A Maximal Concurrency and Low Latency Distributed Scheduling Protocol for Wireless Sensor Networks

Existing work that schedules concurrent transmissions collision-free suffers from low channel utilization. We propose the Optimal Node Activation Multiple Access (ONAMA) protocol to achieve maximal channel spatial reuse through a distributed maximal independent set (DMIS) algorithm. To overcome DMIS's excessive delay in finding a maximal independent set, we devise a novel technique called pipelined precomputation that decouples DMIS from data transmission. We implement ONAMA on resource-constrained TelosB motes using TinyOS. Extensive measurements on two testbeds independently attest to ONAMA's superb performance compared to existing work: improving concurrency, throughput, and delay by a factor of 3.7, 3.0, and 5.3, respectively, while still maintaining reliability.Comment: final version; 6 page

Distortion of quasiconformal mappings with identity boundary values

Teichm\"uller's classical mapping problem for plane domains concerns finding a lower bound for the maximal dilatation of a quasiconformal homeomorphism which holds the boundary pointwise fixed, maps the domain onto itself, and maps a given point of the domain to another given point of the domain. For a domain $D \subset {\mathbb R}^n\,,n\ge 2\,,$ we consider the class of all $K$- quasiconformal maps of $D$ onto itself with identity boundary values and Teichm\"uller's problem in this context. Given a map $f$ of this class and a point $x\in D\,,$ we show that the maximal dilatation of $f$ has a lower bound in terms of the distance of $x$ and $f(x)$ in the distance ratio metric. For instance, convex domains, bounded domains and domains with uniformly perfect boundaries are studied.Comment: 19 pages, 4 figur

On the structure theorem and the Maschke type theorem of Doi Hom-Hopf modules

We give necessary and sufficient conditions for the functor that forgets the $(C, \gamma)$-coaction to be separable. This leads to a generalized notion of integrals. Finally, the applications of our results are considered.Comment: 13pages. arXiv admin note: substantial text overlap with arXiv:1411.720

Central invariants and enveloping algebras of braided Hom-Lie algebras

Let $(H,\alpha)$ be a monoidal Hom-Hopf algebra and $^{H}_{H}\mathcal{HYD}$ the Hom-Yetter-Drinfeld category over $(H,\alpha)$. Then in this paper, we first introduce the definition of braided Hom-Lie algebras and show that each monoidal Hom-algebra in $^{H}_{H}\mathcal{HYD}$ gives rise to a braided Hom-Lie algebra. Second, we prove that if $(A,\beta)$ is a sum of two $H$-commutative monoidal Hom-subalgebras, then the commutator Hom-ideal $[A,A]$ of $A$ is nilpotent. Also, we study the central invariant of braided Hom-Lie algebras as a generalization of generalized Lie algebras. Finally, we obtain a construction of the enveloping algebras of braided Hom-Lie algebras and show that the enveloping algebras are $H$-cocommutative Hom-Hopf algerbas.Comment: 31page

Cohomology and derivations of BiHom-Lie conformal algebras

In this paper, we introduce the notion of a BiHom-Lie conformal algebra and develop its cohomology theory. Also, we discuss some applications to the study of deformations of regular BiHom-Lie conformal algebras. Finally, we introduce derivations of multiplicative BiHom-Lie conformal algebras and study their properties.Comment: 21. arXiv admin note: text overlap with arXiv:1807.03638; text overlap with arXiv:1607.00713, arXiv:1612.02878 by other author

On the structure of split regular Hom-Lie Rinehart algebras

The aim of this paper is to study the structures of split regular Hom-Lie Rinehart algebras. Let $(L,A)$ be a split regular Hom-Lie Rinehart algebra. We first show that $L$ is of the form $L=U+\sum_{[\gamma]\in\Gamma/\thicksim}I_{[\gamma]}$ with $U$ a vector space complement in $H$ and $I_{[\gamma]}$ are well described ideals of $L$ satisfying $I_{[\gamma]},I_{[\delta]}=0$ if $I_{[\gamma]}\neq I_{[\delta]}$. Also, we discuss the weight spaces and decompositions of $A$ and present the relation between the decompositions of $L$ and $A$. Finally, we consider the structures of tight split regular Hom-Lie Rinehart algebras.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1706.07084, arXiv:1504.04236, arXiv:1508.02124 by other author

Smash coproducts of bicomonads and Hom-entwining structures

Let $F,G$ be bicomonads on a monoidal category $\mathcal{C}$. The aim of this paper is to discuss the smash coproducts of $F$ and $G$. As an application, the smash coproduct of Hom-bialgebras is discussed. Further, the Hom-entwining structure and Hom-entwined modules are investigated

Braided monoidal categories and Doi Hopf modules for monoidal Hom-Hopf algebras

We first introduce the notion of Doi Hom-Hopf modules and find the sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. Also we obtain the condition for the monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Second, we give the maps between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras give rise to functors between the category of Doi Hom-Hopf modules and study tensor identities for monodial categories of Doi Hom-Hopf modules. Furthermore, we construct a braiding on the category of Doi Hom-Hopf modules. Finally, as an application of our theory, we consider the braiding on the category of Hom-modules, the category of Hom-comodules and the category of Hom-Yetter-Drinfeld modules respectively.Comment: 23 page

Distributed Consensus Resilient to Both Crash Failures and Strategic Manipulations

In this paper, we study distributed consensus in synchronous systems subject to both unexpected crash failures and strategic manipulations by rational agents in the system. We adapt the concept of collusion-resistant Nash equilibrium to model protocols that are resilient to both crash failures and strategic manipulations of a group of colluding agents. For a system with $n$ distributed agents, we design a deterministic protocol that tolerates 2 colluding agents and a randomized protocol that tolerates $n - 1$ colluding agents, and both tolerate any number of failures. We also show that if colluders are allowed an extra communication round after each synchronous round, there is no protocol that can tolerate even 2 colluding agents and 1 crash failure

Observations on quasihyperbolic geometry modeled on Banach spaces

In this paper, we continue our study of quasihyperbolic metric in Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on the weight function, which improves an earlier result of the two first authors. We also answer to a question posed by the two first authors in an earlier paper with R. Kl\'en, and present results related to the question on smoothness of quasihyperbolic balls