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# Curve25519 extension field

The paper regarding curve25519 presents a theorem in chapter 2 (specification). The extension field $$F_{p^2}$$ is used in this theorem. I don't understand why this extension field is needed for the curve25519. This is how far I got:

The theorem implies that for some elliptic curves $$E$$ exists a unique $$s \in F_p$$ for every point multiplication $$n \cdot Q$$ ($$s$$ is the x-value of the resulting point). Point multiplication can be done using the Montgomery Ladder. Curve25519 has a base point $$P = (9,y)$$, where $$y$$ is not used in the Montgomery Ladder. Because $$P$$ is a point on the Curve, the point multiplication $$P' = n \cdot P$$ has also to be a point on the curve. Now one can multiply another scalar with $$P'$$ which again results to point on the elliptic curve. In this context, only $$F_p$$ should be needed for the curve25519.

Hence, I think that the extension field is only used, if you consider the point multiplication for all point $$Q = (q,r)$$ for every $$q \in F_p$$. That means $$Q \notin E(F_p)$$ but $$Q \in E(F_{p^2})$$. I don't understand why this case in considered, when it is never used.

I don't really know so I'll tell you my best guess: One of the design goals was "free point validation". To do this, we want to make sure that no matter what $$x$$-value in $$F_p$$ we're sent, it is a valid point on the curve.
If $$x\in F_p$$, then to make an elliptic curve point we need $$y$$ such that $$y^2=x^3+488862x^2+x$$. But we have no reason to expect that $$x^3+488862x^2+x$$ will be a quadratic residue, so in general we will need to define $$y$$ over $$F_{p^2}$$. Thus, if I send you any value $$x$$ in $$F_p$$ and tell you it's a point on the curve, you know that there is some $$y\in F_{p^2}$$ such that $$(x,y)\in E(F_{p^2})$$, but you have no guarantee that $$y\in F_p$$.
The key exchange uses $$x$$-only arithmetic, so the key exchange will never need to use the extension field in any computations. Theorem 2.1 tells us that all multiples of a point with an $$x$$-value in $$F_p$$ will also have $$x$$-values in $$F_p$$, which proves correctness of the $$x$$-only arithmetic, more or less. So I think the case of $$Q\in E(F_{p^2})$$ but $$Q\notin E(F_p)$$ is used, but only via an implicitly-defined $$y$$-value.


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# zbMATH — the first resource for mathematics

Sandwiched singularities and desingularization of surfaces by normalized Nash transformations. (English) Zbl 0719.14005
For complex algebraic surfaces, this paper provides the final step in the proof of the conjecture (due to John Nash, about 30 years ago) that the singularities of an algebraic variety can be resolved by a finite succession of proper birational maps $$\mu$$ : $$\bar S\to S$$, $$\mu^*\Omega_{S/k}/$$torsion locally free of rank dim(S) and $$\mu$$ universal with respect to that property (so called “Nash transformations”). It is known by A. Nobile [Pac. J. Math. 60, 297-305 (1975; Zbl 0324.32012)] that (in characteristic 0) $$\mu$$ is an isomorphism iff S is nonsingular, and in particular, for plane curve singularities the conjecture is true. G. González-Sprinberg [Ann. Inst. Fourier 32, No.2, 111-178 (1982; Zbl 0469.14019)] proved for complex surfaces, that normalized Nash transformations resolve rational double points and cyclic quotient singularities. By a theorem of H. Hironaka, any surface singularity is transformed by a finite succession of Nash transformations into “sandwiched singularities”, i.e. singularities of a surface which birationally dominates a nonsingular surface.
The main theorem of the article under review states that sandwiched singularities are resolved by normalized Nash transformations, thus completing the proof of the above mentioned conjecture for $$\dim(S)=2$$, $$k={\mathbb{C}}.$$
Chapter II of the paper gives a classification of sandwiched singularities, a problem which is shown to be equivalent to the classification of plane curve singularities, complete ideals in 2- dimensional regular local rings or valuations with center in a regular 2- dimensional local ring [partially, this is an overview of results of the same author, cf. Am. J. Math. 112, No.1, 107-156 (1990; Zbl 0716.13003)].
In chapter III, the main theorem is proved in two steps: First of all, minimal singularities are considered, i.e. here: rational surface singularities with reduced fundamental cycle. If $$(S,\xi)$$ is such a singularity, $$\Gamma$$ its dual graph and $$\mu:S'\to S$$ the normalized Nash transformation, $$\Gamma '_ i$$ the dual graphs of the singularities of $$S'$$, then $$\#\{$$vertices of $$\Gamma'_ i\}\leq \#\{$$vertices of $$\Gamma\},$$ i.e. such procedure terminates after finitely many steps. The proof is completed by showing that the problem can be reduced to minimal singularities, i.e. any sandwiched singularity is transformed into a minimal one after finitely many normalized Nash transformations.
Reviewer: M.Roczen (Berlin)

##### MSC:
 14E15 Global theory and resolution of singularities (algebro-geometric aspects) 32S45 Modifications; resolution of singularities (complex-analytic aspects) 14B05 Singularities in algebraic geometry 14J17 Singularities of surfaces or higher-dimensional varieties 14H20 Singularities of curves, local rings
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# Lectio Magistralis - Hector J. Sussmann - The Maximum Principle for systems of flows

## Mercoledi' 21 Febbraio ore 11.00 Aula 1C150 - Torre Archimede

ARGOMENTI: Seminari

Il giorno 21 Febbraio 2018, alle ore 11:00,
in aula 1C150 del il Dipartimento di Matematica "Tullio Levi-Civita"

il Prof. Hector J. Sussmann , della Rutgers University,

terrà una LECTIO MAGISTRALIS dal titolo

The Maximum Principle for systems of flows

Gli interessati sono cordialmente invitati a partecipare. La conferenza sarà di carattere generale.

Astratto: The maximum principle (MP) of optimal control theory is usually formulated
in terms of vector fields. But the key point that makes the proof of the MP work
is that the vector fields give rise to flows.On the other hand, flows may have all the
properties needed for the MP to work even if they are not generated by nice vector fields.
So we suggest that a formulation of the MP in terms of flows is preferable, and we argue that such a
formulation has several advantages, such as the possibility of deriving a version of
the MP for hybrid systems.


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# Java VM Options You Should Always Use in Production

This post is a cheatsheet with enumeration of options, which should be always used to configure Java Virtual Machine for Web-oriented server applications (i.e. Web Front-End) in production or production-like environments.

For lazy readers full listing is here (for curious detailed explanation is provided below):

• Java < 8
    -server
-Xms<heap size>[g|m|k] -Xmx<heap size>[g|m|k]
-XX:PermSize=<perm gen size>[g|m|k] -XX:MaxPermSize=<perm gen size>[g|m|k]
-Xmn<young size>[g|m|k]
-XX:SurvivorRatio=<ratio>
-XX:+UseConcMarkSweepGC -XX:+CMSParallelRemarkEnabled
-XX:+UseCMSInitiatingOccupancyOnly -XX:CMSInitiatingOccupancyFraction=<percent>
-XX:+ScavengeBeforeFullGC -XX:+CMSScavengeBeforeRemark
-XX:+PrintGCDateStamps -verbose:gc -XX:+PrintGCDetails -Xloggc:"<path to log>"
-XX:+UseGCLogFileRotation -XX:NumberOfGCLogFiles=10 -XX:GCLogFileSize=100M
-XX:+HeapDumpOnOutOfMemoryError -XX:HeapDumpPath=<path to dump>date.hprof
-Djava.rmi.server.hostname=<external IP>
-Dcom.sun.management.jmxremote.port=<port>
-Dcom.sun.management.jmxremote.authenticate=false
-Dcom.sun.management.jmxremote.ssl=false

• Java >= 8
    -server
-Xms<heap size>[g|m|k] -Xmx<heap size>[g|m|k]
-XX:MaxMetaspaceSize=<metaspace size>[g|m|k]
-Xmn<young size>[g|m|k]
-XX:SurvivorRatio=<ratio>
-XX:+UseConcMarkSweepGC -XX:+CMSParallelRemarkEnabled
-XX:+UseCMSInitiatingOccupancyOnly -XX:CMSInitiatingOccupancyFraction=<percent>
-XX:+ScavengeBeforeFullGC -XX:+CMSScavengeBeforeRemark
-XX:+PrintGCDateStamps -verbose:gc -XX:+PrintGCDetails -Xloggc:"<path to log>"
-XX:+UseGCLogFileRotation -XX:NumberOfGCLogFiles=10 -XX:GCLogFileSize=100M
-XX:+HeapDumpOnOutOfMemoryError -XX:HeapDumpPath=<path to dump>date.hprof
-Djava.rmi.server.hostname=<external IP>
-Dcom.sun.management.jmxremote.port=<port>
-Dcom.sun.management.jmxremote.authenticate=false
-Dcom.sun.management.jmxremote.ssl=false

### Make Server a Server

-server

Turns Java VM features specific to server applications, such as sofisticated JIT compiler. Though this option is implicitely enabled for x64 virtual machines, it still makes sence to use it as according to documentation behaviour maybe changed in the future.

-Xms<heap size>[g|m|k] -Xmx<heap size>[g|m|k]

To avoid dynamic heap resizing and lags, which could be caused by this, we explicitely specify minimal and maximal heap size. Thus Java VM will spend time only once to commit on all the heap.

-XX:PermSize=<perm gen size>[g|m|k] -XX:MaxPermSize=<perm gen size>[g|m|k]

Logic for permanent generation is the same as for overall heap — predefine sizing to avoid costs of dynamic changes. Not applicable to Java >= 8.

-XX:MaxMetaspaceSize=<metaspace size>[g|m|k]

By default Metaspace in Java VM 8 is not limited, though for the sake of system stability it makes sense to limit it with some finite value.

-Xmn<young size>[g|m|k]

Explicitely define size of the young generation.

-XX:SurvivorRatio=<ratio>

Ratio which determines size of the survivour space relatively to eden size. Ratio can be calculated using following formula:

### Make GC Right

-XX:+UseConcMarkSweepGC -XX:+CMSParallelRemarkEnabled

As response time is critical for server application concurrent collector fits best for Web applications. Unfortunatelly G1 is still not production ready, thus we have to use Concurrent Mark-Sweep collector.

-XX:+UseCMSInitiatingOccupancyOnly -XX:CMSInitiatingOccupancyFraction=<percent>

By default CMS GC uses set of heuristic rules to trigger garbage collection. This makes GC less predictable and usually tends to delay collection until old generation is almost occupied. Initiating it in advance allows to complete collection before old generation is full and thus avoid Full GC (i.e. stop-the-world pause). -XX:+UseCMSInitiatingOccupancyOnly prevent usage of GC heuristics. -XX:CMSInitiatingOccupancyFraction informs Java VM when CMS should be triggered. Basically, it allows to create a buffer in heap, which can be filled with data, while CMS is working. Thus percent should be back calculated from the speed in which memory is consumed in old generation during production load. Such percent should be chosen carefully, if it will be small — CMS will work to often, if it will be to big — CMS will be triggered too late and concurrent mode failure may occur. Usually -XX:CMSInitiatingOccupancyFraction should be at the level 70, which mean that application should utilize less that 70% of old generation.

-XX:+ScavengeBeforeFullGC -XX:+CMSScavengeBeforeRemark

Instructs garbage collector to collect young generation before doing Full GC or CMS remark phase and as a result improvde their performance due to absence of need to check references between young generation and tenured.

### GC Logging

-XX:+PrintGCDateStamps -verbose:gc -XX:+PrintGCDetails -Xloggc:"<path to log>"

These options make Java to log garbage collector activities into specified file. All records will be prepended with human readable date and time. Meanwhile you should avoid using -XX:+PrintGCTimeStamps as it will prepend record with useless timestamp since Java application start.

Generate log can be later analysed with GCViewer.

-XX:+UseGCLogFileRotation -XX:NumberOfGCLogFiles=10 -XX:GCLogFileSize=100M

GC log files rotation makes analysis of garbage collection problems easier, also it guaranties that disk is protected from space overconsumption.

### DNS Caching

-Dsun.net.inetaddr.ttl=<TTL in seconds>

Number of seconds during which DNS record will be cached in Java VM. Default behaviour of Java VM 6 was to cache forever, which does not fit server application needs, as you would not want to restart server each time, when IP has changed in DNS record. It has been changed in Java VM 7 to cache for 30 seconds, but only if security manager is not installed. Depending on version of Java VM and presence of security manager DNS records still can be cached infinitely. Commonly recommended option is to disable DNS caching at all, which can be reason for performance degradation. Requests to DNS are performed in synchorized block and only one request is performed in any point in time. Thus, if your application is havily utilizing network it will experience saturation on DNS requests, so TTL value 0 should never be used.

Better solution is to cache for reasonable not long period, for example 1 minute (60 seconds). This mean that system your application is interacting with have to guaranty that two different IPs will continue to work properly during this 1 minute, otherwise lower TTL value should be chosen. It should always be reasonable (not equal to 0) to prevent possible contention of requests to DNS.

This option is convinient to use, but networkaddress.cache.ttl specified in %JRE%/lib/security/java.security should be considered as better solution, at least from official documentation prospective.

### Dump on Out of Memory

-XX:+HeapDumpOnOutOfMemoryError -XX:HeapDumpPath=<path to dump>date.hprof

If your application would ever fail with out-of-memory in production, you would not want to wait for another chance to reproduce the problem. These options instruct Java VM to dump memory into file, when OOM occurred. It can cause considerable pauses on big heaps during OOM event. However, if Java VM is at OOM already, collecting as much information about the issue is more important than trying to serve traffic with completely broken application. We are also making sure the dump would be created with name unique per application start time (this is requeired because Java VM will fail to overwrite existing file).

### Make JMX work

-Djava.rmi.server.hostname=<external IP>

IP address, which would be embedded into RMI stubs sent to clients. Later clients will use this stubs to communicate with server via RMI. As in modern datacenters machine often has two IPs (internal and external) you would want explicitly specify which IP to use, otherwise JVM will make it’s own choice. Correct value of this property is a precondition for successfully using JMX.

-Dcom.sun.management.jmxremote.port=<port>
-Dcom.sun.management.jmxremote.authenticate=false
-Dcom.sun.management.jmxremote.ssl=false

-Dcom.sun.management.jmxremote option is not required starting from Java VM 6, however to make JMX available for remote access specific listen port should be provided. Later this port can be used to connect using any JMX tool (e.g. VisualVM or Java Mission Control).

Also to reduce additional troubles with connecting disable standard authentication, but be sure that only authorized users can connect to environment using firewall. If for security reasons you still want to control access via standard mechanism learn more.

### P.S.

Many options that were previously very useful with updates in Java VM (specifically release of Java 7) are preconfigured by default:

• -XX:+UseCompressedOops
• -Dsun.rmi.dgc.server.gcInterval=3600000 and -Dsun.rmi.dgc.client.gcInterval=3600000
• -Dcom.sun.management.jmxremote


text:
Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm

Bryan Ford <brynosaurus@gmail.com> Wed, 05 July 2017 16:29 UTC

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From: Bryan Ford <brynosaurus@gmail.com>
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Date: Wed, 5 Jul 2017 18:29:23 +0200
Cc: Daniel Slamanig <daniel.slamanig@tugraz.at>, cfrg@irtf.org
To: Thomas Garcia <tgarcia.3141@gmail.com>
References: <8AE29DD0-26FE-4AB6-A4A9-2BB9169BAB13@jovanovic.io> <11cc5d3f-ecf9-2fd0-825c-c8b441bd2813@tugraz.at> <A423CB6E-D649-4320-BB76-2E3783D6AFE0@gmail.com> <CAFTSWve-J9pKVAaCJ=F==ZP_6=f2QMR2chD+J0T7vF6SNb95Ow@mail.gmail.com>
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Subject: Re: [Cfrg] Internet-Draft: Collective Edwards-Curve Digital Signature Algorithm
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Hi Thomas,

> On Jul 5, 2017, at 3:27 PM, Thomas Garcia <tgarcia.3141@gmail.com> wrote:
>
> Hello,
> I have a number of comments regarding the draft.
> 1. In the described protocol the leader, after receiving commitments from the participants and calculating the challenge c, sends that challenge to the participants. The participants then do not verify that c was indeed calculated using the message that they intended to sign, allowing the leader to procure signatures for arbitrary messages. A stage of verification of c should be added to the protocol.

Oops, looks like that was an unfortunate omission that snuck into the first draft somehow.  Indeed, the cosigners definitely must not simply trust the leader to compute c correctly.  What section 5.1.3 should say is that the leader sends out the aggregate commitment R, which all participants use to compute c = SHA512(R || A || M) independently based on that R, ensuring that the responses they produced are only good for a particular message M they’ve seen and approved.  (And the hash might of course be further extended to cover additional information, such as the bit mask, depending on the outcome of other orthogonal discussions raised by others.)  We’ll make sure that fix gets into the next version of the spec - thanks for pointing out the bug.

> 2. EdDSA is designed to withstand collision attacks against the hash function used in the signature. On the other hand, the protocol suggested is susceptible to such attacks. A hostile leader and participant, together, could wait for all other participants to select their commitments. They could then choose a commitment such that SHA512(R||A||msg)=SHA512(R'||A||msg'), providing them with a signature of msg'. This would of course have to be done in real-time, and given the strength of SHA512 is in no way practical. This kind of attack would be difficult to avoid without substantial modifications to the scheme, but this does not seem to be a significant threat.

Nice observation, thanks.  Agreed, it’s not clear that there’s a straightforward way to protect against such attacks in the event the hash function has collision weaknesses - but hopefully SHA512 will be strong enough for long enough that this shouldn’t be an issue in practice.

Cheers
Bryan

> Thomas G.
>
> On Wed, Jul 5, 2017 at 2:11 PM, Bryan Ford <brynosaurus@gmail.com <mailto:brynosaurus@gmail.com>> wrote:
>
>
> To follow up on my last message to Oleg, again I suggest reading section IV of our CoSi paper from IEEE S&P last year (http://dedis.cs.yale.edu/dissent/papers/witness-abs <http://dedis.cs.yale.edu/dissent/papers/witness-abs>), as it discusses several related issues, especially the potential desire to allow the leader to complete a collective signing procedure even with only a subset of “committed” participants remaining present in the “response” phase.  In particular, the leader can form all the individual Schnorr commits into a Merkle tree, and make the real commit c be the root of that Merkle tree.  In this way, the leader is committing not so much to a particular collective Schnorr commit but rather to *all possible* Schnorr commits that can be composed from any subset of the individual Schnorr commits within that Merkle tree.  This way, if some of the participants whose commits are present in that Merkle tree remain available during the response phase but others drop out, the leader can still use the commit c and form a correct and verifiable collective signature against the particular subset of Schnorr commits from nodes that remained available throughout the process, without restarting.
>
> I guess this approach does, in a slightly different way, make the resulting collective signatures slightly malleable to the leader: from a given set of commit-time and response-time information, the leader could put together distinct collective signatures representing different subsets of response-time participants.  Some form of “leader-malleability” of this kind seems unavoidably essential to enabling the leader to complete a collective signing round in the presence of partial failures without restarting.  Perhaps the same limited leader-malleability is more-or-less the same property your suggestion of using chameleon hashes has, although I haven’t had a chance to compare them deeply yet.
>
> But at any rate, the higher-level tradeoff here to consider is whether it’s better to (a) enforce strict non-malleability of collective signatures (by anyone, leader included), at the cost of O(N)-round DoS attack vulnerability during signing due to the need to restart partially failed rounds, or (b) provide some limited form of limited leader-malleability in order to support restart-free operation and avoid DoS attacks during signing, at the cost of a more complex protocol (and perhaps slightly more “special” trust in the leader than we might like).
>
> Again, further thoughts on this and other topics are most welcome.
>
> Thanks
> Bryan
>
>> On Jul 3, 2017, at 7:34 PM, Daniel Slamanig <daniel.slamanig@tugraz.at <mailto:daniel.slamanig@tugraz.at>> wrote:
>>
>> Hi Philipp,
>>
>> looks interesting!
>>
>> After looking at the protocol I also have some security concerns (related to what has been raised by Oleg in a previous mail).
>>
>> Not committing to Z as well as the actual sum of signers public keys A' in the computation of the hash c for the signature seems to be problematic.
>>
>> It seems to me that committing Z in the signature in plain as well as A' does not work given the later application of the signing procedure (where till the end of the protocol it is not clear who actually participates in the signing but c must be known at the beginning).
>>
>> Committing to neither of both however seems problematic as it does not fix the set of actual signers.
>>
>> This could be circumvented by allowing an honest leader to adapt the commitment to the final Z (and A') after it knows the signers without modifying the initially computed c using a chameleon hash (trapdoor commitment). I use P as a generator below, omit the brackets [a]P notation for scalar multiplication and write it from the perspective of the leader, i.e., the signer that initiates the protocol.
>>
>> The leader could choose chameleon hash parameters sk_ch=y for random y and pk_ch=(P,Y=yP) and add pk_ch and chameleon hash CH(Z'):=h(Z')P+u'Y for randomly chosen u' to the computation of c, i.e., set c=H(R||A||pk_ch||CH(Z')||S), where h() is a collision resistant hash function (this is just the standard way of constructing a chameleon hash from DL for arbitrary message spaces as propsed in [1]). If Z' is not yet known one simply sets Z' to some fixed string at the beginning, e.g., Z':=0. At the end of the protocol, when the leader knows the exact signers, it can update Z' to the final value Z and use sk_ch to compute a collision in the chameleon hash, i.e., such that CH(Z)=CH(Z') by solving h(Z')+u'y = h(Z)+uy for u. He then adds u and Z as well as pk_ch to the signature, i.e., sets it as (R,s,u,Z,pk_ch) and discards sk_ch and u'. If Z is known beforehand, one simply computes the chameleon hash once and does not need to compute a collision. Clearly, the use of a chameleon hash allows to simply adapt to the actual set of signers representing Z without modifying c (with the knowledge of sk_ch - but it does not work without the knowledge of sk_ch). This would resolve the issue with the unknown Z at the time of signing.
>>
>> Also, A is committed in the signature, but not the concrete A'=\sum A_i of keys used for computing the signature (I guess also due to the reason that one does not know the correct set of signers when computing the hash c). That can be problematic in a rogue key scenario in the current protocol, i.e., when not all signers need to prove knowledge of the secret key when they register their public keys but their public keys could be functions of other public keys (guess this could be a problem here). For instance, a malicious A^* could just take some key from A, say A_j, and compute and publish A^*=a^*A_j. And then given a collective signature (R,s,Z) where A_j participated, the signer can update s to s^* = s+a^*c as well as Z^* to exclude A_j and include A^* (as Z is not committed in the signature generation) and the signature (R,s^*,Z^*) will be a valid signature that certifies that A^* participated in signing - although he didn't.
>>
>> If Z is committed as proposed above and it is checked during the verification, then this should no longer work. One could also adapt the hash c=H(R||pk_ch||CH(Z'||A)||S) to include a chameleon hash to CH(Z||A'), where A' is the real set of signers that participated in the signature generation and is adapted before finalizing the signature when known as above.
>>
>> I hope that what I proposed is not just complete nonsense :) Also it produces quite a bit of an overhead. There may also be easier ways to avoid the issues.
>>
>> Some editorial issues: the message to be signed is sometimes called a satement S and later then message msg. S could be confusing as part of the signature is s and your semantic is that scalars are lowercase and points are uppercase. Also in 4.2 "Signature Generation" steps 2 and 3 are confusing as I guess that in the protocol all the signer compute their own [r_i]B values and R=\sum R_i instead of R=[r]B which would mean that they would send their r_i's (hope they will not do so).
>>
>> Also I find it somewhat confusing that the bitmask Z identifies the non-signers with a bit set to 1. Why not identifying the signers with a bit set to 1?
>>
>> Cheers,
>> Daniel
>>
>>
>> [1] Hugo Krawczyk, Tal Rabin: Chameleon Signatures. NDSS 2000
>>
>> On 01.07.2017 23:58, Philipp Jovanovic wrote:
>>> Hi CFRG,
>>> Here’s a first version of an Internet-Draft on “Collective Edwards-Curve Digital Signature Algorithms” based on Ed25519 and Ed448: https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/ <https://datatracker.ietf.org/doc/draft-ford-cfrg-cosi/>
>>> We plan to give a short presentation on that topic at the next CFRG meeting in Prague.
>>> Any feedback is more than welcome. Thanks!
>>> All the best,
>>> Philipp
>>> _______________________________________________
>>> Cfrg mailing list
>>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>>> https://www.irtf.org/mailman/listinfo/cfrg <https://www.irtf.org/mailman/listinfo/cfrg>
>>
>>
>> --
>> Dr. Daniel Slamanig
>> Institute for Applied Information Processing and Communications
>> Graz University of Technology
>> Inffeldgasse 16a, 8010 Graz, Austria.
>> Phone: +43 316 873 5509 <tel:+43%20316%208735509>
>> http://www.iaik.tugraz.at <http://www.iaik.tugraz.at/>
>>
>> _______________________________________________
>> Cfrg mailing list
>> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
>> https://www.irtf.org/mailman/listinfo/cfrg <https://www.irtf.org/mailman/listinfo/cfrg>
>
>
> _______________________________________________
> Cfrg mailing list
> Cfrg@irtf.org <mailto:Cfrg@irtf.org>
> https://www.irtf.org/mailman/listinfo/cfrg <https://www.irtf.org/mailman/listinfo/cfrg>
>
>


text:
2:01 AM
cbg

2 hours later…
3:32 AM
recabbage

cbg
@CallCenterExecutive is that your "real" identicon

this is my final form, yes
Unfortunately, there's a typo in "center"

5:06 AM

@piRSquared That's the result of you constantly applying yourself. Well done!

Well stated (-:

cbg

cbg

5:22 AM
wt-yam with the new name @CCE

It's a temporary minor meme.
Cuz... you know... I hail from the land of call centres... etc etc

Nice

5:43 AM
falling asleep at keyboard... its rbrb time!

6:26 AM
plus the fact that I sometimes feel like call centre support, with the kind of questions that come into the site these days...

7:04 AM
cbg
@CallCentreExecutive Now you are going to confuse everyone

@Code-Apprentice why is that?

because of your sudden name change
fortunately it isn't difficult to find out who you really are by checking your profile

Indeed, but this is my real identicon

cbg
call centre exec ?
big boss?

rbrb...time for bed
gnite

7:21 AM
@Code-Apprentice see ya

7:33 AM
cbg

8:05 AM
cbg

1 hour later…
9:32 AM
Someone would know where find doc in deeplearning (theories, informatics...). I didn't find internet

10:05 AM
@bereal thanks

10:24 AM
cbg

What does it mean cbg... I often see @AndrasDeak

sopython.com/salad, also mentioned in our rules page sopython.com/chatroom

Interesting

10:52 AM
airport lounge cbg

cbg

2 hours later…
12:31 PM
mile-high cbg

Hmm, why?

12:49 PM
I've seen someone import np as _np etc, claiming that he signals that thes modules are not their own. While I sort of see where they're coming from, It seems pointlessly cumbersome to keep doing that with third-party modules in your code. Am I right that using a well-documented API and maybe __all__ make it fine to keep using modules without underscored names? Now that I think about it underscores are usually reserved for internal modules, so exactly the other way around.

It's not clear to me why it would be useful to signal that kind of thing

I think the motivation is that someone might see yourmodule.othermodule and think that it belongs there, when it was merely imported. Similar surprises are numpy.int which is really just int and not to be used for anything.

I don't typically do dir(third_party_module) and see another unrelated third party module and assume "oh, these must be made by the same company" and then make incorrect technical decisions based on that. Who's he trying to protect?
Indeed, what kinds of incorrect technical decisions could I make? What's the danger even if I'm maximally dumb?

in the numpy case you may expect numpy.int(3) to give you a numpy int, whereas it's a regular int
But if you look at the relevant documenation it's obvious that numpy.int is not a thing, and looking at the implementation reveals that it's just int. But for this you need to suspect that your naive jumping to conclusions was wrong.

1:08 PM
In the specific case of a module overshadowing a builtin, I would hope the average user would approach using it with due caution
Concluding one of:
- the developers of this module must have a very good reason to ignore the common rule of "don't overshadow builtins", possibly because of a difficult situation with many corner cases, and I should be on my guard
- the developers are kind of dumb and I should be careful using their code at all
Which doesn't prevent them from eventually wrongly concluding "I guess numpy.int is a custom type they defined and which I may use" but it becomes harder for them to do that
The case I think that has the most merit is: if third party module A imports third party module B, and module B has a sufficiently generic name that you're not sure what its affiliation is WRT A.
If pygame imports requests, that might be ambiguous because maybe they wrote their own requests module that doesn't have anything to do with the popular HTTP request module. If scipy imports BeautifulSoup, you can probably reasonably assume that it's actually importing the real BeautifulSoup because it's not too likely that scipy would independently choose the name "BeautifulSoup" for a module they invented
Ideally, nobody would name their module after an already existing popular third party module, but that would be pretty hard to enforce unless everyone is intimately familiar with the third party library ecosystem

1:45 PM
Monday morning shoulda-stayed-in-bed cabbage for all!

cabbage
thanks, @Kevin, that's kind of what I had in mind
the tricky thing about the numpy example is that numpy.int8 and numpy.int64 and the like do exist

To maintain the pattern of the "int" + "number of bits" naming system, long ints should be referred to as numpy.int∞

monday cabbage all

2:03 PM
@MoxieBall afternoon

3:01 PM
If anyone remembers the "what if we allowed a:b:c to represent a slice literal in any context, not just inside square brackets?" conversation from last week, I just now noticed that we already use ":" as a token in a non-slice context: in the format specifier of f-strings. So it would be ambiguous whether f"{1:2}" should evaluate to " 1" or "slice(1, 2, None)"

yup

We can quietly ignore the ambiguity of dict literals because {1:2} shouldn't reasonably be interpreted as "a set containing slice(1,2)" since slices are unhashable
... Which is kind of weird since slices are basically just highfalutin tuples, so why shouldn't they be hashable?

inb4 "dict views"
yeah, slices also seem pretty immutable

Tentatively file under "because not enough people have asked for it"

>>> x = [1,2,3]
>>> y = [4,5,6]
>>> s = slice(x,y)
>>> x[0] = 0
>>> s
slice([0, 2, 3], [4, 5, 6], None)

3:07 PM
Anyone interested in aiosmtpd, asyncio, and debugging intermittent issues? github.com/aio-libs/aiosmtpd/issues/133#issuecomment-399943405
also, morning cabbage all

cbg

Ok, so slices are mutable by proxy. But this is also true for tuples. So ideally, slices should be hashable iff their arguments are hashable. Just like how tuples are now.

is there a purpose to defining a slice using lists like that?

I didn't know it existed
what does that even mean?

I can't imagine any built-in types accepting a slice whose arguments are lists, but theoretically you could write your own class that can do whatever it wants

3:09 PM
oh, right, numpy does some neat things with weird slices

Some wacky 7 dimensional matrix that you want to be able to slice every which way

hmm, then again those are not array-valued slices
I got confused, those are actually getitem tricks
pandas on the other hand uses string:string slices

I think you can slice(start,end) however you want
Python 3.5.2 (default, Nov 23 2017, 16:37:01)
[GCC 5.4.0 20160609] on linux
>>> slice(3, 'elephant')
slice(3, 'elephant', None)

Hmmph. My ipython console is querying an object for attributes, breaking the attempted lazification of my object. :-/

This lets you define __index__ on your custom types so it does sensible things when passed into a slice. Neither list nor str have defined it.

3:15 PM
straight from guido
I think I agree that it would make some syntax especially confusing for no huge benefit

so, TLDR: because we want some_dict[:] to crash instead of doing something weird
Good enough for me.

And in the event that you really need hashable slices, the workaround is quick

I'd agree with that

3:31 PM
morning cabbage

cbg @Code-Apprentice

cbg

@vaultah so that you can concentrate on doing something else :d
airplane-cabbage-with-current-continuation

Gibraltar
or plane is headed for malaga
landing now :d

4:14 PM
Random thought: sin(pi/2) is rational. sin(pi/4) is irrational. Is there a generalized way of determining whether sin(x) is rational for any x?
Are... Are triangles involved

@Kevin /gasp Triangles in trigonometry! The horror!

I ask because a commenter in php and python result difference for same function writes, "Neither PHP nor Python are actually returning the real value [of sin(45 degrees)]. They both approximate." and I thought "well yeah, because you can't store an irrational number precisely in a float. But, hmm, how often is the result irrational?"

@Kevin my intuitive guess is "almost always"

I'd say it usually is, considering that irrationals are uncountably many

In general, there are by far many more irrational numbers than there are rationals

4:18 PM
oh, and pi is irrational so a given rational input will probably give you an irrational result
I'd wager that 0->0 is the only rational example

6-1 cabbage

Cbg.

Oh yeah well my country hasn't lost a game in the world cup yet
And I would bet they're not going to
go USA!

All of those ideas in the picture are good aside from \if
You're gonna get types and you're gonna like it 👿

@AndrasDeak Apparently "if x is rational and not zero, then tan(x) is irrational" has been proven, and was used in an early proof that pi is irrational.
The math is one million miles over my head but I wouldn't be surprised if a similar argument could be applied to sin

4:25 PM
@MoxieBall ...you mean since the start of June? :p

@toonarmycaptain you can't hurt me I don't even like fake football

@Kevin neat
tan(x) = sin(x)/cos(x) = sin(x)/sqrt(1-sin^2(x)) roughly, so something something it's probably similarly true

@MoxieBall That last phrase has started many fist fights. Best not go there.

Speaking of new python features, how do you think proposing dict unpacking would go? I'd be surprised if it hasn't already been proposed

@toonarmycaptain all jokes aside, I like football way better than american football, where 95% of the game is waiting for the game to happen

4:32 PM
Anyone have any experience producing pdfs/documents with equations in them eg x^3 - 4 x^2 + 6 x - 24 = 0 formatted with superscripts etc? I'm trying to find a solution that doesn't include packaging a half gig or so of LaTex with my several meg package.
@MoxieBall Yah. I prefer rugby to NFL.

@KevinMGranger have you seen PEP 448?

cabbage

@toonarmycaptain I find that google docs has a surprisingly good equation formatter

Not what I mean by unpacking-- maybe destructuring would be a better term

cbg CCE

4:36 PM
I can do x = dict(foo=1, bar=2), so I'd like to be able to do {foo, bar} = x

I'm going to quit being a call centre executive. I don't much like it :(

I want symmetry between being able to create/modify a dict with keywords, and being able to extract from a dict with keywords

What would {foo, bar} = x do?

it would be equivalent to foo = x['foo']; bar = x['bar']

My problem is that if there is a None value in the list there will be only 3 values in cleaned_addr how can I fix this??

4:41 PM
oh, I see what you mean

@KevinMGranger what about keys that aren't valid names?
that seems like a strong counterargument
and why would you tie the name of the new variable to the name of the key?
@Self hello

@MoxieBall I see that. You're suggesting I use google docs online to format then pull the doc back and convert to PDF (or just use google doc)?

@Self leave the None or check for the number of items?

If they're not valid names, then you can't do it, and the answer is "tough, deal with it". Unless that backslash proposal gets accepted.

either unpacking makes sense and then you can have a placeholder (even None) in there, or unpacking doesn't make sense and you shouldn't be unpacking anyway

4:44 PM
@toonarmycaptain not sure what your restrictions on the end format are so I can't make a recommendation as to how to use it, I just like what it can do

@KevinMGranger that would be very asymmetric: you could unpack {'foo':1} but not {1:2}

The main use case is for keys that are valid names, which I believe represents enough of a majority of dict usage to be worth it

"Display name may only be changed once every 30 days; you may change again on Jul 25 at 3:28"
uh oh, I'm stuck now

How to handle n amount of missing keys remains an open question, or other exceptions that occur with __getitem__

and why should there be a set on the left-hand-side?

4:47 PM
I'm sure you can use your imagination ;)

This kind of unpacking ("destructuring") has already made its way into JS
I guess Python developers could figure it out, too

Long story short I don't like having to use 4 characters of symbols to extract a dict member, when getting an attribute only uses 1 character

@KevinMGranger I definitely make dictionaries with keys that are invalid names more often than valid ones

@MoxieBall Fair enough. I'm trying to output randomised math worksheets/tests. Seems like there should be a library/ies that can format my x^2 to x superscript 2, and fractions without the function/other_function slash styling, that doesn't involve package sizes expressed in GB

@toonarmycaptain you could do some fancy PIL work to draw a page yourself :P

4:56 PM
@MoxieBall Yeah, a bespoke parser and formatter is what I'd like to avoid lol

@MoxieBall I mean, I've seen matplotlib can be (ab)used to produce text with blank plots, but that seems like grabbing a library purely for a side effect of it's main purpose.

@toonarmycaptain or SymPy?

Man, ThinkGeek has a The Last Unicorn statue. Shiny!

Hmm, is there no module for getting image data out of the Windows copy/paste buffer? pyperclip apparently only does text.
I have a 30 minute task that could become a 10 minute task if I had this power, but I don't want to futz around with the win32 API for 20+ minutes, that'd be a net loss

5:12 PM
not if you ever have to use it again...

@MoxieBall I'm actually looking at that right now.

Also the win32 API is an excruciating experience so every minute I spend with it, I'd rather spend ten minutes watching paint dry
Oh, PIL of all things has clipboard reading ability.
But oops I already gave up and started doing the task manually and undoing my work is more work than finishing at this point

Sunk cost fallacy

I don't think that applies here

5:24 PM
googles topic for 5 minutes Yes I totally understood that

me any time someone links to a proof from the 18th century

:43036031 Unless I'm reading wrong, SymPy will format my equation into LaTex syntax, but then I'd still need to bundle with a LaTex distro, right?

@toonarmycaptain I was reading this, looks like you don't have to use LaTeX but idk if the others will do what you want

@MoxieBall I guess I'm pretty much looking for the python equivalent of MS Equation editor (or whatever exists now, I last used it circa 2003), that will take some sort of syntax and give me either formatted text or an image that I can then insert into a pdf or other document.

Ok, it may or may not apply here depending on whether I can complete writing the program in less than five minutes, given that I only have 15 minutes of manual process left

5:34 PM
@toonarmycaptain well some combination of the previously discussed options should be good enough I imagine
I'm a fan of the google charts api

though I don't understand why you wouldn't want latex on your computer, there are online services such as sharelatex :P
odds are they don't have an API though

@AndrasDeak Really because I'm wanting to distribute something that's less than half a GB, otherwise I'd be using it and done.

5:51 PM
Cabbage
@toonarmycaptain Is this Open Source or commercial? If it's free, I think you could use CodeCogs for free, for commercial use there's a charge. codecogs.com/latex/about.php

@toonarmycaptain: I, can, sympathize.
(Apparently it's easier to remember things you complained about years ago if you write them down, even virtually..)

How complicated are these equations? If they're just say, simple polynomials, you could write a simple parser that outputs Postscript, and PostScript to PDF is easy on any Linux system, since it's bound to have Ghostscript. And many popular PDF viewers will show Postscript.

@PM2Ring At the moment, simple polynomials and rationals (eg x^2 + 4x -17 / x -7 )
@PM2Ring heh "simple parser" - yeah I'm sure I could, I now feel crazy for thinking that there's some simple package for this. Y'know, because polynomials are fine, but when I want to extend to trig, limits, etc, that's another matter.

6:09 PM
@toonarmycaptain Or just cheat and use Unicode, which will give you superscript, and simple fractions, although it can look cheap, depending on the font. E = mc², 10⁵, ⅔
@toonarmycaptain Simple is simple. But you definitely don't want to reinvent LaTeX.

hey guys, opinion on from . import x vs. import x? i.e. relative vs. absolute imports. I haven't seen enough debate to have an opinion

From these two definitely the former

And they aren't equivalent

not my original idea, but
import matplotlib.pyplot as plt
fig = plt.figure()
fig.text(.5,.5,r'$\frac{x^2 + 4x -17}{x-7}$', size=100, horizontalalignment='center', verticalalignment='center')
plt.show()
without setting text.usetex = True in any rc files you'll probably get the native pyplot renderer
you can savefig to pdf; perhaps the only thing you need is an autocrop
which, ironically, I usually do with pdfjam which I'm pretty sure is latex
> pdfjam is a shell-script front end to the LaTeX 'pdfpages' package (for which, see ctan.org/tex-archive/macros/latex/contrib/pdfpages).

6:19 PM
@vaultah could you elaborate?

Sigh, mobile site

ugh, seeing 2 spaces for indent instead of 4, and function names beginning with a capital letter in the codebase is maddening

@CallCentreExecutive sorry to hear that

@AndrasDeak THanks. That's probably what I'll have to go with, although I still feel like using the matplotlib to generate text is like using an ER to put a bandaid on a papercut.
Thanks all, rhubarb for now.

yes, but you don't want to use the bandaid because it's too heavy
rbrb

6:32 PM
This is from CodeCogs. I'm not used to doing stuff like this on my phone. :)

looks good

It's a little blurry, but I just chose fairly simple options, CodeCogs can do better. The 1st version I tried had a transparent background, but when I viewed the downloaded version the Android Gallery app decided to display it on a black background. :) There's probably some way to change that, but I'm still getting used to this phone.

It should export to pdf in which case it'd be vector graphic

6:54 PM
@AndrasDeak Yes, it does PDF & SVG, as well as a few other formats. But none of those will display here in chat. Here's a slightly higher res transparent version.

7:17 PM
This is useful. I don't know when I'll use it. But I have faith that I will

7:49 PM
Cbg

cbg

Can I get some formatting help? I'm on my phone and un able to fix that answer ' hyperlink: stackoverflow.com/a/51030296/5079316

Cbg

@OlivierMelançon done

Thank you!

7:51 PM
2fast4me

Oh, was there a space just after the (?

yup

Subtle

8:55 PM
I'm creating a modified notebook app, and I don't want to actually import the dependencies for testing. So I'm importing them in a separate module that I'll mock for tests. What do I call that module? I'm leaning towards jupyter_libs.py...

9:07 PM
jupyter_libs.py it is...
@CallCentreExecutive what's with the name change?

9:52 PM
@PM2Ring matplotlib can render without LaTex. Have to juggle to crop within matplotlib, but it's functional. I see options to achieve perfect cropping with PIL but suspect that may be slower than it's worth. This'll do me for now though :)

10:10 PM
17 hours ago, by Call Centre Executive
Cuz... you know... I hail from the land of call centres... etc etc
and also
16 hours ago, by Call Centre Executive
plus the fact that I sometimes feel like call centre support, with the kind of questions that come into the site these days...
But I tried changing back today, and found I have to wait 30 days to do so.

@CallCentreExecutive lol @CCE

guess they don't like users making UPDATE queries to their User tables too often

I imagine that's true. But I think they'd also prefer ppl not obscuring their identities.

also trolls

afternoon cabbage

10:18 PM
Cabbage @Code-Apprentice

Hello Guys. I hope you have a nice evening.
How can I use the xmbd variable, as a search variable in the re.findall? Since I'm already in for-loops, I unfortunately have several iterations and have therefore lost the overview.

@CallCentreExecutive there's a workaround
Did you try putting xmdb in place of "HERE"?

@Code-Apprentice I'm all ears!

Hi @Code-Apprentice, ty
yes @Code-Apprentice

@CallCentreExecutive as long as you didn't check "change profile on all sites", you can go to another SE site and change your name there and select the option to change on all sites.
oh...it's two different buttons, not a checkbox

10:22 PM
Thank goodness, I didn't

I went through a name-changing phase early on in my SO career and learned these tricks.

interesting. It didn't work.
No, wait. It did

I see you as coldspeed on main

@CallCentreExecutive it will take a little time to propagate to chat

yup, I realised it takes a while to update here
@Code-Apprentice thanks, you're a lifesaver

10:26 PM
Relish your executive title while it lasts

aww, you liked my new nickname

yeah, despite the weird spelling

Funnily enough, Centre is the right spelling for something that is not a physical center
Example: Shopping Centre

@Code-Apprentice why did you say that? They've been around enough
@CallCentreExecutive I always thought it was a regional thing rather than a semantic distinction

10:28 PM
@AndrasDeak were you keeping it secret? You should have message'd me with the memo

too late for that!

@AndrasDeak because I'm trying to be friendly and too lazy to check history

@CallCentreExecutive pro-tip

centre from french
center from american

10:30 PM
90

Originally, everyone spelled it centre, but because of Noah Webster's spelling reforms, people in the US started spelling it center, particularly in the last century. Although the revised spelling center has been adopted internationally to varying extents, centre is still more popular in most re...

They changed to center because English started to adapt its spelling to the pronunciation. Something something laugh

which seems to agree with @AndrasDeak that it's a regional difference

Ah, so it is a british thing

No
centre is a french word

@AndrasDeak in the early 20th century there was a movement to pass legislation about spelling of words...it never caught on, though.

10:31 PM
yes but it's used in British english
and India is a British colony

@wim yes although we spell it like that here.
As the Call Centre Executive said.

Who? :p

US was arguably an english colony too
They were just better at rejecting the monarchy than India was

bowed out early on this one stackoverflow.com/q/51032504/2336654

you mean better at using systems no one else wants to use

10:34 PM
@wim or quicker to do so at least...

Yes, and it shows in the language too

We have over 100 regional languages, it kinda makes sense that not everyone wants to master a foreign language (English)
of course, not saying that's a good thing
but eh
@piRSquared Unclear, arguably no mcve question with an upvote? Doesn't look right...

Once you realise that so many English words are/were just misspellings from French, you realize (sic) that it's pointless to talk about the "correct" English spelling

whoops, was my upvote >.< gone now
rbrb all. might be on later
@wim where is the mic drop?
and rbrb seriously now

e.g. couleur (french) colour (english) color (us)

10:39 PM
buh bye
You could say the US "dumbed down" the spelling. A lot of "oea" words lost the "o"
etc etc. I can't remember more examples.
There's also a dichotomy when it comes to 'ize' or 'ise'.

@wim Which is handy when you write both, and use the other for coding.

Hi Guys. I would be reluctant to interrupt your conversation, but nevertheless I would be happy about possible help:

Unfortunately I have a bug here. Everything on my output is written twice in JSON. But I think it's a problem with the for-loops. Do you have an idea?

http://dpaste.com/31EMTXM

if you don't like it, you could call it "dumbed down". if you do like it, you could call it simplifying, incremental improvements.

@madik_atma always feel free to interrupt off-topic chatter with python questions :)
I mean, multiple conversations can easily be maintained in parallel

@AndrasDeak ok ty :)

10:49 PM
@madik_atma it's not your first example like that, so: it would help a lot (at least it would help me) if you had some reasonable (English) words in your example. I find it hard to comprehend foreign-language stuff
(foreign with respect to English, I mean)
You should probably also simplify your snippet to cut down to the most essential parts, with an example input that can be run by others.

@wim Meh. I wouldn't necessarily consider random permutations of characters and swapping out one letter for another as a simplification or improvement. Only confusion.

also I'm not sure what you mean by "output is written twice"
you have multiple dicts/lists going on
and with that good night and good luck :P
also make sure you don't have to set speeches to be a new empty list after you insert it into speaker['GERMANISCH']

@wim The American spellings don't necessarily simplify things, though. They can make things more complicated, e.g. centre -> central is simpler than center -> central. Or analyse -> analysis vs analyze -> analysis. I guess you can say that "analyze" makes more sense phonetically, but if American English were serious about doing that then plurals of nouns that end in a voiced consonant should take a z, e.g. dogz.
Aug 7 '16 at 12:42, by PM 2Ring
@AnttiHaapala "The problem with defending the purity of the English language is that English is about as pure as a cribhouse whore. We don't just borrow words; on occasion, English has pursued other languages down alleyways to beat them unconscious and rifle their pockets for new vocabulary." — James Nicoll

11:07 PM
Hello @AndrasDeak yes you are right with the foreign words, but since I like to work in German, my variable names are therefore also in German. Sry for that

I was able to stop the bug with a break. Can you tell me with this snippet, what I'm doing wrong, that I have to go through the loop once with a break?

My JSON agrees after using Break.

Many Thanks !

http://dpaste.com/0T0Z73K


text:
# [Topic-models] Topic-models Digest, Vol 28, Issue 2

1980er at web.de 1980er at web.de
Tue Nov 4 04:28:49 EST 2008

Hi Mateusz,
>I am a undergrad student and a newcomer to the LDA and this list as
>well. I'd like to ask a lot of questions which I guess are of a very
>basic nature to you, guys, but to me most of this stuff is really
>unknown so I am tackling multiple new things/techniques/ideas all at
>once.
Same here.

>After reading LDA paper (Blei et al 2003) a couple of times my grasp
>of the concepts is somewhat better but I still need some
>clarifications.
figured out since then.

>1. \alpha parameters are not known and are used only conceptually in
>the generative process. They are to be estimated ?
Depends on the implementation. You could estimate it or you could know it in
frequent but there is only one per document).

>2. \beta parameters (word probabilities, i.e. p(w^j = 1 | z^i = 1) are
>not known in advance and are to be estimated ? \beta is in fact a
>matrix of conditional probabilities?
Yes, yes. the matrix entry \beta_{i,j} is defined as \$P(w_j|z^i=1)

>3. Whenever we choose \theta from the Dirichlet(\alpha) distribution
>we effectively get all but one (as N is assumed to be fixed)
>parameters for the Multinomial distribution used later on ?
Yes. And since they have to sum up to one, you have all parameters in fact.
Not sure what you think it has to do with N (the number of documents). The
dimensionality of \theta is k. Look at the picture at
http://en.wikipedia.org/wiki/Image:Dirichlet_distributions.png
The height of the surface is proportional to the probability you get that
point, when you sample \theta. And the distances to the cornerpoints represent
the probabilities you get for each of the (here three) topics (represented by
the corners).

>4. Why is p(z_n | \theta) given by \theta_i for the unique i such that
>z_n^i = 1 ?
Because \theta = { \theta_1, \theta_2, ..., \theta_n }, where each entry gives
the probability for one topic. And for topic z_n^i = 1 it is given by
\theta_i.

>5. What is the definition of a variational parameter? What are they?
>(I'm completely new to variational methods)
I don't know

>6. What is the high level overview of the LDA algorithm?
It is given in the paper by Blei in the beginning of chapter three and in the
figure at http://en.wikipedia.org/wiki/Plate_notation
I am currently writing an overview in my thesis. Maybe this helps you:

Being a generative probabilistic model the basic assumption made in LDA is
that documents are generated by random processes. Each of these represents a
different topic z. A random process generates the words in the document by
sampling them from its own specific discrete probability distribution over the
words P(w| z ). A document can be created by one or more topics, each
having associated a distinct probability distribution over the words.
To represent the mixture of topics in a document, a multinomial distribution
\theta  is used.
For each word in the document the generating topic is selected by sampling
from \theta.
The topic mixture \theta itself is drawn from a Dirichlet distribution
once for every document in the corpus. The Dirichlet represents our prior
belief of the topic mixtures that occur in the corpus, i.e. whether the
documents are generated by single topics or from a mixture of many topics
several and which topics prevail.

>What steps do we make in order to make the LDA work correctly?
I do not understand the question.

>Estimate parameters and then do inference, or the other way around? I
>think this is missing in the paper.
First parameter estimation, then inference. You need the parameters for
inference.

>7. Is the LDA-C a 1-1 implementation of what is published in the
>paper? I was trying to read the code but for the first few passes over
>the code I don't see any direct mapping to most of the equations
>published in the paper.
I do not know. But it had comparable results in a short experiment.

>I'd appreciate even the most concise answers (but not too much as this
>can result in another question to the answer ;) ).

best regards,
Mateusz Berezecki


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As you may know, $$\LaTeX$$ and especially the amsmath package offers many ways to align equations. Because of the way LaTeX is parsed, a multiplicity of blanks is treated as a single space token. �����]8�.��;}?��e�꧷�yHD1����qD%����7_y�we���%��.�3��7[U+m�>5i��3+��6e�}���ˠH2��2X����#��.rr;�v. The directives > { {}}c< { {}} tell LaTeX to center-set the column contents (which will be either +, -, or blank) and to treat them as objects of type mathbin. … /Matrix [1 0 0 1 0 0] For instance, we can write instead of without ambiguity. COVID-19 Preprints. http://quicklatex.blogspot.com is a weblog of LaTeX tips and tricks. This is a method for solving systems of linear equations. LaTeX is the de facto standard for the communication and publication of scientific documents. Generally, elimination is a far simpler method when the system involves only two … \begin{align} 1 + 2 & = 3\\ 1 & = 3 - 2 \end{align}. In your own equation, enter f (x)=. LaTeX is a programming language that can be used for writing and typesetting documents. x���P(�� �� \ [ \left\ { \begin {array} {c} a_1x+b_1y+c_1z=d_1 \ a_2x+b_2y+c_2z=d_2 \ a_3x+b_3y+c_3z=d_3 \end {array} \right. /Subtype /Form An easier way to generate the code that you need to paste is by using an offline LaTeX app for your operating system or a web-based LaTeX environment like Overleaf. A system of equations is a group of two or more equations with the same variables. LaTeX math and equations Learn to typeset and align equations, matrices and fractions in LaTeX. To scale them up, we must use the following code: Output: $\left[ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} \right]$. je suis en train de rédiger un mémoire avec latex sur UBUNTU 8.04 Je ne parviens pas à faire une accolade ouvrante devant un système à plusieurs équations du type : f(x) vaut fx0 pour xx1. /Resources 12 0 R In this post I’ll show you, with examples, how to write equations in Jupyter notebook’s markdown. 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Polynomial equations may also contain more than one variables, for example: X2 + 3b + 234 = 0. stream Input LaTeX, Tex, AMSmath or ASCIIMath notation (Click icon to switch to ASCIIMath mode) to make formula. Very Basic Mathematical Latex A document in the article style might be entered between the nmaketitle and nendfdocumentgsections below. The result tends to be slightly incorrect horizontal spacing. Learn which LaTeX commands and MathML elements you can use with Pages, Numbers, and Keynote. AUTHOREA. When numbering is allowed, you can label each row individually. /FormType 1 The align environment will align the equations at the ampersand &. endstream Click Preferences –>Cut and Copy Preferences. 4. Mine ponds amplify mercury risks in Peru's Amazon; Melting ice patch in Norway reveals large collection of ancient arrows ; Comet 2019 … Notice that the two lines are parallel and will never intersect. 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This does also work for parentheses and braces and is not limited to matrices. >> However, there are many other types of equations, and we will investigate a few more types in this section. Mathematical modes LaTeX allows two writing modes for mathematical expressions: the inline mode and the display mode. Copy your equation into your Latex File. /Subtype /Form Insert Equation Interactively. << /Resources 18 0 R For e.g., you can include multiple equations within the same line and select the layout that best suits your document. Open an example of the amsmath package in Overleaf /Subtype /Form A Vandermonde-type system. Greek Letters in Equations . The standard symbol is given by $\cdot$. How do I reference my LaTeX tables or equations? You don't have to pay for using LaTeX, i.e., there are no license fees, etc. There is no alignment when using the simple equation environment. This package allows you to choose the layout for your document that best suits your requirements. L a T e X allows two writing modes for mathematical expressions: the inline mode and the display mode. Open an example of the amsmath package in Overleaf FAQ. 2. Referencing subordinate equations can be done using either of two methods: adding a label after the \begin {subequations} command, viz. x���P(�� �� The mhchem extension allows a more adaptable display and more natural input of chemical formulae and equations. 7 0 obj Every command has a specific syntax to use. The ode23s solver only can solve problems with a mass matrix if the mass matrix is constant. 5. Some examples from the MathJax demos site are reproduced below, as well as the Markdown+TeX source. I will demonstrate some of the most common LaTeX math features: Output: 2. stream x���P(�� �� LaTeX assumes that each equation consists of two parts separated by a &; also that each equation is separated from the one before by an &. 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A blank equation appears. endobj We have seen that substitution is often the preferred method when a system of equations includes a linear equation and a nonlinear equation. I post very short videos to explain LaTex in details one topic at a time. However, when you're multiplying numbers, for instance, a multiplication symbol comes in handy. /Matrix [1 0 0 1 0 0] Cases in Equations. /BBox [0 0 100 100] Exemplede réalisation 053 Résolutiond'unsystèmed'équations 1 Identification Type Imagiciel Modalité Vidéoprojection Thèmeabordé Système d'équations du premier degré Niveau Cycle 4 Lycée Prérequis Système d'équations Objectif Illustrer une notion Réalisationtechnique Difficulté : Vue(s) : Graphique Algèbre Tableur Cas 3D stream I will show you how to use it. The complexities of supercript and subscript notation, ions and isotopes. I was motivated by this question given in 5th grade mathematics competition that I was solving with my advanced students: Three satellites are orbiting … /Type /XObject Previous ones: Basics and overview Use of mathematical symbols in formulas and equations Many of the examples shown here were adapted from the Wikipedia article Displaying a formula, which is actually about formulas in Math Markup. The following code will result in wrong brackets: Output: $[ \begin{matrix} 1 & 0\\ 0 & 1 \end{matrix} ]$. However, it is rather cumbersome for a range or reasons. The system is said to be inconsistent otherwise, having no solutions. MATLAB ® displays a warning message if A is badly scaled or nearly singular, but performs the calculation regardless. endobj /FormType 1 You can now save your post and preview it to see your math equation with formatting. Roots in Equations. x���P(�� �� Pour numéroter les équations à droite, on utilise l’argument fleqn dans la classe du document : \documentclass. It can be used to scale for fractions and other expressions as well: Output: $\left(\frac{1}{\sqrt{x}}\right)$, design and content © 2019 Claudio Vellage, All mathematical expressions have a unique command with unique syntax. /Length 15 HTML LaTeX equation editor that creates graphical equations (gif, png, swf, pdf, emf). In the case of two variables, these systems can be thought of as lines drawn in two-dimensional space. >> Systems of Linear Equations Systems of Linear Equations Systems of Linear Equations. Personally, I write all code by hand though, since it's faster than messing around with the formula editor. title = {The {E}instein equations} Editorial Manager ® When submitting to Editorial Manager®, please, select item type 'Manuscript' for all LaTeX related files (tex, bbl, bst, sty, clo, cls) and 'Figure' for images (eps, jpg, pdf, png, tif). /Subtype /Form ... system extending throughout the plant. Latex ne respecte pas l'espace blanc à gauche dans le code pour signifier que le y et le x sont des entités indépendantes. \documentclass{article} %\addtolength{\textheight}{+ .1\textheight} \title{TITLE} \author{NAME} %\date{} \begin{document} \maketitle \end{document} Paragraphs are separated by a blank line of input. The Lyx program offers a great formula editor, which can ease this work a bit. I also prepared a quick reference of math symbols. endstream x���P(�� �� TexMaths will try to find the external programs it uses to generate LaTeX equations. Source Cours-Systemes-lineaires-Equations-de-droites Fichier Type: Cours File type: Latex, tex (source) Télécharger le document pdf compilé Description Cours de mathématiques en 2nde: équations de droite et système d'équations Niveau Seconde Table des matières. 20 0 obj One, of course, must be careful about spaces, which could, however, require more discipline than the typing of & … Chapter 4 Data Types and Variables Chapter 4 Data Types and Variables ... LaTeX Math Problem Solving with Python Book Construction Contributions Cover Artwork About the Author Table of contents. Solvability of a system of polynomial equations. << /Matrix [1 0 0 1 0 0] Furthermore it is not even possible to enter two equations in that environment, it will result in a compilation error. . In LaTeX, amsmath package facilitates many useful features for displaying and representing equations. /Matrix [1 0 0 1 0 0] TeXnicCenter is another great LaTeX editor specifically developed for Windows … LaTeX Compiler on your system. LaTeX is available as free software. In order to investigate situations such as that of the skateboard manufacturer, we need to recognize that we are dealing with more than one variable and likely more than one equation. There are three types of systems of linear equations in two variables, and three types of solutions. /BBox [0 0 100 100] There are two major modes of typesetting math in LaTeX one is embedding the math directly into your text by encapsulating your formula in dollar signs and the other is using a predefined math environment. Latex. /Length 15 That makes it easy to change … To insert a system of linear equations, do the following: In the Professional format: 1. Today, I wanted to write a system of linear equations in a triangular form using $$\LaTeX$$. … Using the multiline, aligned packages. This means that you can freely mix in mathematical expressions using the MathJax subset of Tex and LaTeX. However, when both equations in the system have like variables of the second degree, solving them using elimination by addition is often easier than substitution. Every command has a specific syntax to use. endobj C'est alors une bonne raison de m'offrir un café. Images may also be dragged into other applications like Word. endstream The second one is used to write expressions that are not part of a text or paragraph, and are therefore put on separate lines. There is a special matrix environment for this purpose, please keep in mind that the matrices only work within math environments as described above: Output: $\begin{matrix} 1 & 0\\ 0 & 1 \end{matrix}$. /BBox [0 0 100 100] In every box, enter the appropriate formula, for example: To insert a new line for this system of linear … There are several fonts with math support and perhaps you will find also an alternative font for the bread-and-butter type of your document. /BBox [0 0 100 100] Basic Math Environment. 3. For more advanced symbols and equations, you can use LaTeX, a system that formats symbols on Edmodo. It is also possible to combine various commands to create more sophisticated expressions such as: The more complex the expression, the more error prone this is, it's important to take care of opening and closing the braces {}. Inline math; Equations; Fractions; Matrices; Scaling of Parentheses, Brackets etc. It can take a long time to debug such errors. /Length 15 2) Use EROs to write a sequence of row-equivalent … It only takes a minute to sign up. 1. /Length 15 Also in this section. The order of ordinary differential equations is defined to be the order of the highest derivative that occurs in the equation. Cela me donnera l'énergie et la motivation pour continuer son développement. The = symbols are inserted automatically; the directive @ { {}= {}} tells LaTeX to treat = as an object of type mathrel. 26 0 obj Finish. The graphical editor is used only for creating mathematical equations in a full graphical What You See Is What You Get or WYSIWYG environment. Outline . /Filter /FlateDecode For example, we might type a system of equations as follows: \begin{align*} ax + by &= 1 \\ cx + dy &= 2 \\ ex + fy &= 3. /FormType 1 Merci ! Fortunately, MathType has Tex translator. endobj /Filter /FlateDecode x���P(�� �� In many euphorbs, the entire structure is made from a single cell – this type of system is known as a non-articulated laticifer, to distinguish it from the multi-cellular structures discussed above. COVID-19 Preprints. << /Matrix [1 0 0 1 0 0] endstream LaTeX, originally developed in the 1980s by Leslie Lamport, allows you to generate camera-ready format and equations using predefined macros rather than all manual text. The first … << >> The solvers all use similar syntaxes. << Sign up to join this community . endstream Except for people familiar with LaTeX, this is often an unfamiliar territory. %PDF-1.5 /FormType 1 Sometimes, when we're multiplying, we don't need a multiplication symbol. Double click your equation then you will go to MathType. /Length 15 BROWSE LOG IN SIGN UP. /Type /XObject If LaTeX is already installed on your system, all you have to do to start with TexMaths is to click on the Equations icon from the TexMaths toolbar. It's possible to typeset integrals, fractions and more. Overview of basic math features, with live-rendering and sandbox in your browser. Equations with Align Environment. >> LaTeX needs to know when text is mathematical. Answers and Replies Related MATLAB, Maple, Mathematica, LaTeX News on Phys.org. An inconsistent system has no solution. Solving system of equations of polynomials and logarithms of rational functions. Do not use subdirectories, all associated files must be in one directory. 1 $\begingroup$ I apologize in advance for the long post. The first one is used to write formulas that are part of a text. LaTeX is obviously pretty good at typesetting maths—it was one of the chief aims of the core TeX system that LaTeX extends. For more advanced symbols and equations, you can use LaTeX, a system that formats symbols on Edmodo. Mathematical Equations in LaTeX. However, it can't always be relied upon to accurately interpret formulas in the way you did. $$$1 + 2 = 3$$$ To surround the matrix by brackets, it's necessary to use special statements, because the plain [ ] symbols do not scale as the matrix grows. How to use Mathjax in WordPress. Furthermore it's possible to display matrices in LaTeX. You can then copy and paste your equations in the shortcode block in WordPress. >> The point where the two lines intersect is the only solution. Latexes are found in nature, but synthetic latexes are common as well. 17 0 obj In the mature plant, the entire … Aligning Equations. A system of linear equationsconsists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. Solving particular type of system of equations in $\mathbb R/\mathbb Z$ Ask Question Asked 5 years ago. Can I write a LaTeX equation over multiple lines? << Write Equations in TexStudio. LaTeX is a high-quality typesetting system; it includes features designed for the production of technical and scientific documentation. /Resources 5 0 R It's possible to typeset integrals, fractions and more. … endobj /Resources 21 0 R TeXnicCenter. The general form of n-th or… All MATLAB ® ODE solvers can solve systems of equations of the form y ' = f (t, y), or problems that involve a mass matrix, M (t, y) y ' = f (t, y). 198 0 obj Under Equation Tools, on the Design tab, in the Structures group, click the Bracket button: Un \quad laisserait un trop grand espace dans cette situation; il n'y a besoin que de quelques petits espaces dans ce type d'exemple, et c'est pour cela que Latex fournit : Latex is a stable dispersion of polymer microparticles in water. %���� It is a complex emulsion consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums that coagulate on exposure to air. If all lines converge to a common point, the system is said to be consistent and has a solution at this point of intersection. endstream It is especially useful to write mathematical notation such as equations and formulae. Therefore, I have to copy my equations in Power Point into my Latex file. WordPressでmultilineでlatexするときの便利なまとめ． Series on Blogging with LaTeX This is the 3rd post in the series. Types of Equations 1. /Type /XObject 2. << The & symbol tells … equation*) only indicates, that I don't want the equations to be numbered. endstream If LaTeX is already installed on your system, all you have to do to start with TexMaths is to click on the Equations icon from the TexMaths toolbar. For example, Edmodo will show the formula shown in the left column below if you send a note with the text shown in the right column. TexMaths will try to find the external programs it uses to generate LaTeX equations. /FormType 1 Then type some LaTeX code in the text field of the TexMaths Equations editor and click on the LaTeX button to generate the equation image. I want to write my paper in latex format but do not have right code to split that equation. /Subtype /Form stream Top. After reading this blog, you should be able to know about: How to Write Equations in TexStudio. How to write number sets N Z D Q R C with Latex: \mathbb, amsfonts and \mathbf; How to write angle in latex langle, rangle, wedge, angle, measuredangle, sphericalangle Thus, the following syntax would produce the same system of equations as the first item in the prior example. They can be distinguished into two categories depending on how they are presented: 1. text — text formulas are displayed inline, that is, within the body of text where it is declared, for example, I can say that a + a = 2 a {\displaystyle a+a=2a} within this sentence. endobj TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. To make equation authoring easier, the equation editor is in math mode by default, so it isn't necessary to add math mode commands to your equations. Open source and XHTML compliant. their LATEX system and usable without installing any additional fonts or doing other setup work. How to add an equation in your document, see Working with Microsoft Equation. /BBox [0 0 100 100] * … In your own equation, enter f (x)=.. 2. Abel-Ruffini theorem for systems of polynomial equations. 23 0 obj for example: \begin{align} y_1(x)=&x^2\\ y_2(x)=&2x+1 \end{align} Thanks in advance . x = A\B solves the system of linear equations A*x = B. Latex espace horizontal : qquad,hspace, thinspace,enspace; Latex accolades horizontales et verticales : \left\{,\right\},\underbrace{} et \overbrace{} Latex racine carrée; Degré en Latex; Offrez-moi un café ! /Length 1512 /FormType 1 /Length 15 HOW TO USE LATEX TO WRITE MATHEMATICAL NOTATION There are thr. 3. Open an example in Overleaf. If your LATEX installation is based on TEXLive, and includes documentation, the list can also be accessed by typing texdoc comprehensive at a system prompt. /BBox [0 0 100 100] /Length 15 To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations i…


text:
# A friend chooses two 5 digit positive integers with no common factors and divides one by the other, telling you the result to 12 significant digits. How can you find out what the two numbers were?

Nov 10, 2016

See below.

#### Explanation:

This problem has a "brute force" solution, using an optimization procedure.

Supose we know $f$ a $12$ digit precission associated to a fraction $\frac{n}{m}$ with $n , m$ two $5$ digit integer numbers. So

$n = {\sum}_{k = 0}^{4} {a}_{k} {10}^{k}$ and
$m = {\sum}_{k = 0}^{4} {b}_{k} {10}^{k}$

Defining now

$e = n - f \cdot m$ we can formulate a Linear Programming model with integer restrictions, that could conveniently minimize the objetive function ${\lambda}_{s} - {\lambda}_{i}$ such that

${S}_{\lambda} = \left\{{\mu}_{i} \le {\lambda}_{i} \le e \le {\lambda}_{s} \le {\mu}_{s}\right\}$

with the integer restrictions

S_a = {0 le a_k le 9 for $k = 0 , 1 , 2 , 3$ and 1 le a_4 le 9} and ${a}_{k} \in \mathbb{N}$
S_b = {0 le b_k le 9 for $k = 0 , 1 , 2 , 3$ and 1 le b_4 le 9} and ${b}_{k} \in \mathbb{N}$

The final model is

$\min {\lambda}_{s} - {\lambda}_{i}$

subjected to

$S = {S}_{\lambda} \cap {S}_{a} \cap {S}_{b}$

Here ${\mu}_{i}$ and ${\mu}_{s}$ are margins with the purpose of precision enhancement. Have in mind that Integer programming is not convex programming. Typical values for ${\mu}_{i}$ and ${\mu}_{s}$ are $- {10}^{- 4}$ and ${10}^{- 4}$ respectively.

1) Given $f = 0.764003200360$ the procedure obtained
$n = 13367$
$m = 17496$

2) Given $f = 5.83081793383$ the procedure obtained
$n = 79200$
$m = 13583$

2) Given $f = 3.14159265359$ the procedure obtained
$n = 92988$
$m = 29599$

Nov 10, 2016

Use continued fractions...

#### Explanation:

If the quotient was known exactly then we could recover the original numerator and denominator by calculating the continued fraction, which would terminate, then simplifying.

As it is, we know the quotient to $12$ significant digits, which should be enough. We just have to recognise when we have encountered the rounding error introduced by the $12$ significant figure approximation...

Given the quotient, calculate the continued fraction as follows:

• Write down the integer part and subtract it.

• If the result is zero (or near enough) then stop.

• Otherwise take the reciprocal and repeat.

The sequence of numbers written down form the coefficients of the continued fraction.

For example, suppose your friend told you that the quotient was: $0.357132525241$ to $12$ significant digits.

Following the steps above:

• Write down the integer part $\textcolor{b l u e}{0}$ and subtract it to give: $0.357132525241$

• Take the reciprocal to give: $2.80008100445$

• Write down the integer part $\textcolor{b l u e}{2}$ and subtract it to give: $0.80008100445$

• Take the reciprocal to give: $1.24987344336$

• Write down the integer part $\textcolor{b l u e}{1}$ and subtract it to give: $0.24987344336$

• Take the reciprocal to give: $4.00202593182$

• Write down the integer part $\textcolor{b l u e}{4}$ and subtract it to give: $0.00202593182$

• Take the reciprocal to give: $493.600026480$ (looks like we're getting warm)

• Write down the integer part $\textcolor{b l u e}{493}$ and subtract it to give: $0.600026480$

• Take the reciprocal to give: $1.66659311436$

• Write down the integer part $\textcolor{b l u e}{1}$ and subtract it to give: $0.66659311436$

• Take the reciprocal to give: $1.50016551095$

• Write down the integer part $\textcolor{b l u e}{1}$ and subtract it to give: $0.50016551095$

• Take the reciprocal to give: $1.99933817528$

• That's pretty close to our final integer $\textcolor{b l u e}{2}$

Taking the integers we have written down, we get the continued fraction:

""[color(blue)(0); color(blue)(2), color(blue)(1), color(blue)(4), color(blue)(493), color(blue)(1), color(blue)(1), color(blue)(2)] = color(blue)(0) + 1/(color(blue)(2) + 1/(color(blue)(1) + 1/(color(blue)(4) + 1/(color(blue)(493) + 1/(color(blue)(1) + 1/(color(blue)(1) + 1/color(blue)(2)))))))

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+1/(2+1/(1+1/(4+1/(493+1 /(1+2/3)))))

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+1/(2+1/(1+1/(4+1/(493+3/5))))

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+1/(2+1/(1+1/(4+5/2468)))

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+1/(2+1/(1+2468/9877))

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+1/(2+9877/12345)

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 0+12345/34567

color(white)(""[0; 2, 1, 4, 493, 1, 1, 2]) = 12345/34567

So the original two $5$ digit numbers were $12345$ and $34567$.


text:
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## Friday, September 04, 2015

Since last sale, I have done 3 buys and 2 sells.
I now own a company that I will reveal later.

At the end of August'2015, my portfolio was up 6% from Dec,31,2014.
Not bad, but missed the going up of Corticeira Amorim, the company I was trading.

Corticeira Amorim is now, in my opinion, above fair value so I give up trading it.

See you soon!

## Thursday, July 09, 2015

### Corticeira Amorim - sell

Considering the turmoil the markets have seen these days, I sold my shares and hope to buy them at a little lower price.

This sale was made at 4.135€ representing 1.0% profit, after commissions and fees.

Not bad, in a one month! See you soon!

## Wednesday, June 17, 2015

### Corticeira Amorim - A new buy

Since this is a rather iliquid stock, I didn't mentioned the buy earlier.
A few days ago, I bought again at 4.095€.

Unfortunately, the stock price is under that since that day. Today, it closed at 3.90€.
Not worried, since it is a great company

At my price it has a PER of 13.8 and profits are climbing >10% YOY the last few years.

I'm ok being a shareholder, and wait for the upside I hope for this stock.

## Tuesday, April 14, 2015

### Corticeira Amorim - no upside potencial

I've been watching this stock for a while and made some trading.

From the begining of 2015, the stock went from €3.00 to €4.20 (this moment price), or, a 40% gain. It was a rather impressive climb, but I think this it is now ended.

In the period, I made 5 trades making a profit of 20%. Not much, but then, I am a rather conservative investor.

In my opinion, this is a stock to sell now, for those who own it, or to wait for some dip in price to buy again.

My price target has been attained: €4.20! I predict it will have a 14 PER and a 1.70 P/B this year. As it is a very small free-float company and in a business that is not growing much near times, I think risk is now too much to buy this stock.

Although, the 3.3% yield can be a reason to maitain it, for those who have some shares.

I will continue to follow it, but with no more trading in the next days/weeks.


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Lets be in the category $\mathbf{M}$ of smooth finite dimensional manifolds with smooth maps:

Suppose we have the set of all smooth maps $Hom_\mathbf{M}(R^n,M)$ from $R^n$ to a smooth manifold $M$. Taking only the first Taylor-Approximation of any such map, gives us the n-velocity Space $T_nM$, that is a fiber bundle over $M$ and a generalization of $TM$.

Now suppose we just have a subset of $Hom(R^n,M)$ given by some constraints on the maps lets say $$Hom_\mathbf{M}( R^n,M | constraint_1(f) ... constraint_n(f) )$$.

Does this always gives us a subbundle of $T_nM$?

If not, what should be required to be a subbundle?

Or say it the other way around: What must we proof, to show that the appropriate Jet set is a subbundle of $T_nM$?

(For my purposes its enough to suppose, that the constraints are of zero-order i.e. don't involve any derivations)

1

# Jet spaces for maps with constraints

Lets be in the category $\mathbf{M}$ of smooth finite dimensional manifolds with smooth maps:

Suppose we have the set of all smooth maps $Hom_\mathbf{M}(R^n,M)$ from $R^n$ to a smooth manifold $M$. Taking only the first Taylor-Approximation of any such map, gives us the n-velocity Space $T_nM$, that is a fiber bundle over $M$ and a generalization of $TM$.

Now suppose we just have a subset of $Hom(R^n,M)$ given by some constraints on the maps lets say $$Hom_\mathbf{M}( R^n,M | constraint_1(f) ... constraint_n(f) )$$.

Does this always gives us a subbundle of $T_nM$?

If not, what should be required to be a subbundle?

Or say it the other way around: What must we proof, to show that the appropriate Jet set is a subbundle of $T_nM$?