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PageRank as a fundamental tool in graph mining, connections to Markov process and linear algebra. Random Walk PageRank An algorithm that provides a score to each web page. It follows: Each link’s vote is proportional to the importance of its source page. If node jjj with importance rjr_jrj​ has nnn out links, each of the jjj’s neighbors gets rj/nr_j/nrj​/n votes. Page jjj’s own importance is the sum of the votes on its in-links. PageRank can be simply expressed as the sum of the scores of the ...

Lecture notes by Kasper. This lecture: different approaches used to speed up the JL transform. Recall: classic JL transform works by drawing a random matrix AAA with coordinates i.i.d. either N(0,1)\mathcal N(0,1)N(0,1) or uniform random among {−1,+1}\{-1,+1\}{−1,+1} and then embedding a vector xxx to m−1/2Axm^{-1/2}Axm−1/2Ax. m=O(ϵ−2log⁡n)m=O(\epsilon^{-2}\log n)m=O(ϵ−2logn) if one wants to preserve all pairwise distances to within (1±ϵ)(1\pm\epsilon)(1±ϵ) and embedding time is O(dm)O(dm)O(dm). ...

Objective: Examine the compatibility of EF1 with Pareto-optimality, introducing the concept of EFX. Activities: Read and present the paper The Unreasonable Fairness of Maximum Nash Welfare. Ioannis et al. ACM Transactions on Economics and Computation 2019 It’s worth to mention that Iannis received Kalai Prize 2024 for this paper 🎆 Hint from Iannis: Ignore appendix, experiments. Focus on the proof, paraphrase it in my own words, a easy way! Maximum Nash welfare (abbr. MNW) selects an allocatio ...

Vocabulario 名词 nombre m. 名字 país m. 国家 año m. 年；岁 lengua f. 语言 estudiante m.f. 学生 médico, a m.f. 医生 futbolista m.f. 足球运动员 一般以 o 结尾是阳性，以 a 结尾的是阴性 表示国家和国籍的词汇 China 中国 chino, na m.f. 中国人；adj. 中国的，中国人的；m. 汉语 España 西班牙 español, la m.f. 西班牙人；adj. 西班牙的，西班牙人的；m. 西班牙语 Inglaterra 英国 inglés, sa m.f. 英国人；adj. 英国的，英国人的；m. 英语 动词 ser intr. 是 llamarse prnl. 叫……名字 hablar tr. 讲（某种语言） tener tr. 有 动词变位 动词原形 我 你 他/她/它/您 我们 你们 他们/她们/它们/诸位 ser soy eres es somos sois son llamarse me llamo te llama ...

Lezione 1 Italiano o italiana? 语法性 仅适用于名词、代词（要分阴阳性和单复数） 意大利语的名词和代词只有两种性别，分别是阳性和阴性 意大利语的名词和代词一定会有性别 名词的阴阳性 按照男女分类：Uomo 阳、Donna 阴、Italiano 阳、Italiana 阴 无特殊规则：Gelato 阳、Chiave 阴、Casa 阴 阴阳性的判断规则：意大利语名词一般可以从词尾来判断阴阳性。 阳性单数名词 Maschile 一般以 o 结尾 阴性单数名词 Femminile 一般以 a 结尾 以 e 结尾的单词，既可能是阳性，也可能是阴性 名词单复数 阳性 -o/-e 变成 -i 例如： 书 Libro 变成 Libri 大学生 Studente 变成 Studenti 阴性 -a 变成 -e -e 变成 -i 例如： 包 borsa 变成 borse 班级 classe 变成 classi 不规则变化 也有少量的单词阴阳性、单复数变化不规则/特殊 问题 Problema 是阳性的，复数为 Problemi 运动 Sp ...

Fælles feedback Hmmmmm… 🙂 Man kunne fx sige … jeg er travlt jeg har travlt Jeg synes det er spændende at se nye film Jeg synes, det er spændende at se nye film …Hvad med på fredag? Virker det for dig Hvad med på fredag? Passer det dig? Jeg venter på dit svar Jeg glæder mig til at høre fra dig også ikke heller ikke Vi kan møde på torsdag Vi kan mødes på torsdag Selvom og alligevel Selvom： 这个词相当于英语中的 “although” 或 “even though”，用于引导一个转折的情况，表示尽管某种情况存在，但仍然会发生另一种情况。例如：“Selvom ...

Community detection finds sets of nodes, i.e., that are highly connected inside the community and coarsely connected outside the community. Community: a group of individuals sharing common interests. A community is a subset C⊆VC\subseteq VC⊆V of the nodes VVV. Non-overlapping communities or partitions are pairwise disjoint set Ci,CjC_i,C_jCi​,Cj​ s.t. Ci∩Cj=∅C_i\cap C_j=\emptyCi​∩Cj​=∅ for each i,ji,ji,j. Overlapping communities are not necessarily pairwise disjoint. Non-overlapping Community D ...

Lecturer: Iannis Goal of dimensionality reduction: represent a high dimensional data set in a lower dimensional space while preserving much of the important structure. PCA (principle component analysis): to maintain as much variance in the data as possible while reducing the dimensionality. The mapping of data from a high dimensional space to a low dimensional space is called an embedding. Johnson-Lindenstrauss Dimensionality Reduction Lecture notes by Allan Grønlund Main results of JL: any mmm ...

Objective: Investigate alternative fairness concepts for allocating indivisible items. Activities: Read and present the paper New Fairness Concepts for Allocating Indivisible Items by Ioannis et al. IJCAI2023 🍬Bonus: Methodology After reading some papers in fair division with indivisible items. I have come up with a naive 👓 methodology about research in this field. Definition of Fairness Notions: This initial phase entails defining various fairness notions and exploring how these concepts ca ...

Personlige egenskaber Han/hun er … flink/sød/venlig 好/甜/友好 stille og rolig 文静 hjælpsom 乐于助人 sjov 有趣的 aktiv 活跃，活泼 kreativ 有创造力的 kvik/intelligent 思维敏捷/聪明 interessant 有意思的 åben/udadvendt 放得开的/外向的 lidt stille 有点不爱说话 ærlig/til at stole på 诚实/可信 naturlig/ligetil 自然随和/直接 selvsikker 自信 god at snakker med 好说话 et positivt menneske 乐观的人 en god ven 好朋友 god til/ikke så god til … 擅长/不擅长 Han/hun har … et godt humør 心态好 humoristisk sans 幽默感 fuld fart på 雷厉风行 et stort hjerte 有颗大心脏，形容人处变不惊 Han/hun … kan god ...