## Thursday, 29 December 2016

### Random BOINC stuffs

I've been supporting BOINC for a few years, but not until the beginning of this year that I've put a computer into computation consistently. Somehow one of the tasks my computer received discovered a new prime number -- 6082*627^34111+1 of 95422 digits long. Not very big but definitely my first discovery in the field of number theory. So allow me to grab the chance to talk about my thoughts on BOINC projects today...

First of all, why? Why am I joining BOINC? For science? Not really - I have absolutely zero interest on extraterrestrial existence [religious influence?] so I won't join those projects who really originates BOINC.

Medicine related projects? Yes I've joined the World Community Grids [WCGs] claiming to help cancers, Zika, AIDS and more. That's surely going to have a positive influence to the world, but given how the industry works I am not really expecting a breakthrough from the project even it's IBM who's managing it.

Physics? No thank you.

Mathematics? Well I somehow believe that Collatz conjecture is true, so it could be largely useless to find counterexamples. We have seen a similar case already -- the ABC conjecture, which was tested by the ABC@home project, now has a pending proof. Prime numbers related projects are kind of interesting, but I still have no idea on finding primes of a specific form that is too big for any practical use. Conjectures are often like, "xxx is true for all k less than ooo" but if ooo is small it is not easy to induce another further results from here. Algebraic structure related projects are then the most meaningful one to me, but I cannot make any further comments since I am not a specialist on algebra.

Proof by computation is surely one of the major modern tools, but besides the 4 colours theorem it is not often that you can find equally important result that is done by computation. And to me, there is no project available on mathematical statements that has enough importance to take my full computation power. So my answer is, for fun.

It's quite fun, isn't it? People now days are tired of crunching MMORPGs manually that they turn into idle games watching the numbers grow. This is simply another idle RPGs that let the numbers grow, only slightly unfriendly to the CPUs and GPUs. You can also make decisions on resource distribution - which project gives you the best reward per second - which can be much more complicated when you put realistic factors into consideration: which project produces less heat/consumes less electricity? Does my ventilation good enough?... no more than picking a suitable map in the RPG and grind properly by carefully choosing the monsters to fight.

Gridcoin or cryptocurrency has been an influential factor these days because it's bonded with BOINC credits and has real money value. People claim that it's the monetary motivation that pushes away people from projects doing `real science' [in their opinion] to some less meaningful projects that offer more credits. To me it does not really matter because gridcoin is never worth the bill of electricity that people consumed to crunch numbers, and given that bitcoin currently being a rather stabilized market [at least, in terms of electronic currencies, and comparing with other cryptocurrencies] I do see the feasibility that gridcoin develops into reliable means of trade. If so, that would be a fully commercialized model of BOINC and gridcoin - private institute issues points for people grinding that can be exchanged into money/prize/whatever. Of course at the end of the day 0.01 or 0.0001 dollar does not make any difference to small scale crunchers. Who cares?

So that's the deal. If you are one that enjoy watching numbers going up and down from some idle flash games/online games. I would recommend you to to join BOINC. Notice that those idel games do take a damn lot of CPU/RAM resources, doing absolutely meaningless work, while BOINC project is at least doing some minimal science, which is better than doing shit :)

## Saturday, 17 December 2016

### A mind set of using linear algebra

Warning: Heavy use of LaTeX follows. Make sure you enabled Javascript to read those equations properly. It is highly recommended to enlarge the page so that the equations are not in congested form.

First of all, seasons greetings everyone. Let's see if I can get the customization article done before the end of 2016...

*

Readers probably know that I use linear algebra extremely heavily -- for casual blog posts, game studies, hardcore research and so on. It is really useful and it simplifies quite a lot of problems when you are stuck to prove it in a traditional way. You can find it in computational maths, topology, combinatorics, and now analysis.

Definition 1. Let $r\in \mathbb{N}_0$. Define $C^r$ to be the space of $r$-times differentiable functions, with the norm

$||f||_{C^r} = \sum _{|s|\leq r} ||D^sf||_{\infty}$

Definition 2. Let $r \in \mathbb{N}_0$ and $\alpha \in (0,1)$. Define $C^{r+\alpha}$ be the space so that the following equipped norm is finite:

$||f||_{C^{r+\alpha}} = \sum _{0\leq |s| < r} ||D^sf||_{\infty} + \sum _{|s|=r} H\ddot{o}l_{\alpha}(D^sf) < \infty$

Theorem 3. Some primitive results. There exist some constants $C>0$ so that:

1) If $f\in C^1$ then $||f||_{C^{\alpha}} \leq C ||f||_{\infty}^{1-\alpha} ||f||_{C^1}^{\alpha}$.

2) If $f\in C^{2+\alpha}$ then $||f||_{C^1} \leq C||f||_{C^{\alpha}}^{(\alpha +1)/2}||f||_{C^{2+\alpha}}^{(1-\alpha)/2}$.

In the rest of this article, $C$ represents some positive constants probably varying from line to line.

Proof. (1) is relatively easy to do using MVT:

$|f(x)-f(y)| = |f(x)-f(y)|^{1-\alpha} |f(x)-f(y)|^{\alpha}$

$\leq (2||f||_{\infty})^{1-\alpha}(||f||_{C^1}|x-y|)^{\alpha}$

$\leq C ||f||_{\infty}^{1-\alpha} ||f||_{C^1}^{\alpha}|x-y|^{\alpha}$

(2) involves some nasty analytical approximation so it will be skipped here.

We split the exponent $1$ into $(1-\alpha) + \alpha$, but what about harder interpolation estimates?

## Sunday, 27 November 2016

### Fan based game customization (1)

Needless to say I am quite an old Osu player - it's my ninth year in the game already. But being stuck in online games does not imply that I am a pure PC console player. In fact I am a big fan of nintendo, or more precisely a big fan of their traditional game series - Mario, Pokemon, Fire Emblem,...their simple but rich art design [at least, in the old days] fits my taste of partial minimalism, and numerically they each represent a possibility of pushing things to extreme.

...what? You say Pokemon RGB has retarded difficulty that BW players would laugh at, and super mario bros. has repetitive design with obsolete control? Well, newcomers to the gaming world must accept that as a fact or phenomenon when you look into the past. Information is pretty much isolated that you won't have access to various walkthroughs, and it is certainly uneasy to figure all out by yourself [walkthroughs worth real money in the past!]. It is often criticised that the Elite four focused on a single element that is easy to battle against [especially Lance, with his team of dragonite fearing coldness very much], but remember the concept of elemental relation is not widely accepted except for a few games [final fantasy and some more, if any], So discovering those becomes an inherited part of the game -- and it's not obvious either due to the rarity of dragon based pokemon. [Some of those relations makes physical sense actually, like the water-fire-grass cycle, but does dragon type pokemon even make sense in the physical world?] And for Mario...bare in mind that completing a game without save is a different story. You were required to complete all 7 worlds just with 3 lives, so your chance is really limited. It is not like the modern ones [since SMW3] that has finite lives but actually allows you to die infinitely [just press 'continue'] -- you lose your points if you die too many times, but not your actual progress. It is not hard to imagine one losing a number of times in a same stage, so completing the whole game could really be a real challenge. At this point the design and control already do not matter because you're already stuck in the game and you want to perform better and faster ---

But that is not what I wanted to talk today. Let us go back to two classic Mario designs - Super Mario Bros. 3 [NES-GBA] and Super Mario World [SNES-GBA]. Despite the fact that they are both in the hall of all-time greatest games, one common feature between the two is that there are a lot of remakes based on the design of these two games, especially the later due to the fact that SNES cartridge can be easily broken. Kaizo who created some trollish superbly hard level has he name named after these kinds of levels - the Kaizo Mario World / Kaizo stage...that soon develops into kind of a standard on what is a well designed stage and what is a trolling stage. Such community contributes a solid part of the retro-gaming, and of course, a solid fanbase of the Mario series. Perhaps inspired by the requests from these gamers, or Nintendo simply ran out of ideas to make new super Mario games, they decided to publish the Super Mario Maker [honestly speaking, Nintendo performed poorly on that year of E3 and SMM is probably the only highlight of it...]. Since then the Mario community inflates quickly and producing stages we have never seen - not only that we have normal stages of difficulty ranging from introductory level to levels with hundreds of moves that requires a extremely narrow time frame typically two or three frames [I am not sure if frame-perfect moves are common though...I am not really a TV console player :/], with different gimmick levels - automated levels, music levels, puzzle levels and a lot more.

That reminds me another game I loved a lot - Osu!. Without doubt that it originates from Osu! the NDS game [or whatever it is called in US], but the modern standard comes from the PC Osu! community [oh hey m980 you should return to make some 'authentic maps', but people nowdays hate them and I don't like them either...] through the process of modding and ranking. The question is, with the heavy involvement and in particular evaluation from the player community, what will a game look like, from both the player end and the official end? The answer is rather simple for Osu! because it is not likely that we will see another commercial Osu! game, and other games that Osu! took reference from are mainly arcade games whose decided to keep with their own theory with the gradual trend of increasing difficulty, which proved to be a success strategy.

But Mario itself, as a commercial game is completely different. Nintendo is not making profit from the Mario Maker platform, and even if they do it does not imply that there is no need to produce any successor. Continuation is essential for this gaming brand as well as for the consoles, or simply Nintendo. What is the impact of Mario Maker to different kind of gamers, and what is the future of Mario? This would be something this article would like to talk about.

We restrict our game customization to the designation of stages as a standard part of the game that simulates the main [the official] part of the game. So plain simulation game [e.g. RollerCoaster Tycoon] does not count. We also require customized 'stages' to be fully playable as intended by the developers in a single player mode [if we also limit ourselves to basically single player games], so pokemon does not count as well -- one may argue that after completing all the post-champion elements players may start to build up a strongest team as for a challenge for themselves, but you can't really fight against your built team and that's probably not an intended part of the game other than the fact that you are allowed to wander around freely in a RPG world.

It is not easy to find games that allow customization in the early years due to the memory restriction [you can't even save your main progress], and the lack of Internet support also make customized stages much less valuable. Therefore these kind of games naturally comes from the PC consoles, typically those flash minigames due to their short main storyline [if there is one]. A typical example is the Super Stacker 2 [I can recall so many interesting stages that I made a few years ago...], or some tower defense that allows customization. We have to be very careful on the definition of game customization when it comes to tower defense because you advances in the game by customizing your objects as well. This is not what we call game customization. When you act as a defender in the game customization refers to customizing the waves including the HP/types of the monsters incoming. And for games featuring the designation of the waves that goes through a TD-like region then customization refers to the alteration of the combination of those defensive objects.

The problem of these minigames is that the surrounding community is too small to trigger anything interesting out of it. Flash games are typically hosted on an integrated site, either just for pure gaming that generates no internal community, or sites that combines forum and gaming structure like Kongregate or Newgrounds in the good old days. [Well, flash games integrated with Discuz! forums have nothing to do with game customization because the aim of those games is quantitative and thus creativity is useless there.] It's still extremely hard to find a big enough community dedicated to a single game that themed with customization. Popular games on Kongregate have their own chat room and assuming that to be players available at the moment it's hard to find games that contain more than 100 players online, or 1000 players active on the message board for at least once...

How about non-flash PC games? I am sorry I can't recall a lot of them honestly :\

So we gave a vague definition on what we want to discuss -- Osu! remains to be one of the best analogy that I can comfortably talk about. In the next entry we shall compare the two as well as a genre of games that does not really fit into the above definition but holds a number of similarities to what we are looking for.

## Sunday, 9 October 2016

### Faster algorithm solving minesweeper puzzles (1)

Minesweeper is something that I'm always addicted to. This is obvious when this blog contains multiple entries talking about different aspects of this absolute classic. Last time, I talked about solving minesweeper using logical deduction generalised as a satisfiability problem. That was quite a long time ago -- when I was playing mienfield. 3 years after that I am now addicted to another minesweeper game called Minesweeper: Collector, that you can find on the Google play store.

Yes of course. Using ILP (integer linear programming) or even SAT (satisfiability) to solve minesweeper is not a very smart idea. Since we are working with equations and we know integral solution exists, we can simply employ linear algebra to make our life easier.

It is a bit hard to define how useful a deduction is by solving all the equations. For instance if we can conclude from 100 equations that now the space of possible solutions has dimension 68, then probably a faster way to solve the puzzle could be done by performing an educated guess in terms of probability. However probability is not something that linear algebra can handle easily so we would simply look for any definite deduction here. The most desirable result from the algorithm is that we can deduce the solution of some particular grids.

For the classic rectangular minesweeper we can think the whole puzzle as a matrix $M\in \mathbb{R} ^{m\times n}$, then we can setup variables $v_{11},...,v_{mn}$. Of course the same idea applies to different kinds of minesweeper shape [hexagonal etc] it is just the naming/coordinate setup that differs. They are supposed to be binary, but this is some technicality that we must handle later.

If a certain grid [for example row $s$ column $t$] is known but its neighborhoods are not all revealed then the grid yields an equation denoted by $E_{st}$. It has the form

$E_{st} ~:~ \sum _{p=s\pm 1, q = t\pm 1}^{1\leq p \leq m, 1\leq q \leq n} \delta _{pq}v_{pq} = c_{st}$

Where $c_{st}$ is the number of mines surrounded, and $\delta _{st} = 1$ if the grid $(s,t)$ is concealed, 0 otherwise. The aim of course, is to identify the mines [i.e. solving $v$] and receive more hints, eventually solving the whole puzzle.

Here is our first algorithm:

Algorithm 1.
-----
Input: A partially solved minesweeper matrix $M\in \mathbb{R}^{m\times n}$ provided that solution exists
Output: Any definite deduction

- Convert puzzle into linear eqautions
- RREF and solve $M$
- Interpret the solution
- Return any conclusion

For example we look at a classic 1-2 combination

$\begin{pmatrix} \square & \square & \square & \square & \square & \square & \square & \square \\ \square & 2 & 1 & 1 & 2 & 2 & 1 & \square \end{pmatrix}$

that should give you deduction like

$\begin{pmatrix} \square & X & O & O & X & X &O & O \\ \square & 2 & 1 & 1 & 2 & 2 & 1 & O \end{pmatrix}$

[where X represents mine and O is safe.] Let $v_1,...,v_{10}$ be the variables naming from left to right, top to bottom. Loot at the matrix reduction:

$\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2\\ 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 1\\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 2\\ 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 2\\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \end{pmatrix} \xrightarrow[~]{rref} \begin{pmatrix} 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 1 & 0 & 1\\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & -1 & 1\\ 0 & 0 & 1 & 0 & 0 & 0 & 1 & 1 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 1\\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 1 \end{pmatrix}$

What a mess! But we can still interpret the solution.

From row 3 we have $v_3+v_7+v_8+v_{10} = 0$, then by non-negativity they are all zero. By removing column 3,7,8,10 and row 3 we instantly get $v_2 = v_5 = v_6 = 1, v_4 = 0$. Now the solution space is given by:

$v = (0,1,0,0,1,1,0,0,1,0)^t + t(1,0,0,0,0,0,0,0,-1,0)^t$ where $t \in \mathbb{R}$, or simply $t \in \left\{ 0,1\right\}$.

as expected. However the deduction is very messy that it cannot be automated in an obvious way. Things get worse if the solution space is more complicated. Look at this simple example:

$\begin{pmatrix} \square & \square & \square & \square & \square & \square \\ \square & 1 & 1 & 2 & 2 & \square \end{pmatrix}$

that yields immediately the following [this should be really obvious for any experienced player!]

$\begin{pmatrix} \square & O & \square & \square & X & \square \\ \square & 1 & 1 & 2 & 2 & \square \end{pmatrix}$

assign the names $v_1,...,v_8$ as before, reduce the matrix:

$\begin{pmatrix} 1 & 1 & 1 & 0 & 0 & 0 & 1 & 0 & 1\\ 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 1\\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 2\\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 2 \end{pmatrix} \xrightarrow[~]{rref} \begin{pmatrix}1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 2\\ 0 & 1 & 0 & 0 & -1 & 0 & 0 & 0 & -1\\ 0 & 0 & 1 & 0 & 0 & -1 & 0 & -1 & 0\\ 0 & 0 & 0 & 1 & 1 & 1 & 0 & 1 & 2 \end{pmatrix}$

The only thing we can deduce is the second equation. Since we know $v_2,v_5\in \left\{ 0,1\right\}$ we must have $v_2 = 0, v_5 = 1$ as predicted, and this is basically all we know.

The trouble here is the deduction heavily relies on facts that we have omitted by modelling the problem into a system of linear equations. Of course rearranging the columns [hence changing the RREF] could solve this problem, but recognising the rearrangement of columns is basically equivalent to knowing the grids that can be definitely [or at least almost definitely - when the solution of that grid has a very low dimension] which is the fundamental aim.

To improve our efficiency instead of adding conditionals that check whether an equation is useful for deduction, we can change the fields that we are working on. Rings wouldn't work [and that is why ILP is bad], but we can look at fields, like $F_2$ or $F_7$!. This will be addressed in the next entry.

## Saturday, 1 October 2016

### Trauma Team review

Well not a very recent game isn't it? Some random recommendation from youtube caught my eyes then I subsequently finished the whole streaming. Back to the time I was stuck in gaming consoles [before went into MUGs] I completed the first game of the Trauma Center series almost perfected every operation, then took on the second opinion but shaking hands definitely makes the game superbly hard on Wii, and I gave up halfway.

Developing the same story line is probably not working after one or two attempts. On one hand the nature of operations being repetitive is somehow pushing the developers to raise the difficulty bar in the sequels. The population is not giving a warm reception against this act -- the precision, speed or continuity necessary to clear the later stage utilizes full functionality of the NDS pad that only a few number of games could had reach such bar. [Wii's better but not a lot, too.] Raising difficulty not only go beyond what gamers could do but also make the game more unreasonable. The story basically entered a dead end - GUILT along with its origin and associated diseases are pretty much cured. Developing something like that takes years as mentioned in the first game, and the way it was spread out decided that it is not easy to create another pandemic anymore. It just makes no sense to try to extend this linear plot.

But the whole story does not stop there. Just look at Phoenix Wright - the introduction of new character adds another layer of complexity of the whole story [in terms of mathematics it is like adding an independent vector into a subspace...right?]. Imagine that your starting pitchers are becoming old and can't be SP anymore. The introduction of a new SP definitely deliver a different game, but it's bitter and sweet finding your old player not only adapting a relief role but also helping the noobs to get through the game. To me, Trauma Center quite successfully replicate such strategy.

Derek and Angie has relieved once or twice already [so they turned into...coach?!? That make sense lol.] so Naomi is a natural choice. Her character didn't change much since her debut, but she was but in an environment with much more interaction and that exposes quite a different side of her. What a pity that the lil' guy failed to impress her enough to gain a starter at the very end.

Each of the individual stories are pretty interesting too, but I feel like getting the story done in like, 6 chapters is too rush. Don't forget that you have the main story pushing you behind so everything is just too quick for those characters to make a change [except for Gabriel who received a real shocker]. Fortunately the ending is kind of complete so I'm leaving happily from the game.

That brings another problem by dividing the whole game into different kinds of puzzles: each type of puzzles has their own significant weakness, and putting all puzzles together is enough to annoy every single player. Operations are extremely easy and generous from beginning to the end - it never escalates even with limited number of operations; endoscoped operations are even more repetitive because the opponent [virus/wounds] never 'fight back', and that is extremely unrealistic. Who would have a full kit equipped on the endoscope? The only thing I can recall from Hank's operation is the super combo that I couldn't recognize where was all the counts from; Maria's one is a nice attempt but the constraint never picks the gamer's back heavily. On the other hand, I found diagnostic and forensic puzzles extremely long and clumsy. It is good that they really collect realistic evidences with details [that stands out from other detective games], but the progress is simply too slow because you cannot reach some obvious conclusion just because the game does not allow you to. The frequent switching scene is also kind of annoying. Why am I going from by office to the scene just to collect 2 pieces of evidence and decided that it's sufficient then go back? I know all of them are logical but redundant logical induction is really bringing any wow factor to the story.

Some other elements of the game is worth mentioning as well. The graphic is nice - American comic styled slides handled the pace well and giving enough details [and easter eggs] given the limited budget [well you know, it's atlus after all...], I definitely like the Japanese styled graphics. Credits must be given to those [Japanese] producer who merged the two together well. Music's average I would say, not that grand and intense as the previous games. A remix of O Fortuna would be a great punch on the old players' stomach, but probably the producer decided not to do so because everything is relaxing and easy here :P

In overall, this is a game that is worth to have a look, especially if you've played similar stuff in the past. Probably too old to buy but streaming videos are worth a shot [say, Karin & Omega's Channel?], and something can be expected from the sequel, if there will be one -- kind of doubtful because it's been 6 years since the last one.

## Monday, 1 August 2016

### 01-08-2016

The nature can sometimes be harsh. Isn't it? Probably a long forgotten nightmare of direct hit under the existence of high tide is approaching fast (not exactly, but people wanted it to go slower allowing more time to improve its CDO).

Living in such metropolitan we often underestimates the power of the nature...interconnected indoor areas and shelters looked safe but you never know what happened next. Who would have expected that the Festival Walk would collapse under thunderstorm? Gales can even be more unpredictable when it comes to destroy things - windows in modern city are designed to withstand tornado-equivalent winds, but random objects brought into the air can pierce glass under fierce pressure just like a piece of paper. Collapsing outdoor structure, and electricity network, flash flooding...essential elements of living in a city could be gone in just a few hours, and these haven't been expected and prepared by residents of the city.

And yes we have Pokemon Go...despite the fact that it does not sound very applauding to me as the authentic game, exposing yourself outside is plainly stupid. The rarity of pokemon in the game is not even close to the chance of getting rare items/cards/characters in a god-damned mobile game, and you've got the chance every single day for free, why risk your life for it?

Vicente may just as well serve as a precaution alarm, but people quickly threw the warning away. And now the real trouble is coming. Hong Kongers, are you ready for that?

## Wednesday, 11 May 2016

### DDR and dance-related games

As a MUG lover you must have encountered this one of the earliest rhythmic games available as an arcade machine - DanceDanceRevolution (DDR). Of course the choice of songs are quite different from now, and that is reasonable considering the change in composition of arcade players that time to now. They realized this before making one of the many sequels DDR Nova so it revives pretty well and remains to be one of the legendary MUG that remains in the arcade center. Other MUGs whose ages are more or less the same meets similar problem as well. Some fixed it and some did not so they rise and fall, like teams in the Premier League...oh this is off-topic now.

So since when I was addicted to this game? I can't really tell. I am of course an Osu player specializing those modes but on the arcade side I used to play taiko primarily then jubeat and beatstream (yes that is rather new, and I do have a rather shallow arcade experience too). But one day my wrist is not feeling well so playing taiko and jubeat would probably be a bad idea [of course, playing DDR with damaged wrist is an even more stupid idea that I didn't realize at that time] and I saw some random player playing caramelldensen [the original one] and that instantly reminds me of the strawberry cake dance from the remix. [Yes the machine is that old!]

So I just gave it a go and never get out of it again. Of course, unless there's absolutely no DDR machine nearby that I can do nothing, like now. Luckily I have my own DDR pad at my home so that I can do some regular minimal practice. Playing with pads definitely weakens the experience you can get from playing the arcade. The difference in hardness [or the spring coefficient] gives you some hint on your positioning without the need to figure it using some extra senses. On the other hand the pad is just simply too slippery at times, so it still takes time for me to fully master that.

A clear substitute would be Pump It Up (PIU) one would say, but I don't really like it. The 5-button setup is a natural choice as a dual for the 4 arrows, but the mapping theory is not very consistent and sometimes forcing awkward movements or maybe I'm just too weak to realize them; choice of music is of course important: SHK and ESTi are not bad. I've been cooperated with mapper for these two composers for quite a long time already -- but if you will the song list with, say, 20% of them you're lacking variety. You can see the choice of songs are quite well-spreaded in terms of the genres but within the same genre they lack variation. It's a wow to see vocaloid and touhou songs --- you do see the might bad apple in both PIU and DDR, but if you compare between the two you can tell PIU's map being unrankable straightaway [using the term from Osu]. For sure you want hardness for competitiveness but that is not for every damn single song. Bad end night for sure go along with dances properly, but are you sure you want a lv23 on this song? That sounds like a group of nuts cramping on the ground. That brings up another issue: the difficulty spread is just stupid. Not only inappropriate levels are assigned to different songs, but the difficulty curve is not well-designed as well.

Poor song selection - mapping - evaluation combines to give a downward cycle in the overall quality and that we have seen numerous time in Osu already...that takes a lot of work for them to capture my heart into it, but I am sure that they'd rather capture others' interest instead. Oh just two more physical complaints -- the inherited light is too hot and the the machine itself is too loud that annoys me seriously on/off the machine. Have to say that the above are all personal opinions so...don't go too hard on me :)

Let's back to DDR. It is kind of interesting that it is a 4K 2-dimensional game [4 inputs with two dimension: notes in the space of 4 arrows and time. Who cares about its topology?], but I am just not good in any of the other 4K-wise game. IIDX, SDVX [should be 6K+2 non-traditional input but well for beginners it is almost 4K]...but I can play DDR and I don't understand why :/ I guess that is associated with one's ability to visualize the theory of a song given all the notes and element played/showing up. I can do that in Osu, taiko and CtB --- all with large hitting objects so maybe that's the key.

If only I can watch my replay, I would be able to analyse songs and mapping using my theory but since I do not have Paseli that is not going to work. So I guess that is all for today -- some shit talk without evidences, just expressing my thought on such essential component in the world of rhythmic games. Here is a little record to remind me how good I was and where am I going to --

DDR: Consistent on lv.15, passing some lv.16. Similar absolute accuracy [in ms] but looks poor in DDR [in grade]: B or C for lv.15 and consistently A or above under lv.15
PIU: Successful attempts around lv.15 but only bothered to play in a relaxing style around lv.6, or sometimes aiming for a perfect --- I've never get a single excellent on jubeat but I can do consistently on PIU songs steadily so you can see how loose the judgement is...
ITG [in the groove, 'fake DDR' or 'stepmania arcarde']: lv.11-12 which converts to high-10 or post-10 in the old DDR scale, but you know these high level songs are not official and they do not tell much. The only thing I can tell is, they are really streamy -- can you imagine a short version of Kokoro with 750 notes and サラマンドラの踊り子 with 730 notes? Don't forget these are low BPM songs meaning that the map is filled with 1/4 and 1/6 mix throughout!

If there is a goal of mine that would be the mighty dancer miku, but that is still too far from me...

## Wednesday, 2 March 2016

### A few cafes in Taiwan

The blog serves more than just mathematics or academic things, so let's talk about food this time.

I went to Taiwan a month ago to meet my friends (from osu! and more), joined FF27, read books,...and of course ate a lot. Without doubt the night markets and old rusty little stalls in the dark corner both yield delicious traditional food, but I also tried lots of western-styled cafe - most of them are giving great surprises. Here allow me to introduce 3 of them:

1. Caldo cafe [台北市復興南路1段107巷5弄2號]

Earl grey, such elegant tea never combines with pastry easily: you want its aroma but not much of its colour, you want its smoothness but you've lost its liquidity --- earl grey cake is quite tricky already, then of course a successful earl grey souffle deserved to be a masterpiece.

Pictured above is an earl grey souffle with grapefruit sorbet and sea salt caramel (on the right it's a cup of fruity Columbia coffee). A well thought combination and the relaxing smell of bergamot spreads throughout the cake, and it spreads evenly and smoothly in your mouth with the assistance of heat from the freshly baked souffle.

I ordered a cinnamon apple pie as well --- not the apple pie in traditional sense, but they use multiple layer of cinnamon crusts with layers of apple on the top and finished with a scoop of vanilla ice cream. The cinnamon mix works really well, but the crust quickly changes its texture from crispy to soft chewy due to the moisture of the ice cream, and both aren't really something that you would fully enjoy, That's why I would recommend the souffle more -- 7 flavors available and once per day, you will always find something you like the most there.

Cost: 350 ~ 400 NTW for souffle + a cup of drink

2. Leslie [復興南路二段160巷11號1樓] (oh this is actually on the ground floor)

Absolute quality. It's hard to find sweets like that at a medium-high price or even in some of the top quality restaurants. Here they specializes in French styled pastry and light food. My first impression is the very warm decoration, and you can feel that from the behavior of customers: a comfortable place for comfort food.

As shown above they serve different tarts, many of which are limited edition. I tried a lemon tart, and failed to overcome the desire to have a try before taking a photo. Silky smooth custard but never too heavy as the zesty lemon flavor immediately comes in taking care of your mouth. The layer of syrup allowed the custard to retain a rather consistent texture and also giving a more mouthful appearance as well.

I also ordered a mille-feuille as shown above. Thin and fragile layers but never too crispy (in contrast to the cinnamon apple pie), you can cut through the cake without much effort and enjoy the combination between the buttery layers and the wonderful cream in between in one single bite.

Certainly I cannot try 4 or 5 different pastries in a single visit so I do missed a number of other deserts like tiramisu made using a mix of coffee wine etc. The shop also serve tea from Mariage Freres, a tea producer that has the same status in France as Twinings in UK. Sakura 2011 is the one I tried and the rose scent works properly with high quality sencha --- and that opened a new door to me as a tea frantic: the moment that I was typing this sentence I was enjoying a cup of wedding imperial with irish cream...

Cost: 350~450 NTW (2 cakes/1 cake and a cup of drink)

3. Simple Kaffa [敦化南路一段177巷48號B1]

Suited in a European styled hotel would this coffee shop brings you to back to a memorable nigh in Prague...? Probably not, but perhaps Tokyo would do. They serve coffee that has won a few medals and their cakes are quite unique that you are not going to find them elsewhere.

Pictured above is a honey flavored cake with a cup of toffee almond latte (hopefully I got this one right). The cake has a sponge texture but with more moisture; the honey foam fills the gap in the cake so that it smells good but it's never too sweet. They also serve a green tea cake that has a really concentrated matcha flavor in its custard that melts under room temperature --- I do not think I'll be able to describe this really interesting combination, but that deserves to be called as innovative in a positive way.

Cost: ~300 NTW (a cake and a cup of coffee)

Hopefully the above allows more choices when you are looking for light food in Taipei and they are really worthy for a go, especially Leslie :)