Related papers: Modified difference ascent sequences and Fishburn …
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
A quasispecies is a set of interrelated genotypes that have reached a situation of equilibrium while evolving according to the usual Darwinian principles of selection and mutation. Quasispecies studies invariably assume that it is possible…
Tandem duplication is an evolutionary process whereby a segment of DNA is replicated and proximally inserted. The different configurations that can arise from this process give rise to some interesting combinatorial questions. Firstly, we…
Transformer models have achieved great progress on computer vision tasks recently. The rapid development of vision transformers is mainly contributed by their high representation ability for extracting informative features from input…
Given a graph $G$, its independence sequence is the integral sequence $a_1,a_2,...,a_n$, where $a_i$ is the number of independent sets of vertices of size i. In the late 80's Alavi, Erdos, Malde, Schwenk showed that this sequence need not…
Multiple sequence alignment is a key process in today's biology, and finding a relevant alignment of several sequences is much more challenging than just optimizing some improbable evaluation functions. Our approach for addressing multiple…
We define the Augmentation property for binary matrices with respect to different rank functions. A matrix $A$ has the Augmentation property for a given rank function, if for any subset of column vectors $x_1,...,x_t$ for for which the rank…
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…
The concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a…
Transformer architectures have facilitated the development of large-scale and general-purpose sequence models for prediction tasks in natural language processing and computer vision, e.g., GPT-3 and Swin Transformer. Although originally…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota-Baxter algebra, called the Rota-Baxter characteristic. We introduce an invariant, called the ascent set, of a…
The problem of data augmentation in feature space is considered. A new architecture, denoted the FeATure TransfEr Network (FATTEN), is proposed for the modeling of feature trajectories induced by variations of object pose. This architecture…
The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo…
We study two related probabilistic models of permutations and trees biased by their number of descents. Here, a descent in a permutation $\sigma$ is a pair of consecutive elements $\sigma(i), \sigma(i+1)$ such that $\sigma(i) >…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
We consider evolution algebras and their related substructures: evolution ideals and evolution subalgebras. After exposing some of the concepts related to them in the literature, we explore the order structures that arise in the sets of…
We propose to extend ``invertibility'' to ``regularity'' for categories in general abstract algebraic manner. Higher regularity conditions and ``semicommutative'' diagrams are introduced. Distinction between commutative and…
We introduce several highness notions on degrees related to the problem of computing isomorphisms between structures, provided that isomorphisms exist. We consider variants along axes of uniformity, inclusion of negative information, and…