Related papers: Sequences with high nonlinear complexity

We introduce a model for random chain complexes over a finite field. The randomness in our complex comes from choosing the entries in the matrices that represent the boundary maps uniformly over $\mathbb{F}_q$, conditioned on ensuring that…

We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…

The linear complexity (LC) of a sequence has been used as a convenient measure of the randomness of a sequence. Based on the theories of linear complexity, $k$-error linear complexity, the minimum error and the $k$-error linear complexity…

We propose a low-complexity sign-dependent metric for sequence selection and study the nonlinear shaping gain achievable for a given computational cost, establishing a benchmark for future research. Small gains are obtained with feasible…

Classical results of second order parabolic quasi-linear equations always require that the nonlinear terms are controlled by a power of the unknown functions and their first derivatives. We improve the previous results. More precisely, in…

A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences…

The true complexity of a polynomial progression in finite fields corresponds to the smallest-degree Gowers norm that controls the counting operator of the progression over finite fields of large characteristic. We give a conjecture that…

Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…

We use fast-growing finite and infinite sequences of natural numbers and more complicated constructs to define models of hypercomputation and interpret non-arithmetic predicates, with the strongest extensions reaching full second order…

Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.

We obtain nontrivial bounds for character sums with multiplicative and additive characters over finite fields over elements with restricted coordinate expansion. In particular, we obtain a nontrivial estimate for such a sum over a finite…

We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…

We prove an upper bound on the degree complexity of Putinar's Positivstellensatz. This bound is much worse than the one obtained previously for Schm\"udgen's Positivstellensatz but it depends on the same parameters. As a consequence, we get…

We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general…

We extend some classical results dealing with boundary Harnack inequatilities to a class of quasilinear elliptic equations and derive some new estimates for solutions of such equations with an isolated singularity on the boundary of a…

Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page…

We give a description of the category of ordinary K3 surfaces over a finite field in terms of linear algebra data over Z. This gives an analogue for K3 surfaces of Deligne's description of the category of ordinary abelian varieties over a…