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A partial Steiner triple system of order n is sequenceable if there is a sequence of length n of its distinct points such that no proper segment of the sequence is a union of point-disjoint blocks. We prove that if a partial Steiner triple…

Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations…

This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…

Anomaly detection is a practical and challenging task due to the scarcity of anomaly samples in industrial inspection. Some existing anomaly detection methods address this issue by synthesizing anomalies with noise or external data.…

Recently, with convolutional neural networks gaining significant achievements in many challenging machine learning fields, hand-crafted neural networks no longer satisfy our requirements as designing a network will cost a lot, and…

Fine-grained classification often requires recognizing specific object parts, such as beak shape and wing patterns for birds. Encouraging a fine-grained classification model to first detect such parts and then using them to infer the class…

This paper proposes a new, visual method to study numerical semigroups and the Frobenius problem. The method is based on building a so-called reduction graph, whose nodes usually correspond to monogenic semigroups, and whose edges can have…

In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…

Semi-supervised classification on graphs aims at assigning labels to all nodes of a graph based on the labels known for a few nodes, called the seeds. The most popular algorithm relies on the principle of heat diffusion, where the labels of…

A $K$-Fibonacci sequence is a binary recurrence sequence where $F_0=0$, $F_1=1$, and $F_n=K\cdot F_{n-1}+F_{n-2}$. These sequences are known to be periodic modulo every positive integer greater than $1$. If the length of one shortest period…

We study frequency moments of partition statistics arising from Euler products $A(q)=\prod_{r\ge1}(1-q^r)^{-c(r)}$ via a transform that expresses the moment generating functions as $B(q)$ times explicit divisor--sum series determined by…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

The classical Fibonacci sequence is known to exhibit many fascinating properties. In this paper, we explore the Fibonacci sequence and integer sequences generated by second order linear recurrence relations with positive integer…

Inspired by Bondal's conjecture, we study the behavior of exceptional sequences of line bundles on rational C*-surfaces under homogeneous degenerations. In particular, we provide a sufficient criterion for such a sequence to remain…

Pedestrian trajectory prediction is challenging due to its uncertain and multimodal nature. While generative adversarial networks can learn a distribution over future trajectories, they tend to predict out-of-distribution samples when the…

A graph is called set-sequential if its vertices can be labeled with distinct nonzero vectors in $\mathbb{F}_2^n$ such that when each edge is labeled with the sum$\pmod{2}$ of its vertices, every nonzero vector in $\mathbb{F}_2^n$ is the…

Component-centric distributed graph processing platforms that use a bulk synchronous parallel (BSP) programming model have gained traction. These address the short-comings of Big Data abstractions/platforms like MapReduce/Hadoop for…

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.…

Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…

Instance search is an interesting task as well as a challenging issue due to the lack of effective feature representation. In this paper, an instance level feature representation built upon fully convolutional instance-aware segmentation is…