Deterministic soliton automata with at most one cycle

AbstractSoliton valves have been proposed as molecular switching elements. Their mathematical model is the soliton graph and the soliton automaton (Dassow and Jürgensen, J. Comput. System Sci.40 (1990), 154–181). In this paper we continue the study of the logic aspects of soliton switching. There are two cases of special importance: those of deterministic and those of strongly deterministic soliton automata. The former have deterministic state transitions in the usual sense of automaton theory. The latter do not only have deterministic state transitions, but also deterministic soliton paths—a much stronger property, as it turns out. In op cit. a characterization of indecomposable, strongly deterministic soliton automata was proved and it was shown that their transition monoids are primitive groups of permutations. Roughly speaking, the main difference between deterministic and strongly deterministic soliton automata is that in the former the underlying soliton graphs may contain cycles of odd lengths while such cycles are not permitted in the soliton graphs belonging to strongly deterministic soliton automata. In the present paper, we focus on a special class of deterministic soliton automata, that of deterministic soliton automata whose underlying graphs contain at most one cycle. For this class we derive structural descriptions. Our main results concern the elimination of certain types of loops, the treatment of soliton paths with repeated edges, the structure of cycles of odd length, and the transition monoid. As an application we show that the memory element proposed in the literature (Carter, in Bioelectronics, edited by Aizawa, Research and Development Report 50, CMC Press, Denver, CO, 1984) can be transformed in into a soliton tree, thus turning a deterministic device into a logically equivalent strongly deterministic device

Decision Problems For Convex Languages

In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages"). We show that we can decide whether a given language L is prefix-, suffix-, factor-, or subword-convex in polynomial time if L is represented by a DFA, but that the problem is PSPACE-hard if L is represented by an NFA. In the case that a regular language is not convex, we prove tight upper bounds on the length of the shortest words demonstrating this fact, in terms of the number of states of an accepting DFA. Similar results are proved for some subclasses of convex languages: the prefix-, suffix-, factor-, and subword-closed languages, and the prefix-, suffix-, factor-, and subword-free languages.Comment: preliminary version. This version corrected one typo in Section 2.1.1, line

A Fast Algorithm Finding the Shortest Reset Words

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.Comment: COCOON 2013. The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1

Gastrointestinal Tract As Entry Route for Hantavirus Infection

Background: Hantaviruses are zoonotic agents that cause hemorrhagic fevers and are thought to be transmitted to humans by exposure to aerosolized excreta of infected rodents. Puumala virus (PUUV) is the predominant endemic hantavirus in Europe. A large proportion of PUUV-infected patients suffer from gastrointestinal symptoms of unclear origin. In this study we demonstrate that PUUV infection can occur via the alimentary tract. Methods: We investigated susceptibility of the human small intestinal epithelium for PUUV infection and analyzed the resistance of virions to gastric juice. As model for intestinal virus translocation we performed infection experiments with human intestinal Caco-2 monolayers. In animal experiments we infected Syrian hamsters with PUUV via the intragastric route and tested seroconversion and protective immunity against subsequent Andes virus challenge. Results: PUUV retained infectivity in gastric juice at pH >3. The virus invaded Caco-2 monolayers in association with endosomal antigen EEA1, followed by virus replication and loss of epithelial barrier function with basolateral virus occurrence. Cellular disturbance and depletion of the tight junction protein ZO-1 appeared after prolonged infection, leading to paracellular leakage (leak flux diarrhea). Moreover, animal experiments led to dose-dependent seroconversion and protection against lethal Andes virus challenge. Conclusions: We provide evidence that hantavirus can infect the organism via the alimentary tract and suggest a novel aspect of hantavirus infection and pathogenesis. Significance: Hantaviruses are zoonotic pathogens causing severe hemorrhagic fevers worldwide. They are transmitted to humans by small mammals. To date, these viruses were thought to infect exclusively through the airborne route by inhalation of aerosols from infectious animal droppings or by rodent bites. In our work we could show that the alimentary tract is an alternative path of infection for hantaviruses, meaning a new association of virus and disease. These findings have impact on current textbook knowledge and bring many implications for hantavirus epidemiology and outbreak prevention measures

Extraction of 2′-O-apiosyl-6′-O-crotonic acid-betanin from the ayrampo seed (Opuntia soehrensii) cuticle and its use as an emitting layer in an organic light-emitting diode

The molecule 2′-O-apiosyl-6′-O-crotonic acid-betanin (called Achkiy) was obtained after an ecofriendly and low-cost purification process of the extract from the ayrampo seed cuticle. Results from EDS give us an idea of the organic elements present in the ayrampo cuticle layer composed of carbon, oxygen and nitrogen. Further characterization analysis of ayrampo extract by Fourier Transform Infrared Spectrophotometry (FTIR) corroborated the presence of characteristic functional groups corresponding to carboxyl, carbonyls, hydroxyls and secondary amines. On the other hand, we have confirmed by absortion peak the glucose, apiosyl, crotonic acid and betanin at 227 nm, 276 nm, 291 nm and 534 nm bands respectively. Mass Spectrometry (MS) characterization was used finally to identify the electroactive Achkiy molecule. This molecule was tested in an Organic Light Emitting Diode (OLED) achieving a luminance of 4.8 Cd m$^{−2}$ when bias voltage of 16.5 V and a current of 34.1 mA was applied. In addition, the irradiance generated by the Achkiy layer reaches a value of ≈ 113.3 μW m$^{−2}$ emitting light with a λ ≈ 390.10 nm. These preliminary results report an interesting molecule extracted from a natural pigment wich emits light in the blue region

Coherent multi-flavour spin dynamics in a fermionic quantum gas

Microscopic spin interaction processes are fundamental for global static and dynamical magnetic properties of many-body systems. Quantum gases as pure and well isolated systems offer intriguing possibilities to study basic magnetic processes including non-equilibrium dynamics. Here, we report on the realization of a well-controlled fermionic spinor gas in an optical lattice with tunable effective spin ranging from 1/2 to 9/2. We observe long-lived intrinsic spin oscillations and investigate the transition from two-body to many-body dynamics. The latter results in a spin-interaction driven melting of a band insulator. Via an external magnetic field we control the system's dimensionality and tune the spin oscillations in and out of resonance. Our results open new routes to study quantum magnetism of fermionic particles beyond conventional spin 1/2 systems.Comment: 9 pages, 5 figure

Algebraic synchronization criterion and computing reset words

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of synchronizing automata. We express the condition that an automaton is synchronizing in terms of linear algebra, and obtain upper bounds for the reset thresholds of automata with a short word of a small rank. The results are applied to make several improvements in the area. We improve the best general upper bound for reset thresholds of finite prefix codes (Huffman codes): we show that an $n$-state synchronizing decoder has a reset word of length at most $O(n \log^3 n)$. In addition to that, we prove that the expected reset threshold of a uniformly random synchronizing binary $n$-state decoder is at most $O(n \log n)$. We also show that for any non-unary alphabet there exist decoders whose reset threshold is in $\varTheta(n)$. We prove the \v{C}ern\'{y} conjecture for $n$-state automata with a letter of rank at most $\sqrt[3]{6n-6}$. In another corollary, based on the recent results of Nicaud, we show that the probability that the \v{C}ern\'y conjecture does not hold for a random synchronizing binary automaton is exponentially small in terms of the number of states, and also that the expected value of the reset threshold of an $n$-state random synchronizing binary automaton is at most $n^{3/2+o(1)}$. Moreover, reset words of lengths within all of our bounds are computable in polynomial time. We present suitable algorithms for this task for various classes of automata, such as (quasi-)one-cluster and (quasi-)Eulerian automata, for which our results can be applied.Comment: 18 pages, 2 figure

Site-Directed Insertion: Decision Problems, Maximality and Minimality

Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider decision problems and language equations involving site-directed insertion. By relying on the tools provided by semantic shuffle on trajectories we show that one variable equations involving site-directed insertion and regular constants can be solved. We consider also maximal and minimal variants of the site-directed insertion operation