A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Rewriting Systems for Reachability in Vector Addition Systems with Pairs

15 pagesInternational audienceWe adapt hypergraph rewriting system to a generalization of Vector Addition Systems with States (VASS) that we call vector addition systems with pairs (VASP). We give rewriting systems and strategies, that allow us to obtain reachability equivalence results between some classes of VASP and VASS. Reachability for the later is well known be equivalent to reachability in Petri nets. VASP generalize also Branching Extension of VASS (BVASS) for which it is unknown if they are more expressive than VASS. We consider here a more restricted notion of reachability for VASP than that for BVASS. However the reachability decision problem corresponding is already equivalent to decidability of the provability in Multiplicative and Exponential Linear Logic (MELL), a question left open for more than 20 years

Cardiovascular risk estimation and eligibility for statins in primary prevention comparing different strategies.

Recommendations for statin use for primary prevention of coronary heart disease (CHD) are based on estimation of the 10-year CHD risk. It is unclear which risk algorithm and guidelines should be used in European populations. Using data from a population-based study in Switzerland, we first assessed 10-year CHD risk and eligibility for statins in 5,683 women and men 35 to 75 years of age without cardiovascular disease by comparing recommendations by the European Society of Cardiology without and with extrapolation of risk to age 60 years, the International Atherosclerosis Society, and the US Adult Treatment Panel III. The proportions of participants classified as high-risk for CHD were 12.5% (15.4% with extrapolation), 3.0%, and 5.8%, respectively. Proportions of participants eligible for statins were 9.2% (11.6% with extrapolation), 13.7%, and 16.7%, respectively. Assuming full compliance to each guideline, expected relative decreases in CHD deaths in Switzerland over a 10-year period would be 16.4% (17.5% with extrapolation), 18.7%, and 19.3%, respectively; the corresponding numbers needed to treat to prevent 1 CHD death would be 285 (340 with extrapolation), 380, and 440, respectively. In conclusion, the proportion of subjects classified as high risk for CHD varied over a fivefold range across recommendations. Following the International Atherosclerosis Society and the Adult Treatment Panel III recommendations might prevent more CHD deaths at the cost of higher numbers needed to treat compared with European Society of Cardiology guidelines

Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)

In this paper, a compressed membership problem for finite automata, both deterministic and non-deterministic, with compressed transition labels is studied. The compression is represented by straight-line programs (SLPs), i.e. context-free grammars generating exactly one string. A novel technique of dealing with SLPs is introduced: the SLPs are recompressed, so that substrings of the input text are encoded in SLPs labelling the transitions of the NFA (DFA) in the same way, as in the SLP representing the input text. To this end, the SLPs are locally decompressed and then recompressed in a uniform way. Furthermore, such recompression induces only small changes in the automaton, in particular, the size of the automaton remains polynomial. Using this technique it is shown that the compressed membership for NFA with compressed labels is in NP, thus confirming the conjecture of Plandowski and Rytter and extending the partial result of Lohrey and Mathissen; as it is already known, that this problem is NP-hard, we settle its exact computational complexity. Moreover, the same technique applied to the compressed membership for DFA with compressed labels yields that this problem is in P; for this problem, only trivial upper-bound PSPACE was known

B cell activity is impaired in human and mouse obesity and is responsive to an essential fatty acid upon murine influenza infection

Obesity is associated with increased risk for infections and poor responses to vaccinations, which may be due to compromised B cell function. However, there is limited information about the influence of obesity on B cell function and underlying factors that modulate B cell responses. Therefore, we studied B cell cytokine secretion and/or Ab production across obesity models. In obese humans, B cell IL-6 secretion was lowered and IgM levels were elevated upon ex vivo anti-BCR/TLR9 stimulation. In murine obesity induced by a high fat diet, ex vivo IgM and IgG were elevated with unstimulated B cells. Furthermore, the high fat diet lowered bone marrow B cell frequency accompanied by diminished transcripts of early lymphoid commitment markers. Murine B cell responses were subsequently investigated upon influenza A/Puerto Rico/8/34 infection using a Western diet model in the absence or presence of docosahexaenoic acid (DHA). DHA, an essential fatty acid with immunomodulatory properties, was tested because its plasma levels are lowered in obesity. Relative to controls, mice consuming theWestern diet had diminished Ab titers whereas theWestern diet plus DHA improved titers. Mechanistically, DHA did not directly target B cells to elevate Ab levels. Instead, DHA increased the concentration of the downstream specialized proresolving lipid mediators (SPMs) 14-hydroxydocosahexaenoic acid, 17-hydroxydocosahexaenoic acid, and protectin DX. All three SPMs were found to be effective in elevating murine Ab levels upon influenza infection. Collectively, the results demonstrate that B cell responses are impaired across human and mouse obesity models and show that essential fatty acid status is a factor influencing humoral immunity, potentially through an SPM-mediated mechanism

String adjunct grammars: II. Equational representation, null symbols, and linguistic relevance

In this paper, we continue the study of String Adjunct Grammars (AG) introduced in Joshi et al. (1972). In particular, equational representations of LAG's, LAG's with null symbols, and some special cases of LAG's are studied. Linguistic relevance of these grammars is also discussed in some detail

Average-case active learning with costs

Abstract. We analyze the expected cost of a greedy active learning algorithm. Our analysis extends previous work to a more general setting in which different queries have different costs. Moreover, queries may have more than two possible responses and the distribution over hypotheses may be non uniform. Specific applications include active learning with label costs, active learning for multiclass and partial label queries, and batch mode active learning. We also discuss an approximate version of interest when there are very many queries.

Operations preserving recognizable languages

Given a subset S of N, filtering a word a0a1 ···an by S consists in deleting the letters ai such that i is not in S. By a natural generalization, denote by L[S], where L is a language, the set of all words of L filtered by S. The filtering problem is to characterize the filters S such that, for every recognizable language L, L[S] is recognizable. In this paper, the filtering problem is solved, and a unified approach is provided to solve similar questions, including the removal problem considered by Seiferas and McNaughton. There are two main ingredients on our approach: the first one is the notion of residually ultimately periodic sequences, and the second one is the notion of representable transductions