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59 articles
A synthetic network experiment shows how edge sampling can create false linear-instability alarms, while a mathematically sound spectral certificate often cannot settle the original graph's verdict.
A thermometer can be locally informative while leaving a distant heat-source explanation unresolved. A controlled heat-kernel study separates reflection symmetry, noisy classification and continuous inversion, then compares six ways of spending the same eight-reading budget.
A small forecasting model can spend extra computation fitting the trajectory in front of it. But a better fit to that context is not automatically a better forecast—or a unique identification of the underlying dynamics. Two controlled synthetic cases separate these questions.
Two positive transport networks can lose exactly the same total mass, share every eigenvalue, and still disagree about a finite-time sensor alarm. A controlled study asks what a spectrum misses, what a rigorous margin can certify, and when that margin becomes uninformative.
A short note on choosing the next observation when several parameter explanations already fit the data.
A small error or an improved average answers only its own question. Event timing and worst-group reliability need their own checks.
A failed check can narrow a useful question. Two published numerical studies show why the original failure must remain visible.
A folding-energy study separates minima from saddles, global energy ordering from metastability, and branch discovery from proof, asking when an optimizer's attractive shape map leaves something important out.
A controlled ring-road study separates hidden velocity, projection-induced memory, noisy observation, and numerical sensitivity, asking when a better traffic forecast also gives a better stability diagnosis.
Two spatial maps can share a convincing least-cost explanation without revealing the history that produced them. A controlled unbalanced optimal transport study separates endpoint fit, numerical convergence and evidence for movement versus local growth.
Delayed regional totals can support a precise-looking estimate without tightly constraining the hidden state. A six-region synthetic SIR benchmark compares ensemble intervals with validated set bounds, including the cost of bounds that become almost useless.
Equal update counts do not guarantee stable feedback. A delayed two-choice model shows why allowing one extra slot between updates can stabilize a system, and why its smallest fairness relaxation is not its fastest schedule.
A system that recovers slowly and an environment that persists can leave the same statistical signature. An exactly sampled stochastic experiment shows what passive monitoring can identify, and which extra observations change the question.
A five-station study asks whether solar prediction intervals remain trustworthy during rapid power changes and missing sensor inputs. Better calibration improves every station, yet the hardest groups still fall far below the intended coverage.
Starting over discards progress, yet it can remove the longest waits in a random search. An exact first-passage experiment separates mean speed, tail risk, restart costs, and the situations where continuing is better.
A frozen six-patch EnKF benchmark shows that an explicit aggregate-and-delay observation operator improves synthetic state and peak forecasts, yet undercovers the latent state and therefore earns only a PARTIAL conclusion.
A matched-work experiment asks whether uniform, residual, or goal-oriented finite-element meshes best preserve a growing-domain modal-transition time. In this first smoke test, uniform wins.
A frozen two-compartment positive-system benchmark separates finite spectral checks from verified all-parameter decay bounds and shows a benchmark-specific cost of restricting the quadratic certificate to be diagonal.
A frozen Michaelis-Menten audit separates exact conservation, positivity, and a fixed-step asymptotic limit from accuracy, stiffness failures, and solver-superiority claims.
A deterministic interval benchmark shows exactly what a worst-case certificate contains, and why fixed random, Latin-hypercube, and local-search results remain incumbents.
A frozen synthetic POD and POD-DEIM audit verifies its full-order reference, then stops because both reduced models fail before any declared ventilation shift is applied.
A failure-preserving LWR benchmark shows how final shock-grid alignment can make a cell-average norm look exact while threshold arrival and queue accounting remain biased.
A technical reading of an AI4Nature@AVSS 2026 camera-trap study, tracing how probability calibration reaches a synthetic patrol allocator while keeping programme, evidence, and publication status separate.
A bounded finite-state calculation and seeded direct simulation agree on one synthetic low-copy genetic-toggle event—but that Phase-1 agreement is a starting point, not a rare-event victory.
A verified 24-case synthetic slab benchmark maps where a harmonic effective diffusivity preserves release curves and where finite-cell transients make it miss t50 and t90.
A global polynomial and an oracle fold-aligned surrogate receive the same 16 model evaluations on one synthetic CSTR benchmark; the local construction is far more faithful, but the oracle cost is outside the comparison.
A controlled audit of when blur, pixel size, segmentation error, and finite windows make Arctic melt-pond images appear to cross a connectivity threshold that the latent surface did not.
A mathematical-modeling study of how a quantum repeater should trade speed against decoherence when link generation and entanglement swapping are probabilistic.
A cellular Potts study tests when differential adhesion produces sorting, engulfment, arrested mixtures, or misleadingly similar end states.
A controlled stress test compares Gaussian, Student-t, historical, and extreme-value risk forecasts under volatility clustering, leverage, heavy tails, and jumps.
A free-boundary study turns early exercise into an obstacle problem, then audits price, Greeks, convergence, and complementarity across three numerical methods.
A hierarchy of empirical and mechanistic dissolution models reveals when a familiar release curve conceals finite-sink transport, parameter trade-offs, and changing regimes.
Deterministic bistability creates two memory states, but finite molecular copy number determines how long a stochastic genetic toggle remains in either one.
A reproducible synthetic implementation separates a causal sEMG fast path from a gated frequency tracker, then tests harmonic cancellation, envelope fidelity, and host-Python timing without claiming participant or embedded-device validation.
A 243-case atlas treats Michaelis-Menten kinetics as a testable model reduction and maps where trajectory or event-time errors become important.
A non-isothermal CSTR can remember its operating path, jump between cold and hot states, and recover ever more slowly before a thermal fold.
A cultural-evolution model shows how publication bias and visible output can select low-effort methods, and when replication audits change that selection pressure.
A verified reaction–diffusion experiment asks when tissue growth preserves a spatial pattern and when it forces peaks to split, merge, or disappear.
A reduced morphoelastic beam experiment tests whether small spatial changes in stiffness and growth load can steer fold number and location without increasing peak curvature.
A synthetic exothermic-reactor study quantifies how much nominal production is surrendered when a decision must remain below a thermal-risk criterion under uncertain kinetics and heat transfer.
A stiff transfer-network benchmark compares standard explicit integrators with a linearly implicit update that preserves non-negativity and total mass.
An evolutionary agent-based model treats novelty, rigour, and replication credit as competing institutional incentives and maps their discovery–reliability frontier.
A stochastic strong-Allee model shows why average sustainable yield can conceal a collapse threshold and why a feedback refuge changes the finite-horizon risk–yield frontier.
A synthetic hedging experiment freezes one uncertainty-aware no-trade band and tests whether it reduces tail loss and turnover across unseen rough-volatility and cost regimes.
A synthetic gene-circuit benchmark compares an unconstrained neural vector field with a sign-structured model under unseen interventions, and finds that feasibility does not guarantee honest uncertainty.
A synthetic quartet experiment separates sampling error from model error and shows how a long alignment can give complete bootstrap support to the wrong phylogenetic tree.
A controlled symbolic-regression benchmark asks whether dimensional constraints improve exact equation recovery, shrink the search space, and prevent unit-fragile formulas.
A FitzHugh–Nagumo benchmark freezes an event-triggered local intervention and tests whether it blocks travelling waves under unseen conduction speeds and sensor delays.
A Wright–Fisher experiment shows why a beneficial allele is usually lost when it begins as one copy, how migration can oppose local adaptation, and why a brief bottleneck leaves a lasting genetic deficit.
A Bayesian sequential-design benchmark chooses forcing experiments that distinguish Van der Pol, Rayleigh, and Duffing mechanisms under a six-experiment budget.
Distributionally robust optimization asks which decision performs acceptably when the probability model is only approximately known.
A close fit can coexist with weak parameter evidence. Identifiability analysis shows when new measurements matter more than another optimizer.
Network interference changes the meaning of a treatment effect. Exposure mappings connect experimental design, estimands, and defensible causal claims.
A reproducible classroom experiment on predictive ventilation, unannounced room changes, shared fan limits, and the price of an occupancy buffer.
An editorial account of a synthetic water-network study that places pressure sensors for useful evidence even after one measurement disappears.
A compact workflow for assumptions, model choice, computation, validation, limitations, and communication.
Building and stress-testing a graph-aware battery thermal warning model without confusing a synthetic result for a safety claim.
You are standing at an optical table, looking at a vacuum chamber where a dielectric nanoparticle is levitated by a tightly focused laser beam. As the pressure decreases into the Knudsen regime, the system becomes highly underdamped. To...
You are standing in a control room, looking at an 8×8 km city grid. Three No-Fly Zones—a park, a hospital, a government building—occupy strategic positions. Fifty customer locations are scattered across the remaining space. Your job:...
You are standing on a coastal promenade in 2024, watching the gentle waves lap against the seawall. The city behind you—$10 billion in property value, home to half a million people—sits just meters above sea level. The wall is 2 meters...
Welcome to another technical deep-dive! In this post, we venture into the orbital battlefield above Earth—where every defunct satellite or forgotten bolt can become the spark for a catastrophic chain reaction. This is the story of the...
The jetbike screams through the void, its engine a thunderclap in the silence of space. At the controls, Jaghatai Khan—the Warhawk, Primarch of the White Scars—pushes his mount to the absolute limit. Ahead, wreathed in toxic mist,...
You are driving on the highway, cruising at 110 km/h. Suddenly, brake lights flare ahead. You stomp on your pedal, checking your rearview mirror, heart rate spiking. The car behind you swerves slightly. You crawl forward for ten...
It was winter in Macau, and the temperature hovered around 25 degrees Celsius—hardly what you'd expect for mosquito season. Yet there I was, getting bitten. That moment got me thinking: if mosquitoes are active in what should be their...
A guide to what a synthetic reaction–diffusion experiment can—and cannot—show about climate-sensitive transmission.
As the demand for persistent aerial platforms grows, a fundamental question in aerospace control emerges:
In the first post, we broke up with perfection and made peace with good-enough solutions using heuristics. In the second, we climbed invisible mountains and saw how local search, restarts, and simulated annealing zig-zag across rugged...
Imagine you are standing in front of a vending machine. You are hungry, and you have exactly one minute before your bus arrives. Inside, there are 40 different snacks—chips, chocolates, nuts, granola bars.
In the last post, we embraced "good enough." This sequel goes deeper into the math of how heuristics move across rugged fitness landscapes —the invisible mountains where every coordinate encodes a solution and its height is the...
As renewable energy sources become increasingly integrated into power systems, a fundamental challenge emerges: how can communities design fair and efficient energy trading mechanisms that maximize renewable energy usage while ensuring...
As humanity has observed the night sky for millennia, different cultures have developed their own systems for dividing the celestial sphere into constellations—patterns of stars that facilitate navigation, storytelling, and astronomical...
As solar photovoltaic (PV) systems become increasingly prevalent worldwide, a fundamental question emerges: are solar panel trackers—electromechanical devices that rotate panels to follow the sun—cost-effective investments, or are they...
As humanity's presence in space expands with thousands of satellites now orbiting Earth, a critical challenge emerges at the intersection of orbital mechanics, game theory, and autonomous decision-making: how do we design collision...
In the rapidly advancing field of computational ecology and agricultural systems modeling, a critical challenge emerges at the intersection of ecosystem dynamics, pollinator conservation, and agricultural productivity: how do we...
In the rapidly advancing field of scientific machine learning and computational physics, a critical challenge emerges at the intersection of deep learning, numerical methods, and inverse problem theory: how do we efficiently solve...
Why This Project Matters: The Critical Challenge of Shared Resource Management in Quantum Systems
Why This Project Matters: The Urgent Challenge of Misinformation in the Digital Age
This post explores a comprehensive physics-based framework I developed for modeling urban microclimates and optimizing thermal comfort through strategic tree placement. While addressing critical challenges in urban heat island...
This post explores a comprehensive mathematical framework I developed for optimizing shared micro-mobility systems through advanced operations research techniques and sophisticated multi-objective optimization. While addressing complex...
This post explores a computational framework I developed for modeling and analyzing multi-species ecosystem dynamics through advanced mathematical techniques and sophisticated perturbation analysis. While addressing complex challenges...
This post explores a comprehensive computational physics framework I developed for modeling and controlling multi-degree-of-freedom robotic manipulators through advanced Lagrangian dynamics and sophisticated control strategies. While...
This post explores a comprehensive mathematical modeling framework I developed for optimizing urban traffic flow systems through advanced multi-objective optimization techniques. While addressing complex transportation challenges in...
This post explores a comprehensive mathematical modeling framework I developed for optimizing sustainable urban mobility systems. While addressing complex transportation challenges in dense urban environments, this project provided an...
This post explores a mathematical modeling exercise I recently completed during the summer break. While the scenario may seem "utopian," it provided a fascinating opportunity to apply advanced quantitative techniques to a complex problem.
This post presents my comprehensive mathematical modeling framework for optimizing NYC's Citi Bike system expansion. Through an integrated approach combining advanced forecasting, multi-objective optimization, and systems thinking, I...
This is a blog post that comes from my insights on the casino industry in Macau. Since I have been supervising two teams for participating the IMMC 2025, I ain't gonna share the blog posts for the problems in the competition. However, I...
This is the fourth blog post in the series of numerical analysis. In this blog post, we will discuss interpolation beyond polynomials, focusing on the theory and applications of radial basis functions (RBFs). We will explore the...
This is the fifth blog post in the series of numerical analysis. The series aims to provide a comprehensive overview of numerical methods, their theoretical foundations, and practical applications. In this post, we explore the...
It has been a while since I last posted a blog; yet, I have finally finished all three problems of IMMC 2025 Autumn. Problem B is the blog post here, and Problem C is the blog post here. Blog post for Problem C is quite short since the...
This is the first blog post series of Numerical Analysis. In this series, we will discuss some advanced topics in scientific computing. We will cover the following topics:
This is another blog post of the series of numerical analysis. In this blog post, we will discuss advanced eigenvalue methods and their applications in scientific computing. We will cover the theoretical foundations of eigenvalue...
This is the third blog post of the series on Numerical Analysis. In this post, we will discuss Iterative Methods for Large Linear Systems. The post will cover the theoretical foundations of iterative methods, including matrix splitting...
This is blog post for the HiMCM 2024 competition. The blog post is about the environmental footprint of High-Powered Computing (HPC) and the challenges and solutions for a sustainable digital future. The blog post covers the problem...
Follows the previous blog post, this is also another one about the IMMC 2025 competition. This time, I will be discussing the solution to Problem C, focusing on household plastic recycling sustainability. This fascinating problem...
Never thought I have not written any blog post for whole November. I have been busy with my work. But anyway, I am back to write a blog post for the International Mathematical Modeling Challenge (IMMC) 2025. This blog post is for the...
This blog presents a mathematical model for fair resource allocation in a Mars research base scenario, implementing multiple distribution strategies including maximum value allocation, Nash social welfare optimization, and social...
It has been a while since I last posted. I have been busy with work and other personal projects. I am excited to share with you a new project that I have been working on. In this blog post, I will discuss the art and science of...
This is another blog post continuing the series on Mathematical Modeling and Python , the problem comes from the MCM (Mathematical Contest in Modeling) competition. The problem is about building and optimizing a trading strategy about...
This is a blog post for the HiMCM 2021 Problem B. The blog post will cover the Lake Mead water crisis, including the factors affecting water volume, modeling water levels using SARIMAX and structural time series models, and developing...
This is a blog post about the 2021 MCM Problem A on modeling fungal decomposition of woody fibers.
This is a blog post about HiMCM 2021 Problem A. The problem statement can be found here. Briefly, the problem is about designing a solar energy storage system for a small town.
This is a blog post about the 2019 High School Mathematical Modeling Contest(HiMCM) Problem B. The problem is about modeling the impact of banning the sale of single-serving plastic water bottles in Concord and San Francisco. To be...
This is another blog post for the 2023 High School Mathematical Contest in Modeling (HiMCM). By taking a glance at the title, one may understand it is about e-buses. The problem statement in some sense is "easy" to understand, but it is...
It is a mathematical modeling problem from MCM 2023 Problem A. The problem is as follows:
This problem unlike the previous posts, is more "recent" in some sense. However, I also encountered this problem in a MCM competition (Even though I have not enrolled). Like the problems in MCM, this problem is also quite interesting...
This is another blog about Mathematical Modeling , Curve Fitting , and Python . In this blog, I will discuss the Problem B of the HiMCM 2022 . The problem is about CO2 and Global Warming .
This problem is quite an "ancient" problem in the HiMCM competition. The problem is about the hydrographic data problem. Even though the problem is quite old, the problem is still relevant to the current situation. Moreover, I consider...
This post is established based on the project I have read on the book "A First Course in Mathematical Modeling" by Frank R. Giordano et al. The project is about the spread of a contagious disease. The spread of a contagious disease can...
School Busing is quite an interesting problem in real life. For me, as an adult with no vehicle, I have to rely on public transportation. Luckily, I live near my workplace. However, for children, they might have to travel a long...
This post is established based on the project I have read on the book "A First Course in Mathematical Modeling" by Frank R. Giordano et al. The project is about simulating the game of darts.
Continuing with the series of posts on numerical analysis, in this post, I am going to discuss Curve Fitting . One may wonder what the difference between interpolation and curve fitting is. To illustrate, one may consider interpolation...
Continuing with the series of posts on numerical analysis, in this post, I will discuss the Gibbs phenomenon . Last time I discussed the Runge phenomenon, which is a problem that occurs when interpolating a function using high-degree...
To begin with, one may wonder why we need to interpolate a function. The answer is simple: interpolation is a fundamental technique in numerical analysis that allows us to approximate a function using a set of discrete data points. By...
A topic guide connecting polynomial interpolation, Chebyshev nodes, and the Gibbs phenomenon.
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