Kemeny's constant and Wiener index on trees

On trees of fixed order, we show a direct relation between Kemeny's constant and Wiener index, and provide a new formula of Kemeny's constant from the relation with a combinatorial interpretation. Moreover, the relation simplifies proofs of several known results for extremal trees in terms of Kemeny's constant for random walks on trees. Finally, we provide various families of co-Kemeny's mates, which are two non-isomorphic connected graphs with the same Kemeny's constant, and we also give a necessary condition for a tree to attain maximum Kemeny's constant for trees with fixed diameter

Neuronal messenger ribonucleoprotein transport follows an aging Lévy walk

Localization of messenger ribonucleoproteins (mRNPs) plays an essential role in the regulation of gene expression for long-term memory formation and neuronal development. Knowledge concerning the nature of neuronal mRNP transport is thus crucial for understanding how mRNPs are delivered to their target synapses. Here, we report experimental and theoretical evidence that the active transport dynamics of neuronal mRNPs, which is distinct from the previously reported motor-driven transport, follows an aging Levy walk. Such nonergodic, transient superdiffusion occurs because of two competing dynamic phases: the motor-involved ballistic run and static localization of mRNPs. Our proposed Levy walk model reproduces the experimentally extracted key dynamic characteristics of mRNPs with quantitative accuracy. Moreover, the aging status of mRNP particles in an experiment is inferred from the model. This study provides a predictive theoretical model for neuronal mRNP transport and offers insight into the active target search mechanism of mRNP particles in vivo.1111sciescopu

Refined canonical stable Grothendieck polynomials and their duals, Part 2

This paper is the sequel of the paper under the same title with part 1, where we introduced refined canonical stable Grothendieck polynomials and their duals with two families of infinite parameters. In this paper we give combinatorial interpretations for these polynomials using generalizations of set-valued tableaux and reverse plane partitions, respectively. Our results extend to their flagged and skew versions.Comment: 34 pages. This is the sequel of the manuscript (arXiv:2104.04251

Refined canonical stable Grothendieck polynomials and their duals

In this paper we introduce refined canonical stable Grothendieck polynomials and their duals with two infinite sequences of parameters. These polynomials unify several generalizations of Grothendieck polynomials including canonical stable Grothendieck polynomials due to Yeliussizov, refined Grothendieck polynomials due to Chan and Pflueger, and refined dual Grothendieck polynomials due to Galashin, Liu, and Grinberg. We give Jacobi--Trudi-type formulas, combinatorial models, Schur expansions, Schur positivity, and dualities of these polynomials. We also consider flagged versions of Grothendieck polynomials and their duals with skew shapes.Comment: 55 pages, 10 figure

Next-generation big data analytics: state of the art, challenges, and future research topics

The term big data occurs more frequently now than ever before. A large number of fields and subjects, ranging from everyday life to traditional research fields (i.e., geography and transportation, biology and chemistry, medicine and rehabilitation), involve big data problems. The popularizing of various types of network has diversified types, issues, and solutions for big data more than ever before. In this paper, we review recent research in data types, storage models, privacy, data security, analysis methods, and applications related to network big data. Finally, we summarize the challenges and development of big data to predict current and future trends.This work was supported in part by the “Open3D: Collaborative Editing for 3D Virtual Worlds” [EPSRC (EP/M013685/1)], in part by the “Distributed Java Infrastructure for Real-Time Big-Data” (CAS14/00118), in part by eMadrid (S2013/ICE-2715), in part by the HERMES-SMARTDRIVER (TIN2013-46801-C4-2-R), and in part by the AUDACity (TIN2016-77158-C4-1-R). Paper no. TII-16-1

Kemeny's constant and enumerating Braess edges in trees

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees

Analysis of Parallel Implementation of Pilsung Block Cipher On Graphics Processing Unit

This paper focuses on the GPU implementation of the Pilsung block cipher used in the Red Star 3.0 operating system developed in North Korea. The Pilsung block cipher is designed based on AES. One notable feature of the Pilsung block cipher is that the table calculations required for encryption take longer than the encryption process itself. This paper emphasizes the parallel implementation of the Pilsung block cipher by leveraging the parallel processing capabilities of GPUs and evaluates the performance of the Pilsung block cipher. Techniques for optimization are proposed, including the use of Pinned memory to reduce data transfer time and work distribution between the CPU and GPU. Pinned memory helps optimize data transfer, and work distribution between the CPU and GPU needs to be considered for efficient parallel processing. Performance measurements were performed using the Nvidia GTX 3060 laptop for evaluation, comparing the results of applying Pinned memory usage and work distribution optimization. As a result, optimizing memory transfer costs was found to have a greater impact on performance improvement. When both techniques were applied together, approximately a 1.44 times performance improvement was observed

LEA Block Cipher in Rust Language: Trade-off between Memory Safety and Performance

Cryptography implementations of block cipher have been written in C language due to its strong features on system-friendly features. However, the C language is prone to memory safety issues, such as buffer overflows and memory leaks. On the other hand, Rust, novel system programming language, provides strict compile-time memory safety guarantees through its ownership model. This paper presents the implementation of LEA block cipher in Rust language, demonstrating features to prevent common memory vulnerabilities while maintaining performance. We compare the Rust implementation with the traditional C language version, showing that while Rust incurs a reasonable memory overhead, it achieves comparable the execution timing of encryption and decryption. Our results highlight Rust’s suitability for secure cryptographic applications, striking the balance between memory safety and execution efficiency

Negative moments of orthogonal polynomials

If a sequence indexed by nonnegative integers satisfies a linear recurrence without constant terms, one can extend the indices of the sequence to negative integers using the recurrence. Recently, Cigler and Krattenthaler showed that the negative version of the number of bounded Dyck paths is the number of bounded alternating sequences. In this paper, we provide two methods to compute the negative versions of sequences related to moments of orthogonal polynomials. We give a combinatorial model for the negative version of the number of bounded Motzkin paths. We also prove two conjectures of Cigler and Krattenthaler on reciprocity between determinants