Radiation Risks and Mitigation in Electronic Systems

Electrical and electronic systems can be disturbed by radiation-induced effects. In some cases, radiation-induced effects are of a low probability and can be ignored; however, radiation effects must be considered when designing systems that have a high mean time to failure requirement, an impact on protection, and/or higher exposure to radiation. High-energy physics power systems suffer from a combination of these effects: a high mean time to failure is required, failure can impact on protection, and the proximity of systems to accelerators increases the likelihood of radiation-induced events. This paper presents the principal radiation-induced effects, and radiation environments typical to high-energy physics. It outlines a procedure for designing and validating radiation-tolerant systems using commercial off-the-shelf components. The paper ends with a worked example of radiation-tolerant power converter controls that are being developed for the Large Hadron Collider and High Luminosity-Large Hadron Collider at CERN.Comment: 19 pages, contribution to the 2014 CAS - CERN Accelerator School: Power Converters, Baden, Switzerland, 7-14 May 201

Approximating Approximate Pattern Matching

Given a text T of length n and a pattern P of length m, the approximate pattern matching problem asks for computation of a particular distance function between P and every m-substring of T. We consider a (1 +/- epsilon) multiplicative approximation variant of this problem, for l_p distance function. In this paper, we describe two (1+epsilon)-approximate algorithms with a runtime of O~(n/epsilon) for all (constant) non-negative values of p. For constant p >= 1 we show a deterministic (1+epsilon)-approximation algorithm. Previously, such run time was known only for the case of l_1 distance, by Gawrychowski and Uznanski [ICALP 2018] and only with a randomized algorithm. For constant 0 <= p <= 1 we show a randomized algorithm for the l_p, thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS 2015, SOSA 2018] for Hamming distance (case of p=0) and of Gawrychowski and Uznanski for l_1 distance

Improved Analysis of Deterministic Load-Balancing Schemes

We consider the problem of deterministic load balancing of tokens in the discrete model. A set of $n$ processors is connected into a $d$-regular undirected network. In every time step, each processor exchanges some of its tokens with each of its neighbors in the network. The goal is to minimize the discrepancy between the number of tokens on the most-loaded and the least-loaded processor as quickly as possible. Rabani et al. (1998) present a general technique for the analysis of a wide class of discrete load balancing algorithms. Their approach is to characterize the deviation between the actual loads of a discrete balancing algorithm with the distribution generated by a related Markov chain. The Markov chain can also be regarded as the underlying model of a continuous diffusion algorithm. Rabani et al. showed that after time $T = O(\log (Kn)/\mu)$, any algorithm of their class achieves a discrepancy of $O(d\log n/\mu)$, where $\mu$ is the spectral gap of the transition matrix of the graph, and $K$ is the initial load discrepancy in the system. In this work we identify some natural additional conditions on deterministic balancing algorithms, resulting in a class of algorithms reaching a smaller discrepancy. This class contains well-known algorithms, eg., the Rotor-Router. Specifically, we introduce the notion of cumulatively fair load-balancing algorithms where in any interval of consecutive time steps, the total number of tokens sent out over an edge by a node is the same (up to constants) for all adjacent edges. We prove that algorithms which are cumulatively fair and where every node retains a sufficient part of its load in each step, achieve a discrepancy of $O(\min\{d\sqrt{\log n/\mu},d\sqrt{n}\})$ in time $O(T)$. We also show that in general neither of these assumptions may be omitted without increasing discrepancy. We then show by a combinatorial potential reduction argument that any cumulatively fair scheme satisfying some additional assumptions achieves a discrepancy of $O(d)$ almost as quickly as the continuous diffusion process. This positive result applies to some of the simplest and most natural discrete load balancing schemes.Comment: minor corrections; updated literature overvie

Brief Announcement: Hamming Distance Completeness and Sparse Matrix Multiplication

We show that a broad class of (+, diamond) vector products (for binary integer functions diamond) are equivalent under one-to-polylog reductions to the computation of the Hamming distance. Examples include: the dominance product, the threshold product and l_{2p+1} distances for constant p. Our results imply equivalence (up to poly log n factors) between complexity of computation of All Pairs: Hamming Distances, l_{2p+1} Distances, Dominance Products and Threshold Products. As a consequence, Yuster\u27s (SODA\u2709) algorithm improves not only Matousek\u27s (IPL\u2791), but also the results of Indyk, Lewenstein, Lipsky and Porat (ICALP\u2704) and Min, Kao and Zhu (COCOON\u2709). Furthermore, our reductions apply to the pattern matching setting, showing equivalence (up to poly log n factors) between pattern matching under Hamming Distance, l_{2p+1} Distance, Dominance Product and Threshold Product, with current best upperbounds due to results of Abrahamson (SICOMP\u2787), Amir and Farach (Ann. Math. Artif. Intell.\u2791), Atallah and Duket (IPL\u2711), Clifford, Clifford and Iliopoulous (CPM\u2705) and Amir, Lipsky, Porat and Umanski (CPM\u2705). The resulting algorithms for l_{2p+1} Pattern Matching and All Pairs l_{2p+1}, for 2p+1 = 3,5,7,... are new. Additionally, we show that the complexity of AllPairsHammingDistances (and thus of other aforementioned AllPairs- problems) is within poly log n from the time it takes to multiply matrices n x (n * d) and (n * d) x n, each with (n * d) non-zero entries. This means that the current upperbounds by Yuster (SODA\u2709) cannot be improved without improving the sparse matrix multiplication algorithm by Yuster and Zwick (ACM TALG\u2705) and vice versa

Brief Announcement: Energy Constrained Depth First Search

Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this is asymptotically optimal over all exploration strategies. This paper considers a variant of such search strategies where the length of each route is bounded by a positive integer B (e.g. due to limited energy resources of the searcher). The objective is to cover all the edges of a tree T using the minimum number of routes, each starting and ending at the root and each being of length at most B. To this end, we analyze the following natural greedy tree traversal process that is based on decomposing a depth first search traversal into a sequence of limited length routes. Given any arbitrary depth first search traversal R of the tree T, we cover R with routes R_1,...,R_l, each of length at most B such that: R_i starts at the root, reaches directly the farthest point of R visited by R_{i-1}, then R_i continues along the path R as far as possible, and finally R_i returns to the root. We call the above algorithm piecemeal-DFS and we prove that it achieves the asymptotically minimal number of routes l, regardless of the choice of R. Our analysis also shows that the total length of the traversal (and thus the traversal time) of piecemeal-DFS is asymptotically minimum over all energy-constrained exploration strategies. The fact that R can be chosen arbitrarily means that the exploration strategy can be constructed in an online fashion when the input tree T is not known in advance. Each route R_i can be constructed without any knowledge of the yet unvisited part of T. Surprisingly, our results show that depth first search is efficient for energy constrained exploration of trees, even though it is known that the same does not hold for energy constrained exploration of arbitrary graphs

A Framework for Searching in Graphs in the Presence of Errors

We consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability p<1/2 and a correct one with probability 1-p). We study this problem both with adversarial errors and independent noise models. First, we show an algorithm that needs at most (log_2 n)/(1 - H(r)) queries in case of adversarial errors, where the adversary is bounded with its rate of errors by a known constant r<1/2. Our algorithm is in fact a simplification of previous work, and our refinement lies in invoking an amortization argument. We then show that our algorithm coupled with a Chernoff bound argument leads to a simpler algorithm for the independent noise model and has a query complexity that is both simpler and asymptotically better than the one of Emamjomeh-Zadeh et al. [STOC 2016]. Our approach has a wide range of applications. First, it improves and simplifies the Robust Interactive Learning framework proposed by Emamjomeh-Zadeh and Kempe [NIPS 2017]. Secondly, performing analogous analysis for edge-queries (where a query to an edge e returns its endpoint that is closer to the target) we actually recover (as a special case) a noisy binary search algorithm that is asymptotically optimal, matching the complexity of Feige et al. [SIAM J. Comput. 1994]. Thirdly, we improve and simplify upon an algorithm for searching of unbounded domains due to Aslam and Dhagat [STOC 1991]

RLE Edit Distance in Near Optimal Time

We show that the edit distance between two run-length encoded strings of compressed lengths m and n respectively, can be computed in O(mn log(mn)) time. This improves the previous record by a factor of O(n/log(mn)). The running time of our algorithm is within subpolynomial factors of being optimal, subject to the standard SETH-hardness assumption. This effectively closes a line of algorithmic research first started in 1993

Tight Tradeoffs for Real-Time Approximation of Longest Palindromes in Streams

We consider computing a longest palindrome in the streaming model, where the symbols arrive one-by-one and we do not have random access to the input. While computing the answer exactly using sublinear space is not possible in such a setting, one can still hope for a good approximation guarantee. Our contribution is twofold. First, we provide lower bounds on the space requirements for randomized approximation algorithms processing inputs of length n. We rule out Las Vegas algorithms, as they cannot achieve sublinear space complexity. For Monte Carlo algorithms, we prove a lower bounds of Omega(M log min {|Sigma|, M}) bits of memory; here M=n/E for approximating the answer with additive error E, and M= log n / log (1 + epsilon) for approximating the answer with multiplicative error (1 + epsilon). Second, we design three real-time algorithms for this problem. Our Monte Carlo approximation algorithms for both additive and multiplicative versions of the problem use O(M) words of memory. Thus the obtained lower bounds are asymptotically tight up to a logarithmic factor. The third algorithm is deterministic and finds a longest palindrome exactly if it is short. This algorithm can be run in parallel with a Monte Carlo algorithm to obtain better results in practice. Overall, both the time and space complexity of finding a longest palindrome in a stream are essentially settled

Ergodic Effects in Token Circulation

International audienceWe consider a dynamical process in a network which distributes all particles (tokens) located at a node among its neighbors, in a round-robin manner.We show that in the recurrent state of this dynamics (i.e., disregarding a polynomially long initialization phase of the system), the number of particles located on a given edge, averaged over an interval of time, is tightly concentrated around the average particle density in the system. Formally, for a system of $k$ particles in a graph of $m$ edges, during any interval of length $T$, this time-averaged value is $k/m \pm \widetilde O(1/T)$, whenever $gcd(m,k) = \widetilde O(1)$ (and so, e.g., whenever $m$ is a prime number). To achieve these bounds, we link the behavior of the studied dynamics to ergodic properties of traversals based on Eulerian circuits on a symmetric directed graph. These results are proved through sum set methods and are likely to be of independent interest.As a corollary, we also obtain bounds on the \emph{idleness} of the studied dynamics, i.e., on the longest possible time between two consecutive appearances of a token on an edge, taken over all edges. Designing trajectories for $k$ tokens in a way which minimizes idleness is fundamental to the study of the patrolling problem in networks. Our results immediately imply a bound of $\widetilde O(m/k)$ on the idleness of the studied process, showing that it is a distributed $\widetilde O(1)$-competitive solution to the patrolling task, for all of the covered cases. Our work also provides some further insights that may be interesting in load-balancing applications

Designer molecular probes for phosphonium ionic liquids

Investigations into the extent of structuring present in phosphonium based ionic liquids (ILs) have been carried out using photochromic molecular probes. Three spiropyran derivatives containing hydroxyl (BSP-1), carboxylic acid (BSP-2) and aliphatic chain (C14H29) (BSP-3) functional groups have been analysed in a range of phosphonium based ionic liquids and their subsequent physico-chemical interactions were reported. It is believed that the functional groups locate the probe molecules into specific regions based upon the interaction of the functional groups with particular and defined regions of the ionic liquid. This structuring results in thermodynamic, kinetic and solvatochromic parameters that are not predictable from classical solvent models. BSP-1 and BSP-2 exhibit generally negative entropies of activation ranging from -50 J K-1 mol-1 to -90 J K-1 mol-1 implying relatively low solvent–solute interactions and possible anion interactions with IL polar functional groups. Higher than expected activation energies of 60 kJ mol-1 to 100 kJ mol-1 obtained for polar probes maybe be due to IL functional groups competing with the charged sites of the merocyanine (MC) isomer thus reducing MC stabilisation effects. Differences in thermal relaxation rate constants (2.5 × 10-3 s-1 in BSP-1 and 3 × 10-4 s-1 in BSP-2 in [P6,6,6,14][dbsa]) imply that while the polar probe systems are primarily located in polar/charged regions, each probe experiences slightly differing polar domains. BSP-3 entropies of activation are positive and between 30 J K-1 mol-1 to 66 J K-1 mol-1. The association of the non-polar functional group is believed to locate the spiropyran moiety in the interfacial polar and non-polar regions. The thermal relaxation of the MC form causes solvent reorientation to accommodate the molecule as it reverts to its closed form. Slow thermal relaxation rate constants were obserevd in contrast to high activation energies (5 × 10-4 s-1 and 111.91 kJ mol-1 respectively, for BSP-3 in [P6,6,6,14][dbsa]). This may be due to steric effects arising from proposed nano-cavity formation by the alkyl chains in phosphonium based ILs