arXiv subjects

Haifeng Xu

Publications and source records attributed to Haifeng Xu.

115 records · Page 7Linked to original sources

arXiv2016

Using Social Networks to Aid Homeless Shelters: Dynamic Influence Maximization under Uncertainty - An Extended Version

This paper presents HEALER, a software agent that recommends sequential intervention plans for use by homeless shelters, who organize these interventions to raise awareness about HIV among homeless youth. HEALER's sequential plans (built using knowledge of social networks of homeless youth) choose intervention participants strategically to maximize influence spread, while reasoning about uncertainties in the network. While previous work presents influence maximizing techniques to choose intervention participants, they do not address three real-world issues: (i) they completely fail to scale up to real-world sizes; (ii) they do not handle deviations in execution of intervention plans; (iii) constructing real-world social networks is an expensive process. HEALER handles these issues via four major contributions: (i) HEALER casts this influence maximization problem as a POMDP and solves it using a novel planner which scales up to previously unsolvable real-world sizes; (ii) HEALER allows shelter officials to modify its recommendations, and updates its future plans in a deviation-tolerant manner; (iii) HEALER constructs social networks of homeless youth at low cost, using a Facebook application. Finally, (iv) we show hardness results for the problem that HEALER solves. HEALER will be deployed in the real world in early Spring 2016 and is currently undergoing testing at a homeless shelter.

cs.AI↗

arXiv2016

The largest cycles consist by the quadratic residues and Fermat primes

This paper studies the largest cycles consisted by the quadratic residues modulo prime numbers. We give some formulae about the maximum length of the cycles. Especially, the formula for modulo Fermat primes is given.

math.NT↗

arXiv2015

Periodicity related to a sieve method of producing primes

In this paper we consider a slightly different sieve method from Eratosthenes' to get primes. We find the periodicity and mirror symmetry of the pattern.

math.NT↗

arXiv2015

Security Games with Information Leakage: Modeling and Computation

Most models of Stackelberg security games assume that the attacker only knows the defender's mixed strategy, but is not able to observe (even partially) the instantiated pure strategy. Such partial observation of the deployed pure strategy -- an issue we refer to as information leakage -- is a significant concern in practical applications. While previous research on patrolling games has considered the attacker's real-time surveillance, our settings, therefore models and techniques, are fundamentally different. More specifically, after describing the information leakage model, we start with an LP formulation to compute the defender's optimal strategy in the presence of leakage. Perhaps surprisingly, we show that a key subproblem to solve this LP (more precisely, the defender oracle) is NP-hard even for the simplest of security game models. We then approach the problem from three possible directions: efficient algorithms for restricted cases, approximation algorithms, and heuristic algorithms for sampling that improves upon the status quo. Our experiments confirm the necessity of handling information leakage and the advantage of our algorithms.

cs.GT↗

arXiv2014

Note on the Hölder norm estimate of the function $x\sin(1/x)$

In this paper, we prove the following inequality: for any $x, y>0$, there holds $$\big|x\sin\frac{1}{x} - y\sin\frac{1}{y} \big| \leq \sqrt{2|x - y|}.$$

math.CA↗

arXiv2014

The limit of the m-norms of a class of symmetric matrices and its applications

We consider a special symmetric matrix and obtain a similar formula as the one obtained by Weyl's criterion. Some applications of the formula are given, where we give a new way to calculate the integral of $\lnΓ(x)$ on $[0,1]$, and we claim that one class of matrices are not Hadamard matrices.

math.CA↗

arXiv2013

The connection between the Basel problem and a special integral

By using Fubini theorem or Tonelli theorem, we find that the zeta function value at 2 is equal to a special integral. Furthermore, We find that this special integral is two times of another special integral. By using this fact we obtain the relationship between Genocchi numbers and Bernoulli numbers. And get some results about Bernoulli polynomials.

math.NT↗