Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.

Development of Riparian and Groundwater-Dependent Ecosystem Assessments for National Forests in the Western U.S.

In 2012, the U.S. Department of Agriculture adopted a new planning rule that outlined a process for developing, amending, and revising land management plans for the 155 National Forests, 20 National Grasslands, and one Tallgrass Prairie managed by the U.S. Forest Service. The rule outlines a framework with three phases: assessment, development/amendment/revision, and monitoring. We are assisting National Forests in the western U.S. with the first phase by completing a series of assessments of riparian and groundwater-dependent ecosystems. Here, we describe our methods and the lessons learned over the course of conducting assessments for seven National Forests. Per the requirements of the planning rule, we conduct a rapid assessment of ecological integrity that uses existing data to evaluate drivers, stressors, structure, function, composition, and connectivity. We have collaborated with National Forests, state agencies, and other research groups to obtain datasets representing various wetland landscape features. Our work supports the plan revision process, from assessment through plan approval, and informs future forest and project planning for the restoration and maintenance of structure, function, composition, and connectivity. We developed our assessment methods in collaboration with resource managers at the National Forest and regional level to ensure useful end products such as published technical reports, literature reviews, photo libraries, or collections of datasets related to riparian and groundwater-dependent ecosystems. Our approach and lessons learned throughout the process are relevant to other resource management planning applications, analyses of landscape condition, as well as assessments of other ecosystems, such as forests or grasslands.

Efficient Outside Computation

Weighted deduction systems provide a framework for describing parsing algorithms that can be used with a variety of operations for combining the values of partial derivations. For some operations, inside values can be computed efficiently, but outside values cannot. We view outside values as functions from inside values to the total value of all derivations, and we analyze outside computation in terms of function composition. This viewpoint helps explain why efficient outside computation is possible in many settings, despite the lack of a general outside algorithm for semiring operations.

The Stoic Theory of Beauty

The monograph aims to show that the Stoa, an ancient Greek philosophical school, made a substantial line of enquiry into the nature of aesthetic properties, and thus there are good reasons to analyse and discuss the sub-field of the Stoic thought that could be called ‘Stoic aesthetics.’ This study of Stoic views on beauty begins with the question of indifferents and the challenge it poses for aesthetics. The controversial Stoic theory of values states that ‘beauty’ is one of the so-called indifferents, that is, the things that do not contribute to human happiness and therefore ought not to be treated as the good. It is argued that a thorough reading of the material shows that beauty is not treated as irrelevant in general; the evidence only shows that beauty is an inferior value to virtue. This leaves the possibility of theorising aesthetic objects. This leads to a systematic interpretation of Stoic aesthetics by looking at other pieces of extant evidence where beauty is mentioned, including the argument ‘that only the beautiful is the good’, theological arguments, the claim that only the wise man is beautiful and the Stoic definition of beauty as summetria. The latter, it is argued, is a succinct formulation of the idea that beauty is a function composition, and this idea has emerged in the previous discussions of various arguments involving aesthetic terms. The monograph ends with a discussion of the Stoic views in ancient Greek philosophical context.

Pseudo-BCI algebras with derivations

In this paper we define two types of implicative derivations on pseudo-BCI algebras, we investigate their properties and we give a characterization of regular implicative derivations of type II. We also define the notion of a $d$-invariant deductive system of a pseudo-BCI algebra $A$ proving that $d$ is a regular derivation of type II if and only if every deductive system on $A$ is $d$-invariant. It is proved that a pseudo-BCI algebra is $p$-semisimple if and only if the only regular derivation of type II is the identity map. Another main result consists of proving that the set of all implicative derivations of a $p$-semisimple pseudo-BCI algebra forms a commutative monoid with respect to function composition. Two types of symmetric derivations on pseudo-BCI algebras are also introduced and it is proved that in the case of $p$-semisimple pseudo-BCI algebras the sets of type II implicative derivations and type II symmetric derivations are equal.