Related papers: On additive complexity of a sequence of matrices
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
Leveraging recent advances in additive combinatorics, we exhibit explicit matrices satisfying the Restricted Isometry Property with better parameters. Namely, for $\varepsilon=3.26\cdot 10^{-7}$, large $k$ and $k^{2-\varepsilon} \le N\le…
This paper presents two alternative approaches for counting the number of two-row weakly increasing matrices, which are $2\times n$ matrices whose entries are integers from $1$ to $k$ and are weakly increasing along all rows and columns,…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
In this research we present a quantum circuit for estimating algorithmic complexity using the coding theorem method. This accelerates inferring algorithmic structure in data for discovering causal generative models. The computation model is…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
All current investigations to analyze the derivational complexity of term rewrite systems are based on a single termination method, possibly preceded by transformations. However, the exclusive use of direct criteria is problematic due to…
We prove bounds on the number of incidences between a set of algebraic curves in $\mathbb{C}^2$ and a Cartesian product $A\times B$ with finite sets $A,B\subset \mathbb{C}$. Similar bounds are known under various conditions, but we show…
Theory of $n$-complements with applications is presented.
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
Degrees of freedom for high-order binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that $N+k_0$ pairs of canonical separated variables for their separation of variables can be…
A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include…
We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given by Grigoriev [10] for Riccatti…
In this paper, we provide an $O(n \mathrm{polylog} n)$ bound on the expected complexity of the randomly weighted Voronoi diagram of a set of $n$ sites in the plane, where the sites can be either points, interior-disjoint convex sets, or…
We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in in our revious publications where computability, in the rigorous sense of…
We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…