Related papers: Self-modified difference ascent sequences
Real-world systems often evolve on different timescales and possess multiple coexisting stable states. Whether or not a system returns to a given stable state after being perturbed away from it depends on the shape and extent of its basin…
We provide a naturally isomorphic description of the persistence map from merge trees to barcodes in terms of a monotone map from the partition lattice to the subset lattice. Our description is local, which offers the potential to speed up…
We characterize the orderings of pairs of sets induced by several distances: Hamming, Jaccard, S\o rensen-Dice and Overlap. We also characterize these distances.
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
Following a result of Eriksen and Sj\"{o}strand (2014) we detail a technique to construct structures following the Fishburn distribution from appropriate Mahonian structures. This technique is introduced on a bivincular pattern of…
Protein-fragment seqlets typically feature about 10 amino acid residue positions that are fixed to within conservative substitutions but usually separated by a number of prescribed gaps with arbitrary residue content. By quantifying a…
This brief note presents two adaptive heap data structures and conjectures on running times.
To perform well on unseen and potentially out-of-distribution samples, it is desirable for machine learning models to have a predictable response with respect to transformations affecting the factors of variation of the input. Here, we…
Given a group $G$, we say that a set $A \subseteq G$ has more sums than differences (MSTD) if $|A+A| > |A-A|$, has more differences than sums (MDTS) if $|A+A| < |A-A|$, or is sum-difference balanced if $|A+A| = |A-A|$. A problem of recent…
We introduce inversions tableaux, a new combinatorial model for Schubert polynomials and Stanley symmetric functions that directly specializes to semi-standard Young tableaux in the Grassmannian case. They are a modification of the balanced…
Consider the regular representation of the sum over all permutations weighted by the sum of their descent, inversion, and fixed point multinomials. We compute the spectrum and the multiplicities of its elements of that matrix. Note that…
Self-supervised learning of depth map prediction and motion estimation from monocular video sequences is of vital importance -- since it realizes a broad range of tasks in robotics and autonomous vehicles. A large number of research efforts…
Large scale image dataset and deep convolutional neural network (DCNN) are two primary driving forces for the rapid progress made in generic object recognition tasks in recent years. While lots of network architectures have been…
In this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomial on the mesh…
A sequence x=x_1 x_2...x_n $ is said to be an ascent sequence of length $n$ if it satisfies x_1=0 and $0\leq x_i\leq asc(x_1x_2...x_{i-1})+1$ for all $2\leq i\leq n$, where $asc(x_1x_2... x_{i-1})$ is the number of ascents in the sequence…
Systems exhibiting degeneracies known as exceptional points have remarkable properties with powerful applications, particularly in sensor design. These degeneracies are formed when eigenstates coincide, and the remarkable effects are…
In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…
We extend Stanley's work on alternating permutations with extremal number of fixed points in two directions: first, alternating permutations are replaced by permutations with a prescribed descent set; second, instead of simply counting…
Fibonacci cubes are induced subgraphs of hypercube graphs obtained by restricting the vertex set to those binary strings which do not contain consecutive 1s. This class of graphs has been studied extensively and generalized in many…
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…