Combinatorics and geometry of finite and infinite squaregraphs

Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not incident with the outer face) have degrees larger than three. The planar dual of a finite squaregraph is determined by a triangle-free chord diagram of the unit disk, which could alternatively be viewed as a triangle-free line arrangement in the hyperbolic plane. This representation carries over to infinite plane graphs with finite vertex degrees in which the balls are finite squaregraphs. Algebraically, finite squaregraphs are median graphs for which the duals are finite circular split systems. Hence squaregraphs are at the crosspoint of two dualities, an algebraic and a geometric one, and thus lend themselves to several combinatorial interpretations and structural characterizations. With these and the 5-colorability theorem for circle graphs at hand, we prove that every squaregraph can be isometrically embedded into the Cartesian product of five trees. This embedding result can also be extended to the infinite case without reference to an embedding in the plane and without any cardinality restriction when formulated for median graphs free of cubes and further finite obstructions. Further, we exhibit a class of squaregraphs that can be embedded into the product of three trees and we characterize those squaregraphs that are embeddable into the product of just two trees. Finally, finite squaregraphs enjoy a number of algorithmic features that do not extend to arbitrary median graphs. For instance, we show that median-generating sets of finite squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure

Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on the maximum overlap problem using directional iterates

In a unified framework, we obtain two-sided estimates of the following quantities of interest in quantum information theory: 1.The minimum-error distinguishability of arbitrary ensembles of mixed quantum states. 2.The approximate reversibility of quantum dynamics in terms of entanglement fidelity. (This is also referred to as "channel-adapted quantum error recovery" when the reversed channel is the composition of an encoding operation and a noise channel.) 3.The maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state. 4. The conditional min-entropy of bipartite quantum states. A refined version of the author's techniques [J. Math. Phys. 50, 032016] for bounding the first quantity is employed to give two-sided estimates of the remaining three quantities. Our primary tool is "small angle" initialization of an abstract generalization of the iterative schemes for computing optimal measurements and quantum error recoveries introduced by Jezek-Rehacek-Fiurasek [Phys. Rev. A 65, 060301], Jezek-Fiurasek-Hradil [Phys. Rev. A 68, 012305], and Reimpell-Werner [Phys. Rev. Lett 94, 080501].Comment: Extensively revised & new content added. Improved min-entropy bounds. Notation made more accessible. Minimax theorem used to clarify relationship between "worst case" bounds and "single instance" bounds. Improved motivation of the choice of "small angle" guess. Eliminated spurious factor appearing when overlap bounds are applied to state distinction. Work connected to that of Beny and Oreshko

Physical Habitat and Fish Assemblage Relationships with Landscape Variables at Multiple Spatial Scales in Wadeable Iowa Streams

Landscapes in Iowa and other midwestern states have been profoundly altered by conversion of native prairies to agriculture. We analyzed landscape data collected at multiple spatial scales to explore relationships with reach-scale physical habitat and fish assemblage data from 93 randomly selected sites on second- through fifth-order wadeable Iowa streams. Ordination of sites by physical habitat showed significant gradients of channel shape, habitat complexity, substrate composition, and stream size. Several landscape variables were significantly associated with the physical habitat ordination. Row crop land use was associated with fine substrates and steep bank angles, whereas wetland land cover and greater sinuosity and catchment land area were associated with complex channel and bank morphology and greater residual pool volume, woody debris, and canopy cover. Thirteen landscape variables were significant predictors of physical habitat variables in multiple linear regressions, with adjusted R 2 values ranging from 0.07 to 0.74. Inclusion of landscape variables with physical habitat variables in multiple regression models predicting fish assemblage metrics and a fish index of biotic integrity resulted in negligible improvements over models based on only physical habitat variables. Physical habitat in wadeable Iowa streams is strongly associated with landscape characteristics. Results of this study and previous studies suggest that (1) landscape factors directly influence physical habitat, (2) physical habitat directly influences fish assemblages, and (3) the influence of landscape factors on fish assemblages is primarily indirect. Understanding how landscape factors, such as human land use, influence physical habitat and fish assemblages will help managers make more informed decisions for improving Iowa\u27s wadeable streams

Identifying core features of adaptive metabolic mechanisms for chronic heat stress attenuation contributing to systems robustness

The contribution of metabolism to heat stress may play a significant role in defining robustness and recovery of systems; either by providing the energy and metabolites required for cellular homeostasis, or through the generation of protective osmolytes. However, the mechanisms by which heat stress attenuation could be adapted through metabolic processes as a stabilizing strategy against thermal stress are still largely unclear. We address this issue through metabolomic and transcriptomic profiles for populations along a thermal cline where two seagrass species, Zostera marina and Zostera noltii, were found in close proximity. Significant changes captured by these profile comparisons could be detected, with a larger response magnitude observed in northern populations to heat stress. Sucrose, fructose, and myo-inositol were identified to be the most responsive of the 29 analyzed organic metabolites. Many key enzymes in the Calvin cycle, glycolysis and pentose phosphate pathways also showed significant differential expression. The reported comparison suggests that adaptive mechanisms are involved through metabolic pathways to dampen the impacts of heat stress, and interactions between the metabolome and proteome should be further investigated in systems biology to understand robust design features against abiotic stress

Testing quantum circuits and detecting insecure encryption

10.1007/978-3-642-35656-8_6Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)7582 LNCS74-8

Computational distinguishability of degradable and antidegradable channels

Quantum Information and Computation109-10735-74