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# QuantLib C++: Monte Carlo Engine with SequenceStatistics

I'm trying to implement a Monte Carlo PricingEngine that stores multidimensional statistics.

I have done the following:

1. Defined a Monte Carlo Trait that among other things stores as the path_pricer_type PathPricer<MultiPath,Array> (my process is one dimensional but has 2 factors). let's call this struct MyMCTrait.
2. Implemented a class that derives from both McSimulation<MyMCTrait,PseudoRandom,SequenceStatistics> and VanillaOption::engine.
3. Implemented a PathPricer<MultiPath,Array> in which the first element of the Array returned by the operator() is the price of the option.

I'm getting compiling errors because in methods value() and valueWithSamples() of class McSimulation we have the following initializations:

a. result_type(mcModel_->sampleAccumulator().mean());

b. result_type error(mcModel_->sampleAccumulator().errorEstimate());

that are trying to cast from std::vector<Real> (returned by the SequenceStatistics methods) to Array (result_type).

I doubt that the right way to go is to implement the cast (if it's possible), could anyone point me to the right direction? Thanks.

## EDIT

I got the Pricing Engine working by using a derived class from SequenceStatistics. I just overrode the inspectors mean() and errorEstimate() and made them return an Array. To do this I used the base class methods + the Array constructor that takes begin and end iterators.

I'm still wondering though if this is the right way to proceed. Thanks for any thoughts.

Yes, your solution is correct, given the implementation of McSimulation and the interface of SequenceStatistics. We should probably have defined SequenceStatistics as returning instances of Array...
As you might have seen, trying to return std::vector<Real> from the path pricer wouldn't work; the result type needs to define arithmetic operations such as addition and subtraction.


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#### Topic: Project Profiler issue

Jeff,

I'm have difficulty accessing the Project Profiler using SF 2.31 build 2290.  Using a single module program, the Profiler works just fine.  But when I try Profiling a large 30 module program that uses AppGraphics, no profile is created. I did check the profier option in the project menu and  I've not tried profiling a large multi-module program without using AppGraphics.

I have not explored this issue further, but wondered whether there is a size limitation for the Profiler, or is compatable with AppGraphics.

I look forward to any suggestions that may help get the profiler working.

Thanks as always,

Frank

#### Re: Project Profiler issue

Frank,

There is no size limitation on the profiler (it is just GNU gprof under the hood), and AppGraphics shouldn't affect it.  However, AppGraphics does introduce threads, which may skew profiler results.  I'll see if I can replicate the issue, though.

Is your project a 32- or 64-bit project?  Which version of Windows are you on?

Jeff Armstrong
Approximatrix, LLC

#### Re: Project Profiler issue

Jeff,

I'm running Windows 7 (64-bit)

Frank

#### Re: Project Profiler issue

Frank,

The project is also 64-bit?

When you enabled profiling, did you first clean your project?  Everything needs to be recompiled to ensure that profiling works, and I don't believe that Simply Fortran actually forces this to occur when that flag is changed.  I'm just trying to eliminate some small issues.

Also, you mentioned that "...no profile is created."  What exactly do you mean?  Do the profile results come back blank?

Jeff Armstrong
Approximatrix, LLC

#### Re: Project Profiler issue

Jeff,

Profiler problem solved.

Project steps taken:
-Build
-Clean

-Project
-options
-General
-Exec
-64 Bit
-Gui
-code generation
-optim - common
-Enable Profiling
-CPU - generic
-compile strictly selection
-fortran
-'all' unchecked
-all static
-compiler
-fortran compiler - empty
-C compiler - empty
-linker: -lappgraphics -lgdi32 -lcomdlg32 -lcomctl32 -luuid -loleaut32 -lole32

-Build
-Profile --> compile and run program (runs okay)

-Profile (selected again after program runs and completed)
( Profiler Error - Profiling data does not yet exist... )

However, the gmon.out file was created in the program project sub-folder where the program accesses a data file.
The gmon.out file is not located in the project folder (.../fortran/myprog but in .../fortran/myprog/data ).

But when the gmon.out file is copied back to the project folder and the Profile Project option is selected, then the profiler does read the gmon.out file and results are displayed properly.

Solution: The Profiler file gmon.out must be located in or copied to the main project file where the program is compiled and run even if the program reads a data file from another folder.

Frank

#### Re: Project Profiler issue

Frank

Ah, I see what's happening.  The gmon.out file would be created in the working directory when the program runs.  By default, the working directory is also the project directory.  However, if you change the working directory, the profiler is still looking for gmon.out in the project directory.

Interesting bug!  I'll see that it's fixed!

Jeff Armstrong
Approximatrix, LLC

#### Re: Project Profiler issue

Frank,

Is your program actually changing the current directory itself?  Looking at Simply Fortran, it already does account for a different working directory when trying to locate and load gmon.out.  Specifically, I'm wondering if your code calls

CALL CHDIR("path\to\data")

while running.  Simply Fortran really wouldn't know where to locate the profiler data in that case.

Jeff Armstrong
Approximatrix, LLC

#### Re: Project Profiler issue

Jeff,

Regarding the question of whether my program is changing the current directory itself, I would have to say yes, but...
It does NOTchange the directory using a CALL CHDIR() statement, but it does open a file for data entry using AppGraphics Openfile statement in a different directory from the programs current directory thereby changing the directory.

For example,

using AppGraphics open menu it could open a data file in a sub-directory of the programs directory, or a completely different directory from the programs current directory.

(.../fortran/myprog opens a data file in .../fortran/myprog/data )
or
(.../fortran/myprog opens a data file in .../fortran/notmyprog/data ).

I hope my explanation was helpful,

Frank

#### Re: Project Profiler issue

Frank,

The Windows file dialogs can change the working directory, which is what's occurring in your case.  We don't really have a good method of detecting this, though, when trying to open the profiler data.  I'll try to think of a solution, but, for now, you'll need to copy gmon.out back to your project directory to generate profile results.

Jeff Armstrong
Approximatrix, LLC

format: plain


text:
# Square Within Square Root

• Jan 21st 2007, 04:55 AM
symmetry
Square Within Square Root
How do I handle square root within square root questions?

I don't have a sample question, though.

Can anyone help me?
• Jan 21st 2007, 05:10 AM
earboth
Quote:

Originally Posted by symmetry
How do I handle square root within square root questions?

I don't have a sample question, though.

Can anyone help me?

Hello,

consider a root to be a power to a rational exponent. Example:

$\sqrt{\sqrt{a}}=\left( a^{\frac{1}{2}} \right)^\frac{1}{2}=a^{\frac{1}{4}}$

In general:

$\sqrt[x]{\sqrt[y]{a}}=a^{\frac{1}{x} \cdot \frac{1}{y}}=\sqrt[x \cdot y]{a}$

EB
• Jan 21st 2007, 05:12 AM
symmetry
ok
Thank you so much.

I had no idea that such formulas existed.

Now it all makes sense.

Thanks!


text:
# Deterministic quantum mechanics

I came across a very recent paper by Gerard 't Hooft The abstract says:

It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a probability, have to be introduced as separate axioms in quantum mechanics besides the Schroedinger equation. Here we show that this is not true in certain models where quantum behavior can be attributed to underlying deterministic equations. It is argued that indeed the apparent spontaneous collapse of wave functions and Born's rule are features that strongly point towards determinism underlying quantum mechanics.

http://de.arxiv.org/abs/1112.1811

I am wondering why this view seems to unpopular?

-
Hmm, at least he finally explains his version of "deterministic model" completely clearly. – Ron Maimon Dec 21 '11 at 19:39
– Qmechanic Aug 20 '12 at 18:40

I'm working on a new, much improved version of my paper. Please note that I am not a fundamentalist, like, as it seems, some of my critics. I don't have an open telephone line with God, like Einstein on one side, and Motl on the other. So what I am doing in my paper (which will come out as a book, eventually), is I simply explore the idea that the usual counter arguments against a simple, deterministic interpretation of qm can be ignored, and I ask what you may get. The answer is quite interesting, but yes, one does encounter some interesting problems. The most severe, technical problems one gets are totally unrelated to the usual emotional arguments against deterministic qm, so I ask: are these totally prohibitive then, or is there a way out? Would that also answer the usual Motl-like objections? The most obnoxious problem I get: how does one arrive at an effective Hamiltonian that is both bounded from below and locally defined (or: extensive) ? There may be very interesting answers; one of them says that yes, the entire theory obeys complete locality - all physics is local - but the ultimate Hamiltonian of qm is non-local. This means that the phases of wave functions of far-away particles enter in the physics equations in a non-trivial way, while nothing of this has effects on the predictions of qm, which, in the usual qm way, are local.

But that does not have to be the answer. An other possible answer I find much more interesting and natural. You know that there are lots of crackpots who claim that you can "disprove the Bell theorem". Most of those totally miss the point, but there is a way. Bell assumes that in the initial state, the entangled particles just separating from one another, and Bob and Alice, who did not yet make their decisions, are fundamentally uncorrelated. That's because Alice and Bob must have "free will". There are two points to be considered to see why this may well be wrong. One is, that correlation functions do not have to vanish outside the light cone (look at QFT, but also look at simple classical systems such as liquids showing critical opalescence near the critical point); the other is directed to those who believe that only "conspiracy" can force Bob and Alice then the mike the "right" decisions. No, there can be something else. If you have a deterministic underlying theory, then there are two kinds of states: the truly `ontological' ones, and the templates, which are quantum superpositions. In ordinary qm, we do not distinguish between the two, but when it comes to the question of realism, you must. Then we note that there is a simple conservation law of nature: once a state is ontological, it will stay that way forever. A template will forever be a template. This means that, no matter what Alice and Bob decide, they will not be able to rotate their polarisers in such a way that the photons come out as superpositions of the other choices they wanted to make. They will have to rotate objects in their environment as well, so that, after changing their minds, they will again work with an ontological state.

Of course, Alice and Bob cannot change their settings without essential changes in their past, and, in probability terms, they might change their state into a much less (or more) likely one.

By the way, the notion of probability enters into my theory in a very simple way: it exactly corresponds to the uncertainties in the initial state, which are reflected in the use of the templates. This leads to the (EXACT) Born rule. Please wait until the improved version of my paper comes out.

-
Greetings Dr. 't Hooft. Perhaps this is a stupid question but it seems to me that finding a deterministic , classical "gears and sprockets" underpinning for QM is only problematic if one demands that it be local, which I think implies that it scales linearly (or sub-exponentially) with the number particles/qubits, whatever. For example, if you wrote down a classical system that reproduces the dynamics of an $N$-level quantum system using $O(N)$, or $O(N^2)$, resources, this wouldn't ruffle anyone's feathers. Would you mind clarifying this for me? (I'd rather not clog your inbox) – lionelbrits Jan 19 '15 at 14:24

It is unpopular among physicists because physicists, by definition, "like" theories and claims that correctly describe our world and Gerard 't Hooft's statements about the nature of the wave function are demonstrably invalid in the world around us, whether or not he may construct a contrived toy model where his claims are right and which has some vague features remotely resembling the real world.

The fact that the basic postulates of quantum mechanics are unavoidable has been known to physics at least from the late 1920s. For example, in his book on principles of quantum mechanics, Paul Dirac disproved all theories of 't Hooft's kind on the first three pages

http://motls.blogspot.com/2011/12/paul-diracs-forgotten-quantum-wisdom.html

and these early stages of the book – explaining that all the concepts and mathematical objects in the quantum theory have a new interpretation, one that doesn't coincide with anything we know in classical physics – are indeed a necessary pre-requisite for the reader to actually understand the rest of the theory.

Many other properties of quantum mechanics that couldn't be obtained from any classical theory compatible with relativity were obtained later, when physicists studied properties of entangled states. Bell's inequalities, Hardy's "paradox", GHZM states, Kochen-Specker theorem, free will theorem, and other results uniformly show that the natural phenomena we observe have features that can't be compatible with any theory of the type that Gerard 't Hooft is discussing. That's another set of rather good reasons for a physicist to treat such alternative theories as unpopular ones.

-
-1: Lubos, here you are mistaken. The ideas of 'tHooft are to reproduce quantum mechanics from a stochastic theory which is massively nonlocal. There is no violation of any standard idea, it requires new ideas to rule this out. It is likely that his idea does not work, but you did not demonstrate it. I share your feeling that this is weird, but one must put personal feelings that something does not work to avoid throwing away future string-theory! Remember strings were also dismissed in 1974 as lunatic stuff. – Ron Maimon Dec 21 '11 at 19:41
"I feel there should be an approximation to QM that is nonexponential." John Sidles has a lot to say about this, e.g. faculty.washington.edu/sidles/ENC_2011/index.html#burningArrow – Mitchell Porter Dec 23 '11 at 2:40
Prof. Motl's answer is a mere diatribe without any physics in it. -1 Now, whether Dirac is a demi-god or not, he stated in print that he thought determinism would be restored, that Einstein would eventually be proved right, so your link is not even accurate. – joseph f. johnson Jan 16 '12 at 7:16
The link Prof. Motl provides, as if it were to Dirac's own thoughts, is only to Prof. Motl's own very loose and tendentious interpretation. At the end of his life, at any rate, Dirac said, and this is an exact quote: « And, I think it might turn out that ultimately Einstein will prove to be right, ... – joseph f. johnson Jan 16 '12 at 16:20
« And I think that it is quite likely that at some future time we may get an improved quantum mechanics in which there will be a return to determinisim and which will, therefore, justify the Einstein point of view. But such a return to determinism could only be made at the expense of giving up some other basic idea which we now assume without question.» – joseph f. johnson Jan 16 '12 at 16:20

My understanding is that the Copenhagen intepretation of quantum mechanics (ie. that particles have no definite position/momentum until they are observed) is just one of many interpretations, any one of which could be correct, and that we have no real reason for preferring one to another - they all produce the same results experimentally.

There is, in fact, a semi-popular deterministic interpretation called the De Broglie–Bohm theory. Unfortunately, it relies on an assumption that is even more unintuitive and terrifying (to physicists) than the Copenhagen intepretation: that all particles, everywhere in the universe, are connected by an invisible wave which acts at a distance instantaneously, no matter how large the distance. For obvious reasons, this is called a non-local theory.

Unfortunately, according to Bell's theorem, there can be no explanation of quantum-mechanics which is both local and deterministic. So we must accept that, if there is an underlying explanation for the weirdness of Quantum Mechanics, it must be either non-deterministic (like the Copenhagen Interpretation surmises) or non-local (like the De Broglie-Bohm theory).

For more information, see Nick Herbert's excellent book, Quantum Reality: Beyond the New Physics.

-
The point is that physics has abandoned locality with holographic principle and string theory, but physics has not come to an end. In fact, the nonlocal theories are more tightly constrained than the local ones. In this atmosphere, it is legitimate to revisit hidden variables, to see if they make sense. t'Hooft is not looking for an interpretation of quantum mechanics, but a new theory, which can replace it. The new theory must have an interpretation as real stuff changing deterministically, and the QM is just informational superstructure on top of this. I don't think his idea works, it might. – Ron Maimon Dec 21 '11 at 23:12
@Ron, is string theory really nonlocal in this sense? Presumably you can't, for example, use a really long string to send a signal faster than light? – Harry Johnston Dec 26 '11 at 5:31
@Harry: String theory is nonlocal, not in the sense of sending signals between two points faster than light, but in the sense that space and time are emergent, so that two nearby points are smeared over a big far-away null surface holographically to big overlapping disks, and even the most local null-surface dynamics are massively nonlocal. This holographic nonlocality is not even describable in terms of 'stuff here' and 'stuff there' so you can't say whether the signal moves faster than light really, because it was always everywhere. – Ron Maimon Dec 26 '11 at 9:44
By the way if you asked a person some centuries ago what would he prefer - undetermined, random fate and unconnected world or underlying connections of the all things with determined fate he would prefere the later. – Anixx Jul 22 '12 at 0:45

Addendum: an other important point of criticism raised (Newman and others): why search for such a theory at all? Its predictions will be nil.

While Maimon thinks that my prediction that true quantum computing will be impossible implies that my theory will deviate from true divine qm. No to both: my theory implies that not all qm models will work for physics. The ones with a deterministic system behind them form a very tiny subset. Such that I predict that there will be obstructions, not deviating from true qm at all, that prohibit quantum calculations outperforming classical computers if you would scale their performance to Planckian dimensions. So yes, quantum computers will be great, but their performance will be limited. The engineers will blame that to problems producing ideal materials, I will blame it to the fact that, in agreement of the Standard Model, ideal materials cannot exist. Most importantly, if the equations could be worked out better than I can at present, they should give important constraints on the parameters of the Standard Model or other theoretical constructs used in fundamental particle physics. That's my real motivation: do good physics.

-
thanks for the updates on your work. – anna v Jan 19 '15 at 10:51

Thanks for the great question, I just skimmed the paper. My reaction: it is still a vague proposal, with hand-waving, ill-defined concepts, and not at all axiomatically 'clean'. For example, he never defines «probability.»

Weinberg and others agree with t'Hooft at least in how to pose the problem: derive the probabilities from the deterministic unitary evolution. There have been real physical models done and published with this end in view, and they tend to take a quantum statistical mechanical approach, so there is some point of contact with some of t'Hooft's attitudes. But the valuable work in this way, as I see it, is using Schroedinger's equation to analyse actual physical measuring devices, such as the important work by Balian and two others at

arXiv:cond-mat/0203460 « Curie-Weiss model of the quantum measurement process.»

: See http://arxiv.org/abs/quant-ph/0507017 for a much less realistic toy model, and my axiomatically clean treatment of it's implications for Hilbert's Sixth problem, the axiomatisation of physics, http://arxiv.org/abs/0705.2554 ,

and Prof. t'Hooft is not even attempting to do that. It seems strange to hope to analyse measurement without thinking of the physics of measuring devices, or solve an axiomatic difficulty about probability without giving it a physical definition. I leave aside rival approaches to the problem, such as the decoherence approach, which some physicists are interested in.

Now QM seems to me, and most physicists, correct physically: the measurement problem is merely an axiomatic problem. Most physicists don't believe there is any new physics to be discovered which is relevant to the issue of determinism or the measurement problem, nor do I. (There are important physicists who are an exception, e.g., I suppose, Penrose.) I believe that a careful axiomatic analysis would be interesting, most physicists do not. I do not see one in this paper.

-
no probability no – propaganda Jan 26 '12 at 3:56

This is a very heuristic argument, but here goes. I believe it is wise to search for determinism in physics, simply because although the physical world we measure appears to contain some elements of indeterminism, the ability to measure anything would not be possible without some degree of placing determinism in our logic. If we measure the position of a particle in the past, the very belief that our memory is even accurate depends upon our reliance on a strong macroscopic deterministic set of assumptions. I believe Bohr thought there was a special relationship between the classic (deterministic) and quantum laws that was not trivial, and one played off the other (and used to restrict and fashion problems) with the other. Perhaps, by investigating this relationship further as tHooft is attempting is very important. There is a second reason which may sound a bit more hoaky, but here goes again. I speculate that all "conscious" thoughts are essentially deterministic and finite, and hence any theory of physics must bow to this prinicple, and that what we see with quantum mechnics is the "maximal" possible violation of this in a presumed exterior world (which also doesn't really exist). In essence, the world seems quantum not because it is, but rather because we have not measured it yet and it is undetermined until we do. The knowledge that we hold and see with our eyes and ears is always deterministic however, it is only the uncertain part. We see similar things in various proofs in mathematics and Goedel's paradox. Our realities (or consciounsness) are a set of deterministic laws meant to be born and to die by their own idiosyncratic laws and can exist independent of any physics. What we call "physics" is are those laws or principles which happen to be in common between different conscious entities and measuring devices. To the extent this is undetermined (as it always is within any finite axiomatic system) is exactly the extent to which we see uncertainty in the world. It is similar to trying to prove the parallel postulate with an incomplete set of axioms. Everything you can say about those laws and think about those laws is deterministic, but you can ask some questions which cannot be determined by those laws...that is the "quantum" part. Once the measurement is made, you have a new axiom...and can go on like this until things get end...though mathematical inconsistency, and death. Of course this whole thing seems hopeless philosophical, but actually I do not think so in reality. Finite laws can be simulated and investigated...as they are with automata, game of life etc...so there is real research that can be done in this area. Perhaps we could create consciousness in our computers using a much smaller set of information than we would normally assume to be the case if we held the classical viewpoint that information exists in outside of our ability to measure it. That would be a strange day indeed if we someday found a mouse could create the (its) universe.

-
Possibly interesting, but does this answer "why this view seems to unpopular?" (i.e. the question)? – Kinnisal Mountain Chicken Jul 17 '15 at 13:50
I was going to add some paragraph breaks to this wall of text, but then I realized that this doesn't actually answer the question asked and appears to mostly be nonsense. – Kyle Kanos Jul 17 '15 at 14:08
Certainly the bottom 2/3s really goes off the rails. It does serve to demonstrate that many people really really really want the universe to be fully deterministic (or at least conform to their idea of determinism). – Jon Custer Jul 17 '15 at 14:17

One place to look is the homepage of Antony Valentini now at Clemson University. He claims that Born's probability rule is only an approximation. David Bohm first made this claim. One can show that entanglement can be used for faster-than-light and even retro-causal back-from-the-future delayed choice signaling once the shackles of Born's rule are cast away.

-

Even great physicists sometimes write weak paper, and this is the case. Any attempt to find some classical deterministic theory behind quantum mechanics failed, so far. And that is because there is not any.

-
I am not sure if there is one, but how would you know that there isn't? For sure Bohmian mechanics works, but the question is if there isn't a reasonable one. No one has argued well that it is impossible, so why should 'tHooft not look? – Ron Maimon Dec 21 '11 at 19:39
If there would be something underneath, it would not be Quantum Mechanics, but some different theory, just like Bohmian QM is different theory, but the problem is that this "different theory" does not give anything new. (or it might give some wrong predictions). Quantum mechanics works perfectly and it is free of paradoxes, and in my opinion, all theories to deal with "something underneath quantum mechanics" are motivated by people who do not like Quantum mechanics. – Newman Dec 21 '11 at 20:39
-1 this is not true, see my answer. – BlueRaja - Danny Pflughoeft Dec 21 '11 at 20:57
@newman: Bohm's theory is logically fine, it is just too big and implausible and contrived. t'Hooft is not looking for a theory which reproduces quantum mechanics. He is looking for a theory which is different from QM in a measurable way, ruling out exponentially faster quantum computation for one. Not all people who look for a different theory do not like Quantum Mechanics philosophically. I personally find the quantum philosophy incredible and profound, and it is my first love. But that doesn't make it the final answer, so it is irresponsible not to dig deeper. – Ron Maimon Dec 21 '11 at 23:05
@Newman: quantum mechanics is a non-probability calculus, because it deals with probability amplitudes which only become probabilities during the act of measurement. A probability amplitude is not a probability, because there is no good way to put together answers to the questions "probability of what?" It is much more physical than probability, because of interference effects. But it is not quite as physical as a separate universe, because you can't solve NP complete problems. So it is intermediate between ignorance and many-worlds, how far it goes this way or that, you decide. – Ron Maimon Dec 22 '11 at 19:06

## protected by Qmechanic♦Jul 17 '15 at 13:47

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site.


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If m and n are both positive integers is (m + n^4)^(1/6) an integer?

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If m and n are both positive integers is $$\sqrt[6]{m + n^4}$$ an integer?

(1) $$m = n^4 + n^5$$

(2) $$m = n^4(n^2 - 1)$$

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Re: If m and n are both positive integers is (m + n^4)^(1/6) an integer?  [#permalink]

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21 Mar 2018, 06:34
Bunuel wrote:
If m and n are both positive integers is $$\sqrt[6]{m + n^4}$$ an integer?

(1) $$m = n^4 + n^5$$

(2) $$m = n^4(n^2 - 1)$$

1)
n^4 + n^5 = m

$$\sqrt[6]{m + n^4}$$ = $$\sqrt[6]{n^4 + n^5 + n^4}$$ = $$\sqrt[6]{n^5 + 2n^4}$$ = insufficient

2) $$m = n^4(n^2 - 1)$$ = $$m = n^6 - n^4$$
$$\sqrt[6]{m + n^4}$$ = $$\sqrt[6]{n^6 - n^4 + n^4}$$ = n

(B) imo
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Re: If m and n are both positive integers is (m + n^4)^(1/6) an integer?  [#permalink]

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05 Dec 2018, 10:00
Hatakekakashi wrote:
Bunuel wrote:
If m and n are both positive integers is $$\sqrt[6]{m + n^4}$$ an integer?

(1) $$m = n^4 + n^5$$

(2) $$m = n^4(n^2 - 1)$$

1)
n^4 + n^5 = m

$$\sqrt[6]{m + n^4}$$ = $$\sqrt[6]{n^4 + n^5 + n^4}$$ = $$\sqrt[6]{n^5 + 2n^4}$$ = insufficient

2) $$m = n^4(n^2 - 1)$$ = $$m = n^6 - n^4$$
$$\sqrt[6]{m + n^4}$$ = $$\sqrt[6]{n^6 - n^4 + n^4}$$ = n

(B) imo

Just by looking at statement 1 , can anybody elaborate by taking some values of n, how it is insufficient?

Kudos for a good explanation! Thank you.
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Re: If m and n are both positive integers is (m + n^4)^(1/6) an integer?   [#permalink] 05 Dec 2018, 10:00
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# Summary

There is level 4 evidence (from one case series study; (Karpova et al., 2013), and two observational studies; (Ghasemi et al., 2015, Yasin et al., 2017) that MRI has strong inter-observer correlation, sensitivity, specificity, predictive value, and diagnostic accuracy in detecting and evaluating SCI in individuals.

There is level 5 evidence (from one case series study; (Schroeder et al., 2016) that the incidence of surgical treatment and spinal decompression is not significantly different between individuals based on the presence of signal intensity on an MRI.

There is conflicting level 3 evidence (from one cohort study; (Mabray et al., 2016), one case control study; (Seif et al., 2018), two case series; (Flanders et al., 1996), (Wilson et al., 2012), and six observational studies; (Aarabi et al., 2017, Schaefer et al., 1992, Selden et al., 1999, Song et al., 2016, Takahashi et al., 1993, Zohrabian et al., 2016) and level 5 evidence (from one observational study (Wang et al., 2016) that MRI is effective in determining microstructural measurements and can reliably predict AIS classification, motor score and status and progression of injury in individuals with SCI and controls.

There is level 5 evidence (from one cohort study; (Martinez-Perez et al., 2017) that early MRI has prognostic value in its ability to evaluate ligamentous injury and edema which are predictors of poor neurologic outcome.

There is level 5 evidence (from one observational study; (Miyanji et al., 2007) that MRI can be used to detect hemorrhage, edema, and cord swelling in individuals with SCI. A greater number of positive detections were significantly associated with increased SCI severity and American Spinal Injury Association classification.

There is level 5 evidence (from two observational studies; (Boldin et al., 2006; Shepard & Bracken 1999) that MRI may be used to predict complete SCI given the detection of hemorrhage and edema in individuals with SCI.

There is level 5 evidence (from one observational study; (Dalkilic et al., 2018) that MRI could be used to assess hematoma length and predict AIS classification at baseline.

There is level 5 evidence (from one observational study; (Matsushita et al., 2017) that MRI is effective in detecting spinal microstructures which can be used to effectively predict American Spinal Injury Association motor scores, and Frankel D scores in individuals with SCI.

There is level 5 evidence (Martinez-Perez et al., 2017) that an early MRI may have prognostic value in individuals with SCI without CT evidence of trauma.

There is level 5 evidence (from an observational study (Ouchida et al., 2016) that MRI may not be an effective diagnostic or prognostic indicator of injury in individuals diagnosed with SCI without radiographic abnormality.

There is level 3 evidence (from one case control study; Choe et al., 2017) that there may be no significant relationship between DTI incidences and total International Standard of Neurological Classification for SCI scores either at baseline or follow-up in individuals with SCI.

There is level 3 evidence (from one case control study; (D’Souza et al., 2017) that there may be a significant positive relationship between fractional anisotropy and Frankel grading system scores, but no relationship between mean diffusivity and Frankel grading system scores.

There is level 3 evidence (from seven case control studies; Choe et al., 2017, (D’Souza et al., 2017, Ellingson et al., 2008a, Facon et al., 2005, Kim et al., 2015, Shanmuganathan et al., 2008, Shanmuganathan et al., 2017) that DTI may be an effective tool to measure microstructure abnormalities in individuals with an SCI compared to healthy controls.

There is level 3 evidence (from one case control study; (Shanmuganathan et al., 2017) that axial diffusivity may be positively correlated with the presence of hemorrhagic contusion, International Standard of Neurological Classification for SCI motor scores, and spinal cord independence measure III at both baseline and follow-up.

There is level 3 evidence (from one case control study; (Shanmuganathan et al., 2017) that axial diffusivity, radial diffusivity, and mean diffusivity may be a significant predictor of International Standard of Neurological Classification for SCI motor scores, but not spinal cord independence measure III scores, for both individuals with and without SCI.

There is conflicting level 3 evidence against (from one case control study; (Ellingson et al., 2008a), and one observational study; (Wang et al., 2016) and level 3 evidence for (from one case control study; (Koskinen et al., 2013) that DTI grading may have prognostic value in determining motor and sensory scores in individuals with SCI.


text:
# NEW VERSION OF THE MAGNETIC CURVES ACCORDING TO THE BISHOP FRAME IN 𝔼3

• Sariaydin, Muhammed T. (Department of Mathematics, Selcuk University) ;
• Korpinar, Talat (Department of Mathematics, Mus Alparslan University)
• Accepted : 2018.12.18
• Published : 2019.03.25

#### Abstract

In this paper, it is investigated Lorentz force equations for $N_1$ and $N_2$-magnetic curves in 3-Dimensional Euclidean space. We give the Lorentz force in the Bishop frame in ${\mathbb{E}}^3$. Then, we obtain a new characterization for a magnetic field V. Also, we also give examples for each curve.

#### References

1. Backlund transformation and multi-soliton solutions, NPTEL Course, 112105165/lec38.,
2. Bishop, R. L. (1975). There is more than one way to frame a curve. The American Mathematical Monthly, 82(3), 246-251. https://doi.org/10.1080/00029890.1975.11993807
3. Bozkurt, Z., Gok, I., Yayli, Y., & Ekmekci, F. N. (2014). A new approach for magnetic curves in 3D Riemannian manifolds. Journal of Mathematical Physics, 55(5), 053501. https://doi.org/10.1063/1.4870583
4. Chern, S. S., & Tenenblat, K. (1986). Pseudospherical surfaces and evolution equations. Studies in Applied Mathematics, 74(1), 55-83. https://doi.org/10.1002/sapm198674155
5. Clelland, J. N., & Ivey, T.A. Backlund transformations and darboux integrability for nonlinear wave equations, arXiv:0707.4408v2.
6. Comtet, A. (1987). On the landau levels on the hyperbolic plane. Annals of physics, (Vol. 173, No. 1).
7. Druta-Romaniuc, S. L., & Munteanu, M. I. (2013). Killing magnetic curves in a Minkowski 3-space. Nonlinear Analysis: Real World Applications, 14(1), 383-396. https://doi.org/10.1016/j.nonrwa.2012.07.002
8. Druta-Romaniuc, S. L., & Munteanu, M. I. (2011). Magnetic curves corresponding to Killing magnetic fields in $E^3$. Journal of Mathematical Physics, (Vol. 52, No. 11).
9. Karacan, M. K., & Tuncer, Y. (2012). Backlund transformations according to bishop frame in Euclidean 3-space. In Siauliai Mathematical Seminar (Vol. 7, No. 15).
10. Korpinar, T., & Sariaydn, M.T. (in press). On the Magnetic curves corresponding to the Backlund transformation in the Euclidean 3-space.
11. Korpinar, T. New characterizations for minimizing energy of biharmonic particles in Heisenberg spacetime. International Journal of Theoretical Physics, 2014;53.9:3208-3218. https://doi.org/10.1007/s10773-014-2118-5
12. Korpinar, T. B-tubular surfaces in Lorentzian Heisenberg Group H3. Acta Scientiarum.Technology, 2015;37.1.
13. Korpinar, T. New characterization of b-m2 developable surfaces. Acta Scientiarum. Technology, 2015;37.2.
14. Korpinar, T, Turhan, E. A New Version of Inextensible Flows of Spacelike Curves with Timelike $B_2$ in Minkowski Space-Time $E^4_1$, Dynamical Systems, 2013;21.3:281-290.
15. Korpinar, T. A new version of energy for slant helix with bending energy in the Lie groups. Journal of Science and Arts, 2017;17.4:721-730.
16. Munteanu, M. I. (2013). Magnetic curves in a Euclidean space: one example, several approaches. Publications De I'Institut Mathematique, 94, 141-150. https://doi.org/10.2298/PIM1308141M
17. Munteanu, M. I., & Nistor, A. I. (2012). The classification of Killing magnetic curves in $S^2{\times}R$. Journal of Geometry and Physics, 62(2), 170-182. https://doi.org/10.1016/j.geomphys.2011.10.002
18. Munteanu, M. I. (2013). Magnetic curves in a Euclidean space: one example, several approaches. Publications De I'Institut Mathematique, 94, 141-150. https://doi.org/10.2298/PIM1308141M
19. Munteanu, M. I., & Nistor, A. I. (2017). On some closed magnetic curves on a 3-torus. Mathematical Physics, Analysis and Geometry, (Vol. 20, No. 2).
20. O'neill, B. (1983). Semi-Riemannian geometry with applications to relativity. (Vol. 103). Academic press.
21. Sunada, T. (1993). Magnetic flows on a Riemann surface. In Proc. KAIST Math. Workshop (Vol. 8, No. 93, p. 108).
22. Weiss, J. (1984). On classes of integrable systems and the Painleve property. Journal of Mathematical Physics, 25(1), 13-24. https://doi.org/10.1063/1.526009


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# 2.2: Respiratory Structures and Their Function

Learning Objectives

• Describe select respiratory structures in aquatic and terrestrial animals
• Explain relationships between respiratory structure and function in generalized aquatic and terrestrial animal systems.

## Skin and Gills

Earthworms and amphibians use their skin (integument) as a respiratory organ. A dense network of capillaries lies just below the skin and facilitates gas exchange between the external environment and the circulatory system. The respiratory surface must be kept moist in order for the gases to dissolve and diffuse across cell membranes.

Organisms that live in water need to obtain oxygen from the water. Oxygen dissolves in water but at a lower concentration than in the atmosphere. The atmosphere has roughly 21 percent oxygen. In water, the oxygen concentration is much smaller than that. Fish and many other aquatic organisms have evolved gills to take up the dissolved oxygen from water (Figure 2.4). Gills are thin tissue filaments that are highly branched and folded. When water passes over the gills, the dissolved oxygen in water rapidly diffuses across the gills into the bloodstream. The circulatory system can then carry the oxygenated blood to the other parts of the body. In animals that contain coelomic fluid instead of blood, oxygen diffuses across the gill surfaces into the coelomic fluid. Gills are found in mollusks, annelids, and crustaceans.

The folded surfaces of the gills provide a large surface area to ensure that the fish gets sufficient oxygen. Diffusion is a process in which material travels from regions of high concentration to low concentration until equilibrium is reached. In this case, blood with a low concentration of oxygen molecules circulates through the gills. The concentration of oxygen molecules in water is higher than the concentration of oxygen molecules in gills. As a result, oxygen molecules diffuse from water (high concentration) to blood (low concentration), as shown in Figure 2.5. Similarly, carbon dioxide molecules in the blood diffuse from the blood (high concentration) to water (low concentration).

## Tracheal systems

Insect respiration is independent of its circulatory system; therefore, the blood does not play a direct role in oxygen transport. Insects have a highly specialized type of respiratory system called the tracheal system, which consists of a network of small tubes that carries oxygen to the entire body. The tracheal system is the most direct and efficient respiratory system in active animals. The tubes in the tracheal system are made of a polymeric material called chitin.

Insect bodies have openings, called spiracles along the thorax and abdomen. These openings connect to the tubular network, allowing oxygen to pass into the body (Figure 2.6) and regulating the diffusion of CO2 and water vapor. Air enters and leaves the tracheal system through the spiracles. Some insects can ventilate the tracheal system with body movements.

## Mammalian systems

In mammals, pulmonary ventilation occurs via inhalation (breathing). During inhalation, air enters the body through the nasal cavity located just inside the nose (Figure 2.7). As air passes through the nasal cavity, the air is warmed to body temperature and humidified. The respiratory tract is coated with mucus to seal the tissues from direct contact with air. Mucus is high in water. As air crosses these surfaces of the mucous membranes, it picks up water. These processes help equilibrate the air to the body conditions, reducing any damage that cold, dry air can cause. Particulate matter that is floating in the air is removed in the nasal passages via mucus and cilia. The processes of warming, humidifying, and removing particles are important protective mechanisms that prevent damage to the trachea and lungs. Thus, inhalation serves several purposes in addition to bringing oxygen into the respiratory system.

Exercise $$\PageIndex{1}$$

Which of the following statements about the mammalian respiratory system is false?

1. When we breathe in, air travels from the pharynx to the trachea.
2. The bronchioles branch into bronchi.
3. Alveolar ducts connect to alveolar sacs.
4. Gas exchange between the lung and blood takes place in the alveolus

From the nasal cavity, air passes through the pharynx (throat) and the larynx (voice box), as it makes its way to the trachea (Figure 2.8). The main function of the trachea is to funnel the inhaled air to the lungs and the exhaled air back out of the body. The human trachea is a cylinder about 10 to 12 cm long and 2 cm in diameter that sits in front of the esophagus and extends from the larynx into the chest cavity where it divides into the two primary bronchi at the mid-thorax. It is made of incomplete rings of hyaline cartilage and smooth muscle (Figure 2.8). The trachea is lined with mucus-producing goblet cells and ciliated epithelia. The cilia propel foreign particles trapped in the mucus toward the pharynx. The cartilage provides strength and support to the trachea to keep the passage open. The smooth muscle can contract, decreasing the trachea’s diameter, which causes expired air to rush upwards from the lungs at a great force. The forced exhalation helps to expel mucus when we cough. Smooth muscle can contract or relax, depending on stimuli from the external environment or the body’s nervous system.

## Lungs: bronchi and alveoli

The end of the trachea bifurcates (divides) to the right and left lungs. The lungs are not identical. The right lung is larger and contains three lobes, whereas the smaller left lung contains two lobes (Figure 2.9). The muscular diaphragm, which facilitates breathing, is inferior (below) to the lungs and marks the end of the thoracic cavity.

In the lungs, air is diverted into smaller and smaller passages or bronchi. Air enters the lungs through the two primary (main) bronchi (singular: bronchus). Each bronchus divides into secondary bronchi, then into tertiary bronchi, which in turn divide, creating smaller and smaller diameter bronchioles as they split and spread through the lung. Like the trachea, the bronchi are made of cartilage and smooth muscle. At the bronchioles, the cartilage is replaced with elastic fibers. Bronchi are innervated by nerves of both the parasympathetic and sympathetic nervous systems that control muscle contraction (parasympathetic) or relaxation (sympathetic) in the bronchi and bronchioles, depending on the nervous system’s cues. In humans, bronchioles with a diameter smaller than 0.5 mm are the respiratory bronchioles. They lack cartilage and therefore rely on inhaled air to support their shape. As the passageways decrease in diameter, the relative amount of smooth muscle increases.

The terminal bronchioles subdivide into microscopic branches called respiratory bronchioles. The respiratory bronchioles subdivide into several alveolar ducts. Numerous alveoli and alveolar sacs surround the alveolar ducts. The alveolar sacs resemble bunches of grapes tethered to the end of the bronchioles (Figure 2.10). In the acinar region, the alveolar ducts are attached to the end of each bronchiole. At the end of each duct are approximately 100 alveolar sacs, each containing 20 to 30 alveoli that are 200 to 300 microns in diameter. Gas exchange occurs only in alveoli. Alveoli are made of thin-walled parenchymal cells, typically one-cell thick, that look like tiny bubbles within the sacs. Alveoli are in direct contact with capillaries (one-cell thick) of the circulatory system. Such intimate contact ensures that oxygen will diffuse from alveoli into the blood and be distributed to the cells of the body. In addition, the carbon dioxide that was produced by cells as a waste product will diffuse from the blood into alveoli to be exhaled. The anatomical arrangement of capillaries and alveoli emphasizes the structural and functional relationship of the respiratory and circulatory systems. Because there are so many alveoli (~300 million per lung) within each alveolar sac and so many sacs at the end of each alveolar duct, the lungs have a sponge-like consistency. This organization produces a very large surface area that is available for gas exchange. The surface area of alveoli in the lungs is approximately 75 m2. This large surface area, combined with the thin-walled nature of the alveolar parenchymal cells, allows gases to easily diffuse across the cells.

Exercise $$\PageIndex{2}$$

Which of the following statements about the human respiratory system is false?
a. When we breathe in, air travels from the pharynx to the trachea.
b. The bronchioles branch into bronchi.
c. Alveolar ducts connect to alveolar sacs.
d. Gas exchange between the lungs and blood takes place in the alveolus

This page titled 2.2: Respiratory Structures and Their Function is shared under a CC BY license and was authored, remixed, and/or curated by Sanja Hinić-Frlog.


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# Chapter 19 Full Bayesian Inference of NHPP(Lecture on 03/09/2021)

Consider a NHPP with intensity function $$\lambda(t)$$ and the time that events occuring at $$t_1,\cdots,t_n$$, then the likelihood can be written as $$$L\propto \exp(-\int_0^T\lambda(t)dt)\prod_{i=1}^n\lambda(t_i) \tag{19.1}$$$

To use the density estimation technique, we reparameterize $$\lambda(t)$$ to $$(f(t),\gamma)$$ and for the priors we use $$p(\gamma)\propto \frac{1}{\gamma}$$ and $$f(t,\boldsymbol{\theta})=\sum_{l=1}^SK(t,\boldsymbol{\theta}_l)\omega_l$$, where $$\sum_{l=1}^S\omega_l=1$$ is the sticking breaking process, that is, $$\omega_1=Z_1,\omega_2=Z_2(1-Z_1),\cdots,\omega_S=(1-Z_1)\cdots(1-Z_{S-1})$$, where $$Z_l|\alpha\stackrel{i.i.d.}{\sim}Beta(1,\alpha)$$, for $$l=1,\cdots,S-1$$. $$\boldsymbol{\theta}=(\mu,\tau)$$, we choose the mixing kernel as $$$K(t;\mu,\tau)=\frac{t^{\mu\tau T^{-1}}(T-t)^{\tau(1-\mu\tau^{-1})-1}}{Beta(\mu\tau T^{-1},\tau(1-\mu T^{-1}))T^{\tau-1}} \tag{19.2}$$$ $$k(t;\cdot,\cdot)$$ has support $$(0,T)$$ and $$\mu\in(0,T)$$, $$\tau>0$$.

The parameters we need to do inference are $$(\mu_1,\tau_1),\cdots,(\mu_S,\tau_S),Z_1,\cdots,Z_{S-1},\alpha$$ and $$\gamma$$. The priors we use for those parameters are $$$\begin{split} &\tau_1,\cdots,\tau_S\sim IG(\alpha_{\tau},\beta),\quad \beta\sim \exp(d)\\ &d,\alpha_{\tau}\equiv\text{constant(fixed)}\\ &\mu_1,\cdots,\mu_S\stackrel{i.i.d.}{\sim}Unif(0,T)\\ &p(\gamma)\propto\frac{1}{\gamma}\\ &Z_1,\cdots,Z_{S-1}|\alpha\sim Beta(1,\alpha) \end{split} \tag{19.3}$$$

Denote $$\mathbf{Z}=(Z_1,\cdots,Z_{S-1})^T,\boldsymbol{\tau}=(\tau_1,\cdots,\tau_S)^T$$ and $$\boldsymbol{\mu}=(\mu_1,\cdots,\mu_S)^T$$, then the full posterior is $$$\begin{split} p(\mathbf{Z},\boldsymbol{\tau},\boldsymbol{\mu},&\alpha,\beta,\gamma)\propto\exp(-\gamma)\gamma^n\prod_{i=1}^{n}\{\sum_{l=1}^SK(t_i;\mu_l\tau_l)\omega_l\}p(\gamma)\\ &\times\prod_{l=1}^{S-1}Beta(Z_l|1,\alpha)p(\alpha)\prod_{l=1}^S[IG(\tau_l|\alpha_{\tau},\beta)\times Unif(\mu_l|0,T)]p(\beta) \end{split} \tag{19.4}$$$

The mixture likelihood framework is not accessable to efficient MCMC. However, we can use the data augumentation technique to make MCMC efficient.

Define $$\zeta_i=l$$ if the $$i$$th data comes from the $$l$$th mixture component, $$l=1,\cdots,S,i=1,\cdots,n$$. Thus, $$f(t_i|\zeta_i=l)=K(t_i;\mu_l,\tau_l)$$ and $$p(\zeta_i=l)=\omega_l$$, and marginalize out $$\zeta_i$$, $$f(t_i)=\sum_{l=1}^Sf(t_i|\zeta_i=l)p(\zeta_i=l)=\sum_{l=1}^SK(t_i;\mu_l,\tau_l)\omega_l$$, which is just the original model.

Therefore, the full posterior can be written as $$$\begin{split} p(\mathbf{Z},\boldsymbol{\tau},\boldsymbol{\mu},&\alpha,\beta,\gamma,\boldsymbol{\zeta})\propto\exp(-\gamma)\gamma^n\prod_{i=1}^{n}\prod_{l=1}^S\{\sum_{l=1}^S[K(t_i;\mu_l\tau_l)\omega_l]^{I(\zeta_i=l)}p(\gamma)\\ &\times\prod_{l=1}^{S-1}Beta(Z_l|1,\alpha)p(\alpha)\prod_{l=1}^S[IG(\tau_l|\alpha_{\tau},\beta)\times Unif(\mu_l|0,T)]p(\beta) \end{split} \tag{19.5}$$$

Now, we can use Gibbs sampler to update those parameters.

Firstly, we have $$$\begin{split} p(\gamma|\cdots)&\propto \exp(-\gamma)\gamma^np(\gamma)\\ &\propto \exp(-\gamma)\gamma^{n-1}\quad (as\,p(\gamma)\propto\frac{1}{\gamma}) \end{split} \tag{19.6}$$$ Thus, $$\gamma|\cdots\sim Gamma(n,1)$$.

Next, to update $$\beta$$, notice that $$$\begin{split} p(\beta|\cdots)&\propto\prod_{l=1}^SIG(\tau_l|a_{\tau},\beta)p(\beta)\\ &\propto \exp(-\beta\sum_{l=1}^{S}\frac{1}{\tau_l})\beta^{\alpha_{\tau}}\exp(-\beta d)\\ &\propto \exp(-\beta(d+\sum_{l=1}^{S}\frac{1}{\tau_l}))\beta^{\alpha_{\tau}} \end{split} \tag{19.7}$$$ Therefore, $$\beta|\cdots\sim Gamma(\alpha_{\tau}+1,d+\sum_{l=1}^S\frac{1}{\tau_l})$$.

Then, $$\alpha$$ is updating using a greedy Gibbs sampler. Think of possible values of $$\alpha$$ on a fine gird $$\{\alpha_1^*,\cdots,\alpha_m^*\}$$ then draw $$\alpha$$ from the discrete distribution with probability of drawing $$\alpha_j^*$$ proportional to $$$P(\alpha=\alpha_j^*|\cdots)=\frac{\prod_{l=1}^{S-1}Beta(Z_l|1,\alpha_j^*)}{\sum_{k=1}^m\prod_{l=1}^{S-1}Beta(Z_l|1,\alpha_k^*)} \tag{19.8}$$$ Typically, each $$\alpha_j^*\in(0,1)$$, but you can create a more extensive search by increasing the range of each $$\alpha_j^*$$. In conclusion, $$\alpha|\cdots\sim \text{Discrete Uniform}(\alpha_1^*,\cdots,\alpha_m^*)$$ with probability given by (19.8).

We then update $$\mu_l$$ and $$\tau_l$$, since $$$\begin{split} p(\mu_l,\tau_l|\cdots)&\propto\prod_{i=1}^n[\frac{(\tau-t_i)^{\tau_l(1-\mu_l\tau^{-1})-1}}{Beta(\mu_l\tau_l\tau^{-1},\tau_l(1-\mu_l\tau^{-1}))}]^{I(\zeta_i=l)}\\ &\times IG(\tau_l|\alpha_l,\beta)Unif(\mu_l|0,T) \end{split} \tag{19.9}$$$ The full conditionals are not in closed form. Rather tan using the Metropolis-Hasting algorithm, you need to use Metropolis Adjusted Langevin Algorithm (MALA) or Hamiltonian Monte Carlo (HMC) algorithm, elliptical slice sampling.

Now comes to update $$Z_l$$, we have $$$\begin{split} p(Z_l|\cdots)&\propto\prod_{i=1}^n[\prod_{j\geq l}\omega_j^{I(\zeta_i=j)}](1-Z_l)^{\alpha-1}\\ &\propto\prod_{i=1}^n[\prod_{j\geq l}\{Z_j(1-Z_1)\cdots(1-Z_{j-1})\}^{I(\zeta_i=j)}](1-Z_l)^{\alpha-1} \end{split} \tag{19.10}$$$ From this product, collect all terms of $$Z_l$$ and $$1-Z_l$$, we have $$$p(Z_l|\cdots)\propto Z_l^{n_1}(1-Z_l)^{n_2} \tag{19.11}$$$ Therefore, $$Z_l|\cdots\sim Beta(n_1+1,n_2+1)$$.

Finally, to update $$\zeta_i$$, we have $$$p(\zeta_i=l|\cdots)\propto K(t_i;\mu_l,\tau_l)\omega_l,\quad l=1,\cdots,S \tag{19.12}$$$ Therefore, $$\zeta_i$$ is a discrete distribution taking values $$1,\cdots,S$$ with probability $$\frac{K(t_i;\mu_1,\tau_1)\omega_1}{\sum_{l=1}^SK(t_i;\mu_l,\tau_l)\omega_l},\cdots,\frac{K(t_i;\mu_S,\tau_S)\omega_S}{\sum_{l=1}^SK(t_i;\mu_l,\tau_l)\omega_l}$$ respectively.

Marked Poisson Process In NHPP, the data is given us as $$t_1,\cdots,t_n$$, which are the points where event occurred. In marked Poisson process, we also have $$y_1,\cdots,y_n$$, which are the marks at the points where event occurred. To model data of this kind, we can still apply the idea of NHPP, the only difference is to chnage the intensity function to $$\lambda(s,y)=\phi(s)h(y|s)$$, where $$\phi(s)$$ is the intensity for a non-homogenous Poisson process and $$h(\cdot)$$ is assumed to be a density. To do the inference, we define $$$\begin{split} \gamma&=\int\int\lambda(s,y)dsdy\\ &=\int\int \phi(s)h(y|s)dyds\\ &=\int\phi(s)(\int h(y|s)dy)ds\\ &=\int \phi(s)ds \end{split} \tag{19.13}$$$

Since $$\gamma=\int \phi(s)ds$$, we have $$\lambda(s,y)=\gamma f(s)h(y|s)$$. Then estimating $$\lambda(\cdot)$$ is equivalent to estimate $$\gamma,f$$ and $$h$$ where $$f$$ and $$h$$ are density functions.

Log-Gaussian Cox Process

Assume $$\log \lambda(s)\sim GP(\mu,C_{\nu}(\cdot,\cdot))$$ and estimating from there. We won’t have closed form expression for anything. The likelihood is $$$L\propto \exp(\int_0^T\lambda(t)dt)\prod_{i=1}^n\lambda(t_i) \tag{19.14}$$$ we have to evaluate this integral. $$$\int_0^T\lambda(t)dt=\frac{1}{S}\sum_{s=1}^S\lambda(t_s^*) \tag{19.15}$$$ where $$t_1^8,\cdots,t_S^*$$ are some knot points chosen in the domain.


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ISBN: 9781938168079 2033

## Solution for problem 116 Chapter 7.4

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Problem 116

Find a power series solution for the following differential equations.

The differential equation $$x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0$$ is a Bessel equation of order 1. Use a power series of the form.

Text Transcription:

x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0

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Courtney C. Module 2 Biology 530 abnormal bone growth gigantism and dwarfism is an excess or deficiency of growth hormone during normal growth period acromegaly is when bones become thicker due to GH induced apositional growth excess growth hormone after normal growth period Human growth hormone has an effect on bone length and mass during the years leading to adulthood. Human growth hormone is described by some as the key to slowing the aging process. Before you sign up, get the facts — and understand proven ways to promote healthy aging. Growth hormone levels throughout the life of an individual vary. It is at its highest level during the growth spurt of the teen age years. There is little evidence that taking growth hormone as an adult actually slows the aging process and may do harm. Growth hormone, produced by cells in the anterior pituitary, is a major factor in causing and maintaining the proliferation of cartilage cells in the epiphysis of bones that are growing longer. . During the growth and development of childhood to early adult life, if there is too little of this hormone available, then individuals will be shorter to the extreme case of a dwarf; if too much and over a longer than normal period of time, then individuals will be unusually tall (gigantism). During adult life, after the epiphyses have closed, if excess growth hormone is produced, then bones will grow by the only method that they can a

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##### ISBN: 9781938168079

The answer to “?Find a power series solution for the following differential equations.The differential equation $$x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0$$ is a Bessel equation of order 1. Use a power series of the form.Text Transcription:x^{2} y^{\prime \prime}+x y^{\prime}+\left(x^{2}-1\right) y=0” is broken down into a number of easy to follow steps, and 36 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 50 chapters, and 2640 solutions. Calculus Volume 3 was written by Aimee Notetaker and is associated to the ISBN: 9781938168079. This textbook survival guide was created for the textbook: Calculus Volume 3, edition: 1. The full step-by-step solution to problem: 116 from chapter: 7.4 was answered by Aimee Notetaker, our top Calculus solution expert on 03/18/22, 10:36AM. Since the solution to 116 from 7.4 chapter was answered, more than 205 students have viewed the full step-by-step answer.

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mctq (development version)

• The documentation was updated to add CRAN installation instructions.
• Some minor documentation issues were resolved.

mctq 0.1.0 (2021-11-04)

CRAN release: 2021-11-05

• Initial CRAN release. 🎉
• You can now install mctq with install.packages("mctq").
• We decided to wait for a little while before releasing a 1.0.0 (stable) mctq version. We don’t intend to make any breaking changes, but we think is better to wait and see if the user community don’t have any issues with the features.

mctq 0.0.0.9002 (pre-release)

• mctq is now a peer-reviewed package by @ropensci! 🎉
• The package repository was transferred to the @ropensci organization. All links related to mctq have been changed. Old links have a redirect protocol to point to the new repository and new website.

mctq 0.0.0.9001 (pre-release)

• @jonkeane was added as a reviewer (‘rev’).

Breaking changes

• assign_date() now returns only Interval objects.
• convert() and all convert_*() functions were removed. See a dedicated note about this below.
• ms() was renamed to msl(). See a dedicated note about this below.
• sd() was renamed to sdu(). See a dedicated note about this below.
• shortest_interval() was renamed to shorter_interval().
• shorter_interval() and longer_interval() now returns only Interval objects.
• sum_time() now have different arguments and was divided in two functions: sum_time() (for non-vectorized sums) and vct_sum_time() (for vectorized sums).
• sum_time() now returns only Duration objects.
• To avoid any unknown compatibility issues, all packages on imports will now require the latest version of them at the moment of release.

New features

• cycle_time(), a function to cycle time spans, was introduced.

Minor improvements and fixes

• round_time() is now a S3 generic.
• The user interface has gotten more stylish, thanks to the cli package (now on imports).
• A new vignette was introduced, explaining why the mctq package use Duration instead of Period (objects from the lubridate package) as the default object for time spans.
• Several typos were fixed in the documentation.
• Several functions were optimized.

Note about removing convert()

convert() was created considering the user experience (sleep and chronobiology scientists). Since most of them don’t have much experience with R and that time can have different types of representations (e.g., decimal hours, radian), convert() aim was to help transpose those difficulties, posing as an “universal translator” (🖖).

However, after much thought and consideration, we believe that the convert() feature may be out of the mctq scope. It can maybe be part of another package (a lubritime package perhaps? 😄). Other mctq tools, like shorter_interval() and sum_time(), could also be a part of that package (but are necessary in mctq for the time being). Hence, we decided to remove convert() and to instruct the user to check the lubridate and hms packages for parsing/conversion.

Note about renaming sd() and ms()

That was a tough, but necessary, call. Although we tried to preserve the original author’s naming pattern for the MCTQ functions, the name sd provokes a dangerous name collision with the widely used stats::sd() function (standard deviation) and the name ms provokes a name collision with lubridate::ms() (a function for parsing minutes and seconds components). That’s why we decided to renamed them. sdu() and msl() are the only exceptions, all the other mctq functions maintain a strong naming resemblance with the original author’s naming pattern.

mctq 0.0.0.9000 (pre-release)

• Added a NEWS.md file to track changes to the package.


text:
Select Board & Class

# Board Paper of Class 12-Science 2015 Chemistry (SET 2) - Solutions

General Instructions :
(i) All questions are compulsory.
(ii) Q. no. 1 to 5 are very short answer questions and carry 1 mark each.
(iii) Q. no. 6 to 10 are short answer questions and carry 2 marks each.
(iv) Q. no. 11 to 22 are also short answer questions and carry 3 marks each.
(v) Q. no. 23 is a value based question and carry 4 marks.
(vi) Q. no. 24 to 26 are long answer questions and carry 5 marks each.
(vii) Use log tables if necessary, use of calculators is not allowed.

• Question 1
What is the formula of a compound in which the element Y forms ccp lattice and atoms of X occupy 2/3rd of octahedral voids ? VIEW SOLUTION

• Question 2
Write the IUPAC name of the given compound :
VIEW SOLUTION

• Question 3
Physisorption is reversible while chemisorption is irreversible. Why ? VIEW SOLUTION

• Question 4
Which would undergo SN2 reaction faster in the following pair and why ?
CH3 – CH2 – Br and CH3 – CH2 – I VIEW SOLUTION

• Question 5
Which allotrope of sulphur is thermally stable at room temperature ? VIEW SOLUTION

• Question 6
(a) Following reactions occur at cathode during the electrolysis of aqueous copper(II) chloride solution :

On the basis of their standard reduction electrode potential (E°) values, which reaction is feasible at the cathode and why ?

(b) State Kohlrausch law of independent migration of ions. Write its one application. VIEW SOLUTION

• Question 7
Why do transition elements show variable oxidation states? In 3d series (Sc to Zn), which element shows the maximum number of oxidation states and why? VIEW SOLUTION

• Question 8

(i) Write down the IUPAC name of the following complex :
[Cr(en)3]Cl3

(ii) Write the formula for the following complex :
Potassium trioxalatochromate(III)

VIEW SOLUTION

• Question 9

Name the reagents used in the following reactions:

VIEW SOLUTION

• Question 10
What is meant by negative deviation from Raoult's law? Give an example. What is the sign of ∆mixH for negative deviation?

OR

Define azeotropes. What type of azeotrope is formed by negative deviation from Raoult's law? Give an example. VIEW SOLUTION

• Question 11
(a) Why are alkyl halides insoluble in water?
(b) Why is Butan-1-ol optically inactive but Butan-2-ol is optically active?
(c) Although chlorine is an electron withdrawing group, yet it is ortho-, para- directing in electrophilic aromatic substitution reactions. Why? VIEW SOLUTION

• Question 12
How do you convert the following :

(i) Benzoic acid to Benzaldehyde
(ii) Ethyne to Ethanal
(iii) Acetic acid to Methane

OR

Write the equations involved in the following reactions :

(i) Stephen reaction
(ii) Wolff-Kishner reduction
(iii) Etard reaction VIEW SOLUTION

• Question 13
Calculate the mass of NaCl (molar mass = 58.5 g mol−1) to be dissolved in 37.2 g of water to lower the freezing point by 2°C, assuming that NaCl undergoes complete dissociation. (Kf for water = 1.86 K kg mol−1) VIEW SOLUTION

• Question 14
Write the names and structures of the monomers of the following polymers:
(i) Terylene
(ii) Bakelite
(iii) Buna-S VIEW SOLUTION

• Question 15
(i) Which one of the following is a monosaccharide:
starch, maltose, fructose, cellulose
(ii) What is the difference between acidic amino acids and basic amino acids?
(iii) Write the name of the vitamin whose deficiency causes bleeding of gums. VIEW SOLUTION

• Question 16
(i) Draw the geometrical isomers of complex [Pt(en)2Cl2]2+.
(ii) On the basis of crystal field theory, write the electronic configuration for d4 ion, if ∆0 > P.
(iii) Write the hybridization type and magnetic behaviour of the complex [Ni(CN)4]2−. (Atomic number of Ni = 28) VIEW SOLUTION

• Question 17
(i) Indicate the principle behind the method used for the refining of Nickel.
(ii) What is the role of dilute NaCN in the extraction of gold?
(iii) What is 'copper matte'? VIEW SOLUTION

• Question 18
Calculate the emf of the following cell at 25°C :

Zn | Zn2+ (0.001 M) || H+ (0.01 M) | H2(g) (1 bar) | Pt(s)

VIEW SOLUTION

• Question 19
Predict the products of the following reactions :
(i)

(ii)

(iii) VIEW SOLUTION

• Question 20
An element X (molar mass = 60 g mol−1) has a density of 6.23 g cm−3. Identify the type of cubic unit cell, if the edge length of the unit cell is 4 ✕ 10−8 cm. VIEW SOLUTION

• Question 21
(a) How would you account the following :
(i) Highest fluoride of Mn is MnF4 whereas the highest oxide is Mn2O7.
(ii) Transition metals and their compounds show catalytic properties.

(b) Complete the following equation :
$3{\mathrm{MnO}}_{4}^{2-}+4{\mathrm{H}}^{+}\to$ VIEW SOLUTION

• Question 22

Give reasons for the following observations :

(i) A delta is formed at the meeting point of seawater and river water.

(ii) NH3 gas adsorbs more readily than N2 gas on the surface of the charcoal.

(iii) Powdered substances are more effective adsorbents.

VIEW SOLUTION

• Question 23

Seeing the growing cases of diabetes and depression among children, Mr. Chopra, the principal of one reputed school organized a seminar in which he invited parents and principals. They all resolved this issue by strictly banning the junk food in schools and by introducing healthy snacks and drinks like soup, lassi, milk etc. in school canteens. They also decided to make compulsory half an hour physical activities for the students in the morning assembly daily. After six months, Mr. Chopra conducted the health survey in most of the schools and discovered a tremendous improvement in the health of students.

(i) What are the values (at least two) displayed by Mr. Chopra ?

(iii) Why should antidepressant drugs not be taken without consulting a doctor ?

(iv) Give two examples of artificial sweeteners.

VIEW SOLUTION

• Question 24
(a) Illustrate the following reactions giving suitable example in each case :
(i) Ammonolysis
(ii) Coupling reaction
(iii) Acetylation of amines
(b) Describe Hinsberg method for the identification of primary, secondary and tertiary amines. Also write the chemical equations of the reactions involved.

OR

(a) Write the structures of main products when benzene diazonium chloride reacts with the following reagents :
(i) HBF4/∆
(ii) Cu/HBr

(b) Write the structures of A, B and C in the following reactions :
VIEW SOLUTION

• Question 25
(a) Define the following terms:
(i) Activation energy
(ii) Rate constant

(b) A first order reaction takes 10 minutes for 25% decomposition. Calculate t1/2 for the reaction.

(Given : log 2 = 0.3010, log 3 = 0.4771, log 4 = 0.6021)

OR

(a) For a chemical reaction R → P, the variation in the concentration, ln [R] vs. time (s) plot is given as

(i) Predict the order of the reaction.
(ii) What is the slope of the curve?
(iii) Write the unit of rate constant for this reaction.

(b) Show that the time required for 99% completion is double of the time required for the completion of 90% reaction. VIEW SOLUTION

• Question 26

(a) Account for the following :

(i) Bond angle in ${\mathrm{NH}}_{4}^{+}$ is higher than NH3.

(ii) H2S has lower boiling point than H2O.

(iii) Reducing character decreases from SO2 to TeO2.

(b) Draw the structures of the following :

(i) H4P2O7 (Pyrophosphoric acid)

(ii) XeF2

OR

(a) Draw the structures of the following :

(i) XeF4

(ii) H2S2O7

(b) Account for the following :

(i) Iron on reaction with HCl forms FeCl2 nd not FeCl3.

(ii) HClO4 is a stronger acid than HClO.

(iii) BiH3 is the strongest reducing agent amongst all the hydrides of group 15.

VIEW SOLUTION
More Board Paper Solutions for Class 12 Science Chemistry

• ### Board Paper of Class 12-Science 2004 Chemistry (SET 1) - Solutions

Board Paper Solutions for Other Subjects

### Board Paper Solutions for Class 12 Science Applied Mathematics

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Syllabus


text:
A mathematical fallacy is a series of steps which is seemingly correct but contains a flawed argument to prove an obvious contradiction or absurdity, such as that 1 = 2. Fallacies differ from simple mistakes in that there is an element of concealment in the presentation of the proof, perhaps hidden by the algebraic notation being used; not only do they lead to an absurd result, they do so in a deliberately deceptive way.[1]

## Example

The following appears to prove that 1 = 2.

Let :
(Multiply both sides by )

(Subtract from both sides)

(Divide both sides by
(Since )

(Divide both sides by )

The deception occurs in the fifth step of the “proof”, the division of both sides of the equation by . As the initial premise is that then that is a division by zero, which is an undefined operation; .

## Bibliography

Maxwell, E. A. (2006). Fallacies in Mathematics. Cambridge University Press.


text:
## CryptoDB

#### Publications

Year
Venue
Title
2021
PKC
Private set intersection reveals the intersection of two private sets, but many real-world applications require the parties to learn $\textit{only}$ partial information} about the intersection. In this paper, we introduce a new approach for computing arbitrary functions of the intersection, provided that it is safe to also reveal the cardinality of the intersection. In the most general case, our new protocol provides the participants with secret shares of the intersection, which can be fed into any generic 2PC protocol. Certain computations on the intersection can also be done even more directly and efficiently, avoiding this secret-sharing step. These cases include computing $\textit{only}$ the cardinality of the intersection, or the cardinality-sum'' application proposed in Ion $\textit{et al.}$ (ePrint 2017). Compared to the state-of-the-art protocol for computing on the intersection (Pinkas et al., Eurocrypt 2019), our protocol has about $2.5-3\times$ less communication and has faster running time on slower (50Mbps) networks. Our new techniques can also be used to privately compute the {\em union} of two sets as easily as computing the intersection. Our protocol concretely improves the leading private set union protocol (Kolesnikov et al., Asiacrypt 2020) by a factor of $2-2.5\times$, depending on the network speed. We then show how private set union can be used in a simple way to realize the Private-ID'' functionality suggested by Buddhavarapu et al.~(ePrint 2020). Our protocol is significantly faster than the prior Private-ID protocol, especially on fast networks. All of our protocols are in the two-party setting and are secure against semi-honest adversaries.

#### Coauthors

Gayathri Garimella (1)
Payman Mohassel (1)
Mike Rosulek (1)
Jaspal Singh (1)


text:
# Viewpoint: Classical Simulation of Quantum Systems?

Physics 9, 66
Richard Feynman suggested that it takes a quantum computer to simulate large quantum systems, but a new study shows that a classical computer can work when the system has loss and noise.

The field of quantum computing originated with a question posed by Richard Feynman. He asked whether or not it was feasible to simulate the behavior of quantum systems using a classical computer, suggesting that a quantum computer would be required instead [1]. Saleh Rahimi-Keshari from the University of Queensland, Australia, and colleagues [2] have now demonstrated that a quantum process that was believed to require an exponentially large number of steps to simulate on a classical computer could in fact be simulated in an efficient way if the system in which the process occurs has sufficiently large loss and noise.

The quantum process considered by Rahimi-Keshari et al. is known as boson sampling, in which the probability distribution of photons (bosons) that undergo a linear optical process [3] is measured or sampled. In experiments of this kind [4, 5], $N$ single photons are sent into a large network of beams splitters (half-silvered mirrors) and combined before exiting through $M$ possible output channels. The calculation of the probability distribution for finding the photons in each of the $M$ output channels is equivalent to calculating the permanent of a matrix. The permanent is the same as the more familiar determinant but with all of the minus signs replaced with plus signs. On any classical computer, the number of computational steps required to calculate the permanent of a matrix is believed to increase exponentially with increasing values of $M$ [3], which would make the problem impossible to solve for large values of $M$.

Rahimi-Keshari and colleagues argue that simulating boson-sampling experiments is not as difficult as calculating the permanent of a matrix if the loss and noise in the experiments are sufficiently large. Their theoretical proof is based on the use of quasiprobability distributions [6, 7], such as the Wigner distribution. As a simple example, the Wigner distribution for a state containing two photons in a single channel is shown in Fig. 1. Quasiprobability distributions have many of the same properties as classical probability distributions, but the Wigner distribution can have negative values, which demonstrates the quantum-mechanical nature of the system. The researchers showed that, for sufficiently large loss and noise, the Wigner distribution describing the photons was positive and, therefore, that the results of the experiment could be simulated classically without requiring an exponentially large number of computational steps.

This proof does not overturn Feynman’s suggestion about the need for quantum simulation in general but clarifies when it applies. A boson-sampling system is a simple but representative case of a quantum system that, when large enough, is seemingly unsolvable with a classical computer. Rahimi-Keshari and co-workers’ study is significant in that it provides upper bounds on the experimental conditions in order for that to be the case.

These results are closely related to the fact that the experimental errors in a quantum computer must be sufficiently small in order to perform quantum error correction. The information in a quantum computer is represented by qubits, which can take on various physical forms, including single photons, trapped ions, electronic spins, and superconducting Josephson junctions. Error correction involves identifying and correcting experimental errors that affect the fragile states of the qubits without disturbing their values. Protocols for quantum error correction have a maximum allowed error rate, which is typically calculated using a “top-down” approach that uses quantum information techniques that are independent of the physical nature of the qubits. The methods used by Rahimi-Keshari et al. might allow a “bottom-up” approach in which the physical properties of the qubits themselves can be used to bound the maximum error rate for a quantum computation that cannot be simulated classically.

Experimental tests of nonlocality typically involve mathematical inequalities that bound the predictions of classical field theories [8] or local hidden variable theories. [9]. Quantum mechanics predicts the violation of these inequalities, but this can only be observed if the experimental errors are sufficiently small, which is similar to the situation for boson sampling or quantum computing. To date, these inequalities have applied only to specific experimental setups, such as tests of Bell’s inequality [9]. It may be possible to apply the techniques used in the study by Rahimi-Keshari and co-workers to derive other types of inequalities or more general bounds on the predictions of any classical theory.

Quantum computers are expected to be able to solve certain problems that are not feasible on a classical computer, such as factoring large integers. To the best of my knowledge, there is no rigorous proof that quantum computers can provide an exponential speed-up compared to classical computers [10]. For example, the argument that boson sampling cannot be simulated classically (even in the limit of no experimental errors) is based on the assumption that various computational complexity classes are not equivalent [3]; certain kinds of calculations require many more steps than others using the best-known algorithms, and this is believed to be true for any algorithm. Perhaps Rahimi-Keshari and colleagues’ approach could be used to avoid the need for this assumption. That would be an important step towards answering Feynman’s original question [1] in a more rigorous way.

This research is published in Physical Review X.

## References

1. R. P. Feynman, “Simulating Physics with Computers,” Int. J. Theor. Phys 21, 467 (1982).
2. S. Rahimi-Keshari, T. C. Ralph, and C. M. Caves, “Sufficient Conditions for Efficient Classical Simulation of Quantum Optics,” Phys. Rev. X 6, 021039 (2016).
3. S. Aaronson and A. Arkhipov, “The Computational Complexity of Linear Optics,” in Proceedings of the ACM Symposium on the Theory of Computing, STOC (Association for Computing Machinery, New York, 2011), p. 33[Amazon][WorldCat].
4. J. B. Spring et al., “Boson Sampling on a Photonic Chip,” Science 339, 798 (2013).
5. M. Tillmann, B. Dakic, R. Heilmann, S. Nolte, A. Szameit, and P. Walther, “Experimental Boson Sampling,” Nature Photon. 7, 540 (2013).
6. R. A. Brewster and J. D. Franson, “Generalized Delta Functions and Their Use in Quasi-Probability Distributions,” arXiv:1605.04321.
7. W. P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, 2001)[Amazon][WorldCat].
8. J. D. Franson, “Violations of a Simple Inequality for Classical Fields,” Phys. Rev. Lett. 67, 290 (1991).
9. J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics (Long Island City) 1, 195 (1964).
10. M. J. Bremner, R. Jozsa, and D. J. Shepherd, “Classical Simulation of Commuting Quantum Computations Implies Collapse of the Polynomial Hierarchy,” Proc. R. Soc. London A 467, 459 (2010).

James Franson received his Ph.D. from the California Institute of Technology and was previously at the Johns Hopkins University Applied Physics Laboratory. He is now a professor of physics at the University of Maryland Baltimore County (UMBC). His research interests include nonlocal interferometry, quantum optics, and quantum communications. He is a Fellow of the American Physical Society and the Optical Society of America. In 2008 he was recognized as an Outstanding Referee by the American Physical Society. http://physics.umbc.edu/people/faculty/franson/

## Related Articles

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### Synopsis: A Lens to Focus Spins

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text:
GxE model for binary variable

6 posts / 0 new
Offline
Joined: 04/17/2019 - 08:58
GxE model for binary variable

Hello! I am trying to fit a GxE model. The phenotype is a binary variable, and the moderator is measured on a 6-point scale .

I want to use the code posted in there, but this code is suit for continuous variable and I don't know how to change it to be suit for binary variable. Could you tell me what lines I should change or add?

Because I'm pressed for time, I am sorry to directly ask for solution instead of learning by myself.

Many many thanks!

Offline
Joined: 01/24/2014 - 12:15
very tricky...

What, specifically, are the phenotype and moderator? If you'd rather not say, then are either of the following statements plausible concerning the moderator?:
1. Its covariance with the phenotype is equally due to A, C, and E.
2. All of the variance in the moderator is entirely due to either A, C, or E.

Another question: would you feel more comfortable treating the ordinal moderator as (1) an approximately interval-scale variable, or (2) a categorical variable with unordered categories?

I will say that I know of no OpenMx example script for a binary phenotype and a multicategory ordinal moderator. Indeed, I do not believe I have ever read a paper fitting such a model. In fact, OpenMx may simply not be capable of a completely satisfactory solution to that data-analysis problem....

...Are you familiar with Markov-Chain Monte Carlo Bayesian methods?

Offline
Joined: 07/31/2009 - 14:25
umx::umxGeE

Have a go with umx::umxGeE

Or perhaps umx::umxGxE_window

Offline
Joined: 05/24/2019 - 22:30
GxE model for binary variable

hello
I just notice that you are tying to fit a GxE model with a binary phenotype variable, what is i am going to do.

I have read the previous posts and related literature, but still can not change the code by myself.

I would like to ask if your problem has been solved? Could you share your chaged code with me.

Thank your!

Offline
Joined: 01/24/2014 - 12:15
moderator?

Is your moderator a continuous variable? If so, you might want to look at Julia Kutschke's code here.

Offline
Joined: 05/24/2019 - 22:30
continuous and categorical variables

Thanks so much for your help!
My moderators include both continuous and categorical variables, and the phenotype variable is a binary variable.
I will try the code first. If there are any questions, I'll consult you again.
Thank you again!


text:
Want to ask us a question? Click here
Browse Questions
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0 votes

Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is

$(A)\; 10\pi \qquad (B) \;12\pi \qquad (C)\; 8\pi \qquad (D)\; 11\pi$

Can you answer this question?

1 Answer

0 votes
Toolbox:
• If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
• $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$
Area of the circle $A=\pi r^2$
Differentiating w.r.t $r$ we get,
$\large\frac{dA}{dr}$$=2\pi r \large\frac{dA}{dr}_{(r=6)}$$=2\pi\times 6$
$\Rightarrow 12\pi$
Hence $B$ is the correct option.
answered Jul 8, 2013

0 votes
1 answer

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1 answer

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1 answer

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1 answer

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text:
# New Perspectives 2020

Jul 20 – 21, 2020
US/Central timezone

## SBC’s 10 kg Argon Bubble Chambers for Dark Matter and Reactor CEvNS

Jul 21, 2020, 10:00 AM
15m
Invited

### Speakers

Matthew Bressler (Drexel University) Matthew Bressler (Drexel University)

### Description

The Scintillating Bubble Chamber (SBC) collaboration is in the process of building the first of a set of bubble chambers with 10 kg superheated liquid argon target masses. Superheated dark matter detectors containing freons such as C$_3$F$_8$ are well-studied and can be operated in thermodynamic states which make the detector intrinsically insensitive to electron recoils (ERs), but provide no event-by-event energy information for nuclear recoils (NRs) above the bubble nucleation-energy threshold. Noble liquids, especially argon and xenon, are well-studied scintillators, but are subject to ER backgrounds at low thresholds when searching for WIMPs or neutrinos. A prototype xenon-filled bubble chamber containing a 30 gram target mass has demonstrated that these two technologies can be combined, resulting in a bubble chamber with simultaneous scintillation (calorimetry) and bubble nucleation from neutron-induced NRs, while maintaining intrinsic insensitivity to ER bubble nucleation. We are now constructing our argon-filled R&D detector at Fermilab, where we will take calibration data with spontaneous fission and photoneutron sources, as well as gamma sources, to constrain the sensitivity of such a detector to NR and ER events at energy thresholds of O(100) eV, where the detector is projected to be sensitive to O(1-10) GeV/$c^2$ dark matter and reactor neutrino CE$\nu$NS. The detector can then be moved to a deep-underground site or nuclear reactor to take dark matter or neutrino data, respectively.

Fermilab report number FERMILAB-SLIDES-20-033-PPD

### Primary authors

Matthew Bressler (Drexel University) Matthew Bressler (Drexel University)


text:
zbMATH — the first resource for mathematics

Proof of the gamma conjecture for Fano 3-folds of Picard rank 1. (English. Russian original) Zbl 1369.14054
Izv. Math. 80, No. 1, 24-49 (2016); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 80, No. 1, 27-54 (2016).
Let $$X$$ be a Fano variety, and let $$A_X\in H^*(X)$$ be the principal asymptotic class of the quantum differential equation associated with $$X$$. Let $$\hat{\Gamma}(X)\in H^*(X)$$ be the gamma class of $$X$$. The gamma conjecture is the validity of the equality $$A_X=\hat{\Gamma}_X$$. For a Fano 3-fold of Picard rank $$1$$, the modified gamma class is given by a formula involving the first Chern class of $$X$$, and a rational multiple of $$\zeta(3)$$.
The paper under review verifies the gamma conjecture for each of the 17 deformation classes in Iskovskikh’s classification of smooth Fano 3-folds of Picard rank 1. The conjecture relates the gamma class of a Fano variety to the asymptotics at infinity of the Frobenius solutions of its associated quantum differential equation, for all 17 deformation classes of Fano 3-folds of Picard rank 1.
The gamma conjecture may be regarded as a mirror symmetry for these Fano 3-folds. Mirror symmetry predicts that with each of the 17 families of Fano varieties, there should be associated a family $${\mathcal{E}}$$ of $$K3$$ surfaces over $${\mathbb{P}}^1$$ in such a way that the “quantum differential equation” on the Fano 3-fold (the A-model side) is the Laplace transform of the Picard-Fuchs differential equation satisfied by the periods of $${\mathcal{E}}$$ (the B-model side). The family $${\mathcal{E}}$$ is a family of Kuga-Sato type whose base space is the modular curve $$X^*_0(N)$$ classifying the unordered pairs ($$E, E^{\prime})$$ of $$N$$-isogenous elliptic curves for some $$N$$, and the fiber is the smooth resolution of the quotient of $$E\times E^{\prime}$$ by $$(-1)$$, with Picard number $$19$$. Their Picard-Fuchs differential equations have modular parametrizations.
The proof involves computing the corresponding limits (“Frobenius limits”) for the Picard-Fuchs differential equations of Apéry-type associated by mirror symmetry with the Fano families, and is achieved using two methods. One is combinatorial, and the other uses modular properties of the differential equations.
Further, numerical evidence is presented suggesting that higher Frobenius limits of Apéry-like differential equations may be related to multiple zeta values.

MSC:
 14J45 Fano varieties 14J30 $$3$$-folds 11G35 Varieties over global fields 34A26 Geometric methods in ordinary differential equations
Full Text:


text:
Euler number is related to

This question was previously asked in
Gujarat Engineering Service 2017 Official Paper (Civil Part 2)
View all GPSC Engineering Services Papers >
1. Inertia force and pressure force
2. Inertia force and elastic force
3. Inertia force and viscous force
4. Inertia force and gravity force

Option 1 : Inertia force and pressure force
Free
Gujarat Engineering Service 2019 Official Paper (Civil Part 1)
792
150 Questions 150 Marks 90 Mins

Detailed Solution

Explanation:

Euler’s Number is defined as the square root of the ratio of the inertia force of a flowing fluid to the pressure force. Mathematically

Euler number $$= \sqrt {\frac{{Inertia\;force}}{{Pressure\;force}}}= \frac{V}{{\sqrt {P/\rho } }}$$

Other important dimensionless numbers are described in the table below:

 Reynold’s number $$R_e=\frac{{{inertia force}}}{{{viscous force}}} = \frac{{{\bf{\rho VL}}\;}}{{\bf{\mu }}}$$ Froude Number $${F_r} = \sqrt {\frac{{inertia\;force}}{{gravitation\;force}}} = \frac{V}{{\sqrt {{\bf{Lg}}} }}$$ Mach Number $${M} = \sqrt {\frac{{inertia\;force}}{{Elastic\;force}}} = \frac{V}{{\sqrt {K/\rho } }}=~\frac VC$$ Weber Number $${W_e} = \sqrt {\frac{{inertia\;force}}{{surface\;tension}}} = \frac{V}{{\sqrt {\sigma /\rho L} }}$$


text:
## Live stacking is showing black image

Discussion of using SharpCap for Deep Sky Imaging
pcfree
Posts: 5
Joined: Sun Jun 03, 2018 3:13 pm

### Live stacking is showing black image

I am using an ASI 294C Pro camera on windows 10. I can take individual images fine, but when I start live stacking it just shows a black screen. When I select the "show individual frame" option it shows a good image. All the statistics like number of images stacked and FWHM look like they are working, but I just see the black screen.

It was working before, so I assume I have just incorrectly adjusted a setting. But I cannot figure out which one.

Here is what I am currently seeing.

Thank you for the help.
image.png (190.83 KiB) Viewed 345 times
image (1).png (904.38 KiB) Viewed 345 times

Posts: 1909
Joined: Sat Feb 11, 2017 3:52 pm
Location: Vale of the White Horse, UK
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### Re: Live stacking is showing black image

Hi,

That's a bit odd! Try changing the stacking type from 'sigma clipping' back to default to see if that helps. Also have a look in the 'log' tab of the Live Stacking UI and the main SharpCap log to see if there are any error/warning messages that might help pin down the cause.

cheers,

Robin

pcfree
Posts: 5
Joined: Sun Jun 03, 2018 3:13 pm

### Re: Live stacking is showing black image

I have tried both types of stacking, and it doesn't make a difference. I will check the logs. I appreciate the tip.

I have tried uninstalling/reinstalling, but it keeps the settings between installs. Is there a way to do a complete uninstall so I can start fresh?

Thank you - Paul

Posts: 1909
Joined: Sat Feb 11, 2017 3:52 pm
Location: Vale of the White Horse, UK
Contact:

### Re: Live stacking is showing black image

Hi Paul,

the manual steps for reset are...

Delete all files in

Code: Select all

C:\Users\<your user name>\AppData\Roaming\SharpCap\CaptureProfiles
This will clear all capture profiles for all cameras (including autosave).

Delete the following registry keys using regedit

Code: Select all

HKEY_CURRENT_USER\Software\AstroSharp Limited\SharpCap
HKEY_CURRENT_USER\Software\RWG\SharpCap

You may not have the second one if you have only started using SharpCap from version 3.0 onwards. Be sure you know what you are doing before deleting stuff in regedit as you can do all sorts of horrible stuff to your computer if you get it wrong.

I'm very perplexed by this issue - could it be a flat or dark frame that is causing issues perhaps?

cheers,

Robin

turfpit
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Joined: Mon Feb 13, 2017 8:13 pm
Location: UK
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### Re: Live stacking is showing black image

Paul

Maybe post a camera settings file when the fault is showing?

Dave

pcfree
Posts: 5
Joined: Sun Jun 03, 2018 3:13 pm

### Re: Live stacking is showing black image

Mon Jun 11, 2018 6:29 pm

I'm very perplexed by this issue - could it be a flat or dark frame that is causing issues perhaps?

cheers,

Robin
I am several hours into this problem, and it is frustrating troubleshooting on a clear night after I have already done all my setup, focus, star alignment, and polar alignment. This is almost certainly self inflicted which also makes it embarrassing. I will probably try the uninstall this afternoon. I should have clear skies tonight, and I will report back

I haven't intentionally done any flat or dark frames, but I am not ruling anything out. What is so strange is that this problem doesn't impact single frames, only when I live stack them.

pcfree
Posts: 5
Joined: Sun Jun 03, 2018 3:13 pm

### Re: Live stacking is showing black image

turfpit wrote:
Mon Jun 11, 2018 7:43 pm
Maybe post a camera settings file when the fault is showing?

Dave
Thank you for the tip. Unfortunately, other than the screenshot, I didn't save any of the black screens last night.

I hope a reinstall will solve the problem, but if it doesn't I will definitely save a raw copy of the output.

pcfree
Posts: 5
Joined: Sun Jun 03, 2018 3:13 pm

### Re: Live stacking is showing black image

I reinstalled with the manual deletions and regedit, and now everything works.

Thank you everyone for the help.

Posts: 1909
Joined: Sat Feb 11, 2017 3:52 pm
Location: Vale of the White Horse, UK
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### Re: Live stacking is showing black image

Glad to hear that it is all working now - I guess we will never know what was causing it!

cheers,

Robin

celkins
Posts: 5
Joined: Fri Apr 20, 2018 10:58 pm

### Re: Live stacking is showing black image

I note that the “display stretch histogram” was linear in both images, but the black screen showed no peak, whereas the other did - applying a non-linear stretch may well have helped...

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text:
# Prove that polynomial doesn't have integer zeroes

Let $a \in - 2 + 5\mathbb{Z}$. Show that the polynomial $f\left( x \right) = x\left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)\left( {x - 4} \right) - a$ doesn't have zeroes in $\mathbb{Z}$.

Hint says to prove directly, or by using projection $\mathbb{Z} \to {\mathbb{Z}_5}$ of the polynomial coefficients.

I must admit that I have no idea how to show that, either directly, or via projection. Resulting polynomial is $g\left( x \right) = {x^5} - x - 2$, and it obviously doesn't have zeroes in $\mathbb{Z}$, but I don't know how to, from that fact, justify that $f$ doesn't have any either.

Can this problem be solved within the framework of the field extension theory? Even if not, I'd appreciate a more elaborate hint.

-

Hint: $f(x)+a=x(x-1)(x-2)(x-3)(x-4)\equiv 0(\mod 5)$ for all $x\in\mathbb{Z}$
There is no solution of $$x\left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)\left( {x - 4} \right) + 2 \equiv 0 \pmod 5$$ because: $x\left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)\left( {x - 4} \right) \equiv 0 \pmod 5$ for all $x$,