Chaos and Exponentially Localized Eigenstates in Smooth Hamiltonian Systems

We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase space structure around the scarring orbit; indicating sharp localization when the orbit undergoes a pitchfork bifurcation and loses stability.Comment: 7pages including 7 figures. Submitted to PR

Local Scaling in Homogeneous Hamiltonian Systems

We study the local scaling properties associated with straight line periodic orbits in homogeneous Hamiltonian systems, whose stability undergoes repeated oscillations as a function of one parameter. We give strong evidence of local scaling of the Poincar\'{e} section with exponents depending simply on the degree of homogeneity of the potential.Comment: 10 pgs. Plain LaTex, Five Figs. in uuencoded, tar-compressed format. To appear in Phys. Rev. Lett

Influence of high gas production during thermophilic anaerobic digestion in pilot-scale and lab-scale reactors on survival of the thermotolerant pathogens Clostridium perfringens and Campylobacter jejuni in piggery wastewater

Safe reuse of animal wastes to capture energy and nutrients, through anaerobic digestion processes, is becoming an increasingly desirable solution to environmental pollution. Pathogen decay is the most important safety consideration and is in general, improved at elevated temperatures and longer hydraulic residence times. During routine sampling to assess pathogen decay in thermophilic digestion, an inversely proportional relationship between levels of Clostridium perfringens and gas production was observed. Further samples were collected from pilot-scale, bench-scale thermophilic reactors and batch scale vials to assess whether gas production (predominantly methane) could be a useful indicator of decay of the thermotolerant pathogens C. perfringens and Campylobacter jejuni. Pathogen levels did appear to be lower where gas production and levels of methanogens were higher. This was evident at each operating temperature (50, 57, 65 °C) in the pilot-scale thermophilic digesters, although higher temperatures also reduced the numbers of pathogens detected. When methane production was higher, either when feed rate was increased, or pH was lowered from 8.2 (piggery wastewater) to 6.5, lower numbers of pathogens were detected. Although a number of related factors are known to influence the amount and rate of methane production, it may be a useful indicator of the removal of the pathogens C. perfringens and C. jejuni

Classical bifurcations and entanglement in smooth Hamiltonian system

We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near a anti-pitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization that have been much studied in quantum chaos and elsewhere. We also point to an interesting near-degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay of localization and symmetry.Comment: 7 pages, 6 figure

本邦人大腿骨傾斜角度ノレントゲン的測定ニ就テ(第一囘報告)

Once every menstrual cycle, eggs are ovulated into the oviduct where they await fertilization. The ovulated eggs are arrested in metaphase of the second meiotic division, and only complete meiosis upon fertilization. It is crucial that the maintenance of metaphase arrest is tightly controlled, because the spontaneous activation of the egg would preclude the development of a viable embryo (Zhang et al. 2015 J. Genet. Genomics 42, 477-485. (doi:10.1016/j.jgg.2015.07.004); Combelles et al. 2011 Hum. Reprod. 26, 545-552. (doi:10.1093/humrep/deq363); Escrich et al. 2011 J. Assist. Reprod. Genet. 28, 111-117. (doi:10.1007/s10815-010-9493-5)). However, the mechanisms that control the meiotic arrest in mammalian eggs are only poorly understood. Here, we report that a complex of BTG4 and CAF1 safeguards metaphase II arrest in mammalian eggs by deadenylating maternal mRNAs. As a follow-up of our recent high content RNAi screen for meiotic genes (Pfender et al. 2015 Nature 524, 239-242. (doi:10.1038/nature14568)), we identified Btg4 as an essential regulator of metaphase II arrest. Btg4-depleted eggs progress into anaphase II spontaneously before fertilization. BTG4 prevents the progression into anaphase by ensuring that the anaphase-promoting complex/cyclosome (APC/C) is completely inhibited during the arrest. The inhibition of the APC/C relies on EMI2 (Tang et al. 2010 Mol. Biol. Cell 21, 2589-2597. (doi:10.1091/mbc.E09-08-0708); Ohe et al. 2010 Mol. Biol. Cell 21, 905-913. (doi:10.1091/mbc.E09-11-0974)), whose expression is perturbed in the absence of BTG4. BTG4 controls protein expression during metaphase II arrest by forming a complex with the CAF1 deadenylase and we hypothesize that this complex is recruited to the mRNA via interactions between BTG4 and poly(A)-binding proteins. The BTG4-CAF1 complex drives the shortening of the poly(A) tails of a large number of transcripts at the MI-MII transition, and this wave of deadenylation is essential for the arrest in metaphase II. These findings establish a BTG4-dependent pathway for controlling poly(A) tail length during meiosis and identify an unexpected role for mRNA deadenylation in preventing the spontaneous activation of eggs

Engineering Functional Quantum Algorithms

Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m^2log m) elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform.Comment: 4 pages, 2 figure

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include

Case studies to enhance online student evaluation: Bond University – Surveying students online to improve learning and teaching

One of the most sensible ways of improving learning and teaching is to ask the students for feedback. At the end of each teaching period (i.e. semester or term) all universities and many schools survey their students. Usually these surveys are managed online. Questions ask for student perceptions about teaching, assessment and workload. The survey administrators report four common problems

Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.Comment: 12 pages, 7 figures, to appear in Physical Review

Large Scale Cross-Correlations in Internet Traffic

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio