$\textrm{GF}(2^m)$ Finite-Field Multipliers with Reduced Activity Variations

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q ((X^{ - 1} ))$$ \end{document} denote the formal field of all formal Laurent series x = Σ n=ν∞anX−n in an indeterminate X, with coefficients an lying in a given finite field \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}. For any \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} with deg β > 1, it is known that for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document} (with respect to the Haar measure), x is β-normal. In this paper, we show the inverse direction, i.e., for any x, for almost all \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\beta \in \mathbb{F}_q ((X^{ - 1} ))$$ \end{document}, x is β-normal.

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Human Neuraminidases Have Reduced Activity Towards Modified Sialic Acids on Glycoproteins

10.26434/chemrxiv.12510011 ◽

2020 ◽

Author(s):

Carmanah D. Hunter ◽

Elizabeth Porter ◽

Christopher Cairo

Keyword(s):

Substrate Specificity ◽

General Trend ◽

Sialic Acids ◽

Enzyme Specificity ◽

Naturally Occurring ◽

Bovine Submaxillary Mucin ◽

Reduced Activity

This work investigated the substrate specificity of hNEU enzymes for a glycoprotein substrate (bovine submaxillary mucin) containing 9-<i>O</i>-acetylated and Neu5Gc residues. Using this model substrate, we observe a general trend for hNEU tolerance of Neu5Ac>Neu5Gc>>>Neu5,9Ac<sub>2</sub>, consistent with our previous results with glycolipid substrates. These results expand our understanding of hNEU enzyme specificity and suggest that naturally occurring modifications of sialic acids can play a role in regulating hNEU activity.

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Valued Field Graph and Some Related Parameters

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.1.30 ◽

2020 ◽

pp. 389-395

Author(s):

G. Suresh Singh ◽

P. K. Prasobha

Keyword(s):

Finite Field ◽

Independence Number ◽

Valued Field ◽

Vertex Set ◽

Adic Valuation

Let $K$ be any finite field. For any prime $p$, the $p$-adic valuation map is given by $\psi_{p}:K/\{0\} \to \R^+\bigcup\{0\}$ is given by $\psi_{p}(r) = n$ where $r = p^n \frac{a}{b}$, where $p,a,b$ are relatively prime. The field $K$ together with a valuation is called valued field. Also, any field $K$ has the trivial valuation determined by $\psi{(K)} = \{0,1\}$. Through out the paper K represents $\Z_q$. In this paper, we construct the graph corresponding to the valuation map called the valued field graph, denoted by $VFG_{p}(\Z_{q})$ whose vertex set is $\{v_0,v_1,v_2,\ldots, v_{q-1}\}$ where two vertices $v_i$ and $v_j$ are adjacent if $\psi_{p}(i) = j$ or $\psi_{p}(j) = i$. Here, we tried to characterize the valued field graph in $\Z_q$. Also we analyse various graph theoretical parameters such as diameter, independence number etc.

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NMR Assisted Antimicrobial Peptide Designing: Structure Based Modifications and Functional Correlation of a Designed Peptide VG16KRKP

Current Medicinal Chemistry ◽

10.2174/0929867326666190624090817 ◽

2020 ◽

Vol 27 (9) ◽

pp. 1387-1404 ◽

Cited By ~ 2

Author(s):

Karishma Biswas ◽

Humaira Ilyas ◽

Aritreyee Datta ◽

Anirban Bhunia

Keyword(s):

Antimicrobial Agents ◽

Biological Properties ◽

Structure Characterization ◽

Drug Resistant ◽

Functional Correlation ◽

Naturally Occurring ◽

High Resolution Nmr ◽

Different Types ◽

Reduced Activity ◽

Poor Stability

Antimicrobial Peptides (AMPs), within their realm incorporate a diverse group of structurally and functionally varied peptides, playing crucial roles in innate immunity. Over the last few decades, the field of AMP has seen a huge upsurge, mainly owing to the generation of the so-called drug resistant ‘superbugs’ as well as limitations associated with the existing antimicrobial agents. Due to their resilient biological properties, AMPs can very well form the sustainable alternative for nextgeneration therapeutic agents. Certain drawbacks associated with existing AMPs are, however, issues of major concern, circumventing which are imperative. These limitations mainly include proteolytic cleavage and hence poor stability inside the biological systems, reduced activity due to inadequate interaction with the microbial membrane, and ineffectiveness because of inappropriate delivery among others. In this context, the application of naturally occurring AMPs as an efficient prototype for generating various synthetic and designed counterparts has evolved as a new avenue in peptide-based therapy. Such designing approaches help to overcome the drawbacks of the parent AMPs while retaining the inherent activity. In this review, we summarize some of the basic NMR structure based approaches and techniques which aid in improving the activity of AMPs, using the example of a 16-residue dengue virus fusion protein derived peptide, VG16KRKP. Using first principle based designing technique and high resolution NMR-based structure characterization we validate different types of modifications of VG16KRKP, highlighting key motifs, which optimize its activity. The approaches and designing techniques presented can support our peers in their drug development work.

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On the Security of Public-Key Algorithms Based on Chebyshev Polynomials over the Finite Field $Z_N$

IEEE Transactions on Computers ◽

10.1109/tc.2010.148 ◽

2010 ◽

Vol 59 (10) ◽

pp. 1392-1401 ◽

Cited By ~ 19

Author(s):

Xiaofeng Liao ◽

Fei Chen ◽

Kwok-wo Wong

Keyword(s):

Finite Field ◽

Chebyshev Polynomials ◽

Public Key

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Image encryption based on the finite field cosine transform

Signal Processing Image Communication ◽

10.1016/j.image.2013.05.008 ◽

2013 ◽

Vol 28 (10) ◽

pp. 1537-1547 ◽

Cited By ~ 21

Author(s):

J.B. Lima ◽

E.A.O. Lima ◽

F. Madeiro

Keyword(s):

Finite Field ◽

Image Encryption ◽

Cosine Transform

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EGFRvIII Promotes Cell Survival during Endoplasmic Reticulum Stress through a Reticulocalbin 1-Dependent Mechanism

Cancers ◽

10.3390/cancers13061198 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1198

Author(s):

Juliana Gomez ◽

Zammam Areeb ◽

Sarah F. Stuart ◽

Hong P. T. Nguyen ◽

Lucia Paradiso ◽

...

Keyword(s):

Endoplasmic Reticulum ◽

Cell Viability ◽

Er Stress ◽

Cell Survival ◽

Glioblastoma Cells ◽

Over Expression ◽

Stress Markers ◽

Apoptotic Protein ◽

Novel Association ◽

Reduced Activity

Reticulocalbin 1 (RCN1) is an endoplasmic reticulum (ER)-residing protein, involved in promoting cell survival during pathophysiological conditions that lead to ER stress. However, the key upstream receptor tyrosine kinase that regulates RCN1 expression and its potential role in cell survival in the glioblastoma setting have not been determined. Here, we demonstrate that RCN1 expression significantly correlates with poor glioblastoma patient survival. We also demonstrate that glioblastoma cells with expression of EGFRvIII receptor also have high RCN1 expression. Over-expression of wildtype EGFR also correlated with high RCN1 expression, suggesting that EGFR and EGFRvIII regulate RCN1 expression. Importantly, cells that expressed EGFRvIII and subsequently showed high RCN1 expression displayed greater cell viability under ER stress compared to EGFRvIII negative glioblastoma cells. Consistently, we also demonstrated that RCN1 knockdown reduced cell viability and exogenous introduction of RCN1 enhanced cell viability following induction of ER stress. Mechanistically, we demonstrate that the EGFRvIII-RCN1-driven increase in cell survival is due to the inactivation of the ER stress markers ATF4 and ATF6, maintained expression of the anti-apoptotic protein Bcl-2 and reduced activity of caspase 3/7. Our current findings identify that EGFRvIII regulates RCN1 expression and that this novel association promotes cell survival in glioblastoma cells during ER stress.

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