112 research outputs found
A new problem in string searching
We describe a substring search problem that arises in group presentation
simplification processes. We suggest a two-level searching model: skip and
match levels. We give two timestamp algorithms which skip searching parts of
the text where there are no matches at all and prove their correctness. At the
match level, we consider Harrison signature, Karp-Rabin fingerprint, Bloom
filter and automata based matching algorithms and present experimental
performance figures.Comment: To appear in Proceedings Fifth Annual International Symposium on
Algorithms and Computation (ISAAC'94), Lecture Notes in Computer Scienc
The -Class Tower of
The seminal papers in the field of root-discriminant bounds are those of
Odlyzko and Martinet. Both papers include the question of whether the field
has finite or infinite -class tower. This is a
critical case that will either substantially lower the best known upper bound
for lim inf of root-discriminants (if infinite) or else give a counter-example
to what is often termed Martinet's conjecture or question (if finite). Using
extensive computation and introducing some new techniques, we give strong
evidence that the tower is in fact finite, establishing other properties of its
Galois group en route
On counterexamples to the Hughes conjecture
described counterexamples for p = 5, 7 and 11. Finite groups which do not satisfy the conjecture, anti-Hughes groups, have interesting properties. We give explicit constructions of a number of anti-Hughes groups via power-commutator presentations, including relatively small examples with orders 5 46 and 7 66 . It is expected that the conjecture is false for all primes larger than 3. We show that it is false for p = 13, 17 and 19
Increased consumption of fruit and vegetables for the primary prevention of cardiovascular diseases
There is increasing evidence that high consumption of fruit and vegetables is beneficial for cardiovascular disease (CVD) prevention
Mouse models of neurodegenerative disease: preclinical imaging and neurovascular component.
Neurodegenerative diseases represent great challenges for basic science and clinical medicine because of their prevalence, pathologies, lack of mechanism-based treatments, and impacts on individuals. Translational research might contribute to the study of neurodegenerative diseases. The mouse has become a key model for studying disease mechanisms that might recapitulate in part some aspects of the corresponding human diseases. Neurode- generative disorders are very complicated and multifacto- rial. This has to be taken in account when testing drugs. Most of the drugs screening in mice are very di cult to be interpretated and often useless. Mouse models could be condiderated a âpathway modelsâ, rather than as models for the whole complicated construct that makes a human disease. Non-invasive in vivo imaging in mice has gained increasing interest in preclinical research in the last years thanks to the availability of high-resolution single-photon emission computed tomography (SPECT), positron emission tomography (PET), high eld Magnetic resonance, Optical Imaging scanners and of highly speci c contrast agents. Behavioral test are useful tool to characterize di erent ani- mal models of neurodegenerative pathology. Furthermore, many authors have observed vascular pathological features associated to the di erent neurodegenerative disorders. Aim
of this review is to focus on the di erent existing animal models of neurodegenerative disorders, describe behavioral tests and preclinical imaging techniques used for diagnose and describe the vascular pathological features associated to these diseases
Behind and beyond a theorem on groups related to trivalent graphs
In 2006 we completed the proof of a five-part conjecture that was made in 1977 about a family of groups related to trivalent graphs. This family covers all 2-generator, 2-relator groups where one relator specifies that a generator is an involution and the other relator has three syllables. Our proof relies upon detailed but general computations in the groups under question. The proof is theoretical, but based upon explicit proofs produced by machine for individual cases. Here we explain how we derived the general proofs from specific cases. The conjecture essentially addressed only the finite groups in the family. Here we extend the results to infinite groups, effectively determining when members of this family of finitely presented groups are simply isomorphic to a specific quotient.Publisher PDFPeer reviewe
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