On representation of the t-J model via spin-charge variables

We show that the t-J Hamiltonian is not in general reduced to H(S,f), where S and f stand for independent ([S,f]=0) SU(2) (spin) generators and spinless fermionic (hole) field, respectively. The proof is based upon an identification of the Hubbard operators with the generators of the su(2|1) superalgebra in the degenerate fundamental representation and ensuing SU(2|1) path integral representation of the partition function.Comment: 15 pages, latex, no figure

Group gradings on finitary simple Lie algebras

We classify, up to isomorphism, all gradings by an arbitrary abelian group on simple finitary Lie algebras of linear transformations (special linear, orthogonal and symplectic) on infinite-dimensional vector spaces over an algebraically closed field of characteristic different from 2.Comment: Several typographical errors have been correcte

An adaptive memory programming framework for the resource-constrained project scheduling problem

The Resource-Constrained Project Scheduling Problem (RCPSP) is one of the most intractable combinatorial optimisation problems that combines a set of constraints and objectives met in a vast variety of applications and industries. Its solution raises major theoretical challenges due to its complexity, yet presenting numerous practical dimensions. Adaptive memory programming (AMP) is one of the most successful frameworks for solving hard combinatorial optimisation problems (e.g. vehicle routing and scheduling). Its success stems from the use of learning mechanisms that capture favourable solution elements found in high-quality solutions. This paper challenges the efficiency of AMP for solving the RCPSP, to our knowledge, for the first time in the literature. Computational experiments on well-known benchmark RCPSP instances show that the proposed AMP consistently produces high-quality solutions in reasonable computational times

AUG_hairpin: prediction of a downstream secondary structure influencing the recognition of a translation start site

<p>Abstract</p> <p>Background</p> <p>The translation start site plays an important role in the control of translation efficiency of eukaryotic mRNAs. The recognition of the start AUG codon by eukaryotic ribosomes is considered to depend on its nucleotide context. However, the fraction of eukaryotic mRNAs with the start codon in a suboptimal context is relatively large. It may be expected that mRNA should possess some features providing efficient translation, including the proper recognition of a translation start site. It has been experimentally shown that a downstream hairpin located in certain positions with respect to start codon can compensate in part for the suboptimal AUG context and also increases translation from non-AUG initiation codons. Prediction of such a compensatory hairpin may be useful in the evaluation of eukaryotic mRNA translation properties.</p> <p>Results</p> <p>We evaluated interdependency between the start codon context and mRNA secondary structure at the CDS beginning: it was found that a suboptimal start codon context significantly correlated with higher base pairing probabilities at positions 13 – 17 of CDS of human and mouse mRNAs. It is likely that the downstream hairpins are used to enhance translation of some mammalian mRNAs <it>in vivo</it>. Thus, we have developed a tool, <it>AUG_hairpin</it>, to predict local stem-loop structures located within the defined region at the beginning of mRNA coding part. The implemented algorithm is based on the available published experimental data on the CDS-located stem-loop structures influencing the recognition of upstream start codons.</p> <p>Conclusion</p> <p>An occurrence of a potential secondary structure downstream of start AUG codon in a suboptimal context (or downstream of a potential non-AUG start codon) may provide researchers with a testable assumption on the presence of additional regulatory signal influencing mRNA translation initiation rate and the start codon choice. <it>AUG_hairpin</it>, which has a convenient Web-interface with adjustable parameters, will make such an evaluation easy and efficient.</p

Semiclassical dynamics of a spin-1/2 in an arbitrary magnetic field

The spin coherent state path integral describing the dynamics of a spin-1/2-system in a magnetic field of arbitrary time-dependence is considered. Defining the path integral as the limit of a Wiener regularized expression, the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints. The resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator. A non-linear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary-value problem. The semiclassical spin dynamics is thus readily amenable to numerical methods.Comment: 16 pages, submitted to Journal of Physics

Potato spindle tuber viroid

Viroids belong to a very interesting class of molecules attracting researchers in phytopathology and molecular evolution. Here we review recent literature data concerning the genetics of Potato spindle tuber viroid (PSTVd) and the mechanisms related to its pathological effect on the host plants. PSTVd can be transmitted vertically through microspores and macrospores, but not with pollen from another infected plant. The 359 nucleotidelong genomic RNA of PSTVd is highly structured and its 3D-conformation is responsible for interaction with host cellular factors to mediate replication, transport between tissues during systemic infection and the severity of pathological symptoms. RNA replication is prone to errors and infected plants contain a population of mutated forms of the PSTVd genome. Interestingly, at 7 DAI, only 25 % of the newly synthesized RNAs were identical to the master copy, but this proportion increased to up to 70 % at 14 DAI and remained the same afterwards. PSTVd infection induces the immune response in host plants. There are PSTVd strains with a severe, a moderate or a mild pathological effect. Interestingly, viroid replication itself does not necessarily induce strong morphological or physiological symptoms. In the case of PSTVd, disease symptoms may occur due to RNA-interference, which decreases the expression levels of some important cellular regulatory factors, such as, for example, potato StTCP23 from the gibberellic acid pathway with a role in tuber morphogenesis or tomato FRIGIDA-like protein 3 with an early flowering phenotype. This association between the small segments of viroid genomic RNAs complementary to the untranslated regions of cellular mRNAs and disease symptoms provides a way for new resistant cultivars to be developed by genetic editing. To conclude, viroids provide a unique model to reveal the fundamental features of living systems, which appeared early in evolution and still remain undiscovered

Fluctuations and Dissipation of Coherent Magnetization

A quantum mechanical model is used to derive a generalized Landau-Lifshitz equation for a magnetic moment, including fluctuations and dissipation. The model reproduces the Gilbert-Brown form of the equation in the classical limit. The magnetic moment is linearly coupled to a reservoir of bosonic degrees of freedom. Use of generalized coherent states makes the semiclassical limit more transparent within a path-integral formulation. A general fluctuation-dissipation theorem is derived. The magnitude of the magnetic moment also fluctuates beyond the Gaussian approximation. We discuss how the approximate stochastic description of the thermal field follows from our result. As an example, we go beyond the linear-response method and show how the thermal fluctuations become anisotropy-dependent even in the uniaxial case.Comment: 22 page

Semiclassical coherent state propagator for systems with spin

We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit. As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.Comment: 19 pages, no figure

Semiclassical theory of spin-orbit interaction in the extended phase space

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density of states. We discuss special cases, such as weak and strong spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B; minor corrections elsewher

Measurement of double beta decay of ¹⁰⁰Mo to excited states in the NEMO 3 experiment

The double beta decay of ¹⁰⁰Mo to the 0_{1}^{+} and 2_{1}^{+} excited states of ¹⁰⁰Ru is studied using the NEMO 3 data. After the analysis of 8024 h of data the half-life for the two-neutrino double beta decay of ¹⁰⁰Mo to the excited 0_{1}^{+} state is measured to be T_{1/2}^{2v} = [5.7_{-0.9}^{+1.3} (stat.) ± 0.8 (syst.)] x 10²⁰ y. The signal-to-background ratio is equal to 3. Information about energy and angular distributions of emitted electrons is also obtained. No evidence for neutrinoless double beta decay to the excited 0_{1}^{+} state has been found. The corresponding half-life limit is T_{1/2}^{0v} (0⁺→0_{1}^{+}) > 8.9 x 10²² y (at 90% C.L.). The search for the double beta decay to the 2_{1}^{+} excited state has allowed the determination of limits on the half-life for the two neutrino mode T_{1/2}^{0v} (0⁺→2_{1}^{+}) > 1.1 x 10²¹ y (at 90% C.L.) and for the neutrinoless mode T_{1/2}^{0v} (0⁺→2_{1}^{+}) > 1.6 x 10²³ y (at 90% C.L.)