Related papers: Optimal bounds for monotonicity and Lipschitz test…
For a permutation $\pi:[k] \to [k]$, a function $f:[n] \to \mathbb{R}$ contains a $\pi$-appearance if there exists $1 \leq i_1 < i_2 < \dots < i_k \leq n$ such that for all $s,t \in [k]$, $f(i_s) < f(i_t)$ if and only if $\pi(s) < \pi(t)$.…
We prove a new lower bound on the critical density $\rho_c$ of the hard disk model, i.e., the density below which it is possible to efficiently sample random configurations of $n$ non-overlapping disks in a unit torus. We use a classic…
In this paper we consider the problem of uniformity testing with limited memory. We observe a sequence of independent identically distributed random variables drawn from a distribution $p$ over $[n]$, which is either uniform or is…
For any $\Omega\subset \mathbb{R}^N$ smooth and bounded domain, we prove uniqueness of positive solutions of free boundary problems arising in plasma physics on $\Omega$ in a neat interval depending only by the best constant of the Sobolev…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
We prove the first nontrivial worst-case lower bounds for two closely related problems. First, $\Omega(n^{3/2})$ degree-1 reductions, series-parallel reductions, and $\Delta$Y transformations are required in the worst case to reduce an…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
We prove the first polynomial bound on the number of monotonic homotopy moves required to tighten a collection of closed curves on any compact orientable surface, where the number of crossings in the curve is not allowed to increase at any…
We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…
Graph algorithms are widely used for decision making and knowledge discovery. To ensure their effectiveness, it is essential that their output remains stable even when subjected to small perturbations to the input because frequent output…
We study the minimum \emph{Monitoring Edge Geodetic Set} (\megset) problem introduced in [Foucaud et al., CALDAM'23]: given a graph $G$, we say that an edge is monitored by a pair $u,v$ of vertices if \emph{all} shortest paths between $u$…
Given an increasing sequence of integers $x_1,\ldots,x_n$ from a universe $\{0,\ldots,u-1\}$, the monotone minimal perfect hash function (MMPHF) for this sequence is a data structure that answers the following rank queries: $rank(x) = i$ if…
We study the convergence properties of the conditional (Kullback-Leibler) entropy in stochastic systems. We have proved very general results showing that asymptotic stability is a necessary and sufficient condition for the monotone…
We enhance constrained-based data quality with approximate band conditional order dependencies (abcODs). Band ODs model the semantics of attributes that are monotonically related with small variations without there being an intrinsic…
There has been a surge of progress in recent years in developing algorithms for testing and learning quantum states that achieve optimal copy complexity. Unfortunately, they require the use of entangled measurements across many copies of…
The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness…
We present an $\tilde{O}(n^{2/3}/\epsilon^2)$-query algorithm that tests whether an unknown Boolean function $f\colon\{0,1\}^n\rightarrow \{0,1\}$ is unate (i.e., every variable is either non-decreasing or non-increasing) or $\epsilon$-far…
In our previous work we have shown how Bayesian networks can be used for adaptive testing of student skills. Later, we have taken the advantage of monotonicity restrictions in order to learn models fitting data better. This article provides…
Within a mathematically rigorous model, we analyse the curse of dimensionality for deterministic exact similarity search in the context of popular indexing schemes: metric trees. The datasets $X$ are sampled randomly from a domain $\Omega$,…