Short, unit-memory, Byte-oriented, binary convolutional codes having maximal free distance

It is shown that (n sub 0, k sub 0) convolutional codes with unit memory always achieve the largest free distance among all codes of the same rate k sub 0/n sub 0 and same number 2MK sub 0 of encoder states, where M is the encoder memory. A unit-memory code with maximal free distance is given at each place where this free distance exceeds that of the best code with k sub 0 and n sub 0 relatively prime, for all Mk sub 0 less than or equal to 6 and for R = 1/2, 1/3, 1/4, 2/3. It is shown that the unit-memory codes are byte-oriented in such a way as to be attractive for use in concatenated coding systems

Real-time minimal bit error probability decoding of convolutional codes

A recursive procedure is derived for decoding of rate R=1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e. fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications such as in the inner coding system for concatenated coding

Relativistic Coulomb Green's function in dd-dimensions

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.Comment: 9 page

Spectral convexity for attractive SU(2N) fermions

We prove a general theorem on spectral convexity with respect to particle number for 2N degenerate components of fermions. The number of spatial dimensions is arbitrary, and the system may be uniform or constrained by an external potential. We assume only that the interactions are governed by an SU(2N)-invariant two-body potential whose Fourier transform is negative definite. The convexity result implies that the ground state is in a 2N-particle clustering phase. We discuss implications for light nuclei as well as asymmetric nuclear matter in neutron stars.Comment: 10 pages, 2 figures; references adde

Map of metastable states for thin circular magnetic nano-cylinders

Nano-magnetic systems of artificially shaped ferromagnetic islands, recently became a popular subject due to their current and potential applications in spintronics, magneto-photonics and superconductivity. When the island size is close to the exchange length of magnetic material (around 15 nm), its magnetic structure becomes markedly different. It determines both static and dynamic magnetic properties of elements, but strongly depends on their shape and size. Here we map this dependence for circular cylindrical islands of a few exchange lengths in size. We outline the region of metastability of "C"-type magnetic states, proving that they are indeed genuine and not a result of pinning on particle imperfections. A way to create the smallest particles with guaranteed magnetic vortex state at zero field becomes evident. It is expected that the map will help focus the efforts in planning of experiments and devices.Comment: 3 pages, 1 figur

Nonlinear dynamic intertwining of rods with self-contact

Twisted marine cables on the sea floor can form highly contorted three-dimensional loops that resemble tangles. Such tangles or hockles are topologically equivalent to the plectomenes that form in supercoiled DNA molecules. The dynamic evolution of these intertwined loops is studied herein using a computational rod model that explicitly accounts for dynamic self-contact. Numerical solutions are presented for an illustrative example of a long rod subjected to increasing twist at one end. The solutions reveal the dynamic evolution of the rod from an initially straight state, through a buckled state in the approximate form of a helix, through the dynamic collapse of this helix into a near-planar loop with one site of self-contact, and the subsequent intertwining of this loop with multiple sites of self-contact. This evolution is controlled by the dynamic conversion of torsional strain energy to bending strain energy or, alternatively by the dynamic conversion of twist (Tw) to writhe (Wr). KEY WORDS Rod Dynamics, Self-contact, Intertwining, DNA Supercoiling, Cable HocklingComment: 35 pages, 9 figures, submitted to Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

Computer programs for prediction of structural vibrations due to fluctuating pressure environments. Volume 1 - Theoretical analyses Final report

Theoretical analyses for computer program to calculate random vibrations of reinforced rectangular cylindrical panels in fluctuating pressure environmen

Knowledge-based vision and simple visual machines

The vast majority of work in machine vision emphasizes the representation of perceived objects and events: it is these internal representations that incorporate the 'knowledge' in knowledge-based vision or form the 'models' in model-based vision. In this paper, we discuss simple machine vision systems developed by artificial evolution rather than traditional engineering design techniques, and note that the task of identifying internal representations within such systems is made difficult by the lack of an operational definition of representation at the causal mechanistic level. Consequently, we question the nature and indeed the existence of representations posited to be used within natural vision systems (i.e. animals). We conclude that representations argued for on a priori grounds by external observers of a particular vision system may well be illusory, and are at best place-holders for yet-to-be-identified causal mechanistic interactions. That is, applying the knowledge-based vision approach in the understanding of evolved systems (machines or animals) may well lead to theories and models that are internally consistent, computationally plausible, and entirely wrong

An Analysis of the Decay B→D∗XℓνˉℓB \rightarrow D^* X \ell \bar\nu_\ell with Predictions from Heavy Quark and Chiral Symmetry

This paper considers the implications of the heavy quark and chiral symmetries for the semi-leptonic decay $B \rightarrow D^* X \ell \bar \nu_\ell$. The general kinematic analysis for decays of the form {\sl pseudoscalar meson $\rightarrow$ vector meson $+$ pseudoscalar meson $+$ lepton $+$ anti-lepton} is presented. This formalism is applied to the above exclusive decay which allows the differential decay rate to be expressed in a form that is ideally suited for the experimental determination of the different form factors for the process through angular distribution measurements. Heavy quark and chiral symmetry predictions for the form factors are presented, and the differential decay rate is calculated in the kinematic region where chiral perturbation theory is valid.Comment: 15 pages, uses jytex.tex and tables.tex; 3 figures not included but available on reques