Minimal Unitary Realizations of Exceptional U-duality Groups and Their Subgroups as Quasiconformal Groups

We study the minimal unitary representations of noncompact exceptional groups that arise as U-duality groups in extended supergravity theories. First we give the unitary realizations of the exceptional group E_{8(-24)} in SU*(8) as well as SU(6,2) covariant bases. E_{8(-24)} has E_7 X SU(2) as its maximal compact subgroup and is the U-duality group of the exceptional supergravity theory in d=3. For the corresponding U-duality group E_{8(8)} of the maximal supergravity theory the minimal realization was given in hep-th/0109005. The minimal unitary realizations of all the lower rank noncompact exceptional groups can be obtained by truncation of those of E_{8(-24)} and E_{8(8)}. By further truncation one can obtain the minimal unitary realizations of all the groups of the "Magic Triangle". We give explicitly the minimal unitary realizations of the exceptional subgroups of E_{8(-24)} as well as other physically interesting subgroups. These minimal unitary realizations correspond, in general, to the quantization of their geometric actions as quasi-conformal groups as defined in hep-th/0008063.Comment: 28 pages. Latex commands removed from the abstract for the arXiv. No changes in the manuscrip

Characterization of two-qubit perfect entanglers

Here we consider perfect entanglers from another perspective. It is shown that there are some {\em special} perfect entanglers which can maximally entangle a {\em full} product basis. We have explicitly constructed a one-parameter family of such entanglers together with the proper product basis that they maximally entangle. This special family of perfect entanglers contains some well-known operators such as {\textsc{cnot}} and {\textsc{dcnot}}, but {\em not} {\small{\sqrt{\rm{\textsc{swap}}}}}. In addition, it is shown that all perfect entanglers with entangling power equal to the maximal value, 2/9, are also special perfect entanglers. It is proved that the one-parameter family is the only possible set of special perfect entanglers. Also we provide an analytic way to implement any arbitrary two-qubit gate, given a proper special perfect entangler supplemented with single-qubit gates. Such these gates are shown to provide a minimum universal gate construction in that just two of them are necessary and sufficient in implementation of a generic two-qubit gate.Comment: 6 pages, 1 eps figur

Minimum orbit dimension for local unitary action on n-qubit pure states

The group of local unitary transformations partitions the space of n-qubit quantum states into orbits, each of which is a differentiable manifold of some dimension. We prove that all orbits of the n-qubit quantum state space have dimension greater than or equal to 3n/2 for n even and greater than or equal to (3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since n-qubit states composed of products of singlets achieve these lowest orbit dimensions.Comment: 19 page

Exploring The Effects Of Genetic Variation On Gene Regulation In Cancer In The Context Of 3D Genome Structure

Background Numerous genome-wide association studies (GWAS) conducted to date revealed genetic variants associated with various diseases, including breast and prostate cancers. Despite the availability of these large-scale data, relatively few variants have been functionally characterized, mainly because the majority of single-nucleotide polymorphisms (SNPs) map to the non-coding regions of the human genome. The functional characterization of these non-coding variants and the identification of their target genes remain challenging. Results In this communication, we explore the potential functional mechanisms of non-coding SNPs by integrating GWAS with the high-resolution chromosome conformation capture (Hi-C) data for breast and prostate cancers. We show that more genetic variants map to regulatory elements through the 3D genome structure than the 1D linear genome lacking physical chromatin interactions. Importantly, the association of enhancers, transcription factors, and their target genes with breast and prostate cancers tends to be higher when these regulatory elements are mapped to high-risk SNPs through spatial interactions compared to simply using a linear proximity. Finally, we demonstrate that topologically associating domains (TADs) carrying high-risk SNPs also contain gene regulatory elements whose association with cancer is generally higher than those belonging to control TADs containing no high-risk variants. Conclusions Our results suggest that many SNPs may contribute to the cancer development by affecting the expression of certain tumor-related genes through long-range chromatin interactions with gene regulatory elements. Integrating large-scale genetic datasets with the 3D genome structure offers an attractive and unique approach to systematically investigate the functional mechanisms of genetic variants in disease risk and progression

Muon capture on light nuclei

This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A=3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9) s^{-1} for A=3, where the uncertainties arise from the adopted fitting procedure.Comment: 6 pages, submitted to Few-Body Sys

Globally controlled universal quantum computation with arbitrary subsystem dimension

We introduce a scheme to perform universal quantum computation in quantum cellular automata (QCA) fashion in arbitrary subsystem dimension (not necessarily finite). The scheme is developed over a one spatial dimension $N$-element array, requiring only mirror symmetric logical encoding and global pulses. A mechanism using ancillary degrees of freedom for subsystem specific measurement is also presented.Comment: 7 pages, 1 figur

Yang-Mills theory for bundle gerbes

Given a bundle gerbe with connection on an oriented Riemannian manifold of dimension at least equal to 3, we formulate and study the associated Yang-Mills equations. When the Riemannian manifold is compact and oriented, we prove the existence of instanton solutions to the equations and also determine the moduli space of instantons, thus giving a complete analysis in this case. We also discuss duality in this context.Comment: Latex2e, 7 pages, some typos corrected, to appear in J. Phys. A: Math. and Ge

Localization of ligand binding site in proteins identified in silico

Knowledge-based models for protein folding assume that the early-stage structural form of a polypeptide is determined by the backbone conformation, followed by hydrophobic collapse. Side chain-side chain interactions, mostly of hydrophobic character, lead to the formation of the hydrophobic core, which seems to stabilize the structure of the protein in its natural environment. The fuzzy-oil-drop model is employed to represent the idealized hydrophobicity distribution in the protein molecule. Comparing it with the one empirically observed in the protein molecule reveals that they are not in agreement. It is shown in this study that the irregularity of hydrophobic distributions is aim-oriented. The character and strength of these irregularities in the organization of the hydrophobic core point to the specificity of a particular protein\u27s structure/function. When the location of these irregularities is determined versus the idealized fuzzy-oil-drop, function-related areas in the protein molecule can be identified. The presented model can also be used to identify ways in which protein-protein complexes can possibly be created. Active sites can be predicted for any protein structure according to the presented model with the free prediction server at http://www.bioinformatics.cm-uj. krakow.pl/activesite. The implication based on the model presented in this work suggests the necessity of active presence of ligand during the protein folding process simulation. © Springer-Verlag 2007

Quantum circuits with uniformly controlled one-qubit gates

Uniformly controlled one-qubit gates are quantum gates which can be represented as direct sums of two-dimensional unitary operators acting on a single qubit. We present a quantum gate array which implements any n-qubit gate of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit gates and a single diagonal n-qubit gate. The circuit is based on the so-called quantum multiplexor, for which we provide a modified construction. We illustrate the versatility of these gates by applying them to the decomposition of a general n-qubit gate and a local state preparation procedure. Moreover, we study their implementation using only nearest-neighbor gates. We give upper bounds for the one-qubit and controlled-NOT gate counts for all the aforementioned applications. In all four cases, the proposed circuit topologies either improve on or achieve the previously reported upper bounds for the gate counts. Thus, they provide the most efficient method for general gate decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some result

An Integrated Network Representation Of Multiple Cancer-Specific Data For Graph-Based Machine Learning

Genomic profiles of cancer cells provide valuable information on genetic alterations in cancer. Several recent studies employed these data to predict the response of cancer cell lines to drug treatment. Nonetheless, due to the multifactorial phenotypes and intricate mechanisms of cancer, the accurate prediction of the effect of pharmacotherapy on a specific cell line based on the genetic information alone is problematic. Emphasizing on the system-level complexity of cancer, we devised a procedure to integrate multiple heterogeneous data, including biological networks, genomics, inhibitor profiling, and gene-disease associations, into a unified graph structure. In order to construct compact, yet information-rich cancer-specific networks, we developed a novel graph reduction algorithm. Driven by not only the topological information, but also the biological knowledge, the graph reduction increases the feature-only entropy while preserving the valuable graph-feature information. Subsequent comparative benchmarking simulations employing a tissue level cross-validation protocol demonstrate that the accuracy of a graph-based predictor of the drug efficacy is 0.68, which is notably higher than those measured for more traditional, matrix-based techniques on the same data. Overall, the non-Euclidean representation of the cancer-specific data improves the performance of machine learning to predict the response of cancer to pharmacotherapy. The generated data are freely available to the academic community at https:/osf.io/dzx7b/