text:
International Association for Cryptologic Research

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Further sources to find out about changes are CryptoDB, ePrint RSS, ePrint Web, Event calender (iCal).

2015-05-06
15:17 [Pub][ePrint]

Provable data possession (PDP) and Proof of Retrievability (POR) are techniques for a client to verify whether an untrusted server (i.e. the cloud storage provider) possesses the original data entirely, and many PDP and POR schemes have been proposed to resolve above issue so far. But another question comes up: driven by profits, a malicious client may accuse an honest server and deny the correct verification in many circumstances. As far as we know, none of the existing private verification schemes that are not based on a third party has settled this matter.

In this paper, we give a method to reform any private verification PDP/POR scheme into a non-repudiable PDP/POR scheme. And then we propose an instantiation, the first Non-repudiable PDP (NRPDP) scheme of private verification, which can provide mutual proof to protect both the client and server. Based on homomorphic verifiable tags and commitment function, our solution allows both the client and the server to prove themselves and verify the other side respectively. To achieve better performance, we improve the NRPDP scheme to obtain an E-NRPDP scheme, which can save the storage cost of the server and reduce the I/O costs to raise efficiency.

We prove the security of NRPDP scheme in the random oracle model, and implement a prototype based on our NRPDP scheme. Then we utilize big data as much as 10G to evaluate the performance in a realistic cloud platform. The experiments show our scheme can be executed efficiently as the original PDP/POR scheme and guarantee non-repudiation efficaciously. Our method is universal and practical, which means that it can be applied in any private PDP/POR schemes to guarantee non-repudiation.

15:17 [Pub][ePrint]

In this paper, we present a new classification of 4-bit optimal S-boxes. All optimal 4-bit S-boxes can be classified into 183 different categories, among which we specify 3 platinum categories. Under the design criteria of the PRESENT (or SPONGENT) S-box, there are 8064 different S-boxes up to adding constants before and after an S-box. The 8064 S-boxes belong to 3 different categories, we show that the S-box should be chosen from one out of the 3 categories or other categories for better resistance against linear cryptanalysis. Furthermore, we study in detail how the S-boxes in the 3 platinum

categories influence the security of PRESENT, RECTANGLE and SPONGENT88 against differential and linear cryptanalysis. Our results show that the S-box selection has a great influence on the security of the schemes. For block ciphers or hash functions with 4-bit S-boxes as confusion layers and bit permutations as diffusion layers, designers can extend the range of S-box selection to the 3 platinum categories and select their S-box very carefully. For PRESENT, RECTANGLE and SPONGENT88 respectively, we get a set of potentially best/better S-box candidates from the 3 platinum categories. These potentially best/better S-boxes can be further investigated to see if they can be used to improve the security-performance tradeoff of the 3 cryptographic algorithms.

15:17 [Pub][ePrint]

Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in $\\mathbb{F}_2[x]$ that are involutions over finite fields of characteristic $2$. Such description is obtained using modular arithmetic\'s tools. We give results related to the cardinality and the number of fixed points (in the context of cryptographic application) of this corpus. We also present a class of Dickson involutions with high degree.

12:17 [Pub][ePrint]

This paper analyses the cryptography used in the Open Smart Grid Protocol

(OSGP). The authenticated encryption (AE) scheme deployed by OSGP is a

non-standard composition of RC4 and a home-brewed MAC, the OMA digest\'\'.

We present several practical key-recovery attacks against the OMA digest. The

first and basic variant can achieve this with a mere $13$ queries to an OMA

digest oracle and negligible time complexity. A more sophisticated version

breaks the OMA digest with only $4$ queries and a time complexity of about

$2^{25}$ simple operations. A different approach only requires one arbitrary

valid plaintext-tag pair, and recovers the key in an average of $144$

\\emph{message verification} queries, or one ciphertext-tag pair and $168$

\\emph{ciphertext verification} queries.

Since the encryption key is derived from the key used by the OMA digest, our

attacks break both confidentiality and authenticity of OSGP.

2015-05-05
21:17 [Pub][ePrint]

The recent result of Garg et al. (FOCS 2013) changed the previously pessimistic attitude towards general purpose cryptographic obfuscation. Since their first candidate construction, several authors proposed newer and newer schemes with more persuasive security arguments and better efficiency. At the same time, indistinguishability obfuscation proved its extreme usefulness by becoming the basis of many solutions for long-standing open problems in cryptography e.g. functional or witness encryption and others.

In this survey, we give an overview of recent research, focusing on the theoretical results on general purpose obfuscation, particularly, indistinguishability obfuscation.

21:17 [Pub][ePrint]

Pair encodings and predicate encodings, recently introduced by Attrapadung (Eurocrypt 2014) and Wee (TCC 2014) respectively, greatly simplify the process of designing and analyzing predicate and attribute-based encryption schemes. However, they are still somewhat limited in that they are restricted to composite order groups, and the information theoretic properties are not sufficient to argue about many of the schemes. Here we focus on pair encodings, as the more general of the two. We first study the structure of these objects, then propose a new relaxed but still information theoretic security property. Next we show a generic construction for predicate encryption in prime order groups from our new property; it results in either selective or full security depending on the encoding, and gives security under SXDH or DLIN. Finally, we demonstrate the range of our new property by using it to design the first selectively secure CP-ABE scheme with constant size ciphertexts.

21:17 [Pub][ePrint]

It is well known that three and four rounds of balanced Feistel cipher or Luby-Rackoff (LR) encryption for two blocks messages are pseudorandom permutation (PRP) and strong pseudorandom permutation (SPRP) respectively. A {\\bf block} is $n$-bit long for some positive integer $n$ and a (possibly keyed) {\\bf block-function} is a nonlinear function mapping all blocks to themselves, e.g. blockcipher. XLS (eXtended Latin Square) with three blockcipher calls was claimed to be SPRP and later which is shown to be wrong. Motivating with these observations, we consider the following questions in this paper: {\\em What is the minimum number of invocations of block-functions required to achieve PRP or SPRP security over $\\ell$ blocks inputs}? To answer this question, we consider all those length-preserving encryption schemes, called {\\bf linear encryption mode}, for which only nonlinear operations are block-functions. Here, we prove the following results for these encryption schemes:

(1) At least $2\\ell$ (or $2\\ell-1$) invocations of block-functions are required to achieve SPRP (or PRP respectively). These bounds are also tight.

(2) To achieve the above bound for PRP over $\\ell > 1$ blocks, either we need at least two keys or it can not be {\\em inverse-free} (i.e., need to apply the inverses of block-functions in the decryption). In particular, we show that a single-keyed block-function based, inverse-free PRP needs $2\\ell$ invocations.

(3) We show that 3-round LR using a single-keyed pseudorandom function (PRF) is PRP if we xor a block of input by a masking key.

21:17 [Pub][ePrint]

This memo collects references to published cryptanalytic results

which are directly relevant to the security evaluation of CAESAR first

round algorithm STRIBOB and its second round tweaked variant, WHIRLBOB.

During the first year after initial publication of STRIBOB and WHIRLBOB,

no cryptanalytic

breaks or other serious issues have emerged. The main difference in

the security between the two variants is that WHIRLBOB allows easier

creation of constant-time software implementations resistant to cache

timing attacks.

21:17 [Pub][ePrint]

In this work, we present a generic open-source software framework that can evaluate the correctness and performance of homomorphic encryption software. Our framework, called HEtest, auto- mates the entire process of a test: generation of data for testing (such as circuits and inputs), execution of a test, comparison of performance to an insecure baseline, statistical analysis of the test results, and production of a LaTeX report. To illustrate the capability of our framework, we present a case study of our analysis of the open-source HElib homomorphic encryption software. We stress though that HEtest is written in a modular fashion, so it can easily be adapted to test any homomorphic encryption software.

21:17 [Pub][ePrint]

An order-revealing encryption scheme gives a public procedure by which two ciphertexts can be compared to reveal the ordering of their underlying plaintexts. We show how to use order-revealing encryption to separate computationally efficient PAC learning from efficient $(\\epsilon, \\delta)$-differentially private PAC learning. That is, we construct a concept class that is efficiently PAC learnable, but for which every efficient learner fails to be differentially private. This answers a question of Kasiviswanathan et al. (FOCS \'08, SIAM J. Comput. \'11).

To prove our result, we give a generic transformation from an order-revealing encryption scheme into one with strongly correct comparison, which enables the consistent comparison of ciphertexts that are not obtained as the valid encryption of any message. We believe this construction may be of independent interest.

21:17 [Pub][ePrint]

LowMC is a collection of block cipher families introduced at Eurocrypt 2015 by Albrecht et al. Its design is optimized for instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. A unique feature of LowMC is that its internal affine layers are chosen at random, and thus each block cipher family contains a huge number of instances. The Eurocrypt paper proposed two specific block cipher families of LowMC, having 80-bit and 128-bit keys.

In this paper, we mount interpolation attacks (algebraic attacks introduced by Jakobsen and Knudsen) on LowMC, and show that a practically significant fraction of $2^{-38}$ of its 80-bit key instances could be broken $2^{23}$ times faster than exhaustive search. Moreover, essentially all instances that are claimed to provide 128-bit security could be broken about $1000$ times faster. In order to obtain these results, we had to develop novel techniques and optimize the original interpolation attack in new ways. While some of our new techniques exploit specific internal properties of LowMC, others are more generic and could be applied, in principle, to any block cipher.


text:
How can a defecting pilot improve their odds of survival?

A bit of context first, this question is inspired by the famous North Korean pilot No Kum-sok, and his defection to the United States during the Korean war. A quick summary, he breaks formation, flies to a South Korean air-force base, and lands successfully, despite landing at the wrong end and nearly colliding with an F-86 in the process. No Kum-sok successfully defects, but it seems as if he ended up just getting lucky, as the base radar happened to be down on his approach.

So at this point the question becomes, what would happen if in a similar situation, the details were more dire, and what could he do to improve his odds of survival?

A Federation pilot grows tired of how things are going and decides to defect to the Empire. He is flying a state of the art air superiority fighter jet (2018). Less than an hour before, his squadron was engaged in a dogfight where in a strange fluke his radio was destroyed but left his aircraft completely sound functionally. He manages to break formation and contact with all other aircraft. At this point he is committed, and his only option is to head south to the Imperial AFB using his on-board navigation systems. A few details to hammer out:

• The plane still has more than half of it's fuel remaining, so he can afford to loiter or use his AB's if necessary.
• The plane also has most of its armament remaining in both bullets and missiles, as well as countermeasures.
• Due to the damage, the plane is entirely incapable of communicating in the normal sense of radio/phone.
• The Imperial base is not far, but is well defended and patrolled, with dozens of active and passive missile systems that can strike from tens of miles away, as well as missile equipped fighters.
• The Imperials would happily welcome a defector, especially one with the air-frame he's piloting, but do not even remotely find it likely that this will happen.
• The Defector only knows the most basic words in the Imperial's language: "Yes, No, Ok"
• The ejection seat has also jammed, making a bail out impossible

What strategy(s) could the Defector employ that would keep him alive long enough so that he could even attempt to convince them of his intentions?

• I have the impression this is story based. – L.Dutch - Reinstate Monica Jul 17 '18 at 7:46
• How critical is the airframe to his defection scheme? I have a feeling his best bet is to punch out over a wilderness area, make his way to a town on foot, and go to a civilian government official and ask for asylum. Fewer air-to-air missiles that way. – Cadence Jul 17 '18 at 7:47
• There are international standards on how pilots should communicate in the event of loss of radiotelephony communications. There's a dedicated transponder code for "loss of radio". On up to mid-sized airports, pilots operating under VFR (visual flight rules) will be monitoring for other traffic, and large airports typically have specific published loss-of-communications protocols for approaches to fly and how to communicate intentions. If one makes it as far as to within visual range of the tower or an aircraft, I imagine signalling SOS by flashing the landing lights could draw some attention. – a CVn Jul 17 '18 at 9:24
• There was an original Battlestar Galactica episode in which Starbuck and Apollo use a Cylon Raider to sneak on to a Basestar. They had a transponder they could use to prevent them from being shot down on their return to the Galactica. They lost the transponder but had luckily joked about "waggling" their wings, so were correctly identified and not blasted. – Michael Richardson Jul 17 '18 at 17:54
• It's amusing that more or less the opposite scenario actually happened at the height of the cold war. A state of the art Western jet developed serious engine trouble and the pilot ejected over West Germany. The plane's engine then recovered and the plane was maintaining altitude and heading for East Germany! Cue a frantic panic to shoot it down before it gave the USSR an intelligence gift or started WW3. ISTR it crashed a few tens of miles short of the border and would otherwise have crossed it, – nigel222 Jul 18 '18 at 16:29

Land and wait

Don't go anywhere near a place that has the capability of bringing you down. You'll be detected flying in their airspace soon enough, you don't need to go to their military base.

Simply land your airplane on an empty highway or similar location where you'll be able to land without causing major damage, get out, wave a white flag around and hold your hands up when the police arrives.

The military and a translator will be called in soon enough when the police wants to figure out what to do with a warplane and an enemy pilot who seems to have surrendered without a fight.

• I'm starting to think this is the most viable option, depending on the terrain setup of course. A high speed, low altitude run to a major highway is his best bet. It avoids most of the triple A bubble of the imperials, and will get him wheels down ASAP. The reason for the high speed is I suspect if an Imperial squadron gets within missile range before he lands he's cooked. – Raznarok Jul 17 '18 at 16:56
• Any civilian airport with a long-enough runway should also do. – RBarryYoung Jul 17 '18 at 19:59
• @RBarryYoung Flying directly at a civilian airport seems like a way to get shot down much sooner than flying toward a relatively empty section of highway. – Azor Ahai Jul 17 '18 at 20:36
• @AzorAhai Civilian airports typically do not have anti-aircraft weapons. But they do have paved runways without obstructions. – RBarryYoung Jul 17 '18 at 20:41
• @RBarryYoung Well, yes, but they're also near population centers which means the military would be much more likely to fear an incoming enemy craft over one approaching the badlands. Especially during an active war. – Azor Ahai Jul 17 '18 at 20:42

Cross into hostile airspace, but don't go towards anything. Keep on a level course, away from anything that could be construed as a strategic target. Set the transponder to whatever the most visible setting is; if it's a modern Mode 3, set its ident to 7600 ("distress - lost communications"), or to an equivalent military code. Disarm the craft as completely as possible; anything that can be done in terms of jettisoning munitions, deactivating ECW, etc. should all be done, preferably where it can be seen by the enemy, but not close enough to be interpreted as an attack.

The low threat (one plane, in a region devoid of any obvious targets) should keep you not-shot-down for the longest possible time. Your best-case scenario is that a fighter (or more likely several) is dispatched to intercept - in the general aviation sense, not the military sense - the anomalous plane. At this point there are standard protocols that the two pilots can use to communicate visually using just the movements of their plane, which would be sufficient for the hostile plane to guide you down to a landing zone, and for you to signal your intent to follow those instructions. My guess is that you'd get sent down to a civil airfield of some description (just in case it is a trap) and there'd be plenty of police on hand.

• Given a transponder, I think this is a viable option. However, I'm on the fence on whether it is operational in the first place. Without it I suspect this move would be suicidal as he is likely to receive several BVR missile launches from the squadron coming to intercept him, and considering his aircraft originated from an active dogfight, it's reasonable that they would shoot first and ask questions later, and I don't favor his chances of fending off an entire squadrons worth of AIM-9's. – Raznarok Jul 17 '18 at 16:53
• You don't just want to be going "nowhere in particular" when you cross the border, you also want to be highly visible while doing so. Modern combat aircraft tend to fly as low as possible to avoid radar, so you want to cross the border while flying high. – Mark Jul 17 '18 at 22:50
• @Mark It would help to come from a country with a history of not having suicide missions, lest they feel you're a distraction from a real threat. I think in any event there's a serious chance of not making out alive. – corsiKa Jul 20 '18 at 4:35

Vulnerability

The defector knows that the flight pattern of one wanting to attack is going to be evasive and attempt to avoid retaliation. The defector also doesn't want to be mistaken for a kamikaze. To communicate that his intentions are not to attack or self-destruct, he deliberately slows down the plane to minimum flying speed and directly towards an anti-air cannon. It is a desperate move, but if he doesn't open fire or speed up, the cannon could easily blast it out of the sky, putting the control entirely in the hands of the Imperials.

Assume the position

He puts down his landing gear right away. Fighters don't do this during combat because it creates drag, but again, the purpose is to defect, not to attack.

Communication

His wing lights can be turned on and off and can be used as a crude form of communication. The actual message is not too important, just the intent to communicate should imply that the intent is not to attack.

Should it be feasible, the lights could express Morse code communicating the intention to defect directly.

Conclusion

Would the Imperials blast a single fighter out of the sky which deliberately puts itself in harms way, lowering landing gear, and with light signals? Maybe. It is a risky endeavor to be sure. However, the ball is left to the Imperials to decide if it is worthwhile to take the risk. There is always the possibility of a bomb on board, and a kamikaze fighter might employ such tactics to get close enough to inflict true damage.

Perhaps they don't believe a defection is likely, though after seeing these signs, they have to at least have doubts in their mind about it being an attack.

• You rely completely on how trigger-happy is the commander of the base. Iran Air 655 was downed by a then state-of-the-art radar system which mistook an Airbus A300 for an F-14 (like mistaking a Ferrari Testarrosa for a 18-wheeler truck) and that was a warship of a third country not directly involved in the war. So go figure. en.wikipedia.org/wiki/Iran_Air_Flight_655 – Rekesoft Jul 17 '18 at 9:24
• I'd probably use the landing lights (which are directed forward) rather than the navigation lights on the wings (which are mainly directed off to the sides), but the idea of using lights to communicate (even simple messages like just "SOS" repeatedly) is not a bad one. – a CVn Jul 17 '18 at 9:30
• Assuming the Imperials somehow stumble upon him and can actually see his aircraft I think this would work. The only issue that @Rekesoft stated was the idea that they'd just shoot at him in BVR and he would die before they even had a clue something was up. – Raznarok Jul 17 '18 at 17:47
• I like this answer aside from the part about flying directly towards an anti-air cannon. – Michael Jul 17 '18 at 19:13
• @Rekesoft Lets not forget the Russians downing passenger planes over Ukraine and, well, the other times they've done the same... – whn Jul 17 '18 at 20:42

1) Fuel permitting, put the gear down. That's a clear indication of non-hostile intent and in general will disable the aircraft's weaponry. If you don't have the fuel to reach the intended target keep it up until intercepted.

2) Unlike what some other posters say, do not jettison ordinance. Having your external stores gone says nothing, but if you jettison once enemy fighters show up that's the equivalent of dropping your gun--a sign of surrender.

3) Head for the smallest civilian airport with an adequate runway, stay well away from anything important while doing so.

4) Pilots have hand signals for radio-out conditions. Exactly obey whatever the intercepting pilots direct you to do unless that is impossible.

Before i start... This is all guess work, i'm not a qualified pilot... let alone a fighter pilot.

Fly close enough that he doesn't get shot down, but enough that the imperial forces would send a squadron of fighters out to investigate. often a single aircraft is a sign of something odd, (i'm assuming he's not being chased by the federation)

Imperial squadron would fly out, perhaps engage perhaps not. if the pilot was within visual range of the Imperial fighters, he could do many things to show he was no threat. activating his landing lights etc he could get there attention, flashing them on and off or attempting morse code. even flashing code for now constantly could be enough

he could release all his bombs and missiles without firing them, they would fall to the ground (hopefully not in a crowded area) the imperial fighters would be able to see he can't attack them.

Another common friendly signal is to wave his wings, all of these are signs that the plane in question is not normal, and any experienced pilot would not see this and think, "Thats odd... oh well, better kill him and get back for breakfast" they'd be reporting it back to base and their officer would probably suggests having it follow an imperial aircraft into landing, while the other imperials would flank it ready to shoot as soon as the pilot did something aggressive.

I think it would be very difficult to defect in this manner in an active warzone, after engaging in a dogfight.

No Kum-suk was defecting after a ceasefire had been declared but your pilot will be doing so when combat is still ongoing, his travelling towards the Imperial AFB will look a lot like an intruder mission.

Without the capability of radio communication and due to the language barrier they will be unable to persuade the Imperial forces of their intention to defect it's likely they will engage the pilot as a hostile before they can get too close to the airbase. Given missle defenses they can engage at range without observing the aircraft so attempts to visually give clues to the intent to defect will be of limited success.

Even with a radio to communicate his intention to defect they would treat it with suspicion sending up escort aircraft, asking him to jettison munitions etc.

This is actually easier then it seems. Contrary to popular media military bodies don't fire the guns and send out missiles at every little thing. Keep in mind that, minus a device like a transponder radar can only see something not rather that something is friendly or not.

So what you would do is.

• Fly slowly, and at a decent radar height, say 10,000.
• If you can manage to drop your landing gear, lower flaps, whatever. Now you may not be able to, (if you're going to fast for example) but with gear and flaps down, you're not going far and you're certainly not attacking anything.
• Wobble your wings left and right. That's the pretty much "everyone" signal for I see you (search and rescue).
• Don't fly in a straight line, but in S turns. If you see an airport do a "2-minute turn" holding pattern. Again massively common. Both the S turns and the holding pattern is very common before landing and should make it clear.
• When you get told to do something via lights or hand signals or plane movements, then do it.
• If you can manage, keep your speed below 250 KIAS, not great, but most airspace in many countries (though far from universal) one of the main things you have to do is stay below 250KIAS when below 10,000 feet. Doing this is a clear indication you mean to go down and not up.
• Finally, if your transponder has a mode-c, doink with your altimeter so that your "altitude" goes down. The normal altimeter may not be able to fake all the way down to 0, but it can do an impressive range, and that gets sent with the transponder signal. So the radar watcher will see an altitude that goes from 10,000 feet to 0 feet, even if your plane doesn't move like that.
• Contrary to popular media military bodies don't fire the guns and send out missiles at every little thing. Quite a few incidents would disagree, from the US shooting down civilian planes to Israeli military personnel shooting unarmed children because they wondered a few feet into a military zone. – forest Jul 20 '18 at 5:59

I suggest you start learning how to say "I defect", "I surrender", "here's a gift for you" and "please don't shoot". If you can only say yes and no, if you can't communicate your defection in their language, you might as well stay at home that day.

This is a time of war, and you are an enemy aricraft approaching a major strategic location in a war zone. You will get shot down from across the horizon.

So firstly avoid AAA coverage. Your briefing should have included intelligence on that. They wouldn't send you to your death without intel, planes are too expensive to be gambled like that.

Your second consideration is that a plane loaded with fuel and missiles causes collateral damages when crashing. They might take the risk shooting you down above an air base, they might not. Depends on the base commander's mood really. They will shoot you above a desert or an empty field. However, if you flew above a population center, it would make the decision to shoot you down a bit more difficult.

In any case, they'll scramble fighters to intercept (because remember, you aren't within AAA range). You won't have much time to make contact, so you better do it quick. Assuming you have no radio or other wireless comm options, you still have good old visual communication. You might fliddle with your jet's lights, or use a flashlight from your cockpit. The latter would make it really obvious that it is an attempt at communication rather than a technical issue with your plane's electrics. Use Morse code to send a single, short, unequivocal message: SOS. Your next messages might be "defection", "no kill" or "I follow you". Keep it short, keep it to the point.

To increase your chances, you'll need to make yourself less threatening. Drop your missiles in a lake or an empty field. Shut down all your weapon systems and countermeasures. Pull the landing gear down. Flap your wings. Anything that makes it look like you aren't interested in combat.

From that point on, you are a POW. You might get preferential treatment if you are willing to give up information which they can't interrogate you for (at least, according to Geneva Conventions), but don't expect champagne and caviar. You are still an enemy combattant.

I would suggest you strike a deal on paper and ask for a legal representation. Make it clear you want to cooperate but you also want guarantees they won't throw you in a dungeon once you've outlived your usefulness, or worst send you back in a prisoner exchange.

• Your radio is out, you won't be able to talk nor you'll be able to hear what they say to you, knowing how to speak the language is irrelevant; by the time you can talk to them, you'll be on land with guns pointing at you. Use of morse code would be a bad or suboptimal idea, not only you need time to communicate a message, but you are relying on the intercepting party to figure out you're using morse to begin with. – Inferry Jul 20 '18 at 1:54
• @Inferry Hence why you open with SOS. You don't need encyclopedic knowledge to know and recognise ... --- ... Also hence why you'd use a flashlight too, which is highly unusual and shouldn't be mistaken with anything but light signals. – AmiralPatate Jul 20 '18 at 5:56
• @Inferry I will also add that in my scenario, it is possible they would deploy a translator in the welcoming party. In other scenarios, say parking your Su-35 on the PCH unannounced, how well would you rate your chances against some Oregonian schmuck with a rifle if you only speak Russian? When you have guns pointed at you is exactly when knowing the language is relevant. – AmiralPatate Jul 20 '18 at 7:23
• This is assuming the person knows about international standards and has not been living in a closed-off country, where precautions for defecting might be in use like not teaching your pilots international protocols, and even then SOS in morse still takes more time than to just rock your wings, which is actual protocol that you had been taught if you know international standards. Once on ground, if you face someone with a gun, talking is unlikely to increase your chances, as with the plane, the best is to show no treat, open hands up or forwards is your best approach. – Inferry Jul 23 '18 at 19:48

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Browse Questions

CsBr crystallises in a body centred cubic lattice. The unit cell length is 436.6 pm. Given that the atomic mass of Cs = 133 and that of Br = 80 amu and Avogadro number being = $6.023 \times 10^{23}mol^{–1}$.CsBr, the density of CsBr is

$4.25g/cm^3$


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## vishal09x one year ago log (base 3) (x+2) = 2?

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1. jdoe0001

$$\bf \Large{ log_3(x+3)=2 \\ \quad \\ \textit{log cancellation rule of }{\color{blue}{ a^{log_ax}=x}}\qquad thus \\ \quad \\ log_3(x+3)=2\implies {\color{blue}{ 3}}^{log_{\color{blue}{ 3}}(x+3)}={\color{blue}{ 3}}^2\\ \quad \\\implies x+3=3^2 }$$

2. jdoe0001

and I think you can take it from there

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No.10642529
Guys I'm really confused what was suppose to be the point of this ending other than being a cliffhanger for a year?

In before Suzaku Lelouche BANG BANG BANG


text:
Dimension of an algebraic group

Definition

The dimension of an algebraic group over a field is defined in the following equivalent ways:

No. Shorthand Definition
1 algebraic variety its dimension as an algebraic variety over the field over which it is defined
2 formal group law the dimension of the formal group law associated with the algebraic group
3 Lie algebra dimension the dimension (as a vector space over the field) of the Lie algebra of the algebraic group.

Facts

• The dimension is an invariant under any isomorphism of algebraic groups. It is possible, however, to have the same abstract group arising as algebraic groups of different dimensions over a given field.
• Given an algebraic group $G$ over a field extension $L$ of $K$, $G$ naturally acquires the structure of an algebraic group over $K$. The dimension of $G$ over $K$ is the product of the dimension of $G$ over $L$ and the degree of the extension $L/K$. Further information: formula for dimension for change of base field of algebraic group
• The dimension of an algebraic group equals the dimension of its connected component of identity.

Particular cases

• The trivial group, viewed as an algebraic group over any field, is zero-dimensional.
• The additive group of a field, as well as the multiplicative group of a field, are both one-dimensional as algebraic groups under the usual structure.
• The additive group of a $n$-dimensional vector space has dimension $n$ as an algebraic group.
• The general linear group over a field of degree $n$ has dimension $n^2$ as an algebraic group.

Effect of operations

Operation Input groups and their orders Output group and its order Proof and comment
external direct product of two algebraic groups $G$ has dimension $m$, $H$ has dimension $n$ $G \times H$ has dimension $m + n$ dimension of direct product is sum of dimensions; the same formula works for internal direct product, which is equivalent to external direct product.
external direct product of finitely many algebraic groups $G_1, G_2, \dots, G_n$ with orders $m_1, m_2, \dots, m_n$ respectively $G_1 \times G_2 \times \dots \times G_n$ has order $\sum_{i=1}^n m_i = m_1 + m+2 + \dots + m_n$ dimension of direct product is sum of dimensions; same formula works for internal direct product
external semidirect product of two groups $G$, dimension $m$, $H$, dimension $n$, acting on it via algebraic automorphisms $G \rtimes H$ has dimension $m +n$ dimension of semidirect product is sum of dimensions; same formula works for internal semidirect product
group extension closed normal subgroup $N$, dimension $m$, quotient group $G/N$, dimension $n$ $m + n$ dimension of extension is sum of dimensions of normal subgroup and quotient


text:
# The set-theoretic universe is not necessarily a class-forcing extension of HOD

• J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” ArXiv e-prints, 2017.
[Bibtex]
@ARTICLE{HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD,
author = {Joel David Hamkins and Jonas Reitz},
title = {The set-theoretic universe {$V$} is not necessarily a class-forcing extension of {HOD}},
journal = {ArXiv e-prints},
year = {2017},
volume = {},
number = {},
pages = {},
month = {September},
note = {Manuscript under review},
abstract = {},
keywords = {under-review},
source = {},
doi = {},
eprint = {1709.06062},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/the-universe-need-not-be-a-class-forcing-extension-of-hod},
}

Abstract. In light of the celebrated theorem of Vopěnka, proving in ZFC that every set is generic over $\newcommand\HOD{\text{HOD}}\HOD$, it is natural to inquire whether the set-theoretic universe $V$ must be a class-forcing extension of $\HOD$ by some possibly proper-class forcing notion in $\HOD$. We show, negatively, that if ZFC is consistent, then there is a model of ZFC that is not a class-forcing extension of its $\HOD$ for any class forcing notion definable in $\HOD$ and with definable forcing relations there (allowing parameters). Meanwhile, S. Friedman (2012) showed, positively, that if one augments $\HOD$ with a certain ZFC-amenable class $A$, definable in $V$, then the set-theoretic universe $V$ is a class-forcing extension of the expanded structure $\langle\HOD,\in,A\rangle$. Our result shows that this augmentation process can be necessary. The same example shows that $V$ is not necessarily a class-forcing extension of the mantle, and the method provides a counterexample to the intermediate model property, namely, a class-forcing extension $V\subseteq V[G]$ by a certain definable tame forcing and a transitive intermediate inner model $V\subseteq W\subseteq V[G]$ with $W\models\text{ZFC}$, such that $W$ is not a class-forcing extension of $V$ by any class forcing notion with definable forcing relations in $V$. This improves upon a previous example of Friedman (1999) by omitting the need for $0^\sharp$.

In 1972, Vopěnka proved the following celebrated result.

Theorem. (Vopěnka) If $V=L[A]$ where $A$ is a set of ordinals, then $V$ is a forcing extension of the inner model $\HOD$.

The result is now standard, appearing in Jech (Set Theory 2003, p. 249) and elsewhere, and the usual proof establishes a stronger result, stated in ZFC simply as the assertion: every set is generic over $\HOD$. In other words, for every set $a$ there is a forcing notion $\mathbb{B}\in\HOD$ and a $\HOD$-generic filter $G\subseteq\mathbb{B}$ for which $a\in\HOD[G]\subseteq V$. The full set-theoretic universe $V$ is therefore the union of all these various set-forcing generic extensions $\HOD[G]$.

It is natural to wonder whether these various forcing extensions $\HOD[G]$ can be unified or amalgamated to realize $V$ as a single class-forcing extension of $\HOD$ by a possibly proper class forcing notion in $\HOD$. We expect that it must be a very high proportion of set theorists and set-theory graduate students, who upon first learning of Vopěnka’s theorem, immediately ask this question.

Main Question. Must the set-theoretic universe $V$ be a class-forcing extension of $\HOD$?

We intend the question to be asking more specifically whether the universe $V$ arises as a bona-fide class-forcing extension of $\HOD$, in the sense that there is a class forcing notion $\mathbb{P}$, possibly a proper class, which is definable in $\HOD$ and which has definable forcing relation $p\Vdash\varphi(\tau)$ there for any desired first-order formula $\varphi$, such that $V$ arises as a forcing extension $V=\HOD[G]$ for some $\HOD$-generic filter $G\subseteq\mathbb{P}$, not necessarily definable.

In this article, we shall answer the question negatively, by providing a model of ZFC that cannot be realized as such a class-forcing extension of its $\HOD$.

Main Theorem. If ZFC is consistent, then there is a model of ZFC which is not a forcing extension of its $\HOD$ by any class forcing notion definable in that $\HOD$ and having a definable forcing relation there.

Throughout this article, when we say that a class is definable, we mean that it is definable in the first-order language of set theory allowing set parameters.

The main theorem should be placed in contrast to the following result of Sy Friedman.

Theorem. (Friedman 2012) There is a definable class $A$, which is strongly amenable to $\HOD$, such that the set-theoretic universe $V$ is a generic extension of $\langle \HOD,\in,A\rangle$.

This is a postive answer to the main question, if one is willing to augment $\HOD$ with a class $A$ that may not be definable in $\HOD$. Our main theorem shows that in general, this kind of augmentation process is necessary.

It is natural to ask a variant of the main question in the context of set-theoretic geology.

Question. Must the set-theoretic universe $V$ be a class-forcing extension of its mantle?

The mantle is the intersection of all set-forcing grounds, and so the universe is close in a sense to the mantle, perhaps one might hope that it is close enough to be realized as a class-forcing extension of it. Nevertheless, the answer is negative.

Theorem. If ZFC is consistent, then there is a model of ZFC that does not arise as a class-forcing extension of its mantle $M$ by any class forcing notion with definable forcing relations in $M$.

We also use our results to provide some counterexamples to the intermediate-model property for forcing. In the case of set forcing, it is well known that every transitive model $W$ of ZFC set theory that is intermediate $V\subseteq W\subseteq V[G]$ a ground model $V$ and a forcing extension $V[G]$, arises itself as a forcing extension $W=V[G_0]$.

In the case of class forcing, however, this can fail.

Theorem. If ZFC is consistent, then there are models of ZFC set theory $V\subseteq W\subseteq V[G]$, where $V[G]$ is a class-forcing extension of $V$ and $W$ is a transitive inner model of $V[G]$, but $W$ is not a forcing extension of $V$ by any class forcing notion with definable forcing relations in $V$.

Theorem. If ZFC + Ord is Mahlo is consistent, then one can form such a counterexample to the class-forcing intermediate model property $V\subseteq W\subseteq V[G]$, where $G\subset\mathbb{B}$ is $V$-generic for an Ord-c.c. tame definable complete class Boolean algebra $\mathbb{B}$, but nevertheless $W$ does not arise by class forcing over $V$ by any definable forcing notion with a definable forcing relation.

More complete details, please go to the paper (click through to the arxiv for a pdf).

• J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” ArXiv e-prints, 2017.
[Bibtex]
@ARTICLE{HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD,
author = {Joel David Hamkins and Jonas Reitz},
title = {The set-theoretic universe {$V$} is not necessarily a class-forcing extension of {HOD}},
journal = {ArXiv e-prints},
year = {2017},
volume = {},
number = {},
pages = {},
month = {September},
note = {Manuscript under review},
abstract = {},
keywords = {under-review},
source = {},
doi = {},
eprint = {1709.06062},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/the-universe-need-not-be-a-class-forcing-extension-of-hod},
}

# A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo

• V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, p. 1–21, 2018.
[Bibtex]
@ARTICLE{GitmanHamkins2018:A-model-of-the-generic-Vopenka-principle-in-which-the-ordinals-are-not-Mahlo,
author = {Gitman, Victoria and Hamkins, Joel David},
year = {2018},
title = {A model of the generic Vopěnka principle in which the ordinals are not Mahlo},
journal = {Archive for Mathematical Logic},
issn = {0933-5846},
doi = {10.1007/s00153-018-0632-5},
month = {5},
pages = {1--21},
eprint = {1706.00843},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1xT},
abstract = {The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a Δ2-definable class containing no regular cardinals. In such a model, there can be no Σ2-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler.},
}

Abstract. The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a $\Delta_2$-definable class containing no regular cardinals. In such a model, there can be no $\Sigma_2$-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler.

The Vopěnka principle is the assertion that for every proper class of first-order structures in a fixed language, one of the structures embeds elementarily into another. This principle can be formalized as a single second-order statement in Gödel-Bernays set-theory GBC, and it has a variety of useful equivalent characterizations. For example, the Vopěnka principle holds precisely when for every class $A$, the universe has an $A$-extendible cardinal, and it is also equivalent to the assertion that for every class $A$, there is a stationary proper class of $A$-extendible cardinals (see theorem 6 in my paper The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme) In particular, the Vopěnka principle implies that ORD is Mahlo: every class club contains a regular cardinal and indeed, an extendible cardinal and more.

To define these terms, recall that a cardinal $\kappa$ is extendible, if for every $\lambda>\kappa$, there is an ordinal $\theta$ and an elementary embedding $j:V_\lambda\to V_\theta$ with critical point $\kappa$. It turns out that, in light of the Kunen inconsistency, this weak form of extendibility is equivalent to a stronger form, where one insists also that $\lambda<j(\kappa)$; but there is a subtle issue about this that comes up with the virtual forms of these axioms, where the virtual weak and virtual strong forms are no longer equivalent. Relativizing to a class parameter, a cardinal $\kappa$ is $A$-extendible for a class $A$, if for every $\lambda>\kappa$, there is an elementary embedding
$$j:\langle V_\lambda, \in, A\cap V_\lambda\rangle\to \langle V_\theta,\in,A\cap V_\theta\rangle$$
with critical point $\kappa$, and again one may equivalently insist also that $\lambda<j(\kappa)$. Every such $A$-extendible cardinal is therefore extendible and hence inaccessible, measurable, supercompact and more. These are amongst the largest large cardinals.

In the first-order ZFC context, set theorists commonly consider a first-order version of the Vopěnka principle, which we call the Vopěnka scheme, the scheme making the Vopěnka assertion of each definable class separately, allowing parameters. That is, the Vopěnka scheme asserts, of every formula $\varphi$, that for any parameter $p$, if $\{\,x\mid \varphi(x,p)\,\}$ is a proper class of first-order structures in a common language, then one of those structures elementarily embeds into another.

The Vopěnka scheme is naturally stratified by the assertions $\text{VP}(\Sigma_n)$, for the particular natural numbers $n$ in the meta-theory, where $\text{VP}(\Sigma_n)$ makes the Vopěnka assertion for all $\Sigma_n$-definable classes. Using the definable $\Sigma_n$-truth predicate, each assertion $\text{VP}(\Sigma_n)$ can be expressed as a single first-order statement in the language of set theory.

In my previous paper, The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme, I proved that the Vopěnka principle is not provably equivalent to the Vopěnka scheme, if consistent, although they are equiconsistent over GBC and furthermore, the Vopěnka principle is conservative over the Vopěnka scheme for first-order assertions. That is, over GBC the two versions of the Vopěnka principle have exactly the same consequences in the first-order language of set theory.

In this article, Gitman and I are concerned with the virtual forms of the Vopěnka principles. The main idea of virtualization, due to Schindler, is to weaken elementary-embedding existence assertions to the assertion that such embeddings can be found in a forcing extension of the universe. Gitman and Schindler had emphasized that the remarkable cardinals, for example, instantiate the virtualized form of supercompactness via the Magidor characterization of supercompactness. This virtualization program has now been undertaken with various large cardinals, leading to fruitful new insights.

Carrying out the virtualization idea with the Vopěnka principles, we define the generic Vopěnka principle to be the second-order assertion in GBC that for every proper class of first-order structures in a common language, one of the structures admits, in some forcing extension of the universe, an elementary embedding into another. That is, the structures themselves are in the class in the ground model, but you may have to go to the forcing extension in order to find the elementary embedding.

Similarly, the generic Vopěnka scheme, introduced by Bagaria, Gitman and Schindler, is the assertion (in ZFC or GBC) that for every first-order definable proper class of first-order structures in a common language, one of the structures admits, in some forcing extension, an elementary embedding into another.

On the basis of their work, Bagaria, Gitman and Schindler had asked the following question:

Question. If the generic Vopěnka scheme holds, then must there be a proper class of remarkable cardinals?

There seemed good reason to expect an affirmative answer, even assuming only $\text{gVP}(\Sigma_2)$, based on strong analogies with the non-generic case. Specifically, in the non-generic context Bagaria had proved that $\text{VP}(\Sigma_2)$ was equivalent to the existence of a proper class of supercompact cardinals, while in the virtual context, Bagaria, Gitman and Schindler proved that the generic form $\text{gVP}(\Sigma_2)$ was equiconsistent with a proper class of remarkable cardinals, the virtual form of supercompactness. Similarly, higher up, in the non-generic context Bagaria had proved that $\text{VP}(\Sigma_{n+2})$ is equivalent to the existence of a proper class of $C^{(n)}$-extendible cardinals, while in the virtual context, Bagaria, Gitman and Schindler proved that the generic form $\text{gVP}(\Sigma_{n+2})$ is equiconsistent with a proper class of virtually $C^{(n)}$-extendible cardinals.

But further, they achieved direct implications, with an interesting bifurcation feature that specifically suggested an affirmative answer to the question above. Namely, what they showed at the $\Sigma_2$-level is that if there is a proper class of remarkable cardinals, then $\text{gVP}(\Sigma_2)$ holds, and conversely if $\text{gVP}(\Sigma_2)$ holds, then there is either a proper class of remarkable cardinals or a proper class of virtually rank-into-rank cardinals. And similarly, higher up, if there is a proper class of virtually $C^{(n)}$-extendible cardinals, then $\text{gVP}(\Sigma_{n+2})$ holds, and conversely, if $\text{gVP}(\Sigma_{n+2})$ holds, then either there is a proper class of virtually $C^{(n)}$-extendible cardinals or there is a proper class of virtually rank-into-rank cardinals. So in each case, the converse direction achieves a disjunction with the target cardinal and the virtually rank-into-rank cardinals. But since the consistency strength of the virtually rank-into-rank cardinals is strictly stronger than the generic Vopěnka principle itself, one can conclude on consistency-strength grounds that it isn’t always relevant, and for this reason, it seemed natural to inquire whether this second possibility in the bifurcation could simply be removed. That is, it seemed natural to expect an affirmative answer to the question, even assuming only $\text{gVP}(\Sigma_2)$, since such an answer would resolve the bifurcation issue and make a tighter analogy with the corresponding results in the non-generic/non-virtual case.

In this article, however, we shall answer the question negatively. The details of our argument seem to suggest that a robust analogy with the non-generic/non-virtual principles is achieved not with the virtual $C^{(n)}$-cardinals, but with a weakening of that property that drops the requirement that $\lambda<j(\kappa)$. Indeed, our results seems to offer an illuminating resolution of the bifurcation aspect of the results we mentioned from Bagaria, Gitmand and Schindler, because it provides outright virtual large-cardinal equivalents of the stratified generic Vopěnka principles. Because the resulting virtual large cardinals are not necessarily remarkable, however, our main theorem shows that it is relatively consistent with even the full generic Vopěnka principle that there are no $\Sigma_2$-reflecting cardinals and therefore no remarkable cardinals.

Main Theorem.

1. It is relatively consistent that GBC and the generic Vopěnka principle holds, yet ORD is not Mahlo.
2. It is relatively consistent that ZFC and the generic Vopěnka scheme holds, yet ORD is not definably Mahlo, and not even $\Delta_2$-Mahlo. In such a model, there can be no $\Sigma_2$-reflecting cardinals and therefore also no remarkable cardinals.

For more, go to the arcticle:

• V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, p. 1–21, 2018.
[Bibtex]
@ARTICLE{GitmanHamkins2018:A-model-of-the-generic-Vopenka-principle-in-which-the-ordinals-are-not-Mahlo,
author = {Gitman, Victoria and Hamkins, Joel David},
year = {2018},
title = {A model of the generic Vopěnka principle in which the ordinals are not Mahlo},
journal = {Archive for Mathematical Logic},
issn = {0933-5846},
doi = {10.1007/s00153-018-0632-5},
month = {5},
pages = {1--21},
eprint = {1706.00843},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1xT},
abstract = {The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a Δ2-definable class containing no regular cardinals. In such a model, there can be no Σ2-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler.},
}

# The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme

• J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016.
[Bibtex]
@ARTICLE{Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme,
author = {Joel David Hamkins},
title = {The {Vop\v{e}nka} principle is inequivalent to but conservative over the {Vop\v{e}nka} scheme},
journal = {ArXiv e-prints},
year = {2016},
volume = {},
number = {},
pages = {},
month = {},
note = {Under review},
abstract = {},
keywords = {under-review},
source = {},
eprint = {1606.03778},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1lV},
}

Abstract. The Vopěnka principle, which asserts that every proper class of first-order structures in a common language admits an elementary embedding between two of its members, is not equivalent over GBC to the first-order Vopěnka scheme, which makes the Vopěnka assertion only for the first-order definable classes of structures. Nevertheless, the two Vopěnka axioms are equiconsistent and they have exactly the same first-order consequences in the language of set theory. Specifically, GBC plus the Vopěnka principle is conservative over ZFC plus the Vopěnka scheme for first-order assertions in the language of set theory.

The Vopěnka principle is the assertion that for every proper class $\mathcal{M}$ of first-order $\mathcal{L}$-structures, for a set-sized language $\mathcal{L}$, there are distinct members of the class $M,N\in\mathcal{M}$ with an elementary embedding $j:M\to N$ between them. In quantifying over classes, this principle is a single assertion in the language of second-order set theory, and it makes sense to consider the Vopěnka principle in the context of a second-order set theory, such as Godel-Bernays set theory GBC, whose language allows one to quantify over classes. In this article, GBC includes the global axiom of choice.

In contrast, the first-order Vopěnka scheme makes the Vopěnka assertion only for the first-order definable classes $\mathcal{M}$ (allowing parameters). This theory can be expressed as a scheme of first-order statements, one for each possible definition of a class, and it makes sense to consider the Vopěnka scheme in Zermelo-Frankael ZFC set theory with the axiom of choice.

Because the Vopěnka principle is a second-order assertion, it does not make sense to refer to it in the context of ZFC set theory, whose first-order language does not allow quantification over classes; one typically retreats to the Vopěnka scheme in that context. The theme of this article is to investigate the precise meta-mathematical interactions between these two treatments of Vopěnka’s idea.

Main Theorems.

1. If ZFC and the Vopěnka scheme holds, then there is a class forcing extension, adding classes but no sets, in which GBC and the Vopěnka scheme holds, but the Vopěnka principle fails.
2. If ZFC and the Vopěnka scheme holds, then there is a class forcing extension, adding classes but no sets, in which GBC and the Vopěnka principle holds.

It follows that the Vopěnka principle VP and the Vopěnka scheme VS are not equivalent, but they are equiconsistent and indeed, they have the same first-order consequences.

Corollaries.

1. Over GBC, the Vopěnka principle and the Vopěnka scheme, if consistent, are not equivalent.
2. Nevertheless, the two Vopěnka axioms are equiconsistent over GBC.
3. Indeed, the two Vopěnka axioms have exactly the same first-order consequences in the language of set theory. Specifically, GBC plus the Vopěnka principle is conservative over ZFC plus the Vopěnka scheme for assertions in the first-order language of set theory. $$\text{GBC}+\text{VP}\vdash\phi\qquad\text{if and only if}\qquad\text{ZFC}+\text{VS}\vdash\phi$$

These results grew out of my my answer to a MathOverflow question of Mike Shulman, Can Vopěnka’s principle be violated definably?, inquiring whether there would always be a definable counterexample to the Vopěnka principle, whenever it should happen to fail. I interpret the question as asking whether the Vopěnka scheme is necessarily equivalent to the Vopěnka principle, and the answer is negative.

The proof of the main theorem involves the concept of a stretchable set $g\subset\kappa$ for an $A$-extendible cardinal, which has the property that for every cardinal $\lambda>\kappa$ and every extension $h\subset\lambda$ with $h\cap\kappa=g$, there is an elementary embedding $j:\langle V_\lambda,\in,A\cap V_\lambda\rangle\to\langle V_\theta,\in,A\cap V_\theta\rangle$ such that $j(g)\cap\lambda=h$. Thus, the set $g$ can be stretched by an $A$-extendibility embedding so as to agree with any given $h$.

# Norman Lewis Perlmutter

Norman Lewis Perlmutter successfully defended his dissertation under my supervision and will earn his Ph.D. at the CUNY Graduate Center in May, 2013.  His dissertation consists of two parts.  The first chapter arose from the observation that while direct limits of large cardinal embeddings and other embeddings between models of set theory are pervasive in the subject, there is comparatively little study of inverse limits of systems of such embeddings.  After such an inverse system had arisen in Norman’s joint work on Generalizations of the Kunen inconsistency, he mounted a thorough investigation of the fundamental theory of these inverse limits. In chapter two, he investigated the large cardinal hierarchy in the vicinity of the high-jump cardinals.  During this investigation, he ended up refuting the existence of what are now called the excessively hypercompact cardinals, which had appeared in several published articles.  Previous applications of that notion can be made with a weaker notion, what is now called a hypercompact cardinal.

Norman Lewis Perlmutter, “Inverse limits of models of set theory and the large cardinal hierarchy near a high-jump cardinal”  Ph.D. dissertation for The Graduate Center of the City University of New York, May, 2013.

Abstract.  This dissertation consists of two chapters, each of which investigates a topic in set theory, more specifically in the research area of forcing and large cardinals. The two chapters are independent of each other.

The first chapter analyzes the existence, structure, and preservation by forcing of inverse limits of inverse-directed systems in the category of elementary embeddings and models of set theory. Although direct limits of directed systems in this category are pervasive in the set-theoretic literature, the inverse limits in this same category have seen less study. I have made progress towards fully characterizing the existence and structure of these inverse limits. Some of the most important results are as follows. If the inverse limit exists, then it is given by either the entire thread class or a rank-initial segment of the thread class. Given sufficient large cardinal hypotheses, there are systems with no inverse limit, systems with inverse limit given by the entire thread class, and systems with inverse limit given by a proper subset of the thread class. Inverse limits are preserved in both directions by forcing under fairly general assumptions. Prikry forcing and iterated Prikry forcing are important techniques for constructing some of the examples in this chapter.

The second chapter analyzes the hierarchy of the large cardinals between a supercompact cardinal and an almost-huge cardinal, including in particular high-jump cardinals. I organize the large cardinals in this region by consistency strength and implicational strength. I also prove some results relating high-jump cardinals to forcing.  A high-jump cardinal is the critical point of an elementary embedding $j: V \to M$ such that $M$ is closed under sequences of length $\sup\{\ j(f)(\kappa) \mid f: \kappa \to \kappa\ \}$.  Two of the most important results in the chapter are as follows. A Vopenka cardinal is equivalent to an Woodin-for-supercompactness cardinal. The existence of an excessively hypercompact cardinal is inconsistent.


text:
# How to Multiply with the 3n + 1 series (Collatz Conjecture)

August 06, 2022

Tags: math

I stumbled across an interesting paper, which shows that you can multiply two numbers by using the Collatz conjecture (and assuming it to be true for the numbers you are dealing with).

This post contains my summary and understanding of how this method works.

# Background

## Collatz conjecture

### Definition

The Collatz conjecture, also known as the $3n + 1$ problem, is a simple to describe, yet unsolved, problem in discrete mathematics. The conjecture states that if you start with a positive integer $n$ and apply the following rule to it:

• If the number ($n$) is even, divide it by two: $\frac{n}{2}$
• If the number ($n$) is odd, multiply it by 3 and add one: $3n + 1$

The number will eventually land in the cycle $4 \rightarrow 2 \rightarrow 1 \rightarrow 4$. The conjecture states: this the only cycle. There is no proof to confirm this, however, we have tested up to a very large number and the conjecture seems to hold. Thus, for all practical purposes: the conjecture is true.

The rule can be mathematically written as:

$f(n) = \begin{cases} \frac{n}{2} &\text{if } n \equiv 0 \text{ (mod 2)} \\ 3n + 1 &\text{otherwise} \end{cases}$

### Examples

$10$

• $5$
• $16$
• $8$
• $4$
• $2$
• $1$ (cycle starts)

$18$

• $9$
• $28$
• $14$
• $7$
• $22$
• $11$
• $34$
• $17$
• $52$
• $26$
• $13$
• $40$
• $20$
• $10$ (use above)

# Method

## Definitions

### Collatz Function

Define the Collatz function, $F$, as the Collatz conjecture with path of dividing by 2 compressed into one step, that is:

Given $x$, a positive odd integer:

$F(x) = \frac{3x + 1}{2^{\text{ctz}(3x + 1)}}$
• $\text{ctz}(x)$ gives the number of factors of 2 in a number, i.e. count the trailing zeros of a number in binary

### Collatz sequence and $k$

• The Collatz sequence, is the sequence of numbers produced by the Collatz function until it reaches the number $1$ for the first time
• Define $k$ as the number of steps until the Collatz series lands on $1$

In other words, the Collatz sequence can be shown mathematically like so:

$x, F_1(x), F_2(x), ..., F_{k-1}(x), 1$

## How to Divide: $\frac{m}{a}$

Let's multiply the Collatz function series by $a$, we get:

$ax, aF_1(x), aF_2(x), ..., aF_{k-1}(x), a$

Let $m = ax$, we get

\begin{aligned} a F(x) & = a \frac{3x + 1}{2^{\text{ctz}{(a(3x + 1))}}} \\ & = \frac{3ax + a}{2^{\text{ctz}{(3ax + a)}}} \\ & = \frac{3m + a}{2^{\text{ctz}{(3m + a)}}} \\ & = G(m) \end{aligned}

NOTES: $ctz(3m+a) = ctz(3m+1)$ when $a$ is odd

Assuming $a \mid m$ ($a$ divides $m$), we can:

1. Start with $m$
2. Use $G(m)$ until we get to $a$
• Record what we've done to get there
• i.e. save the result of $\text{ctz}(3x + 1)$ along the way and $k$ (the number of steps)
3. Backtrack using the same form of operations (in reverse) with $F(x)$ whilst starting at $1$

i.e. we have a division algorithm using the Collatz conjecture

## How to Multiply: $ax$

Now, how do we multiply? Simple:

• Start with $x$ and use $F(x)$ until we get to $1$
• Record what we've done (save the $k$ steps)
• Now, start with $a$ and backtrack with $G(x)$ (with the saved $k$ steps), which will get us to $ax$


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# How does one estimate theta in the Ho-Lee model from a yield curve?

I have a yield curve constructed using linear interpolation with data points every 3-months for US treasuries.

I would like to use that calibrate a Ho-Lee model, but I can't wrap my head around how to calibrate theta.

Is there any implementation that I could use (preferably matlab, r or c++) or a detailed description of the algorithm that I could use for reference? I have found some notes on the optimal form of theta*, but it's described in continuous rather than discrete terms, so it's of limited use in my case.

Given the Ho-Lee interest rate model of the form \begin{align*} dr_t = \theta_t dt + \sigma dW_t, \end{align*} the price at time $t>0$ of a zero-coupon bond, with maturity $T$ and unit face, has the form \begin{align*} B(t, T) &=E\Big(e^{-\int_t^T r_s ds} \mid r_t \Big)\\ &=e^{-(T-t)r_t - \int_t^T (T-u)\theta_u du + \frac{\sigma^2}{6}(T-t)^3}. \end{align*} See this question for the details. In particular, \begin{align*} B(0, t) = e^{t\, r_0 - \int_0^t(t-u)\theta_u du + \frac{\sigma^2}{6}t^3}. \end{align*} Moreover, \begin{align*} \theta_t = \sigma^2 t - \frac{\partial^2 \ln B(0, t)}{\partial t^2}, \end{align*} which can be computed piecewise-analytically based on the interpolation scheme of the yield curve.


text:
## Discrepancy between GD-by-GD and GD-by-SGD

The ICLR deadline is approaching, and of course, it’s time to write a short blog post that has absolutely nothing to do with any of my manuscripts in preparation. i’d like to thank Ed Grefenstette, Tim Rocktäschel and Phu Mon Htut for fruitful discussion. Let’s consider the following meta-optimization objective function: $$\mathcal{L}'(D’; \theta_0 – \eta \nabla_{\theta} \mathcal{L}(D; \theta_0))$$ which we want to minimize w.r.t. θ₀. it has become popular recently thanks to the success of MAML and its earlier and more recent variants to use gradient descent to minimize such a meta-optimization objective function. the gradient can be written down as* \nabla_{\theta_0} \mathcal{L}'(D’; \theta_0 – \eta \nabla_\theta \mathcal{L}(D; \theta_0) =

## BERT has a Mouth and must Speak, but it is not an MRF

Update on June 9 2021: i still don’t know the fate of the hypothetical manuscript by Chandel et al., but i’ve noticed that Kartik Goyal, Chris Dyer & Taylor Berg-Kirkpatrick fixed this issue (https://arxiv.org/abs/2106.02736) in this blog post by using BERT’s conditional as a proposal distribution in Metropolis-Hastings, to sample from the distribution defined using the potentials defined by the BERT’s single-token conditionals’ logits. It was pointed out by our colleagues at NYU, Chandel, Joseph and Ranganath, that there is an error in the recent technical report <BERT has a Mouth, and It Must Speak: BERT as a Markov Random Field Language Model> written

## Are we ready for self-driving cars?

Last Monday (April 29), I had an awesome experience of having been invited and participating in the debate event organized by the Review and Debates at NYU (http://www.thereviewatnyu.com/). By being born and raised in South Korea, I can confidently tell you that i cannot remember a single moment where I participated in any kind of formal debate nor a single chance in which i was taught how to make an argument for or against any specific topic. My mom often tells me I draw way too gloomy picture of Korean K-12 education I had, but it is true that our

## On the causality view of “Context-Aware Learning for Neural Machine Translation”

[Notice: what an unfortunate timing! This post is definitely NOT an april fool’s joke.] Sebastien Jean and I had a paper titled <context-aware learning for neural machine translation> rejected from NAACL’19, perhaps understandable because we did not report any substantial gain in the BLEU score. As I finally found some time to read Pearl’s <Book of Why> due to a personal reason  (yes, personal reasons sometimes can help), I thought I wrote a short note on how the idea in this paper was originally motivated. As I was never educated in causal inference or learning, I was scared of using a term

## Lecture note “Brief Introduction to Machine Learning without Deep Learning”

This past Spring (2017), I taught the undergrad <Intro to Machine Learning> course. This was not only the first time for me to teach <Intro to Machine Learning> but also the first time for me to teach an undergrad course (!) This course was taught a year before by David Sontag who has now moved to MIT. Obviously, I thought about re-using David’s materials as they were, which you can find at http://cs.nyu.edu/~dsontag/courses/ml16/. These materials are really great, and the coverage of various topics in ML is simply amazing. I highly recommend all the materials on this web page. All the things


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# Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3 - Mathematics

Sum

Find the sum of all natural numbers between 250 and 1000 which are exactly divisible by 3

#### Solution

Clearly, the numbers between 250 and 1000 which are divisible by 3 are 252, 255, 258, …., 999.

This is an A.P. with first term a = 252, common difference = 3 and last term = 999.

Let there be n terms in this A.P. Then,

⇒ an = 999

⇒ a + (n – 1)d = 999

⇒ 252 + (n – 1) × 3 = 999 ⇒ n = 250

∴ Required sum = S_n = \frac { n }{ 2 } [a + l]

= \frac { 250 }{ 2 } [252 + 999] = 156375

Concept: Sum of First n Terms of an AP
Is there an error in this question or solution?


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# Difference between Subspace topology and Ordered topology…

Recently I am started reading Topology by James R.Munkers Second edition.Right now I study The Subspace topology point and Can't understand the differences between subspace topology and Ordered topology especially the example 2 and example 3. I think with the basis element of topology we can make difference,I am right or wrong ?

• What exact lines in this copy are you asking about? – Lee Mosher Apr 22 '16 at 13:32
• In example 2 Set Y is open in the subspace topology but not open in order topology I can't get the idea – Prabhakaran Apr 22 '16 at 13:36
• It is explained in the sentence "Any basis element for the order topology on $Y$ that contains $2$...". – Lee Mosher Apr 22 '16 at 13:41

He first shows--explicitly using the definition of "subspace topology"--that $\{2\}$ is open in the subspace topology.
He then shows that $\{2\}$ is not open in the order topology. This part is slightly more round-about. He intends to do this by showing that any open set in the order topology that contains $2$ must also contain other points, which then establishes that $\{2\}$ cannot be an open set in the order topology. To accomplish this, he makes use of the (unstated here) fact that if you have an open set that contains $2,$ then you must also have a basic open set that contains $2,$ since any open set (this now being true for any topology) is a union of basic open sets. (If, from among the basic open sets whose union is the given open set, you don't have one of them that contains the element $2,$ then the union isn't going to contain the element $2$ either.) OK, so from our assumption that we have an open set (in the order topology) that contains $2,$ it follows that this open set has as a subset a basic open set that contains the element $2.$ Munkres shows that any basic open set that contains the element $2$ must contain other points (this is pretty much all he says, the rest I've said is for the reader to fill in), and from what I said previously this implies that the open set we started with must contain points other than $2,$ which is what we wanted to show in order to show that $\{2\}$ is not open in the order topology.
In Example 2, the reason why the set $Y$ is not open in the order topology is explained in the sentence "Any basis element for the order topology on $Y$ that contains $2$..."
Perhaps some extra words in the final clause of that sentence might help: "... such a set necessarily contains points of $Y$ less than $2$, namely the points in the interval $(a,1)$."


text:
Signaling game

(Redirected from Signaling games)
An extensive form representation of a signaling game

In game theory, a signaling game is a simple type of a dynamic Bayesian game. [1]

It is a game with two players, called the sender (S) and the receiver (R):

• The sender can have one of several types. The sender's type, t, determines the payoff function of the sender. It is the private information of the sender - it is not known to the receiver.
• The receiver has only a single type, so his payoff function is known to both players.

The game has two steps:

• The sender plays in the first step. He can play one of several actions, which are called "messages". The set of possible messages is M = {m1, m2, m3,..., mj}.
• The receiver plays in the second step, after viewing the sender's message. The set of possible actions is A = {a1, a2, a3,...., ak}.

The two players receive payoffs dependent on the sender's type, the message chosen by the sender and the action chosen by the receiver.[2][3]

Perfect Bayesian equilibrium

The equilibrium concept that is relevant for signaling games is Perfect Bayesian equilibrium - a refinement of both Bayesian Nash equilibrium and subgame-perfect equilibrium.

A sender of type ${\displaystyle t_{j}}$ sends a message ${\displaystyle m^{*}(t_{j})}$ in the set of probability distributions over M. (${\displaystyle m(t_{j})}$ represents the probabilities that type ${\displaystyle t_{j}}$ will take any of the messages in M.) The receiver observing the message m takes an action ${\displaystyle a^{*}(m)}$ in the space of probability distributions over A.

A game is in perfect Bayesian equilibrium if it meets all four of the following requirements:

• The receiver must have a belief about which types can have sent message m. These beliefs can be described as a probability distribution ${\displaystyle \mu (t_{i}|m)}$, the probability that the sender has type ${\displaystyle t_{i}}$ if he chooses message ${\displaystyle m}$. The sum over all types ${\displaystyle t_{i}}$ of these probabilities has to be 1 conditional on any message m.
• The action the receiver chooses must maximize the expected utility of the receiver given his beliefs about which type could have sent message ${\displaystyle m}$, ${\displaystyle \mu (t|m)}$. This means that the sum ${\displaystyle \sum _{t_{i}}\mu (t_{i}|m)U_{R}(t_{i},m,a)}$ is maximized. The action ${\displaystyle a}$ that maximizes this sum is ${\displaystyle a^{*}(m)}$.
• For each type, ${\displaystyle t}$, the sender chooses to send the message ${\displaystyle m^{*}}$ that maximizes the sender's utility ${\displaystyle U_{S}(t,m,a^{*}(m))}$ given the strategy chosen by the receiver, ${\displaystyle a^{*}}$.
• For each message ${\displaystyle m}$ the sender can send, if there exists a type ${\displaystyle t}$ such that ${\displaystyle m^{*}(t)}$ assigns strictly positive probability to ${\displaystyle m}$ (i.e. for each message which is sent with positive probability), the belief the receiver has about the type of the sender if he observes message ${\displaystyle m}$, ${\displaystyle \mu (t|m)}$ satisfies Bayes' rule: ${\displaystyle \mu (t|m)=p(t)/\sum _{t_{i}}p(t_{i})}$

The perfect Bayesian equilibria in such a game can be divided in three different categories: pooling equilibria, separating equilibria and semi-separating

• A pooling equilibrium is an equilibrium where senders with different types all choose the same message. This means that the sender's message does not give any information to the receiver, so the receiver's beliefs are not updated after seeing the message.
• A separating equilibrium is an equilibrium where senders with different types always choose different messages. This means that the sender's message always reveals the sender's type, so the receiver's beliefs become deterministic after seeing the message.
• A semi-separating (also called partial-pooling) equilibrium is an equilibrium where some types of senders choose the same message and other types choose different messages.

Note that, if there are more types of senders than there are messages, the equilibrium can never be a separating equilibrium (but may be semi-separating equilibria). There are also hybrid equilibria, in which the sender randomizes between pooling and separating.

Examples

Reputation game

Sane, Prey P1+P1, D2 P1+M1, 0
Sane, Accommodate D1+D1, D2 D1+M1, 0
Crazy, Prey X1, P2 X1, 0

In this game,[1]:326-329[4] the sender and the receiver are firms. The sender is an incumbent firm and the receiver is an entrant firm.

• The sender can be one of two types: Sane or Crazy. A sane sender can send one of two messages: Prey and Accommodate. A crazy sender can only Prey.
• The receiver can do one of two actions: Stay or Exit.

The payoffs are given by the table at the right. We assume that:

• M1>D1>P1, i.e, a sane sender prefers to be a monopoly (M1), but if it is not monopoly, it prefers to accommodate (D1) than to prey (P1). Note that the value of X1 is irrelevant since a Crazy firm has only one possible action.
• D2>0>P2, i.e, the receiver prefers to stay in a market with a sane competitor (D2) than to exit the market (0), but prefers to exit than to be stay in a market with a crazy competitor (P2).
• Apriori, the sender has probability p to be sane and 1-p to be crazy.

We now look for perfect Bayesian equilibria. It is convenient to differentiate between separating equilibria and pooling equilibria.

• A separating equilibrium, in our case, is one in which the sane sender always accommodates. This separates it from a crazy sender. In the second period, the receiver has complete information, and his best strategy is: "If Accommodate then Stay, if Prey then Exit". The payoff of the sender when he accommodates is D1+D1, but if he deviates to Prey his payoff changes to P1+M1; therefore, a necessary condition for a separating equilibrium is D1+D1≥P1+M1. It is possible to show that this condition is also sufficient.
• A pooling equilibrium is one in which the sane sender always preys. In the second period, the receiver has no new information: he still believes that the sender is sane with probability p and crazy with probability 1-p. Therefore, the receiver's expected payoff if he stays is: [p D2 + (1-p) P2]; the receiver stays if-and-only-if this expression is positive. The sender can gain from preying, only if the receiver exits. Therefore, a necessary condition for a pooling equilibrium is p D2 + (1-p) P2 ≤ 0. It is possible to show that, if D1+D1<P1+M1 (so there is no separating equilibrium), this condition is also sufficient.

To summarize:

• If preying is costly for a sane sender (D1+D1≥P1+M1), he will accommodate and there will be a separating PBE.
• If preying is not too costly for a sane sender but harmful for the receiver (p D2 + (1-p) P2 ≤ 0), the sender will prey and there will be a pooling PBE. The sender is willing to lose some value by preying in the first period, in order to build a reputation of a predatory firm, and convince the receiver to exit.
• If preying is not costly for the sender nor harmful for the receiver, there will be a unique hybrid PBE - both the sender and the receiver will randomize between their two actions.

Education game

This game was first presented by Michael Spence.[5][1]:329-331 In this game, the sender is a worker and the receiver is an employer.

• The worker can be one of two types: Wise (with probability p) or Dumb (with probability 1-p). Each type can select his level of education, e.g. GoToCollege or StayAtHome. Going to college has a cost; the cost is lower for a wise worker than for a dumb one.
• The employer has to decide how much salary to offer the worker. The goal of the employer is to offer a high salary to a Wise worker and a low salary to a Dumb worker. However, the employer does not know the true talent of the worker - only his level of education.

In this model it is assumed that the level of education does not influence the productivity of the worker; it is used only as a signal regarding the worker's talent.

To summarize: only workers with high ability are able to attain a specific level of education without it being more costly than their increase in wage. In other words, the benefits of education are only greater than the costs for workers with a high level of ability, so only workers with a high ability will get an education.

Applications of signaling games

Signaling games describe situations where one player has information the other player does not have. These situations of asymmetric information are very common in economics and behavioral biology.

Philosophy

The first known use of signaling games occurs in David K. Lewis' Ph. D. dissertation (and later book) Convention.[6] Replying to W.V.O. Quine,[7][8] Lewis attempts to develop a theory of convention and meaning using signaling games. In his most extreme comments, he suggests that understanding the equilibrium properties of the appropriate signaling game captures all there is to know about meaning:

I have now described the character of a case of signaling without mentioning the meaning of the signals: that two lanterns meant that the redcoats were coming by sea, or whatever. But nothing important seems to have been left unsaid, so what has been said must somehow imply that the signals have their meanings.[9]

The use of signaling games has been continued in the philosophical literature. Others have used evolutionary models of signaling games to describe the emergence of language. Work on the emergence of language in simple signaling games includes models by Huttegger,[10] Grim, et al.,[11] Skyrms,[12][13] and Zollman.[14] Harms,[15][16] and Huttegger,[17] have attempted to extend the study to include the distinction between normative and descriptive language.

Economics

The first application of signaling games to economic problems was Michael Spence's #Education game. A second application was the #Reputation game.

Biology

Valuable advances have been made by applying signaling games to a number of biological questions. Most notably, Alan Grafen's (1990) handicap model of mate attraction displays.[18] The antlers of stags, the elaborate plumage of peacocks and bird-of-paradise, and the song of the nightingale are all such signals. Grafen’s analysis of biological signaling is formally similar to the classic monograph on economic market signaling by Michael Spence.[19] More recently, a series of papers by Getty[20][21][22][23] shows that Grafen’s analysis, like that of Spence, is based on the critical simplifying assumption that signalers trade off costs for benefits in an additive fashion, the way humans invest money to increase income in the same currency. This assumption that costs and benefits trade off in an additive fashion might be valid for some biological signaling systems, but is not valid for multiplicative tradeoffs, such as the survival cost – reproduction benefit tradeoff that is assumed to mediate the evolution of sexually selected signals.

Charles Godfray (1991) modeled the begging behavior of nestling birds as a signaling game.[24] The nestlings begging not only informs the parents that the nestling is hungry, but also attracts predators to the nest. The parents and nestlings are in conflict. The nestlings benefit if the parents work harder to feed them than the parents ultimate benefit level of investment. The parents are trading off investment in the current nestlings against investment in future offspring.

Pursuit deterrent signals have been modeled as signaling games.[25] Thompson's gazelles are known sometimes to perform a 'stott', a jump into the air of several feet with the white tail showing, when they detect a predator. Alcock and others have suggested that this action is a signal of the gazelle's speed to the predator. This action successfully distinguishes types because it would be impossible or too costly for a sick creature to perform and hence the predator is deterred from chasing a stotting gazelle because it is obviously very agile and would prove hard to catch.

The concept of information asymmetry in molecular biology has long been apparent.[26] Although molecules are not rational agents, simulations have shown that through replication, selection, and genetic drift, molecules can behave according to signaling game dynamics. Such models have been proposed to explain, for example, the emergence of the genetic code from an RNA and amino acid world.[27]

Costly versus cost-free signaling

One of the major uses of signaling games both in economics and biology has been to determine under what conditions honest signaling can be an equilibrium of the game. That is, under what conditions can we expect rational people or animals subject to natural selection to reveal information about their types?

If both parties have coinciding interest, that is they both prefer the same outcomes in all situations, then honesty is an equilibrium. (Although in most of these cases non-communicative equilbria exist as well.) However, if the parties' interests do not perfectly overlap, then the maintenance of informative signaling systems raises an important problem.

Consider a circumstance described by John Maynard Smith regarding transfer between related individuals. Suppose a signaler can be either starving or just hungry, and she can signal that fact to another individual which has food. Suppose that she would like more food regardless of her state, but that the individual with food only wants to give her the food if she is starving. While both players have identical interests when the signaler is starving, they have opposing interests when she is only hungry. When the signaler is hungry she has an incentive to lie about her need in order to obtain the food. And if the signaler regularly lies, then the receiver should ignore the signal and do whatever he thinks best.

Determining how signaling is stable in these situations has concerned both economists and biologists, and both have independently suggested that signal cost might play a role. If sending one signal is costly, it might only be worth the cost for the starving person to signal. The analysis of when costs are necessary to sustain honesty has been a significant area of research in both these fields.

References

1. ^ a b c Subsection 8.2.2 in
2. ^ Gibbons, Robert (1992). A Primer in Game Theory. New York: Harvester Wheatsheaf. ISBN 0-7450-1159-4.
3. ^ Osborne, M. J. & Rubenstein, A. (1994). A Course in Game Theory. Cambridge: MIT Press. ISBN 0-262-65040-1.
4. ^ which is a simplified version of a reputation model suggested in 1982 by Kreps, Wilson, Milgrom and Roberts
5. ^ Spence, A. M. (1973). "Job Market Signaling". Quarterly Journal of Economics. 87 (3): 355–374. doi:10.2307/1882010.
6. ^ Lewis, D. (1969). Convention. A Philosophical Study. Cambridge: Harvard University Press.
7. ^ Quine, W. V. O. (1936). "Truth by Convention". Philosophical Essays for Alfred North Whitehead. London: Longmans, Green & Co. pp. 90–124. ISBN 0-8462-0970-5. (Reprinting)
8. ^ Quine, W. V. O. (1960). "Carnap and Logical Truth". Synthese. 12 (4): 350–374. doi:10.1007/BF00485423.
9. ^ Lewis (1969), p. 124.
10. ^ Huttegger, S. M. (2007). "Evolution and the Explanation of Meaning". Philosophy of Science. 74 (1): 1–24. doi:10.1086/519477.
11. ^ Grim, P.; Kokalis, T.; Alai-Tafti, A.; Kilb, N.; St. Denis, Paul (2001). "Making Meaning Happen". Technical Report #01-02. Stony Brook: Group for Logic and Formal Semantics SUNY, Stony Brook.
12. ^ Skyrms, B. (1996). Evolution of the Social Contract. Cambridge: Cambridge University Press. ISBN 0-521-55471-3.
13. ^ Skyrms, B. (2010). Signals Evolution, Learning & Information. New York: Oxford University Press. ISBN 978-0-19-958082-8.
14. ^ Zollman, K. J. S. (2005). "Talking to Neighbors: The Evolution of Regional Meaning". Philosophy of Science. 72 (1): 69–85. doi:10.1086/428390.
15. ^ Harms, W. F. (2000). "Adaption and Moral Realism". Biology and Philosophy. 15 (5): 699–712. doi:10.1023/A:1006661726993.
16. ^ Harms, W. F. (2004). Information and Meaning in Evolutionary Processes. Cambridge: Cambridge University Press. ISBN 0-521-81514-2.
17. ^ Huttegger, S. M. (2005). "Evolutionary Explanations of Indicatives and Imperatives". Erkenntnis. 66 (3): 409–436. doi:10.1007/s10670-006-9022-1.
18. ^ Grafen, A. (1990). "Biological signals as handicaps". Journal of Theoretical Biology. 144 (4): 517–546. doi:10.1016/S0022-5193(05)80088-8. PMID 2402153.
19. ^ Spence, A. M. (1974). Market Signaling: Information Transfer in Hiring and Related Processes. Cambridge: Harvard University Press.
20. ^ Getty, T. (1998). "Handicap signalling: when fecundity and viability do not add up". Animal Behaviour. 56 (1): 127–130. doi:10.1006/anbe.1998.0744. PMID 9710469.
21. ^ Getty, T. (1998). "Reliable signalling need not be a handicap". Animal Behaviour. 56 (1): 253–255. doi:10.1006/anbe.1998.0748. PMID 9710484.
22. ^ Getty, T. (2002). "Signaling health versus parasites". The American Naturalist. 159 (4): 363–371. doi:10.1086/338992. PMID 18707421.
23. ^ Getty, T. (2006). "Sexually selected signals are not similar to sports handicaps". Trends in Ecology & Evolution. 21 (2): 83–88. doi:10.1016/j.tree.2005.10.016.
24. ^ Godfray, H. C. J. (1991). "Signalling of need by offspring to their parents". Nature. 352 (6333): 328–330. doi:10.1038/352328a0.
25. ^ Yachi, S. (1995). "How can honest signalling evolve? The role of the handicap principle". Proceedings of the Royal Society of London B. 262 (1365): 283–288. doi:10.1098/rspb.1995.0207.
26. ^ John Maynard Smith. (2000) The Concept of Information in Biology. Philosophy of Science. 67(2):177-194
27. ^ Jee, J.; Sundstrom, A.; Massey, S.E.; Mishra, B. (2013). "What can information-asymmetric games tell us about the context of Crick's 'Frozen Accident'?". Journal of the Royal Society Interface. 10 (88): 20130614. doi:10.1098/rsif.2013.0614. PMC 3785830. PMID 23985735.


text:
Limited access

A ball is tossed from the top of a building with speed $v_0$ at an angle $\theta$ above the horizontal. Another ball is tossed from the top of the same building with speed $v_0$ at the same angle $\theta$ below the horizontal.

Let $t_1$ and $t_2$ be their times of flight and let $v_1$ and $v_2$ be the velocities of the two balls when they strike the ground.

Which of the following is TRUE?

A

$t_1>t_2$
$v_1= v_2$

B

$t_1= t_2$
$v_1= v_2$

C

$t_1> t_2$
$v_1> v_2$

D

$t_1< t_2$
$v_1= v_2$

E

$t_1>t_2$
$v_1< v_2$

Select an assignment template


text:
# Limit Switch problems on RAMPS 1.4 and custom built 3D Printer running Marlin 1.1.0-rc6

So I am trying to fix a custom built 3D printer for my institute and am running into a problem I can't wrap my head around.

So the limit switches for Y-axis and Z-Axis work just fine, but the X-Axis does not.

All three switches are Makerbot (3-pin), and all three light up the LED when they get pressed. However the X-axis does not get recognized by Marlin. When I diagnose with M119 command it does not show as triggered even though the LED is on. All the other ones do.

All three switches are connected to min (X-min, Y-min, and Z-min).

Could this be a firmware problem? Or perhaps my RAMPS 1.4 has burned out the X-axis signaling? (I doubt this because the LED on the switch still turns on).

Let me know if you need any more info to diagnose the problem.

P.S. I have also replaced the X-Axis limit switch with a brand new one and the same result happens: LED turns on upon activation but it doesn't get recognized by the machine.

Considering you're having issues with the board, and the limit switches appear to be registering, but the board isn't doing anything about it, a first good step would be to update the firmware to 1.1.9 as @0scar states. If the update in the firmware doesn't do the trick, then move on to doing as he suggests with changing the Xmax/min stuff around. This just seems like a good first logical step to getting it fixed.

To rule out problem with the switches itself, you can change the Z-min and swap it with the Y- or Z-min. Once you found out that you get the same issues you know that your X endstop module is working (unless they both are faulty, but the odds are small for that), but the signal change is not registered by the board. This could be a faulty port/pin of the X-min port / attached microprocessor pin. What you could do to try to diagnose that is using the X-max header on the board. In order to use that header for X-min, you need to change some code in pins_RAMPS.h, change:

//
// Limit Switches
//
#define X_MIN_PIN           3
#ifndef X_MAX_PIN
#define X_MAX_PIN         2
#endif

to:

//
// Limit Switches
//
#define X_MIN_PIN           2
#ifndef X_MAX_PIN
#define X_MAX_PIN         3
#endif

Recompile and upload. Please use the latest sources, 1.1.9, 1.1.0 is very old.

• very old doesn't mean that don't work, I have 2 3D printers with 1.1.0 working fine. – Fernando Baltazar May 30 '19 at 6:23
• @FernandoBaltazar Very true, but considering the many changes since 1.1.0 it is way more easy to get support as most people tinkering are using newer versions. Also newer releases contain bug fixes. – 0scar May 30 '19 at 7:14


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# MAPPING THE $OH + CO \leftrightarrow HOCO$ REACTION PATHWAY THROUGH INFRARED SPECTROSCOPY OF THE OH-CO REACTANT COMPLEX

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/20166

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 Title: MAPPING THE $OH + CO \leftrightarrow HOCO$ REACTION PATHWAY THROUGH INFRARED SPECTROSCOPY OF THE OH-CO REACTANT COMPLEX Creators: Pond, Bethany V.; Marshall, Mark D.; Lester, Marsha I. Issue Date: 2001 Publisher: Ohio State University Abstract: A hydrogen-bonded OH-CO complex has been identified along the reaction coordinate for the $OH + CO \leftrightarrow HOCO \rightarrow H + CO_{2}$ reaction. The vibrational spectrum of the OH-CO complex has been examined in the OH overtone region at $1.4 \mu m$ using infrared action spectroscopy, which relies on detection of $OH (v = 1)$ fragments from vibrational predissociation by laser-induced fluorescence. The observed infrared spectrum of OH-CO consists of the pure OH overtone band at $6941.7 cm^{-1}$ and combination bands involving the simultaneous excitation of OH stretch and intermolecular vibrations, which appear 50 to $250 cm^{-1}$ higher in energy than the pure overtone. The rotational structure of the pure overtone band is indicative of a parallel transition of a linear OH-CO complex having a $P = 3/2$ projection of the total angular momentum on the intermolecular axis, which arises from the unquenched electronic angular momentum of OH. The OH-CO binding energy, $D_{0} \leq 430 cm^{-1}$, is also established from the quantum state distribution of the OH fragments following pure overtone excitation. The strongest combination bands with 51.1, 57.1, and $247.3 cm^{-1}$ of intermolecular energy are attributed to geared bend and H-atom bend excitation, which are the modes that drive the transformation from OH-CO to HOCO. These combination bands exhibit rotational structures that are characteristic of perpendicular transitions $(\Delta P = \pm 1)$ to states with vibrational angular momentum from the bending motions of the complex. A complete analysis of the experimental results promises to yield a spectroscopic quality characterization of the $OH + CO \rightarrow HOCO$ reaction pathway. $^{a}$Permanant address: Department of Chemistry, Amherst College, Amherst, MA 01002-5000 Description: Author Institution: University of Pennsylvania; Department of Chemistry, University of Pennsylvania URI: http://hdl.handle.net/1811/20166 Other Identifiers: 2001-RH-02