Critical stability constraints for discrete-time linear systems

Critical stability constraints are a small set of conditions that are enough to maintain the stability of a system when some parameters are perturbed from a nominal stable setting. The paper uses a recently introduced efficient integer-preserving (IP) form of the Bistritz test to derive critical constraints for stability of discrete-time linear systems. The new procedure produces polynomial (rather than rational) constraints of particularly low degree whose variates are the free parameters (or the literal coefficients) of the system's characteristic polynomial. Comparison with the modified Jury test, also an efficient IP stability test, shows that the constraints are obtained with less computation and, more contributing to simplicity, the constraints appear as polynomials with degrees lower by a factor of two.     

Constraining the phase of Bs-Bs mixing

New physics contributions to Bs-Bs mixing can be parametrized by the size (rs2) and the phase (2thetas) of the total mixing amplitude relative to the standard model amplitude. The phase has so far been unconstrained. We first use the D0 measurement of the semileptonic CP asymmetry ASL to obtain the first constraint on the semileptonic CP asymmetry in Bs decays, ASLs=-0.008+/-0.011. Then we combine recent measurements by the CDF and D0 Collaborations--the mass difference (DeltaMs), the width difference (DeltaGammas), and ASL;s--to constrain 2thetas. The errors on DeltaGammas and ASL;s should still be reduced to have a sensitive probe of the phase, yet the central values are such that the regions around 2thetas approximately 3pi/2 and, in particular, 2thetas approximately pi/2, are disfavored.     

Towards a dephasing diode: asymmetric and geometric dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.     

Random walks in varying dimensions

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogeneous random walks in the plane which interlace two symmetric step distributions of bounded support.Research partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.Research supported in part by National Science Foundation Grant No. DMS 9300191, by a Sloan Foundation Fellowship, and by a Presidential Faculty Fellowship.     

Self-similar amplification in fiber Bragg gratings written in fiber amplifiers

We show, by using numerical simulations, that self-similar pulses with a duration on the order of few nanoseconds and an energy on the order of 10?μJ can be obtained at the output of a fiber Bragg grating (FBG) written in a fiber amplifier. The evolution of the amplified pulses is determined by the combined effect of Kerr nonlinearity, normal-dispersion, gain, and gain saturation, which limit the pulse energy. The output pulse mainly depends on the initial pulse energy rather than on the initial pulse profile. The reduced group velocity in FBGs can significantly increase the total gain for a given amplifier length. Hence we find that the proposed amplification scheme can be highly advantageous for amplification of nanosecond-scale pulses in fiber amplifiers.     

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.     

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.     

Adaptive versus Non-Adaptive Security of Multi-Party Protocols

Security analysis of multi-party cryptographic protocols distinguishes between two types of adversarial settings: In the non-adaptive setting the set of corrupted parties is chosen in advance, before the interaction begins. In the adaptive setting the adversary chooses who to corrupt during the course of the computation. We study the relations between adaptive security (i.e., security in the adaptive setting) and nonadaptive security, according to two definitions and in several models of computation.     

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.     

Upper bound on the characters of the symmetric groups

Let C be a conjugacy class in the symmetric group S _n , and λ be a partition of n. Let f ^λ be the degree of the irreducible representation S ^λ , χ ^λ (C)– the character of S ^λ at C, and r ^λ (C)– the normalized character χ ^λ (C) f ^λ . We prove that there exist constants b > 0 and 1 > q > 0 such that for n > 4, for every conjugacy class C in S _n and every irreducible representation S ^λ of S _n ∣r ^λ (C)∣≦ ( max {q,λ ₁ n, λ ₁ ′ n}) ^{b ⋅ supp(C)} where supp (C) is the number of non-fixed digits under the action of a permutation in C, λ ₁ is the size of the largest part in λ, and λ ₁ ′ is the number of parts in λ. The proof is obtained by enumeration of rim hook tableaux, the Hook formula and probabilistic arguments. Combinatorial, algebraic and statistical applications follow this result. In particular, we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes. Oblatum 14-III-1995 & 30-X-1995