Related papers: Self-modified difference ascent sequences
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Preferential attachment is often suggested to be the underlying mechanism of the growth of a network, largely due to that many real networks are, to a certain extent, scale-free. However, such attribution is usually made under debatable…
We show how to use the combinatorial notion of jump sets to parametrize the possible structures of the group of principal units of local fields, viewed as filtered modules. We establish a natural bijection between the set of jump sets and…
In past research on self-supervised learning for image classification, the use of rotation as an augmentation has been common. However, relying solely on rotation as a self-supervised transformation can limit the ability of the model to…
Furstenberg, Glasscock, Bergelson, Beiglboeck have been studied abundance in arithmatic progression on various large sets like piecewise syndetic, central, thick, etc. but also there are so many sets in which abundance in progression is…
The distance matrix of a connected graph is the symmetric matrix with columns and rows indexed by the vertices and entries that are the pairwise distances between the corresponding vertices. We give a construction for graphs which differ in…
The study of patterns in permutations associated with forests of binary shrubs was initiated by D. Bevan et al.. In this paper, we study five different types of rise statistics that can be associated with such permutations and find the…
This paper introduces the extended set difference, a generalization of the Hukuhara and generalized Hukuhara differences, defined for compact convex sets in $\mathbb{R}^d$. The proposed difference guarantees existence for any pair of such…
Developmental bias plays a major role in phenotypic evolution. Some researchers have argued that phenotypes, regulated by development, can only evolve along restricted trajectory under certain scenarios, such as the case for mammalian molar…
We consider an estimator for the location of a shift in the mean of long-range dependent sequences. The estimation is based on the two-sample Wilcoxon statistic. Consistency and the rate of convergence for the estimated change point are…
Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.
While gradient descent has proven highly successful in learning connection weights for neural networks, the actual structure of these networks is usually determined by hand, or by other optimization algorithms. Here we describe a simple…
Deep Imitation Learning requires a large number of expert demonstrations, which are not always easy to obtain, especially for complex tasks. A way to overcome this shortage of labels is through data augmentation. However, this cannot be…
Current approaches for predicting sets from feature vectors ignore the unordered nature of sets and suffer from discontinuity issues as a result. We propose a general model for predicting sets that properly respects the structure of sets…
The descent set of an oscillating (or up-down) tableau is introduced. This descent set plays the same role in the representation theory of the symplectic groups as the descent set of a standard tableau plays in the representation theory of…
Although gradient descent (GD) almost always escapes saddle points asymptotically [Lee et al., 2016], this paper shows that even with fairly natural random initialization schemes and non-pathological functions, GD can be significantly…
A data augmentation module is utilized in contrastive learning to transform the given data example into two views, which is considered essential and irreplaceable. However, the predetermined composition of multiple data augmentations brings…
An open question in the Deep Learning community is why neural networks trained with Gradient Descent generalize well on real datasets even though they are capable of fitting random data. We propose an approach to answering this question…
Certain classes of problems, including perceptual data understanding, robotics, discovery, and learning, can be represented as incremental, dynamically constructed belief networks. These automatically constructed networks can be dynamically…
We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one.…