0. 初めに お久しぶりです。段々と寒くなり、冬の訪れを感じます。 ところで、厚生労働省のホームページ（https://www.mhlw.go.jp/stf/shingi2/0000128981_00001.html） から医師国家試験の出題基準なる文書に出会ることはご存知でしょうか。 そこに、各項目…

Here is the proof Hypatia and I came up with. What we claim is that there is a line dividing the points into two balanced groups on each side, making two smaller instances of the problem, and so by induction we are done. To find the line, …

en.wikipedia.org 隠れマルコフモデルがあって、 そこからの出力の時系列データがある時、 中での状態の推移がどうなっているのかを知りたいことがある。 そんな時に、確率的に最もありそうな状態の時系列を得るアルゴリズムが、Viterbi algorithmだ。 Pseud…

問診事項のメモ。 OPQRST 発症様式、増悪・緩和、質と量、場所・放散痛、随伴症状、時間経過 かきくけこさしすせたあべ 家族歴 既往歴 薬 健康診断 渡航歴 酒たばこ 職業 ストレス 性交歴・月経歴 体重変化 アレルギー 便・尿

www.cambridge.org this paper shows the proof of 9 circles packing in an square. They show some configuration of 9 points, that achieve packing. Next, they make 9 square. Each square contains 1 point. Then, they make iterative algorithm tha…

https://ir.cwi.nl/pub/10189/10189D.pdf Proof of 5 square packing in a square. In this papar, after define some nice length, slightly smaller-size square are prepared, and the 4 nice points are selected. And, it is shown that each of the sq…

en.wikipedia.org from wikipedia. As a continous extension of discrete graph, we can consider real tree, which is in the metric space. there are several conditions that real tree must satisfy. (such as Gromov product) The interesting thing …

youtu.be This video explains the algorithm of Delaunay triangulation nicely, even I could understand the concept. First draw big triangle that contains all vertex, and draw circumcircle of triangle. If some point (we call P) are inside of …

I like reading books on mathematics. I often go to the library and borrow several books. Now I bring two book on functional analysis. These days, I am thinking about the purpose of reading. Of course, you can gain lots of knowledge, and th…

using Optim n = [3 4 5 6 7 8 9 13 15 17] k = [1 2 5 7 11 15 21 47 65 85] lambda = 2.5 f(lam, x) = 1/size(k)[2] * sum((x[1] .+ x[2].*(n) .+ x[3].*(n).^2 .- (k)) .^ 2) - lam * sum(abs.(x)) #f(lam, x) = 1/size(k)[2] * sum((x[1] .+ x[2].*(n) .…

en.wikipedia.org Vertex cover is the subset of vertex sets such that for all edges, at least one endpoint belongs to that subset. It is related to maximal matching of graph. For bipartite graph, there is a nice theorem. en.wikipedia.orgKőn…

When we learn support vector machine, we often want to know the meaning of support. en.wikipedia.org In mathematics, support of function means some set that maps nonzero value by the function. (also, I found nice theorem related to support…

https://www.jstage.jst.go.jp/article/jsiaml/8/0/8_29/_pdf This study shows truncation error of particle method by using Taylor expansion, and mean value theorem, and triangular inequality. Also, open ball is used. And the change of variabl…

Hadwiger Nelson problem is the unsolved problem in mathematics, about minimum chromatic number of unit distance graph. en.wikipedia.org For planar graph, four color theorem is famous, but the unit distance graph allows intersection of edge…

scrapbox.io I found interesting problem related to separation of variables. We can see separation of variables not only in ODE problem, but PDE problem. www.sciencedirect.com For PDE, it is convenient because we can decompose into time dep…

Phase separation in cell is interesting. www.jstage.jst.go.jp Phase separation is dependent on the diffusion coefficient. Whether diffusion is normal or abnormal is meaningful. https://www.rikou.ryukoku.ac.jp/journal/journal74/RJ74-01.pdf …

bmcbioinformatics.biomedcentral.com Ornstein Uhlenbeck process en.wikipedia.org If the parameter is given, and initial condition is provided, then the the distribution at time t > 0 is following Normal distribution whose mean and variance …

Stochastic Model Energy of RNA is divided into two, accessibility and hybridization。 RNA structure is stochastically fluctuated, so the distribution of the shape of RNA is calculated by Boltzmann distribution. RNA secondary structure anal…

I am studying information theory. When we start learning information theory, we will encounter entropy soon. We know discrete version, but there is continous one, called differential entropy. en.wikipedia.org If the mean and variance of th…

If the diagonal matrix A is irreducible (which is we cannot make upper or lower triangular matrix by changing the order of row and column), and the all element is nonnegative, then, there is real positive eigenvalue p(A), and its eigenvect…

I learned the d - separation when I learned statistical causal theory. Given causal directed graph, The path p is called "d separated by node set Z" if either of the following condition are satisfied. 1) p has chain A → B → C or fork A ← B…

We are thinking of EMT/MET transition. With certain modelling, rosa.uniroma1.it https://hal.science/hal-02520861v2/document When we want traveling wave solution with asymptotic states, we take some function depenedent on (x - ct), where x …

We often think about phenomena in biological tissue. In tissue, cellular proliferation and differentiation is the important event. To analyze the dynamics of cellular event, we make Brancing Process. for instance, S : stem cell D : daughte…

When we do not know the probability distribution but we have some restrictions (such as observation of variable, sum of probability is equal to 1, or other knowledge), we can infer the probability distribution by Max entropy method. link.s…

When we thinking of cancer, we often consider variety of phenotype because cancer often mutate and change genetic expression patterns. arxiv.org link.springer.com link.springer.com research-repository.st-andrews.ac.uk Then we get some part…

https://www.plus.ac.at/wp-content/uploads/2021/02/2013-05_Flatz.pdf Nonnegative Tensor Analysisというものを知った。 そもそも、Nonnegative Matrix Factorizationというものは、ある行列を、2つの細い行列の積で表現しようという考え。 それを高次元…

journals.math.tku.edu.tw https://arxiv.org/pdf/1711.01226 math.stackexchange.com link.springer.com 解が有界かどうかを考えると嬉しいことがある。 手法としては、何かしらの不等式を作って、解がある値以上で別のある値以下に抑えられることを示して…

pubmed.ncbi.nlm.nih.gov scRNAの点群データから、細胞の分化の様子を、木グラフで表現するアルゴリズム、URD、の論文。 まず、k近傍グラフを構成して、ある点を根として、そこからグラフ上で拡散(確率的な遷移、ランダムウォーク)させる。 その時に、各点に…

グラフの可視化について調べていた。 ja.wikipedia.org tera-kun.hatenadiary.com https://www.jstage.jst.go.jp/article/jssst/12/4/12_4_335/_pdf/-char/en 基本的なアイデアとしては、 とある2次元の配置に対して、エネルギーなる実数を返す関数を用意す…

https://arxiv.org/pdf/0803.0476 en.wikipedia.org グラフのモジュラリティを小さくするようにクラスター割り当てを行うアルゴリズム。 モジュラリティの更新を早くする方法がarxivの方に書いてある。 モジュラリティとは、同じクラスター内のノード同士が…