Fish play Minority Game as humans do

Previous computer simulations of the Minority Game (MG) have shown that the average agent number in the winning group (i.e., the minority group) had a maximal value such that the global gain was also maximal when an optimal amount of information was available to all agents . This property was further examined and its connection to financial markets has also been discussed . Here we report the results of an unprecedented real MG played by university staff members who clicked one of two identical buttons (A and B) on a computer screen while clocking in or out of work. We recorded the number of people who clicked button A for 1288 games, beginning on April 21, 2008 and ending on October 31, 2010, and calculated the variance among the people who clicked A as a function of time. We find that variance per person decreases to a minimum and rises to a value close to 1/4 which is the expected value when agents click buttons randomly. Our results are consistent with previous simulation results for the theoretical MG and suggest that our agents had employed more information for their strategies as their experience playing the game grew. We also carried out another experiment in which we forced 101 fish to enter one of the two symmetric chambers (A and B). We repeated the fish experiment 500 times and found that the variance of the number of fish that entered chamber A also decreased to a minimum and then increased to a saturated value, suggesting that fish have memory and can employ more strategies when facing the same situation again and again

Interfacing differently oriented biaxial van der Waals crystals for negative refraction

Negative refraction has a wide range of applications in diverse fields such as imaging, sensing, and waveguides and typically entails the fabrication of intricate metamaterials endowed with hyperbolic features. In contrast to artificially engineered hyperbolic materials, natural van der Waals (vdW) materials are more accessible owing to their inherent strong in-plane covalent bonding and weak interlayer interactions. However, most vdW materials manifest uniaxial crystal properties, which restrict their behavior solely to out-of-plane hyperbolicity. This characteristic poses a considerable challenge to their seamless integration via planar fabrication techniques, unless a suitable pattern is employed. Recent advances have identified natural biaxial α-MoO3 as a promising vdW material capable of exhibiting in-plane hyperbolicity. In this study, we performed numerical simulations demonstrating that negative refraction could be achieved by interfacing differently oriented α-MoO3 slabs coated with tunable graphene on a gold substrate. Our comprehensive analysis yielded three notable outcomes: negative refraction, simultaneous positive and negative refractions, and diffractionless propagation. These outcomes could be operated in a broad range of frequencies and achieved at all angles to offer a superior platform for the flexible manipulation of mid-infrared polaritons. Our findings provide valuable insights into the potential application of other two-dimensional vdW materials for advances in nanoscale super-resolution imaging, molecular sensing, and on-chip photonic integrated circuits

Turing model for generating biological patterns

In 1952, A. M. Turing[1] proposed that the reaction-diffusion system could explain the main phenomena of biological morphogenesis. Unfortunately, he died in 1954. However, Turing's intriguing ideas influenced the thinking of theoretical biologists and scientists of many fields. The Turing mechanism has been successfully used for generating patterns in mammals[2,3], fish[4-6], bacterial colonies[7-9], phyllotaxis[10,11] and many others. We simulate the patterns on the elytras of the lady beetles using a reaction-diffusion equation with two types of morphogens based on the Turing model[12]. A part of a half spherical surface is used to approximate the geometry of the hard wings.Various patterns common to lady beetles in Taiwan can be produced on this curved surface. A complex system like the leopard's skin marking still offers an optimal level of challenge for generating it, even though previous simulations using a one-stage Turing model[13-16] might have produced final rosette patterns similar the patterns of real leopards. Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it[17], we construct a two-stage Turing reaction-diffusion model[18] which generates spot patterns initially. In the first stage, spots are generated in a similar manner for both the leopard cub and the jaguar cub. In the second stage, we tune model paraments to generate, separately, the sequence of patterns transformation during the growth of the animals.英國數學家涂林於1952年[1]提出「解釋生物形態發生的反應擴散模型」的創見，不幸卻於1954年早逝，但他的想法已經引起理論生物學家與許多領域的科學家的注意與興趣，開始從事於涂林機制的研究。至今在生物圖案形成的應用累積了許多豐碩的成果，例如成功模擬出哺乳動物毛皮圖案[2,3]、魚類的圖紋[4-6]、細菌群聚的圖樣[7-9]、與植物的葉序[10,11]…等等。 台灣特有的瓢蟲身上豔麗多樣的圖案吸引我們的注意，嘗試將部分的半球面視為瓢蟲的鞘翅(elytra)，以兩種成形素(morphogens)的涂林方程，給予不同的初始濃度分佈與參數，成功製造出不同種類的瓢蟲花紋[12]。 此外對於複雜的豹紋花樣，過去一些以單階段涂林模型的研究，雖然曾經製造出與花豹相類似的玫瑰斑紋[13-16]，但是斑紋隨年齡成長的變化過程的問題，仍然懸而未決。根據動植物種類史的分析(phylogenetic analysis)，顯示貓科動物身上的不同種的斑紋─包括複雜的玫瑰紋(rosettes)與擴散狀的污斑(blotches)─是從點(flecks)演化而來的[17]，我們提出了兩階段的涂林模型[18]，成功的模擬出花豹(leopard)與美洲豹(jaguar)身上複雜的斑紋結構：第一階段首先利用涂林模型製造出點的圖案，對照於剛出生的幼豹的斑紋；第二階段以點為初始條件，調變模型中部分的參數，隨著參數的變化過程，圖案的改變呈現出真實豹紋在成長中的變化。目錄 中文摘要 ⅰ 英文摘要 ⅱ 目錄 ⅲ 圖表目次 ⅵ 第一章 簡介 1 一、 引言 1 二、 涂林模型 2 三、 涂林模型的發展歷史 2 第二章 數學分析 6 一、 反應動力學項( Reaction Kinetics term ) 6 二、 涂林方程式的線性穩定分析 8 三、 初始值對模選擇的影響 18 第三章 瓢蟲花紋模擬 20 一、 模型與線性穩定分析 21 二、 數值模擬 22 三、 模擬的結果 32 (一) 五斑廣盾瓢蟲 32 (二) 七星瓢蟲 34 (三) 杜虹十星瓢蟲 34 (四) 縱條黃瓢蟲 36 (五) 細紋裸瓢蟲 37 第四章 豹紋的模擬 40 一、 模型與線性穩定分析 43 二、 兩階段涂林模型 50 三、 δ對數值模擬的影響 55 四、 數值模擬與結果 58 第五章 二維傅立葉轉換分析 64 第六章 結論 70 附錄A 反應擴散方程去因次的推導 71 附錄B 美洲豹、花豹與獵豹 73 附錄C 催化物-抑制物系統與基質消耗系統 78 附錄D 以兩階段涂林模型模擬台灣的雲豹的毛皮圖案 82 附錄E 論文的相關報導摘錄 83 一、 PHYSICS NEW UPDATE, 26.09.2001 83 二、 Sciscape新聞報導, 28.09.2001 84 三、 SCIENCE NEWS, 06.10.2001 86 四、 Nature, online News, 04.08.2006 89 五、 Nature 442, Research Highlights, 10.08.2006 92 六、 知識通訊評論, 16.08.2006 93 七、 Math Digest, 08.2006 95 八、 LiveScience, 08.08.2006 97 九、 SCIENCE&VIE, 10. 2006 99 十、 2007傑出團隊研究成果 100 十一、動手玩碎形 (天下文化出版) 101 參考資料 102 圖表目次 圖 1-1 七星瓢蟲的成長圖 4 圖 1-2 在化學實驗系統所觀察到的涂林結構圖 5 圖 1-3 催化物-抑制物系統典型的示意圖 5 圖 2-1 特徵值與固定點穩定性之對應關係圖(不含k) 11 圖 2-2 特徵值與固定點穩定性之對應關係圖(含k) 13 圖 2-3 Ãk(k2)行列式的函數曲線圖 17 圖 2-4 不同D值的色散關係圖 17 圖 2-5 滿足涂林不穩定的色散關係圖 18 圖 2-6 典型線性分析得到的色散關係圖 19 圖 3-1 白斑褐瓢蟲( Halyzia sanscrita ) 20 圖 3-2 滿足涂林不穩定的色散關係圖 23 圖 3-3 (fu+gv)與σv的函數關係圖 25 圖 3-4 (fu+gv)與κ的函數關係圖 26 圖 3-5 (fugv+fvgu)與κ的函數關係圖 26 圖 3-6 Dv/Du與κ的函數關係圖 27 圖 3-7 點的大小與Du、Dv/Du的關係 28 圖 3-8 點、線與κ的關係 30 圖 3-9 模擬瓢蟲鞘翅的半球面座標 31 圖 3-10 瓢蟲鞘翅的差異 31 圖 3-11 五斑廣盾瓢蟲 33 圖 3-12 七星瓢蟲 34 圖 3-13 杜虹十星瓢蟲 35 圖 3-14白條菌瓢蟲 37 圖 3-15 細紋裸瓢蟲 39 圖 4-1 貓科動物尾巴的圖案 40 圖 4-2 模擬花豹的玫瑰斑紋 41 圖 4-3 模擬花豹的玫瑰斑紋 41 圖 4-4 模擬花豹的玫瑰斑紋 42 圖 4-5 模擬幼小美洲豹的斑紋 42 圖 4-6 點、線與r2的關係 45 圖 4-7 涂林參數空間與色散關係圖 50 圖 4-8 條紋棘蝶魚( Pomacanthus imperator ) 51 圖 4-9 疊波棘蝶魚( Pomacanthus semicirculatus ) 52 圖 4-10 Weigel提出的假設：貓科動物斑紋的演化途徑 53 圖 4-11 Werdelin與Olsson將貓科動物的斑紋歸類成六種花紋 54 圖 4-12 Werdelin與Olsson認為貓科動物的斑紋的演化途徑 54 圖 4-13 不同δ的色散關係圖 55 圖 4-14 δ與線疏密的關係圖 56 圖 4-15 δ與點疏密的關係圖 57 圖 4-16 不同δ的色散關係圖 60 圖 4-17不同D的色散關係圖 60 圖 4-18 模擬美洲豹的過程中，改變參數D與δ時的色散關係 61 圖 4-19 第一階段以涂林模型模擬點的圖案 61 圖 4-20 模擬花豹的第二階的過程 62 圖 4-21 模擬美洲豹的第二階的過程 62 圖 4-22 α-β參數平面 63 圖 5-1 美洲豹四個典型的圖案與對應的二維傅立葉轉換 65 圖 5-2 二維傅立葉頻譜，水平橫切線的強度分佈 68 圖 5-3 二維傅立葉逆轉換 69 圖 B-J 美洲豹成長過程 74 圖 B-L 花豹成長過程 76 圖 C-1 不同反應系統的null clines 79 圖 C-2 固定態附近的行為模式 80 圖 C-3催化物-抑制物的機制與基質消耗的機制 80 圖 C-4模擬瓢蟲鞘翅斑紋的系統，在相空間中的null clines 81 圖 C-5模擬豹紋的系統，在相空間中的null clines 81 圖 D 以兩階段涂林模型模擬台灣的雲豹的毛皮圖案 8

Fish play Minority Game as humans do

We report the results of an unprecedented real Minority Game (MG) played by university staff members who clicked one of two identical buttons (A and B) on a computer screen while clocking in or out of work. We recorded the number of people who clicked button A for 1288 games, beginning on April 21, 2008 and ending on October 31, 2010, and calculated the variance among the people who clicked A as a function of time. The evolution of the variance shows that the global gain of selfish agents increases when a small portion of agents make persistent choice in the games. We also carried out another experiment in which we forced 101 fish to enter one of the two symmetric chambers (A and B). We repeated the fish experiment 500 times and found that the variance of the number of fish that entered chamber A evolved in a way similar to the human MG, suggesting that fish have memory and can employ more strategies when facing the same situation again and again

Fish play Minority Game as humans do

We report the results of an unprecedented real Minority Game (MG) played by university staff members who clicked one of two identical buttons (A and B) on a computer screen while clocking in or out of work. We recorded the number of people who clicked button A for 1288 games, beginning on April 21, 2008 and ending on October 31, 2010, and calculated the variance among the people who clicked A as a function of time. The evolution of the variance shows that the global gain of selfish agents increases when a small portion of agents make persistent choice in the games. We also carried out another experiment in which we forced 101 fish to enter one of the two symmetric chambers (A and B). We repeated the fish experiment 500 times and found that the variance of the number of fish that entered chamber A evolved in a way similar to the human MG, suggesting that fish have memory and can employ more strategies when facing the same situation again and again