Related papers: Maintaining partial sums in logarithmic time
Tasks that model the relation between pairs of tokens in a string are a vital part of understanding natural language. Such tasks, in general, require exhaustive pair-wise comparisons of tokens, thus having a quadratic runtime complexity in…
In this note we answer a question concerning lineability of the set of non-absolutely summing operators.
We consider approximating data structures with collections of the items that they contain. For examples, lists, binary trees, tuples, etc, can be approximated by sets or multisets of the items within them. Such approximations can be used to…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…
Visualizing changes over time is fundamental to learning from the past and anticipating the future. However, temporal semantics can be complicated, and existing visualization tools often struggle to accurately represent these complexities.…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
We introduce a new formulation for the finite element immersed boundary method which makes use of a distributed Lagrange multiplier. We prove that a full discretization of our model, based on a semi-implicit time advancing scheme, is…
This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
Sylvester showed that the partition of an integer into a set of positive integers can be represented as a sum of the polynomial term and quasiperiodic components called the Sylvester waves. The wave itself is a weighted sum of the…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have…
A linear-interval order is the intersection of a linear order and an interval order. For this class of orders, several structural results have been known. This paper introduces a new subclass of linear-interval orders. We call a partial…
Horadam sequences and their partial sums are computed via generating functions. The results are as simple as possible.
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
Structured matrices with symbolic sizes appear frequently in the literature, especially in the description of algorithms for linear algebra. Recent work has treated these symbolic structured matrices themselves as computational objects,…
This work is about the synchronization of nonlinear coupled dynamical systems driven by $\alpha$-stable noise. Firstly, we provide a novel technique to construct the relationship between synchronized system and slow-fast system. Secondly,…
In this paper, the exact values of the structured singular values of some generalized stochastic complex matrices is explicit in term of the constant row (column) sum.