Why does the house impose severe limits on floor debates??...

### Why was samual slater considered a criminal by british textiles manufacturers

why was samual slater considered a criminal by british textiles manufacturers...

### How long is an individual monarchs term of rule

how long is an individual monarchs term of rule...

### A surgical microscope weighing 200 lb is hung from a ceiling by four springs with stiffness 25 lb/ft. The ceiling has a vibration amplitude of 0.05mm at 2 Hz (a typical resonant frequency of a building). a) If there is no damping, how much transmitted vibration (amplitude of displacement) does the microscope experience

A surgical microscope weighing 200 lb is hung from a ceiling by four springs with stiffness 25 lb/ft. The ceiling has a vibration amplitude of 0.05mm at 2 Hz (a typical resonant frequency of a building). a) If there is no damping, how much transmitted vibration (amplitude of displacement) does the m...

### Warren, a golf fan, was curious about how often professional golfers make successful putts from various distances. He looked at a large sample of putts from different distances (in meters) and recorded the success rate for each distance. He noticed a strong negative linear relationship. Here is computer output from a least-squares regression analysis for predicting success rate based on putt distance

Warren, a golf fan, was curious about how often professional golfers make successful putts from various distances. He looked at a large sample of putts from different distances (in meters) and recorded the success rate for each distance. He noticed a strong negative linear relationship. Here is comp...

### In a recent year, an author wrote 171 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check. The probability is:_______.

In a recent year, an author wrote 171 checks. Use the Poisson distribution to find the probability that, on a randomly selected day, he wrote at least one check. The probability is:_______....

### I NEED HELP FAST (25 points)

I NEED HELP FAST (25 points)...


text:
# Determine the indefinite integral: $I=\int \frac{\sin^5x\arcsin^5x}{e^{5x}\ln^5x}dx$ [closed]

Determine the indefinite integral: $$I = \int{\sin^{5}\left(x\right)\arcsin^{5}\left(x\right) \over {\rm e}^{5x}\ln^{5}\left(x\right)}\,{\rm d}x$$

I have not seen this ever, so do not know how solve. Please help me come up with a method of solving the problem.

-

## closed as off-topic by Carl Mummert, kjetil b halvorsen, Fabian, Harish Chandra Rajpoot, yoknapatawphaDec 31 '15 at 0:34

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

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Carl Mummert, kjetil b halvorsen, Fabian, Harish Chandra Rajpoot, yoknapatawpha
If this question can be reworded to fit the rules in the help center, please edit the question.

What makes you think there's a closed-form solution for problems like this? – Ted Shifrin Dec 13 '13 at 14:24
What article? Even if you make all the exponents $5$ equal to $1$, I expect one could prove that there is no elementary antiderivative using differential algebra. – Ted Shifrin Dec 13 '13 at 14:31
Is a series solution okay? Can you post a link to the forum you found it in? – Brian Rushton Jan 4 '14 at 4:19
Series solution seams to be the only way. Otherwise, you should use numerical methods. – whatever Jan 4 '14 at 23:51
I think posting a question with no definite solution has become a good way to gain reputation.. – Apurv Jan 10 '14 at 5:20


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# NAG C Library Function Document

## 1Purpose

nag_tsa_spectrum_univar_cov (g13cac) calculates the smoothed sample spectrum of a univariate time series using one of four lag windows – rectangular, Bartlett, Tukey or Parzen window.

## 2Specification

 #include #include
 void nag_tsa_spectrum_univar_cov (Integer nx, Integer mtx, double px, Integer iw, Integer mw, Integer ic, Integer nc, double c[], Integer kc, Integer l, Nag_LoggedSpectra lg_spect, Integer nxg, double xg[], Integer *ng, double stats[], NagError *fail)

## 3Description

The smoothed sample spectrum is defined as
 $f^ω=12π C0+2∑k=1 M-1wkCkcosωk ,$
where $M$ is the window width, and is calculated for frequency values
 $ωi=2πiL, i=0,1,…,L/2,$
where $\left[\right]$ denotes the integer part.
The autocovariances ${C}_{k}$ may be supplied by you, or constructed from a time series ${x}_{1},{x}_{2},\dots ,{x}_{n}$, as
 $Ck=1n∑t=1 n-kxtxt+k,$
the fast Fourier transform (FFT) being used to carry out the convolution in this formula.
The time series may be mean or trend corrected (by classical least squares), and tapered before calculation of the covariances, the tapering factors being those of the split cosine bell:
 $121-cosπ t-12/T, 1≤t≤T 121-cosπ n-t+12/T, n+ 1-T≤t≤n 1, otherwise,$
where $T=\left[\frac{np}{2}\right]$ and $p$ is the tapering proportion.
The smoothing window is defined by
 $wk=W kM , k≤M-1,$
which for the various windows is defined over $0\le \alpha <1$ by
rectangular:
 $Wα=1$
Bartlett:
 $Wα = 1-α$
Tukey:
 $Wα=121+cosπα$
Parzen:
 $Wα= 1- 6α2+ 6α3, 0≤α≤12 Wα= 2 1-α 3, 12<α< 1.$
The sampling distribution of $\stackrel{^}{f}\left(\omega \right)$ is approximately that of a scaled ${\chi }_{d}^{2}$ variate, whose degrees of freedom $d$ is provided by the function, together with multiplying limits $mu$, $ml$ from which approximate $95%$ confidence intervals for the true spectrum $f\left(\omega \right)$ may be constructed as $\left[ml×\stackrel{^}{f}\left(\omega \right),mu×\stackrel{^}{f}\left(\omega \right)\right]$. Alternatively, log $\stackrel{^}{f}\left(\omega \right)$ may be returned, with additive limits.
The bandwidth $b$ of the corresponding smoothing window in the frequency domain is also provided. Spectrum estimates separated by (angular) frequencies much greater than $b$ may be assumed to be independent.

## 4References

Bloomfield P (1976) Fourier Analysis of Time Series: An Introduction Wiley
Jenkins G M and Watts D G (1968) Spectral Analysis and its Applications Holden–Day

## 5Arguments

1:    $\mathbf{nx}$IntegerInput
On entry: $n$, the length of the time series.
Constraint: ${\mathbf{nx}}\ge 1$.
2:    $\mathbf{mtx}$IntegerInput
On entry: if covariances are to be calculated by the function (${\mathbf{ic}}=0$), mtx must specify whether the data are to be initially mean or trend corrected.
${\mathbf{mtx}}=0$
For no correction.
${\mathbf{mtx}}=1$
For mean correction.
${\mathbf{mtx}}=2$
For trend correction.
Constraint: if ${\mathbf{ic}}=0$, $0\le {\mathbf{mtx}}\le 2$
If covariances are supplied (${\mathbf{ic}}\ne 0$), mtx is not used.
3:    $\mathbf{px}$doubleInput
On entry: if covariances are to be calculated by the function (${\mathbf{ic}}=0$), px must specify the proportion of the data (totalled over both ends) to be initially tapered by the split cosine bell taper.
If covariances are supplied $\left({\mathbf{ic}}\ne 0\right)$, px must specify the proportion of data tapered before the supplied covariances were calculated and after any mean or trend correction. px is required for the calculation of output statistics. A value of $0.0$ implies no tapering.
Constraint: $0.0\le {\mathbf{px}}\le 1.0$.
4:    $\mathbf{iw}$IntegerInput
On entry: the choice of lag window.
${\mathbf{iw}}=1$
Rectangular.
${\mathbf{iw}}=2$
Bartlett.
${\mathbf{iw}}=3$
Tukey.
${\mathbf{iw}}=4$
Parzen.
Constraint: $1\le {\mathbf{iw}}\le 4$.
5:    $\mathbf{mw}$IntegerInput
On entry: $M$, the ‘cut-off’ point of the lag window. Windowed covariances at lag $M$ or greater are zero.
Constraint: $1\le {\mathbf{mw}}\le {\mathbf{nx}}$.
6:    $\mathbf{ic}$IntegerInput
On entry: indicates whether covariances are to be calculated in the function or supplied in the call to the function.
${\mathbf{ic}}=0$
Covariances are to be calculated.
${\mathbf{ic}}\ne 0$
Covariances are to be supplied.
7:    $\mathbf{nc}$IntegerInput
On entry: the number of covariances to be calculated in the function or supplied in the call to the function.
Constraint: ${\mathbf{mw}}\le {\mathbf{nc}}\le {\mathbf{nx}}$.
8:    $\mathbf{c}\left[{\mathbf{nc}}\right]$doubleInput/Output
On entry: if ${\mathbf{ic}}\ne 0$, c must contain the nc covariances for lags from $0$ to $\left({\mathbf{nc}}-1\right)$, otherwise c need not be set.
On exit: if ${\mathbf{ic}}=0$, c will contain the nc calculated covariances.
If ${\mathbf{ic}}\ne 0$, the contents of c will be unchanged.
9:    $\mathbf{kc}$IntegerInput
On entry: if ${\mathbf{ic}}=0$, kc must specify the order of the fast Fourier transform (FFT) used to calculate the covariances.
If ${\mathbf{ic}}\ne 0$, that is covariances are supplied, kc is not used.
Constraint: ${\mathbf{kc}}\ge {\mathbf{nx}}+{\mathbf{nc}}$.
10:  $\mathbf{l}$IntegerInput
On entry: $L$, the frequency division of the spectral estimates as $\frac{2\pi }{L}$. Therefore it is also the order of the FFT used to construct the sample spectrum from the covariances.
Constraint: ${\mathbf{l}}\ge 2×{\mathbf{mw}}-1$.
11:  $\mathbf{lg_spect}$Nag_LoggedSpectraInput
On entry: indicates whether unlogged or logged spectral estimates and confidence limits are required.
${\mathbf{lg_spect}}=\mathrm{Nag_Unlogged}$
Unlogged.
${\mathbf{lg_spect}}=\mathrm{Nag_Logged}$
Logged.
Constraint: ${\mathbf{lg_spect}}=\mathrm{Nag_Unlogged}$ or $\mathrm{Nag_Logged}$.
12:  $\mathbf{nxg}$IntegerInput
On entry: the dimension of the array xg.
Constraints:
• if ${\mathbf{ic}}=0$, ${\mathbf{nxg}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{kc}},{\mathbf{l}}\right)$;
• if ${\mathbf{ic}}\ne 0$, ${\mathbf{nxg}}\ge {\mathbf{l}}$.
13:  $\mathbf{xg}\left[{\mathbf{nxg}}\right]$doubleInput/Output
On entry: if the covariances are to be calculated, then xg must contain the nx data points. If covariances are supplied, xg may contain any values.
On exit: contains the ng spectral estimates, $\stackrel{^}{f}\left({\omega }_{\mathit{i}}\right)$, for $\mathit{i}=0,1,\dots ,\left[L/2\right]$ in ${\mathbf{xg}}\left[0\right]$ to ${\mathbf{xg}}\left[{\mathbf{ng}}-1\right]$ respectively (logged if ${\mathbf{lg_spect}}=\mathrm{Nag_Logged}$). The elements ${\mathbf{xg}}\left[\mathit{i}-1\right]$, for $\mathit{i}={\mathbf{ng}}+1,\dots ,{\mathbf{nxg}}$ contain $0.0$.
14:  $\mathbf{ng}$Integer *Output
On exit: the number of spectral estimates, $\left[L/2\right]+1$, in xg.
15:  $\mathbf{stats}\left[4\right]$doubleOutput
On exit: four associated statistics. These are the degrees of freedom in ${\mathbf{stats}}\left[0\right]$, the lower and upper $95%$ confidence limit factors in ${\mathbf{stats}}\left[1\right]$ and ${\mathbf{stats}}\left[2\right]$ respectively (logged if ${\mathbf{lg_spect}}=\mathrm{Nag_Logged}$), and the bandwidth in ${\mathbf{stats}}\left[3\right]$.
16:  $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_CONFID_LIMITS
The calculation of confidence limit factors has failed.
Spectral estimates (logged if requested) are returned in xg, and degrees of freedom and bandwidth in stats.
NE_INT
On entry, ${\mathbf{ic}}=0$ and ${\mathbf{mtx}}<0$: ${\mathbf{mtx}}=〈\mathit{\text{value}}〉$.
On entry, ${\mathbf{ic}}=0$ and ${\mathbf{mtx}}>2$: ${\mathbf{mtx}}=〈\mathit{\text{value}}〉$.
On entry, ${\mathbf{iw}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{iw}}=1$, $2$, $3$ or $4$.
On entry, ${\mathbf{mw}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{mw}}\ge 1$.
On entry, ${\mathbf{nx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nx}}\ge 1$.
NE_INT_2
On entry, ${\mathbf{l}}=〈\mathit{\text{value}}〉$ and ${\mathbf{mw}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{l}}\ge 2×{\mathbf{mw}}-1$.
On entry, ${\mathbf{mw}}=〈\mathit{\text{value}}〉$ and ${\mathbf{nx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{mw}}\le {\mathbf{nx}}$.
On entry, ${\mathbf{nc}}=〈\mathit{\text{value}}〉$ and ${\mathbf{mw}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nc}}\ge {\mathbf{mw}}$.
On entry, ${\mathbf{nc}}=〈\mathit{\text{value}}〉$ and ${\mathbf{nx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nc}}\le {\mathbf{nx}}$.
On entry, ${\mathbf{nxg}}=〈\mathit{\text{value}}〉$ and ${\mathbf{l}}=〈\mathit{\text{value}}〉$.
Constraint: if ${\mathbf{ic}}\ne 0$, ${\mathbf{nxg}}\ge {\mathbf{l}}$.
NE_INT_3
On entry, ${\mathbf{kc}}=〈\mathit{\text{value}}〉$, ${\mathbf{nx}}=〈\mathit{\text{value}}〉$ and ${\mathbf{nc}}=〈\mathit{\text{value}}〉$.
Constraint: if ${\mathbf{ic}}=0$, ${\mathbf{kc}}\ge \left({\mathbf{nx}}+{\mathbf{nc}}\right)$.
On entry, ${\mathbf{nxg}}=〈\mathit{\text{value}}〉$, ${\mathbf{kc}}=〈\mathit{\text{value}}〉$ and ${\mathbf{l}}=〈\mathit{\text{value}}〉$.
Constraint: if ${\mathbf{ic}}=0$, ${\mathbf{nxg}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{kc}},{\mathbf{l}}\right)$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL
On entry, ${\mathbf{px}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{px}}\le 1.0$.
On entry, ${\mathbf{px}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{px}}\ge 0.0$.
NE_SPECTRAL_ESTIMATES
One or more spectral estimates are negative.
Unlogged spectral estimates are returned in xg, and the degrees of freedom, unloged confidence limit factors and bandwidth in stats.

## 7Accuracy

The FFT is a numerically stable process, and any errors introduced during the computation will normally be insignificant compared with uncertainty in the data.

## 8Parallelism and Performance

nag_tsa_spectrum_univar_cov (g13cac) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_tsa_spectrum_univar_cov (g13cac) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the x06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

nag_tsa_spectrum_univar_cov (g13cac) carries out two FFTs of length kc to calculate the covariances and one FFT of length l to calculate the sample spectrum. The time taken by the function for an FFT of length $n$ is approximately proportional to $n\mathrm{log}\left(n\right)$ (but see Section 9 in nag_sum_fft_realherm_1d (c06pac) for further details).

## 10Example

This example reads a time series of length $256$. It selects the mean correction option, a tapering proportion of $0.1$, the Parzen smoothing window and a cut-off point for the window at lag $100$. It chooses to have $100$ auto-covariances calculated and unlogged spectral estimates at a frequency division of $2\pi /200$. It then calls nag_tsa_spectrum_univar_cov (g13cac) to calculate the univariate spectrum and statistics and prints the autocovariances and the spectrum together with its $95%$ confidence multiplying limits.

### 10.1Program Text

Program Text (g13cace.c)

### 10.2Program Data

Program Data (g13cace.d)

### 10.3Program Results

Program Results (g13cace.r)


text:
RESol - Maple Programming Help

RESol

data structure to represent the solution of a recurrence equation

 Calling Sequence RESol(eqns, fcns, inits) LREtools[REcreate](eqns, fcns, inits)

Parameters

 eqns - single equation or a set of equations fcns - function name or set of function names inits - set of initial conditions

Description

 • The RESol command calls LREtools[REcreate] to build the RESol data structure.
 • This data structure represents the solution of a recurrence equation.  It is to rsolve and LREtools as DESol is to dsolve and DEtools.
 • The parameters of an RESol are a set of normalized equations, a set of function names and a set of initial conditions.
 • On output, an information table, INFO is added.  The entries in this table are:

 type - the strings 'linear' or 'nonlinear' functions - a name or set of names of the recurrence function(s) vars - a name or set of names of the recurrence variable(s) order - the order of the equation shifteqn - an equation in &Shift[vars](functions) which represents the shift operator associated to the linear recurrence equation coeffs - a list of the rhs of the equation and the coefficients of the shifteqn

 • Note that the first three items are always present, and the next three are there only if the recurrence is linear.

Examples

 > $\mathrm{RESol}\left(\left\{a\left(n+1\right)-a\left(n\right)=n\right\},\left\{a\left(n\right)\right\},\left\{\right\}\right)$
 ${\mathrm{RESol}}{}\left(\left\{{a}{}\left({n}{+}{1}\right){-}{a}{}\left({n}\right){=}{n}\right\}{,}\left\{{a}{}\left({n}\right)\right\}{,}\left\{{a}{}\left({0}\right){=}{a}{}\left({0}\right)\right\}{,}{\mathrm{INFO}}\right)$ (1)
 > $\mathrm{re}≔\mathrm{LREtools}[\mathrm{REcreate}]\left(a\left(n+2\right)-{n}^{2}a\left(n+1\right)+\left(n-17\right)a\left(n\right)=\mathrm{sin}\left(n\right),a\left(n\right),\left\{a\left(0\right)=0\right\}\right)$
 ${\mathrm{re}}{≔}{\mathrm{RESol}}{}\left(\left\{{a}{}\left({n}{+}{2}\right){-}{{n}}^{{2}}{}{a}{}\left({n}{+}{1}\right){+}\left({n}{-}{17}\right){}{a}{}\left({n}\right){=}{\mathrm{sin}}{}\left({n}\right)\right\}{,}\left\{{a}{}\left({n}\right)\right\}{,}\left\{{a}{}\left({0}\right){=}{0}{,}{a}{}\left({1}\right){=}{a}{}\left({1}\right)\right\}{,}{\mathrm{INFO}}\right)$ (2)
 > $\mathrm{print}\left(\mathrm{op}\left(4,\mathrm{re}\right)\right)$
 ${\mathrm{table}}\left(\left[{\mathrm{order}}{=}{2}{,}{\mathrm{type}}{=}{\mathrm{constcoeffs}}{,}{\mathrm{polycoeffs}}{=}{\mathrm{false}}{,}{\mathrm{max_shift}}{=}{2}{,}{\mathrm{nonvars}}{=}\left({}\right){,}{\mathrm{shifteqn}}{=}{{\mathrm{&Shift}}{[}{n}{]}{}\left({a}\right)}^{{2}}{-}{{n}}^{{2}}{}{\mathrm{&Shift}}{[}{n}{]}{}\left({a}\right){+}{n}{-}{17}{,}{\mathrm{vars}}{=}{n}{,}{\mathrm{rhs}}{=}{\mathrm{sin}}{}\left({n}\right){,}{\mathrm{min_shift}}{=}{0}{,}{\mathrm{functions}}{=}{a}{,}{\mathrm{coeffs}}{=}\left[{-}{\mathrm{sin}}{}\left({n}\right){,}{n}{-}{17}{,}{-}{{n}}^{{2}}{,}{1}\right]{,}{\mathrm{linear}}{=}{\mathrm{true}}\right]\right)$ (3)
 > $\mathrm{re2}≔\mathrm{LREtools}[\mathrm{REcreate}]\left({a\left(n+2\right)}^{2}-a\left(n\right)=0,a\left(n\right),\left\{\right\}\right)$
 ${\mathrm{re2}}{≔}{\mathrm{RESol}}{}\left(\left\{{{a}{}\left({n}{+}{2}\right)}^{{2}}{-}{a}{}\left({n}\right){=}{0}\right\}{,}\left\{{a}{}\left({n}\right)\right\}{,}\left\{{}\right\}{,}{\mathrm{INFO}}\right)$ (4)
 > $\mathrm{print}\left(\mathrm{op}\left(4,\mathrm{re2}\right)\right)$
 ${\mathrm{table}}\left(\left[{\mathrm{order}}{=}{2}{,}{\mathrm{max_shift}}{=}{2}{,}{\mathrm{nonvars}}{=}\left({}\right){,}{\mathrm{vars}}{=}{n}{,}{\mathrm{min_shift}}{=}{0}{,}{\mathrm{functions}}{=}{a}{,}{\mathrm{linear}}{=}{\mathrm{false}}\right]\right)$ (5)


text:
Kritische Frequenzen von Systemen, die in bezug auf die Zeitumkehr invariant sind.(Russian)Zbl 0284.34048

MSC:

 34C25 Periodic solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34A30 Linear ordinary differential equations and systems


text:
# Help me understand this

1. Apr 26, 2005

### Reshma

I seem to have a problem understanding this problem let alone solving it

A star emits 2x1045 photons per sec, 80% of which are in the visible range. The star is 1200 light years away, and the night adapted eye, whose pupil makes an opening 4mm in diameter, can barely see the star. How many photons per sec are necessary to trigger the eye as a detector?

I figured out the number of photons in the visible range is = 0.8x2x1045

Can someone help me proceed?

2. Apr 26, 2005

### Galileo

Out of those photons, how many will go to a surface of known area a given distance away?

3. Apr 26, 2005

### jdavel

Reshma,

2E45 is a lot of photons, right? What do you think the problem means when it says the star emits that many photons/second? What are you picturing?

4. Apr 26, 2005

### Reshma

Thank for looking into this-Jdavel and Galileo.

Jdavel-I'm picturing the number of visible photons here, but few will be detected by the night adapted eye.

Galileo- are you referring to the surface area of the pupil?

5. Apr 26, 2005

### learningphysics

The 2E45 photons form a shape... they are burst by the star every second.

What is the area of the shape when photons reach 1200 light years away.

Can you use the area of this shape and the area of the eye to calculate how many of the 2E45 photons hit the eye?

That is the required number of photons per second.

6. Apr 27, 2005

### Reshma

OK, the distant star is a sphere and HERE you take the radius(R) as 1200 light years, right? Using this assumption:
R=1.14x1019m. Area is given by $$4 \pi R^2$$
Can you clarify this?

7. Apr 27, 2005

### Reshma

Also area of puplil $$A= \pi (2\times 10^{-3})^2$$

8. Apr 27, 2005

### maverick280857

I would suppose that the elementary flux model we use will give the answer here: you know the fraction f of the total number of photons emitted by the source (N). A light year is the distance travelled by light at a velocity 299792458 m/s in vacuum in one year (which means a LOT of seconds: 86400s/day * 365 days or if you want to be ultraprecise (you can't be) then its 365.25 days). The source gives out fN photons per second but the source is apparently isotropic so it gives out fN photons over a spherical region of space. If you "cut in" somewhere with some radius r then the effective area over which the fN photons are "available" completely is $A_{T}=4\pi r^2$ so the number of photons arriving at the eye is actually $\frac{fN}{A_T}A_{eye}$. Whats wrong with that? :shy:

9. Apr 27, 2005

### SpaceTiger

Staff Emeritus

10. Apr 27, 2005

### learningphysics

Yes. Looks right.

(area of eye)/(area of sphere) = (no.visible photons that hit eye)/(total number of visible photons)

I made a mistake in my previous post. Be sure to use 1.6E45 (visible photons) instead of 2E45.

The number of visible photons that hit the eye is what you're looking for.

Last edited: Apr 27, 2005
11. Apr 28, 2005

### Reshma

Thanks for the help everyone. My final answer is: 12 visible photons per sec hit the eye.
SpaceTiger- Thank you so much for the link. Your post was extremely well written and gives me a clear picture in context to this question.


text:
Map Engine Rendering Broken

So I've been making my own tile map engine in LibGDX as the one currently implemented doesn't support collision detection with scaling. So I've come up with my own Layer and Map class and a drawing function for the map. Currently this is what it produces:

Here's the rendering code:

public void draw(SpriteBatch batch) {
for(Layer layer : layers) {
for(int x = 0; x < layer.getTileMap().length; x++) {
for(int y = 0; y < layer.getTileMap()[x].length; y++) {
batch.draw(layer.getTiles()[layer.getTileMap()[x][y]],
xOffset + (x * ((layer.getTileWidth() * scale))), yOffset + (y * ((layer.getTileHeight() * scale))),
(layer.getTileWidth() * scale), (layer.getTileHeight() * scale));
}
}
}
}

EDIT: Yes, I'm aware the map looks weird, it's just random textures thrown in from a tile-sheet.

• What would your expected output look like in this case? It's tough to know what's wrong with the output you've shown if we don't know what you were trying to do instead, or how it differs. – DMGregory Jan 22 '17 at 10:38
• Good point, it's meant to look like the bottom row. The answer basically came to me this morning as I realised that the x and y need to be switched in order for it to function correctly as the x represents the columns rather than the rows. – Ammar Tarajia Jan 22 '17 at 12:03

Here's the new rendering code:

public void draw(SpriteBatch batch) {
for(Layer layer : layers) {
for(int y = 0; y < layer.getTileMap().length; y++) {
for(int x = 0; x < layer.getTileMap()[y].length; x++) {
batch.draw(layer.getTiles()[layer.getTileMap()[x][y]],
xOffset + (x * ((layer.getTileWidth() * scale))), yOffset + (y * ((layer.getTileHeight() * scale))),
(layer.getTileWidth() * scale), (layer.getTileHeight() * scale));
}
}
}
}

The x and y simply needed to be switched.