On the Disambiguation of Weighted Automata

We present a disambiguation algorithm for weighted automata. The algorithm admits two main stages: a pre-disambiguation stage followed by a transition removal stage. We give a detailed description of the algorithm and the proof of its correctness. The algorithm is not applicable to all weighted automata but we prove sufficient conditions for its applicability in the case of the tropical semiring by introducing the *weak twins property*. In particular, the algorithm can be used with all acyclic weighted automata, relevant to applications. While disambiguation can sometimes be achieved using determinization, our disambiguation algorithm in some cases can return a result that is exponentially smaller than any equivalent deterministic automaton. We also present some empirical evidence of the space benefits of disambiguation over determinization in speech recognition and machine translation applications

On finitely ambiguous B\"uchi automata

Unambiguous B\"uchi automata, i.e. B\"uchi automata allowing only one accepting run per word, are a useful restriction of B\"uchi automata that is well-suited for probabilistic model-checking. In this paper we propose a more permissive variant, namely finitely ambiguous B\"uchi automata, a generalisation where each word has at most $k$ accepting runs, for some fixed $k$. We adapt existing notions and results concerning finite and bounded ambiguity of finite automata to the setting of $\omega$-languages and present a translation from arbitrary nondeterministic B\"uchi automata with $n$ states to finitely ambiguous automata with at most $3^n$ states and at most $n$ accepting runs per word

Fixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted

HFST—Framework for Compiling and Applying Morphologies

HFST–Helsinki Finite-State Technology ( hfst.sf.net ) is a framework for compiling and applying linguistic descriptions with finite-state methods. HFST currently connects some of the most important finite-state tools for creating morphologies and spellers into one open-source platform and supports extending and improving the descriptions with weights to accommodate the modeling of statistical information. HFST offers a path from language descriptions to efficient language applications in key environments and operating systems. HFST also provides an opportunity to exchange transducers between different software providers in order to get the best out of each finite-state library.Peer reviewe

Bounded Delay and Concurrency for Earliest Query Answering

International audienceEarliest query answering is needed for streaming XML processing with optimal memory management. We study the feasibility of earliest query answering for node selection queries. Tractable queries are distinguished by a bounded number of concurrently alive answer candidates at every time point, and a bounded delay for node selection. We show that both properties are decidable in polynomial time for queries defined by deterministic automata for unranked trees. Our results are obtained by reduction to the bounded valuedness problem for recognizable relations between unranked trees

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

Indices of insulin sensitivity and secretion from a standard liquid meal test in subjects with type 2 diabetes, impaired or normal fasting glucose

<p>Abstract</p> <p>Background</p> <p>To provide an initial evaluation of insulin sensitivity and secretion indices derived from a standard liquid meal tolerance test protocol in subjects with normal (NFG), impaired fasting glucose (IFG) or type 2 diabetes mellitus.</p> <p>Methods</p> <p>Areas under the curve (AUC) for glucose, insulin and C-peptide from pre-meal to 120 min after consumption of a liquid meal were calculated, as were homeostasis model assessments of insulin resistance (HOMA2-IR) and the Matsuda index of insulin sensitivity.</p> <p>Results</p> <p>Subjects with NFG (n = 19), IFG (n = 19), and diabetes (n = 35) had mean ± SEM HOMA2-IR values of 1.0 ± 0.1, 1.6 ± 0.2 and 2.5 ± 0.3 and Matsuda insulin sensitivity index values of 15.6 ± 2.0, 8.8 ± 1.2 and 6.0 ± 0.6, respectively. The log-transformed values for these variables were highly correlated overall and within each fasting glucose category (r = -0.91 to -0.94, all p < 0.001). Values for the product of the insulin/glucose AUC ratio and the Matsuda index, an indicator of the ability of the pancreas to match insulin secretion to the degree of insulin resistance, were 995.6 ± 80.7 (NFG), 684.0 ± 57.3 (IFG) and 188.3 ± 16.1 (diabetes) and discriminated significantly between fasting glucose categories (p < 0.001 for each comparison).</p> <p>Conclusion</p> <p>These results provide initial evidence to support the usefulness of a standard liquid meal tolerance test for evaluation of insulin secretion and sensitivity in clinical and population studies.</p

Aβ40 Oligomers Identified as a Potential Biomarker for the Diagnosis of Alzheimer's Disease

Alzheimer's Disease (AD) is the most prevalent form of dementia worldwide, yet the development of therapeutics has been hampered by the absence of suitable biomarkers to diagnose the disease in its early stages prior to the formation of amyloid plaques and the occurrence of irreversible neuronal damage. Since oligomeric Aβ species have been implicated in the pathophysiology of AD, we reasoned that they may correlate with the onset of disease. As such, we have developed a novel misfolded protein assay for the detection of soluble oligomers composed of Aβ x-40 and x-42 peptide (hereafter Aβ40 and Aβ42) from cerebrospinal fluid (CSF). Preliminary validation of this assay with 36 clinical samples demonstrated the presence of aggregated Aβ40 in the CSF of AD patients. Together with measurements of total Aβ42, diagnostic sensitivity and specificity greater than 95% and 90%, respectively, were achieved. Although larger sample populations will be needed to confirm this diagnostic sensitivity, our studies demonstrate a sensitive method of detecting circulating Aβ40 oligomers from AD CSF and suggest that these oligomers could be a powerful new biomarker for the early detection of AD