Limiting distributions of the number of pure strategy Nash equilibria in n-person games

We study the number of pure strategy Nash equilibria in a “random” n-person non-cooperative game in which all players have a countable number of strategies. We consider both the cases where all players have strictly and weakly ordinal preferences over their outcomes. For both cases, we show that the distribution of the number of pure strategy Nash equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to infinity. We also find, for each case, the distribution of the number of pure strategy Nash equilibria when the number of strategies of one player goes to infinity, while those of the other players remain finite.     

Context-dependent effects of asparagine glycosylation on Pin WW folding kinetics and thermodynamics

Asparagine glycosylation is one of the most common and important post-translational modifications of proteins in eukaryotic cells. N-glycosylation occurs when a triantennary glycan precursor is transferred en bloc to a nascent polypeptide (harboring the N-X-T/S sequon) as the peptide is cotranslationally translocated into the endoplasmic reticulum (ER). In addition to facilitating binding interactions with components of the ER proteostasis network, N-glycans can also have intrinsic effects on protein folding by directly altering the folding energy landscape. Previous work from our laboratories (Hanson et al. Proc. Natl. Acad. Sci. U.S.A. 2009, 109, 3131-3136; Shental-Bechor, D.; Levy, Y. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 8256-8261) suggested that the three sugar residues closest to the protein are sufficient for accelerating protein folding and stabilizing the resulting structure in vitro; even a monosaccharide can have a dramatic effect. The highly conserved nature of these three proximal sugars in N-glycans led us to speculate that introducing an N-glycosylation site into a protein that is not normally glycosylated would stabilize the protein and increase its folding rate in a manner that does not depend on the presence of specific stabilizing protein-saccharide interactions. Here, we test this hypothesis experimentally and computationally by incorporating an N-linked GlcNAc residue at various positions within the Pin WW domain, a small β-sheet-rich protein. The results show that an increased folding rate and enhanced thermodynamic stability are not general, context-independent consequences of N-glycosylation. Comparison between computational predictions and experimental observations suggests that generic glycan-based excluded volume effects are responsible for the destabilizing effect of glycosylation at highly structured positions. However, this reasoning does not adequately explain the observed destabilizing effect of glycosylation within flexible loops. Our data are consistent with the hypothesis that specific, evolved protein-glycan contacts must also play an important role in mediating the beneficial energetic effects on protein folding that glycosylation can confer.     

Wavelength tunable high power laser using a double-clad Er:Yb doped fiber

We experimentally demonstrated a stable, wavelength-tunable fiber laser using a polarization-maintaining, double-clad Er:Yb doped fiber amplifier in the cavity. The output wavelength is tunable over the range from 1535 to 1567 nm using a fixed grating and the dichroic mirror placed on a rotational mount; under rotation of the dichroic mirror the tuning ratio of 50 nm/deg was found. We studied the wavelength tuning range dependence on the amplifier fiber length and achieved a maximal output power of 850 mW. This configuration can be Q-switched for high peak power and its narrow bandwidth is suitable for nonlinear optics applications, such as parametric teraherthz generator.     

The influence of substrate surface roughness on microstrip transmission line loss using conventional analyses and length‐scale fractal analysis

Two components of conductor topography can impact conductor loss for signals in the GHz frequency range: conductor–ceramic interface roughness and conductor edge angle. This study is an experimental investigation of the influence of these conductor topographies on conductor loss in microstrip circuits produced by thick‐film technology. The aluminum nitride ceramic substrates have different surface roughnesses due to different surface finish processes. The substrate surfaces were characterized using conventional and length‐scale fractal analysis. The conductor–ceramic interface was measured with a contact profilometer. The conductor edge angle and conductor edge profile were measured optically. It was found that there is a direct correlation between conductor loss and conductor edge angle, whereas there is an inverse correlation between loss and substrate roughness or relative length of the conductor–ceramic interface. This is the opposite result to the conventional expectation of surface roughness effects on conductor loss. There is also a negative correlation between conductor edge angle and surface roughness or relative length. The loss behavior can be explained by the interaction of the conductor paste with the surfaces during processing. The paste tends to spread more on the smoother surfaces, and thus creates an elongated edge of diminishing cross‐section and a small edge angle. This leads to greater conductor loss. Copyright © 2009 John Wiley & Sons, Ltd.     

The application of homodyne spectroscopy to the study of low-frequency microturbulence in the TEXT tokamak

Summary The wave propagation direction of microturbulence in a tokamak plasma has been accurately measured by application of a new homodyne spectroscopy technique. This method has been used in conjunction with a collective far-infrared laser scattering experiment on TEXT. The low-frequency density fluctuations are observed to propagate primarily in the electron diamagnetic drift direction, however, the broadband spectra also possess an appreciable level of fluctuations traveling in the ion drift direction. Application of the homodyne spectroscopy technique represents an inexpensive and easily implemented alternative to the more technically demanding heterodyne schemes available in the far-infrared.     

A numerical investigation of transient detonation in granulated material

A two-phase model based upon principles of continuum mixture theory is numerically solved to predict the evolution of detonation in a granulated reactive material. Shock to detonation transition (SDT) is considered whereby combustion is initiated due to compression of the material by a moving piston. In particular, this study demonstrates the existence of a SDT event which gives rise to a steady two-phase Chapman-Jouguet (CJ) detonation structure consisting of a single lead shock in the gas and an unshocked solid; this structure has previously been independently predicted by a steady-state theory. The unsteady model equations, which constitute a non-strictly hyperbolic system, are numerically solved using a modern high-resolution method. The numerical method is based on Godunov's method, and utilizes an approximate solution for the two-phase Riemann problem. Comparisons are made between numerical predictions and known theoretical results for 1) an inert two-phase shock tube problem, 2) an inert compaction wave structure, and 3) a reactive two-phase detonation structure; in all cases, good agreement exists. Received 4 August 1995 / Accepted 17 February 1996     

Bacterial protein structures reveal phylum dependent divergence

Protein sequence space is vast compared to protein fold space. This raises important questions about how structures adapt to evolutionary changes in protein sequences. A growing trend is to regard protein fold space as a continuum rather than a series of discrete structures. From this perspective, homologous protein structures within the same functional classification should reveal a constant rate of structural drift relative to sequence changes. The clusters of orthologous groups (COG) classification system was used to annotate homologous bacterial protein structures in the Protein Data Bank (PDB). The structures and sequences of proteins within each COG were compared against each other to establish their relatedness. As expected, the analysis demonstrates a sharp structural divergence between the bacterial phyla Firmicutes and Proteobacteria. Additionally, each COG had a distinct sequence/structure relationship, indicating that different evolutionary pressures affect the degree of structural divergence. However, our analysis also shows the relative drift rate between sequence identity and structure divergence remains constant.     

Free states of the canonical anticommutation relations

Each gauge invariant generalized free state _A of the anticommutation relation algebra over a complex Hilbert spaceK is characterized by an operatorA onK. It is shown that the cyclic representations induced by two gauge invariant generalized free states _A and _B are quasi-equivalent if and only if the operatorsA ^1/2–B ^1/2 and (I–A)^1/2–(I–B)^1/2 are of Hilbert-Schmidt class. The combination of this result with results from the theory of isomorphisms of von Neumann algebras yield necessary and sufficient conditions for the unitary equivalence of the cyclic representations induced by gauge invariant generalized free states.Work supported in part by US Atomic Energy Commission, under Contract AT (30-1)-2171 and by the National Science Foundation.     

Fast-Fourier-Transform Spectral-Analysis Techniques as a Plasma Fluctuation Diagnostic Tool

A review is given of the key ideas involved in computing power spectral density functions from fast-Fourier-transformed plasma fluctuation data. Next a model is described which enables one to determine, from the computer-generated power spectra, the amplitude, frequency, and wavenumber of each of several waves present in the plasma. The potential of digitally implemented spectral analysis techniques as a plasma diagnostic tool is demonstrated in an experimental study of the evolution, and ultimate turbulent destruction, of a multi-mode drift wave spectrum.