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 22-Class Tower of Q(−5460)\mathbb{Q}(\sqrt{-5460})

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 $\mathbb{Q}(\sqrt{-5460})$ has finite or infinite $2$-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 ‘pathway models’, 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