The Sign and Micro-Origin of Complexity as Entropy (Conjectured Resolution of a Paradox)

Evolution produces ever more ordered matter, while also increasing its complexity all the time. There are various ways of measuring complexity, such as Kolmogorov's algorithmic complexity, drawn from information theory, and identified with entropy, enchancing irreversibility in harmony with the second law of thermodynamics. On the other hand, however, the creation of order should have reduced entropy; quoting Schroedinger, it represents "negentropy." To resolve this apparent contradiction we first review a similar set up (though with a totally different interaction) occurring in black holes, a model in which the physics are now explicit and fully understood at the quantum level.     

Microstructure of GaN grown by lateral confined epitaxy 2. GaN on patterned sapphire

Transmission electron microscopy (TEM), atomic force microscopy (AFM), and photoluminescence (PL) spectroscopy were used in order to study the microstructure and optical properties of GaN films grown by metal-organic chemical vapor deposition (MOCVD) on c-plane sapphire by lateral confined epitaxy (LCE). In this method, the substrate is etched prior to growth to form uniform mesas separated by trenches for laterally restricting growth area. As previously observed for LCE GaN on Si(111), the density of threading dislocations was significantly reduced in the areas close to the edge of mesas due to the lateral propagation of the dislocations. Hence, the overall material quality improves with decreasing mesa size, which is consistent with the observed increase in photoluminescence band edge peak intensity. Electron diffraction indicated ∼1° rotation about the [ ] axis between the mesa and trench material, which was also observed in the image contrast of these two regions with g= . Additionally, LCE samples prepared in [ ] and [ ] cross sections were used for comparing the growth rates in these two perpendicular directions. As theoretically expected, growth in the [ ] direction appears to proceed considerably faster than that in the [% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9qqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaig% daceaIYaGbaebacaaIWaaaaa!38D1!\[11\bar 20\]] direction.     

The sharp Hausdorff measure condition for length of projections

In a recent paper, Pertti Mattila asked which gauge functions have the property that for any Borel set with Hausdorff measure 0$">, the projection of to almost every line has positive length. We show that finiteness of , which is known to be sufficient for this property, is also necessary for regularly varying . Our proof is based on a random construction adapted to the gauge function.

     

Immittance-type tabular stability test for 2-D LSI systems based on a zero location test for 1-D complex polynomials

A new algebraic test is developed to determine whether or not a two-variable (2-D) characteristic polynomial of a recursive linear shift invariant (LSI, discrete-time) system is stable (i.e., it does not vanish in the closed exterior of the unit bi-circle). The method is based on the original form of a unit-circle zero location test for one variable (1-D) polynomials with complex coefficients proposed by the author. The test requires the construction of a table, in the form of a sequence of centrosymmetric matrices or 2-D polynomials, that is obtained using a certain three-term recursion, and examination of the zero location with respect to the unit circle of a few associated 1-D polynomials. The minimal set necessary and sufficient conditions for 2-D stability involves one 1-D polynomial whose zeros must reside inside the unit circle (which may be examined before the table is constructed), and one symmetric 1-D polynomial (which becomes available after completing the table) that is required not to have zeros on the unit circle. A larger set of intermediate necessary conditions for stability (which may be examined during the table's construction) are also given. The test compares favorably with Jury's recently improved 2-D stability test in terms of complexity and munerical stability.     

Laser-Based Printing: From Liquids to Microstructures

Assembly of materials into microstructures under laser guidance is attracting wide attention. The ability to pattern various materials and form 2D and 3D structures with micron/sub-micron resolution and less energy and material waste compared with standard top-down methods make laser-based printing promising for many applications, for example medical devices, sensors, and microelectronics. Assembly from liquids provides a smaller feature size than powders and has advantages over other states of matter in terms of relatively simple setup, easy handling, and recycling. However, the simplicity of the setup conceals a variety of underlying mechanisms, which cannot be identified simply according to the starting or resulting materials. This progress report surveys the various mechanisms according to the source of the material—preformed or locally synthesized. Within each category, methods are defined according to the driving force of material deposition. The advantages and limitations of each method are critically discussed, and the methods are compared, shedding light on future directions and developments required to advance this field.     

Implementation of Statistical Process Control for Proteomic Experiments Via LC MS/MS

Statistical process control (SPC) is a robust set of tools that aids in the visualization, detection, and identification of assignable causes of variation in any process that creates products, services, or information. A tool has been developed termed Statistical Process Control in Proteomics (SProCoP) which implements aspects of SPC (e.g., control charts and Pareto analysis) into the Skyline proteomics software. It monitors five quality control metrics in a shotgun or targeted proteomic workflow. None of these metrics require peptide identification. The source code, written in the R statistical language, runs directly from the Skyline interface, which supports the use of raw data files from several of the mass spectrometry vendors. It provides real time evaluation of the chromatographic performance (e.g., retention time reproducibility, peak asymmetry, and resolution), and mass spectrometric performance (targeted peptide ion intensity and mass measurement accuracy for high resolving power instruments) via control charts. Thresholds are experiment- and instrument-specific and are determined empirically from user-defined quality control standards that enable the separation of random noise and systematic error. Finally, Pareto analysis provides a summary of performance metrics and guides the user to metrics with high variance. The utility of these charts to evaluate proteomic experiments is illustrated in two case studies.

Cusp Forms on GL(2n) with GL(n) × GL (n) Periods,and Simple Algebras

The notion of a period of a cusp form on GL(2,D(??)), with respect to the diagonal subgroup D(??)^X × D(??)^X, is defined. Here D is a simple algebra over a global field F with a ring ?? of adeles. For D^x = GL(1), the period is the value at 1/2 of the L-function of the cusp form on GL(2, ??). A cuspidal representation is called cyclic if it contains a cusp form with a non zero period. It is investigated whether the notion of cyclicity is preserved under the Deligne - Kazhdan correspondence, relating cuspidal representations on the group and its split form, where D is a matrix algebra. A local analogue is studied too, using the global technique. The method is based on a new bi-period summation formula. Local multiplicity one statements for spherical distributions, and non - vanishing properties of bi - characters, known only in a few cases, play a key role.     

The rotor-router shape is spherical

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.