https://skckenneth.github.io/zh/writing/數學思考、計算實驗與教學的新文章。 zh-Hant Sun, 11 Oct 2026 02:00:00 GMT https://skckenneth.github.io/zh/writing/two-networks-one-spectrum-different-alarms/https://skckenneth.github.io/zh/writing/two-networks-one-spectrum-different-alarms/兩個正值運輸網絡，可以有完全相同的特徵值、損失完全相同的總物質，卻對同一個有限時間感測警報給出相反答案。這個受控研究分清頻譜、路徑、精確響應與決策界限，並檢查有效界限何時仍然沒有用。Sun, 11 Oct 2026 02:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/zh/writing/after-a-good-fit-what-to-measure/https://skckenneth.github.io/zh/writing/after-a-good-fit-what-to-measure/當多組參數都能擬合觀測，下一步未必是換一個最佳化器，而是找出能分辨解釋的新量度。Sun, 11 Oct 2026 00:00:00 GMTdata-aimathematical-thinkingteaching-research-practice https://skckenneth.github.io/zh/writing/choose-the-question-before-the-score/https://skckenneth.github.io/zh/writing/choose-the-question-before-the-score/誤差小或平均表現改善，都只回答各自的問題。到達時間與最弱群組的可靠性，需要直接對應的檢查。Sun, 11 Oct 2026 00:00:00 GMTrisk-decisionscities-engineeringdata-ai https://skckenneth.github.io/zh/writing/keep-the-result-that-changes-the-question/https://skckenneth.github.io/zh/writing/keep-the-result-that-changes-the-question/檢查失敗可以收窄研究能回答的問題。兩項已發布數值研究說明，為何後來的發現不能抹去原本的失敗。Sun, 11 Oct 2026 00:00:00 GMTteaching-research-practicecomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/how-many-equilibria-did-the-optimizer-miss/https://skckenneth.github.io/zh/writing/how-many-equilibria-did-the-optimizer-miss/一幅漂亮的最低能量形狀圖，是否已經交代所有重要平衡？以可獨立枚舉的兩模態控制，分清極小值、鞍點、亞穩定態與分支追蹤，再檢查載荷相位、初值及數值細化如何改變解讀。Sat, 03 Oct 2026 08:20:00 GMTdynamics-networkscomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/what-must-a-traffic-model-remember/https://skckenneth.github.io/zh/writing/what-must-a-traffic-model-remember/在可精確核對的環形道路上，分清被刪去的速度、駕駛員差異與觀測雜訊，如何令過去的資料變得有用。有限歷史可以改善預測，卻不一定代表模型辨認了物理記憶，也不一定仍是有效的降維。Sat, 26 Sep 2026 00:00:00 GMTcities-engineering https://skckenneth.github.io/zh/writing/did-the-hotspot-move-or-did-it-grow/https://skckenneth.github.io/zh/writing/did-the-hotspot-move-or-did-it-grow/兩張空間分布圖可以得到漂亮而精確的最低成本解釋，卻仍然無法辨認真正的生成歷史。這個非平衡最優傳輸合成研究，分開檢查端點擬合、數值收斂，以及搬移與局部生長的機制解讀。Sat, 19 Sep 2026 00:00:00 GMTdata-airisk-decisionscities-engineering https://skckenneth.github.io/zh/writing/can-aggregate-observations-bound-an-epidemic/https://skckenneth.github.io/zh/writing/can-aggregate-observations-bound-an-epidemic/延遲的地區總數可以支持看似精確的估計，卻未必緊緊限制隱藏狀態。透過六區 SIR 合成基準，比較 ensemble 區間與經驗證集合界限，保留界限闊得幾乎失去作用的結果。Sat, 12 Sep 2026 00:00:00 GMTdata-airisk-decisionslife-environment https://skckenneth.github.io/zh/writing/when-taking-turns-makes-a-system-unstable/https://skckenneth.github.io/zh/writing/when-taking-turns-makes-a-system-unstable/相同的更新次數，不一定帶來穩定的回饋。透過一個具有資訊延遲的雙選項模型，理解為甚麼容許兩次更新相隔多一個時段，可以穩定系統，以及最小的公平限制放寬為甚麼不等於最快的排程。Thu, 10 Sep 2026 00:00:00 GMTdynamics-networks https://skckenneth.github.io/zh/writing/when-early-warnings-cannot-tell-the-difference/https://skckenneth.github.io/zh/writing/when-early-warnings-cannot-tell-the-difference/系統恢復變慢，與環境擾動變持久，可以留下相同的統計痕跡。透過精確取樣的隨機模型，本文追問被動監測能識別甚麼，以及哪一種額外量度才能分辨背後機制。Wed, 09 Sep 2026 00:00:00 GMTdata-ailife-environmentdynamics-networks https://skckenneth.github.io/zh/writing/when-solar-power-changes-fast/https://skckenneth.github.io/zh/writing/when-solar-power-changes-fast/以五個太陽能站點的公開數據，檢查快速功率變化與感測輸入缺失時的預測區間。校準令每個站點都改善，但最困難群組的覆蓋率仍遠低於原來的目標。Wed, 09 Sep 2026 00:00:00 GMTcities-engineeringrisk-decisionsteaching-research-practice https://skckenneth.github.io/zh/writing/when-starting-over-finds-the-target-faster/https://skckenneth.github.io/zh/writing/when-starting-over-finds-the-target-faster/重新開始看似浪費進度，卻可能消除隨機搜尋中最漫長的等待。透過精確首次到達實驗，本文分辨平均速度、尾端風險、重啟成本，以及繼續前進反而更好的情況。Wed, 09 Sep 2026 00:00:00 GMTrisk-decisionsdynamics-networks https://skckenneth.github.io/zh/writing/assimilating-what-you-can-observe/https://skckenneth.github.io/zh/writing/assimilating-what-you-can-observe/一個固定的六區 EnKF benchmark 顯示，明確表示聚合與延遲的 observation operator 能改善合成狀態與峰值預測，但 latent-state coverage 不及預設門檻，因此結論只能是 PARTIAL。Sun, 30 Aug 2026 00:00:00 GMTdata-airisk-decisionslife-environment https://skckenneth.github.io/zh/writing/can-a-mesh-preserve-the-event/https://skckenneth.github.io/zh/writing/can-a-mesh-preserve-the-event/在相同 production work 下，比較 uniform、residual 與 goal-oriented finite-element meshes 能否保留 growing-domain modal-transition time；今次 smoke experiment 反而由 uniform mesh 勝出。Sun, 30 Aug 2026 00:00:00 GMTcomputation-codelife-environment https://skckenneth.github.io/zh/writing/from-simulation-to-certificate/https://skckenneth.github.io/zh/writing/from-simulation-to-certificate/一項凍結的合成雙艙正系統 audit，把有限 parameter sampling、共同 Lyapunov inequality、diagonal restriction 與可容許的 robust-decay claim 逐層分開。Sun, 30 Aug 2026 00:00:00 GMTcomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/one-integrator-across-the-fast-slow-boundary/https://skckenneth.github.io/zh/writing/one-integrator-across-the-fast-slow-boundary/一項凍結 Michaelis-Menten audit 把 exact conservation、positivity 與 fixed-step asymptotic limit，同 accuracy、stiffness failure 及 solver-superiority claim 分開驗證。Sun, 30 Aug 2026 00:00:00 GMTcomputation-code https://skckenneth.github.io/zh/writing/random-stress-tests-are-not-certificates/https://skckenneth.github.io/zh/writing/random-stress-tests-are-not-certificates/一個 deterministic interval benchmark 說明 worst-case certificate 必須同時有 feasible lower bound 與 valid set-wise upper bound，而固定抽樣與 local search 只能交出 incumbents。Sun, 30 Aug 2026 00:00:00 GMTrisk-decisionscomputation-code https://skckenneth.github.io/zh/writing/when-a-reduced-ventilation-model-leaves-its-training-regime/https://skckenneth.github.io/zh/writing/when-a-reduced-ventilation-model-leaves-its-training-regime/一項凍結的 synthetic POD 與 POD-DEIM audit 先驗證 full-order reference，然後因兩個 reduced models 在 nominal holdout 已失敗而停止。Sun, 30 Aug 2026 00:00:00 GMTcities-engineeringcomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/when-a-traffic-solver-invents-a-jam/https://skckenneth.github.io/zh/writing/when-a-traffic-solver-invents-a-jam/一個保留失敗結果的 LWR benchmark 顯示，終點時刻的 shock-grid alignment 可令 cell-average norm 看似近乎精確，但門檻到達時間與排隊核算仍然有偏差。Sun, 30 Aug 2026 00:00:00 GMTcomputation-codecities-engineering https://skckenneth.github.io/zh/writing/from-pixels-to-patrols/https://skckenneth.github.io/zh/writing/from-pixels-to-patrols/以技術角度閱讀一項 AI4Nature@AVSS 2026 camera-trap 研究，追蹤機率校準如何進入合成巡邏配置，同時分開議程、證據與出版狀態。Sat, 29 Aug 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/zh/writing/how-rare-is-a-flip/https://skckenneth.github.io/zh/writing/how-rare-is-a-flip/帶誤差界的有限狀態計算與固定種子的直接模擬，在一個合成低 copy 數基因開關事件上互相吻合；但這項第一階段結果只是起點，並非 rare-event 方法的勝利。Sat, 29 Aug 2026 00:00:00 GMTrisk-decisionslife-environmentdynamics-networks https://skckenneth.github.io/zh/writing/when-effective-diffusivity-stops-being-effective/https://skckenneth.github.io/zh/writing/when-effective-diffusivity-stops-being-effective/一個經驗證的 24 案例合成週期薄板基準，標出調和有效擴散係數何時能保留釋放曲線，以及有限單元瞬態何時令 t50 與 t90 超出預先鎖定的誤差門檻。Sat, 29 Aug 2026 00:00:00 GMTcomputation-codecities-engineering https://skckenneth.github.io/zh/writing/when-polynomial-chaos-crosses-a-fold/https://skckenneth.github.io/zh/writing/when-polynomial-chaos-crosses-a-fold/在一個合成 CSTR benchmark 中，全域多項式與 oracle fold-aligned surrogate 各使用 16 次模型評估；局部表示明顯較準，但比較不包括折疊點的發現成本。Sat, 29 Aug 2026 00:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/zh/writing/topology-at-the-edge-of-resolution/https://skckenneth.github.io/zh/writing/topology-at-the-edge-of-resolution/一項受控審核，研究模糊、像素尺度、分割誤差與有限視窗如何令北極融池影像看似跨越實際上未曾出現的連通臨界點。Mon, 24 Aug 2026 00:00:00 GMTdata-ailife-environment https://skckenneth.github.io/zh/writing/when-entanglement-expires/https://skckenneth.github.io/zh/writing/when-entanglement-expires/以數學模型研究量子中繼鏈如何在連結生成與糾纏交換均有機會失敗的情況下，權衡速度、退相干、可靠度與長尾延遲。Sun, 09 Aug 2026 00:00:00 GMTdynamics-networksrisk-decisions https://skckenneth.github.io/zh/writing/can-adhesion-alone-sort-cells-into-tissues/https://skckenneth.github.io/zh/writing/can-adhesion-alone-sort-cells-into-tissues/以細胞 Potts 模型檢驗差異黏附何時導致分選、包覆、停滯混合，以及外表相似但機制不同的終態。Sun, 02 Aug 2026 00:00:00 GMTlife-environmentcomputation-code https://skckenneth.github.io/zh/writing/how-much-tail-risk-a-gaussian-model-hides/https://skckenneth.github.io/zh/writing/how-much-tail-risk-a-gaussian-model-hides/在波動聚集、槓桿效應、厚尾與跳躍下，以受控壓力測試比較高斯、Student-t、歷史及極值風險預測。Sun, 02 Aug 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/zh/writing/when-an-american-put-should-be-exercised/https://skckenneth.github.io/zh/writing/when-an-american-put-should-be-exercised/將提早行使寫成自由邊界障礙問題，並以三種數值方法審核價格、希臘字母、收斂與互補條件。Sun, 02 Aug 2026 00:00:00 GMTcomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/when-simple-drug-release-laws-stop-being-enough/https://skckenneth.github.io/zh/writing/when-simple-drug-release-laws-stop-being-enough/由經驗定律到機理模型的層級研究，揭示熟悉的釋放曲線何時遮蔽有限 sink 傳輸、參數權衡與轉變中的機制。Sun, 02 Aug 2026 00:00:00 GMTdata-aicities-engineering https://skckenneth.github.io/zh/writing/how-noise-flips-a-genetic-switch/https://skckenneth.github.io/zh/writing/how-noise-flips-a-genetic-switch/確定性雙穩態建立兩個記憶狀態，但有限分子數決定隨機基因開關能在每個狀態停留多久。Thu, 30 Jul 2026 00:00:00 GMTlife-environmentcomputation-codedynamics-networks https://skckenneth.github.io/zh/writing/tracking-mains-noise-without-losing-the-muscle-signal/https://skckenneth.github.io/zh/writing/tracking-mains-noise-without-losing-the-muscle-signal/一項可重現的合成實作研究，把因果 sEMG 快速路徑與帶閘門的頻率追蹤器分開，測試諧波消除、包絡保真度與主機 Python 計時，而不冒充參與者或嵌入式裝置驗證。Thu, 30 Jul 2026 00:00:00 GMTdata-ai https://skckenneth.github.io/zh/writing/when-michaelis-menten-stops-being-valid/https://skckenneth.github.io/zh/writing/when-michaelis-menten-stops-being-valid/一個 243 組參數圖譜把 Michaelis-Menten 動力學視為可檢驗的模型降階，標示軌跡或事件時間誤差何時變得重要。Thu, 30 Jul 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/zh/writing/when-one-reactor-has-three-temperatures/https://skckenneth.github.io/zh/writing/when-one-reactor-has-three-temperatures/非等溫連續攪拌反應器可以記住操作路徑，在冷、熱狀態之間跳轉，並在熱失穩折點前愈來愈慢地恢復。Thu, 30 Jul 2026 00:00:00 GMTdynamics-networkscities-engineering https://skckenneth.github.io/zh/writing/when-publication-count-selects-the-method/https://skckenneth.github.io/zh/writing/when-publication-count-selects-the-method/一個文化演化模型顯示，發表偏差與可見產出如何選擇低投入方法，以及具後果的重複驗證抽查何時會改變這股選擇壓力。Thu, 30 Jul 2026 00:00:00 GMTmathematical-thinking https://skckenneth.github.io/zh/writing/growing-domain-turing-topology/https://skckenneth.github.io/zh/writing/growing-domain-turing-topology/一個經數值核實的反應—擴散實驗，研究組織生長何時保留空間圖樣，何時迫使峰值分裂、合併或消失。Tue, 28 Jul 2026 00:00:00 GMTrisk-decisionslife-environmentdynamics-networks https://skckenneth.github.io/zh/writing/heterogeneous-morphoelastic-folding/https://skckenneth.github.io/zh/writing/heterogeneous-morphoelastic-folding/一個簡化形態彈性樑實驗，測試細小的剛度與生長負載空間變化能否引導摺疊數量和位置，而不增加峰值曲率。Mon, 27 Jul 2026 00:00:00 GMTlife-environmentrisk-decisions https://skckenneth.github.io/zh/writing/robust-cstr-safety-envelope/https://skckenneth.github.io/zh/writing/robust-cstr-safety-envelope/一個合成放熱反應器研究，量化在動力學與傳熱不確定下，為保持低於熱風險準則需要放棄多少名義產量。Sun, 26 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/zh/writing/positive-conservative-time-stepping/https://skckenneth.github.io/zh/writing/positive-conservative-time-stepping/一個剛性轉移網絡基準，比較標準顯式積分器與保持非負性及總質量的線性隱式更新。Sat, 25 Jul 2026 00:00:00 GMTrisk-decisionsteaching-research-practice https://skckenneth.github.io/zh/writing/scientific-incentives-reliability/https://skckenneth.github.io/zh/writing/scientific-incentives-reliability/一個演化個體為本模型，把新穎性、嚴謹度與重複研究信用視為競爭的制度誘因，並繪出發現—可靠性前沿。Fri, 24 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/zh/writing/when-sustainable-harvesting-becomes-a-trap/https://skckenneth.github.io/zh/writing/when-sustainable-harvesting-becomes-a-trap/具有強 Allee 效應的隨機模型說明：平均永續產量如何掩蓋崩潰門檻，以及帶保護線的回饋政策如何改變有限期風險—產量前沿。Fri, 24 Jul 2026 00:00:00 GMTdynamics-networkscomputation-coderisk-decisions https://skckenneth.github.io/zh/writing/rough-volatility-robust-hedging/https://skckenneth.github.io/zh/writing/rough-volatility-robust-hedging/一個合成對沖實驗先凍結不確定性感知的無交易帶，再測試它能否在未見粗糙波動及成本情境降低尾部損失與換手。Thu, 23 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/zh/writing/intervention-calibrated-neural-odes/https://skckenneth.github.io/zh/writing/intervention-calibrated-neural-odes/一個合成基因迴路基準在未見介入下比較無約束與符號結構向量場，發現可行性不等於誠實不確定性。Wed, 22 Jul 2026 00:00:00 GMTdata-airisk-decisions https://skckenneth.github.io/zh/writing/when-more-dna-makes-the-wrong-tree-more-certain/https://skckenneth.github.io/zh/writing/when-more-dna-makes-the-wrong-tree-more-certain/四物種合成實驗把抽樣誤差與模型誤差分開，顯示一條很長的序列比對仍可對錯誤演化樹產生百分之百 bootstrap 支持度。Wed, 22 Jul 2026 00:00:00 GMTlife-environment https://skckenneth.github.io/zh/writing/dimensional-equation-discovery/https://skckenneth.github.io/zh/writing/dimensional-equation-discovery/一個受控 symbolic-regression 基準，研究量綱約束能否改善精確方程恢復、縮小搜尋空間及防止單位脆弱公式。Tue, 21 Jul 2026 00:00:00 GMTrisk-decisionsteaching-research-practice https://skckenneth.github.io/zh/writing/sparse-wave-blocking-excitable-media/https://skckenneth.github.io/zh/writing/sparse-wave-blocking-excitable-media/一個 FitzHugh–Nagumo 基準凍結事件觸發局部介入，再測試它能否在未見傳導速度與感測延遲下阻擋行進波。Mon, 20 Jul 2026 00:00:00 GMTrisk-decisionslife-environment https://skckenneth.github.io/zh/writing/when-randomness-defeats-natural-selection/https://skckenneth.github.io/zh/writing/when-randomness-defeats-natural-selection/Wright–Fisher 計算實驗說明：有利等位基因由單一拷貝開始時為何仍多數消失、遷移如何抵消局部適應，以及短暫瓶頸為何會留下長期遺傳缺口。Mon, 20 Jul 2026 00:00:00 GMTlife-environment https://skckenneth.github.io/zh/writing/sequential-nonlinear-model-discrimination/https://skckenneth.github.io/zh/writing/sequential-nonlinear-model-discrimination/一個 Bayesian sequential-design 基準在六次實驗預算下，選擇能分辨 Van der Pol、Rayleigh 與 Duffing 機制的外力。Sun, 19 Jul 2026 00:00:00 GMTrisk-decisionsdynamics-networks https://skckenneth.github.io/zh/writing/a-decision-that-survives-the-shift/https://skckenneth.github.io/zh/writing/a-decision-that-survives-the-shift/分佈穩健最佳化追問：當機率模型只屬近似已知時，哪一個決策仍能維持可接受的表現？Thu, 16 Jul 2026 00:00:00 GMTrisk-decisions https://skckenneth.github.io/zh/writing/when-the-fit-is-not-the-model/https://skckenneth.github.io/zh/writing/when-the-fit-is-not-the-model/曲線可以非常貼近資料，但參數證據仍然薄弱；可識別性分析說明何時新增量度比再換一個最佳化器更重要。Thu, 16 Jul 2026 00:00:00 GMTdata-aidynamics-networks https://skckenneth.github.io/zh/writing/when-treatment-spills-over/https://skckenneth.github.io/zh/writing/when-treatment-spills-over/網絡干擾改變了「處理效應」的意思；暴露映射把實驗設計、估計目標與可辯護的因果結論連接起來。Thu, 16 Jul 2026 00:00:00 GMTdata-aidynamics-networks https://skckenneth.github.io/zh/writing/when-the-timetable-lies/https://skckenneth.github.io/zh/writing/when-the-timetable-lies/一項可重現的課室實驗，研究預測式通風、未通報的轉房、共用風機限制，以及佔用人數緩衝的代價。Wed, 15 Jul 2026 00:00:00 GMTcities-engineeringrisk-decisions https://skckenneth.github.io/zh/writing/designing-for-the-missing-sensor/https://skckenneth.github.io/zh/writing/designing-for-the-missing-sensor/一項合成水網研究的編輯解讀：即使一項量度消失，仍把壓力感測器放在能提供有用證據的位置。Mon, 13 Jul 2026 00:00:00 GMTrisk-decisionscities-engineeringdynamics-networks https://skckenneth.github.io/zh/writing/modeling-workflow/https://skckenneth.github.io/zh/writing/modeling-workflow/一套精簡流程，把假設、模型選擇、計算、驗證、限制與溝通串連起來。Mon, 13 Jul 2026 00:00:00 GMTteaching-research-practice https://skckenneth.github.io/zh/writing/the-alarm-before-the-heat/https://skckenneth.github.io/zh/writing/the-alarm-before-the-heat/建立並壓力測試一個圖結構感知的電池熱預警模型，同時避免把合成結果誤當成安全主張。Mon, 13 Jul 2026 00:00:00 GMTrisk-decisionsdata-ai https://skckenneth.github.io/zh/writing/climate-driven-dengue/https://skckenneth.github.io/zh/writing/climate-driven-dengue/說明一個合成反應—擴散實驗，對氣候敏感傳播機制可以告訴我們甚麼，以及不能支持哪些結論。Fri, 26 Dec 2025 00:00:00 GMTlife-environmentrisk-decisions https://skckenneth.github.io/zh/writing/interpolation-guide/https://skckenneth.github.io/zh/writing/interpolation-guide/把多項式插值、Chebyshev 節點與 Gibbs 現象連接起來的主題導讀。Sun, 21 Jul 2024 00:00:00 GMTcomputation-code