Related papers: On VC-density over indiscernible sequences

Searches for continuous gravitational waves target nearly monochromatic gravitational wave emission from e.g. non-axysmmetric fast-spinning neutron stars. Broad surveys often require to explicitly search for a very large number of different…

Most density-based clustering methods largely rely on how well the underlying density is estimated. However, density estimation itself is also a challenging problem, especially the determination of the kernel bandwidth. A large bandwidth…

Degree sequence (DS) problems are around for at least hundred twenty years, and with the advent of network science, more and more complicated, structured DS problems were invented. Interestingly enough all those problems so far are…

How do two deep neural networks differ in how they arrive at a decision? Measuring the similarity of deep networks has been a long-standing open question. Most existing methods provide a single number to measure the similarity of two…

Research on the generalization ability of deep neural networks (DNNs) has recently attracted a great deal of attention. However, due to their complex architectures and large numbers of parameters, measuring the generalization ability of…

We define a class of so-called thinnable ideals $\mathcal{I}$ on the positive integers which includes several well-known examples, e.g., the collection of sets with zero asymptotic density, sets with zero logarithmic density, and several…

We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles. For R the 3-local…

A finite non-increasing sequence of positive integers $d = (d_1\geq \cdots\geq d_n)$ is called a degree sequence if there is a graph $G = (V,E)$ with $V = \{v_1,\ldots,v_n\}$ and $deg(v_i)=d_i$ for $i=1,\ldots,n$. In that case we say that…

We study pattern densities in binary sequences, finding optimal limit sequences with fixed pattern densities.

In this paper we study structural properties of LV-degrees of the algebra of collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. We construct atoms…

We study effective randomness-preserving transformations of path-incompressible trees. Some path-incompressible trees with infinitely many paths do not compute perfect path-random trees with computable oracle-use. Sparse perfect…

A theoretical framework is presented for a (copula-based) notion of dissimilarity between continuous random vectors and its main properties are studied. The proposed dissimilarity assigns the smallest value to a pair of random vectors that…

The space of constructible functions form a dense subspace of the space of generalized valuations. In this note we prove a somewhat stronger property that the sequential closure, taken sufficiently many (in fact, infinitely many) times, of…

In recent years, deep learning poses a deep technical revolution in almost every field and attracts great attentions from industry and academia. Especially, the convolutional neural network (CNN), one representative model of deep learning,…

Cluster number counts offer sensitive probes of the dark energy if and only if the_evolution_ of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding…

Kneser's theorem in the integers asserts that denoting by $ \underline{\mathrm{d}}$ the lower asymptotic density, if $\underline{\mathrm{d}}(X_1+\cdots+X_k)<\sum_{i=1}^k\underline{\mathrm{d}}(X_i)$ then the sumset $X_1+\cdots+X_k$ is…

Let $d$ be a positive integer. We study the proportion of irreducible characters of infinite families of irreducible Coxeter groups whose values evaluated on a fixed element $g$ are divisible by $d$. For Coxeter groups of types $A_n, B_n$…

Mid-level visual element discovery aims to find clusters of image patches that are both representative and discriminative. In this work, we study this problem from the prospective of pattern mining while relying on the recently popularized…

This paper presents a novel geometrical approach to investigate the convexity of a density-based cluster. Our approach is grid-based and we are about to calibrate the value space of the cluster. However, the cluster objects are coming from…

The design, analysis and application of a volumetric convolutional neural network (VCNN) are studied in this work. Although many CNNs have been proposed in the literature, their design is empirical. In the design of the VCNN, we propose a…