2,465 research outputs found
Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups
The problem of computing \emph{the exponent lattice} which consists of all
the multiplicative relations between the roots of a univariate polynomial has
drawn much attention in the field of computer algebra. As is known, almost all
irreducible polynomials with integer coefficients have only trivial exponent
lattices. However, the algorithms in the literature have difficulty in proving
such triviality for a generic polynomial. In this paper, the relations between
the Galois group (respectively, \emph{the Galois-like groups}) and the
triviality of the exponent lattice of a polynomial are investigated. The
\bbbq\emph{-trivial} pairs, which are at the heart of the relations between
the Galois group and the triviality of the exponent lattice of a polynomial,
are characterized. An effective algorithm is developed to recognize these
pairs. Based on this, a new algorithm is designed to prove the triviality of
the exponent lattice of a generic irreducible polynomial, which considerably
improves a state-of-the-art algorithm of the same type when the polynomial
degree becomes larger. In addition, the concept of the Galois-like groups of a
polynomial is introduced. Some properties of the Galois-like groups are proved
and, more importantly, a sufficient and necessary condition is given for a
polynomial (which is not necessarily irreducible) to have trivial exponent
lattice.Comment: 19 pages,2 figure
Exploiting symmetries in SDP-relaxations for polynomial optimization
In this paper we study various approaches for exploiting symmetries in
polynomial optimization problems within the framework of semi definite
programming relaxations. Our special focus is on constrained problems
especially when the symmetric group is acting on the variables. In particular,
we investigate the concept of block decomposition within the framework of
constrained polynomial optimization problems, show how the degree principle for
the symmetric group can be computationally exploited and also propose some
methods to efficiently compute in the geometric quotient.Comment: (v3) Minor revision. To appear in Math. of Operations Researc
A comparison of microsatellite instability in early onset gastric carcinomas from relatively low and high incidence European populations.
We have investigated the genetic basis of gastric carcinomas occurring in patients aged under 40 years from a Portuguese population with a relatively high incidence of gastric cancer. We analysed a panel of 12 microsatellite loci in DNA extracted from gastric carcinomas arising in 16 patients aged 24-39 years from Braga, Portugal. Overall, microsatellite instability (MI) in at least 1 locus was detected in 44% (7 of 16) of carcinomas. A single patient demonstrated a mutator phenotype suggestive of the hereditary nonpolyposis colorectal cancer syndrome with instability in 82% of loci. This carcinoma showed loss of expression of the hMLH1 mismatch repair protein. In a previous study, we found no evidence of MI among 10 cases of early onset gastric carcinomas from an English population, which has a relatively low incidence of gastric cancer. Comparing the 2 series, we found that there was a significant difference (p = 0.04) in the prevalence of MI (at least 1 marker affected). This geographical difference in low-level MI may be related to a significantly higher prevalence of background chronic atrophic gastritis (8 of 16 vs. 0 of 8) and Helicobacter pylori infection (15 of 16 vs. 2 of 8) in Portuguese carcinomas compared with English cases. Genetic mechanisms underlying the hereditary non-polyposis colorectal cancer syndrome may play a role in a small number of early onset gastric carcinomas. The difference in prevalence of low-level MI between these relatively high and low incidence European populations requires further investigation
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
On right conjugacy closed loops of twice prime order
The right conjugacy closed loops of order 2p, where p is an odd prime, are
classified up to isomorphism.Comment: Clarified definitions, added some remarks and a tabl
Deletion of the GABAA α2-subunit does not alter self dministration of cocaine or reinstatement of cocaine seeking
Rationale
GABAA receptors containing α2-subunits are highly represented in brain areas that are involved in motivation and reward, and have been associated with addiction to several drugs, including cocaine. We have shown previously that a deletion of the α2-subunit results in an absence of sensitisation to cocaine.
Objective
We investigated the reinforcing properties of cocaine in GABAA α2-subunit knockout (KO) mice using an intravenous self-administration procedure.
Methods
α2-subunit wildtype (WT), heterozygous (HT) and KO mice were trained to lever press for a 30 % condensed milk solution. After implantation with a jugular catheter, mice were trained to lever press for cocaine (0.5 mg/kg/infusion) during ten daily sessions. Responding was extinguished and the mice tested for cue- and cocaine-primed reinstatement. Separate groups of mice were trained to respond for decreasing doses of cocaine (0.25, 0.125, 0.06 and 0.03 mg/kg).
Results
No differences were found in acquisition of lever pressing for milk. All genotypes acquired self-administration of cocaine and did not differ in rates of self-administration, dose dependency or reinstatement. However, whilst WT and HT mice showed a dose-dependent increase in lever pressing during the cue presentation, KO mice did not.
Conclusions
Despite a reported absence of sensitisation, motivation to obtain cocaine remains unchanged in KO and HT mice. Reinstatement of cocaine seeking by cocaine and cocaine-paired cues is also unaffected. We postulate that whilst not directly involved in reward perception, the α2-subunit may be involved in modulating the “energising” aspect of cocaine’s effects on reward-seeking
Role of f02 in fluid saturation of oceanic basalt.
Assessing the conditions under which magmas become fluid-saturated has important bearings on the geochemical modelling of magmas because volatile exsolution may profoundly alter the behaviour of certain trace elements that are strongly partitioned in the coexisting fluid1. Saal et al.2 report primitive melt inclusions from dredged oceanic basalts of the Siqueiros transform fault, from which they derive volatile abundances of the depleted mantle, based on the demonstration that magmas are not fluid-saturated at their eruption depth and so preserve the mantle signature in terms of their volatile contents. However, in their analysis, Saal et al.2 consider only fluid−melt equilibria, and do not take into account the homogeneous equilibria between fluid species, which, as we show here, may lead to a significant underestimation of the pressure depth of fluid saturation
On finite monoids of cellular automata.
For any group G and set A, a cellular automaton over G and A is a transformation τ:AG→AGτ:AG→AG defined via a finite neighbourhood S⊆GS⊆G (called a memory set of ττ) and a local function μ:AS→Aμ:AS→A. In this paper, we assume that G and A are both finite and study various algebraic properties of the finite monoid CA(G,A)CA(G,A) consisting of all cellular automata over G and A. Let ICA(G;A)ICA(G;A) be the group of invertible cellular automata over G and A. In the first part, using information on the conjugacy classes of subgroups of G, we give a detailed description of the structure of ICA(G;A)ICA(G;A) in terms of direct and wreath products. In the second part, we study generating sets of CA(G;A)CA(G;A). In particular, we prove that CA(G,A)CA(G,A) cannot be generated by cellular automata with small memory set, and, when G is finite abelian, we determine the minimal size of a set V⊆CA(G;A)V⊆CA(G;A) such that CA(G;A)=⟨ICA(G;A)∪V⟩CA(G;A)=⟨ICA(G;A)∪V⟩
On The Stability Of Non-Supersymmetric AdS Vacua
We consider two infinite families of Non-Supersymmetric vacua, called
Type 2) and Type 3) vacua, that arise in massive IIA supergravity with flux. We
show that both families are perturbatively stable. We then examine
non-perturbative decays of these vacua to other supersymmetric and
non-supersymmetric vacua mediated by instantons in the thin wall
approximation. We find that many decays are ruled out since the tension of the
interpolating domain wall is too big compared to the energy difference in AdS
units. In fact, within our approximations no decays of Type 2) vacua are
allowed, although some decays are only marginally forbidden. This can be
understood in terms of a "pairing symmetry" in the landscape which relate Type
2) vacua with supersymmetric ones of the same energy.Comment: 50 pages, Minor changes in section 2.2.
Children Consuming Cassava as a Staple Food are at Risk for Inadequate Zinc, Iron, and Vitamin A Intake
Cassava contains little zinc, iron, and β-carotene, yet it is the primary staple crop of over 250 million Africans. This study used a 24-hour dietary recall to test the hypothesis that among healthy children aged 2–5 years in Nigeria and Kenya, cassava’s contribution to the childrens’ daily diets is inversely related to intakes of zinc, iron, and vitamin A. Dietary and demographic data and anthropometric measurements were collected from 449 Kenyan and 793 Nigerian children. Among Kenyan children 89% derived at least 25% of their dietary energy from cassava, while among the Nigerian children 31% derived at least 25% of energy from cassava. Spearman’s correlation coefficient between the fraction of dietary energy obtained from cassava and vitamin A intake was r = −0.15, P < 0.0001, zinc intake was r = −0.11, P < 0.0001 and iron intake was r = −0.36, P < 0.0001. In Kenya, 59% of children consumed adequate vitamin A, 22% iron, and 31% zinc. In Nigeria, 17% of children had adequate intake of vitamin A, 57% iron, and 41% zinc. Consumption of cassava is a risk factor for inadequate vitamin A, zinc and/or iron intake
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