3,403 research outputs found
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 .
We then specialise to planar monomial functions and present
constructions and partial results towards their classification. In particular,
we show that is the only odd exponent for which is planar
(for some nonzero ) 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 that induce planar functions on
infinitely many extensions of ; 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 -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
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