A continued fraction generator for smooth pulse sequences

Digital circuit produces rational output pulse rate at fraction of continuous input pulse rate. Output pulses have average rate with least possible deviation from absolute correct time spacing. Circuit uses include frequency synthesizing, fraction generation, and approximation of irrational sequences

How to centralize and normalize quandle extensions

We show that quandle coverings in the sense of Eisermann form a (regular epi)-reflective subcategory of the category of surjective quandle homomorphisms, both by using arguments coming from categorical Galois theory and by constructing concretely a centralization congruence. Moreover, we show that a similar result holds for normal quandle extensions.Comment: 17 page

Planning in POMDPs Using Multiplicity Automata

Planning and learning in Partially Observable MDPs (POMDPs) are among the most challenging tasks in both the AI and Operation Research communities. Although solutions to these problems are intractable in general, there might be special cases, such as structured POMDPs, which can be solved efficiently. A natural and possibly efficient way to represent a POMDP is through the predictive state representation (PSR) - a representation which recently has been receiving increasing attention. In this work, we relate POMDPs to multiplicity automata- showing that POMDPs can be represented by multiplicity automata with no increase in the representation size. Furthermore, we show that the size of the multiplicity automaton is equal to the rank of the predictive state representation. Therefore, we relate both the predictive state representation and POMDPs to the well-founded multiplicity automata literature. Based on the multiplicity automata representation, we provide a planning algorithm which is exponential only in the multiplicity automata rank rather than the number of states of the POMDP. As a result, whenever the predictive state representation is logarithmic in the standard POMDP representation, our planning algorithm is efficient.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

An electronic model for self-assembled hybrid organic/perovskite semiconductors: reverse band edge electronic states ordering and spin-orbit coupling

Based on density functional theory, the electronic and optical properties of hybrid organic/perovskite crystals are thoroughly investigated. We consider the mono-crystalline 4FPEPI as material model and demonstrate the optical process is governed by three active Bloch states at the {\Gamma} point of the reduced Brillouin zone with a reverse ordering compared to tetrahedrally bonded semiconductors. Giant spin-orbit coupling effects and optical activities are subsequently inferred from symmetry analysis.Comment: 17 pages, 6 figure

Dynamic Approximate All-Pairs Shortest Paths: Breaking the O(mn) Barrier and Derandomization

We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with a total update time of $\tilde O(mn/\epsilon)$ and constant query time by Roditty and Zwick [FOCS 2004]. The fastest deterministic algorithm is from a 1981 paper by Even and Shiloach [JACM 1981]; it has a total update time of $O(mn^2)$ and constant query time. We improve these results as follows: (1) We present an algorithm with a total update time of $\tilde O(n^{5/2}/\epsilon)$ and constant query time that has an additive error of $2$ in addition to the $1+\epsilon$ multiplicative error. This beats the previous $\tilde O(mn/\epsilon)$ time when $m=\Omega(n^{3/2})$. Note that the additive error is unavoidable since, even in the static case, an $O(n^{3-\delta})$-time (a so-called truly subcubic) combinatorial algorithm with $1+\epsilon$ multiplicative error cannot have an additive error less than $2-\epsilon$, unless we make a major breakthrough for Boolean matrix multiplication [Dor et al. FOCS 1996] and many other long-standing problems [Vassilevska Williams and Williams FOCS 2010]. The algorithm can also be turned into a $(2+\epsilon)$-approximation algorithm (without an additive error) with the same time guarantees, improving the recent $(3+\epsilon)$-approximation algorithm with $\tilde O(n^{5/2+O(\sqrt{\log{(1/\epsilon)}/\log n})})$ running time of Bernstein and Roditty [SODA 2011] in terms of both approximation and time guarantees. (2) We present a deterministic algorithm with a total update time of $\tilde O(mn/\epsilon)$ and a query time of $O(\log\log n)$. The algorithm has a multiplicative error of $1+\epsilon$ and gives the first improved deterministic algorithm since 1981. It also answers an open question raised by Bernstein [STOC 2013].Comment: A preliminary version was presented at the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (FOCS 2013

NFAT5 genes are part of the osmotic regulatory system in Atlantic salmon (Salmo salar)

Acknowledgements This study was supported by a grant from the Biotechnology and Biological Sciences Research Council (BBSRC, BB/H008063/1), UK to DGH and SAM. Funding also came from Research Council Norway for project number 241016 for DGH and EJ. This work was carried out as part of a PhD thesis funded by the Marine Alliance of Science and Technology Scotland (MASTS).Peer reviewedPublisher PD

Answer Set Programming for Non-Stationary Markov Decision Processes

Non-stationary domains, where unforeseen changes happen, present a challenge for agents to find an optimal policy for a sequential decision making problem. This work investigates a solution to this problem that combines Markov Decision Processes (MDP) and Reinforcement Learning (RL) with Answer Set Programming (ASP) in a method we call ASP(RL). In this method, Answer Set Programming is used to find the possible trajectories of an MDP, from where Reinforcement Learning is applied to learn the optimal policy of the problem. Results show that ASP(RL) is capable of efficiently finding the optimal solution of an MDP representing non-stationary domains

Electronic energy spectra and wave functions on the square Fibonacci tiling

We study the electronic energy spectra and wave functions on the square Fibonacci tiling, using an off-diagonal tight-binding model, in order to determine the exact nature of the transitions between different spectral behaviors, as well as the scaling of the total bandwidth as it becomes finite. The macroscopic degeneracy of certain energy values in the spectrum is invoked as a possible mechanism for the emergence of extended electronic Bloch wave functions as the dimension changes from one to two