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I'm no Keynes, but Germany seems to have illogical economic goals

1. Nov 18, 2005

wasteofo2

http://news.bbc.co.uk/2/hi/europe/4449662.stm

I'm a teenager. There's obviously many things I don't know. Perhaps there are some principals involved with this that I'm not aware of.

However, this seems rather opposed to almost everything I've heard about economics.

Obviously, the two main ways to stimulate the economy are to increase govt. spending, or to cut taxes so as to increase private spending. Usually, as in the Great Depression, defecit spending has been preferred, since an already sluggish economy wouldn't fair well with higher taxes to fund the public spending. Spending cuts are usually proposed so that taxes can be lowered to encourage increased private spending.

So to me, the fact that the Germans want to hike taxes and cut spending, would seem to indicate that both Private and Pubilc expenditures will drop, and I don't see how this could be construed as a mean of revitalizing an economy.

I suppose that if the German government gets its defecit under control, interest rates can be allowed to fall, and firms might be more inclined to invest in Germany, since it's government has itself under control. Is that the angle they're working? Because if so, it would seem that this would really be a process that would take many years for any noticable change to take place.

Could someone more versed in economics explain if there's something I'm missing here, because it seems that the German government is just out of touch with basic economic principals to me.

2. Nov 18, 2005

kleinwolf

Right, to make economy, there is an apparently historical method that works well : just let everybody do what they want (how do you want to make the other way anyhow ? , there are crimes everyday I heard...) and raise military power on top...this is well working....

3. Nov 18, 2005

Art

This is the approach Clinton took in the US and it worked well. However I believe the key to his success was that less borrowing by gov't led to lower interest rates which meant a net income gain to the vast majority of the population resulting in higher spending and thus 8,000,000 more jobs.

Germany is more complicated as they do not have control over their interest rates as these are set by the european central bank. I don't know a lot about the details of Germany's economy but even without interest rate declines reducing the deficit allows for reducing the allocation for debt servicing which frees up money for investment. If tightened too much it can lead to a downward spiral and deeper recession so it is a delicate balancing act made more so by not having the cushion of increased income from lower interest rates to cushion the impact.

Supply side economics whereby gov'ts reduce tax and try to spend their way out of recesson has a dismal track record although that is what the US has done first under Bush snr and now under Bush jnr. Britain's attempts at following this model some years back resulted in them having to ask the IMF to bail them out.

Last edited: Nov 18, 2005
4. Nov 18, 2005

My own thoughts are that if you finance your current gov't expenditure with longterm debt you are heading for a major fall. for eg the costs of the war in Iraq ($00 billions so far) is being financed entirely by borrowings. Borrowing for investment is fine (provided the investments are sound) but using your credit card to feed the electricity meter is a dangerous path to take. Last edited: Nov 18, 2005 11. Nov 18, 2005 Art Yes I just had a quick look at your balance of trade statement for 2005 and it looks pretty good. Luckily for you the gov't is not following the supply side economists' advice. Their economic policy sounds very Clintonesque. http://www.dfait-maeci.gc.ca/eet/pdf/SOT-2005-English.pdf Last edited: Nov 18, 2005 12. Nov 18, 2005 loseyourname Staff Emeritus As far as I know, it isn't. Supply-side economics simply advocates that the revenue streams of suppliers of goods and services be increased (by not taking quite as much off the top), thereby allowing them to create more jobs and better products and services, which in theory should end up benefitting everybody. If we look at the government as being a supplier of goods and services, then cutting their own revenue stream does not constitute a supply-side approach. What they should be doing is handing the ball off, allowing private firms to provide goods and services that the government was previously providing. The only reason public spending increased under Reagan and the Bushes is because all of them also carried out wars which required massive military buildups. The only jobs being created by the government are for soldiers, arms dealers, and contractors that work to rebuild the countries that we occupy. You shouldn't mistake the fiscal stupidity of politicians for real economic theory. 13. Nov 18, 2005 Art That's why I added 'in practice' to my mail above. Gov'ts which follow half an economic plan and half a political plan are unlikely to succeed well on either count. However besides the numerous jobs created directly by gov't expenditure on defence there are also a huge amount of secondary jobs funded by the gov't in supplying for instance health care under the gov't health insurance plans and also of course in the businesses of those people supplying gov't agencies; Halliburton springs to mind As you say ideally (in theory) this expenditure and hence supply should be farmed out to private companies but there are 2 problems with that. Firstly the 'good' problem is private companies are motivated by profit only and so in areas such as health the most vulnerable in society get trampled on and secondly the 'not so good problem' is politicians like to be able to target large amounts of expenditure as it can be very handy when you are looking to win votes in a key marginal 14. Nov 18, 2005 Smurf *shrug* if you say so. They're not listening to traditionalists either. Like I said, their budgets are designed by lawyers. We'll see what happens with the New Budget (assuming it gets through) 15. Nov 18, 2005 Art I'm not endosing their policies as I don't know anything about them other than what I gleaned form the article I read but balanced budgets and positive trade balances sounds good. Do you not agree? 16. Nov 18, 2005 Smurf We have a balanced budget? :surprised When did that happen? 17. Nov 19, 2005 wasteofo2 That's false. Non-defense spending fluxuated under Reagan; some years it dropped, some years it rose. At the end of his term, nondefense discretionary spending had risen by$32 billion. However, with Bush, non-defense spending has been constantly rising. If you'd care to remember, during his first term, Bush didn't veto a single bill, so anything congress wanted to spend money on, he was alright with. During 2000, Clinton's last year as President, the nondefense discretionary spending was $319 Billion. In 2003, Bush and the new Republican majority had hiked it up to$420 Billion.

This chart is entitled Outlays For Discretionary Spending Programs: 1962-2009, check it out. At the bottom there's a sumation of all the nondefense discretionary spending that took place in any one year. http://www.whitehouse.gov/omb/budget/fy2005/sheets/hist08z7.xls

Last edited: Nov 19, 2005
18. Nov 19, 2005

Art

Have a look at the link I posted. I can't speak to it's veracity but the article says they work on balanced budgets.

19. Nov 19, 2005

Smurf

Yeah, they work towards a balanced budget alright. :rofl: :rofl: They balance it by dumping the surplus off the side of the road in Quebec. :rofl: :rofl:

20. Nov 19, 2005

loseyourname

Staff Emeritus
Okay, so I really haven't paid much attention to what money is being spent on by the government. Sorry for making a false statement. I guess I could have built an even stronger case that neither of these guys is actually a supply-sider had I done some actual research.


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SBAT004 June   2022

Integrated instrumentation amplifiers have long been inaccessible for many designers building extremely cost-optimized products due to their price tag. However, not every design needs the precision and accuracy that comes with the vast majority of instrumentation amplifiers. Many designers instead build discrete instrumentation amplifier circuits using three amplifiers of a quad-channel op amp and a network of resistors. This was the only option that fit the budget of these designs until the release of the INA35x family. INA35x re-defines the instrumentation amplifier landscape by offering an integrated solution within the price range of a discrete solution as shown in Table 1-1.

Figure 1-1 Instrumentation Amplifier Landscape
Table 1-1 Instrumentation Amplifier Key Specification Comparison
Key SpecificationsDiscreteINA350Existing INAs

Maximum gain error

Minimum CMRR

About 60 dB85 dB> 100 dB

Maximum offset

About 3 mV1.2 mV< 0.25 mV

Web price(1)

$0.14>$0.50
Web price at time of writing
Approximate price based on online price of general-purpose op amp (LM324LV) + 1% discrete resistors

In addition to the performance benefits, the INA35x also extends TI’s instrumentation amplifier package lineup with new smaller packages that help reduce the amount of printed-circuit-board (PCB) space compared to discrete solutions by up to 70%, as shown in Figure 1-2. This figure compares a typical layout including the resistor network, decoupling capacitors, and a voltage reference buffer. The TLV9041 is used as the reference buffer for INA350, and the fourth channel in a quad-amplifier is used for the discrete solution.

Figure 1-2 PCB Layout Comparison of a Discrete Solution Using TSSOP-14 (Left) vs INA350 in the WSON Package Plus TLV9041 in the X2SON Package (Right)

Learn more about how INA35x can help reduce space and improve performance while simplifying the BOM, and start your evaluation with the following content:

## Evaluate the Design

Generic Part NumberOrderable Part NumberGain OptionsPackageShutdown
INA350INA350ABSIDDFR10 or 202.9 × 2.8 mm (SOT-23-THN)Yes
INA350ABSIDSGR10 or 202 × 2 mm (WSON)
INA350CDSIDDFR30 or 502.9 × 2.8 mm (SOT-23-THN)
INA350CDSIDSGR30 or 502 × 2 mm (WSON)

For additional assistance, ask questions to TI engineers on the TI E2E™ Amplifiers Support Forum.

format: plain


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# Constraining the Transport Processes of the Intracluster Medium with Cold Fronts

The latest generation of X-ray telescopes, including Chandra and XMM-Newton, have revealed the existence of sharp surface brightness discontinuities which betray the existence of sharp density jumps in the intracluster medium (ICM) Spectral analysis demonstrates that these are also jumps in temperature, with the denser side of the front having a lower temperature. These features have been dubbed "cold fronts" (for an extensive review see Markevitch & Vikhlinin 2007). Simulations indicate that cold fronts may form from merging activity, whether by ram-pressure stripping or "ram-pressure slingshots" of cool, dense gas. Cold fronts should be susceptible to heat conduction, which would elminate the sharp temperature gradient on a short timescale, and fluid instabilities, such as Kelvin-Helmholtz (K-H), which would disrupt their smooth appearance.

 Figure 1b: Magnetic field strength.
 Figure 1a: Gas temperature.

However, most cold fronts are observed to be very smooth and sharp, so there must be a mechanism to support the existence of these features. One possible mechanism is magnetic fields. The velocity shear associated with a cold front can amplify the weak cluster magnetic fields to near-equipartition strengths, and stretch the field lines tangential to the front surface (Figure 1b). Due to the small Larmor radii of electrons in the $\mu$G cluster magnetic field, heat conduction is strongly anisotropic, occurring essentially only along the field lines. Therefore, a magnetic field stretched parallel to the front surface would shield the temperature gradient from heat conduction.In ZuHone et al 2011 we performed a series of simulations of sloshing cold front formation in a magnetized ICM. We varied the overall magnetic field strength of the cluster and the degree to which it is tangled on small scales. We found that for initial magnetic field energies ~1% of the thermal energy, the field is stretched and amplified to such a degree that most cold fronts can be stabilized against the development of fluid instabilities (Figure 2). Large-radii cold fronts, where the field is weaker, are more susceptible to the development of instabilities.

However, we found that the ability of magnetic fields to suppress heat conduction across cold fronts in this scenario is limited. In ZuHone et al 2013 we re-simulated our magnetized sloshing cold fronts with anisotropic thermal conduction. We found that despite the formation of magnetic field lines draped tangentially to the front surfaces, conduction is not fully suppressed and the temperature jumps can be significantly reduced, to the point where the corresponding surface brightness jumps would not be seen in observations. This is due to the fact that the magnetic field layers are not perfectly aligned with the cold front surfaces, and some heat flux is able to "leak through." This potentially places strong constraints on heat conduction in the bulk of the ICM.

Another candidate for preventing the development of fluid instabilities at cold front surfaces is viscosity. Little is currently known about the Reynolds number of the cluster plasma. Even a modest isotropic ion viscosity is capable of preventing the development of K-H instabilities at sloshing cold fronts, as was shown to a certain extent by ZuHone et al 2010 and in fuller depth by Roediger et al 2013.

However, for similar reasons as conduction, the ion viscosity in the ICM should be highly anisotropic. Therefore, the suppression of instabilities will be weaker and dependent upon the magnetic field direction. In ZuHone et al 2014, we performed a set of simulations of gas sloshing with magnetic fields and various models for viscosity. We found that the combination of even weak magnetic fields and Braginskii (anisotropic) viscosity is sufficient to produce cold fronts that are consistent with observations in terms of supressing K-H instabilties. We also found that this situation may be approximated by an isotropic Spitzer viscosity with a suppression factor of f ~ 0.1 (Figure 3). However, we also showed that the effect of the magnetic field is crucial; even if the viscosity is the same, simulations with and without magnetic fields produce qualitatively different results in terms of the degree of disruption of cold front surfaces by instabilities.


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Can we (theoretically) spin the black hole so strong that it will be broken apart by centrifugal force?

I can't imagine the forces involved in black holes' lives. So please, help me to find out, if it is possible or not to destroy black hole in this specific way.

• I am not sure, but I think that in order to increase its spin efficiently, you need to throw stuff at it, and if you do you will also increase its mass; in the strong field limit of GR, the corresponding mass increase prevents centrifugal force from breaking it apart. At best it becomes a Kerr black hole with 'a' asymptotically close to 1. For black holes, gravity always win! (if you want to torque it up without throwing things, you ll have to be fairly far away and it won't be very efficient) May 25 '14 at 0:50

Can we (theoretically) spin the black hole so strong so it will be broken apart by centrifugal force?

For a Kerr-Newman (rotating, charged, isolated) black hole of mass $M$, angular momentum $J$, and charge $Q$, the surface area of the event horizon is given by $$A = 8M\left[M^2 + (M^2-a^2-Q^2)^{1/2} - Q^2/2\right]\text{,}$$ where $a = J/M$. An extremal black hole occurs when $M^2 = a^2 + Q^2$. Beyond that, if the black hole is even more overspun or overcharged, is an "overextremal" Kerr-Newman spacetime, which wouldn't really be a black hole at all, but rather a naked singularity.

Thus, I interpret your question as asking whether or not a black hole can be be spun up to the extremal limit and beyond, so as to destroy the event horizon. It's very probable that it can't be done.

Wald proved in 1974 that as one flings matter into a black hole to try to increase its angular momentum, the nearer to an extremal black hole it is, the harder it is to continue this process: a fast-spinning black hole will repel matter that would take it beyond the extremal limit. There are other schemes, and though I'm not aware of any completely general proof within classical general relativity, the continual failure of schemes like this is well-motivated by the connection between black hole dynamics and thermodynamics.

For example, the Hawking temperature of the black hole is $T_\text{H} = \kappa/2\pi$, where $$\kappa = \frac{\sqrt{M^2-a^2-Q^2}}{2M\left(M+\sqrt{M^2-a^2-Q^2}\right)-Q^2}$$ is the black hole's surface gravity. Thus, even reaching the extremal limit is thermodynamically equivalent to cooling a system to absolute zero.

I don't have all of the math off the top of my head, but from my conceptual understanding, it is not possible.

Black holes have a large enough gravitational attraction that even light cannot escape even from well beyond the "surface" (that is if the black hole has a low enough mass that it still has a surface and has not collapsed into a singularity). That would mean that it would have to spin fast enough that the surface is moving significantly faster than the speed of light in order to have enough linear momentum (often colloquially called "centrifugal force" in a circular reference frame) to escape, which according to the theory of relativity is not possible.

Hawking radiation is only possible because the electromagnetic radiation is moving very nearly to orthogonally to the "surface" of the black hole and light can only be "bent" by gravity, it can't be pulled to a stop.

• There are several conceptual problems with this answer. It suggests that the "surface" is something other than the event horizon--then what is it? It suggests that Hawking radiation is limited to massless radiation like electromagnetic--not true. It suggests that black holes can't stop light--the horizon is a lightlike surface that does that. May 25 '14 at 8:44

Black holes can evaporate through a quantum process known as Hawking Radiation and that's it.

As far as we know there is nothing that can stop a black hole. For this notion to make sense you must first look at what is currently known about black holes. Once you get a grasp of it, then you will see that due to our current understanding of the Cosmos there is nothing we can do to black holes.

It is true that Hawking Radiation can affect a black hole, but that is only for very very small black holes.

By the way, in Physics there is no centrifugal force -- this is actually a misconception many people have. However, there is centripetal force.

• Obligatory rebuttal-via-xkcd link: xkcd.com/123 May 24 '14 at 21:41
• @IlmariKaronen Thanks for the down-vote, however, you do realize that the cartoon doesn't prove anything right? There is a difference between Centripetal force and centrifugal. May 24 '14 at 22:01
• To be fair, the cartoon points out that centrifugal force is as inertial force, which is true. Arguably it's sensible to interpret inertial forces as "not real", but I'm not sure what bearing that has on this question, since gravitational force is an inertial force as well. May 26 '14 at 3:54
• This "answer" is pretty vague, makes questionable statements, and has no real bearing on the original query. Jun 3 '15 at 19:48

Interesting. This process could impact the black hole formation in the first place. Consider a rotating star that dies and starts to shrink due to gravitational forces. As it shrinks, all its mass will be more and more compacted in a smaller radius. This will have two consequences: 1) the gravitational force atracting different parts of the body will will grow up with the inverse of squared radius and 2) its rotational speed will increase due to angular momentum conservation and the expanding force, due to the rotation, will grow up with the inverse of radius cubed. This means the expanding force will grow more quickly than the contracting one and, at least in Newtonian view, the expanding force will win. From this point of view, it looks like a rotating star would never form a black hole...

Let's try the following:

Equate the forces:

$$\begin{eqnarray*} F_c &=& \frac{mv^2}R\\ F_g &=& \frac{GMm}{R^2}\\ \newline mv^2/R &=& \frac{GMm}{R^2}\\ v^2 &=& \frac{GM}R \end{eqnarray*}$$

Since the radius is $R_s = 2GM/c^2$

$$\begin{eqnarray*} v^2 &=& \frac{GM}{2GM/c^2}\\ v &=& \sqrt{c^2/2}\\ v &=& \frac{c}{\sqrt2}\\ v &=& 0,707c \end{eqnarray*}$$

I don't know if I made all the considerations, but as far as my knowledge goes, if the blackhole is spinning faster than $0,707c$, the event horizon won't be able to maintain itself on the current radius.

However, when the radius expands, the rotation will slow down by conservation of angular momentum... so I don't think it will rip apart... perhaps become a "grey hole"?

Please forgive me if any fundamental mistake was made, I'm new to all this... :P

• This looks Newtonian. Did you consider the curvature of spacetime near a Black Hole? See also "Kerr solution" for Black Holes. Oct 7 '14 at 14:32
• I like the term "Grey hole". Jun 3 '15 at 20:11
• This is an old answer, but I thought I'd drop this here because it addresses orbital velocity of black holes. you'd need to have the theoretical edge of the black hole at the event horizon spinning at C to escape, which is obviously impossible. physics.stackexchange.com/questions/207816/… Oct 5 '17 at 15:10


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# Are

## Are

Unit of area that corresponds to 100 square metres.

### Notation

The symbol for are is “a” which stands for “are”.

• 1 are is equal to 100 m$$^{2}$$ and we write: 1 a = 100 m$$^{2}$$.
• 1 hectare is equivalent to 100 ares and we write: 1 ha = 100 a.


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## § Relationship betwee permutations and runs

• Let the permutation be $\pi \equiv (3 9 2 5 6 7 10 11 13 15 14 16 12 1 4 8)$.
• Split into runs: $r_1:(3 9)$, $r_2:(2 5 6 7 10 11 13 15)$, $r_3:(14 16)$, $r_4:(12)$, $r_5:(1 4 8)$.
• The runs begin at indeces $p[1] = 1$, $p[2] = 3$, $p[3] = 11$, $p[4] = 13$, $p[5] = 14$. Total number of runs is $R=5$.
• Encode each number in $[1..15]$ by the run to which it belongs to. This is us mapping the integer $k$ to $run(\pi^{-1}(k))$.
• We get that:
1 -> run 5 | (1 4 8)
2 -> run 2 | (2 5 ... 15)
3 -> run 1 | (3 9)
4 -> run 5 | (1 4 8)
--
5 -> run 2 | (2 5 ... 15)
6 -> run 2 | (2 5 ... 15)
7 -> run 2 | (2 5 ... 15)
8 -> run 5 | (1 4 8)
--
9 -> run 1 | (3 9)
10 -> run 2| (2 5 ... 15)
11 -> run 2| (2 5 ... 15)
12 -> run 4| (12)
--
13 -> run 2| (2 5 ... 15)
14 -> run 3| (14 16)
15 -> run 2| (2 5 ... 15)
16 -> run 3| (14 16)

• This gives us the array $S = [5, 2, 1, 5| 2, 2, 2, 5| 1, 2, 2, 4| 2, 3, 2, 3]$
• The $k$th occurrence of symbol $s$ in $S$ corresponds to the row of the permutation $P[s] + k$. The occurrence will be at $\pi(P[s] + k)$.
• Suppose we want to find $\pi(P[s] + k) = y$.

#### § Relationship to burrows wheeler?

• See that we do sort of the same thing, where we identify a string based on the ranks of its characters?!


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# The Relation Between KMS States For Different Temperatures

C. Jaekel
Published 1998 · Physics, Mathematics

Abstract. Given a thermal field theory for some temperature $$\beta^-1$$ , we construct the theory at an arbitrary temperature $$1/\beta'$$ . Our work is based on a construction invented by Buchholz and Junglas, which we adapt to thermal field theories. In a first step we construct states which closely resemble KMS states for the new temperature in a local region $$\mathcal O_{\circ} \subset \mathbb{R}^4$$ , but coincide with the given KMS state in the space-like complement of a slightly larger region Ô. By a weak*-compactness argument there always exists a convergent subnet of states as the size of $$\mathcal O_{\circ}$$ and Ô tends towards $$\mathbb{R}^4$$ . Whether or not such a limit state is a global KMS state for the new temperature, depends on the surface energy contained in the layer in between the boundaries of $$\mathcal O_{\circ}$$ and Ô. We show that this surface energy can be controlled by a generalized cluster condition.
This paper references

This paper is referenced by
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### Congruences of algebraic automorphic forms and supercuspidal representations

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb A_F)$ and that of automorphic forms with supercuspidal components at p, provided that p is larger than the Coxeter number of the absolute Weyl group of $G$. We illustrate how such congruences can be applied in the construction of Galois representations. Our proof is based on type theory for representations of p-adic groups, generalizing the prototypical case of GL(2) in [arXiv:1506.04022, Section 7] to general reductive groups. We exhibit a plethora of new supercuspidal types consisting of arbitrarily small compact open subgroups and characters thereof. We expect these results of independent interest to have further applications. For example, we extend the result by Emerton--Pa\v{s}k\=unas on density of supercuspidal points from definite unitary groups to general $G$ as above.

### Congruences on K-theoretic Gromov--Witten invariants

We study K-theoretic Gromov--Witten invariants of projective hypersurfaces using a virtual localization formula under finite group actions. In particular, it provides all K-theoretic Gromov--Witten invariants of the quintic threefold modulo 41, up to genus 19 and degree 40. Applying the same idea to a K-theoretic version of FJRW theory, we determine it modulo 41 for the quintic polynomial with minimal group and narrow insertions, in every genus.

### An improved existence criterion and an optimal result

We are concerned with a semi-linear elliptic equation on a smooth bounded domain $\Omega$ of $\mathbb{R}^n,\,n\geq 5,$ which involves a critical nonlinearity and a linear term of the form $K(x)u^{(n+2)/(n-2)}$ and $\mu u,$ respectively. By using a test function procedure, we give an existence criterion involving the parameter $\mu$ and the function $K(x).$ For a particular case of $\Omega,\,K(x)$ and $n,$ we prove its optimality through a Pohozaev type identity.

### $C^*$-correspondence functoriality of Cuntz-Pimsner algebras

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. The objects in our domain category are $C^*$-correspondences, and the morphisms are the isomorphism classes of $C^*$-correspondences satisfying certain conditions. As an application, we recover a well-known result of Muhly and Solel. In fact, we show that functoriality leads us to a more generalized result: strongly Morita equivalent $C^*$-correspondences have Morita equivalent Cuntz-Pimsner algebras.

### Finite elements for Helmholtz equations with a nonlocal boundary condition

Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal boundary condition. This condition is exact and requires the evaluation of layer potentials involving the free space Green's function. However, it seems to work in general unstructured geometry, and Galerkin finite element discretization leads to convergence under the usual mesh constraints imposed by G{\aa}rding-type inequalities. The nonlocal boundary conditions are readily approximated by fast multipole methods, and the resulting linear system can be preconditioned by the purely local operator involving transmission boundary conditions.

### [6] 2009.08494

This letter proposes a pragmatic link adaptation algorithm considering power density offsets (PDOs) for next-generation uplink wireless channels. The proposed algorithm consists of PDO calculation between a physical uplink shared channel and its associated sounding reference signal, key channel state metric generation, and modulation and coding scheme (MCS) adaptation with respect to the PDO. Scaling is applied to estimated channel matrices based on multiple reference PDO points to generate corresponding reference mutual information (MI) values, followed by interpolation or extrapolation to obtain the adapted MI and ultimately MCS. The proposed algorithm has low complexity in terms of hardware implementation, while yielding satisfactory block error rates and throughput for a wide range of PDOs as shown by simulation results.

### A consequence of the relative Bogomolov conjecture

We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov conjecture implies the uniform Manin-Mumford conjecture for curves. The proof is built up on our previous work "Uniformity in Mordell-Lang for curves".

### Intelligent Reflecting Surface Aided Pilot Contamination Attack and Its Countermeasure

Pilot contamination attack (PCA) in a time division duplex wireless communication system is considered, where an eavesdropper (Eve) attacks the reverse pilot transmission phase in order to wiretap the data transmitted from a transmitter, Alice, to a receiver, Bob. We propose a new PCA scheme for Eve, wherein Eve does not emit any signal by itself but uses an intelligent reflecting surface (IRS) to reflect the pilot sent by Bob to Alice. The proposed new PCA scheme, referred to as IRS-PCA, increases the signal leakage from Alice to the IRS during the data transmission phase, which is then reflected by the IRS to Eve in order to improve the wiretapping capability of Eve. The proposed IRS-PCA scheme disables many existing countermeasures on PCA due to the fact that with IRS-PCA, Eve no longer needs to know the pilot sequence of Bob, and therefore, poses severe threat to the security of the legitimate wireless communication system. In view of this, the problems of 1) IRS-PCA detection and 2) secure transmission under IRSPCA are considered in this paper. For IRS-PCA detection, a generalized cumulative sum (GCUSUM) detection procedure is proposed based on the framework of quickest detection, aiming at detecting the occurrence of IRS-PCA as soon as possible once it occurs. For secure transmission under IRS-PCA, a cooperative channel estimation scheme is proposed to estimate the channel of the IRS, based on which zero-forcing beamforming is designed to reduce signal leakage.

### A computational framework for evaluating the role of mobility on the propagation of epidemics on point processes

This paper is focused on SIS epidemic dynamics (also known as the contact process) on stationary Poisson point processes of the Euclidean plane, when the infection rate of a susceptible point is proportional to the number of infected points in a ball around it. Two models are discussed, the first with a static point process, and the second where points are subject to some random motion. For both models, we use conservation equations for moment measures to analyze the stationary point processes of infected and susceptible points. A heuristic factorization of the third moment measure is then proposed to derive simple polynomial equations allowing one to derive closed form approximations for the fraction of infected nodes and the steady state. These polynomial equations also lead to a phase diagram which tentatively delineates the regions of the space of parameters (population density, infection radius, infection and recovery rate, and motion rate) where the epidemic survives and those where there is extinction. According to this phase diagram, the survival of the epidemic is not always an increasing function of the motion rate. These results are substantiated by simulations on large two dimensional tori. These simulations show that the polynomial equations accurately predict the fraction of infected nodes when the epidemic survives. The phase diagram is also partly substantiated by the simulation of the mean survival time of the epidemic on large tori. The phase diagram accurately predicts the parameter regions where the mean survival time increases or decreases with the motion rate.

### Skein lasagna modules for 2-handlebodies

Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov-Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary definition in terms of certain diagrams in the 4-manifold. We give a description of the skein lasagna module for 4-manifolds without 1- and 3-handles, and present some explicit calculations for disk bundles over $S^2$.

### Riesz bases of port-Hamiltonian systems

The location of the spectrum and the Riesz basis property of well-posed homogeneous infinite-dimensional linear port-Hamiltonian systems on a 1D spatial domain are studied. It is shown that the Riesz basis property is equivalent to the fact that system operator generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap.

### A categorical sl_2 action on some moduli spaces of sheaves

We study certain sequences of moduli spaces of sheaves on K3 surfaces, building on work of Markman. We show that these sequences can be given the structure of a geometric categorical sl_2 action in the sense of Cautis, Kamnitzer, and Licata. As a corollary, we get an equivalence between derived categories of some moduli spaces that are birational via stratified Mukai flops.

### The equivariant cohomology for semidirect product actions

The rational Borel equivariant cohomology for actions of a compact connected Lie group is determined by restriction of the action to a maximal torus. We show that a similar reduction holds for any compact Lie group $G$ when there is a closed subgroup $K$ such that the cohomology of the classifying space $BK$ is free over the cohomology of $BG$ for field coefficients. We study the particular case when $G$ is a semi-direct product and $K$ is its maximal elementary abelian 2-subgroup for cohomology with coefficients in a field of characteristic two. This provides a different approach to investigate the syzygy order of the equivariant cohomology of a space with a torus action and a compatible involution, and we relate this description with results for 2-torus actions.

### Realizations of non-commutative rational functions around a matrix centre, II: The lost-abbey conditions

In a previous paper the authors generalized classical results of minimal realizations of non-commutative (nc) rational functions, using nc Fornasini--Marchesini realizations which are centred at an arbitrary matrix point. In particular, it was proved that the domain of regularity of a nc rational function is contained in the invertibility set of a corresponding pencil of any minimal realization of the function. In this paper we prove an equality between the domain of a nc rational function and the domain of any of its minimal realizations. As for evaluations over stably finite algebras, we show that the domain of the realization w.r.t any such algebra coincides with the so called matrix domain of the function w.r.t the algebra. As a corollary we show that the domain of regularity and the stable extended domain coincide. In contrary to both the classical case and the scalar case -- where every matrix coefficients which satisfy the controllability and observability conditions can appear in a minimal realization of a nc rational function -- the matrix coefficients in our case have to satisfy certain equations, called linearized lost-abbey conditions, which are related to Taylor--Taylor expansions in nc function theory.

### The quotient criterion in equivariant cohomology for elementary $2$-abelian group actions

Let $G$ be a 2-elementary abelian group and $X$ be a manifold with a locally standard action of $G$. We provide a criterion to determine the syzygy order of the $G$-equivariant cohomology of $X$ with coefficients over a field of characteristic two using a complex associated to the cohomology of the face filtration of the manifold with corners $X/G$. This result is the real version of the quotient criterion for locally standard torus actions developed by M. Franz in arXiv:1205.4462z .

### Positive Solutions For a Schrödinger-Bopp-Podolsky system in $\mathbb R^{3}$

We consider the following Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$ $$\left\{ \begin{array}{c} -\varepsilon^{2} \Delta u + V(x)u + \phi u = f(u)\\ -\varepsilon^{2} \Delta \phi + \varepsilon^{4} \Delta^{2}\phi = 4\pi u^{2}\\ \end{array} \right.$$ where $\varepsilon > 0$ with $V:\mathbb{R}^{3} \rightarrow \mathbb{R}, f:\mathbb{R} \rightarrow \mathbb{R}$ satisfy suitable assumptions. By using variational methods, we prove that the number of positive solutions is estimated below by the Ljusternick-Schnirelmann category of $M$, the set of minima of the potential $V$.

### Radio number of Hamming graphs of diameter 3

For $G$ a simple, connected graph, a vertex labeling $f:V(G)\rightarrow \mathbb{Z}_+$ is called a $\textit{radio labeling of}$ $G$ if it satisfies $|f(u)-f(v)|\geq \operatorname{diam}(G) + 1 - d(u,v)$ for all distinct vertices $u,v\in V(G)$. The $\textit{radio number}$ of $G$ is the minimal span over all radio labelings of $G$. If a bijective radio labeling onto $\{1,2,...,|V(G)|\}$ exists, $G$ is called a $\textit{radio graceful graph}$. We determine the radio number of all diameter $3$ Hamming graphs and show that an infinite subset of them is radio graceful.

### Numerical Testing of a New Positivity-Preserving Interpolation Algorithm

An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving algorithm that is designed to be used when interpolating from a solution defined on one grid to different spatial grid. The motivating application is a numerical weather prediction (NWP) code that uses spectral elements as the discretization choice for its dynamics core and Cartesian product meshes for the evaluation of its physics routines. This combination of spectral elements, which use nonuniformly spaced quadrature/collocation points, and uniformly-spaced Cartesian meshes combined with the desire to maintain positivity when moving between these necessitates our work. This new approach is evaluated against several typical algorithms in use on a range of test problems in one or more space dimensions. The results obtained show that the new method is competitive in terms of observed accuracy while at the same time preserving the underlying positivity of the functions being interpolated.

### A stabilizer free weak Galerkin finite element method on polytopal mesh: Part III

A weak Galerkin (WG) finite element method without stabilizers was introduced in [J. Comput. Appl. Math., 371 (2020). arXiv:1906.06634] on polytopal mesh. Then it was improved in [arXiv:2008.13631] with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG method on polytopal mesh. This method has convergence rates two orders higher than the optimal convergence rates for the corresponding WG solution in both an energy norm and the $L^2$ norm. The numerical examples are tested for low and high order elements in two and three dimensional spaces.

### Deformations of Hopf algebras by partial actions

In this work we study the deformation of a Hopf algebra $H$ by a partial action of $H$ on its ground field $\Bbbk$ through the partial smash product algebra $\underline{\Bbbk # H}$. We introduce the concept of $\lambda$-Hopf algebra such as a Hopf algebra obtained as a partial smash product algebra, as well as we show that, indeed, every Hopf algebra is a $\lambda$-Hopf algebra. Moreover, we develop a method to compute partial actions of a given Hopf algebra on its ground field and, as an application, we exhibit all partial actions of such type for some families of Hopf algebras.

### The Poincare lemma for codifferential, anticoexact forms, and applications to physics

The linear homotopy theory for codifferential operator on Riemannian manifolds is developed in analogy to the theory for exterior derivative. A new class of anticoexact forms that exist locally in a star-shaped region is defined. Their application to physics, including vacuum Dirac-K\"{a}hler equation, coupled Maxwell-Kalb-Ramond system of equations occurring in a bosonic string theory and its reduction to the Dirac equation, is presented.

### Practical Dynamic SC-Flip Polar Decoders: Algorithm and Implementation

SC-Flip (SCF) is a low-complexity polar code decoding algorithm with improved performance, and is an alternative to high-complexity (CRC)-aided SC-List (CA-SCL) decoding. However, the performance improvement of SCF is limited since it can correct up to only one channel error ($\omega=1$). Dynamic SCF (DSCF) algorithm tackles this problem by tackling multiple errors ($\omega \geq 1$), but it requires logarithmic and exponential computations, which make it infeasible for practical applications. In this work, we propose simplifications and approximations to make DSCF practically feasible. First, we reduce the transcendental computations of DSCF decoding to a constant approximation. Then, we show how to incorporate special node decoding techniques into DSCF algorithm, creating the Fast-DSCF decoding. Next, we reduce the search span within the special nodes to further reduce the computational complexity. Following, we describe a hardware architecture for the Fast-DSCF decoder, in which we introduce additional simplifications such as metric normalization and sorter length reduction. All the simplifications and approximations are shown to have minimal impact on the error-correction performance, and the reported Fast-DSCF decoder is the only SCF-based architecture that can correct multiple errors. The Fast-DSCF decoders synthesized using TSMC $65$nm CMOS technology can achieve a $1.25$, $1.06$ and $0.93$ Gbps throughput for $\omega \in \{1,2,3\}$, respectively. Compared to the state-of-the-art fast CA-SCL decoders with equivalent FER performance, the proposed decoders are up to $5.8\times$ more area-efficient. Finally, observations at energy dissipation indicate that the Fast-DSCF is more energy-efficient than its CA-SCL-based counterparts.

### Constructing highly regular expanders from hyperbolic Coxeter groups

A graph $X$ is defined inductively to be $(a_0,\dots,a_{n-1})$-regular if $X$ is $a_0$-regular and for every vertex $v$ of $X$, the sphere of radius $1$ around $v$ is an $(a_1,\dots,a_{n-1})$-regular graph. Such a graph $X$ is said to be highly regular (HR) of level $n$ if $a_{n-1}\neq 0$. Chapman, Linial and Peled studied HR-graphs of level 2 and provided several methods to construct families of graphs which are expanders "globally and locally". They ask whether such HR-graphs of level 3 exist. In this paper we show how the theory of Coxeter groups, and abstract regular polytopes and their generalisations, can lead to such graphs. Given a Coxeter system $(W,S)$ and a subset $M$ of $S$, we construct highly regular quotients of the 1-skeleton of the associated Wythoffian polytope $\mathcal{P}_{W,M}$, which form an infinite family of expander graphs when $(W,S)$ is indefinite and $\mathcal{P}_{W,M}$ has finite vertex links. The regularity of the graphs in this family can be deduced from the Coxeter diagram of $(W,S)$. The expansion stems from applying superapproximation to the congruence subgroups of the linear group $W$. This machinery gives a rich collection of families of HR-graphs, with various interesting properties, and in particular answers affirmatively the question asked by Chapman, Linial and Peled.

### On the Enumeration of Sweep-Covers and Their Relation to Raney Numbers

We define a new structure for collections of nodes in trees which are called "Sweep-Covers" for their 'covering' of all the nodes in the tree by some ancestor-descendent relationship. Then, we analyze an algorithm for finding all sweep covers of a given size in any tree. The complexity of the algorithm is analyzed on a class of infinite $\Delta$-ary trees with constant path lengths between the $\Delta$-star internal nodes. The lower bound of the complexity on these infinite trees is proven to be the Raney numbers due to how Raney trees embed onto the infinite trees of bounded out-degree.

### Improved recovery guarantees and sampling strategies for TV minimization in compressive imaging

In this paper, we consider the use of Total Variation (TV) minimization for compressive imaging; that is, image reconstruction from subsampled measurements. Focusing on two important imaging modalities -- namely, Fourier imaging and structured binary imaging via the Walsh--Hadamard transform -- we derive uniform recovery guarantees asserting stable and robust recovery for arbitrary random sampling strategies. Using this, we then derive a class of theoretically-optimal sampling strategies. For Fourier sampling, we show recovery of an image with approximately $s$-sparse gradient from $m \gtrsim_d s \cdot \log^2(s) \cdot \log^4(N)$ measurements, in $d \geq 1$ dimensions. When $d = 2$, this improves the current state-of-the-art result by a factor of $\log(s) \cdot \log(N)$. It also extends it to arbitrary dimensions $d \geq 2$. For Walsh sampling, we prove that $m \gtrsim_d s \cdot \log^2(s) \cdot \log^2(N/s) \cdot \log^3(N)$ measurements suffice in $d \geq 2$ dimensions. To the best of our knowledge, this is the first recovery guarantee for structured binary sampling with TV minimization.

### The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds

We show that for a generic conformal metric perturbation of a hyperbolic 3-manifold $\Sigma$, the order of vanishing of the Ruelle zeta function at zero equals $4-b_1(\Sigma)$, contrary to the hyperbolic case where it is equal to $4-2b_1(\Sigma)$. The result is proved by developing a suitable perturbation theory that exploits the natural pairing between resonant and co-resonant differential forms. To obtain a metric conformal perturbation we need to establish the non-vanishing of the pushforward of a certain product of resonant and co-resonant states and we achieve this by a suitable regularisation argument. Along the way we describe geometrically all resonant differential forms (at zero) for a closed hyperbolic 3-manifold and study the semisimplicity of the Lie derivative.

### Loci of the Brocard Points over Selected Triangle Families

We study the loci of the Brocard points over two selected families of triangles: (i) 2 vertices fixed on a circumference and a third one which sweeps it, (ii) Poncelet 3-periodics in the homothetic ellipse pair. Loci obtained include circles, ellipses, and teardrop-like curves. We derive expressions for both curves and their areas. We also study the locus of the vertices of Brocard triangles over the homothetic and Brocard-poristic Poncelet families.

### Bounds for Learning Lossless Source Coding

This paper asks a basic question: how much training is required to beat a universal source coder? Traditionally, there have been two types of source coders: fixed, optimum coders such as Huffman coders; and universal source coders, such as Lempel-Ziv The paper considers a third type of source coders: learned coders. These are coders that are trained on data of a particular type, and then used to encode new data of that type. This is a type of coder that has recently become very popular for (lossy) image and video coding. The paper consider two criteria for performance of learned coders: the average performance over training data, and a guaranteed performance over all training except for some error probability $P_e$. In both cases the coders are evaluated with respect to redundancy. The paper considers the IID binary case and binary Markov chains. In both cases it is shown that the amount of training data required is very moderate: to code sequences of length $l$ the amount of training data required to beat a universal source coder is $m=K\frac{l}{\log l}$, where the constant in front depends the case considered.

### SISTA: learning optimal transport costs under sparsity constraints

In this paper, we describe a novel iterative procedure called SISTA to learn the underlying cost in optimal transport problems. SISTA is a hybrid between two classical methods, coordinate descent ("S"-inkhorn) and proximal gradient descent ("ISTA"). It alternates between a phase of exact minimization over the transport potentials and a phase of proximal gradient descent over the parameters of the transport cost. We prove that this method converges linearly, and we illustrate on simulated examples that it is significantly faster than both coordinate descent and ISTA. We apply it to estimating a model of migration, which predicts the flow of migrants using country-specific characteristics and pairwise measures of dissimilarity between countries. This application demonstrates the effectiveness of machine learning in quantitative social sciences.

### Observers Design for Inertial Navigation Systems: A Brief Tutorial

The design of navigation observers able to simultaneously estimate the position, linear velocity and orientation of a vehicle in a three-dimensional space is crucial in many robotics and aerospace applications. This problem was mainly dealt with using the extended Kalman filter and its variants which proved to be instrumental in many practical applications. Although practically efficient, the lack of strong stability guarantees of these algorithms motivated the emergence of a new class of geometric navigation observers relying on Riemannian geometry tools, leading to provable strong stability properties. The objective of this brief tutorial is to provide an overview of the existing estimation schemes, as well as some recently developed geometric nonlinear observers, for autonomous navigation systems relying on inertial measurement unit (IMU) and landmark measurements.

### Prism graphs in tropical plane curves

Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the so-called big face graphs cannot be the skeleta of tropical curves for genus $12$ and greater. In this paper we answer an open question they posed to extend their result to the prism graphs, proving that they are the skeleton of a smooth tropical plane curve precisely when the genus is at most $11$. Our main tool is a classification of lattice polygons with two points than can simultaneously view all others, without having any one point that can observe all others.

### The Newform $K$-Type and $p$-adic Spherical Harmonics

Let $K := \mathrm{GL}_n(\mathcal{O})$ denote the maximal compact subgroup of $\mathrm{GL}_n(F)$ with $F$ a nonarchimedean local field. We study the decomposition of the space of square-integrable functions on the unit sphere in $F^n$ into irreducible $K$-modules; for $F = \mathbb{Q}_p$, these are the $p$-adic analogues of spherical harmonics. As an application, we characterise the newform and conductor exponent of a generic irreducible admissible smooth representation of $\mathrm{GL}_n(F)$ in terms of distinguished $K$-types. Finally, we compare our results to analogous results in the archimedean setting.

### The Capacity of Multi-user Private Information Retrieval for Computationally Limited Databases

We present a private information retrieval (PIR) scheme that allows a user to retrieve a single message from an arbitrary number of databases by colluding with other users while hiding the desired message index. This scheme is of particular significance when there is only one accessible database -- a special case that turns out to be more challenging for PIR in the multi-database case. The upper bound for privacy-preserving capacity for these scenarios is $C=(1+\frac{1}{S}+\cdots+\frac{1}{S^{K-1}})^{-1}$, where $K$ is the number of messages and $S$ represents the quantity of information sources such as $S=N+U-1$ for $U$ users and $N$ databases. We show that the proposed information retrieval scheme attains the capacity bound even when only one database is present, which differs from most existing works that hinge on the access to multiple databases in order to hide user privacy. Unlike the multi-database case, this scheme capitalizes on the inability for a database to cross-reference queries made by multiple users due to computational complexity.

### Can You Take Komjath's Inaccessible Away

In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree, if there is an inaccessible cardinal. This is stronger than Komjath's theorem that asserts the same consistency from two inaccessible cardinals. We will show that our large cardinal assumption is optimal, i.e. if every Kurepa tree has an Aronszajn subtree then $\omega_2$ is inaccessible in the constructible universe \textsc{L}. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree $T$ such that if $U \subset T$ is a Kurepa tree with the inherited order from $T$, then $U$ has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: assume $\textrm{MA}_{\omega_2}$ holds and $\omega_2$ is not a Mahlo cardinal in $\textsc{L}$. Then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's $\rho$ function which might be useful in other contexts.

### Simultaneous Linearization of Diffeomorphisms of Isotropic Manifolds

Suppose that $M$ is a closed isotropic Riemannian manifold and that $R_1,...,R_m$ generate the isometry group of $M$. Let $f_1,...,f_m$ be smooth perturbations of these isometries. We show that the $f_i$ are simultaneously conjugate to isometries if and only if their associated uniform Bernoulli random walk has all Lyapunov exponents zero. This extends a linearization result of Dolgopyat and Krikorian from $S^n$ to real, complex, and quaternionic projective spaces. In addition, we identify and remedy an oversight in that earlier work.

### Galvin's Question on non-$σ$-Well Ordered Total Order

Assume $\mathcal{C}$ is the class of all linear orders $L$ such that $L$ is not a countable union of well ordered sets, and every uncountable subset of $L$ contains a copy of $\omega_1$. We show it is consistent that $\mathcal{C}$ has minimal elements. This answers an old question due to Galvin.

### On the Boomerang Uniformity of Permutations of Low Carlitz Rank

Finding permutation polynomials with low differential and boomerang uniformityis an important topic in S-box designs of many block ciphers. For example, AES chooses the inverse function as its S-box, which is differentially 4-uniform and boomerang 6-uniform. Also there has been considerable research on many non-quadratic permutations which are obtained by modifying certain set of points from the inverse function. In this paper, we give a novel approach that shows that plenty of existing modifications of the inverse function are in fact affine equivalent to permutations of low Carlitz rank and those modifications cannot be APN (almost perfect nonlinear) unless the Carlitz rank is very large. Using nice properties of the permutations of Carlitz form, we present the complete list of permutations of Carlitz rank 3 having the boomerang uniformity six, and also give the complete classification of the differential uniformity of permutations of Carlitz rank 3. We also provide, up to affine equivalence, all the involutory permutations of Carlitz rank 3 having the boomerang uniformity six.

### Conjecture: 100% of elliptic surfaces over $\mathbb{Q}$ have rank zero

Based on an equation for the rank of an elliptic surface over $\mathbb{Q}$ which appears in the work of Nagao, Rosen, and Silverman, we conjecture that 100% of elliptic surfaces have rank $0$ when ordered by the size of the coefficients of their Weierstrass equations, and present a probabilistic heuristic to justify this conjecture. We then discuss how it would follow from either understanding of certain $L$-functions, or from understanding of the local behaviour of the surfaces. Finally, we make a conjecture about ranks of elliptic surfaces over finite fields, and highlight some experimental evidence supporting it.

### On Khovanov Homology of Quasi-Alternating Links

We prove that the length of any gap in the differential grading of the Khovanov homology of any quasi-alternating link is one. As a consequence, we obtain that the length of any gap in the Jones polynomial of any such link is one. This establishes a weaker version of Conjecture 2.3 in [5]. Moreover, we obtain a lower bound for the determinant of any such link in terms of the breadth of its Jones polynomial. This establishes a weaker version of Conjecture 3.8 in [16]. The main tool in obtaining this result is proving the Knight Move Conjecture [2] for the class of quasi-alternating links.

### The Stability of Low-Density Parity-Check Codes and Some of Its Consequences

We study the stability of low-density parity-check (LDPC) codes under blockwise or bitwise maximum $\textit{a posteriori}$ (MAP) decoding, where transmission takes place over a binary-input memoryless output-symmetric channel. Our study stems from the consideration of constructing universal capacity-achieving codes under low-complexity decoding algorithms, where universality refers to the fact that we are considering a family of channels with equal capacity. Consider, e.g., the right-regular sequence by Shokrollahi and the heavy-tail Poisson sequence by Luby $\textit{et al}$. Both sequences are provably capacity-achieving under belief propagation (BP) decoding when transmission takes place over the binary erasure channel (BEC). In this paper we show that many existing capacity-achieving sequences of LDPC codes are not universal under BP decoding. We reveal that the key to showing this non-universality result is determined by the stability of the underlying codes. More concretely, for an ordered and complete channel family and a sequence of LDPC code ensembles, we determine a stability threshold associated with them, which further gives rise to a sufficient condition such that the sequence is not universal under BP decoding. Furthermore, we show that the same stability threshold applies to blockwise or bitwise MAP decoding as well. We present how stability can determine an upper bound on the corresponding blockwise or bitwise MAP threshold, revealing the operational significance of the stability threshold.

### Remarks on some compact symplectic solvmanifolds

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.

### An integral Suzuki-type fixed point theorem with application

In this paper, we present an integral Suzuki-type fixed point theorem for multivalued mappings defined on a complete metric space in terms of the \'{C}iri\'{c} integral contractions. As an application, we will prove an existence and uniqueness theorem for a functional equation arising in dynamic programming of continuous multistage decision processes.

### Low Density Parity Check Code (LDPC Codes) Overview

This paper basically expresses the core fundamentals and brief overview of the research of R. G. GALLAGER [1] on Low-Density Parity-Check (LDPC) codes and various parameters related to LDPC codes like, encoding and decoding of LDPC codes, code rate, parity check matrix, tanner graph. We also discuss advantages and applications as well as the usage of LDPC codes in 5G technology. We have simulated encoding and decoding of LDPC codes and have acquired results in terms of BER vs SNR graph in MATLAB software. This report was submitted as an assignment in Nirma University

### Global Linear Convergence of Evolution Strategies on More Than Smooth Strongly Convex Functions

Evolution strategies (ESs) are zero-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zero-order optimizers for difficult problems. Albeit ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zero-order and also first order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES, namely the (1 + 1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions.

### Hybrid Digital-Analog Beamforming and MIMO Radar with OTFS Modulation

Motivated by future automotive applications, we study some joint radar target detection and parameter estimation problems where the transmitter, equipped with a mono-static MIMO radar, wishes to detect multiple targets and then estimate their respective parameters, while simultaneously communicating information data using orthogonal time frequency space (OTFS) modulation. Assuming that the number of radio frequency chains is smaller than the number of antennas over the mmWave frequency band, we design hybrid digital-analog beamforming at the radar transmitter adapted to different operating phases. The first scenario considers a wide angular beam in order to perform the target detection and parameter estimation, while multicasting a common message to all possible active users. The second scenario considers narrow angular beams to send information streams individually to the already detected users and simultaneously keep tracking of their respective parameters. Under this setup, we propose an efficient maximum likelihood scheme combined with hybrid beamforming to jointly perform target detection and parameter estimation. Our numerical results demonstrate that the proposed algorithm is able to reliably detect multiple targets with a sufficient number of antennas and achieves the Cram\'er-Rao lower bound for radar parameter estimation such as delay, Doppler and angle-of-arrival (AoA).

### Additive Models for Symmetric Positive-Definite Matrices, Riemannian Manifolds and Lie groups

In this paper an additive regression model for a symmetric positive-definite matrix valued response and multiple scalar predictors is proposed. The model exploits the abelian group structure inherited from either the Log-Cholesky metric or the Log-Euclidean framework that turns the space of symmetric positive-definite matrices into a Riemannian manifold and further a bi-invariant Lie group. The additive model for responses in the space of symmetric positive-definite matrices with either of these metrics is shown to connect to an additive model on a tangent space. This connection not only entails an efficient algorithm to estimate the component functions but also allows to generalize the proposed additive model to general Riemannian manifolds that might not have a Lie group structure. Optimal asymptotic convergence rates and normality of the estimated component functions are also established. Numerical studies show that the proposed model enjoys superior numerical performance, especially when there are multiple predictors. The practical merits of the proposed model are demonstrated by analyzing diffusion tensor brain imaging data.

### HDGlab: An open-source implementation of the hybridisable discontinuous Galerkin method in MATLAB

This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems.

### Automatic Differentiation to Simultaneously Identify Nonlinear Dynamics and Extract Noise Probability Distributions from Data

The sparse identification of nonlinear dynamics (SINDy) is a regression framework for the discovery of parsimonious dynamic models and governing equations from time-series data. As with all system identification methods, noisy measurements compromise the accuracy and robustness of the model discovery procedure. In this work, we develop a variant of the SINDy algorithm that integrates automatic differentiation and recent time-stepping constrained motivated by Rudy et al. for simultaneously (i) denoising the data, (ii) learning and parametrizing the noise probability distribution, and (iii) identifying the underlying parsimonious dynamical system responsible for generating the time-series data. Thus within an integrated optimization framework, noise can be separated from signal, resulting in an architecture that is approximately twice as robust to noise as state-of-the-art methods, handling as much as 40% noise on a given time-series signal and explicitly parametrizing the noise probability distribution. We demonstrate this approach on several numerical examples, from Lotka-Volterra models to the spatio-temporal Lorenz 96 model. Further, we show the method can identify a diversity of probability distributions including Gaussian, uniform, Gamma, and Rayleigh.

### Disordered complex networks: energy optimal lattices and persistent homology

Disordered complex networks are of fundamental interest as stochastic models for information transmission over wireless networks. Well-known networks based on the Poisson point process model have limitations vis-a-vis network efficiency, whereas strongly correlated alternatives, such as those based on random matrix spectra (RMT), have tractability and robustness issues. In this work, we demonstrate that network models based on random perturbations of Euclidean lattices interpolate between Poisson and rigidly structured networks, and allow us to achieve the best of both worlds : significantly improve upon the Poisson model in terms of network efficacy measured by the Signal to Interference plus Noise Ratio (abbrv. SINR) and the related concept of coverage probabilities, at the same time retaining a considerable measure of mathematical and computational simplicity and robustness to erasure and noise. We investigate the optimal choice of the base lattice in this model, connecting it to the celebrated problem optimality of Euclidean lattices with respect to the Epstein Zeta function, which is in turn related to notions of lattice energy. This leads us to the choice of the triangular lattice in 2D and face centered cubic lattice in 3D. We demonstrate that the coverage probability decreases with increasing strength of perturbation, eventually converging to that of the Poisson network. In the regime of low disorder, we approximately characterize the statistical law of the coverage function. In 2D, we determine the disorder strength at which the PTL and the RMT networks are the closest measured by comparing their network topologies via a comparison of their Persistence Diagrams . We demonstrate that the PTL network at this disorder strength can be taken to be an effective substitute for the RMT network model, while at the same time offering the advantages of greater tractability.

### Equivalence of three quantum algorithms: Privacy amplification, error correction, and data compression

Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study quantum algorithms of these three types (PA, EC, and DC) in the one-shot scenario, and show that they all become equivalent if modified properly. As an application of this equivalence, we take previously known security bounds of PA, and translate them into coding theorems for EC and DC which have not been obtained previously. Further, we apply these results to simplify and improve our previous result that the two prevalent approaches to the security proof of quantum key distribution (QKD) are equivalent. We also propose a new method to simplify the security proof of QKD.

### Deviation bound for non-causal machine learning

Concentration inequality are widely used for analysing machines learning algorithms. However, current concentration inequalities cannot be applied to the most popular deep neural network, notably in NLP processing. This is mostly due to the non-causal nature of this data. In this paper, a framework for modelling non-causal random fields is provided. A McDiarmid-type concentration inequality is obtained for this framework. In order to do so, we introduce a local i.i.d approximation of the non-causal random field.

### An infection process near criticality: Influence of the initial condition

We investigate how the initial number of infected individuals affects the behavior of the critical susceptible-infected-recovered process. We analyze the outbreak size distribution, duration of the outbreaks, and the role of fluctuations.


text:
# scipy.fft.rfft¶

scipy.fft.rfft(x, n=None, axis=- 1, norm=None, overwrite_x=False, workers=None, *, plan=None)[source]

Compute the 1-D discrete Fourier Transform for real input.

This function computes the 1-D n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).

Parameters
aarray_like

Input array

nint, optional

Number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input along the axis specified by axis is used.

axisint, optional

Axis over which to compute the FFT. If not given, the last axis is used.

norm{“backward”, “ortho”, “forward”}, optional

Normalization mode (see fft). Default is “backward”.

overwrite_xbool, optional

If True, the contents of x can be destroyed; the default is False. See fft for more details.

workersint, optional

Maximum number of workers to use for parallel computation. If negative, the value wraps around from os.cpu_count(). See fft for more details.

plan: object, optional

This argument is reserved for passing in a precomputed plan provided by downstream FFT vendors. It is currently not used in SciPy.

New in version 1.5.0.

Returns
outcomplex ndarray

The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. If n is even, the length of the transformed axis is (n/2)+1. If n is odd, the length is (n+1)/2.

Raises
IndexError

If axis is larger than the last axis of a.

irfft

The inverse of rfft.

fft

The 1-D FFT of general (complex) input.

fftn

The N-D FFT.

rfft2

The 2-D FFT of real input.

rfftn

The N-D FFT of real input.

Notes

When the DFT is computed for purely real input, the output is Hermitian-symmetric, i.e., the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore n//2 + 1.

When X = rfft(x) and fs is the sampling frequency, X[0] contains the zero-frequency term 0*fs, which is real due to Hermitian symmetry.

If n is even, A[-1] contains the term representing both positive and negative Nyquist frequency (+fs/2 and -fs/2), and must also be purely real. If n is odd, there is no term at fs/2; A[-1] contains the largest positive frequency (fs/2*(n-1)/n), and is complex in the general case.

If the input a contains an imaginary part, it is silently discarded.

Examples

>>> import scipy.fft
>>> scipy.fft.fft([0, 1, 0, 0])
array([ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j]) # may vary
>>> scipy.fft.rfft([0, 1, 0, 0])
array([ 1.+0.j,  0.-1.j, -1.+0.j]) # may vary

Notice how the final element of the fft output is the complex conjugate of the second element, for real input. For rfft, this symmetry is exploited to compute only the non-negative frequency terms.

scipy.fft.ifftn

scipy.fft.irfft


text:
Question
Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one's birth. The only known force a planet exerts on Earth is gravitational. (a) Calculate the magnitude of the gravitational force exerted on a 4.20 kg baby by a 100 kg father 0.200 m away at birth (he is assisting, so he is close to the child). (b) Calculate the magnitude of the force on the baby due to Jupiter if it is at its closest distance to Earth, some $6.29 \times 10^{11} \textrm{ m}$ away. How does the force of Jupiter on the baby compare to the force of the father on the baby? Other objects in the room and the hospital building also exert similar gravitational forces. (Of course, there could be an unknown force acting, but scientists first need to be convinced that there is even an effect, much less that an unknown force causes it.)

a) $7.01 \times 10^{-7} \textrm{ N}$

b) $1.34 \times 10^{-6} \textrm{ N}$. The force of gravity due to Jupiter is greater than that of the father by a factor of $1.9$.

Solution Video

# OpenStax College Physics Solution, Chapter 6, Problem 39 (Problems & Exercises) (1:36)

View sample solution

## Calculator Screenshots

Video Transcript
ed1ch06pe39 This is College Physics Answers with Shaun Dychko. The force of gravity between the father and his newborn baby will be the gravitational constant, times the mass of the father, times the mass of the baby, divided by the distance between the father and the baby squared. So 6.673 times ten to the minus eleven times 100 kilograms, mass of the father, times 4.2 kilograms mass of the baby, divided by the 20 centimeters squared between the father and baby which we read in meters as 0.2 meters. This is 7.01 times ten to the minus seven Newtons which is a very small number, much smaller than the other forces the baby is experiencing during childbirth I can tell you. The force due to Jupiter is gravitational constant times the mass of Jupiter which is 1.898 times ten to the twenty-seven kilograms, multiplied by the mass of the baby divided by the distance between Jupiter and the earth at its closest, which is 6.29 times ten to the eleven meters, we square that. That gives 1.34 times ten to the six, negative six Newtons. The ratio between those two forces, force due to Jupiter and the force due to the father, is 1.34 times ten to the minus six divided by 7.01 times ten to the minus seven which is about 1.9. So the force of gravity due to Jupiter is greater than that of the father by a factor of 1.9. But even though the force due to Jupiter is two times greater than the force of gravity due to the father, this is still something that's negligible because it's two times greater than something that's really, really, really, really small.

Submitted by bryanlovell on Tue, 09/18/2018 - 10:54

In the video @ 45 seconds you have (1.898*10^27) but on the calculator you just do (1.898^27) Can you still get the correct answer doing it like that?

Submitted by ShaunDychko on Tue, 09/18/2018 - 11:04

Hi bryanlovell, thanks for the question. With a closer look at the calculator screenshot, notice the capital "E" between 1.897 and 27. This is my favorite shorthand way of writing "times 10^". It has an advantage over typing "* 10^27" since the calculator understands that 1.897E27 should be treated as a single number. This means that when dividing by 1.897E27, the 10^27 factor stays in the denominator where it belongs with the 1.897 factor. To explain by example, for the problem $\dfrac{20}{10} = 2$, typing "20 / 1E1 = 2" which is correct, whereas "20 / 1 * 10^1 = 200" which is not the expected answer since the capital E wasn't used. Of course, one could type "20 / (1 * 10^1) = 2" to get the correct answer with brackets, but avoiding the trouble of typing those brackets is the whole point of the capital E shortcut.

I hope you enjoy the solutions,

Shaun


text:
# A hawk flying at 19 m/s at an altitude of 165 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation `y = 165- x^2/57` until it hits the ground, where...

A hawk flying at 19 m/s at an altitude of 165 m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation `y = 165- x^2/57`

until it hits the ground, where y is its height above the ground and x is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground.

mathsworkmusic | Certified Educator

calendarEducator since 2012

starTop subjects are Math, Science, and Business

The distance equation is

`d = 165-1/57x^2`

This is a parabola with focal length `f=|-57/4| = 57/4`

We want to calculate the arclength from `x=0` to  `x=sqrt((57)(165)) = 96.98`

Let `h = p/2`  where `p` is the distance along the x-axis from the vertex to the point where we are measuring the arclength

`implies` `h = 96.98/2 = 48.49 `

` ` and let `q = sqrt(f^2+h^2) = 50.54`

Then the arclength `s` satisfies

`s = ((hq)/f) + fln((h+q)/f) = 199.6m` (look for length of an arc of a parabola in reference below)

Alternatively, evaluate `s = int_0^96.98 sqrt(1+((dy)/(dx))^2) dx` (this involves integrating `sec^3u` after making the substitution `4/57x = tanu`)

The prey travels 199.6m

check Approved by eNotes Editorial


text:
# How do you find the quotient of (p^3-4p^2+9)div(p-1) using long division?

Sep 18, 2017

${p}^{2} - 3 p + 3$ and remainder$\frac{12}{p - 1}$

#### Explanation:

$\left({p}^{3} - 4 {p}^{2} + 9\right) \div \left(p - 1\right)$

$\textcolor{w h i t e}{\ldots \ldots \ldots .} \textcolor{w h i t e}{\ldots \ldots \ldots .} {p}^{2} - 3 p + 3$
$p - 1 | \overline{{p}^{3} - 4 {p}^{2} + 0 + 9}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \underline{{p}^{3} - {p}^{2}}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots} - 3 {p}^{2} + 0$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .} \underline{- 3 {p}^{2} - 3 p}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 3 p + 9$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} \underline{3 p - 3}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots} 12$

$\frac{{p}^{3} - 4 {p}^{2} + 9}{p - 1} = {p}^{2} - 3 p + 3$ and remainder$\frac{12}{p - 1}$


text:
# How can I add delimiters around the amsmath align environment?

I have a group of equations and I'd like to show under some transformation, the system looks like something else. So I'd like to group the AMS Align environment inside a pair of brackets such that the align environment is vertically centered on the line and I can do something like:

(That uses the matrix environment, so the alignment is centered.)

I am using LyX.

-
Then why not use matrix like the example? – Steve Tjoa Sep 30 '10 at 4:35
Actually, that is the array environment in LyX. To insert a matrix in math mode, type \matrix or one of the AMS variants. (like \bmatrix) but I still do not see how to set the column alignment. – Gus Oct 1 '10 at 22:03

$$\left\{ \begin{matrix} x = & y \\ y = & -x-\mu(x^4-1)y \end{matrix} \right\} \Rightarrow \left\{ \begin{matrix} w = & -x \\ x = & w-\mu F(x) \end{matrix} \right\}$$

Produces something closely to the thing shown above.

-

To have the right spacing appropriate for equations, you can use the aligned environment (instead of matrix):

\left\{ \begin{aligned} x & = y \\ y & = -x-\mu(x^4-1)y \end{matrix} \right\} \Rightarrow \left\{ \begin{aligned} w & = -x \\ x & = w-\mu F(x) \end{aligned} \right\}

I have no idea how to input this in LyX.

-


text:
Beamer user guide says at p140:

Example: For a more interesting usage of the ⟨default overlay specification⟩, consider the following usage:

\multiinclude[<alert@+|> +->]{gra}

This will always paint the most recently added part of the graphic in red (assuming you do not use special colors in the graphic itself).

However, a simple test with gra.pdf files (saved from inkscape) doesn't seem to be rendered red at each overlay. The pdf files contain only black lines. No matter what I try, seems every color is a "special color", and beamer does not correctly alert/highlight elements in the pdfs, like in this (correct) example using xfig:

http://p3f.gmxhome.de/fig2mpdf/fig2mpdf.html

What's your experience on this issue? Can I correctly alert pdfs produced by tools like inkscape?

I do not have a minimal example right now, but may supply one a while later. Thanks for any help/hint!

-

I think that the beamer manual is probably in need of revision here. The \multiinclude macro wraps up the highlighted input using \begin{alertenv} ... \end{aletrenv} (which is how \alert is implemented). Thus the colour only applies to things which LaTeX can make coloured, i.e. where

\begingroup
\color{red}
<thing>
\endgroup

works as expected. This is not the case for PDF graphics: I suspect that Till Tantau was thinking of 'graphics' generated by Tikz when he wrote the documentation, where LaTeX can colour the material.

So the bottom line is that you'll have to colour the graphics yourself if they are generated externally.

-


text:
# 1min force question to solve

1. Oct 12, 2005

### ultimate70192

alright this question involved a shopping cart up a ramp with an unknown angle and i have all the other variables but, cannot find the angle

.17 = .1cosx = sinx i need angle x, simple trig i believe but, i can't do it

2. Oct 12, 2005

### Astronuc

Staff Emeritus
Based on 0.17 = 0.1 cos x,

the x = cos-1 1.7

Based on 0.1 cos x = sin x,

x = tan-1 0.1

If one has developed the correct relationships, the x from either equation should be the same. If not there is something wrong.

3. Oct 12, 2005

### VietDao29

Since you have:
$$\forall x \in \mathbb{R}, \ \ \nexists x \ | \ \ \ |\cos x| > 1$$
So, what can you say about x?
Viet Dao,


text:
# Algorithm What is the mathematical explanation behind this implementation of simulating eyeballs roll in eyes?

## Recommended Posts

Posted (edited)

I want to simulate eyeballs roll in eyes and I have found and forked this implementation in codepen.io. This is exactly what I need.

Smart way but I don't understand why it needs to work like this way. Why is it using ratioX and ratioY which are calculated from dividing mouseX and mouseY with their sum?  Is there a simpler or even cleverer way to do similar simulation?

Edited by caymanbruce

##### Share on other sites
Posted (edited)

I think they are using the x/y ratio as a cheap way to do fake trigonometry. If the mouse is far away from the eyes, they should rotate slower. If the mouse is close to the eyes, it will rotate faster. That would happen naturally with sin/cos. So I think what they have is already pretty simple and clever.

Edited by missionctrl

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