Space Laser Power Transmission System Studies

Power transmission by laser technique is addressed. Space to Earth and space to space configurations are considered

Principles of Antifragile Software

The goal of this paper is to study and define the concept of "antifragile software". For this, I start from Taleb's statement that antifragile systems love errors, and discuss whether traditional software dependability fits into this class. The answer is somewhat negative, although adaptive fault tolerance is antifragile: the system learns something when an error happens, and always imrpoves. Automatic runtime bug fixing is changing the code in response to errors, fault injection in production means injecting errors in business critical software. I claim that both correspond to antifragility. Finally, I hypothesize that antifragile development processes are better at producing antifragile software systems.Comment: see https://refuses.github.io

Quaternionic Root Systems and Subgroups of the Aut(F4)Aut(F_{4})

Cayley-Dickson doubling procedure is used to construct the root systems of some celebrated Lie algebras in terms of the integer elements of the division algebras of real numbers, complex numbers, quaternions and octonions. Starting with the roots and weights of SU(2) expressed as the real numbers one can construct the root systems of the Lie algebras of SO(4),SP(2)= SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the division algebras. The roots themselves display the group structures besides the octonionic roots of E_{8} which form a closed octonion algebra. The automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the largest crystallographic group in 4-dimensional Euclidean space, is realized as the direct product of two binary octahedral group of quaternions preserving the quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192 with different conjugacy classes occur as maximal subgroups in the finite subgroups of the Lie group $G_{2}$ of orders 12096 and 1344 and proves to be useful in their constructions. The triality of SO(8) manifesting itself as the cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and F_{4} respectively

Pattern Selection in the Complex Ginzburg-Landau Equation with Multi-Resonant Forcing

We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe or hexagon patterns are linearly stable, whereas square patterns and patterns involving more than three modes are unstable. In the case of hexagon patterns up- and down-hexagons can be simultaneously stable. The third-order, weakly nonlinear analysis predicts stable square patterns and super-hexagons for larger amplitudes. Direct simulations show, however, that in this regime the third-order weakly nonlinear analysis is insufficient, and these patterns are, in fact unstable

Entanglement Distillation Protocols and Number Theory

We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension $D$ benefits from applying basic concepts from number theory, since the set \zdn associated to Bell diagonal states is a module rather than a vector space. We find that a partition of \zdn into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analitically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension $D$. When $D$ is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.Comment: REVTEX4 file, 7 color figures, 2 table

Guidelines for testing and release procedures

Guidelines and procedures are recommended for the testing and release of the types of computer software efforts commonly performed at NASA/Ames Research Center. All recommendations are based on the premise that testing and release activities must be specifically selected for the environment, size, and purpose of each individual software project. Guidelines are presented for building a Test Plan and using formal Test Plan and Test Care Inspections on it. Frequent references are made to NASA/Ames Guidelines for Software Inspections. Guidelines are presented for selecting an Overall Test Approach and for each of the four main phases of testing: (1) Unit Testing of Components, (2) Integration Testing of Components, (3) System Integration Testing, and (4) Acceptance Testing. Tools used for testing are listed, including those available from operating systems used at Ames, specialized tools which can be developed, unit test drivers, stub module generators, and the use of format test reporting schemes