3,199 research outputs found
New directions in mechanism design
Mechanism design uses the tools of economics and game theory to design rules
of interaction for economic transactions that will,in principle, yield some de-
sired outcome. In the last few years this field has received much interest of
researchers in computer science, especially with the Internet developing as a
platform for communications and connections among enormous numbers of computers
and humans. Arguably the most positive result in mechanism de- sign is truthful
and there are only one general truthful mechanisms so far : the generalized
Vickrey-Clarke-Groves (VCG) mechanism. But VCG mecha- nism has one shortage:
The implementation of truthfulness is on the cost of decreasing the revenue of
the mechanism. (e.g., Ning Chen and Hong Zhu. [1999]). We introduce three new
characters of mechanism:partly truthful, criti- cal, consistent, and introduce
a new mechanism: X mechanism that satisfy the above three characters. Like VCG
mechanism, X mechanism also generalizes from Vickery Auction and is consistent
with Vickery auction in many ways, but the extended methods used in X mechanism
is different from that in VCG mechanism . This paper will demonstrate that X
mechanism better than VCG mechanism in optimizing utility of mechanism, which
is the original intention of mechanism design. So partly truthful,critical and
consistent are at least as important as truthful in mechanism design, and they
beyond truthful in many situations.As a result, we conclude that partly
truthful,critical and consistent are three new directions in mechanism design
Depth-graded motivic Lie algebra
Consider the neutral Tannakian category mixed Tate motives over Z, in this
paper we suggest a way to understand the structure of depth-graded motivic Lie
subalgebra generated by the depth one part. We will show that from an
isomorphism conjecture proposed by K. Tasaka we can deduce the F. Brown matrix
conjecture and the non-degenerated conjecture about depth-graded motivic Lie
subalgebra generated by the depth one part.Comment: 13 page
The depth structure of motivic multiple zeta values
In this paper, we construct some maps related to the motivic Galois action on
depth-graded motivic multiple zeta values. And from these maps we give some
short exact sequences about depth-graded motivic multiple zeta values in depth
two and three. In higher depth we conjecture that there are exact sequences of
the same type. And we will show from three conjectures about depth-graded
motivic Lie algebra we can nearly deduce the exact sequences conjectures in
higher depth. At last we give a new proof of the result that the modulo
zeta(2)$ version motivic double zeta values is generated by the totally odd
part. And we reduce the well-known conjecture that the modulo zeta (2) version
motivic triple zeta values is generated by the totally odd part to an
isomorphism conjecture in linear algebra.Comment: 25 page
Approximate Message Passing with Unitary Transformation
Approximate message passing (AMP) and its variants, developed based on loopy
belief propagation, are attractive for estimating a vector x from a noisy
version of z = Ax, which arises in many applications. For a large A with i. i.
d. elements, AMP can be characterized by the state evolution and exhibits fast
convergence. However, it has been shown that, AMP mayeasily diverge for a
generic A. In this work, we develop a new variant of AMP based on a unitary
transformation of the original model (hence the variant is called UT-AMP),
where the unitary matrix is available for any matrix A, e.g., the conjugate
transpose of the left singular matrix of A, or a normalized DFT (discrete
Fourier transform) matrix for any circulant A. We prove that, in the case of
Gaussian priors, UT-AMP always converges for any matrix A. It is observed that
UT-AMP is much more robust than the original AMP for difficult A and exhibits
fast convergence.
A special form of UT-AMP with a circulant A was used in our previous work
[13] for turbo equalization. This work extends it to a generic A, and provides
a theoretical investigation on the convergence.Comment: 5 page
On the structure of zero-sum free set with minimum subset sums in abelian groups
Let be an additive abelian group and a subset. Let
denote the set of group elements which can be expressed as a sum of
a nonempty subset of . We say is zero-sum free if .
It was conjectured by R.B.~Eggleton and P.~Erd\"{o}s in 1972 and proved by
W.~Gao et. al. in 2008 that provided that is a
zero-sum free subset of an abelian group with . In this paper, we
determined the structure of zero-sum free set where and
.Comment: 19 page
On the unsplittable minimal zero-sum sequences over finite cyclic groups of prime order
Let be a prime and let be a cyclic group of order . Let
be a minimal zero-sum sequence with elements over , i.e., the sum of
elements in is zero, but no proper nontrivial subsequence of has sum
zero. We call is unsplittable, if there do not exist in and such that and is also a minimal zero-sum sequence.
In this paper we show that if is an unsplittable minimal zero-sum sequence
of length , then
or
. Furthermore, if is a
minimal zero-sum sequence with , then \ind(S) \leq 2.Comment: 11 page
Motivic multiple zeta values reletive to \mu_2
We establish a short exact sequence about depth-graded motivic double zeta
values of even weight relative to . We find a basis for the depth-graded
motivic double zeta values relative to of even weight and a basis for
the depth-graded motivic triple zeta values relative to of odd weight.
As an application of our main results, we prove Kaneko and Tasaka's conjectures
about the sum odd double zeta values and the classical double zeta values. We
also prove an analogue of Kaneko and Tasaka's conjecture in depth three. At
last we formulate a conjecture which is related to sum odd multiple zeta values
in higher depth.Comment: 27 page
Motivic double zeta values of odd weight
For odd , we establish a short exact sequence about motivic double
zeta values with odd, . From
this we classify all the relations among depth-graded motivic double zeta
values with odd, . As a
corollary, we confirm a conjecture of Zagier on the rank of a matrix which
concerns relations among multiple zeta values of odd weight.Comment: 15 page
Strategically Simple Mechanisms
We define and investigate a property of mechanisms that we call "strategic
simplicity," and that is meant to capture the idea that, in strategically
simple mechanisms, strategic choices require limited strategic sophistication.
We define a mechanism to be strategically simple if choices can be based on
first-order beliefs about the other agents' preferences and first-order
certainty about the other agents' rationality alone, and there is no need for
agents to form higher-order beliefs, because such beliefs are irrelevant to the
optimal strategies. All dominant strategy mechanisms are strategically simple.
But many more mechanisms are strategically simple. In particular, strategically
simple mechanisms may be more flexible than dominant strategy mechanisms in the
bilateral trade problem and the voting problem
Computer Network Reliability Optimization Calculation Based on Genetic Algorithm
How to effectively reduce the network node link cost by improving the reliability of computer network transmission system is one of the important targets of computer network reliability optimization calculation. Therefore, in the computer network reliability optimization calculation, it is necessary to integrate the computer network link medium cost, network reliability optimization mathematical model and other factors. This paper describes genetic algorithm and its implementation process, as well as the application of genetic algorithm to the network link cost and network reliability optimization calculation. In addition, it is indicated from the simulation results that genetic algorithm can effectively solve the reliability optimization calculation problem which is difficult to solve by the traditional algorithm of network, so as to speed up the calculation speed of computer network and optimize the network calculation result
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