相关论文: Unlocking Your Bike the Easy Way

We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization…

Natural materials often feature a combination of soft and stiff phases, arranged to achieve excellent mechanical properties, such as high strength and toughness. Many natural materials have even independently evolved to have similar…

Universal Cycles, or U-cycles, as originally defined by de Bruijn, are an efficient method to exhibit a large class of combinatorial objects in a compressed fashion, and with no repeats. de Bruijn's theorem states that U-cycles for $n$…

Binary decisions are the simplest form of decisions that are made in our daily lives. Examples include choosing a two-way path in a maze, accepting or declining an offer, etc. These decisions are also made by computers, machines and various…

In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of…

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…

A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established…

We analyze the trajectory of suspended spherical particles moving through a square array of obstacles, in the deterministic limit and at zero Reynolds number. We show that, in the dilute approximation of widely separated obstacles, the…

It is known that cyclic arrangements are the only {\em unavoidable} simple arrangements of pseudolines: for each fixed $m\ge 1$, every sufficiently large simple arrangement of pseudolines has a cyclic subarrangement of size $m$. In the same…

On the lines of the huge and varied efforts in the field of automation with respect to technology development and innovation of vehicles to make them run autonomously, this paper presents an innovation to a bicycle. A normal daily use…

Codes for storage systems aim to minimize the repair locality, which is the number of disks (or nodes) that participate in the repair of a single failed disk. Simultaneously, the code must sustain a high rate, operate on a small finite…

In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4}+\nu Z_{4}$ for $\nu^{2} \in \{0,1,\nu,2\nu,3\nu,2+\nu,2+3\nu,3+2\nu\}$ to be a reversible cyclic code have been…

A unibike curve is a track that can be made by either a bicycle or a unicycle. More precisely, the end of a unit tangent vector at any point on a unibike curve lies on the curve (so the bike's front wheel always lies on the track made by…

Existing logic-locking attacks are known to successfully decrypt functionally correct key of a locked combinational circuit. It is possible to extend these attacks to real-world Silicon-based Intellectual Properties (IPs, which are…

We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the…

We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to…

Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…

A novel implementation of a special class of Galois ring, in which the multiplication can be realized by a cyclic convolution, is applied to the construction of network codes. The primitive operations involved are byte-wise shifts and…

We formulate an optimization of a bicycle ascent time under the constraints of the average, maximum, and minimum powers. In contrast to the first part of this study, we do not restrict the departure to flying starts with an initial speed…

Simple cycles on a digraph form a trace monoid under the rule that two such cycles commute if and only if they are vertex disjoint. This rule describes the spatial configuration of simple cycles on the digraph. Cartier and Foata have showed…