Algebraic theory of minimal nondeterministic finite automata with applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA’s behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas

This flyer promotes the event "A Minimal History of the Cuban Revolution (Historia mínima de Ia Revolución Cubana), Book Presentation by Author Rafael Rojas", part at the SIPA at Books & Books series. This event held at Books & Books in Coral Gables.

Algebraic Theory of Minimal Nondeterministic Finite Automata with Applications

Since the 1950s, the theory of deterministic and nondeterministic finite automata (DFAs and NFAs, respectively) has been a cornerstone of theoretical computer science. In this dissertation, our main object of study is minimal NFAs. In contrast with minimal DFAs, minimal NFAs are computationally challenging: first, there can be more than one minimal NFA recognizing a given language; second, the problem of converting an NFA to a minimal equivalent NFA is NP-hard, even for NFAs over a unary alphabet. Our study is based on the development of two main theories, inductive bases and partials, which in combination form the foundation for an incremental algorithm, ibas, to find minimal NFAs. An inductive basis is a collection of languages with the property that it can generate (through union) each of the left quotients of its elements. We prove a fundamental characterization theorem which says that a language can be recognized by an n-state NFA if and only if it can be generated by an n-element inductive basis. A partial is an incompletely-specified language. We say that an NFA recognizes a partial if its language extends the partial, meaning that the NFA's behavior is unconstrained on unspecified strings; it follows that a minimal NFA for a partial is also minimal for its language. We therefore direct our attention to minimal NFAs recognizing a given partial. Combining inductive bases and partials, we generalize our characterization theorem, showing that a partial can be recognized by an n-state NFA if and only if it can be generated by an n-element partial inductive basis. We apply our theory to develop and implement ibas, an incremental algorithm that finds minimal partial inductive bases generating a given partial. In the case of unary languages, ibas can often find minimal NFAs of up to 10 states in about an hour of computing time; with brute-force search this would require many trillions of years.

A minimal model of partial synchrony

Acknowledgement We wish to acknowledge A. Pikovsky and M. Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).

A minimal model of partial synchrony

We wish to acknowledge A Pikovsky and M Zaks for useful discussions. This work has been financially supported by the EU project COSMOS (642563).

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Application of self-quenched JH consensus primers for real-time quantitative PCR of IGH gene to minimal residual disease evaluation in multiple myeloma.

Monitoring multiple myeloma patients for relapse requires sensitive methods to measure minimal residual disease and to establish a more precise prognosis. The present study aimed to standardize a real-time quantitative polymerase chain reaction (PCR) test for the IgH gene with a JH consensus self-quenched fluorescence reverse primer and a VDJH or DJH allele-specific sense primer (self-quenched PCR). This method was compared with allele-specific real-time quantitative PCR test for the IgH gene using a TaqMan probe and a JH consensus primer (TaqMan PCR). We studied nine multiple myeloma patients from the Spanish group treated with the MM2000 therapeutic protocol. Self-quenched PCR demonstrated sensitivity of >or=10(-4) or 16 genomes in most cases, efficiency was 1.71 to 2.14, and intra-assay and interassay reproducibilities were 1.18 and 0.75%, respectively. Sensitivity, efficiency, and residual disease detection were similar with both PCR methods. TaqMan PCR failed in one case because of a mutation in the JH primer binding site, and self-quenched PCR worked well in this case. In conclusion, self-quenched PCR is a sensitive and reproducible method for quantifying residual disease in multiple myeloma patients; it yields similar results to TaqMan PCR and may be more effective than the latter when somatic mutations are present in the JH intronic primer binding site.

Minimal residual disease monitoring in multiple myeloma: a comparison between allelic-specific oligonucleotide real-time quantitative polymerase chain reaction and flow cytometry.

BACKGROUND AND OBJECTIVES: Minimal residual disease (MRD) studies are useful in multiple myeloma (MM). However, the definition of the best technique and clinical utility are still unresolved issues. The aim of this study was to analyze and compare the clinical utility of MRD studies in MM with two different techniques: allelic-specific oligonucleotide real-time quantitative PCR (ASO-RQ-PCR), and flow cytometry (FCM). DESIGN AND METHODS: Bone marrow samples from 32 MM patients who had achieved complete response after transplantation were evaluated by ASO-RQ-PCR, using TaqMan technology, and multiparametric FCM. RESULTS: ASO-RQ-PCR was only applicable in 75% of patients for a variety of technical reasons, while FCM was applicable in up to 90%. Therefore, simultaneous PCR/FCM analysis was possible in only 24 patients. The number of residual tumor cells identified by both techniques was very similar (mean=0.29%, range=0.001-1.61%, correlation coefficient=0.861). However, RQ-PCR was able to detect residual myelomatous cells in 17 patients while FCM only did so in 11; thus, 6 cases were FCM negative but PCR positive, all of them displaying a very low number of clonal cells (median=0.014%, range=0.001-0.11). Using an MRD threshold of 0.01% (10(-4)) two risk groups with significantly different progression-free survival could be identified by either PCR (34 vs. 15m, p=0.04) or FCM (27 vs. 10m, p=0.05). INTERPRETATION AND CONCLUSIONS: Although MRD evaluation by ASO-RQ-PCR is slightly more sensitive and specific than FCM, it is applicable in a lower proportion of MM patients and is more time-consuming, while both techniques provide similar prognostic information.

Incomplete DJH rearrangements as a novel tumor target for minimal residual disease quantitation in multiple myeloma using real-time PCR.

The hypervariable regions of immunoglobulin heavy-chain (IgH) rearrangements provide a specific tumor marker in multiple myeloma (MM). Recently, real-time PCR assays have been developed in order to quantify the number of tumor cells after treatment. However, these strategies are hampered by the presence of somatic hypermutation (SH) in VDJH rearrangements from multiple myeloma (MM) patients, which causes mismatches between primers and/or probes and the target, leading to a nonaccurate quantification of tumor cells. Our group has recently described a 60% incidence of incomplete DJH rearrangements in MM patients, with no or very low rates of SH. In this study, we compare the efficiency of a real-time PCR approach for the analysis of both complete and incomplete IgH rearrangements in eight MM patients using only three JH consensus probes. We were able to design an allele-specific oligonucleotide for both the complete and incomplete rearrangement in all patients. DJH rearrangements fulfilled the criteria of effectiveness for real-time PCR in all samples (ie no unspecific amplification, detection of less than 10 tumor cells within 10(5) polyclonal background and correlation coefficients of standard curves higher than 0.98). By contrast, only three out of eight VDJH rearrangements fulfilled these criteria. Further analyses showed that the remaining five VDJH rearrangements carried three or more somatic mutations in the probe and primer sites, leading to a dramatic decrease in the melting temperature. These results support the use of incomplete DJH rearrangements instead of complete somatically mutated VDJH rearrangements for investigation of minimal residual disease in multiple myeloma.

Geometric properties of 2-dimensional minimal surfaces in a sub-Riemannian manifold which models the Visual Cortex

In this paper we study the notion of degree forsubmanifolds embedded in an equiregular sub-Riemannian manifold and we provide the definition of their associated area functional. In this setting we prove that the Hausdorff dimension of a submanifold coincides with its degree, as stated by Gromov. Using these general definitions we compute the first variation for surfaces embedded in low dimensional manifolds and we obtain the partial differential equation associated to minimal surfaces. These minimal surfaces have several applications in the neurogeometry of the visual cortex.

Strategic tillage in no-till farming systems in Australia's northern grains-growing regions: I. Drivers and implementation

Development of no-tillage (NT) farming has revolutionized agricultural systems by allowing growers to manage greater areas of land with reduced energy, labour and machinery inputs to control erosion, improve soil health and reduce greenhouse gas emission. However, NT farming systems have resulted in a build-up of herbicide-resistant weeds, an increased incidence of soil- and stubble-borne diseases and enrichment of nutrients and carbon near the soil surface. Consequently, there is an increased interest in the use of an occasional tillage (termed strategic tillage, ST) to address such emerging constraints in otherwise-NT farming systems. Decisions around ST uses will depend upon the specific issues present on the individual field or farm, and profitability and effectiveness of available options for management. This paper explores some of the issues with the implementation of ST in NT farming systems. The impact of contrasting soil properties, the timing of the tillage and the prevailing climate exert a strong influence on the success of ST. Decisions around timing of tillage are very complex and depend on the interactions between soil water content and the purpose for which the ST is intended. The soil needs to be at the right water content before executing any tillage, while the objective of the ST will influence the frequency and type of tillage implement used. The use of ST in long-term NT systems will depend on factors associated with system costs and profitability, soil health and environmental impacts. For many farmers maintaining farm profitability is a priority, so economic considerations are likely to be a primary factor dictating adoption. However, impacts on soil health and environment, especially the risk of erosion and the loss of soil carbon, will also influence a grower's choice to adopt ST, as will the impact on soil moisture reserves in rainfed cropping systems. © 2015 Elsevier B.V.

Effect of sugarcane cropping systems on herbicide losses in surface runoff

Herbicide runoff from cropping fields has been identified as a threat to the Great Barrier Reef ecosystem. A field investigation was carried out to monitor the changes in runoff water quality resulting from four different sugarcane cropping systems that included different herbicides and contrasting tillage and trash management practices. These include (i) Conventional - Tillage (beds and inter-rows) with residual herbicides used; (ii) Improved - only the beds were tilled (zonal) with reduced residual herbicides used; (iii) Aspirational - minimum tillage (one pass of a single tine ripper before planting) with trash mulch, no residual herbicides and a legume intercrop after cane establishment; and (iv) New Farming System (NFS) - minimum tillage as in Aspirational practice with a grain legume rotation and a combination of residual and knockdown herbicides. Results suggest soil and trash management had a larger effect on the herbicide losses in runoff than the physico-chemical properties of herbicides. Improved practices with 30% lower atrazine application rates than used in conventional systems produced reduced runoff volumes by 40% and atrazine loss by 62%. There were a 2-fold variation in atrazine and >10-fold variation in metribuzin loads in runoff water between reduced tillage systems differing in soil disturbance and surface residue cover from the previous rotation crops, despite the same herbicide application rates. The elevated risk of offsite losses from herbicides was illustrated by the high concentrations of diuron (14mugL-1) recorded in runoff that occurred >2.5months after herbicide application in a 1st ratoon crop. A cropping system employing less persistent non-selective herbicides and an inter-row soybean mulch resulted in no residual herbicide contamination in runoff water, but recorded 12.3% lower yield compared to Conventional practice. These findings reveal a trade-off between achieving good water quality with minimal herbicide contamination and maintaining farm profitability with good weed control.