Constructive Relationships Between Algebraic Thickness and Normality
نویسندگان
چکیده
We study the relationship between two measures of Boolean functions; algebraic thickness and normality. For a function f , the algebraic thickness is a variant of the sparsity, the number of nonzero coefficients in the unique F2 polynomial representing f , and the normality is the largest dimension of an affine subspace on which f is constant. We show that for s < 3, any function with algebraic thickness ns is constant on some affine subspace of dimension Ω (
منابع مشابه
Relationships between Serum Luteinizing Hormone Level, Endometrial Thickness and Body Mass Index in Polycystic Ovary Syndrome Patients with and without Endometrial Hyperplasia
Objective The endometrial hyperplasia measured by ultrasound in polycystic ovary syndrome (PCOS) women is strongly related to pathologic endometrial thickness, but there is no consensus on the relation between serum luteinizing hormone (LH) and either of these factors: pathologic endometrial hyperplasia and body mass index (BMI). MaterialsAndMethods In this observational cross-sectional study, ...
متن کاملThe Relationship Between the Invitational Education and Social Constructive Learning Environment Among the Students of Bojnourd Islamic Azad University.
Purpose: The present study has been carried out with the aim of considering the relationships among the invitational education, social constructive classroom learning environment and their components in Iran Bojnourd Islamic Azad University. Methodology: The research method in this study is descriptive and correlation. The research population is comprised of all the male and female students...
متن کاملEssential normality and the decomposability of algebraic varieties
We consider the Arveson–Douglas conjecture on the essential normality of homogeneous submodules corresponding to algebraic subvarieties of the unit ball. We prove that the property of essential normality is preserved by isomorphisms between varieties, and we establish a similar result for maps between varieties that are not necessarily invertible. We also relate the decomposability of an algebr...
متن کاملThe complexity of Boolean functions from cryptographic viewpoint
Cryptographic Boolean functions must be complex to satisfy Shannon’s principle of confusion. But the cryptographic viewpoint on complexity is not the same as in circuit complexity. The two main criteria evaluating the cryptographic complexity of Boolean functions on F n 2 are the nonlinearity (and more generally the r-th order nonlinearity, for every positive r < n) and the algebraic degree. Tw...
متن کاملDetermination of Relationships between the Ultrasound Velocity and the Physical Properties of Bovine Cortical Bone Femur
Accurate measurements of physical characteristics of bone are essential for diagnosis, assessment of change following treatment, and therefore, indirectly, for evaluation of new forms of therapy. This is particularly true of osteoporosis and aging skeleton, in which fractures occur easily. Methods: In this study an ultrasonic system was set-up and calibrated on Plexiglas tubes of variable thick...
متن کامل