Akhet Khufu: Archaeo-astronomical Hints at a Common Project of the Two Main Pyramids of Giza, Egypt

The architectural complexes composed by the two main pyramids of Giza together with their temples are investigated from an interdisciplinary point of view, taking into account their astronomical alignments as well as their relationships with the visible landscape. Combining already known facts together with new clues, the work strongly supports the idea that the two complexes were conceived as parts of a common project.     

Two- and Three-Dimensional Constructions Based on Leonardo Grids

In 1989 I made a drawing of a net on a cube, consisting of 12 lines/elements. They were connected in a way that, a couple of months later, I recognised them in 899v in Leonardo’s Codex Atlanticus. I don’t know which moment impressed me the most: my own discovery of a very simple and powerful connecting system or the discovery of the Leonardo drawings, which implied that my own discovery was in fact a rediscovery. What we see in Leonardo’s drawings are some examples of roof constructions built with a lot of straight elements. These drawings can be ‘translated’ into the following definition: On each element we define four points at some distance of each other – two points somewhere in the middle and two points closer to the ends. To make constructions with these elements we need only connect a middle point of one element to an end point of another one in a regular over-under pattern. Out of the simple definition of the elements, I designed many different patterns for my so-called “+ - - +” structures: domes, spheres, cylinders and other models were made.     

Gaining insight through case-based explanation

Traditional explanation strategies in machine learning have been dominated by rule and decision tree based approaches. Case-based explanations represent an alternative approach which has inherent advantages in terms of transparency and user acceptability. Case-based explanations are based on a strategy of presenting similar past examples in support of and as justification for recommendations made. The traditional approach to such explanations, of simply supplying the nearest neighbour as an explanation, has been found to have shortcomings. Cases should be selected based on their utility in forming useful explanations. However, the relevance of the explanation case may not be clear to the end user as it is retrieved using domain knowledge which they themselves may not have. In this paper the focus is on a knowledge-light approach to case-based explanations that works by selecting cases based on explanation utility and offering insights into the effects of feature-value differences. In this paper we examine to two such a knowledge-light frameworks for case-based explanation. We look at explanation oriented retrieval (EOR) a strategy which explicitly models explanation utility and also at the knowledge-light explanation framework (KLEF) that uses local logistic regression to support case-based explanation.

Nexus VII: Relationships Between Architecture and Mathematics

Sylvie Duvernoy reports on the seventh international, interdisciplinary Nexus conference for architecture and mathematics. Point Loma Nazarene University, San Diego, USA 23-25 June 2008     

Development and application of the theory of parametric regulation of evolution of economic systems based on a neoclassical model of optimal growth

Presented were some results on roughness of the mathematical model of the neoclassical theory of optimal growth with and without parametric regulation, selection of the optimal law of parametric regulation, and the optimal law of parametric regulation vs. the uncontrollable parameters of this mathematical model based on the parametric regulation theory.     

Non-smooth guiding potentials in problems on forced oscillations

New classes of non-smooth guiding potentials are determined. The introduced concepts are used for solving the problem on periodic oscillations of controlled objects described by the system of differential equations and by the system of differential inclusions.     

Models of closed multimachine computer systems with transient-fault-tolerance and fault-tolerance on the basis of replication under byzantine faults

Consideration was given to the key definitions, notions, and models that may be useful for transient-fault-tolerant and fault-tolerant computing in the unmanned multimachine computer systems having many interconnected autonomous computers without shared memory and centralized control organ and operating with high degree of computational parallelism, that is, executing on different computers simultaneously various tasks which interchange their information. These computations should establish reliable results under byzantine faults and controllable degradation of the system at detection of faults.     

Approximate control optimization based on transformation of object model

It is considered an approach to approximate solving of control problems using different simplifying transformation of object model based on principles of extension or contraction of searching area and possible schemes of its realization. This approach focuses on getting, generally speaking, of a rough approximation to a global solution with two-sided estimation. Main attention focused on effective non-traditional schemes of continuous system velocity set transformation and discrete system transition set transformation. The obtained global approximate solutions can be considered as initial approximations in various iterative optimization procedures to be improved.     

On construction of measurement means on the basis of adaptation principle

An idea of the adaptive approach to the construction (design) of measuring systems is developed. An analysis is given of the features of technical adaptive systems and also the specific character of the means of measurements of both their subclass and the object of application of the adaptation principle. On the basis of the analysis, the concept is set up of the construction of these means, according to which the given principle is considered as an instrument of their perfection and its application is extended to all stages of their design from the choice of the principle (principles) of the action to the organization of the procedure of the output control (primary verification) in their series production. The effectiveness of the concept is illustrated by examples of the solution of the earlier unsolved problems and statement of new problems.     

Information protection based on nanosecond synchronization of time scales in meteor burst channel

The work is dedicated to metrological validation of meteor-based method of information protection—new technique for distant encryption key generation which might be capable of providing thorough security. The method is based on high-precision phase measurements of radio signal propagation time performed simultaneously in both forward and backward directions. These measurements are possible only if the communicants’ time scales are synchronized with nanosecond precision, which is shown to be possible by meteor time transfer. In order to account for short-term instability of quantum frequency standards, considering irregularity and variable precision of meteor measurements, we use optimal linear filtration and experimental measurement analogue, based on the results of meteor synchronization experiment conducted on the Mendeleevo(Moscow)-Kazan radio path. The possibility of using a meteor channel in two modes for remote time scale synchronization and encryption key generation is shown together with estimates for the capacity of this procedure.     

Parametric synthesis method of integral systems on the basis of root locus curves of Kharitonov polynomials

The method is developed for the synthesis of a stable set of characteristic polynomials of an interval dynamic system on the basis of the initial unstable set with the use of the system model in the form of a free root portrait. The synthesis is carried out by changing the boundaries (adjustment) of the interval of uncertainty of a free polynomial term, which enables affording the stability without a change of the configuration of the root portrait of the system. As a criterion of the adjustment, the distance is assigned that is measured along trajectories of the root portrait; in particular, a new polynomial can be defined by the nearest polynomial to the prescribed one with due regard for requirements of the quality of the system.     

Selection and Setting of an Intelligent Fuzzy Regulator based on Nonlinear Model Simulations of a Helicopter in Hover

Most research on fuzzy regulators has focused on the integrating rules in intelligent control systems. This paper evaluates a fuzzy helicopter regulator for a single-rotor PZL Kania helicopter. Unlike other models which only match stable flight ability, the model presented in this paper attempts to match the links between disturbances and hover conditions. Two simulations were performed to validate the model. In the first simulation, a helicopter was evaluated in a fixed hover position. In the second simulation, model robustness was validated by introducing wind gust. Results, both with the initial and with the modified model demonstrated the viability of the proposed regulator.

Studying the stability boundaries of the gyro-stabilized satellite on a circular orbit

Consideration was given to all parts of the stability boundaries of stationary motion of the gyro-stabilized manyaxis satellite. For each of the necessary stability conditions, conversion to zero or equality was analyzed using the second Lyapunov method. Terms of orders higher than two were used to check sign-definiteness of the Lyapunov function on the stability boundaries. Using the terms up to the sixth order, analysis established asymptotic stability on some parts of the boundaries. Terms of the order at most four enabled us to prove instability on other parts of the boundary.     

Joint detection and estimation of the Yule-Furry processes

An algorithm of joint detection of the Yule-Furry birth process and estimation of its start instant was designed. Results of the numerical studies were presented. Features of the solution of the problems of joint detection and estimation of this class were revealed.     

Some methods of automatic analysis and controllable transformation of programs

Principles and methods of the development of program systems are considered, which facilitate the analysis and transformation of the structure of programs. In the implementation of scale projects, it is impossible to have a complete concept of the structure of a program without the use of special systems. These systems contain the means of analysis of the initial program and, as a result of automatic transformation, produce another program displaying prescribed properties. As examples, the problems of fast automatic differentiation and the problems of obfuscation (“darkening,” intricacy) of programs are considered.     

Partial orders and Jordan normal form

Consideration is given to the relation between the structure of the acyclic binary relation and the adjacency matrix of its corresponding graph. In this case, the existing methods for studying the binary relations and their corresponding graphs in terms of the spectrum, that is, the set of eigenvalues, of the adjacency matrix are inapplicable because for the acyclic relations this matrix is nilpotent and its spectrum is identically zero. Therefore, a more refined characteristic of the matrix is required. The present paper considers the Jordan normal form (JNF) as such.