24 papers · ranked by Valyu relevance
N. A. Carella
| 3.1 Basic Concepts………………………………………….……………………………….40 | | --- | | 3.2 Existence of Normal Bases………………………………..……………………………..41 | | 3.3 Iterative Construction of Normal Bases………………….……………………………...42 | | 3.4 Additive Order and Decomposition Theorem…………….……………………………..44 | | 3.5 Normal Tests……………………………………………….……………………………46 |…
Giorgos Kapetanakis, Lucas Reis
The celebrated Primitive Normal Basis Theorem states that for any n ≥ 2 and any finite field Fq, there exists an element α ∈ Fq n that is simultaneously primitive and normal over Fq. In this paper, we prove some variations of this result, completing the proof of a conjecture proposed by Anderson and Mullen (2014). Our…
Mahmood Alizadeh, Saeid Mehrabi
The paper is devoted to produce infinite sequences of k-normal polynomials Fu(x) ∈ Fq[x] of degrees npu (u ≥ 0), for a suitably chosen initial k-normal polynomial F0(x) ∈ Fq[x] of degree n over Fq by iteratively applying the transformation x → x p−x xp−x+δ , where δ ∈ Fq and 0 ≤ k ≤ n − 1.
Lucas Reis
The so called k-normal elements appear in the literature as a generalization of normal elements over finite fields. Recently, questions concerning the construction of k-normal elements and the existence of k-normal elements that are also primitive have attracted attention from many authors. In this paper we give…
Verónica Becher, Theodore A. Slaman
We ask whether normality to one base is related to normality to another. Maxfield in 1953 proved that a real number is normal to a base exactly when it is normal to every base multiplicatively dependent to that base (two numbers are multiplicatively dependent when one is a rational power of the other.) Schmidt…
Anoop Kumar Kushwaha
In recent years, the applications of first-principles density functional theory (DFT) is diversified and expanded in a wide range due to the development of robust algorithms and more powerful computer systems. In general, DFT is used in condensed matter physics, chemistry, material science and biology to predict and…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Pierpaolo Uberti
In this paper we study the property of normality of a number in base 2. A simple rule that associates a vector to a number is presented and the property of normality is stated for the vector associated to the number. The problem of testing a number for normality is shown to be equivalent to the test of geometrical…
Authors not listed
Vibrational exciton models are widely used for the simulation of biomolecular vibrational spectra, in particular of two-dimensional infrared (2D-IR) spectra. The parameters entering such models, specifically harmonic local-mode frequencies and harmonic coupling constants, are provided by vibrational maps, which have…
Janus R. L. Kobbersmed, Chetan Gohil, Andre Marquand, Diego Vidaurre
Many brain diseases and disorders lack objective measures of brain function as indicators of pathology. The search for brain function biomarkers is complicated by the fact that these conditions are often heterogenous and described as a spectrum from normal to abnormal rather than a sick-healthy dichotomy. Normative…
Xu Yang, Cai Cheng, Jin Duan, You-Fei Hao + 3 more
'Sylvain Girard'] There are six possible solutions for the surface normal vectors obtained from polarization information during 3D reconstruction. To resolve the ambiguity of surface normal vectors, scholars have introduced additional information, such as shading information. However, this makes the 3D reconstruction…
Robert Shaw, Grant Hill
The basis set used in quantum chemical calculations for molecular applications is vital to the accuracy and efficiency of the calculation, but the development of novel basis sets is hindered by an opaque process and inaccessibility of the tools required. We present here BasisOpt, a tool for the automated optimization…
Mingqiang Guo, Zhenzhen Song, Chengde Han, Saishang Zhong + 2 more
'Zheng Liu'] In this paper, we propose a novel guided normal filtering followed by vertex updating for mesh denoising. We introduce a two-stage scheme to construct adaptive consistent neighborhoods for guided normal filtering. In the first stage, we newly design a consistency measurement to select a coarse consistent…
Jonas Vester, Jógvan Magnus Haugaard Olsen
The partial Hessian approximation is often used to perform vibrational analysis of large QM/MM systems where the high computational cost of calculating the full Hessian is impractical. Here, we investigate the accuracy and applicability of the partial Hessian vibrational analysis (PHVA) approach as it is typically used…
Garri Davydyan
The evolution of biologic systems (BS) includes functional mechanisms that in some conditions may lead to the development of cancer. Using mathematical group theory and matrix analysis, previously, it was shown that normally functioning BS are steady functional structures regulated by three basis regulatory components…
Yang Shen, Julia Wang, Saket Navlakha
A fundamental challenge at the interface of machine learning and neuroscience is to uncover computational principles that are shared between artificial and biological neural networks. In deep learning, normalization methods, such as batch normalization, weight normalization, and their many variants, help to stabilize…
Saige Rutherford, Pieter Barkema, Ivy F. Tso, Chandra Sripada + 3 more
In this work, we expand the normative model repository introduced in Rutherford et al. (2022a) to include normative models charting lifespan trajectories of structural surface area and brain functional connectivity, measured using two unique resting-state network atlases (Yeo-17 and Smith-10), and an updated online…
Jurgen Serth, Christel Reese, Tatyana Hubscher, Bastian Hill + 3 more
The detection of alterations in DNA methylation (DNAm) in normal human tissues may provide molecular insights for cancer development, the estimation of personal cancer risk, and a basis for early diagnosis of malignancies to reduce cancer lethality. Thus, whether DNAm allows discrimination between healthy normal and…
Daisuke Miyazaki, Kazuya Uegomori, Guanghui Wang
A photometric stereo needs three images taken under three different light directions lit one by one, while a color photometric stereo needs only one image taken under three different lights lit at the same time with different light directions and different colors. As a result, a color photometric stereo can obtain the…
Sikai Zhang, Qizhe Lin, Jiayao Lin, Andrea Cataldo
The potential for rotor component shedding in rotating machinery poses significant risks, necessitating the development of an early and precise fault diagnosis technique to prevent catastrophic failures and reduce maintenance costs. This study introduces a data-driven approach to detect rotor component shedding at its…
Daisuke Miyazaki, Yuka Onishi, Shinsaku Hiura
One of the main problems faced by the photometric stereo method is that several measurements are required, as this method needs illumination from light sources from different directions. A solution to this problem is the color photometric stereo method, which conducts one-shot measurements by simultaneously…
Anna-Sophia Hehn, Beliz Sertcan, Fabian Belleflamme, Sergey K. Chulkov + 2 more
Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials due to its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions…
Bryce Morsky, Erol Akçay
Social norms regulate and coordinate most aspects of human social life, yet they emerge and change as a result of individual behaviours, beliefs, and expectations. A satisfactory account for the evolutionary dynamics of social norms therefore has to link individual beliefs and expectations to population-level dynamics…
Prokopis C. Prokopiou, Kyle T. S. Pattinson, Richard G. Wise, Georgios D. Mitsis
In this work, we investigate the regional characteristics of the dynamic interactions between arterial CO2 and BOLD (dynamic cerebrovascular reactivity - dCVR) during normal breathing and hypercapnic, externally induced step CO2 challenges. To obtain CVR curves at each voxel, we use a custom set of basis functions…