Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables

In this paper, a technique on constructing nonlinear resilient Boolean functions is described. By using several sets of disjoint spectra functions on a small number of variables, an almost optimal resilient function on a large even number of variables can be constructed. It is shown that given any $m$, one can construct infinitely many $n$-variable ($n$ even), $m$-resilient functions with nonlinearity $>2^{n-1}-2^{n/2}$. A large class of highly nonlinear resilient functions which were not known are obtained. Then one method to optimize the degree of the constructed functions is proposed. Last, an improved version of the main construction is given.Comment: 14 pages, 2 table

Resilience: Health in a New Key

This is the story of resilience, the remarkable capacity of individuals and communities to bounce back from adversity and even thrive in a world of turmoil and change. How we can begin to build on our strengths -- instead of becoming prisoners of our weaknesses -- is the subject of this issue brief

Dynamics and the Godbillon-Vey Class of C^1 Foliations

Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbolic resilient leaf. Our approach is based on methods of C^1-dynamical systems, and does not use the classification theory of C^2-foliations. We first prove that for a codimension--one C^1-foliation with non-trivial Godbillon measure, the set of infinitesimally expanding points E(F) has positive Lebesgue measure. We then prove that if E(F) has positive measure for a C^1-foliation F, then F must have a hyperbolic resilient leaf, and hence its geometric entropy must be positive. The proof of this uses a pseudogroup version of the Pliss Lemma. The theorem then follows, as a C^2-foliation with non-zero Godbillon-Vey class has non-trivial Godbillon measure. These results apply for both the case when M is compact, and when M is an open manifold.Comment: This manuscript is a revision of the section 3 material from the previous version, and includes edits to the pictures in the tex

Understanding Android Obfuscation Techniques: A Large-Scale Investigation in the Wild

In this paper, we seek to better understand Android obfuscation and depict a holistic view of the usage of obfuscation through a large-scale investigation in the wild. In particular, we focus on four popular obfuscation approaches: identifier renaming, string encryption, Java reflection, and packing. To obtain the meaningful statistical results, we designed efficient and lightweight detection models for each obfuscation technique and applied them to our massive APK datasets (collected from Google Play, multiple third-party markets, and malware databases). We have learned several interesting facts from the result. For example, malware authors use string encryption more frequently, and more apps on third-party markets than Google Play are packed. We are also interested in the explanation of each finding. Therefore we carry out in-depth code analysis on some Android apps after sampling. We believe our study will help developers select the most suitable obfuscation approach, and in the meantime help researchers improve code analysis systems in the right direction

Resilience trinity: safeguarding ecosystem functioning and services across three different time horizons and decision contexts

Ensuring ecosystem resilience is an intuitive approach to safeguard the functioning of ecosystems and hence the future provisioning of ecosystem services (ES). However, resilience is a multi‐faceted concept that is difficult to operationalize. Focusing on resilience mechanisms, such as diversity, network architectures or adaptive capacity, has recently been suggested as means to operationalize resilience. Still, the focus on mechanisms is not specific enough. We suggest a conceptual framework, resilience trinity, to facilitate management based on resilience mechanisms in three distinctive decision contexts and time‐horizons: 1) reactive, when there is an imminent threat to ES resilience and a high pressure to act, 2) adjustive, when the threat is known in general but there is still time to adapt management and 3) provident, when time horizons are very long and the nature of the threats is uncertain, leading to a low willingness to act. Resilience has different interpretations and implications at these different time horizons, which also prevail in different disciplines. Social ecology, ecology and engineering are often implicitly focussing on provident, adjustive or reactive resilience, respectively, but these different notions of resilience and their corresponding social, ecological and economic tradeoffs need to be reconciled. Otherwise, we keep risking unintended consequences of reactive actions, or shying away from provident action because of uncertainties that cannot be reduced. The suggested trinity of time horizons and their decision contexts could help ensuring that longer‐term management actions are not missed while urgent threats to ES are given priority