Normal Basis Research Articles

Novel Bit-Parallel and Digit-Serial Systolic Finite Field Multipliers Over $GF(2^m)$ Based on Reordered Normal Basis

Efficient implementation of finite field multipliers based on a reordered normal basis (RNB) is highly desirable in the current/emerging cryptosystems since it offers almost free realization of squaring operation. Therefore, in this paper, we propose novel bit-parallel and digit-serial finite field multipliers over $GF(2^{m})$ based on RNB. By efficient transformation of the core multiplication algorithm using a unique circular shifting feature, we have derived an efficient algorithm for low-complexity systolic mapping. Both bit-parallel and digit-serial structures of the multipliers are then obtained and optimized to enhance the area–time efficiency. We have also utilized the unique feature of the proposed multiplication algorithm to obtain the systolic multipliers by Karatsubalike decomposition. Detailed analysis and comparison show the superior performance of the proposed implementation. For example, the proposed regular and Karatsuba-based bit-parallel designs involve at least 48.4% less area-delay product (ADP) and 42.2% less power-delay product (PDP) than the best existing ones (37.7% and 55.3% less ADP and PDP on field-programmable gate array platform), respectively. The proposed multipliers, because of their lower area–time complexities, can be used for efficient realization of cryptographic applications.

AID, APOBEC3A and APOBEC3B efficiently deaminate deoxycytidines neighboring DNA damage induced by oxidation or alkylation

BackgroundAID/APOBEC3 (A3) enzymes instigate genomic mutations that are involved in immunity and cancer. Although they can deaminate any deoxycytidine (dC) to deoxyuridine (dU), each family member has a signature preference determined by nucleotides surrounding the target dC. This WRC (W = A/T, R = A/G) and YC (Y = T/C) hotspot preference is established for AID and A3A/A3B, respectively. Base alkylation and oxidation are two of the most common types of DNA damage induced environmentally or by chemotherapy. Here we examined the activity of AID, A3A and A3B on dCs neighboring such damaged bases. MethodsSubstrates were designed to contain target dCs either in normal WRC/YC hotspots, or in oxidized/alkylated DNA motifs. AID, A3A and A3B were purified and deamination kinetics of each were compared between substrates containing damaged vs. normal motifs. ResultsAll three enzymes efficiently deaminated dC when common damaged bases were present in the -2 or -1 positions. Strikingly, some damaged motifs supported comparable or higher catalytic efficiencies by AID, A3A and A3B than the WRC/YC motifs which are their most favored normal sequences. Based on the resolved interactions of AID, A3A and A3B with DNA, we modeled interactions with alkylated or oxidized bases. Corroborating the enzyme assay data, the surface regions that recognize normal bases are predicted to also interact robustly with oxidized and alkylated bases. ConclusionsAID, A3A and A3B can efficiently recognize and deaminate dC whose neighbouring nucleotides are damaged. General significanceBeyond AID/A3s initiating DNA damage, some forms of pre-existing damaged DNA can constitute favored targets of AID/A3s if encountered.

On Asano’s theorem

Let [Formula: see text] be a division algebra over an infinite field [Formula: see text] such that every element of [Formula: see text] is a sum of finitely many algebraic elements. As a generalization of Asano’s theorem, it is proved that every noncentral subspace of [Formula: see text] invariant under all inner automorphisms induced by algebraic elements contains [Formula: see text], the additive subgroup of [Formula: see text] generated by all additive commutators of [Formula: see text]. From the viewpoint we study the existence of normal bases of certain subspaces of division algebras. It is proved among other things that [Formula: see text] is generated by multiplicative commutators as a vector space over the center of [Formula: see text].

Construction of Irreducible Polynomials in Galois elds, GF(2m) Using Normal Bases

This thesis is about Construction of Polynomials in Galois fields Using Normal Bases in finite fields. In this piece of work, we discussed the following in the text; irreducible polynomials, primitive polynomials, field, Galois field or finite fields, and the order of a finite field. We found the actual construction of polynomials in GF(2m) with degree less than or equal to m − 1 and also illustrated how this construction can be done using normal bases. Finally, we found the general rule for construction of GF(pm) using normal bases and even the rule for producing reducible polynomials.

Superconducting qubits beyond the dispersive regime

We present a theoretical description for circuits consisting of weak anharmonic qubits coupled to cavity multimodes. We obtain a unitary transformation that diagonalizes harmonic sector of the circuit. Weak anharmonicity does not alter the normal mode basis, however it can modify energy levels. We study two examples of a transmon and two transmons coupled to bus resonator, and we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.

Normal bases from 1-dimensional algebraic groups

This paper surveys and illustrates a geometric method for constructing normal bases allowing fast finite field arithmetic. Indeed, Couveignes and Lercier presented in February 2008 a process for constructing efficient normal bases of Fqn over Fq from some degree two functions on an elliptic curve over Fq. We apply the Couveignes-Lercier method to all the remaining 1-dimensional algebraic groups. That results in natural normal bases with quasi-linear complexity.

Tame Galois module structure revisited

A number field K is Hilbert–Speiser if all of its tame abelian extensions L / K admit NIB (normal integral basis). It is known that \({\mathbb {Q}}\) is the only such field, but when we restrict \(\text {Gal}(L/K)\) to be a given group G, the classification of G-Hilbert–Speiser fields is far from complete. In this paper, we present new results on so-called G-Leopoldt fields. In their definition, NIB is replaced by “weak NIB” (defined below). Most of our results are negative, in the sense that they strongly limit the class of G-Leopoldt fields for some particular groups G, sometimes even leading to an exhaustive list of such fields or at least to a finiteness result. In particular, we are able to correct a small oversight in a recent article by Ichimura concerning Hilbert–Speiser fields.

Cartel Control of Attorney Licensure and the Public Interest

The purpose of licensure is to assure competent practitioners, particularly where irreparable harm to clients may occur in its absence. At the same time, there may be an advantage to greater supply, because that can lead to lower prices. In the case of attorneys, additional supply can improve attorney access not just to the poor, but to the middle class now lacking it. Regrettably, the legal profession --which openly operates in cartel fashion as its own public regulator -- has violated thesebasic precepts in extemis, with California serving as a preeminent example. First, state bars -- in combination with the American Bar Association national cartel -- require 4 years of largely irrelevant higher for law school entry, most of which have little or nothing to do with law and include subjects ranging from Sex and the human to yoga. Meanwhile, the rest of the world requires 1 or 2 years of lead-in). Second, the entire 7 year total travail -- driven by high tuition increases lacking competitive check -- now costs from $190,000 to $380,000 in tuition and room &board per student. Third, attorneys will practice in one of 24 dispararate areas of law, from admiralty to probate with different applicable law and often entirely disparate courts. 1 But attorney training focuses on traditional subjects only partially relevant to the majority of them, with scant attention to legislation and administrative proceedings. Even less attention is paid to the actual area of law a student will choose and have to know in order to practice competently. Upon graduation, students take an increasingly expensive preparatory course -- to pass a supply constricting bar examination that only tangentially relates to underlying competence. In the largest state of California that examination then flunks about 2/3 of its takers. Meanwhile, the bars regulating attorneys in the respective states: (a) Do not rank negligent acts as a normal basis for discipline (outside of extreme incapacity). (b) Do not require malpractice insurance -- effectively denying consumer remedies for negligence since plaintiff malpractice attorneys require insurance or other payment assurance. (c) Where setting up client security funds to compensate injured clients -- most only include theft in that coverage (not malpractice, even where there is a judgment). (d) Upon licensure as an attorney, state bars sometimes require continuing legal education by programs advocating for their remunerative purchase -- but do not consistently require them to be in the area of an attorney's actual practice. (e) Most significantly, they never test attorneys in the area of actual practice relied upon by consumers -- ever. Even in areas of law where clients are unable to gauge competence and a single case can mean ruination. (f) They confront modern technology approaches to provide legal information and assistance not to stimulate and regulate for accuracy, but as an affront warranting elimination in favor of exclusive reliance on counsel. Finally, no area of state regulation more ostentatiously violates federal antitrust law than does the legal profession. Following the North Carolina 2005 Supreme Court case holding that any state body controlled by participants in the profession regulated was not a legitimate sovereign entity for antitrust purposes, the legal profession continues to violate that holding. That Sherman Act coverage includes the per se violative offense of price fixing from supply control (i.e. licensing). The only defense is to provide by a state body not so conflicted. In theory, that could be a state supreme court. However, such courts tend to be inherently passive and not amenable to active supervision as mandated, or they delegate information gathering and decisions impermissibly to attorneys -- because that is their unsurprising mindset.

Normal Basis of the Maximal Real Subfield of a Circular Field

We find a necessary and sufficient condition on the natural number n in order that the conjugates of an entire algebraic number α = 2 cos(π/n) form a normal basis of the field ℚ(α); we show that this normal basis at the same time is fundamental.

Fully ceramic microencapsulated fuel in prismatic high-temperature gas-cooled reactors: Design basis accidents and fuel cycle cost

Fully ceramic microencapsulated (FCM) fuel may enhance the already strong inherent reactor safety characteristics of a conventional High-Temperature Gas-Cooled Reactor (HTGR). FCM fuel uses an SiC matrix that exhibits higher stability under irradiation with limited swelling relative to a conventional graphite matrix. Additionally, the SiC matrix is expected to exhibit improved mechanical performance relative to graphite. The feasibility of FCM-fueled HTGRs has been explored in a previous study (Lu et al., 2018), and three FCM fuel concepts were identified to be able to maintain the cycle length of the reference conventional General Atomics 350 MWt prismatic modular HTGR.In this work, the previous investigation of the reactor core safety characteristics of HTGRs fueled by these three FCM fuels was significantly extended to detailed thermal hydraulics and neutronics analysis of normal operation and design basis accident scenarios. We found that these FCM-fueled cores would have a maximum fuel temperature ∼20–40 K higher than that of the reference HTGR core at the beginning of cycle (BOC) and ∼30–60 K higher at the end of cycle (EOC) during normal operating conditions. Pressurized (P-) and depressurized (D-) loss of forced cooling (LOFC) accidents as well as the control rod withdrawal accident were explored. The FCM-fueled cores would at most have a maximum fuel temperature ∼30–50 K higher than that of the reference core in a P-LOFC accident, ∼10–30 K in a D-LOFC accident and ∼30–50 K in a rod withdrawal accident. The conclusion of the study is that FCM fuel has a small impact on the reactor performance and safety characteristics during normal operation and design basis accident conditions within the existing and generic 350 MWt prismatic modular HTGR design we considered.Additionally, a fuel cycle cost comparison was also performed in the current study. We found that the FCM fuels may be up to 40%–74% more expensive than the conventional fuel. Further analysis of the economics of FCM fuel are needed, because the uncertainties in the assumptions for this study are high.

Evaluation of Changes on Maxillo-Facial Skeleton of Class II Patients with Deep Bite Treated with Anterior Bite Plane as a Functional Appliance

Background: Class II division 1 malocclusion can be produced by protrusion of upper anterior teeth with normal maxillary basis relationship, that can be as a result of mandibular deficiency with normal dental position or posterior rotation of the mandible due to the excessive vertical growth of the maxilla. Deep bite usually associated with class II malocclusion, in which the mandibular incisor crowns are excessively overlapped vertically by the maxillary incisors where the teeth are in centric occlusion, which can be seen in children as well as in adults. So that for the successful treatment of Class II/ 1 required controlling the deep bite before starting the virtual treatment of this malocclusion to get better retention. Aim: The aim of this study was to investigate the morphological changes in maxillary and mandibular bones relationship after using the anterior bite plane appliance. Material and Methods: Evaluative analysis of cephalograms by superimposing two lateral cephalograms before and after the treatment of 27 patients (12 girls and 15 boys) class II division 1 malocclusion with mean age 11.7 years old. They treated by utilization of anterior bite plane while the period of fixed orthodontic therapy. Cephalometric data were analyzed with the following methods: Delaire, Danguy and classical and the morphological changes were evaluated. Results: The results of superposition of every patient before and after treatment showed a significant (P<0.05) reduction of deep bite and the facial convexity reduced in an average of 2.49°, anterior-posterior discrepancy reduced also very significantly (P=0.001), with a mean value of 1.81° and increasing in total mandibular length with a mean value of 2.95 mm. The decrease of the overbite can be due especially to the mandibular rotation and also supra-eruption of posterior teeth. Change in the mandibular length and the maxillary position improved facial profile but did not correct it completely as the mandible moved forward and also downward due to vertical and horizontal ramus growth and condylar remodeling. Conclusion: It can be concluded that the use of an anterior bite plane in conjunction with a straight wire and edgewise orthodontic techniques improved the overbite. Further research is recommended to support the result. How to cite this article:Senussi IB, Abdelgader I. Evaluation of Changeson Maxillo-Facial Skeleton of Class II Patients with Deep Bite Treated with Anterior Bite Plane as a Functional Appliance. J Adv Res Dent Oral Health 2019; 4(1): 1-9.

The unit theorem for finite-dimensional algebras

The unit theorem that forms the subject of the present article, is a theorem from algebra that has a combinatorial flavour, and that originated in fact from algebraic combinatorics. Beyond a proof, we also address applications, one of which is a proof of the normal basis theorem from Galois theory.

Fully Ceramic Microencapsulated fuel in prismatic high-temperature gas-cooled reactors: Sensitivity of reactor behavior during design basis accidents to fuel properties and the potential impact of the SiC defect annealing process

We conducted reactor performance calculations to assess the potential design basis accident performance of HTGR fuel designs. Three Fully Ceramic Microencapsulated (FCM) fueled HTGR designs were developed in a previous work (Lu et al., 2018). The maximum fuel temperature in the cores fueled by these three FCM fuels was predicted to be higher than that in the reference 350-MWt mHTGR core in both normal operating conditions and during representative design basis accidents (Lu and Brown, 2019). To better understand the potential safety margins in mHTGR design basis accidents, we performed thermal-hydraulics sensitivity studies to investigate how maximum fuel temperature varies considering various parameters, e.g. thermal properties, within the ranges corresponding to the differences between the FCM-fueled prismatic mHTGR cores and the reference core with conventional fuel compacts. We found that the difference in the steady-state axial power distribution contributed the most to the difference in the maximum fuel temperature, in both normal operation and design basis accidents.Experimental data suggested that the annealing process of irradiation defects in SiC would be rapid at mHTGR relevant fuel temperatures. The bounding potential impact of the SiC annealing on the maximum fuel temperature was analyzed considering both the thermal conductivity recovery and the Wigner energy release due to the annealing of SiC. We found that the defect annealing process in SiC would at most increase the peak maximum fuel temperature of an FCM-fueled core by 40 K in loss of forced cooling accidents and by 10 K in a control rod withdrawal accident. Additional experiments on the SiC defect annealing kinetics and Wigner energy release in more relevant conditions are needed.

Segmentation of dust storm areas on Mars images using principal component analysis and neural network

We present a method for automated segmentation of dust storm areas on Mars images observed by an orbiter. We divide them into small patches. Normal basis vectors are obtained from the many small patches by principal component analysis. We train a classifier using coefficients of these basis vectors as feature vectors. All patches in test images are categorized into one of the dust storm, cloud, and surface classes by the classifier. Each pixel may be included in several dust storm patches. The pixel is classified as a dust storm or the other classes based on the number of dust storm patches that include the pixel. We evaluate the segmentation method by the receiver operator characteristic curve and the area under the curve (AUC). AUC for dust storm is 0.947–0.978 if dust storm areas determined by our visual inspection are assumed to be ground truth. Precision, recall, and F-measure for dust storm are 0.88, 0.84, and 0.86, respectively, if we remove false negative pixels efficiently and maintain the size of true positive dust storms using two different threshold values. The tuning parameters of the classifier used in this study are determined so that the accuracy for dust storm is maximized. We can also tune the classifier for cloud segmentation by changing the parameters.

Conformational Dynamics of Damage Processing by Human DNA Glycosylase NEIL1

Endonuclease VIII-like protein 1 (NEIL1) is a DNA repair enzyme found in higher eukaryotes, including humans. It belongs to the helix–two turn–helix (H2TH) structural superfamily together with Escherichia coli formamidopyrimidine–DNA glycosylase (Fpg) and endonuclease VIII (Nei), and removes a variety of oxidized purine and pyrimidine bases from DNA. Structural, modeling and kinetic studies have established that the bacterial H2TH superfamily enzymes proceed through several conformational intermediates while recognizing and removing their cognate lesions. Here we apply stopped-flow kinetics with detection of intrinsic Trp fluorescence and Förster resonance energy transfer fluorescence to follow the conformational dynamics of human NEIL1 and DNA when the enzyme interacts with undamaged DNA, or DNA containing cleavable or non-cleavable abasic sites, or dihydrouracil lesions. NEIL1 processed a natural abasic site and a damaged base in DNA equally well but showed an additional fluorescently discernible step when DHU was present, likely reflecting additional rearrangements during base eversion into the enzyme's active site. With undamaged DNA and DNA containing a non-cleavable abasic site analog, (3-hydroxytetrahydrofuran-2-yl)methyl phosphate, NEIL1 was diverted to a non-productive DNA conformation early in the reaction. Our results support the view of NEIL1 as an enzyme that actively destabilizes damaged DNA and uses multiple checkpoints along the reaction coordinate to drive substrate lesions into the active site while rejecting normal bases and non-substrate lesions.

Weakly Normal Basis Vector Fields in RKHS with an Application to Shape Newton Methods

We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spac...

R-compact uniform spaces in the category ZUni f

A number of basic properties of R-compact spaces in the category Tych of Tychonoff spaces and their continuous mappings are extended to the category ZUni f of uniform spaces with the special normal bases and their coz-mappings.

Construction of Normal Bases over Finite Fields

Construction of Normal Bases over Finite Fields

COMPUTING NORMAL INTEGRAL BASES OF ABELIAN NUMBER FIELDS

Let L be an abelian number field of degree n with Galois group G. In this paper we study how to compute efficiently a normal integral basis for L, if there is at least one, assuming that the group G and an integral basis for L are known.

Normal Bases on Galois Ring Extensions

Normal bases are widely used in applications of Galois fields and Galois rings in areas such as coding, encryption symmetric algorithms (block cipher), signal processing, and so on. In this paper, we study the normal bases for Galois ring extension R / Z p r , where R = GR ( p r , n ) . We present a criterion on the normal basis for R / Z p r and reduce this problem to one of finite field extension R ¯ / Z ¯ p r = F q / F p ( q = p n ) by Theorem 1. We determine all optimal normal bases for Galois ring extension.