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1. Meta Distributions–Part 1: Definition and Examples

   https://doi.org/10.1109/LCOMM.2021.3069662  

   Haenggi, Martin (April 2021, IEEE Communications Letters)

   null (Ed.)

   Meta distributions (MDs) have emerged as a powerful tool in the analysis of wireless networks. Compared to standard distributions, they enable a clean separation of the different sources of randomness, resulting in sharper, more refined results. In particular, they capture the disparity of the performances of individual links or users. In this first part of a two-letter series, we start from first principles and give the formal definition of MDs and present several simple yet illustrative examples. Part 2 [1] explores the properties of the MD in more depth and offers multiple interpretations and applications. 

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2. Statistical Significance of Clustering with Multidimensional Scaling

   https://doi.org/10.1080/10618600.2023.2219708  

   Shen, Hui; Bhamidi, Shankar; Liu, Yufeng (January 2024, Journal of Computational and Graphical Statistics)

   Clustering is a fundamental tool for exploratory data analysis. One central problem in clustering is deciding if the clusters discovered by clustering methods are reliable as opposed to being artifacts of natural sampling variation. Statistical significance of clustering (SigClust) is a recently developed cluster evaluation tool for high-dimension, low-sample size data. Despite its successful application to many scientific problems, there are cases where the original SigClust may not work well. Furthermore, for specific applications, researchers may not have access to the original data and only have the dissimilarity matrix. In this case, clustering is still a valuable exploratory tool, but the original SigClust is not applicable. To address these issues, we propose a new SigClust method using multidimensional scaling (MDS). The underlying idea behind MDS-based SigClust is that one can achieve low-dimensional representations of the original data via MDS using only the dissimilarity matrix and then apply SigClust on the low-dimensional MDS space. The proposed MDS-based SigClust can circumvent the challenge of parameter estimation of the original method in high-dimensional spaces while keeping the essential clustering structure in the MDS space. Both simulations and real data applications demonstrate that the proposed method works remarkably well for assessing the statistical significance of clustering. Supplementary materials for this article are available online. 

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3. Neuc-MDS: Non-Euclidean Multidimensional Scaling Through Bilinear Forms

   Deng, Chengyuan; Gao, Jie; Lu, Kevin; Luo, Feng; Sun, Hongbin; Xin, Cheng (December 2024, The Thirty-eighth Annual Conference on Neural Information Processing Systems (NeurIPS))

   We introduce Non-Euclidean-MDS (Neuc-MDS), an extension of classical Multidimensional Scaling (MDS) that accommodates non-Euclidean and non-metric inputs. The main idea is to generalize the standard inner product to symmetric bilinear forms to utilize the negative eigenvalues of dissimilarity Gram matrices. Neuc-MDS efficiently optimizes the choice of (both positive and negative) eigenvalues of the dissimilarity Gram matrix to reduce STRESS, the sum of squared pairwise error. We provide an in-depth error analysis and proofs of the optimality in minimizing lower bounds of STRESS. We demonstrate Neuc-MDS’s ability to address limitations of classical MDS raised by prior research, and test it on various synthetic and real-world datasets in comparison with both linear and non-linear dimension reduction methods. 

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4. Ecological Impact of Green Computing Using Graphical Processing Units in Molecular Dynamics Simulations

   https://doi.org/10.4018/IJGC.2018010103  

   Marquetti, Izabele; Rodrigues, Jhonatam; Desai, Salil S. (January 2018, International Journal of Green Computing)

   Molecular dynamics (MD) models require comprehensive computational power to simulate nanoscale phenomena. Traditionally, central processing unit (CPU) clusters have been the standard method of performing these numerically intensive computations. This article investigates the use of graphical processing units (GPUs) to implement large-scale MD models for exploring nanofluidic-substrate interactions. MD models of water nanodroplets over flat silicon substrate are tracked wherein the simulation attains a steady state computational performance. Different classes of GPU units from NVIDIA (C2050, K20, and K40) are evaluated for energy efficiency performance with respect to three green computing measures: simulation completion time, power consumption, and CO2 emissions. The CPU+K40 configuration displayed the lowest energy consumption profile for all the measures. This research demonstrates the use of energy efficient graphical computing versus traditional CPU computing for high-performance molecular dynamics simulations. 

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5. An approach to generate correctly rounded math libraries for new floating point variants

   https://doi.org/10.1145/3434310  

   Lim, Jay_P; Aanjaneya, Mridul; Gustafson, John; Nagarakatte, Santosh (January 2021, Proceedings of the ACM on Programming Languages)

   Given the importance of floating point (FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and posits). These representations do not have correctly rounded math libraries. Further, the use of existing FP libraries for these new representations can produce incorrect results. This paper proposes a novel approach for generating polynomial approximations that can be used to implement correctly rounded math libraries. Existing methods generate polynomials that approximate the real value of an elementary function 𝑓 (𝑥) and produce wrong results due to approximation errors and rounding errors in the implementation. In contrast, our approach generates polynomials that approximate the correctly rounded value of 𝑓 (𝑥) (i.e., the value of 𝑓 (𝑥) rounded to the target representation). It provides more margin to identify efficient polynomials that produce correctly rounded results for all inputs. We frame the problem of generating efficient polynomials that produce correctly rounded results as a linear programming problem. Using our approach, we have developed correctly rounded, yet faster, implementations of elementary functions for multiple target representations. 

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