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1. Mixed-Level Covering, Locating, and Detecting Arrays via Cyclotomy

   Akhtar, Yasmeen; Colbourn, Charles J; Syrotiuk, Violet R (June 2024, Springer)

   Hoffman, Frederick; Holliday, Sarah; Rosen, Zvi; Shahrokhi, Farhad; Wierman, John (Ed.)

   For a finite field of order.q, and.v a divisor of.q − 1, additive translates of a cyclotomic vector yield a.q × q cyclotomic array on.v symbols. For every positive integer.t, for certain.q sufficiently large with respect to.v, such a cyclotomic array is always a covering array of strength.t. Asymptotically such arrays have far too many rows to be competitive with certain other covering array constructions. Nevertheless, for small values of .t , this cyclotomic method produces smallest known covering arrays for numerous parameters suitable for practical application. This paper extends these ideas and shows that cyclotomy can produce covering arrays of higher index, and locating and detecting arrays with large separation. Computational results also demonstrate that certain cyclotomic arrays for the same order.q but different values of .v can be juxtaposed to produce mixed-level covering, locating, and detecting arrays. 

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2. Fault Zone Imaging With Distributed Acoustic Sensing: Body‐To‐Surface Wave Scattering

   https://doi.org/10.1029/2022JB025052  

   Atterholt, James; Zhan, Zhongwen; Yang, Yan (November 2022, Journal of Geophysical Research: Solid Earth)

   Abstract Fault zone structures at many scales largely dictate earthquake ruptures and are controlled by the geologic setting and slip history. Characterizations of these structures at diverse scales inform better understandings of earthquake hazards and earthquake phenomenology. However, characterizing fault zones at sub‐kilometer scales has historically been challenging, and these challenges are exacerbated in urban areas, where locating and characterizing faults is critical for hazard assessment. We present a new procedure for characterizing fault zones at sub‐kilometer scales using distributed acoustic sensing (DAS). This technique involves the backprojection of the DAS‐measured scattered wavefield generated by natural earthquakes. This framework provides a measure of the strength of scattering along a DAS array and thus constrains the positions and properties of local scatterers. The high spatial sampling of DAS arrays makes possible the resolution of these scatterers at the scale of tens of meters over distances of kilometers. We test this methodology using a DAS array in Ridgecrest, CA which recorded much of the 2019 M_w7.1 Ridgecrest earthquake aftershock sequence. We show that peaks in scattering along the DAS array are spatially correlated with mapped faults in the region and that the strength of scattering is frequency‐dependent. We present a model of these scatterers as shallow, low‐velocity zones that is consistent with how we may expect faults to perturb the local velocity structure. We show that the fault zone geometry can be constrained by comparing our observations with synthetic tests. 

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3. Stratification and optimal resampling for sequential Monte Carlo

   https://doi.org/10.1093/biomet/asab004  

   Li, Yichao; Wang, Wenshuo; Deng, K E; Liu, Jun S (February 2021, Biometrika)

   Summary Sequential Monte Carlo algorithms are widely accepted as powerful computational tools for making inference with dynamical systems. A key step in sequential Monte Carlo is resampling, which plays the role of steering the algorithm towards the future dynamics. Several strategies have been used in practice, including multinomial resampling, residual resampling, optimal resampling, stratified resampling and optimal transport resampling. In one-dimensional cases, we show that optimal transport resampling is equivalent to stratified resampling on the sorted particles, and both strategies minimize the resampling variance as well as the expected squared energy distance between the original and resampled empirical distributions. For general $$d$$-dimensional cases, we show that if the particles are first sorted using the Hilbert curve, the variance of stratified resampling is $$O(m^{-(1+2/d)})$$, an improvement over the best previously known rate of $$O(m^{-(1+1/d)})$$, where $$m$$ is the number of resampled particles. We show that this improved rate is optimal for ordered stratified resampling schemes, as conjectured in Gerber et al. (2019). We also present an almost-sure bound on the Wasserstein distance between the original and Hilbert-curve-resampled empirical distributions. In light of these results, we show that for dimension $d>1$ the mean square error of sequential quasi-Monte Carlo with $$n$$ particles can be $$O(n^{-1-4/\{d(d+4)\}})$$ if Hilbert curve resampling is used and a specific low-discrepancy set is chosen. To our knowledge, this is the first known convergence rate lower than $$o(n^{-1})$$. 

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4. Algorithms for Constructing Anonymizing Arrays

   Lanus, E.; Colbourn, C.J. (May 2020, In: Gąsieniec L., Klasing R., Radzik T. (eds), Combinatorial Algorithms. IWOCA 2020. Lecture Notes in Computer Science, vol 12126)

   Attribute-based methods are inherently identity-less as authorization decisions are made in terms of attributes possessed by the subject rather than identity. However, anonymity against the system is not guaranteed when attribute distribution allows for the composition of a policy that few subjects can satisfy. An anonymizing array ensures that any assignment of values to t attributes that appears in the array appears at least r times. When an anonymizing array is used for subjects registered to a system and policies contain conjunctions of at most t attributes, the system cannot identify the subject using the policy to to gain authorization with greater than 1𝑟 probability. Anonymizing arrays are similar to covering arrays with higher coverage and constraints, but have an additional desired property, homogeneity, due to their application domain. In this paper, we develop constructions for anonymizing arrays and propose a post-optimization mechanism to reduce homogeneity. 

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5. Detecting arrays for effects of multiple interacting factors

   https://doi.org/10.1016/j.ic.2024.105202  

   Colbourn, Charles J; Syrotiuk, Violet R (December 2024, Information and Computation)

   Detecting arrays provide test suites for complex engineered systems in which many factors interact. The determination of which interactions have a significant impact on system behaviour requires not only that each interaction appear in a test, but also that its effect can be distinguished from those of other significant interactions. In this paper, compact representations of detecting arrays using vectors over the finite field are developed. Covering strong separating hash families exploit linear independence over the field, while the weaker elongated covering perfect hash families permit some linear dependence. For both, probabilistic analyses are employed to establish effective upper bounds on the number of tests needed in a detecting array for a wide variety of parameters. The analyses underlie efficient algorithms for the explicit construction of detecting arrays. 

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