Algorithm and Complexity for a Network Assortativity Measure

We show that finding a graph realization with the minimum Randi\'c index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-Hard. For instances in which the optimal solution to the minimum Randi\'c index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. In our computational experiments, the heuristic performs well and the Randi\'c index of the realization after our heuristic is within 3% of the unconstrained optimal value on average. Although we focus on minimizing the Randi\'c index, our results extend to maximizing the Randi\'c index as well. Applications of the Randi\'c index to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia are provided.Comment: Added additional section on application

Influence of damping and mass-stiffness discontinuities upon the dynamic stability of a free-free beam under a gimballed thrust of periodically-varying magnitude Technical memorandum no. 103

Damping and mass stiffness discontinuity effects on dynamic stability of free-free beam under gimballed pulsating end thrus

Phase behavior of a system of particles with core collapse

The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential in two dimensions is studied. The interaction consists of a hard core plus an additional repulsion at low energies. It is shown that at zero temperature, instead of the expected isostructural transition due to core collapse occurring when increasing pressure, the system passes through a series of ground states that are not triangular lattices. In particular, and depending on parameters, structures with squares, chains, hexagons and even quasicrystalline ground states are found. At finite temperatures the solid-fluid coexistence line presents a zone with negative slope (which implies melting with decreasing in volume) and the fluid phase has a temperature of maximum density, similar to that in water.Comment: 11 pages, 15 figures included. To appear in PRE. Some figures in low quality format. Better ones available upon request from [email protected]

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

Dynamic stability of a flexible booster subjected to a gimbled, periodically-varying end thrust Technical memorandum no. 104

Dynamic structural behavior of large rocket booster synthesized by two thin-walled cylinders and subjected to periodically varying end thrus

Resonance Raman Characterization of the Peroxo and Hydroperoxo Intermediates in Cytochrome P450

Resonance Raman (RR) studies of intermediates generated by cryoreduction of the oxyferrous complex of the D251N mutant of cytochrome P450cam (CYP101) are reported. Owing to the fact that proton delivery to the active site is hindered in this mutant, the unprotonated peroxo-ferric intermediate is observed as the primary species after radiolytic reduction of the oxy-complex in frozen solutions at 77 K. In as much as previous EPR and ENDOR studies have shown that annealing of this species to ∼180 K results in protonation of the distal oxygen atom to form the hydroperoxo intermediate, this system has been exploited to permit direct RR interrogation of the changes in the Fe−O and O−O bonds caused by the reduction and subsequent protonation. Our results show that the ν(O−O) mode decreases from a superoxo-like frequency near ∼1130 cm−1 to 792 cm−1 upon reduction. The latter frequency, as well as its lack of sensitivity to H/D exchange, is consistent with heme-bound peroxide formulation. This species also exhibits a ν(Fe−O) mode, the 553 cm−1 frequency of which is higher than that observed for the nonreduced oxy P450 precursor (537 cm−1), implying a strengthened Fe−O linkage upon reduction. Upon subsequent protonation, the resulting Fe−O−OH fragment exhibits a lowered ν(O−O) mode at 774 cm−1, whereas the ν(Fe−O) increases to 564 cm−1. Both modes exhibit a downshift upon H/D exchange, as expected for a hydroperoxo-ferric formulation. These experimental RR data are compared with those previously acquired for the wild-type protein, and the shifts observed upon reduction and subsequent protonation are discussed with reference to theoretical predictions

Resonance Raman Detection of the Hydroperoxo Intermediate in the Cytochrome P450 Enzymatic Cycle

The resonance Raman spectra of the hydroperoxo complex of camphor-bound CYP101 have been obtained by cryoradiolytic reduction of the oxygenated ferrous form that had been rapidly frozen in water/glycerol frozen solution; EPR spectroscopy was employed to confirm the identity of the trapped intermediate. The ν(O−O) mode, appearing at 799 cm-1, is observed for the first time in a peroxo-heme adduct. It is assigned unambiguously by employing isotopomeric mixtures of oxygen gas containing 50% 16O18O, confirming the presence of an intact O−O fragment. The ν(Fe−O) mode is observed at 559 cm-1 (H2O). Furthermore, both modes shift down by 3 cm-1, documenting the formulation as a hydroperoxo complex, in agreement with EPR data

Phase transitions in social sciences: two-populations mean field theory

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction and conclusions from the social sciences perspectives are drawn

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts

The Explanatory Value of Abstracting Away from Idiosyncratic and Messy Detail

Some explanations are relatively abstract: they abstract away from the idiosyncratic or messy details of the case in hand. The received wisdom in philosophy is that this is a virtue for any explanation to possess. I argue that the apparent consensus on this point is illusory. When philosophers make this claim, they differ on which of four alternative varieties of abstractness they have in mind. What's more, for each variety of abstractness there are several alternative reasons to think that the variety of abstractness in question is a virtue. I identify the most promising reasons, and dismiss some others. The paper concludes by relating this discussion to the idea that explanations in biology, psychology and social science cannot be replaced by relatively micro explanations without loss of understanding.This work has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no 284123.This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s11098-015-0554-