Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations associated with a certain kind of (two-dimensional) ``complex'' geometric object, in the sense in which classical algebraic structures (groups, algebras, Lie algebras and the like) are always implicitly based on (one-dimensional) ``real'' geometric objects. In effect, the standard analogy between point-particle theory and string theory is being shown to manifest itself at a more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling group" have been improve

On compression rate of quantum autoencoders: Control design, numerical and experimental realization

Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the compression rate for a given quantum autoencoder and present a learning control approach for training the autoencoder to achieve the maximal compression rate. The upper bound of the compression rate is theoretically proven using eigen-decomposition and matrix differentiation, which is determined by the eigenvalues of the density matrix representation of the input states. Numerical results on 2-qubit and 3-qubit systems are presented to demonstrate how to train the quantum autoencoder to achieve the theoretically maximal compression, and the training performance using different machine learning algorithms is compared. Experimental results of a quantum autoencoder using quantum optical systems are illustrated for compressing two 2-qubit states into two 1-qubit states

Lorentz-Violating Supergravity

The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with exact Lorentz symmetry and microcausality. For example, the bosonic sfermions have spin 1/2 and the fermionic gauginos have spin 1. The theory is based on a phenomenological action that is shown to follow from a simple microscopic and statistical picture.Comment: 15 pages; to be published in Proceedings of Beyond the Desert 2003 (Castle Ringberg, Tegernsee, Germany, 9-14 June 2003), edited by H. V. Klapdor-Kleingrothau

The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys

The collisionless accretion shock at the outer boundary of a galaxy cluster should primarily heat the ions instead of electrons since they carry most of the kinetic energy of the infalling gas. Near the accretion shock, the density of the intracluster medium is very low and the Coulomb collisional timescale is longer than the accretion timescale. Electrons and ions may not achieve equipartition in these regions. Numerical simulations have shown that the Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can be biased if non-equipartition effects are not properly taken into account. Using a set of hydrodynamical simulations, we have calculated three potential systematic biases in the Y-mass relations introduced by non-equipartition effects during the cross-calibration or self-calibration when using the galaxy cluster abundance technique to constraint cosmological parameters. We then use a semi-analytic technique to estimate the non-equipartition effects on the distribution functions of Y (Y functions) determined from the extended Press-Schechter theory. Depending on the calibration method, we find that non-equipartition effects can induce systematic biases on the Y functions, and the values of the cosmological parameters Omega_8, sigma_8, and the dark energy equation of state parameter w can be biased by a few percent. In particular, non-equipartition effects can introduce an apparent evolution in w of a few percent in all of the systematic cases we considered. Techniques are suggested to take into account the non-equipartition effect empirically when using the cluster abundance technique to study precision cosmology. We conclude that systematic uncertainties in the Y-mass relation of even a few percent can introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical Journal, abstract abridged slightly. Typos corrected in version

Ferromagnetic Quantum Critical Point in CePd2_2P2_2 with Pd →\rightarrow Ni Substitution

An investigation of the structural, thermodynamic, and electronic transport properties of the isoelectronic chemical substitution series Ce(Pd$_{1-x}$Ni$_x$)$_2$P$_2$ is reported, where a possible ferromagnetic quantum critical point is uncovered in the temperature - concentration ($T-x$) phase diagram. This behavior results from the simultaneous contraction of the unit cell volume, which tunes the relative strengths of the Kondo and RKKY interactions, and the introduction of disorder through alloying. Near the critical region at $x_{\rm{cr}}$ $\approx$ 0.7, the rate of contraction of the unit cell volume strengthens, indicating that the cerium $f$-valence crosses over from trivalent to a non-integer value. Consistent with this picture, x-ray absorption spectroscopy measurements reveal that while CePd$_2$P$_2$ has a purely trivalent cerium $f$-state, CeNi$_2$P$_2$ has a small ($<$ 10 \%) tetravalent contribution. In a broad region around $x_{\rm{cr}}$, there is a breakdown of Fermi liquid temperature dependences, signaling the influence of quantum critical fluctuations and disorder effects. Measurements of clean CePd$_2$P$_2$ furthermore show that applied pressure has a similar initial effect to alloying on the ferromagnetic order. From these results, CePd$_2$P$_2$ emerges as a keystone system to test theories such as the Belitz-Kirkpatrick-Vojta model for ferromagnetic quantum criticality, where distinct behaviors are expected in the dirty and clean limits.Comment: 9 pages, 8 figure

In the Shadow of the Transiting Disk: Imaging epsilon Aurigae in Eclipse

Eclipses of the single-line spectroscopic binary star, epsilon Aurigae, provide an opportunity to study the poorly-defined companion. We used the MIRC beam combiner on the CHARA array to create interferometric images during eclipse ingress. Our results demonstrate that the eclipsing body is a dark disk that is opaque and tilted, and therefore exclude alternative models for the system. These data constrain the geometry and masses of the components, providing evidence that the F-star is not a massive supergiant star.Comment: As submitted to Nature. Published in Nature April 8, 2010

Airports at Risk: The Impact of Information Sources on Security Decisions

Security decisions in high risk organizations such as airports involve obtaining ongoing and frequent information about potential threats. Utilizing questionnaire survey data from a sample of airport employees in European Airports across the continent, we analyzed how both formal and informal sources of security information affect employee's decisions to comply with the security rules and directives. This led us to trace information network flows to assess its impact on the degree employees making security decisions comply or deviate with the prescribed security rules. The results of the multivariate analysis showed that security information obtained through formal and informal networks differentially determine if employee will comply or not with the rules. Information sources emanating from the informal network tends to encourage employees to be more flexible in their security decisions while formal sources lead to be more rigid with complying with rules and protocols. These results suggest that alongside the formal administrative structure of airports, there exists a diverse and pervasiveness set of informal communications networks that are a potent factor in determining airport security levels

How consistent are the transcriptome changes associated with cold acclimation in two species of the Drosophila virilis group?

This work was financially support by a Marie Curie Initial Training Network grant, “Understanding the evolutionary origin of biological diversity” (ITN-2008–213780 SPECIATION), grants from the Academy of Finland to A.H. (project 132619) and M.K. (projects 268214 and 272927), a grant from NERC, UK to M.G.R. (grant NE/J020818/1), and NERC, UK PhD studentship to D.J.P. (NE/I528634/1).For many organisms the ability to cold acclimate with the onset of seasonal cold has major implications for their fitness. In insects, where this ability is widespread, the physiological changes associated with increased cold tolerance have been well studied. Despite this, little work has been done to trace changes in gene expression during cold acclimation that lead to an increase in cold tolerance. We used an RNA-Seq approach to investigate this in two species of the Drosophila virilis group. We found that the majority of genes that are differentially expressed during cold acclimation differ between the two species. Despite this, the biological processes associated with the differentially expressed genes were broadly similar in the two species. These included: metabolism, cell membrane composition, and circadian rhythms, which are largely consistent with previous work on cold acclimation/cold tolerance. In addition, we also found evidence of the involvement of the rhodopsin pathway in cold acclimation, a pathway that has been recently linked to thermotaxis. Interestingly, we found no evidence of differential expression of stress genes implying that long-term cold acclimation and short-term stress response may have a different physiological basis.PostprintPeer reviewe

Explosion risk assessment model for underground mine atmosphere

In the coal mining industry, explosions or mine fires present the most hazardous safety threats for coal miners or mine rescue members. Hence, the determination of the mine atmosphere explosibility and its evolution are critical for the success of mine rescues or controlling the severity of a mine accident. However, although there are numbers of methods which can be used to identify the explosibility, none of them could well indicate the change to the explosion risk time evolution. The reason is that the underground sealed atmospheric compositions are so complicated and their dynamical changes are also affected by various influence factors. There is no one method that could well handle all such considerations. Therefore, accurately knowing the mine atmospheric status is still a complicated problem for mining engineers. Method of analyzing the explosion safety margin for an underground sealed atmosphere is urgently desired. This article is going to propose a series of theoretical explosion risk assessment models to fully analyze the evolution of explosion risk in an underground mine atmosphere. Models are based on characteristics of the Coward explosibility diagram with combining mathematical analyzing approaches to address following problems: (1) for an "not-explosive" atmosphere, judging the evolution of explosion risk and estimating the change-of-state time span from "not-explosive" to "explosive" and (2) for an "explosive" atmosphere, estimating the "critical" time span of moving out of explosive zone and stating the best risk mitigation strategy. Such research efforts could not only help mine operators understand the explosibility risk of a sealed mine atmosphere but also provide a useful tool to wisely control explosive atmosphere away from any dangers. In order to demonstrate research findings, case studies for derived models are shown and are also used to instruct readers how to apply them. The results provide useful information for effectively controlling an explosive underground sealed atmosphere