Derivatives of Entropy Rate in Special Families of Hidden Markov Chains

Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Zuk, et. al. [13], [14] showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called ``Black Holes.'' We also discuss in depth special cases of binary Markov chains observed in binary symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell.Comment: The relaxed condtions for entropy rate and examples are taken out (to be part of another paper). The section about general principle and an example to determine the domain of analyticity is taken out (to be part of another paper). A section about binary Markov chains corrupted by binary symmetric noise is adde

Effect of polymer concentration and length of hydrophobic end block on the unimer-micelle transition broadness in amphiphilic ABA symmetric triblock copolymer solutions

The effects of the length of each hydrophobic end block N_{st} and polymer concentration \bar{\phi}_{P} on the transition broadness in amphiphilic ABA symmetric triblock copolymer solutions are studied using the self-consistent field lattice model. When the system is cooled, micelles are observed, i.e.,the homogenous solution (unimer)-micelle transition occurs. When N_{st} is increased, at fixed \bar{\phi}_{P}, micelles occur at higher temperature, and the temperature-dependent range of micellar aggregation and half-width of specific heat peak for unimer-micelle transition increase monotonously. Compared with associative polymers, it is found that the magnitude of the transition broadness is determined by the ratio of hydrophobic to hydrophilic blocks, instead of chain length. When \bar{\phi}_{P} is decreased, given a large N_{st}, the temperature-dependent range of micellar aggregation and half-width of specific heat peak initially decease, and then remain nearly constant. It is shown that the transition broadness is concerned with the changes of the relative magnitudes of the eductions of nonstickers and solvents from micellar cores.Comment: 8 pages, 4 figure

Complexity in Prefix-Free Regular Languages

We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127

The effect of asymmetry of the coil block on self-assembly in ABC coil-rod-coil triblock copolymers

Using the self-consistent field approach, the effect of asymmetry of the coil block on the microphase separation is focused in ABC coil-rod-coil triblock copolymers. For different fractions of the rod block $f_{\text B}$, some stable structures are observed, i.e., lamellae, cylinders, gyroid, and core-shell hexagonal lattice, and the phase diagrams are constructed. The calculated results show that the effect of the coil block fraction $f_{\text A}$ is dependent on $f_{\text B}$. When $f_{\text B}=0.2$, the effect of asymmetry of the coil block is similar to that of the ABC flexible triblock copolymers; When $f_{\text B}=0.4$, the self-assembly of ABC coil-rod-coil triblock copolymers behaves like rod-coil diblock copolymers under some condition. When $f_{\text B}$ continues to increase, the effect of asymmetry of the coil block reduces. For $f_{\text B}=0.4$, under the symmetrical and rather asymmetrical conditions, an increase in the interaction parameter between different components leads to different transitions between cylinders and lamellae. The results indicate some remarkable effect of the chain architecture on self-assembly, and can provide the guidance for the design and synthesis of copolymer materials.Comment: 9 pages, 3 figure

On the Impact of Entity Linking in Microblog Real-Time Filtering

Microblogging is a model of content sharing in which the temporal locality of posts with respect to important events, either of foreseeable or unforeseeable nature, makes applica- tions of real-time filtering of great practical interest. We propose the use of Entity Linking (EL) in order to improve the retrieval effectiveness, by enriching the representation of microblog posts and filtering queries. EL is the process of recognizing in an unstructured text the mention of relevant entities described in a knowledge base. EL of short pieces of text is a difficult task, but it is also a scenario in which the information EL adds to the text can have a substantial impact on the retrieval process. We implement a start-of-the-art filtering method, based on the best systems from the TREC Microblog track realtime adhoc retrieval and filtering tasks , and extend it with a Wikipedia-based EL method. Results show that the use of EL significantly improves over non-EL based versions of the filtering methods.Comment: 6 pages, 1 figure, 1 table. SAC 2015, Salamanca, Spain - April 13 - 17, 201

Towards a grid-enabled simulation framework for nano-CMOS electronics

The electronics design industry is facing major challenges as transistors continue to decrease in size. The next generation of devices will be so small that the position of individual atoms will affect their behaviour. This will cause the transistors on a chip to have highly variable characteristics, which in turn will impact circuit and system design tools. The EPSRC project "Meeting the Design Challenges of Nano-CMOS Electronics" (Nana-CMOS) has been funded to explore this area. In this paper, we describe the distributed data-management and computing framework under development within Nano-CMOS. A key aspect of this framework is the need for robust and reliable security mechanisms that support distributed electronics design groups who wish to collaborate by sharing designs, simulations, workflows, datasets and computation resources. This paper presents the system design, and an early prototype of the project which has been useful in helping us to understand the benefits of such a grid infrastructure. In particular, we also present two typical use cases: user authentication, and execution of large-scale device simulations