Global Geometry of 3-Body Motions with Vanishing Angular Momentum Ⅰ

Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）.
In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

Deep Task-Based Quantization

Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be significantly improved by processing the signals prior to quantization. However, the design of such hybrid quantizers is quite complex, and their implementation requires complete knowledge of the statistical model of the analog signal. In this work we design data-driven task-oriented quantization systems with scalar ADCs, which determine their analog-to-digital mapping using deep learning tools. These mappings are designed to facilitate the task of recovering underlying information from the quantized signals. By using deep learning, we circumvent the need to explicitly recover the system model and to find the proper quantization rule for it. Our main target application is multiple-input multiple-output (MIMO) communication receivers, which simultaneously acquire a set of analog signals, and are commonly subject to constraints on the number of bits. Our results indicate that, in a MIMO channel estimation setup, the proposed deep task-bask quantizer is capable of approaching the optimal performance limits dictated by indirect rate-distortion theory, achievable using vector quantizers and requiring complete knowledge of the underlying statistical model. Furthermore, for a symbol detection scenario, it is demonstrated that the proposed approach can realize reliable bit-efficient hybrid MIMO receivers capable of setting their quantization rule in light of the task.     

A behavior-oriented model for long-term coastal profile evolution: Validation,identification, and prediction

A behavior-oriented diffusion model, governing the time evolution of the cross-shore position of coastal profiles, is studied. Here, two time-independent, space-varying coefficients, which embody the relevant physical properties, are identified simultaneously. Two sets of real data, the first measured over 10 years at Duck, in NC (USA), the second obtained over 39 years measurements at Delfland (Holland), have been processed numerically by a suitable “inversion algorithm”, earlier developed by the authors. This is based on the minimization of a certain cost functional in order to identify both coefficients. The numerical results, obtained by solving the diffusion equation with the so-determined coefficients, favorably agree with the real data, which fact validates and calibrates somehow the diffusion model under investigation. A short-term prediction is finally obtained for coastal profiles, using such a model.     

Acceleration of randomized Kaczmarz method via the Johnson–Lindenstrauss Lemma

The Kaczmarz method is an algorithm for finding the solution to an overdetermined consistent system of linear equations Ax = b by iteratively projecting onto the solution spaces. The randomized version put forth by Strohmer and Vershynin yields provably exponential convergence in expectation, which for highly overdetermined systems even outperforms the conjugate gradient method. In this article we present a modified version of the randomized Kaczmarz method which at each iteration selects the optimal projection from a randomly chosen set, which in most cases significantly improves the convergence rate. We utilize a Johnson–Lindenstrauss dimension reduction technique to keep the runtime on the same order as the original randomized version, adding only extra preprocessing time. We present a series of empirical studies which demonstrate the remarkable acceleration in convergence to the solution using this modified approach.     

Optimization of improved suspension system with inerter device of the quarter-car model in vibration analysis

In this paper, we analyze an improved suspension system with the incorporated inerter device of the quarter-car model to obtain optimal design parameters for maximum comfort level for a driver and passengers. That is achieved by finding the analytical solution for the system of ordinary differential equations, which enables us to generate an optimization problem whose objective function is based on the international standards of admissible acceleration levels (ISO 2631-1, Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration–Part 1, 1997). The considered approach ensures the highest level of comfort for the driver and passengers due to a favorable reduction in body vibrations. Numerical examples, based on actually measured road profiles, are presented at the end of the paper to prove the validity of the proposed approach and its suitability for the problem at hand.     

Robust Mean-Squared Error Estimation of Multiple Signals in Linear Systems Affected by Model and Noise Uncertainties

This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent of N. The research was partially supported by BSF grant #2002038     

Tobramycin and Nebramine as Pseudo‐oligosaccharide Scaffolds for the Development of Antimicrobial Cationic Amphiphiles

Antimicrobial cationic amphiphiles derived from aminoglycoside pseudo‐oligosaccharide antibiotics interfere with the structure and function of bacterial membranes and offer a promising direction for the development of novel antibiotics. Herein, we report the design and synthesis of cationic amphiphiles derived from the pseudo‐trisaccharide aminoglycoside tobramycin and its pseudo‐disaccharide segment nebramine. Antimicrobial activity, membrane selectivity, mode of action, and structure–activity relationships were studied. Several cationic amphiphiles showed marked antimicrobial activity, and one amphiphilic nebramine derivative proved effective against all of the tested strains of bacteria; furthermore, against several of the tested strains, this compound was well over an order of magnitude more potent than the parent antibiotic tobramycin, the membrane‐targeting antimicrobial peptide mixture gramicidin D, and the cationic lipopeptide polymyxin B, which are in clinical use.     

Variants of the Hajnal-Szemerédi Theorem

The Hajnal-Szemerédi Theorem [Hajnal & Szemerédi, Colloq Math Soc J Bolyai, 1970] states that a graph with hk vertices and minimum degree at least (h − 1)k contains k vertex disjoint copies of K_h. Its proof is not algorithmic. Here, we present an algorithm that, for a fixed h, finds in such a graph k − C(h) vertex disjoint copies of K_h in polynomial time in k, C(h) being a constant depending on h only. The proof suggests a variant of the theorem for h-partite graphs, which is conjectured here and proven in a slightly weaker form in some special cases. © 1999 John Wiley & Sons, Inc. J Graph Theory 31: 275–282, 1999