New Exhibit at the Zoo

Poetry by Matthew Del Busto

Resolvent Positive Linear Operators Exhibit the Reduction Phenomenon

The spectral bound, s(a A + b V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in b \in R. This is shown here, through an elementary lemma, to imply that s(a A + b V) is also convex in a > 0, and notably, \partial s(a A + b V) / \partial a <= s(A) when it exists. Diffusions typically have s(A) <= 0, so that for diffusions with spatially heterogeneous growth or decay rates, greater mixing reduces growth. Models of the evolution of dispersal in particular have found this result when A is a Laplacian or second-order elliptic operator, or a nonlocal diffusion operator, implying selection for reduced dispersal. These cases are shown here to be part of a single, broadly general, `reduction' phenomenon.Comment: 7 pages, 53 citations. v.3: added citations, corrections in introductory definitions. v.2: Revised abstract, more text, and details in new proof of Lindqvist's inequalit

Dual quantum-correlation paradigms exhibit opposite statistical-mechanical properties

We report opposite statistical mechanical behaviors of the two major paradigms in which quantum correlation measures are defined, viz., the entanglement-separability paradigm and the information-theoretic one. We show this by considering the ergodic properties of such quantum correlation measures in transverse quantum XY spin-1/2 systems in low dimensions. While entanglement measures are ergodic in such models, the quantum correlation measures defined from an information-theoretic perspective can be nonergodic.Comment: 8 pages, 5 figures, REVTeX 4.1; v2: published version, 9 page

Does a Simple Lattice Protein Exhibit Self-Organized Criticality?

There are many unanswered questions when it comes to protein folding. These questions are interesting because the tertiary structure of proteins determines its functionality in living organisms. How do proteins consistently reach their final tertiary structure from the primary sequence of amino acids? What explains the complexity of tertiary structures? Our research uses a simple hydrophobic-polar lattice-bound computational model to investigate self-organized criticality as a possible mechanism for generating complexity in protein folding and protein tertiary structures

Does GRS 1915+105 exhibit "canonical" black-hole states?

We have analysed RXTE data of the superluminal source GRS 1915+105 in order to investigate if, despite its extreme variability, it also exhibits the canonical source states that characterise other black-hole candidates. The phenomenology of GRS 1915+105 has been described in terms of three states (named A, B and C) based on their hardness ratios and position in the colour-colour diagram. We have investigated the connection between these states and the canonical behaviour and found that the shape of the power spectral continuum and the values of the best-fit model parameters to the noise components in all three states indicate that the source shows properties similar to the canonical very high state.Comment: 5 pages, 3 figures, accepted for publication in A&

Aluminum/steel wire composite plates exhibit high tensile strength

Composite plate of fine steel wires imbedded in an aluminum alloy matrix results in a lightweight material with high tensile strength. Plates have been prepared having the strength of titanium with only 85 percent of its density

Do Lattice Protein Simulations Exhibit Self-Organized Criticality?

Proteins are known to fold into tertiary structures that determine their functionality in living organisms. The goal of my research is to better understand the protein folding process through a lattice HP model simulation with a Monte-Carlo based algorithm. Specifically, amino acids in the chain at each time step are allowed to fold to certain locations according to two main criteria: folds must maintain bond length and should be thermally and energetically favorable. This simulation will then be used to examine whether the folding process can be viewed through the lens of self-organized criticality (SOC). In particular, I am interested in whether there are features of the folding process that are independent of the size of the protein. The power law behavior found in SOC systems was not clearly found for the protein lengths studied. Further studies of the model should be investigated