On Match Lengths, Zero Entropy and Large Deviations - with Application to Sliding Window Lempel-Ziv Algorithm

The Sliding Window Lempel-Ziv (SWLZ) algorithm that makes use of recurrence times and match lengths has been studied from various perspectives in information theory literature. In this paper, we undertake a finer study of these quantities under two different scenarios, i) \emph{zero entropy} sources that are characterized by strong long-term memory, and ii) the processes with weak memory as described through various mixing conditions. For zero entropy sources, a general statement on match length is obtained. It is used in the proof of almost sure optimality of Fixed Shift Variant of Lempel-Ziv (FSLZ) and SWLZ algorithms given in literature. Through an example of stationary and ergodic processes generated by an irrational rotation we establish that for a window of size $n_w$, a compression ratio given by $O(\frac{\log n_w}{{n_w}^a})$ where $a$ depends on $n_w$ and approaches 1 as $n_w \rightarrow \infty$, is obtained under the application of FSLZ and SWLZ algorithms. Also, we give a general expression for the compression ratio for a class of stationary and ergodic processes with zero entropy. Next, we extend the study of Ornstein and Weiss on the asymptotic behavior of the \emph{normalized} version of recurrence times and establish the \emph{large deviation property} (LDP) for a class of mixing processes. Also, an estimator of entropy based on recurrence times is proposed for which large deviation principle is proved for sources satisfying similar mixing conditions.Comment: accepted to appear in IEEE Transactions on Information Theor

Study of effective interaction from single particle transfer reactions on f-p shell nuclei

The present study concentrates on the average effective two-body interaction matrix elements being extracted, using sum-rule techniques, from transfer reactions on target states having single orbital as well as two orbitaloccupancy. This investigation deals with transfer reactions on f-p shell nuclei involving (i) $1f_{7/2}$ and $2p_{3/2}$ transfer on target states using $^{40}$Ca as inert core, and (ii) $2p_{3/2}$ and$1f_{5/2}$ transfer on states using $^{56}$Ni as core.Comment: 12 pages, ptptex Subj-Classes: Nuclear Shell Structure e-mail:[email protected]

Listen, Attend, and Walk: Neural Mapping of Navigational Instructions to Action Sequences

We propose a neural sequence-to-sequence model for direction following, a task that is essential to realizing effective autonomous agents. Our alignment-based encoder-decoder model with long short-term memory recurrent neural networks (LSTM-RNN) translates natural language instructions to action sequences based upon a representation of the observable world state. We introduce a multi-level aligner that empowers our model to focus on sentence "regions" salient to the current world state by using multiple abstractions of the input sentence. In contrast to existing methods, our model uses no specialized linguistic resources (e.g., parsers) or task-specific annotations (e.g., seed lexicons). It is therefore generalizable, yet still achieves the best results reported to-date on a benchmark single-sentence dataset and competitive results for the limited-training multi-sentence setting. We analyze our model through a series of ablations that elucidate the contributions of the primary components of our model.Comment: To appear at AAAI 2016 (and an extended version of a NIPS 2015 Multimodal Machine Learning workshop paper

Effective two-body interactions in the s-d shell nuclei from sum rules equations in tranfer reactions

Average effective two-body interaction matrix elements in the s-d shell have been extracted, from data on experimentally measured isospin centroids, by combining the recently derived new sum rules equations for pick-up reactions with similar known equations for stripping reactions performed on general multishell target states. Using this combination of stripping and pick-up equations, the average effective matrix elements for the shells, 1d^2_5/2, 2s^2_1/2 and 1d^2_3/2 respectively have been obtained. A new feature of the present work is that the restriction imposed in earlier works on target states, that it be populated only by active neutrons has now been abandoned.Comment: 12 pages, RevTeX, e-mail: [email protected]

Superconducting ceramics in the Bi1.5SrCaCu2O sub x system by melt quenching technique

Bi sub 1.5 SrCaCu sub 2 O sub x has been prepared in the glassy state by rapid quenching of the melt. The kinetics of crystallization of various phases in the glass have been evaluated by a variable heating rate differential scanning calorimetry method. The formation various phases on thermal treatments of the glass has been investigated by powder X-ray diffraction and electrical resistivity measurements. Heating at 450 C formed Bi sub 2 Sr sub 2 CuO sub 6, which disappeared on further heating at 765 C, where Bi sub 2 Sr sub 2 CaCu sub 2 O sub 8 formed. Prolonged heating at 845 C resulted in the formation of a small amount of a phase with T sub c onset of approx. 108 K, believed to be Bi sub 2 Sr sub 2 Ca sub 2 Cu sub 3 O sub 10. This specimen showed zero resistivity at 54 K. The glass ceramic approach could offer several advantages in the fabrication of the high-T sub c superconductors in desired practical shapes such as continuous fibers, wires, tapes, etc