Two classes of LCD BCH codes over finite fields

BCH codes form an important subclass of cyclic codes, and are widely used in compact discs, digital audio tapes and other data storage systems to improve data reliability. As far as we know, there are few results on $q$-ary BCH codes of length $n=\frac{q^{m}+1}{q+1}$. This is because it is harder to deal with BCH codes of such length. In this paper, we study $q$-ary BCH codes with lengths $n=\frac{q^{m}+1}{q+1}$ and $n=q^m+1$. These two classes of BCH codes are always LCD codes. For $n=\frac{q^{m}+1}{q+1}$, the dimensions of narrow-sense BCH codes of length $n$ with designed distance $\delta=\ell q^{\frac{m-1}{2}}+1$ are determined, where $q>2$ and $2\leq \ell \leq q-1$. Moreover, the largest coset leader is given for $m=3$ and the first two largest coset leaders are given for $q=2$. The parameters of BCH codes related to the first few largest coset leaders are investigated. Some binary BCH codes of length $n=\frac{2^m+1}{3}$ have optimal parameters. For ternary narrow-sense BCH codes of length $n=3^m+1$, a lower bound on the minimum distance of their dual codes is developed, which is good in some cases

The dual codes of two classes of LCD BCH codes

Cyclic BCH codes and negacyclic BCH codes form important subclasses of cyclic codes and negacyclic codes, respectively, and can produce optimal linear codes in many cases. To the best of our knowledge, there are few results on the dual codes of cyclic and negacyclic BCH codes. In this paper, we study the dual codes of narrow-sense cyclic BCH codes of length $q^m+1$ over a finite field $\mathbb{F}_q$, where $q$ is an odd prime power, and the dual codes of narrow-sense negacyclic BCH codes of length $\frac{q^{m}+1}{2}$ over $\mathbb{F}_q$, where $q$ is an odd prime power satisfying $q\equiv 3~({\rm mod}~4)$. Some lower bounds on the minimum distances of the dual codes are established, which are very close to the true minimum distances of the dual codes in many cases. Sufficient and necessary conditions for the even-like subcodes of narrow-sense cyclic BCH codes of length $q^{m}+1$ being cyclic dually-BCH codes are given in terms of designed distances, where $q$ is odd and $m$ is odd or $m\equiv 2~({\rm mod~}4)$. The concept of negacyclic dually-BCH codes is proposed, and sufficient and necessary conditions in terms of designed distances are presented to ensure that narrow-sense negacyclic BCH codes of length $\frac{q^{m}+1}{2}$ are dually-BCH codes, where $q\equiv 3~({\rm mod}~4)$

Reactive Oxygen Species Production and Brugia Pahangi Survivorship in Aedes polynesiensis with Artificial Wolbachia Infection Types

Heterologous transinfection with the endosymbiotic bacterium Wolbachia has been shown previously to induce pathogen interference phenotypes in mosquito hosts. Here we examine an artificially infected strain of Aedes polynesiensis, the primary vector of Wuchereria bancrofti, which is the causative agent of Lymphatic filariasis (LF) throughout much of the South Pacific. Embryonic microinjection was used to transfer the wAlbB infection from Aedes albopictus into an aposymbiotic strain of Ae. polynesiensis. The resulting strain (designated MTB ) experiences a stable artificial infection with high maternal inheritance. Reciprocal crosses of MTB with naturally infected wild-type Ae. polynesiensis demonstrate strong bidirectional incompatibility. Levels of reactive oxygen species (ROS) in the MTB strain differ significantly relative to that of the wild-type, indicating an impaired ability to regulate oxidative stress. Following a challenge with Brugia pahangi, the number of filarial worms achieving the infective stage is significantly reduced in MTB as compared to the naturally infected and aposymbiotic strains. Survivorship of MTB differed significantly from that of the wild-type, with an interactive effect between survivorship and blood feeding. The results demonstrate a direct correlation between decreased ROS levels and decreased survival of adult female Aedes polynesiensis. The results are discussed in relation to the interaction of Wolbachia with ROS production and antioxidant expression, iron homeostasis and the insect immune system. We discuss the potential applied use of the MTB strain for impacting Ae. polynesiensis populations and strategies for reducing LF incidence in the South Pacific

Nearly quantized conductance plateau of vortex zero mode in an iron-based superconductor

Majorana zero-modes (MZMs) are spatially-localized zero-energy fractional quasiparticles with non-Abelian braiding statistics that hold a great promise for topological quantum computing. Due to its particle-antiparticle equivalence, an MZM exhibits robust resonant Andreev reflection and 2e2/h quantized conductance at low temperature. By utilizing variable-tunnel-coupled scanning tunneling spectroscopy, we study tunneling conductance of vortex bound states on FeTe0.55Se0.45 superconductors. We report observations of conductance plateaus as a function of tunnel coupling for zero-energy vortex bound states with values close to or even reaching the 2e2/h quantum conductance. In contrast, no such plateau behaviors were observed on either finite energy Caroli-de Genne-Matricon bound states or in the continuum of electronic states outside the superconducting gap. This unique behavior of the zero-mode conductance reaching a plateau strongly supports the existence of MZMs in this iron-based superconductor, which serves as a promising single-material platform for Majorana braiding at a relatively high temperature

SPOC learner's final grade prediction based on a novel sampling batch normalization embedded neural network method

Recent years have witnessed the rapid growth of Small Private Online Courses (SPOC) which is able to highly customized and personalized to adapt variable educational requests, in which machine learning techniques are explored to summarize and predict the learner's performance, mostly focus on the final grade. However, the problem is that the final grade of learners on SPOC is generally seriously imbalance which handicaps the training of prediction model. To solve this problem, a sampling batch normalization embedded deep neural network (SBNEDNN) method is developed in this paper. First, a combined indicator is defined to measure the distribution of the data, then a rule is established to guide the sampling process. Second, the batch normalization (BN) modified layers are embedded into full connected neural network to solve the data imbalanced problem. Experimental results with other three deep learning methods demonstrates the superiority of the proposed method.Comment: 11 pages, 5 figures, ICAIS 202

Structural organization of the C1a-e-c supercomplex within the ciliary central apparatus

Nearly all motile cilia contain a central apparatus (CA) composed of two connected singlet microtubules with attached projections that play crucial roles in regulating ciliary motility. Defects in CA assembly usually result in motility-impaired or paralyzed cilia, which in humans causes disease. Despite their importance, the protein composition and functions of the CA projections are largely unknown. Here, we integrated biochemical and genetic approaches with cryo-electron tomography to compare the CA of wild-type Chlamydomonas with CA mutants. We identified a large ( \u3e 2 MD) complex, the C1a-e-c supercomplex, that requires the PF16 protein for assembly and contains the CA components FAP76, FAP81, FAP92, and FAP216. We localized these subunits within the supercomplex using nanogold labeling and show that loss of any one of them results in impaired ciliary motility. These data provide insight into the subunit organization and 3D structure of the CA, which is a prerequisite for understanding the molecular mechanisms by which the CA regulates ciliary beating

Asymmetric Trapdoor Pseudorandom Generators: Definitions, Constructions, and Applications to Homomorphic Signatures with Shorter Public Keys

We introduce a new primitive called the asymmetric trapdoor pseudorandom generator (ATPRG), which belongs to pseudorandom generators with two additional trapdoors (a public trapdoor and a secret trapdoor) or backdoor pseudorandom generators with an additional trapdoor (a secret trapdoor). Specifically, ATPRG can only generate public pseudorandom numbers $pr_1,\dots,pr_N$ for the users having no knowledge of the public trapdoor and the secret trapdoor; so this function is the same as pseudorandom generators. However, the users having the public trapdoor can use any public pseudorandom number $pr_i$ to recover the whole $pr$ sequence; so this function is the same as backdoor pseudorandom generators. Further, the users having the secret trapdoor can use $pr$ sequence to generate a sequence $sr_1,\dots,sr_N$ of the secret pseudorandom numbers. ATPRG can help design more space-efficient protocols where data/input/message should respect a predefined (unchangeable) order to be correctly processed in a computation or malleable cryptographic system. As for applications of ATPRG, we construct the first homomorphic signature scheme (in the standard model) whose public key size is only $O(T)$ that is independent of the dataset size. As a comparison, the shortest size of the existing public key is $O(\sqrt{N}+\sqrt{T})$, proposed by Catalano et al. (CRYPTO\u2715), where $N$ is the dataset size and $T$ is the dimension of the message. In other words, we provide the first homomorphic signature scheme with $O(1)$-sized public keys for the one-dimension messages

Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science