292 research outputs found
On the Falk invariant of hyperplane arrangements attached to gain graphs
The fundamental group of the complement of a hyperplane arrangement in a
complex vector space is an important topological invariant. The third rank of
successive quotients in the lower central series of the fundamental group was
called Falk invariant of the arrangement since Falk gave the first formula and
asked to give a combinatorial interpretation. In this article, we give a
combinatorial formula for the Falk invariant of hyperplane arrangements
attached to certain gain graphs.Comment: To appear in the Australasian Journal of Combinatorics. arXiv admin
note: text overlap with arXiv:1703.0940
An Architecture for Distributed Energies Trading in Byzantine-Based Blockchain
With the development of smart cities, not only are all corners of the city
connected to each other, but also connected from city to city. They form a
large distributed network together, which can facilitate the integration of
distributed energy station (DES) and corresponding smart aggregators.
Nevertheless, because of potential security and privacy protection arisen from
trustless energies trading, how to make such energies trading goes smoothly is
a tricky challenge. In this paper, we propose a blockchain-based multiple
energies trading (B-MET) system for secure and efficient energies trading by
executing a smart contract we design. Because energies trading requires the
blockchain in B-MET system to have high throughput and low latency, we design a
new byzantine-based consensus mechanism (BCM) based on node's credit to improve
efficiency for the consortium blockchain under the B-MET system. Then, we take
combined heat and power (CHP) system as a typical example that provides
distributed energies. We quantify their utilities, and model the interactions
between aggregators and DESs in a smart city by a novel multi-leader
multi-follower Stackelberg game. It is analyzed and solved by reaching Nash
equilibrium between aggregators, which reflects the competition between
aggregators to purchase energies from DESs. In the end, we conduct plenty of
numerical simulations to evaluate and verify our proposed model and algorithms,
which demonstrate their correctness and efficiency completely
Differential Privacy-Based Online Allocations towards Integrating Blockchain and Edge Computing
In recent years, the blockchain-based Internet of Things (IoT) has been
researched and applied widely, where each IoT device can act as a node in the
blockchain. However, these lightweight nodes usually do not have enough
computing power to complete the consensus or other computing-required tasks.
Edge computing network gives a platform to provide computing power to IoT
devices. A fundamental problem is how to allocate limited edge servers to IoT
devices in a highly untrustworthy environment. In a fair competition
environment, the allocation mechanism should be online, truthful, and privacy
safe. To address these three challenges, we propose an online multi-item double
auction (MIDA) mechanism, where IoT devices are buyers and edge servers are
sellers. In order to achieve the truthfulness, the participants' private
information is at risk of being exposed by inference attack, which may lead to
malicious manipulation of the market by adversaries. Then, we improve our MIDA
mechanism based on differential privacy to protect sensitive information from
being leaked. It interferes with the auction results slightly but guarantees
privacy protection with high confidence. Besides, we upgrade our
privacy-preserving MIDA mechanism such that adapting to more complex and
realistic scenarios. In the end, the effectiveness and correctness of
algorithms are evaluated and verified by theoretical analysis and numerical
simulations
Holonomy Lie algebra of a fiber-type arrangement
We prove that the holonomy Lie algebra of a fiber-type arrangement is an
iterated almost-direct product of a series of free Lie algebras with ranks the
exponents of the arrangement. This is a Lie algebra version analogue of the
well-known result of Falk-Randell that the fundamental group of the complement
of a fiber-type arrangement is an iterated almost-direct product of a series of
free groups with ranks the exponents of the arrangements. By using
Jambu-Papadima's deformation method, we generalize the result to hypersolvable
arrangements. As byproducts, we reprove the LCS formula for those arrangements.Comment: 10 pages, No figure
A k-hop Collaborate Game Model: Extended to Community Budgets and Adaptive Non-Submodularity
Revenue maximization (RM) is one of the most important problems on online
social networks (OSNs), which attempts to find a small subset of users in OSNs
that makes the expected revenue maximized. It has been researched intensively
before. However, most of exsiting literatures were based on non-adaptive
seeding strategy and on simple information diffusion model, such as
IC/LT-model. It considered the single influenced user as a measurement unit to
quantify the revenue. Until Collaborate Game model appeared, it considered
activity as a basic object to compute the revenue. An activity initiated by a
user can only influence those users whose distance are within k-hop from the
initiator. Based on that, we adopt adaptive seed strategy and formulate the
Revenue Maximization under the Size Budget (RMSB) problem. If taking into
account the product's promotion, we extend RMSB to the Revenue Maximization
under the Community Budget (RMCB) problem, where the influence can be
distributed over the whole network. The objective function of RMSB and RMCB is
adatpive monotone and not adaptive submodular, but in some special cases, it is
adaptive submodular. We study the RMSB and RMCB problem under both the speical
submodular cases and general non-submodular cases, and propose RMSBSolver and
RMCBSolver to solve them with strong theoretical guarantees, respectively.
Especially, we give a data-dependent approximation ratio for RMSB problem under
the general non-submodular cases. Finally, we evaluate our proposed algorithms
by conducting experiments on real datasets, and show the effectiveness and
accuracy of our solutions
A Double Auction for Charging Scheduling among Vehicles Using DAG-Blockchains
Electric vehicle (EV) is becoming more and more popular in our daily life,
which replaces the traditional fuel vehicles to reduce carbon emissions and
protect the environment. The EVs need to be charged, but the number of charging
piles in a charging station (CS) is limited and charging is usually more
time-consuming than fueling. According to this scenario, we propose a secure
and efficient charging scheduling system based on DAG-blockchain and double
auction mechanism. In a smart area, it attempts to assign EVs to the available
CSs in the light of their submitted charging requests and status information.
First, we design a lightweight charging scheduling framework that integrates
DAG-blockchain and modern cryptography technology to ensure security and
scalability during performing scheduling and completing tradings. In this
process, a constrained double auction problem is formulated because of the
limited charging resources in a CS, which motivates the EVs and CSs in this
area to participate in the market based on their preferences and statuses. Due
to this constraint, our problem is more complicated and harder to achieve the
truthfulness as well as system efficiency compared to the existing double
auction model. To adapt to it, we propose two algorithms, namely the truthful
mechanism for charging (TMC) and efficient mechanism for charging (EMC), to
determine the assignments between EVs and CSs and pricing strategies. Then,
both theoretical analysis and numerical simulations show the correctness and
effectiveness of our proposed algorithms
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