6,254 research outputs found
Martin Gardner and His Influence on Recreational Math
Recreational mathematics is a relatively new field in the world of mathematics. While sometimes overlooked as frivolous since those who practice it need no advanced knowledge of the subject, recreational mathematics is a perfect transition for people to experience the joy in logically establishing a solution. Martin Gardner recognized that this pattern of proving solutions to questions is how mathematics progresses. From his childhood on, Gardner greatly influenced the mathematical world. Although not a mathematician, he inspired many to pursue careers and make advancements in mathematics during his 25-year career with Scientific American. He encouraged novices to expand their knowledge, enlightened professionals of computer science developments, and established his own proofs
Constrained Non-Monotone Submodular Maximization: Offline and Secretary Algorithms
Constrained submodular maximization problems have long been studied, with
near-optimal results known under a variety of constraints when the submodular
function is monotone. The case of non-monotone submodular maximization is less
understood: the first approximation algorithms even for the unconstrainted
setting were given by Feige et al. (FOCS '07). More recently, Lee et al. (STOC
'09, APPROX '09) show how to approximately maximize non-monotone submodular
functions when the constraints are given by the intersection of p matroid
constraints; their algorithm is based on local-search procedures that consider
p-swaps, and hence the running time may be n^Omega(p), implying their algorithm
is polynomial-time only for constantly many matroids. In this paper, we give
algorithms that work for p-independence systems (which generalize constraints
given by the intersection of p matroids), where the running time is poly(n,p).
Our algorithm essentially reduces the non-monotone maximization problem to
multiple runs of the greedy algorithm previously used in the monotone case.
Our idea of using existing algorithms for monotone functions to solve the
non-monotone case also works for maximizing a submodular function with respect
to a knapsack constraint: we get a simple greedy-based constant-factor
approximation for this problem.
With these simpler algorithms, we are able to adapt our approach to
constrained non-monotone submodular maximization to the (online) secretary
setting, where elements arrive one at a time in random order, and the algorithm
must make irrevocable decisions about whether or not to select each element as
it arrives. We give constant approximations in this secretary setting when the
algorithm is constrained subject to a uniform matroid or a partition matroid,
and give an O(log k) approximation when it is constrained by a general matroid
of rank k.Comment: In the Proceedings of WINE 201
How to Incentivize Data-Driven Collaboration Among Competing Parties
The availability of vast amounts of data is changing how we can make medical
discoveries, predict global market trends, save energy, and develop educational
strategies. In some settings such as Genome Wide Association Studies or deep
learning, sheer size of data seems critical. When data is held distributedly by
many parties, they must share it to reap its full benefits.
One obstacle to this revolution is the lack of willingness of different
parties to share data, due to reasons such as loss of privacy or competitive
edge. Cryptographic works address privacy aspects, but shed no light on
individual parties' losses/gains when access to data carries tangible rewards.
Even if it is clear that better overall conclusions can be drawn from
collaboration, are individual collaborators better off by collaborating?
Addressing this question is the topic of this paper.
* We formalize a model of n-party collaboration for computing functions over
private inputs in which participants receive their outputs in sequence, and the
order depends on their private inputs. Each output "improves" on preceding
outputs according to a score function.
* We say a mechanism for collaboration achieves collaborative equilibrium if
it ensures higher reward for all participants when collaborating (rather than
working alone). We show that in general, computing a collaborative equilibrium
is NP-complete, yet we design efficient algorithms to compute it in a range of
natural model settings.
Our collaboration mechanisms are in the standard model, and thus require a
central trusted party; however, we show this assumption is unnecessary under
standard cryptographic assumptions. We show how to implement the mechanisms in
a decentralized way with new extensions of secure multiparty computation that
impose order/timing constraints on output delivery to different players, as
well as privacy and correctness
Tool support for reasoning in display calculi
We present a tool for reasoning in and about propositional sequent calculi.
One aim is to support reasoning in calculi that contain a hundred rules or
more, so that even relatively small pen and paper derivations become tedious
and error prone. As an example, we implement the display calculus D.EAK of
dynamic epistemic logic. Second, we provide embeddings of the calculus in the
theorem prover Isabelle for formalising proofs about D.EAK. As a case study we
show that the solution of the muddy children puzzle is derivable for any number
of muddy children. Third, there is a set of meta-tools, that allows us to adapt
the tool for a wide variety of user defined calculi
Escalating The War On SPAM Through Practical POW Exchange
Proof-of-work (POW) schemes have been proposed in the past. One prominent
system is HASHCASH (Back, 2002) which uses cryptographic puzzles . However,
work by Laurie and Clayton (2004) has shown that for a uniform proof-of-work
scheme on email to have an impact on SPAM, it would also be onerous enough to
impact on senders of "legitimate" email. I suggest that a non-uniform
proof-of-work scheme on email may be a solution to this problem, and describe a
framework that has the potential to limit SPAM, without unduly penalising
legitimate senders, and is constructed using only current SPAM filter
technology, and a small change to the SMTP (Simple Mail Transfer Protocol).
Specifically, I argue that it is possible to make sending SPAM 1,000 times more
expensive than sending "legitimate" email (so called HAM). Also, unlike the
system proposed by Debin Liu and Jean Camp (2006), it does not require the
complications of maintaining a reputation system.Comment: To be presented at the IEEE Conference On Networking, Adelaide,
Australia, November 19-21, 200
The System Paradigm
The introduction explains the sense in which the concept of a paradigm, whose originator, T.S. Kuhn, was inspired by the history of the national sciences, is applied to the context of the social sciences. Here the new paradigm does not necessarily replace the old; several paradigms may function effectively side by side. The milestones in the development of the system paradigm have been the works of Marx, Mises, Hayek, Polányi, Schumpeter and Eucken. Although these make a heterogeneous list in terms of their philosophies and political positions, they share a 'system approach'. They deal not just with individual details of the economy but with the system as a whole, and not just with the economy but with the political, ideological and social dimensions, paying special heed to the interactions between each sphere. The great task for the system paradigm is to study the post-socialist transition. For this, it is indispensable; its explanatory power cannot be replaced by any other paradigm. On the other hand, those applying the system paradigm (like the exponents of other paradigms) are often gravely mistaken. The predictive force of the system paradigm is limited, which urges modesty upon those who employ it.http://deepblue.lib.umich.edu/bitstream/2027.42/39662/3/wp278.pd
Tiny Groups Tackle Byzantine Adversaries
A popular technique for tolerating malicious faults in open distributed
systems is to establish small groups of participants, each of which has a
non-faulty majority. These groups are used as building blocks to design
attack-resistant algorithms.
Despite over a decade of active research, current constructions require group
sizes of , where is the number of participants in the system.
This group size is important since communication and state costs scale
polynomially with this parameter. Given the stubbornness of this logarithmic
barrier, a natural question is whether better bounds are possible.
Here, we consider an attacker that controls a constant fraction of the total
computational resources in the system. By leveraging proof-of-work (PoW), we
demonstrate how to reduce the group size exponentially to while
maintaining strong security guarantees. This reduction in group size yields a
significant improvement in communication and state costs.Comment: This work is supported by the National Science Foundation grant CCF
1613772 and a C Spire Research Gif
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