Bandwidth and density for block graphs

The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special class of block graphs (graphs in which every block is a clique), namely those where deleting the vertices of degree one produces a path of cliques. The result is best possible in various ways. Furthermore, for two classes of graphs that are ``almost'' caterpillars, the bandwidth problem is NP-complete.Comment: 14 pages, 9 included figures. Note: figures did not appear in original upload; resubmission corrects thi

Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines

The Carnot-like heat engines are classified into three types (normal-, sub- and super-dissipative) according to relations between the minimum irreversible entropy production in the "isothermal" processes and the time for completing those processes. The efficiencies at maximum power of normal-, sub- and super-dissipative Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$, $\eta_C /2$ and $\eta_C$, 0 and $\eta_C/(2-\eta_C)$, respectively. These bounds are also shared by linear, sub- and super-linear irreversible Carnot-like engines [Tu and Wang, Europhys. Lett. 98, 40001 (2012)] although the dissipative engines and the irreversible ones are inequivalent to each other.Comment: 1 figur

Multiple regulatory domains on the Byr2 protein kinase

Byr2 protein kinase, a homolog of mammalian mitogen-activated protein kinase/extracellular signal-regulated kinase kinase (MEKK) and Saccharomyces cerevisiae STE11, is required for pheromone-induced sexual differentiation in the fission yeast Schizosaccharomyces pombe. Byr2 functions downstream of Ste4, Ras1, and the membrane-associated receptor-coupled heterotrimeric G-protein alpha subunit, Gpa1. Byr2 has a distinctive N-terminal kinase regulatory domain and a characteristic C-terminal kinase catalytic domain. Ste4 and Ras1 interact with the regulatory domain of Byr2 directly. Here, we define the domains of Byr2 that bind Ste4 and Ras1 and show that the Byr2 regulatory domain binds to the catalytic domain in the two-hybrid system. Using Byr2 mutants, we demonstrate that these direct physical interactions are all required for proper signaling. In particular, the physical association between Byr2 regulatory and catalytic domains appears to result in autoinhibition, the loss of which results in kinase activation. Furthermore, we provide evidence that Shk1, the S. pombe homolog of the STE20 protein kinase, can directly antagonize the Byr2 intramolecular interaction, possibly by phosphorylating Byr2

Are Bosonic Replicas Faulty?

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.Comment: 4.3 pages; final version to appear in PR

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe