Planar functions over fields of characteristic two

Classical planar functions are functions from a finite field to itself and give rise to finite projective planes. They exist however only for fields of odd characteristic. We study their natural counterparts in characteristic two, which we also call planar functions. They again give rise to finite projective planes, as recently shown by the second author. We give a characterisation of planar functions in characteristic two in terms of codes over $\mathbb{Z}_4$. We then specialise to planar monomial functions $f(x)=cx^t$ and present constructions and partial results towards their classification. In particular, we show that $t=1$ is the only odd exponent for which $f(x)=cx^t$ is planar (for some nonzero $c$) over infinitely many fields. The proof techniques involve methods from algebraic geometry.Comment: 23 pages, minor corrections and simplifications compared to the first versio

Exceptional planar polynomials

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field $K$ that induce planar functions on infinitely many extensions of $K$; we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial classification of exceptional planar polynomials. This includes results for the classical planar functions on finite fields of odd characteristic and for the recently proposed planar functions on finite fields of characteristic two

Semifields, relative difference sets, and bent functions

Recently, the interest in semifields has increased due to the discovery of several new families and progress in the classification problem. Commutative semifields play an important role since they are equivalent to certain planar functions (in the case of odd characteristic) and to modified planar functions in even characteristic. Similarly, commutative semifields are equivalent to relative difference sets. The goal of this survey is to describe the connection between these concepts. Moreover, we shall discuss power mappings that are planar and consider component functions of planar mappings, which may be also viewed as projections of relative difference sets. It turns out that the component functions in the even characteristic case are related to negabent functions as well as to $\mathbb{Z}_4$-valued bent functions.Comment: Survey paper for the RICAM workshop "Emerging applications of finite fields", 09-13 December 2013, Linz, Austria. This article will appear in the proceedings volume for this workshop, published as part of the "Radon Series on Computational and Applied Mathematics" by DeGruyte

End-to-end Learning for Short Text Expansion

Effectively making sense of short texts is a critical task for many real world applications such as search engines, social media services, and recommender systems. The task is particularly challenging as a short text contains very sparse information, often too sparse for a machine learning algorithm to pick up useful signals. A common practice for analyzing short text is to first expand it with external information, which is usually harvested from a large collection of longer texts. In literature, short text expansion has been done with all kinds of heuristics. We propose an end-to-end solution that automatically learns how to expand short text to optimize a given learning task. A novel deep memory network is proposed to automatically find relevant information from a collection of longer documents and reformulate the short text through a gating mechanism. Using short text classification as a demonstrating task, we show that the deep memory network significantly outperforms classical text expansion methods with comprehensive experiments on real world data sets.Comment: KDD'201

Examining the Relationships Among Mindfulness, Disability, Social Support, and Stress in Emerging Adults

College students, as part of the broader population of emerging adults, are thought to be particularly vulnerable to stress compared to other age groups as they transition through adolescence into adulthood. Various internal and external factors including mindfulness, disability, and social support play an important role in students’ stress levels. The relationships among these three predictor variables and stress were analyzed in a sample of 1,049 individuals between the ages of 18-29. Responses were obtained from the dataset “Emerging Adulthood Measured at Multiple Institutions 2: The Data” (Grahe et al., 2018). The data were cleaned in Python and analyzed in SPSS using multiple regression analyses. Higher perceived levels of mindfulness and social support were significant predictors of less stress in students, while a higher perceived level of disability was a significant predictor of more stress. The combined regression model showed that mindfulness, disability, and social support accounted for a significant amount of the variance in distress. Determinants of stress are multifactorial; identification and evaluation of variables that account for a significant amount of the variance in stress within a vulnerable population can contribute to the development of effective stress management techniques

The Progress, Challenges, and Perspectives of Directed Greybox Fuzzing

Most greybox fuzzing tools are coverage-guided as code coverage is strongly correlated with bug coverage. However, since most covered codes may not contain bugs, blindly extending code coverage is less efficient, especially for corner cases. Unlike coverage-guided greybox fuzzers who extend code coverage in an undirected manner, a directed greybox fuzzer spends most of its time allocation on reaching specific targets (e.g., the bug-prone zone) without wasting resources stressing unrelated parts. Thus, directed greybox fuzzing (DGF) is particularly suitable for scenarios such as patch testing, bug reproduction, and specialist bug hunting. This paper studies DGF from a broader view, which takes into account not only the location-directed type that targets specific code parts, but also the behaviour-directed type that aims to expose abnormal program behaviours. Herein, the first in-depth study of DGF is made based on the investigation of 32 state-of-the-art fuzzers (78% were published after 2019) that are closely related to DGF. A thorough assessment of the collected tools is conducted so as to systemise recent progress in this field. Finally, it summarises the challenges and provides perspectives for future research.Comment: 16 pages, 4 figure

Optical-Amplifier-Compatible Long-Distance Secure Key Generation Based on Random Phase Fluctuations for WDM Systems

We proposed and experimentally demonstrated a secure key generation and distribution system that is compatible with optical amplifiers and standard wavelength-division multiplexing (WDM) transmission systems. The key is generated from the phase fluctuations induced by environmental instabilities. The key generation system is tested in a 240 km bidirectional fiber-pair link with multiple optical amplifiers. To demonstrate the compatibility with WDM systems, 38 WDM channels are transmitted together with the key distribution channel. The secret key is protected against eavesdropping and coherence detection attack by the wide-band property of the signal carrier and the fast-changing rate of the phase fluctuations