More on super-replication formulae

We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $\Gamma_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it could be one way to find a connection between modular functions and infinite dimensional Lie algebras.Comment: 28 page

Prediction of protein-protein interaction types using association rule based classification

This article has been made available through the Brunel Open Access Publishing Fund - Copyright @ 2009 Park et alBackground: Protein-protein interactions (PPI) can be classified according to their characteristics into, for example obligate or transient interactions. The identification and characterization of these PPI types may help in the functional annotation of new protein complexes and in the prediction of protein interaction partners by knowledge driven approaches. Results: This work addresses pattern discovery of the interaction sites for four different interaction types to characterize and uses them for the prediction of PPI types employing Association Rule Based Classification (ARBC) which includes association rule generation and posterior classification. We incorporated domain information from protein complexes in SCOP proteins and identified 354 domain-interaction sites. 14 interface properties were calculated from amino acid and secondary structure composition and then used to generate a set of association rules characterizing these domain-interaction sites employing the APRIORI algorithm. Our results regarding the classification of PPI types based on a set of discovered association rules shows that the discriminative ability of association rules can significantly impact on the prediction power of classification models. We also showed that the accuracy of the classification can be improved through the use of structural domain information and also the use of secondary structure content. Conclusion: The advantage of our approach is that we can extract biologically significant information from the interpretation of the discovered association rules in terms of understandability and interpretability of rules. A web application based on our method can be found at http://bioinfo.ssu.ac.kr/~shpark/picasso/SHP was supported by the Korea Research Foundation Grant funded by the Korean Government(KRF-2005-214-E00050). JAR has been supported by the Programme Alβan, the European Union Programme of High level Scholarships for Latin America, scholarship E04D034854CL. SK was supported by Soongsil University Research Fund

Recent progress in mitochondria-targeted drug and drug-free agents for cancer therapy

The mitochondrion is a dynamic eukaryotic organelle that controls lethal and vital functions of the cell. Being a critical center of metabolic activities and involved in many diseases, mitochondria have been attracting attention as a potential target for therapeutics, especially for cancer treatment. Structural and functional differences between healthy and cancerous mitochondria, such as membrane potential, respiratory rate, energy production pathway, and gene mutations, could be employed for the design of selective targeting systems for cancer mitochondria. A number of mitochondria-targeting compounds, including mitochondria-directed conventional drugs, mitochondrial proteins/metabolism-inhibiting agents, and mitochondria-targeted photosensitizers, have been discussed. Recently, certain drug-free approaches have been introduced as an alternative to induce selective cancer mitochondria dysfunction, such as intramitochondrial aggregation, self-assembly, and biomineralization. In this review, we discuss the recent progress in mitochondria-targeted cancer therapy from the conventional approach of drug/cytotoxic agent conjugates to advanced drug-free approaches

The structure of gauge-invariant ideals of labelled graph C∗C^*-algebras

In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple labelled graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged labelled graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share

Industry Leader Premium

The advantage of becoming an industry leader is widely studied. However, how can we measure it? This paper measures how much premium an industry leader has in its valuation through a P/E ratio. The findings suggest industry leaders have significantly higher P/E ratios by 0.65 than their peers. The analysis of earnings forecasts suggests this is not due to their high earnings growth potentials but from other sources. However, in stock recommendations, the premium is not recognised by analysts but interpreted as the sign of over-valuation. The paper contributes the new structure of a P/E ratio by identifying the industry leader premium

M\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation

In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real matrices of determinant one via M\"{o}bius transformations. Our approach is based on a deconvolution technique which relies on the Helgason--Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random M\"{o}bius transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincar\'{e} plane exactly describes the physical system that is of statistical interest.Comment: Published in at http://dx.doi.org/10.1214/09-AOS783 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Summer Sprite for Orchestra

Summer Sprite for Orchestra was completed in December, 2004. The piece originated from a singular encounter with little angels at Chang-Kyung Palace, which is the oldest and the most beautiful palace in Korea, and where the kings of the Chosun Dynasty (1393-1897) lived. This encounter was in the summer of 2002. I certainly could not prove that those angels I met were real. Possibly they were the reflection of drops of water after a sudden shower on that summer day. However, I definitely remember that short, unforgettable, and mysterious moment and the angels' beautiful dance-like celebration. Summer Sprite is based on these special memories and the encounter with the little angels that summer. Summer Sprite consists of 3 movements: "Greeting," "Encounter," and "Celebration." These follow the course of my encounter with the little angels. In Summer Sprite, I wished to describe the image of the angels as well as the progression of greeting, encounter, and celebration with them. The moods that follow in Summer Sprite are by turns lyrical, poetic, fantastic, mysterious, and dream-like. In each movement, I describe the meeting of angels and composer through the use of the soloists -- violin (sometimes viola) and cello. As suggested by the subtitle of the first movement, "Greeting" portrays the moment when a surprised I met the angels. It begins with tam-tam, marimba, harp, and piano and sets a mysterious and dark mood. The second movement, "Encounter," is shorter than the first movement. This movement provides a more tranquil mood as well as more unique timbres resulting from the use of mutes and special instruments (English horn, harp, crotales, suspended cymbal, and celesta). The delicate expression of the percussion is particularly important in establishing the static mood of this movement . The last movement, °?Celebration,°± is bright and energetic. It is also the longest. Here, I require the most delicate changes of dynamics and tempo, the most vigorous harmonies, and the fastest rhythmic figures, as well as the most independent, lyrical, and poetic melodies. For bright orchestral tone color, I used various kinds of percussion such as timpani, xylophone, marimba, vibraphone, cymbals, side drum, tambourine, triangle, and bass drum. This last movement is divided rondo-like into five sections: The first (mm.1-3), second (mm.4 - rehearsal number 1), third (rehearsal numbers 2-4), fourth (rehearsal numbers 5-7), and fifth, (rehearsal numbers 8 -18). To sum up, Summer Sprite describes an unforgettable and mysterious moment in a my life. My intention was to portray this through a concerto-like framework. A model for this would be Brahms°Ø °?Double Concerto°± in A minor, op.102, in which the solo cello stands for my angel and the solo violin (sometimes solo viola) for me