Sums and products along sparse graphs

In their seminal paper from 1983, Erdős and Szemerédi showed that any n distinct integers induce either n ^1+ɛ distinct sums of pairs or that many distinct products, and conjectured a lower bound of n ^2−o(1). They further proposed a generalization of this problem, in which the sums and products are taken along the edges of a given graph G on n labeled vertices. They conjectured a version of the sum-product theorem for general graphs that have at least n ^1+ɛ edges.     

A performance analysis of channel fragmentation in dynamic spectrum access systems

Dynamic Spectrum Access systems offer temporarily available spectrum to opportunistic users capable of spreading transmissions over a number of non-contiguous subchannels. Such methods can be highly beneficial in terms of spectrum utilization, but excessive fragmentation degrades performance and hence off-sets the benefits. To get some insight into acceptable levels of fragmentation, we present experimental and analytical results derived from a mathematical model. According to the model, a system operates at capacity serving requests for bandwidth by assigning a collection of one or more gaps of unused bandwidth to each request as bandwidth becomes available. Our main result is a proof that, even if fragments can be arbitrarily small, the system remains stable in the sense that the average total number of fragments remains bounded. Within the class of dynamic fragmentation models, including models of dynamic storage allocation that have been around for many decades, this result appears to be the first of its kind. In addition, we provide extensive experimental results that describe behavior, at times unexpected, of fragmentation as parameter values are varied. Different scanning rules for searching gaps of available spectrum, all covered by the above stability result, are also studied. Our model applies to dynamic linked-list storage allocation, and provides a novel analysis in that domain. We prove that, interestingly, a version of the 50?% rule of the classical, non-fragmented allocation model holds for the new model as well. Overall, the paper provides insights into the behavior of practical fragmentation algorithms.     

Electrospinning‐induced shape memory effect in thermoplastic polyurethane characterization and thermoviscoelastic modeling

Electrospun thermoplastic polyurethane (TPU) nanofibers are known to contract considerably (～40%) on heating up to ～90 °C. This study investigates this thermomechanical behavior and the TPU shape memory capabilities. The shape memory effect was first studied in TPU films as a model system by applying classical thermomechanical cycles (programming and recovery). The films were able to fix the applied deformation during long‐term storage at room temperature, well above the material's calorimetric glass transition temperature and in the absence of a percolated structure of hard domains. Structural analysis (Fourier transform infrared, differential scanning calorimeter, and dynamic mechanical analysis) revealed broad thermal transitions indicating the presence of a mixed phase of hard segments dispersed in the soft segment matrix. Using a linear viscoelastic model together with time–temperature superposition, the shape memory effect was attributed to the thermoviscoelastic properties of TPU. In particular, the mixed phase was found to give rise to a very broad relaxation spectrum dominated by long relaxation times, which explains the suppression of strain recovery at room temperature. Finally, the electrospinning process was examined and was found to be similar to a programming cycle characterized by the strong elongation flow accompanied by massive solvent evaporation, whereas the contraction effect was interpreted as the recovery phase in a shape memory perspective. Thus, the contraction of electrospun TPU mats may be considered to be an electrospinning‐induced shape memory effect. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1590–1602     

Neutron multiplicities in inelastic collisions of132Xe with197Au

The multiplicities of neutrons emitted from the light and heavy fragments, respectively, in the inelastic scattering of 7.5 MeV/amu¹³² Xe ions from¹⁹⁷Au have been studied as a function of total energy loss. The measured multiplicity ratios are close to the Au-Xe mass ratio for all Q-values, consistent with a rapid thermalization of the excitation energy. The absolute multiplicity values are lower than expected and suggest significant pre-equilibrium effects.     

Assessment ofBeauveria bassiana Nov. EO-1 strain,which produces a red pigment for microbial control

A new strain of the fungusBeauveria bassiana Nov. EO-1 (ATCC 74037), which produces a red pigment in solid and liquid culture, has been isolated from an infected whitefly. The red pigment was extracted and has been identified by mass spectrometry as oosporein, a potent dibenzoquinone mycotoxin. In order to assess the potential of this entomogenous fungi for microbial control purposes, a mycelium bead formulation was developed as a source for pathogenic conidial spores and oosporein production. The mycelium bead preparation was found to be a stable fungal carrier. Conidiation and germination studies have revealed the mycelium bead viability is 100% over a 1-yr period when stored at 4°C. Conidial spore production from the mycelium beads has been falling substantially per time from an initial value of 1.5 × 10⁸ spores per bead to 3 × 10⁵ spores per bead after a year storage at 4°C. However, the mycelium bead formulation continues to produce oosporein on agar media, at the same intensity throughout the 1 yr period. In in vitro and in vivo small scale greenhouse experimentsBeauveria bassiana Nov. EO-1 were compared with known entomogenous fungi,Beauveria sp. andPaceilomyces sp. Beauveria bassiana Nov. EO-1 was found to have a high pathogenicity against foliage insect pests (e.g., whiteflies and mealy bugs), and against soil insects (e.g., citrus root weevils). The utilization of a mycelium bead based on this strain,Beauveria bassiana Nov. EO-1, as a source of conidial spores and oosporein may have broad applications for the control of various insect pests.     

Cutoff on all Ramanujan graphs

We show that on every Ramanujan graph \({G}\), the simple random walk exhibits cutoff: when \({G}\) has \({n}\) vertices and degree \({d}\), the total-variation distance of the walk from the uniform distribution at time \({t=\frac{d}{d-2} \log_{d-1} n + s\sqrt{\log n}}\) is asymptotically \({{\mathbb{P}}(Z > c \, s)}\) where \({Z}\) is a standard normal variable and \({c=c(d)}\) is an explicit constant. Furthermore, for all \({1 \leq p \leq \infty}\), \({d}\)-regular Ramanujan graphs minimize the asymptotic \({L^p}\)-mixing time for SRW among all \({d}\)-regular graphs. Our proof also shows that, for every vertex \({x}\) in \({G}\) as above, its distance from \({n-o(n)}\) of the vertices is asymptotically \({\log_{d-1} n}\).     

The isoperimetric constant of the random graph process

The isoperimetric constant of a graph G on n vertices, i(G), is the minimum of , taken over all nonempty subsets S ⊂ V (G) of size at most n/2, where ∂S denotes the set of edges with precisely one end in S. A random graph process on n vertices, , is a sequence of graphs, where is the edgeless graph on n vertices, and is the result of adding an edge to , uniformly distributed over all the missing edges. The authors show that in almost every graph process equals the minimal degree of as long as the minimal degree is o(log n). Furthermore, it is shown that this result is essentially best possible, by demonstrating that along the period in which the minimum degree is typically Θ(log n), the ratio between the isoperimetric constant and the minimum degree falls from 1 to , its final value. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Relaxation suppression in a stretched copolymer matrix above Tg

Electrospun thermoplastic polyurethane (TPU) copolymer nanofiber mats are known to contract considerably upon heating up to ～90 °C, whereas cast TPU films expand as expected. This work examined contraction in single electrospun nanofibers. In contrast to nanofiber mats, where mat contraction appears like a critical phenomenon, no temperature threshold for contraction was measured for a single electrospun nanofiber. Unexpectedly, we demonstrate that cast TPU films can also massively contract upon heating, but only after thermomechanical programming which relies on film stretching (～100%) at a high temperature (～90 °C). This nonequilibrium stretched state is highly preserved, despite sample temperatures that significantly exceeded the glass transition temperature of the soft phase, and hard segments concentration in the TPU macromolecules is too low to form a percolated “solid” system. A possible physical explanation of the observed phenomenon is proposed. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1254–1259     

High precision measurements of the temperature dependence of the sound velocity in selected liquid metals

The temperature dependence of the sound velocity in liquid lead, tin, bismuth and antimony has been measured with high precision (errors of less than 0.35%) by the ultrasonic pulse transmission technique. The measurements were performed from the melting temperature to approximately 1000 °C. A smooth temperature dependence of the sound velocity was found in liquid lead and antimony. In liquid lead, a linear dependence with a negative temperature coefficient was observed whereas for liquid antimony the sound velocity displays a distinct maximum. The high precision of the measurements enabled uncovering localized features in the temperature dependence of the sound velocity in liquid tin and bismuth. The measurements provide some information on the temperature dependent structure of the molten state of these four elements.