Hasil untuk "Law"

K. Aki

Peter Danielson, J. Finnis

J. Law, J. Hassard

D. Spalding

P. Hsu, H. Robbins

S. Sutera, R. Skalak

G. Turkel, K. Beckett

S. Aji, R. McEliece

E. Schneider, J. Kay

David M cKnight

J. Accot, Shumin Zhai

R. Rigobon, D. Rodrik

Michel L. Goldstein, S. Morris, G. Yen

Abstract.This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnov test for goodness-of-fit tailored to power-law distributions in which the power-law exponent is estimated using MLE. The techniques presented here will advance the application of complex network theory by allowing reliable estimation of power-law models from data and further allowing quantitative assessment of goodness-of-fit of proposed power-law models to empirical data.

Noelle Law, Yuki Miura

Natural disasters are increasing in frequency and severity, causing hundreds of billions of dollars in damage annually and posing growing threats to infrastructure and human livelihoods. Accurate data on roofing materials is critical for modeling building vulnerability to natural hazards such as earthquakes, floods, wildfires, and hurricanes, yet such data remain unavailable. To address this gap, we introduce RoofNet, the largest and most geographically diverse novel multimodal dataset to date, comprising over 51,500 samples from 184 geographically diverse sites pairing high-resolution Earth Observation (EO) imagery with curated text annotations for global roof material classification. RoofNet includes geographically diverse satellite imagery labeled with 14 key roofing types -- such as asphalt shingles, clay tiles, and metal sheets -- and is designed to enhance the fidelity of global exposure datasets through vision-language modeling (VLM). We sample EO tiles from climatically and architecturally distinct regions to construct a representative dataset. A subset of 6,000 images was annotated in collaboration with domain experts to fine-tune a VLM. We used geographic- and material-aware prompt tuning to enhance class separability. The fine-tuned model was then applied to the remaining EO tiles, with predictions refined through rule-based and human-in-the-loop verification. In addition to material labels, RoofNet provides rich metadata including roof shape, footprint area, solar panel presence, and indicators of mixed roofing materials (e.g., HVAC systems). RoofNet supports scalable, AI-driven risk assessment and serves as a downstream benchmark for evaluating model generalization across regions -- offering actionable insights for insurance underwriting, disaster preparedness, and infrastructure policy planning.

William Law

The rapid advancement of creating Zero-Knowledge (ZK) programs has led to the development of numerous tools designed to support developers. Popular options include being able to write in general-purpose programming languages like Rust from Risc Zero. Other languages exist like Circom, Lib-snark, and Cairo. However, developers entering the ZK space are faced with many different ZK backends to choose from, leading to a steep learning curve and a fragmented developer experience across different platforms. As a result, many developers tend to select a single ZK backend and remain tied to it. This thesis introduces zkSDK, a modular framework that streamlines ZK application development by abstracting the backend complexities. At the core of zkSDK is Presto, a custom Python-like programming language that enables the profiling and analysis of a program to assess its computational workload intensity. Combined with user-defined criteria, zkSDK employs a dynamic selection algorithm to automatically choose the optimal ZK-proving backend. Through an in-depth analysis and evaluation of real-world workloads, we demonstrate that zkSDK effectively selects the best-suited backend from a set of supported ZK backends, delivering a seamless and user-friendly development experience.

Yann-Meing Law, Zhichao Peng, Daniel Appelö et al.

In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small local linear systems for which the dimension is independent of the order. The implementation of order adaptive algorithms is straightforward in this setting, making the resulting p-adaptive Hermite method appealing for the simulations of soliton-like wave propagation.

Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

By using the Efetov's super-symmetric formalism we computed analytically the mean spectral density $\rho(E)$ for the Lévy and the Lévy -Rosenzweig-Porter random matrices which off-diagonal elements are strongly non-Gaussian with power-law tails. This makes the standard Hubbard-Stratonovich transformation inapplicable to such problems. We used, instead, the functional Hubbard-Stratonovich transformation which allowed to solve the problem analytically for large sizes of matrices. We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.

C. Bordenave, Djalil CHAFAÏ

Betsey Stevenson, J. Wolfers

Robert Law

Europa's surface exhibits many regions of complex topography termed 'chaos terrains'. One set of hypotheses for chaos terrain formation requires upward migration of liquid water from perched water bodies within the icy shell formed by convection and tidal heating. However, consideration of the behavior of terrestrial ice sheets suggests the upwards movement of water from englacial water bodies is uncommon. Instead, rapid downwards hydrofracture from supraglacial lakes - unbounded given a sufficient volume of water - can occur in relatively low tensile stress states given a sufficiently deep initial fracture due to the negative relative buoyancy of water. I suggest that downwards, not upwards, fracture may be more reasonable for perched water bodies but show that full hydrofracture is unlikely if the perched water body is located beneath a mechanically strong icy lid. However, full hydrofracture is possible in the event of lid break up over a perched water body and likely in the event of a meteor impact that generates sufficient meltwater and a tensile shock. This provides a possible mechanism for the transfer of biologically important nutrients to the subsurface ocean and the formation of chaos terrains.