Towards a statement of the S-adic conjecture through examples

The $S$-adic conjecture claims that there exists a condition $C$ such that a sequence has a sub-linear complexity if and only if it is an $S$-adic sequence satisfying Condition $C$ for some finite set $S$ of morphisms. We present an overview of the factor complexity of $S$-adic sequences and we give some examples that either illustrate some interesting properties or that are counter-examples to what could be believed to be "a good Condition $C$".Comment: 2

A new Parallel Algorithm for the Parentheses-Matching Problem

1 The parentheses-matching problem is of crucial importance in the construction of expression tree in order to evaluate, for instance, arithmetic expressions. A new parallel algorithm is introduced in this paper to solve the parenthesesmatching problem optimally (in O(log 2 n) parallel time with O(n= log 2 n) processors) on an EREW-PRAM model. An algorithm for an input string of n parentheses with a maximal nested level of log n is also presented. Keywords: parallel algorithms on PRAM (Parallel Random Access Machine) model, parentheses-matching problem. 1 Introduction The parentheses-matching problem, initially tackled in [1], is used to determine the mate of each parenthesis in a balanced string of n (opening or closing) parentheses. The parentheses are matched with a sequential algorithm in O(n) time complexity using a stack by scanning the string once. One can view the parentheses-matching problem as a subproblem of parsing, recognition (over a 2 letters alphabet) of formal lang..

Self-Stabilizing Depth-First Token Circulation In Arbitrary Rooted Networks

We present a deterministic distributed depth-first token passing protocol on a rooted network. This protocol uses neither the processor identifiers nor the size of the network, but assumes the existence of a distinguises hed processor, called the root of the network. The protocol is self-stabilizing, meaning that starting from an arbitrary state (in response to an arbitrary perturbation modifying the memory state), it is guaranteed to reach a state with no more than one token in the network. Our protocol implements a fair token circulation scheme, i.e., in every round, every processor obtains the token at least once. The proposed protocol has extremely small state requirement---only 3(\Delta +1) states per processor, i.e., O(log\Delta) bits per processor, where \Delta is the degree of the network. The protocol can be used to implement a fair distributed mutual exclusion in any rooted network. This protocol can also be used to construct a DFS spanning tree

Impact of methodological choices in comparative effectiveness studies: application in natalizumab versus fingolimod comparison among patients with multiple sclerosis

Abstract Background Natalizumab and fingolimod are used as high-efficacy treatments in relapsing–remitting multiple sclerosis. Several observational studies comparing these two drugs have shown variable results, using different methods to control treatment indication bias and manage censoring. The objective of this empirical study was to elucidate the impact of methods of causal inference on the results of comparative effectiveness studies. Methods Data from three observational multiple sclerosis registries (MSBase, the Danish MS Registry and French OFSEP registry) were combined. Four clinical outcomes were studied. Propensity scores were used to match or weigh the compared groups, allowing for estimating average treatment effect for treated or average treatment effect for the entire population. Analyses were conducted both in intention-to-treat and per-protocol frameworks. The impact of the positivity assumption was also assessed. Results Overall, 5,148 relapsing–remitting multiple sclerosis patients were included. In this well-powered sample, the 95% confidence intervals of the estimates overlapped widely. Propensity scores weighting and propensity scores matching procedures led to consistent results. Some differences were observed between average treatment effect for the entire population and average treatment effect for treated estimates. Intention-to-treat analyses were more conservative than per-protocol analyses. The most pronounced irregularities in outcomes and propensity scores were introduced by violation of the positivity assumption. Conclusions This applied study elucidates the influence of methodological decisions on the results of comparative effectiveness studies of treatments for multiple sclerosis. According to our results, there are no material differences between conclusions obtained with propensity scores matching or propensity scores weighting given that a study is sufficiently powered, models are correctly specified and positivity assumption is fulfilled

Impact of methodological choices in comparative effectiveness studies: application in natalizumab versus fingolimod comparison among patients with multiple sclerosis

Abstract Background Natalizumab and fingolimod are used as high-efficacy treatments in relapsing–remitting multiple sclerosis. Several observational studies comparing these two drugs have shown variable results, using different methods to control treatment indication bias and manage censoring. The objective of this empirical study was to elucidate the impact of methods of causal inference on the results of comparative effectiveness studies. Methods Data from three observational multiple sclerosis registries (MSBase, the Danish MS Registry and French OFSEP registry) were combined. Four clinical outcomes were studied. Propensity scores were used to match or weigh the compared groups, allowing for estimating average treatment effect for treated or average treatment effect for the entire population. Analyses were conducted both in intention-to-treat and per-protocol frameworks. The impact of the positivity assumption was also assessed. Results Overall, 5,148 relapsing–remitting multiple sclerosis patients were included. In this well-powered sample, the 95% confidence intervals of the estimates overlapped widely. Propensity scores weighting and propensity scores matching procedures led to consistent results. Some differences were observed between average treatment effect for the entire population and average treatment effect for treated estimates. Intention-to-treat analyses were more conservative than per-protocol analyses. The most pronounced irregularities in outcomes and propensity scores were introduced by violation of the positivity assumption. Conclusions This applied study elucidates the influence of methodological decisions on the results of comparative effectiveness studies of treatments for multiple sclerosis. According to our results, there are no material differences between conclusions obtained with propensity scores matching or propensity scores weighting given that a study is sufficiently powered, models are correctly specified and positivity assumption is fulfilled