State Complexity of Reversals of Deterministic Finite Automata with Output

We investigate the worst-case state complexity of reversals of deterministic finite automata with output (DFAOs). In these automata, each state is assigned some output value, rather than simply being labelled final or non-final. This directly generalizes the well-studied problem of determining the worst-case state complexity of reversals of ordinary deterministic finite automata. If a DFAO has $n$ states and $k$ possible output values, there is a known upper bound of $k^n$ for the state complexity of reversal. We show this bound can be reached with a ternary input alphabet. We conjecture it cannot be reached with a binary input alphabet except when $k = 2$, and give a lower bound for the case $3 \le k < n$. We prove that the state complexity of reversal depends solely on the transition monoid of the DFAO and the mapping that assigns output values to states.Comment: 18 pages, 3 tables. Added missing affiliation/funding informatio

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Towards the implementation of a sustainable cold chain for the livestock value chain in Bangladesh

The cold chain is essential for food quality and safety. Good management of the postharvest cold chain can reduce food losses. The International Institute of Refrigeration (IIR) estimated that the lack of a cold chain causes significant global food losses of up to 20% of the global food supply (IIR, 2009). Besides economic and health considerations, the environmental sustainability of the food cold supply chain should be considered to prevent further increases in emissions that could potentially increase global warming. This paper presents an assessment of the livestock cold chain related gaps in Bangladesh which is one of the initiative within the World Bank LDDP (Livestock and Dairy Development Project) project (LDDP, P161246). Information on technological and non-technological issues which can be tackled are presented. Practical recommendations to develop the cold chain in Bangladesh for milk and meat are provided

Shuffling cards, factoring numbers, and the quantum baker's map

It is pointed out that an exactly solvable permutation operator, viewed as the quantization of cyclic shifts, is useful in constructing a basis in which to study the quantum baker's map, a paradigm system of quantum chaos. In the basis of this operator the eigenfunctions of the quantum baker's map are compressed by factors of around five or more. We show explicitly its connection to an operator that is closely related to the usual quantum baker's map. This permutation operator has interesting connections to the art of shuffling cards as well as to the quantum factoring algorithm of Shor via the quantum order finding one. Hence we point out that this well-known quantum algorithm makes crucial use of a quantum chaotic operator, or at least one that is close to the quantization of the left-shift, a closeness that we also explore quantitatively.Comment: 12 pgs. Substantially elaborated version, including a new route to the quantum bakers map. To appear in J. Phys.

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

IRMPD spectroscopy sheds new (InfraRed) light on the sulfate pattern of carbohydrates

Contains fulltext : 169008.pdf (publisher's version ) (Closed access

Computing the kk-binomial complexity of the Thue--Morse word

Two words are $k$-binomially equivalent whenever they share the same subwords, i.e., subsequences, of length at most $k$ with the same multiplicities. This is a refinement of both abelian equivalence and the Simon congruence. The $k$-binomial complexity of an infinite word $\mathbf{x}$ maps the integer $n$ to the number of classes in the quotient, by this $k$-binomial equivalence relation, of the set of factors of length $n$ occurring in $\mathbf{x}$. This complexity measure has not been investigated very much. In this paper, we characterize the $k$-binomial complexity of the Thue--Morse word. The result is striking, compared to more familiar complexity functions. Although the Thue--Morse word is aperiodic, its $k$-binomial complexity eventually takes only two values. In this paper, we first obtain general results about the number of occurrences of subwords appearing in iterates of the form $\Psi^\ell(w)$ for an arbitrary morphism $\Psi$. We also thoroughly describe the factors of the Thue--Morse word by introducing a relevant new equivalence relation

A Carbon Nanofilament-Bead Necklace

Carbon nanofilaments with carbon beads grown on their surfaces were successfully synthesized reproducibly by a floating catalyst CVD method. The nanofilaments hosting the pearl-like structures typically show an average diameter of about 60 nm, which mostly consists of low-ordered graphite layers. The beads with diameter range 150−450 nm are composed of hundreds of crumpled and random graphite layers. The mechanism for the formation of these beaded nanofilaments is ascribed to two nucleation processes of the pyrolytic carbon deposition, arising from a temperature gradient between different parts of the reaction chamber. Furthermore, the Raman scattering properties of the beaded nanofilaments have been measured, as well as their confocal Raman G-line images. The Raman spectra reveal that that the trunks of the nanofilaments have better graphitic properties than the beads, which is consistent with the HRTEM analysis. The beaded nanofilaments are expected to have high potential applications in composites, which should exhibit both particle- and fiber-reinforcing functions for the host matrixes

Distinct roles for the IIId2 sub-domain in pestivirus and picornavirus internal ribosome entry sites.

Viral internal ribosomes entry site (IRES) elements coordinate the recruitment of the host translation machinery to direct the initiation of viral protein synthesis. Within hepatitis C virus (HCV)-like IRES elements, the sub-domain IIId(1) is crucial for recruiting the 40S ribosomal subunit. However, some HCV-like IRES elements possess an additional sub-domain, termed IIId2, whose function remains unclear. Herein, we show that IIId2 sub-domains from divergent viruses have different functions. The IIId2 sub-domain present in Seneca valley virus (SVV), a picornavirus, is dispensable for IRES activity, while the IIId2 sub-domains of two pestiviruses, classical swine fever virus (CSFV) and border disease virus (BDV), are required for 80S ribosomes assembly and IRES activity. Unlike in SVV, the deletion of IIId2 from the CSFV and BDV IRES elements impairs initiation of translation by inhibiting the assembly of 80S ribosomes. Consequently, this negatively affects the replication of CSFV and BDV. Finally, we show that the SVV IIId2 sub-domain is required for efficient viral RNA synthesis and growth of SVV, but not for IRES function. This study sheds light on the molecular evolution of viruses by clearly demonstrating that conserved RNA structures, within distantly related RNA viruses, have acquired different roles in the virus life cycles

Parameterized and Approximation Algorithms for the Load Coloring Problem

Let $c, k$ be two positive integers and let $G=(V,E)$ be a graph. The $(c,k)$-Load Coloring Problem (denoted $(c,k)$-LCP) asks whether there is a $c$-coloring $\varphi: V \rightarrow [c]$ such that for every $i \in [c]$, there are at least $k$ edges with both endvertices colored $i$. Gutin and Jones (IPL 2014) studied this problem with $c=2$. They showed $(2,k)$-LCP to be fixed parameter tractable (FPT) with parameter $k$ by obtaining a kernel with at most $7k$ vertices. In this paper, we extend the study to any fixed $c$ by giving both a linear-vertex and a linear-edge kernel. In the particular case of $c=2$, we obtain a kernel with less than $4k$ vertices and less than $8k$ edges. These results imply that for any fixed $c\ge 2$, $(c,k)$-LCP is FPT and that the optimization version of $(c,k)$-LCP (where $k$ is to be maximized) has an approximation algorithm with a constant ratio for any fixed $c\ge 2$