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"uniformity"
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Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits
We study a class of measure-theoretic objects that we call
eBook
Survey on recent trends towards generalized differential and boomerang uniformities
Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block and stream ciphers and cryptographic hash functions. The discovery of differential cryptanalysis is generally attributed to Biham and Shamir in the late 1980s, who published several attacks against various block ciphers and hash functions, including a theoretical weakness in the Data Encryption Standard (DES). Boomerang cryptanalysis is a method for the cryptanalysis of block ciphers based on differential cryptanalysis. It was invented by Wagner in (FSE, LNCS 1636, 156–170, 1999) and has allowed new avenues of attack for many ciphers previously deemed safe from differential cryptanalysis. Differential and boomerang uniformities are crucial tools to handle and analyze vectorial functions (designated by substitution boxes, or briefly S-boxes in the context of symmetric cryptography) to resist differential and boomerang attacks, respectively. Ellingsen et al. (IEEE Transactions on Information Theory 66(9), 2020) introduced a new variant of differential uniformity, called c-differential uniformity (where c is a non-zero element of a finite field of characteristic p), of p-ary (n, m)-function for any prime p obtained by extending the well-known derivative of vectorial functions into the (multiplicative) c-derivative. Later, Stănică [Discrete Applied Mathematics, 2021] introduced the notion of c-boomerang uniformity. Both c-differential and c-boomerang uniformities have been extended to the idea of simple differential and boomerang uniformities, respectively, which are recovered when c equals 1.This survey paper combines the known results on this new concept of differential and boomerang uniformities and analyzes their possible cryptographic applications. This survey presents an overview of these significant concepts that might have greater implications for future theoretical research on this subject and applied perspectives in symmetric cryptography and related topics. Along with the paper, we analyze these discoveries and the results provided synthetically. The article intends to help readers explore further avenues in this promising and emerging direction of research. At the end of the article, we present more than nine lines of perspectives and research directions to benefit symmetric cryptography and other related domains such as combinatorial theory (namely, graph theory).
Journal Article
True Colors of Oceanography
Data graphics shape the way science is communicated, and the color schemes we employ can either faithfully represent or tacitly obscure the data a figure is intended to convey (Tufte, 1983). Tasteful use of color can make data graphics visually appealing and can draw viewers in, engaging the audience and encouraging further inspection of a figure. But wherever color is used to represent numerical values, its role transitions from a mere aesthetic nicety to carrying the responsibility of conveying data honestly and accurately. Yet, biases introduced by some common colormaps have gone widely unrecognized within the oceanographic community. Here, we describe the pitfalls of some commonly used colormaps, provide guidelines on effective, accurate colormap selection, and present a suite of perceptually uniform cmocean colormaps that have been designed for oceanographic data display.
Journal Article
The PopuList: A Database of Populist, Far-Left, and Far-Right Parties Using Expert-Informed Qualitative Comparative Classification (EiQCC)
With a proliferation of scholarly work focusing on populist, far-left, and far-right parties, questions have arisen about the correct ways to ideologically classify such parties. To ensure transparency and uniformity in research, the discipline could benefit from a systematic procedure. In this letter, we discuss how we have employed the method of ‘Expert-informed Qualitative Comparative Classification’ (EiQCC) to construct the newest version of The PopuList (3.0) – a database of populist, far-left, and far-right parties in Europe since 1989. This method takes into account the in-depth knowledge of national party experts while allowing for systematic comparative analysis across cases and over time. We also examine how scholars have made use of the previous versions of the dataset, explain how the new version of The PopuList differs from previous ones, and compare it to other data. We conclude with a discussion of the strengths and limitations of The PopuList dataset.
Journal Article
Blend Segregation in Tablets Manufacturing and Its Effect on Drug Content Uniformity—A Review
Content uniformity (CU) of the active pharmaceutical ingredient is a critical quality attribute of tablets as a dosage form, ensuring reproducible drug potency. Failure to meet the accepted uniformity in the final product may be caused either by suboptimal mixing and insufficient initial blend homogeneity, or may result from further particle segregation during storage, transfer or the compression process itself. This review presents the most relevant powder segregation mechanisms in tablet manufacturing and summarizes the currently available, up-to-date research on segregation and uniformity loss at the various stages of production process—the blend transfer from the bulk container to the tablet press, filling and discharge from the feeding hopper, as well as die filling. Formulation and processing factors affecting the occurrence of segregation and tablets’ CU are reviewed and recommendations for minimizing the risk of content uniformity failure in tablets are considered herein, including the perspective of continuous manufacturing.
Journal Article
High‐Uniformity Threshold Switching HfO2‐Based Selectors with Patterned Ag Nanodots
High‐performance selector devices are essential for emerging nonvolatile memories to implement high‐density memory storage and large‐scale neuromorphic computing. Device uniformity is one of the key challenges which limit the practical applications of threshold switching selectors. Here, high‐uniformity threshold switching HfO2‐based selectors are fabricated by using e‐beam lithography to pattern controllable Ag nanodots (NDs) with high order and uniform size in the cross‐point region. The selectors exhibit excellent bidirectional threshold switching performance, including low leakage current (<1 pA), high on/off ratio (>108), high endurance (>108 cycles), and fast switching speed (≈75 ns). The patterned Ag NDs in the selector help control the number of Ag atoms diffusing into HfO2 and confine the positions to form reproducible filaments. According to the statistical analysis, the Ag NDs selectors show much smaller cycle‐to‐cycle and device‐to‐device variations (CV < 10%) compared to control samples with nonpatterned Ag thin film. Furthermore, when integrating the Ag NDs selector with resistive switching memory in one‐selector‐one‐resistor (1S1R) structure, the reduced selector variation helps significantly reduce the bit error rate in 1S1R crossbar array. The high‐uniformity Ag NDs selectors offer great potential in the fabrication of large‐scale 1S1R crossbar arrays for future memory and neuromorphic computing applications. A high‐performance selector is fabricated by patterning highly ordered Ag nanodots to control the formation of reproducible filaments. The selector exhibits low leakage current <1 pA, high on/off ratio >108, high endurance >108 cycles, fast switching speed ≈75 ns, and excellent uniformity with CV < 10%. It is further integrated into one‐selector‐one‐resistor structure to demonstrate the feasibility of large‐scale array operation.
Journal Article
Non-Uniformities in Heat Exchangers: A Two-Decade Review of Causes, Effects, and Mitigation Strategies
While extensive research has focused on improving the efficiency and performance of heat exchangers (HXs), identifying the underlying causes of performance degradation remains equally important. Flow and temperature non-uniformities are among the most critical factors affecting performance, often reducing thermo-hydraulic efficiency by approximately 5–10%. These non-uniformities commonly manifest as thermal inconsistencies, airflow maldistribution, and uneven refrigerant distribution. Researchers have observed a notable performance degradation—up to 27%—due to flow maldistribution. Therefore, a clear understanding of their causes and effects is essential for developing effective mitigation strategies to enhance system performance. Despite the notable progress in this area, few studies have systematically classified the dominant non-uniformities associated with specific HX types. This article presents a two-decade review of the causes, impacts, and mitigation approaches related to non-uniformities across different HX configurations. The primary objective is to identify the most critical form of non-uniformity affecting performance in each category. This review specifically examines plate heat exchangers (PHXs), finned and tube heat exchangers (FTHXs), microchannel heat exchangers (MCHXs), and printed circuit heat exchangers (PCHXs). It also discusses mathematical models designed to account for non-uniformities in HXs. This article concludes by identifying key research gaps and outlining future directions to support the development of more reliable and energy-efficient HXs.
Journal Article
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
We prove a theorem giving the asymptotic number of binary quartic forms having bounded invariants; this extends, to the quartic case, the classical results of Gauss and Davenport in the quadratic and cubic cases, respectively. Our techniques are quite general and may be applied to counting integral orbits in other representations of algebraic groups. We use these counting results to prove that the average rank of elliptic curves over ℚ, when ordered by their heights, is bounded. In particular, we show that when elliptic curves are ordered by height, the mean size of the 2-Selmer group is 3. This implies that the limsup of the average rank of elliptic curves is at most 1.5.
Journal Article