A Robust Class of Linear Recurrence Sequences

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers

Dissipative polynomials

Limited precision floating point computer implementations of large polynomial arithmetic expressions are nonlinear and dissipative. They are not reversible (irreversible, lack conservation), lose information, and so are robust to perturbations (anti-fragile) and resilient to fluctuations. This gives a largely stable locally flat evolutionary neutral fitness search landscape. Thus even with a large number of test cases, both large and small changes deep within software typically have no effect and are invisible externally. Shallow mutations are easier to detect but their RMS error need not be simple

Design and Evaluation of Approximate Logarithmic Multipliers for Low Power Error-Tolerant Applications

In this work, the designs of both non-iterative and iterative approximate logarithmic multipliers (LMs) are studied to further reduce power consumption and improve performance. Non-iterative approximate LMs (ALMs) that use three inexact mantissa adders, are presented. The proposed iterative approximate logarithmic multipliers (IALMs) use a set-one adder in both mantissa adders during an iteration; they also use lower-part-or adders and approximate mirror adders for the final addition. Error analysis and simulation results are also provided; it is found that the proposed approximate LMs with an appropriate number of inexact bits achieve a higher accuracy and lower power consumption than conventional LMs using exact units. Compared with conventional LMs with exact units, the normalized mean error distance (NMED) of 16-bit approximate LMs is decreased by up to 18% and the power-delay product (PDP) has a reduction of up to 37%. The proposed approximate LMs are also compared with previous approximate multipliers; it is found that the proposed approximate LMs are best suitable for applications allowing larger errors, but requiring lower energy consumption and low power. Approximate Booth multipliers fit applications with less stringent power requirements, but also requiring smaller errors. Case studies for error-tolerant computing applications are provided

Probabilistic hypergraph containers

Given a $k$-uniform hypergraph $\mathcal{H}$ and sufficiently large $m \gg m_0(\mathcal{H})$, we show that an $m$-element set $I \subseteq V(\mathcal{H})$, chosen uniformly at random, with probability $1 - e^{-\omega(m)}$ is either not independent or belongs to an almost-independent set in $\mathcal{H}$ which, crucially, can be constructed from carefully chosen $o(m)$ vertices of $I$. With very little effort, this implies that if the largest almost-independent set in $\mathcal{H}$ is of size $o(v(\mathcal{H}))$ then $I$ itself is an independent set with probability $e^{-\omega(m)}$. More generally, $I$ is very likely to inherit structural properties of almost-independent sets in $\mathcal{H}$. The value $m_0$ coincides with that for which Janson's inequality gives that $I$ is independent with probability at most $e^{-\Theta(m_0)}$. On the one hand, our result is a significant strengthening of Janson's inequality in the range $m \gg m_0$. On the other hand, it can be seen as a probabilistic variant of hypergraph container theorems, developed by Balogh, Morris and Samotij and, independently, by Saxton and Thomason. While being strictly weaker than the original container theorems in the sense that it does not apply to all independent sets of size $m$, it is nonetheless sufficient for many applications, admits a short proof using probabilistic ideas, and has weaker requirements on $m_0$.Comment: 11 pages. Comments are welcome

Recent tendencies in the use of optimization techniques in geotechnics:a review

The use of optimization methods in geotechnics dates back to the 1950s. They were used in slope stability analysis (Bishop) and evolved to a wide range of applications in ground engineering. We present here a non-exhaustive review of recent publications that relate to the use of different optimization techniques in geotechnical engineering. Metaheuristic methods are present in almost all the problems in geotechnics that deal with optimization. In a number of cases, they are used as single techniques, in others in combination with other approaches, and in a number of situations as hybrids. Different results are discussed showing the advantages and issues of the techniques used. Computational time is one of the issues, as well as the assumptions those methods are based on. The article can be read as an update regarding the recent tendencies in the use of optimization techniques in geotechnics