Stability of the Chari-Pressley-Loktev bases for local Weyl modules of sl2[t]sl_2[t]

We prove stability of the Chari-Pressley-Loktev bases for natural inclusions of local Weyl modules of the current algebra $sl_2[t]$. These modules being known to be Demazure submodules in the level 1 representations of the affine Lie algebra $\widehat{sl_2}$, we obtain, by passage to the direct limit, bases for the level 1 representations themselves.Comment: 20 pages; minor revision

A Better Good-Turing Estimator for Sequence Probabilities

We consider the problem of estimating the probability of an observed string drawn i.i.d. from an unknown distribution. The key feature of our study is that the length of the observed string is assumed to be of the same order as the size of the underlying alphabet. In this setting, many letters are unseen and the empirical distribution tends to overestimate the probability of the observed letters. To overcome this problem, the traditional approach to probability estimation is to use the classical Good-Turing estimator. We introduce a natural scaling model and use it to show that the Good-Turing sequence probability estimator is not consistent. We then introduce a novel sequence probability estimator that is indeed consistent under the natural scaling model.Comment: ISIT 2007, to appea

A Method for Dynamic Characterization and Response Prediction Using Ground Vibration Test(GVT)Data for Unknown Structures.

The Objective Of This Proposed Work Is To Develop A Reliable Method For Dynamic Characterization And Prediction Of Dynamic Response Of Structures Of Known/Unknown Configurations, By Processing The Free Vibration Data Generated Experimentally From The Ground Vibration Tests (GVT)Of The Prototype Vehicles. The Methodology Would Make Use Of The Measured Dynamic Data In Terms Of Mode Shapes, Natural Frequencies, Modal Damping, Point Impedances Etc.And Generate Modal (Scaled) Stiffness And Inertia Information That Will Be Used For Prediction Of Response Characteristics Of The Prototype Structure . With These Objectives, The Present Work Develops The Mathematical Formulation Of The Method, And Demonstrates Its Reliability By Performing The Experiment On A Simple Cantilever Beam To Determine Its Dynamic Characteristics. Results On Scaled Modal Stiffness And Inertia, Generated Through The Method Using Experimental (GVT) Data Show Excellent Agreement With Those Generated By FE And Analytical Models .It Must Be Noted That A Valid Benchmarking Is Performed With The Condition That The Experimental Procedure Is 'Blind' To The Actual Stiffness And Inertia Distributions As Used In FEM Or Analytical Models . Agreement Of The Predicted Response Of The Structure With That From Direct Experiment And Those From The FE And Analytical Models Indicates That This Method Will Be A Promising Tool To Predict The Dynamic And Aeroelastic Characteristics Of Any Prototype Vehicle In The Future. Once The Reliability Of The Method Is Established,It Can Be Extended To Determine The Dynamic And Aeroelastic Characteristics Of All Aircraft For Which Dynamic Characteristics Are Available From A Ground -; Vibration Test (GVT)

Stable manifolds and homoclinic points near resonances in the restricted three-body problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with $q/p$ equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ small enough in the unaveraged restricted three-body problem

Weak ties: Subtle role of information diffusion in online social networks

As a social media, online social networks play a vital role in the social information diffusion. However, due to its unique complexity, the mechanism of the diffusion in online social networks is different from the ones in other types of networks and remains unclear to us. Meanwhile, few works have been done to reveal the coupled dynamics of both the structure and the diffusion of online social networks. To this end, in this paper, we propose a model to investigate how the structure is coupled with the diffusion in online social networks from the view of weak ties. Through numerical experiments on large-scale online social networks, we find that in contrast to some previous research results, selecting weak ties preferentially to republish cannot make the information diffuse quickly, while random selection can achieve this goal. However, when we remove the weak ties gradually, the coverage of the information will drop sharply even in the case of random selection. We also give a reasonable explanation for this by extra analysis and experiments. Finally, we conclude that weak ties play a subtle role in the information diffusion in online social networks. On one hand, they act as bridges to connect isolated local communities together and break through the local trapping of the information. On the other hand, selecting them as preferential paths to republish cannot help the information spread further in the network. As a result, weak ties might be of use in the control of the virus spread and the private information diffusion in real-world applications.Comment: Final version published in PR

Specific Antibodies to Recombinant Allergens of \u3cem\u3eAspergillus fumigatus\u3c/em\u3e in Cystic Fibrosis Patients with ABPA

Background Aspergillus fumigatus, a widely distributed fungus, has been implicated in causing life threatening infections as well as severe asthma and allergic diseases in man. Allergic affliction like allergic bronchopulmonary aspergillosis (ABPA) is a disabling lung disease frequently seen in patients with asthma and cystic fibrosis. Immunodiagnosis of the former is comparatively easier due to the availability of purified antigens and sensitive methods. However, this is not true with cystic fibrosis patients where the prevalence of ABPA is fairly high and the morbidity and mortality are significant. Methods In the present study, we have evaluated purified recombinant allergens from A. fumigatus, namely Asp f 1, f 2, f 3, f 4, and f 6 using ELISA and a semi-automated method (ImmunoCAP). We studied 17 patients each from cystic fibrosis with ABPA, and cystic fibrosis with asthma, 22 cystic fibrosis with no ABPA or asthma, and 11 age matched controls. Results The results indicate that no antigen, antibody or method is capable of differentiating cystic fibrosis (CF) with ABPA from other CF patients, although some allergens showed strong reaction or showed more prevalence among the patients studied. Conclusion When results of several allergens such as Asp f 1, f 2, f 3, f 4, and f 6 in their binding to IgA, IgG, and IgE antibodies were analyzed, a more strong discrimination of CF patients with ABPA was possible from the other groups studied

Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from author