text:
# Addendum: Low-value approvals and high prices might incentivize ineffective drug development

Nature Reviews Clinical Oncology (2018) https://doi.org/10.1038/s41571-018-0030-2 Published online 15 May 2018

In hindsight, we realize that we could have been more precise when using the terms ‘profit’ and ‘revenue’ in our article ‘Low-value approvals and high prices might incentivize ineffective drug development’. Total revenue is defined as the receipts from sales1. Profit is defined as the excess of the receipts from sales over the spending of a business during any period1. Hence, profit is the total revenue minus the costs of a business, over a given period. Profit calculations include credit transactions and asset revaluations as well as cash transactions and changes in the value of real assets1.

Nevertheless, this imprecision does not affect the validity of our insight. In our analysis we show that the break-even point for revenue and cost of development (under the specific conditions of our ‘thought experiment’) would be US$440 million. The annual revenue from the sale of many approved cancer drugs now routinely exceeds$1 billion, and thus we conclude that “pharmaceutical companies could, hypothetically, turn a profit by testing inert chemical compounds in phase III trials”. In the conditions we define in our thought experiment, companies would therefore receive sufficient revenues to make a profit.

## References

1. 1.

Black, J., Hashimzade, N. & Myles, G.A. A dictionary of economics, 4th edn online. (Oxford, 2013).


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# How do you find the slope of the line perpendicular to a line with slope -1/2?

Mar 10, 2018

See a solution process below:

#### Explanation:

Let's call the slope of a perpendicular line: $\textcolor{b l u e}{{m}_{p}}$

The slope of a line perpendicular to a line with slope $\textcolor{red}{m}$ is the negative inverse, or:

$\textcolor{b l u e}{{m}_{p}} = - \frac{1}{\textcolor{red}{m}}$

Substituting the slope for the line in the problem gives:

$\textcolor{b l u e}{{m}_{p}} = \frac{- 1}{\textcolor{red}{- \frac{1}{2}}} = 2$

format: plain


text:
File: NMFfit-class.R

package info (click to toggle)
r-cran-nmf 0.23.0-1
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It contains a slot with the fitted NMF model (see slot #' \code{fit}) as well as data about the methods and parameters used to compute #' the factorization. #' #' The purpose of this class is to handle in a generic way the results of NMF #' algorithms. Its slot \code{fit} contains the fitted NMF model as an object #' of class \code{\linkS4class{NMF}}. #' #' Other slots contains data about how the factorization has been computed, #' such as the algorithm and seeding method, the computation time, the final #' residuals, etc\dots{} #' #' Class \code{NMFfit} acts as a wrapper class for its slot \code{fit}. It #' inherits from interface class \code{\linkS4class{NMF}} defined for generic #' NMF models. Therefore, all the methods defined by this interface can be #' called directly on objects of class \code{NMFfit}. The calls are simply #' dispatched on slot \code{fit}, i.e. the results are the same as if calling #' the methods directly on slot \code{fit}. #' #' @slot fit An object that inherits from class \code{\linkS4class{NMF}}, and #' contains the fitted NMF model. #' #' NB: class \code{NMF} is a virtual class. The default class for this #' slot is \code{NMFstd}, that implements the standard NMF model. #' #' @slot residuals A \code{numeric} vector that contains the final #' residuals or the residuals track between the target matrix and its NMF #' estimate(s). Default value is \code{numeric()}. #' #' See method \code{\link{residuals}} for details on accessor methods and main #' interface \code{\link{nmf}} for details on how to compute NMF with residuals #' tracking. #' #' @slot method a single \code{character} string that contains the #' name of the algorithm used to fit the model. #' Default value is \code{''}. #' #' @slot seed a single \code{character} string that contains the #' name of the seeding method used to seed the algorithm that fitted the NMF #' model. #' Default value is \code{''}. See \code{\link{nmf}} for more details. #' #' @slot rng an object that contains the RNG settings used for the #' fit. #' Currently the settings are stored as an integer vector, the value of #' \code{\link{.Random.seed}} at the time the object is created. #' It is initialized by the \code{initialized} method. #' See \code{\link{getRNG}} for more details. #' #' @slot distance either a single \code{"character"} string that #' contains the name of the built-in objective function, or a \code{function} #' that measures the residuals between the target matrix and its NMF estimate. #' See \code{\link{objective}} and \code{\link{deviance,NMF-method}}. #' #' @slot parameters a \code{list} that contains the extra parameters #' -- usually specific to the algorithm -- that were used to fit the model. #' #' @slot runtime object of class \code{"proc_time"} that contains #' various measures of the time spent to fit the model. #' See \code{\link[base]{system.time}} #' #' @slot options a \code{list} that contains the options used to #' compute the object. #' #' @slot extra a \code{list} that contains extra miscellaneous data #' for internal usage only. #' For example it can be used to store extra parameters or temporary data, #' without the need to explicitly extend the \code{NMFfit} class. #' Currently built-in algorithms only use this slot to #' store the number of iterations performed to fit the object. #' #' Data that need to be easily accessible by the end-user should rather be set #' using the methods \code{$<-} that sets elements in the \code{list} slot #' \code{misc} -- that is inherited from class \code{\linkS4class{NMF}}. #' #' @slot call stored call to the last \code{nmf} method that generated the #' object. #' #' @export #' @examples #' # run default NMF algorithm on a random matrix #' n <- 50; r <- 3; p <- 20 #' V <- rmatrix(n, p) #' res <- nmf(V, r) #' #' # result class is NMFfit #' class(res) #' isNMFfit(res) #' #' # show result #' res #' #' # compute summary measures #' summary(res, target=V) #' setClass('NMFfit' , representation( fit = 'NMF', # NMF model residuals = 'numeric', # residuals from the target matrix method = 'character', # method used to compute the factorization seed = 'character', # seeding method used to compute the factorization rng = 'ANY', # numerical random seed distance = '.functionSlotNULL', # method used to compute the distance between the target matrix and its NMF estimate parameters = 'list', # method used to compute the factorization runtime = 'proc_time', # running time to perform the NMF options = 'list', # run options extra = 'list' # extra list of results output by the method , call = 'call' # store last call to nmf() ) , prototype = prototype( residuals = numeric(), method = '', seed = '', parameters = list(), extra = list() ) , validity = function(object){ # slot 'objective' must either be a non-empty character string or a function obj <- objective(object) if( is.character(obj) && obj == '') return(paste("Slot 'objective' must either be a non-empty character string or a function definition", sep='')) # everything went fine: return TRUE TRUE } , contains = 'NMF' ) #' The function \code{NMFfit} is a factory method for NMFfit objects, that should #' not need to be called by the user. #' It is used internally by the functions \code{\link{nmf}} and \code{seed} to #' instantiate the starting point of NMF algorithms. #' #' @param fit an NMF model #' @param ... extra argument used to initialise slots in the instantiating #' \code{NMFfit} object. #' @param rng RNG settings specification (typically a suitable value for #' \code{\link{.Random.seed}}). #' #' @rdname NMFfit-class NMFfit <- function(fit=nmfModel(), ..., rng=NULL){ # use current RNG settings if not otherwise provided if( is.null(rng) ) rng <- getRNG() new('NMFfit', fit=fit, ..., rng=rng) } #' Computes and return the estimated target matrix from an NMF model fitted with #' function \code{\link{nmf}}. #' #' It is a shortcut for \code{fitted(fit(object), ...)}, dispatching the call to #' the \code{fitted} method of the actual NMF model. setMethod('fitted', signature(object='NMFfit'), function(object, ...){ fitted(fit(object), ...) } ) #' Returns the basis matrix from an NMF model fitted with #' function \code{\link{nmf}}. #' #' It is a shortcut for \code{.basis(fit(object), ...)}, dispatching the call to #' the \code{.basis} method of the actual NMF model. setMethod('.basis', signature(object='NMFfit'), function(object, ...){ .basis(fit(object), ...) } ) #' Sets the the basis matrix of an NMF model fitted with #' function \code{\link{nmf}}. #' #' It is a shortcut for \code{.basis(fit(object)) <- value}, dispatching the call to #' the \code{.basis<-} method of the actual NMF model. #' It is not meant to be used by the user, except when developing #' NMF algorithms, to update the basis matrix of the seed object before #' returning it. #' setReplaceMethod('.basis', signature(object='NMFfit', value='matrix'), function(object, value){ .basis(fit(object)) <- value object } ) #' Returns the the coefficient matrix from an NMF model fitted with #' function \code{\link{nmf}}. #' #' It is a shortcut for \code{.coef(fit(object), ...)}, dispatching the call to #' the \code{.coef} method of the actual NMF model. setMethod('.coef', signature(object='NMFfit'), function(object, ...){ .coef(fit(object), ...) } ) #' Sets the the coefficient matrix of an NMF model fitted with #' function \code{\link{nmf}}. #' #' It is a shortcut for \code{.coef(fit(object)) <- value}, dispatching the call to #' the \code{.coef<-} method of the actual NMF model. #' It is not meant to be used by the user, except when developing #' NMF algorithms, to update the coefficient matrix in the seed object before #' returning it. #' setReplaceMethod('.coef', signature(object='NMFfit', value='matrix'), function(object, value){ .coef(fit(object)) <- value object } ) #' Method for single NMF fit objects, which returns the indexes of fixed #' basis terms from the fitted model. setMethod('ibterms', 'NMFfit', function(object){ ibterms(fit(object)) } ) #' Method for single NMF fit objects, which returns the indexes of fixed #' coefficient terms from the fitted model. setMethod('icterms', 'NMFfit', function(object){ icterms(fit(object)) } ) #' Returns the offset from the fitted model. setMethod('offset', signature(object='NMFfit'), function(object){ offset(fit(object)) } ) #' Returns the number of iteration performed to fit an NMF model, typically #' with function \code{\link{nmf}}. #' #' Currently this data is stored in slot \code{'extra'}, but this might change #' in the future. setMethod('niter', signature(object='NMFfit'), function(object, ...){ object@extra$iteration } ) #' Sets the number of iteration performed to fit an NMF model. #' #' This function is used internally by the function \code{\link{nmf}}. #' It is not meant to be called by the user, except when developing #' new NMF algorithms implemented as single function, to set the number #' of iterations performed by the algorithm on the seed, before returning it #' (see \code{\linkS4class{NMFStrategyFunction}}). #' setReplaceMethod('niter', signature(object='NMFfit', value='numeric'), function(object, value){ if( (length(value) != 1) || value < 0 ) stop("NMF::niter - invalid value for 'niter': single non-negative value is required.", call.=FALSE) object@extra\$iteration <- value object } ) #' Show method for objects of class \code{NMFfit} setMethod('show', 'NMFfit', function(object) { cat("


text:
# Steven Crothers , against BB

Discussion in 'Pseudoscience' started by river, Nov 30, 2017.

1. ### NotEinsteinValued Senior Member

Messages:
1,233
You are using force, which is a Newtonian concept, instead of the appropriate four-vector from GR. You are using the E-field, instead of the appropriate F-tensor from GR. That's what I meant.

Honestly, I hadn't even seen that type. I read it as "imperviousness".

I was pointing out the apparent conflict between your statement that "Singularities are moot here" and that there is "an infinitely depressed metric" present here.

No real comments here, as I still have to dive deeper into GR.
Just a repeat of my positive criticism: you have to do the maths as well. GR can behave in unintuitive ways, and without the maths backing you up, all you have is a hand-wavy argument. Or at the very least, scientists won't take you very seriously when one has no math to support the claim. That's because quite often when presented with such claims, when the maths is checked, the arguments and conclusion of the thought experiments turn out to be wrong, and scientists (and people in general) don't like wasting their time.

3. ### Q-reeusValued Senior Member

Messages:
2,939
But electrostatic forces as considered in #79, #96 are just proper qE forces and are necessarily modified by depressed metric. See this is where it will pay to go over those scenarios and ask yourself how can it be otherwise. E field is surely the only relevant component of EM F-tensor to consider re RN metric.
It's √(g_tt) (or √(g_00) as used in my earlier notation) that is according to GR infinitely depressed at the assumed 'EH'. I consider GR wrong and one indication of that is a supposed 'singularity' residing at some indefinite future as the termination of a weird 'interior metric' that imo is physically absurd. At best, one might concede an EH as the 'real' asymptotic termination point beyond which any infalling matter never passes in finite exterior time (classical GR scenario - no HR or 'firewalls' etc. stuff here please!).
I understand your pov but trust me or not, the proof stress as source leads to serious inconsistencies is quite solid. I did field a quickie version of it both at PhysicsForums way back, and later here at SF. The savage and unreasonable reactions in both cases left a bad taste in my mouth. At some point I may come back to it with an updated/expanded version, but other things beckon ahead of that.

5. ### Xelasnave.1947Valued Senior Member

Messages:
4,433
Thats a good thing it means you probably hit a nerve.
I remember something said re defamation....the lady would not mind people saying she had a red nose unless she did indeed have a red nose.
Alec

Q-reeus likes this.

7. ### NotEinsteinValued Senior Member

Messages:
1,233
Which are modeled fundamentally differently in GR; that's my point. There are a couple of surprising features of EM in GR that aren't obvious when you don't use the GR formulation. And because you aren't using GR formulation, it's not obvious that all these surprising features have been taken into account (because you have to apply them manually, instead of them happening automatically through the maths).

And it will also pay to use the proper GR terminology and calculations to prove that your description of the scenario is indeed what GR predicts.

I agree; we both came to that conclusion when discussing the $F^\text{tr}$ term.

Then I don't understand what you mean by "infinitely depressed"?

It's a known limitation of GR: a quantum description of gravity is needed. In other words: GR breaks down before you get to the singularity. Saying GR is wrong because it gives absurd answers in a domain where it is not applicable is the same as saying Newtonian gravity is absurd because it doesn't model the precession of Mercury accurately.

The event horizon isn't a physical barrier: particles can travel through the event horizon just fine. This is more obvious when using Kruskal–Szekeres coordinates.

If you have proof (that I can understand), I wouldn't have to trust you. Convincing scientists that GR is wrong is going to require proof that they can understand, that's written in their language.

That can be easily explained: there are a lot of cranks out there that believe GR is wrong, but can't form a coherent argument as to why. Without any evidence in a language that GR experts can easily understand (i.e. GR terminology), it will be quite difficult to convince GR experts that one's claim is even worth looking into. Many scientists are sick and tired of such cranks, and their claims have so far amounted to nothing, so when somebody comes along and isn't able to set themselves apart from those cranks, that person will get treated as just another one.
Is that fair? No. But it is (unfortunately) common practice, is quite efficient for the scientists, and better for the general sanity of the scientists.

8. ### przyksquishyValued Senior Member

Messages:
3,171
What do you think needs to be reconciled? Assuming the eternal black hole, either there's an electromagnetic field extending both inside and outside the event horizon (and by definition, "charge" somewhere, if the electromagnetic field is divergent) since $t = -\infty$ or there isn't. This doesn't require anything inside the event horizon to be causally influencing anything outside of it.

No. The electromagnetic field outside the event horizon can only depend on there being an electromagnetic field and/or charges/currents (if any) at earlier times outside of the event horizon.

I don't see any issue with this. I don't see it as being all that different from, e.g., plane wave solutions to the vacuum Maxwell equations. These are solutions that describe plane waves of infinite extent, propagating through space, that have been there since $t = -\infty$ and continue to exist through to $t = +\infty$, with no causal link to any material "charge". This is admittedly not the most realistic situation, but it is perfectly legal as far as electromagnetism is concerned and it shows that one should maybe be careful about thinking too simplistically of electromagnetic fields as always being "produced" by charges or the like.

9. ### NotEinsteinValued Senior Member

Messages:
1,233
Under those conditions, there cannot be any change in the charge of the eternal black hole (i.e. no charge is allowed to fall under the event horizon). I suppose that's an option, but then the RN-metric can only describe these eternal black holes, as a black hole growing by "eating" charged matter is fundamental not the same as the black hole always having that charge.

(I assume you also don't believe in eternal black holes, then?)

I don't see a problem either; I mostly see my own ignorance about the topic, triggered by Q-reeus' scenario.

Sure, but one also must realize that the described scenario therefore doesn't exist in reality, and that it (at best) can be an approximation of reality. Then the question becomes: is the approximation justified? Does the process of constructing a charge black hole by throwing a lot of (partially) charged matter together result in something that can reasonably accurately be modeled by the RN-metric?

10. ### przyksquishyValued Senior Member

Messages:
3,171
Why? Like the Schwarzschild metric, the RN solution is static in the Schwarzschild-type coordinate system it is usually described in, so if the spacetime geometry and electromagnetic field somehow comes to coincide with the RN solution outside some radial coordinate $r$ (e.g. left behind by some shrinking charged sphere) then it should stay that way unless something else comes along to change it.

The Schwarzschild metric describes the gravitational field outside any spherically symmetric mass, not just the eternal black hole. I would expect something similar is true of the RN solution. This getting beyond what I actually remember from studying a couple of GR courses nearly ten years ago, though, so I can't say for certain that this is how it works, but I think I remember something about it working this way.

I don't see any problem with them theoretically, at least as far as classical GR is concerned. Of course, reality is different and "eternal black hole" doesn't play so well with "universe is only ~13 billion years old" and "Hawking says they should eventually evaporate".

11. ### NotEinsteinValued Senior Member

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1,233
Sure, but wouldn't there in practice only be a few black holes that form in such a clean way? Those other black holes would then not (necessarily) be properly described by the RN metric.

Honestly, I would expect the same; the power of the Schwarzschild metric in describing situations that aren't exactly spherical symmetric or static suggests that the RN metric might by equally powerful.

My point exactly.

(I really need to stop slacking off, and dive back into my GR books.

This is way too interesting not to know the details about it!)

Messages:
21,703
Now why would your amateurish attempt at goading me make me indignant qreeus? After all by your own admissions you are an amateur....
excerpts:
Not too long ago was banned from another forum - PhysicsForum.com to be precise. In my judgement that ban was both illegal re internal rules and done out of principally one person's spite.
"Have no formal education in physics but like lots of folks it is a kind of passion and am interested in both learning new things from experts, but also wanting to contribute possibly new angles that may get folks thinking. That would be particularly in the arena of GR but maybe also classical physics. Only claim to fame is to think clearly".
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

So, Stephen Crothers is a gardener...what is your claim to fame?
But anyway Your poster boy Yilmaz is not considered within GR because he has shown to be in error...no conspiracy or any other crap needed...
And of course you in this thread have been rather misleading at best with relation to your claims "gravity does not make gravity. Gravity/spacetime is nonlinear and as such and as was shown to you many moons ago by at least two professionals, you were wrong in your assumption. You remember don't you? Of course you do! In the meantime the professional opinion is as follows....
http://www.einstein-online.info/spotlights/gravity_of_gravity.html
and....
https://www.researchgate.net/post/W...e_comparatively_stronger_electric_force_limit
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I believe the obvious question that now needs to be asked is why you are in conflict with GR. An agenda of sorts? In relation to your ID support?
Hi NotEinstein...
The following may explain further as to what you are dealing with......
Simple geometric proof GR's GW's are impossible
A simple proof Einstein got it wrong with GR

Free-fall to singularity is BS (or - don't just trust 'authorities')

:::::::::::::::::::::::::::::::::::
The above links explain where qreeus is coming from, and the obvious agenda that in my opinion he has: Not to mention the rather provocative goading style of the headlines.

Let me also say that this post will probably earn me an infraction when exchemist reports it. So be it. My time is spent elsewhere now on a forum where science is the prime consideration and the cranks, god botherers, IDers, and others of that ilk are required to support their generally unsupported nonsense and claims, or they are dispatched within a week or so to the trash bin.
Just thought I would pop in so to speak and explain the errors of qreeus.
In essence, the only good thing this thread has going for it, is that at least one reasonably bright mod has seen the need to shift it to speudoscience

Last edited: Dec 8, 2017

Messages:
21,703
Ooops sorry, I'm back again! Just forgot to clear up one little point.
A BH can have three properties, mass, spin and charge.
Obviously a charged BH would be quickly negated by attracting matter of opposite charge and would not exist for too long.
A Reissner-Nordström black hole is a black hole with mass and electric charge, but no spin. The geometry was discovered independently by Reissner (1916)1 and Nordström (1918)2.
Real black holes probably spin, but probably have almost no electric charge, because our Universe appears to be electrically neutral, and a charged black hole would quickly neutralize by attracting charge of the opposite sign. Nevertheless, the internal geometry of an electrically charged black hole resembles mathematically that of a rotating black hole. For this reason the behavior inside a charged black hole is often taken as a surrogate for that inside a rotating black hole.

The big difference between a charged (Reissner-Nordström) and an uncharged (Schwarzschild) black hole is that the mathematical solution to the charged black hole has, inside its horizon, a one-way wormhole that connects to a white hole that propels you to another space and time. Sadly, the wormhole is violently unstable, and would not occur in reality. Click on Waterfall to learn more about why the charged black hole has a wormhole. Click on Realistic to see what happens in reality, and to learn more about the mass inflation instability that in reality prevents any wormhole from forming.
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14. ### Q-reeusValued Senior Member

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2,939
The 'surprising features' are precisely what imo #79, #96, #98 uncover as 'crazy'. If you do nothing but brush up on GR and it's formal inclusion of EM a per RN you will never see the issues. It absolutely requires stepping out of that cycle and applying some kind of independent consistency checks.
Not obvious? Infinite redshift occurs, not at the supposed 'singularity' as you had thought, but all the way out at the EH where, at perfectly finite r and perfectly finite Newtonian potential, √(g_tt) -> 0.
A pathology of GR.
No, I'm saying it's fundamentally flawed leading to absurdities, for among other things, the reason given in appendix A here: https://arxiv.org/abs/1606.01417
I'm well aware of the proper time of free-faller stock argument, and how that manifests in e.g. KS coordinate system. And it's BS. Infinite exterior time has passed just getting to the EH. Something conveniently ignored by defenders of GR.
Right. Right....As stated before I well understand that pov. If you wish to PM me I will furnish links to the two instances I mentioned. You can then feel free to further PM concerning any 'fatal flaws' you think may be present. There are many other ways to show the issues with stress as source, but just the one raised in those threads is a clincher all by itself. Your choice. I won't regurgitate it all here.

15. ### Q-reeusValued Senior Member

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2,939
Piss off blowfly. I stand by all you dredged up and regurgitated there with endless malice as motivator. As one living in a glass house throwing stones, it would pay to just keep quiet. Or you would like some tit-for-tat? Like how many times I have exposed your ignorance of plain old special relativity? I went years contributing at PhysicsForums before things came to a head. You lasted just 11 days - having contributed nothing of any use. Unless you think posting a link to the Mule Skinner song was a great addition there.

16. ### Xelasnave.1947Valued Senior Member

Messages:
4,433
It is comforting to know you are OK and I wish you all the best for the holiday season.
Re Crothers.
Have you watched Crothers utube presentation? On GR his comments on CBR is interesting and I wondered I you had any comments on his take on the subject particularly upon the signal to noise ratio and the difficulty, or as he suggests, the impossibility of presenting reliable data in regions of the Milly Way central region.
Even though he is a Queenslander he may be on the money.
I suppose I wonder how the map could be considered valid in that region and why they even sought to include that region given the signal to noise ratio could only mean, certainly in my view, it could be considered only an educated guess really.
I would be interested in your comments as gardener or not he seems to also rely upon an expert in these matter and frankly having to work out signal to noise ratios in doing astro photography I think his view must be taken seriously, even though he is a gardener from Queensland, he seems to make a valid and supportable claim.
Alex

17. ### Xelasnave.1947Valued Senior Member

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4,433
May I offer my counsel here not to respond to folk who display bitterness for to do so somewhat lowers the level of discussion.

Perhaps leave it to readers to judge who is capable of discussing the issues and who is not.

I would not like to see the discussion here, which has been most interesting, degenerate into name calling as there is absolutely no value to be gained.

And there is no point in making the obvious observation that you were provoked I and others can see that.

So I appeal to you to continue and use my advice as insect repellant.
Alex

18. ### Q-reeusValued Senior Member

Messages:
2,939
Mediation has it's place but so does putting someone in their place where and when needed. Peace.

19. ### Xelasnave.1947Valued Senior Member

Messages:
4,433
Trading insults with paddoboy is like wrestling a pig in the mud but after some time you must be aware that he loves it.
Peace to you as well.
Alex

Q-reeus likes this.
20. ### NotEinsteinValued Senior Member

Messages:
1,233
If you haven't done the math, how can you be sure you've included all surprising features?

Perhaps, but at least I can be certain your described scenario operates in GR in the way you claim it does. Without that, there is very little sense in discussing it in detail.

If you mean an internal consistency check; that's being done all the time, and you've just said those check out one sentence earlier. You haven't given any experimental data, so it's not a consistency check against reality either. I can only assume you are talking about a consistency check against our notions about how things should behave. But that's dangerous, because GR (and QM) often violate those notions, but with reality backing those up.

Ah, OK. I just have never heard of that term, so I (falsely) assumed it would be at a point where the metric did something weird; i.e. the singularity. I still don't know what the term means, but OK, it's at the event horizon.

How is that not a result of using a weird metric? At best one can say the used metric is bogus; it doesn't (necessarily) invalidate all of GR.

Yes, but not to the particle falling in, and that's the point. Obviously, there being only one reality, there's no physical barrier at the location of the event horizon. Particles can pass it just fine. It's just that an observer infinitely far away will never get to see that happening, but it obviously does happen.

At this moment, I'm not interested in a PM-discussion.

21. ### Q-reeusValued Senior Member

Messages:
2,939
The essential relevant maths is right there in the given scenarios. If you insist on some exact solution using EFE's then good luck hiring supercomputer time.
Well gravitational redshift aka time dilation is experimentally confirmed. The rest then follows logically. The issue is internal self-consistency - or lack thereof.
So just point to where you think I have misapplied things in given scenarios.
No idea what you mean there. That set out in that Appendix A nails the problem with standard GR formulation of time dilation - a truncated approximation. Hence Schwarzschild metric also.
You still miss the key issue. In coordinate aka exterior time, an infaller never quite gets to the EH. GR gate-keepers claim that's just an 'optical illusion' but that is simply not true. The rest of the universe has become infinitely old thus will have disappeared. Hence a fantasy to claim that proper time for infall not only to horizon but then somehow on to 'singularity' is physically sensible.
Fine.

22. ### RajeshTrivediValued Senior Member

Messages:
1,525
Gravity is left out (out of EH) as fossil field, Spin is left out as angular momentum in ergosphere and charge is left out as eletrostatic field outside EH. This mathematical jugglery removes the obvious problem associated with infinite time dilation at or inside EH. You have to appreciate that Einstein never offered BH or such solutions around BH based on GR. It was the overenthusiastic crowd of mathematically oriented physicists who wanted to get into the GR / BH bandwagon. Now as somewhere you have rightly mentioned that the GR has become a 800 pounds gorilla, I would say after nobel on GW, it has doubled its crushing power. I ask a very simple question: the EHs (even for charged or rotating or both) will change its spatial position/size based on mass reduction (HR) or based on mass increase (accretion), the real impact of change in EH happens only after mass has entered the EH, then how does angular momentum or electrostatic filed reorient or realign due to change in EH?

23. ### NotEinsteinValued Senior Member

Messages:
1,233
No, it isn't. That math isn't expressed in GR terminology.

I don't see how that's relevant? Many of the GR derivations can be done on paper; see for example that PDF you linked to.

Yes indeed, so you agree that GR is valid? (Seeing that that's the only theory mentioned in this thread that can explain it.)

I know that SR is proven to be internally consistent; not sure about GR. So no comment for now.

Well, I'll have to dive into GR for details, but my guess would be that, since (almost) nothing is expressed in GR maths, it's some surprising feature of GR somewhere.

The choice of metric is critical in GR. For example, the Schwarzschild metric has a singularity (which is physically weird), but the Minkowski metric has no such problems. Many of the "absurdities" in GR come from the choice of metric, not from GR itself.

I know of no "GR gate-keepers" claiming this, and I agree with you that anybody who really claims this is not worth their salt in GR.

Except for the infaller. Are you claiming the perspective of the infaller somehow becomes wrong as it crosses the event horizon?


text:
# Error in \title : Overleaf

I am using Overleaf and am receiving the following error when I try setting the title to my file.

Illegal parameter number in definition of \@title. <to be read again> 1

How should I fix this ?

• Welcome to TeX.SX. Please provide a MWE of your problem. Without one it is nearly impossible to help you. – Benjamin Jan 31 '16 at 2:16
• Correct the definition of \@title so that it no longer uses an illegal parameter number? Usually this means you have #1 when you want ##1 or ##1 when you want ###1 or ##1 when your want #1 or ###1 when you want ##1 or ... Or else it means that you've tried to use something like #1 in a macro which was not defined to absorb any arguments at all. However, that is less likely in this case as it is a standard macro. If you don't think you've redefined it at all, do you have a literal hash symbol in \title{} or something? – cfr Jan 31 '16 at 3:01
• @cfr : Yes, I have a hash symbol in my title : \title{#1} – stark Jan 31 '16 at 3:46
• That's the problem, then. Is your paper really titled #1? No offence intended: I'm sure there's an audience out there for that kind of thing. Just not my cup of tea, probably. – cfr Jan 31 '16 at 4:00
• @cfr : No, my paper is not just titled #1, there was some text before it in the title but I didn't post it here since I thought the text wasn't relevant to the error. – stark Jan 31 '16 at 4:01

A # is a special character. TeX assumes you mean to use it to refer to an argument parameter. If you wish to literally typeset a hash symbol, you must escape the character or otherwise request it indirectly.

For example:

\documentclass{article}
\title{A \# to end all \# s}
\author{S. O. M. E. Body}
\begin{document}
\maketitle
\end{document}

• Perfect, that fixed it. I was not aware of # being a special character. Thanks. – stark Jan 31 '16 at 3:59


text:
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# Quadratic Diophantine Equations - Solve by Completing the Square

Cite as: Quadratic Diophantine Equations - Solve by Completing the Square. Brilliant.org. Retrieved from https://brilliant.org/wiki/quadratic-diophantine-equations-solve-by/
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text:
# Biblio

Found 814 results

Filters: Keyword is privacy  [Clear All Filters]
2019-12-11
.  2019.  2019 IEEE Symposium on Security and Privacy (SP). :157–174.
We present Ouroboros Crypsinous, the first formally analyzed privacy-preserving proof-of-stake blockchain protocol. To model its security we give a thorough treatment of private ledgers in the (G)UC setting that might be of independent interest. To prove our protocol secure against adaptive attacks, we introduce a new coin evolution technique relying on SNARKs and key-private forward secure encryption. The latter primitive-and the associated construction-can be of independent interest. We stress that existing approaches to private blockchain, such as the proof-of-work-based Zerocash are analyzed only against static corruptions.
2019-12-10
.  2018.  2018 Fourth International Conference on Advances in Electrical, Electronics, Information, Communication and Bio-Informatics (AEEICB). :1-5.

A 2D-Compressive Sensing and hyper-chaos based image compression-encryption algorithm is proposed. The 2D image is compressively sampled and encrypted using two measurement matrices. A chaos based measurement matrix construction is employed. The construction of the measurement matrix is controlled by the initial and control parameters of the chaotic system, which are used as the secret key for encryption. The linear measurements of the sparse coefficients of the image are then subjected to a hyper-chaos based diffusion which results in the cipher image. Numerical simulation and security analysis are performed to verify the validity and reliability of the proposed algorithm.

.  2018.  2018 International Conference on Network Infrastructure and Digital Content (IC-NIDC). :389-393.

Compressed sensing (CS) integrates sampling and compression into a single step to reduce the processed data amount. However, the CS reconstruction generally suffers from high complexity. To solve this problem, compressive signal processing (CSP) is recently proposed to implement some signal processing tasks directly in the compressive domain without reconstruction. Among various CSP techniques, compressive detection achieves the signal detection based on the CS measurements. This paper investigates the compressive detection problem of random signals when the measurements are corrupted. Different from the current studies that only consider the dense noise, our study considers both the dense noise and sparse error. The theoretical performance is derived, and simulations are provided to verify the derived theoretical results.

.  2019.  2019 International Conference on Sustainable Engineering and Creative Computing (ICSECC). :223-227.

The security and confidentiality of the data can be guaranteed by using a technique called watermarking. In this study, compressive sampling is designed and analyzed on video watermarking. Before the watermark compression process was carried out, the watermark was encoding the Bose Chaudhuri Hocquenghem Code (BCH Code). After that, the watermark is processed using the Discrete Sine Transform (DST) and Discrete Wavelet Transform (DWT). The watermark insertion process to the video host using the Stationary Wavelet Transform (SWT), and Singular Value Decomposition (SVD) methods. The results of our system are obtained with the PSNR 47.269 dB, MSE 1.712, and BER 0.080. The system is resistant to Gaussian Blur and rescaling noise attacks.

.  2018.  Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining. :1059-1068.

Click-through rate prediction is an essential task in industrial applications, such as online advertising. Recently deep learning based models have been proposed, which follow a similar Embedding&MLP paradigm. In these methods large scale sparse input features are first mapped into low dimensional embedding vectors, and then transformed into fixed-length vectors in a group-wise manner, finally concatenated together to fed into a multilayer perceptron (MLP) to learn the nonlinear relations among features. In this way, user features are compressed into a fixed-length representation vector, in regardless of what candidate ads are. The use of fixed-length vector will be a bottleneck, which brings difficulty for Embedding&MLP methods to capture user's diverse interests effectively from rich historical behaviors. In this paper, we propose a novel model: Deep Interest Network (DIN) which tackles this challenge by designing a local activation unit to adaptively learn the representation of user interests from historical behaviors with respect to a certain ad. This representation vector varies over different ads, improving the expressive ability of model greatly. Besides, we develop two techniques: mini-batch aware regularization and data adaptive activation function which can help training industrial deep networks with hundreds of millions of parameters. Experiments on two public datasets as well as an Alibaba real production dataset with over 2 billion samples demonstrate the effectiveness of proposed approaches, which achieve superior performance compared with state-of-the-art methods. DIN now has been successfully deployed in the online display advertising system in Alibaba, serving the main traffic.

.  2018.  Proceedings of the 2018 International Conference on Management of Data. :757-772.

We introduce a new sub-linear space sketch—the Weight-Median Sketch—for learning compressed linear classifiers over data streams while supporting the efficient recovery of large-magnitude weights in the model. This enables memory-limited execution of several statistical analyses over streams, including online feature selection, streaming data explanation, relative deltoid detection, and streaming estimation of pointwise mutual information. Unlike related sketches that capture the most frequently-occurring features (or items) in a data stream, the Weight-Median Sketch captures the features that are most discriminative of one stream (or class) compared to another. The Weight-Median Sketch adopts the core data structure used in the Count-Sketch, but, instead of sketching counts, it captures sketched gradient updates to the model parameters. We provide a theoretical analysis that establishes recovery guarantees for batch and online learning, and demonstrate empirical improvements in memory-accuracy trade-offs over alternative memory-budgeted methods, including count-based sketches and feature hashing.

.  2018.  Proceedings of the 2Nd International Conference on Digital Signal Processing. :17-21.

The difference of sensor devices and the camera position offset will lead the geometric differences of the matching images. The traditional SIFT image matching algorithm has a large number of incorrect matching point pairs and the matching accuracy is low during the process of image matching. In order to solve this problem, a SIFT image matching based on Maximum Likelihood Estimation Sample Consensus (MLESAC) algorithm is proposed. Compared with the traditional SIFT feature matching algorithm, SURF feature matching algorithm and RANSAC feature matching algorithm, the proposed algorithm can effectively remove the false matching feature point pairs during the image matching process. Experimental results show that the proposed algorithm has higher matching accuracy and faster matching efficiency.

.  2018.  Proceedings of the 3rd International Conference on Intelligent Information Processing. :46-51.

With the increase of mobile equipment and transmission data, Common Public Radio Interface (CPRI) between Building Base band Unit (BBU) and Remote Radio Unit (RRU) suffers amounts of increasing transmission data. It is essential to compress the data in CPRI if more data should be transferred without congestion under the premise of restriction of fiber consumption. A data compression scheme based on Discrete Sine Transform (DST) and Lloyd-Max quantization is proposed in distributed Base Station (BS) architecture. The time-domain samples are transformed by DST according to the characteristics of Orthogonal Frequency Division Multiplexing (OFDM) baseband signals, and then the coefficients after transformation are quantified by the Lloyd-Max quantizer. The simulation results show that the proposed scheme can work at various Compression Ratios (CRs) while the values of Error Vector Magnitude (EVM) are better than the limits in 3GPP.

.  2018.  Proceedings of the 2Nd International Conference on Digital Signal Processing. :80-83.

Compressed sensing (CS) can recover a signal that is sparse in certain representation and sample at the rate far below the Nyquist rate. But limited to the accuracy of atomic matching of traditional reconstruction algorithm, CS is difficult to reconstruct the initial signal with high resolution. Meanwhile, scholar found that trained neural network have a strong ability in settling such inverse problems. Thus, we propose a Super-Resolution Convolutional Neural Network (SRCNN) that consists of three convolutional layers. Every layer has a fixed number of kernels and has their own specific function. The process is implemented using classical compressed sensing algorithm to process the input image, afterwards, the output images are coded via SRCNN. We achieve higher resolution image by using the SRCNN algorithm proposed. The simulation results show that the proposed method helps improve PSNR value and promote visual effect.

.  2018.  Proceedings of the Thirteenth ACM International Conference on Underwater Networks & Systems. :5:1-5:8.

This paper presents a novel Kriged Compressive Sensing (KCS) approach for the reconstruction of underwater acoustic intensity fields sampled by multiple gliders following sawtooth sampling patterns. Blank areas in between the sampling trajectories may cause unsatisfying reconstruction results. The KCS method leverages spatial statistical correlation properties of the acoustic intensity field being sampled to improve the compressive reconstruction process. Virtual data samples generated from a kriging method are inserted into the blank areas. We show that by using the virtual samples along with real samples, the acoustic intensity field can be reconstructed with higher accuracy when coherent spatial patterns exist. Corresponding algorithms are developed for both unweighted and weighted KCS methods. By distinguishing the virtual samples from real samples through weighting, the reconstruction results can be further improved. Simulation results show that both algorithms can improve the reconstruction results according to the PSNR and SSIM metrics. The methods are applied to process the ocean ambient noise data collected by the Sea-Wing acoustic gliders in the South China Sea.

.  2018.  Proceedings of the 26th ACM International Conference on Multimedia. :1777-1785.

Traditional image compressed sensing (CS) coding frameworks solve an inverse problem that is based on the measurement coding tools (prediction, quantization, entropy coding, etc.) and the optimization based image reconstruction method. These CS coding frameworks face the challenges of improving the coding efficiency at the encoder, while also suffering from high computational complexity at the decoder. In this paper, we move forward a step and propose a novel deep network based CS coding framework of natural images, which consists of three sub-networks: sampling sub-network, offset sub-network and reconstruction sub-network that responsible for sampling, quantization and reconstruction, respectively. By cooperatively utilizing these sub-networks, it can be trained in the form of an end-to-end metric with a proposed rate-distortion optimization loss function. The proposed framework not only improves the coding performance, but also reduces the computational cost of the image reconstruction dramatically. Experimental results on benchmark datasets demonstrate that the proposed method is capable of achieving superior rate-distortion performance against state-of-the-art methods.

.  2018.  Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. :964-977.

We describe a new way of compressing two-party communication protocols to get protocols with potentially smaller communication. We show that every communication protocol that communicates C bits and reveals I bits of information about the participants' private inputs to an observer that watches the communication, can be simulated by a new protocol that communicates at most poly(I) $\cdot$ loglog(C) bits. Our result is tight up to polynomial factors, as it matches the recent work separating communication complexity from external information cost.

Huang, Xuping.  2018.  Proceedings of the 2Nd International Workshop on Multimedia Privacy and Security. :54-60.

The integrity and reliability of speech data have been important issues to probative use. Watermarking technologies supplies an alternative solution to guarantee the the authenticity of multiple data besides digital signature. This work proposes a novel digital watermarking based on a reversible compression algorithm with sample scanning to detect tampering in time domain. In order to detect tampering precisely, the digital speech data is divided into length-fixed frames and the content-based hash information of each frame is calculated and embedded into the speech data for verification. Huffman compression algorithm is applied to each four sampling bits from least significant bit in each sample after pulse-code modulation processing to achieve low distortion and high capacity for hiding payload. Experimental experiments on audio quality, detection precision and robustness towards attacks are taken, and the results show the effectiveness of tampering detection with a precision with an error around 0.032 s for a 10 s speech clip. Distortion is imperceptible with an average 22.068 dB for Huffman-based and 24.139 dB for intDCT-based method in terms of signal-to-noise, and with an average MOS 3.478 for Huffman-based and 4.378 for intDCT-based method. The bit error rate (BER) between stego data and attacked stego data in both of time-domain and frequency domain is approximate 28.6% in average, which indicates the robustness of the proposed hiding method.

2019-12-05
.  2018.  Proceedings of the 23Nd ACM on Symposium on Access Control Models and Technologies. :51-59.

Despite decades of research on the Internet security, we constantly hear about mega data breaches and malware infections affecting hundreds of millions of hosts. The key reason is that the current threat model of the Internet relies on two assumptions that no longer hold true: (1) Web servers, hosting the content, are secure, (2) each Internet connection starts from the original content provider and terminates at the content consumer. Internet security is today merely patched on top of the TCP/IP protocol stack. In order to achieve comprehensive security for the Internet, we believe that a clean-slate approach must be adopted where a content based security model is employed. Named Data Networking (NDN) is a step in this direction which is envisioned to be the next generation Internet architecture based on a content centric communication model. NDN is currently being designed with security as a key requirement, and thus to support content integrity, authenticity, confidentiality and privacy. However, in order to meet such a requirement, one needs to overcome several challenges, especially in either large operational environments or resource constrained networks. In this paper, we explore the security challenges in achieving comprehensive content security in NDN and propose a research agenda to address some of the challenges.

2019-11-26
.  2018.  2018 International Conference on Applied Engineering (ICAE). :1-6.
Smartphone has become the tool which is used daily in modern human life. Some activities in human life, according to the usage of the smartphone can be related to the information which has a high privilege and needs a privacy. It causes the owners of the smartphone needs a system which can protect their privacy. Unfortunately, the secure the system, the unease of the usage. Hence, the system which has an invulnerable environment but also gives the ease of use is very needful. The aspect which is related to the ease of use is an authentication mechanism. Sometimes, this aspect correspondence to the effectiveness and the efficiency. This study is going to analyze the application related to this aspect which is a lock screen application. This lock screen application uses the context data based on the environment condition around the user. The context data used are GPS location and Mac Address of Wi-Fi. The system is going to detect the context and is going to determine if the smartphone needs to run the authentication mechanism or to bypass it based on the analysis of the context data. Hopefully, the smartphone application which is developed still can provide mobility and usability features, and also can protect the user privacy even though it is located in the environment which its context data is unknown.
2019-11-25
.  2019.  2019 IEEE/CIC International Conference on Communications Workshops in China (ICCC Workshops). :239–244.
The Internet of Things is stepping out of its infancy into full maturity, requiring massive data processing and storage. Unfortunately, because of the unique characteristics of resource constraints, short-range communication, and self-organization in IoT, it always resorts to the cloud or fog nodes for outsourced computation and storage, which has brought about a series of novel challenging security and privacy threats. For this reason, one of the critical challenges of having numerous IoT devices is the capacity to manage them and their data. A specific concern is from which devices or Edge clouds to accept join requests or interaction requests. This paper discusses a design concept for developing the IoT data management platform, along with a data management and lineage traceability implementation of the platform based on blockchain and smart contracts, which approaches the two major challenges: how to implement effective data management and enrich rational interoperability for trusted groups of linked Things; And how to settle conflicts between untrusted IoT devices and its requests taking into account security and privacy preserving. Experimental results show that the system scales well with the loss of computing and communication performance maintaining within the acceptable range, works well to effectively defend against unauthorized access and empower data provenance and transparency, which verifies the feasibility and efficiency of the design concept to provide privacy, fine-grained, and integrity data management over the IoT devices by introducing the blockchain-based data management platform.
.  2019.  2019 IEEE 35th International Conference on Data Engineering (ICDE). :626–637.
Data outsourcing to cloud has been a common IT practice nowadays due to its significant benefits. Meanwhile, security and privacy concerns are critical obstacles to hinder the further adoption of cloud. Although data encryption can mitigate the problem, it reduces the functionality of query processing, e.g., disabling SQL queries. Several schemes have been proposed to enable one-dimensional query on encrypted data, but multi-dimensional range query has not been well addressed. In this paper, we propose a secure and scalable scheme that can support multi-dimensional range queries over encrypted data. The proposed scheme has three salient features: (1) Privacy: the server cannot learn the contents of queries and data records during query processing. (2) Efficiency: we utilize hierarchical cubes to encode multi-dimensional data records and construct a secure tree index on top of such encoding to achieve sublinear query time. (3) Verifiability: our scheme allows users to verify the correctness and completeness of the query results to address server's malicious behaviors. We perform formal security analysis and comprehensive experimental evaluations. The results on real datasets demonstrate that our scheme achieves practical performance while guaranteeing data privacy and result integrity.
.  2019.  2019 IEEE 9th Annual Computing and Communication Workshop and Conference (CCWC). :0055–0061.
With the widespread of cloud computing, the delegation of storage and computing is becoming a popular trend. Concerns on data integrity, security, user privacy as well as the correctness of execution are highlighted due to the untrusted remote data manipulation. Most of existing proposals solve the integrity checking and verifiable computation problems by challenge-response model, but are lack of scalability and reusability. Via blockchain, we achieve efficient and transparent public verifiable delegation for both storage and computing. Meanwhile, the smart contract provides API for request handling and secure data query. The security and privacy issues of data opening are settled by applying cryptographic algorithms all through the delegations. Additionally, any access to the outsourced data requires the owner's authentication, so that the dat transference and utilization are under control.
2019-11-19
.  2018.  Proceedings of the 19th Annual International Conference on Digital Government Research: Governance in the Data Age. :89:1-89:10.

As a frequent participant in eSociety, Willeke is often preoccupied with paperwork because there is no easy to use, affordable way to act as a qualified person in the digital world. Confidential interactions take place over insecure channels like e-mail and post. This situation poses risks and costs for service providers, civilians and governments, while goals regarding confidentiality and privacy are not always met. The objective of this paper is to demonstrate an alternative architecture in which identifying persons, exchanging information, authorizing external parties and signing documents will become more user-friendly and secure. As a starting point, each person has their personal data space, provided by a qualified trust service provider that also issues a high level of assurance electronic ID. Three main building blocks are required: (1) secure exchange between the personal data space of each person, (2) coordination functionalities provided by a token based infrastructure, and (3) governance over this infrastructure. Following the design science research approach, we developed prototypes of the building blocks that we will pilot in practice. Policy makers and practitioners that want to enable Willeke to get rid of her paperwork can find guidance throughout this paper and are welcome to join the pilots in the Netherlands.

2019-11-18
.  2018.  2018 17th IEEE International Conference On Trust, Security And Privacy In Computing And Communications/ 12th IEEE International Conference On Big Data Science And Engineering (TrustCom/BigDataSE). :98–103.
The public key infrastructure (PKI) based authentication protocol provides the basic security services for vehicular ad-hoc networks (VANETs). However, trust and privacy are still open issues due to the unique characteristics of vehicles. It is crucial for VANETs to prevent internal vehicles from broadcasting forged messages while simultaneously protecting the privacy of each vehicle against tracking attacks. In this paper, we propose a blockchain-based anonymous reputation system (BARS) to break the linkability between real identities and public keys to preserve privacy. The certificate and revocation transparency is implemented efficiently using two blockchains. We design a trust model to improve the trustworthiness of messages relying on the reputation of the sender based on both direct historical interactions and indirect opinions about the sender. Experiments are conducted to evaluate BARS in terms of security and performance and the results show that BARS is able to establish distributed trust management, while protecting the privacy of vehicles.
2019-11-12
.  2018.  2018 IEEE 31st Computer Security Foundations Symposium (CSF). :359-373.

Exclusive-or (XOR) operations are common in cryptographic protocols, in particular in RFID protocols and electronic payment protocols. Although there are numerous applications, due to the inherent complexity of faithful models of XOR, there is only limited tool support for the verification of cryptographic protocols using XOR. The Tamarin prover is a state-of-the-art verification tool for cryptographic protocols in the symbolic model. In this paper, we improve the underlying theory and the tool to deal with an equational theory modeling XOR operations. The XOR theory can be freely combined with all equational theories previously supported, including user-defined equational theories. This makes Tamarin the first tool to support simultaneously this large set of equational theories, protocols with global mutable state, an unbounded number of sessions, and complex security properties including observational equivalence. We demonstrate the effectiveness of our approach by analyzing several protocols that rely on XOR, in particular multiple RFID-protocols, where we can identify attacks as well as provide proofs.

Padon, Oded.  2018.  2018 Formal Methods in Computer Aided Design (FMCAD). :1-1.

Formal verification of infinite-state systems, and distributed systems in particular, is a long standing research goal. In the deductive verification approach, the programmer provides inductive invariants and pre/post specifications of procedures, reducing the verification problem to checking validity of logical verification conditions. This check is often performed by automated theorem provers and SMT solvers, substantially increasing productivity in the verification of complex systems. However, the unpredictability of automated provers presents a major hurdle to usability of these tools. This problem is particularly acute in case of provers that handle undecidable logics, for example, first-order logic with quantifiers and theories such as arithmetic. The resulting extreme sensitivity to minor changes has a strong negative impact on the convergence of the overall proof effort.

.  2019.  2019 3rd International Conference on Electronics, Communication and Aerospace Technology (ICECA). :930-935.

In VLSI industry the design cycle is categorized into Front End Design and Back End Design. Front End Design flow is from Specifications to functional verification of RTL design. Back End Design is from logic synthesis to fabrication of chip. Handheld devices like Mobile SOC's is an amalgamation of many components like GPU, camera, sensor, display etc. on one single chip. In order to integrate these components protocols are needed. One such protocol in the emerging trend is I3C protocol. I3C is abbreviated as Improved Inter Integrated Circuit developed by Mobile Industry Processor Interface (MIPI) alliance. Most probably used for the interconnection of sensors in Mobile SOC's. The main motivation of adapting the standard is for the increase speed and low pin count in most of the hardware chips. The bus protocol is backward compatible with I2C devices. The paper includes detailed study I3C bus protocol and developing verification environment for the protocol. The test bench environment is written and verified using system Verilog and UVM. The Universal Verification Methodology (UVM) is base class library built using System Verilog which provides the fundamental blocks needed to quickly develop reusable and well-constructed verification components and test environments. The Functional Coverage of around 93.55 % and Code Coverage of around 98.89 % is achieved by verification closure.

.  2018.  2018 IEEE 3rd International Conference on Integrated Circuits and Microsystems (ICICM). :341-344.

With the development of large scale integrated circuits, the functions of the IoT chips have been increasingly perfect. The verification work has become one of the most important aspects. On the one hand, an efficient verification platform can ensure the correctness of the design. On the other hand, it can shorten the chip design cycle and reduce the design cost. In this paper, based on a transmission protocol of the IoT node, we propose a verification method which combines simulation verification and FPGA-based prototype verification. We also constructed a system verification platform for the IoT smart node chip combining two kinds of verification above. We have simulated and verificatied the related functions of the node chip using this platform successfully. It has a great reference value.

.  2019.  2019 IEEE 19th International Conference on Software Quality, Reliability and Security Companion (QRS-C). :482-486.

For aerospace FPGA software products, traditional simulation method faces severe challenges to verify product requirements under complicated scenarios. Given the increasing maturity of formal verification technology, this method can significantly improve verification work efficiency and product design quality, by expanding coverage on those "blind spots" in product design which were not easily identified previously. Taking UART communication as an example, this paper proposes several critical points to use formal verification for asynchronous communication protocol. Experiments and practices indicate that formal verification for asynchronous communication protocol can effectively reduce the time required, ensure a complete verification process and more importantly, achieve more accurate and intuitive results.


text:
# Journal article

## Slowly oscillating solutions of Cauchy problems with countable spectrum

Abstract:
Let u be a bounded slowly oscillating mild solution of an inhomogeneous Cauchy problem, u̇(t) = Au(t) + f(t), on ℝ or ℝ+, where A is a closed operator such that σap(A) ∩ iℝ is countable, and the Carleman or Laplace transform of f has a continuous extension to an open subset of the imaginary axis with countable complement. It is shown that u is (asymptotically) almost periodic if u is totally ergodic (or if X does not contain c0 in the case of a problem on ℝ). Similar results hold for second-order Cauchy problems and Volterra equations.
Publication status:
Published

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
Volume:
130
Issue:
3
Pages:
471-484
Publication date:
2000-01-01
ISSN:
0308-2105
Language:
English
Pubs id:
pubs:932
UUID:
uuid:3717bbb1-f506-4ba4-b48b-c622c5846739
Local pid:
pubs:932
Source identifiers:
932
Deposit date:
2012-12-19


text:
# 13.1 Newton's law of universal gravitation  (Page 2/6)

 Page 2 / 6

## Newton’s law of gravitation

Newton’s law of gravitation can be expressed as

${\stackrel{\to }{F}}_{12}=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}{\stackrel{^}{r}}_{12}$

where ${\stackrel{\to }{F}}_{12}$ is the force on object 1 exerted by object 2 and ${\stackrel{^}{r}}_{12}$ is a unit vector that points from object 1 toward object 2.

As shown in [link] , the ${\stackrel{\to }{F}}_{12}$ vector points from object 1 toward object 2, and hence represents an attractive force between the objects. The equal but opposite force ${\stackrel{\to }{F}}_{21}$ is the force on object 2 exerted by object 1.

These equal but opposite forces reflect Newton’s third law, which we discussed earlier. Note that strictly speaking, [link] applies to point masses—all the mass is located at one point. But it applies equally to any spherically symmetric objects, where r is the distance between the centers of mass of those objects. In many cases, it works reasonably well for nonsymmetrical objects, if their separation is large compared to their size, and we take r to be the distance between the center of mass of each body.

## The cavendish experiment

A century after Newton published his law of universal gravitation, Henry Cavendish determined the proportionality constant G by performing a painstaking experiment. He constructed a device similar to that shown in [link] , in which small masses are suspended from a wire. Once in equilibrium, two fixed, larger masses are placed symmetrically near the smaller ones. The gravitational attraction creates a torsion (twisting) in the supporting wire that can be measured.

The constant G is called the universal gravitational constant    and Cavendish determined it to be $G=6.67\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{N}·{\text{m}}^{2}{\text{/kg}}^{2}$ . The word ‘universal’ indicates that scientists think that this constant applies to masses of any composition and that it is the same throughout the Universe. The value of G is an incredibly small number, showing that the force of gravity is very weak. The attraction between masses as small as our bodies, or even objects the size of skyscrapers, is incredibly small. For example, two 1.0-kg masses located 1.0 meter apart exert a force of $6.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-11}\phantom{\rule{0.2em}{0ex}}\text{N}$ on each other. This is the weight of a typical grain of pollen.

Although gravity is the weakest of the four fundamental forces of nature, its attractive nature is what holds us to Earth, causes the planets to orbit the Sun and the Sun to orbit our galaxy, and binds galaxies into clusters, ranging from a few to millions. Gravity is the force that forms the Universe.

## Problem-solving strategy: newton’s law of gravitation

To determine the motion caused by the gravitational force, follow these steps:

1. Identify the two masses, one or both, for which you wish to find the gravitational force.
2. Draw a free-body diagram, sketching the force acting on each mass and indicating the distance between their centers of mass.
3. Apply Newton’s second law of motion to each mass to determine how it will move.

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## anonymous 4 years ago Help? Suppose w varies directly with x, x varies inversely with y, and y varies inversely with z. Show algebraically how w relates to z.

• This Question is Closed
1. asnaseer

do you know how to write "w varies directly with x" as an equation?

2. anonymous

I don't o.o

3. asnaseer

ok, this can be written as:$w=ax$where 'a' is some constant

4. anonymous

so a, being some constant, is part of how it relates to z?

5. asnaseer

yes - thats right. similarly, "x varies inversely with y" can be written as:$x=\frac{b}{y}$where 'b' is some other constant

6. asnaseer

finally "y varies inversely with z" can be written as:$y=\frac{c}{z}$

7. anonymous

well that makes sense now that you put it that way thanks!

8. asnaseer

where 'c' is some other constant

9. asnaseer

now all you need to do is to combine all these equations:$w=ax$$x=\frac{b}{y}$$y=\frac{c}{z}$ to get a relation between w and z.

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# Wrong alternative invocation of MathJax

It is commonly known that MathJax can be invoked with $...$ for inline mode and $$...$$ for display mode.

The more latex-like invocation would be $$...$$ for inline mode and $...$ for display mode. This does not work as backslashes and brackets have a special meaning on stack exchange and often need to be escaped.

According to the site's config, there are other invocations allowed:

tex2jax: { inlineMath: [ ["$", "$"], ["\\$","\$/extract_itex]"] ], displayMath: [ ["",""], ["\\[", "\$"] ],
processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }

This literally means that \\$....\$/extract_itex] and \\[...\$ will also invoke MathJax. I think the first definition is faulty and should rather be $...$.

P.S.: All of the posts using this construct (4; cleaned now) are false positives, therefore these alternative invocations are not used at all. Is there any reason to keep them? Alternatively (or additionally), one could add \\ce{...} (or better \ce{...}, like \ref{...} see below)[1] to invoke MathJax - that would probably make more sense.

Additional notes:

1. processRefs: true is the default, so \eqref{label} or \ref{label} works automatically (see sandbox).
Setting up direct rendering of \ce{...} can probably not be handled in the configuration file in this style, this has to be treated directly by the pre-processor. Therefore this would be a feature-request that needs to be relegated to the MathJax team. However, while \ref only processes a label, which should only be a string, and therefore the regular expression \(eq)?ref{[^}]*} is completely sufficient, that cannot be said for all of the code that mhchem's \ce{...} may be able to process.
2. processEnvironments: true is the default, so something like \begin{align}...\end{align} will also invoke maths mode. (\begin{align}...\end{align} is possible in MathJax, but would be an error in latex. It also is really terrible, as it sets a display style environment in inline mode.)
• Right. They should be swapped\\\\\\\\replaced. – M.A.R. ಠ_ಠ Feb 13 '18 at 6:54
• \\ce{H2O} --> $\ce{H2O}$ would be awesome! It doesn't work currently, but it'd be great if it did :D – Gaurang Tandon Feb 13 '18 at 9:22
• As far as readability goes while typing or editing, or searching for a specific line, I think  is superior to \( analogues and bare commands. Not sure why \\$ has been used though. Does indeed seem inconsistent at first glance. – Linear Christmas Feb 13 '18 at 12:42 • @LinearChristmas I find \( increases readability and avoids misinterpretation, since the beginning of maths mode is clearly marked. You have a lot of ambiguity with  (which is usually disabled in default mode for that reason). I guess the "bug" is due to the fact that the forward slash needs to be escaped on SE, because it is used to escape. It is a simple typo, I believe. – Martin - マーチン Feb 13 '18 at 12:51 • Currently, there preview editor only looks for  and  (or \ on some sites) for math delimiters, so if you use \\( or \\[, the contents of the math is not protected from the Markdown processing, and may prevent the math from displaying, or require additional backslashes to be escape Markdown syntax. So the preview code would need to be modified to support \\( and \\[. Similarly for \ce. – Davide Cervone Feb 13 '18 at 13:43 • I assume the reason that dollar signs were used in preference to \( and \[ is the interaction between Markdown's use of  with that of MathJax. For example, since [ is used in Markdown to create links, if you wanted an explicit [ in your output, you are supposed to use \[. That conflicts with using \[ as the display-math delimiter. – Davide Cervone Feb 13 '18 at 13:47 • @Davide If the editor only looks for  and , then wouldn't it be better to completely remove the alternate stuff. It wouldn't really make a difference in the usage (at least not here). The way it is now is just very confusing and I don't see any benefit. the \ce might be better implemented in the MathJax source analogous to \ref; it wouldn't be much of a gain if you had to write \\\\ce... – Martin - マーチン Feb 13 '18 at 14:24 • @Martin-マーチン, I agree, the configuration is inappropriate. I'm only saying that more has to be done to allow \\( and \\[ than just changing the configuration parameter. I am in favor of removing those from the configuration entirely. Yes, it would be possible to handle \ce as \ref currently is, but again, there need to be other changes that support that (this time changes to MathJax itself). If those changes were done, you would only need \ce not \\\\ce. – Davide Cervone Feb 13 '18 at 14:43 • @Davide I have tested \\[ and \\\\( and they do work as they are expected on our site, see sandbox demo. Whatever is going on under the hood, I don't know. However, while removing them on this site is no problem, if that is a network wide configuration, then more care must be applied. The thing about \ce is unfortunately not as easy as \ref as the former takes code, the latter only a string (the preprocessor uses a regex that would break at }), and an implementation must be handled in the source there, so I'm cutting this here. – Martin - マーチン Feb 14 '18 at 3:58 • @Martin-マーチン, yes, if you use them, they will "work", in the sense that MathJax will process them (both in the page and in the preview), but the system goes to special lengths to protect the contents of math delimited by dollar signs from being modified by Markdown, whereas it doesn't do that for these other delimiters. For example, if you enter \\\\(x _1 + x_ 2\\$ you will get \$x 1 + x 2\$, (italic 1 + x with math not processed). Or if you do something like \\$x[1](lost)\\$, you will get no brackets or parens and without "lost". – Davide Cervone Feb 14 '18 at 10:34 • So you have to be careful about the math you type within those delimiters in ways that you don't with dollar delimiters. – Davide Cervone Feb 14 '18 at 10:38 • @Davide Thank yo so much for clearing that up. I think I understand it better now. I'm not a programmer, so that helps a lot. – Martin - マーチン Feb 14 '18 at 10:54 • @Martin-マーチン Are the current mathjax site settings the reason why \begin{align}...\end{align} works just as well with or without the \$ signs? – Gaurang Tandon Mar 12 '18 at 14:44
• @GaurangTandon the current settings allow environments to be escaped; I think the developers did consider this option when they enabled it. See 2 in additional notes – Martin - マーチン Mar 12 '18 at 15:35