Reply to K. Amos et al. (nucl-th/0401055)

An expression for the spin-orbit interaction coupling between different levels, which was shown to be aberrant more than thirty years ago persists in the literature without clear indication of what is used. It leads to expressions quite simpler than they should be. After an attempt to warn the community of the nuclear physicists on this strange situation (nucl-th/0312038), the authors of the publication in which the "aberrant" interaction is described and used, try to justify their work (nucl-th/0401055), by a very strange "symmetrization" of something already symmetric. They claim also that their method allows to solve some problem related to the Pauli principle and give some references, among which a book which reports the solution of such problem almost forty years ago, with a very small effect. An examination of their own results shows that their optimism is not completely justified. Nevertheless, any user of ECIS, sensitive to their arguments, is requested to ask their opinion to these five coauthors before publishing.Comment: latex arXiv.tex, 1 file, 8 page

Two-Bit Messages are Sufficient to Implement Atomic Read/Write Registers in Crash-prone Systems

Atomic registers are certainly the most basic objects of computing science. Their implementation on top of an n-process asynchronous message-passing system has received a lot of attention. It has been shown that t \textless{} n/2 (where t is the maximal number of processes that may crash) is a necessary and sufficient requirement to build an atomic register on top of a crash-prone asynchronous message-passing system. Considering such a context, this paper presents an algorithm which implements a single-writer multi-reader atomic register with four message types only, and where no message needs to carry control information in addition to its type. Hence, two bits are sufficient to capture all the control information carried by all the implementation messages. Moreover, the messages of two types need to carry a data value while the messages of the two other types carry no value at all. As far as we know, this algorithm is the first with such an optimality property on the size of control information carried by messages. It is also particularly efficient from a time complexity point of view

The distribution of "time of flight" in three dimensional stationary chaotic advection

The distributions of "time of flight" (time spent by a single fluid particle between two crossings of the Poincar\'e section) are investigated for five different 3D stationary chaotic mixers. Above all, we study the large tails of those distributions, and show that mainly two types of behaviors are encountered. In the case of slipping walls, as expected, we obtain an exponential decay, which, however, does not scale with the Lyapunov exponent. Using a simple model, we suggest that this decay is related to the negative eigenvalues of the fixed points of the flow. When no-slip walls are considered, as predicted by the model, the behavior is radically dfferent, with a very large tail following a power law with an exponent close to -3

Byzantine-Tolerant Set-Constrained Delivery Broadcast

Set-Constrained Delivery Broadcast (SCD-broadcast), recently introduced at ICDCN 2018, is a high-level communication abstraction that captures ordering properties not between individual messages but between sets of messages. More precisely, it allows processes to broadcast messages and deliver sets of messages, under the constraint that if a process delivers a set containing a message m before a set containing a message m\u27, then no other process delivers first a set containing m\u27 and later a set containing m. It has been shown that SCD-broadcast and read/write registers are computationally equivalent, and an algorithm implementing SCD-broadcast is known in the context of asynchronous message passing systems prone to crash failures. This paper introduces a Byzantine-tolerant SCD-broadcast algorithm, which we call BSCD-broadcast. Our proposed algorithm assumes an underlying basic Byzantine-tolerant reliable broadcast abstraction. We first introduce an intermediary communication primitive, Byzantine FIFO broadcast (BFIFO-broadcast), which we then use as a primitive in our final BSCD-broadcast algorithm. Unlike the original SCD-broadcast algorithm that is tolerant to up to t<n/2 crashing processes, and unlike the underlying Byzantine reliable broadcast primitive that is tolerant to up to t<n/3 Byzantine processes, our BSCD-broadcast algorithm is tolerant to up to t<n/4 Byzantine processes. As an illustration of the high abstraction power provided by the BSCD-broadcast primitive, we show that it can be used to implement a Byzantine-tolerant read/write snapshot object in an extremely simple way

Strong existence and uniqueness for stochastic differential equation with H{\"o}lder drift and degenerate noise

In this paper, we prove pathwise uniqueness for stochastic degenerate systems with a H{\"o}lder drift, for a H{\"o}lder exponent larger than the critical value 2/3. This work extends to the degenerate setting the earlier results obtained by Zvonkin, Veretennikov, Krylov and R{\"o}ckner from non-degenerate to degenerate cases. The existence of a threshold for the H{\"o}lder exponent in the degenerate case may be understood as the price to pay to balance the degeneracy of the noise. Our proof relies on regularization properties of the associated PDE, which is degenerate in the current framework and is based on a parametrix method