Smith equivalence and finite Oliver groups with Laitinen number 0 or 1

In 1960, Paul A. Smith asked the following question. If a finite group G acts smoothly on a sphere with exactly two fixed points, is it true that the tangent G-modules at the two points are always isomorphic? We focus on the case G is an Oliver group and we present a classification of finite Oliver groups G with Laitinen number a_G = 0 or 1. Then we show that the Smith Isomorphism Question has a negative answer and a_G > 1 for any finite Oliver group G of odd order, and for any finite Oliver group G with a cyclic quotient of order pq for two distinct odd primes p and q. We also show that with just one unknown case, this question has a negative answer for any finite nonsolvable gap group G with a_G > 1. Moreover, we deduce that for a finite nonabelian simple group G, the answer to the Smith Isomorphism Question is affirmative if and only if a_G = 0 or 1.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-35.abs.htm

Author recognition using Locality Sensitive Hashing & Alergia (Stochastic Finite Automata)

In today’s world data grows very fast. It is difficult to answer questions like 1) Is the content completely written by this author, 2) Did he get few sentences or pages from another author, 3) Is there any way to identify actual author. There are many plagiarism software’s available in the market which identify duplicate content. It doesn’t understand writing pattern involved. There is always a necessity to make an effort to find the original author. Locality sensitive hashing is one such standard for applying hashing to recognize authors writing pattern

Social Samaritan Justice: When and Why Needy Fellow Citizens Have a Right to Assistance

In late 2012, Hurricane Sandy hit the East Coast of the U.S., causing much suffering and devastation. Those who could have easily helped Sandy’s victims had a duty to do so. But was this a rightfully enforceable duty of justice, or a non-enforceable duty of beneficence? The answer to this question is often thought to depend on the kind of help offered: the provision of immediate bodily services is not enforceable; the transfer of material resources is. I argue that this double standard is unjustified, and defend a version of what I call “Social Samaritanism.” On this view, within political communities, the duty to help the needy—whether via bodily services or resource transfers—is always an enforceable demand of justice, except when the needy are reckless; across independent political communities, it is always a matter of beneficence. I defend this alternative double standard, and consider its implications for the case of Sandy

What is the smallest prime?

What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime.Comment: 11 pages, 5 figure

Universality and Decidability of Number-Conserving Cellular Automata

Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the definition of the property to include cellular automata with any set of states in \Zset, and show that they can be always extended to ``usual'' NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive.Comment: 13 page

Reinforced Mnemonic Reader for Machine Reading Comprehension

In this paper, we introduce the Reinforced Mnemonic Reader for machine reading comprehension tasks, which enhances previous attentive readers in two aspects. First, a reattention mechanism is proposed to refine current attentions by directly accessing to past attentions that are temporally memorized in a multi-round alignment architecture, so as to avoid the problems of attention redundancy and attention deficiency. Second, a new optimization approach, called dynamic-critical reinforcement learning, is introduced to extend the standard supervised method. It always encourages to predict a more acceptable answer so as to address the convergence suppression problem occurred in traditional reinforcement learning algorithms. Extensive experiments on the Stanford Question Answering Dataset (SQuAD) show that our model achieves state-of-the-art results. Meanwhile, our model outperforms previous systems by over 6% in terms of both Exact Match and F1 metrics on two adversarial SQuAD datasets.Comment: Published in 27th International Joint Conference on Artificial Intelligence (IJCAI), 201

It’s Complicated: Reflections on Teaching Negotiation for Women

What does it mean to be a woman negotiator? In the two decades that I have been teaching negotiation, I have encountered a wide range of human behavior in the negotiation setting. Individuals run the gamut in terms of their strategies, tactics, worldviews, charisma, perspicacity, flexibility, and other factors that affect negotiation behavior and negotiation outcomes. But one area that negotiation students are always curious about—be they top executives, law students, government employees, lawyers, or doctors—is the role of gender in negotiation. The maddening but intriguing answer to this question is the same as the answer to many other questions about negotiation: it’s complicated. The most important quality of negotiation is its dynamic and fluid nature, each encounter completely unique to its own participants and its own contexts, yet always with the possibility of analysis along a set of identifiable dimensions

Bloom Filters in Adversarial Environments

Many efficient data structures use randomness, allowing them to improve upon deterministic ones. Usually, their efficiency and correctness are analyzed using probabilistic tools under the assumption that the inputs and queries are independent of the internal randomness of the data structure. In this work, we consider data structures in a more robust model, which we call the adversarial model. Roughly speaking, this model allows an adversary to choose inputs and queries adaptively according to previous responses. Specifically, we consider a data structure known as "Bloom filter" and prove a tight connection between Bloom filters in this model and cryptography. A Bloom filter represents a set $S$ of elements approximately, by using fewer bits than a precise representation. The price for succinctness is allowing some errors: for any $x \in S$ it should always answer `Yes', and for any $x \notin S$ it should answer `Yes' only with small probability. In the adversarial model, we consider both efficient adversaries (that run in polynomial time) and computationally unbounded adversaries that are only bounded in the number of queries they can make. For computationally bounded adversaries, we show that non-trivial (memory-wise) Bloom filters exist if and only if one-way functions exist. For unbounded adversaries we show that there exists a Bloom filter for sets of size $n$ and error $\varepsilon$, that is secure against $t$ queries and uses only $O(n \log{\frac{1}{\varepsilon}}+t)$ bits of memory. In comparison, $n\log{\frac{1}{\varepsilon}}$ is the best possible under a non-adaptive adversary