A projective Dirac operator on CP^2 within fuzzy geometry

We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative generalisation within the framework of fuzzy geometry. Along the way we identify the physical spinors and construct the canonical spin_c bundle in this formulation. The chirality operator is also given in two equivalent forms. Finally, using representation theory we obtain the eigenspinors and calculate the full spectrum. We use an argument from the fuzzy complex projective space CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show that our commutative projected spin_c bundle has the correct SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos correcte

Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits

We propose the implementation of a digital quantum simulation of spin chains coupled to bosonic field modes in superconducting circuits. Gates with high fidelities allows one to simulate a variety of Ising magnetic pairing interactions with transverse field, Tavis-Cummings interaction between spins and a bosonic mode, and a spin model with three-body terms. We analyze the feasibility of the implementation in realistic circuit quantum electrodynamics setups, where the interactions are either realized via capacitive couplings or mediated by microwave resonators.Comment: Chapter in R. S. Anderssen et al. (eds.), Mathematics for Industry 11 (Springer Japan, 2015

A holographic model for the fractional quantum Hall effect

Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a modular symmetry group commuting with the renormalization group flow and hence mapping different phases of two-dimensional electron gases into each other. Based on this insight, we construct a phenomenological holographic model which captures many features of the fractional quantum Hall effect. Using an SL(2,Z)-invariant Einstein-Maxwell-axio-dilaton theory capturing the important modular transformation properties of quantum Hall physics, we find dyonic diatonic black hole solutions which are gapped and have a Hall conductivity equal to the filling fraction, as expected for quantum Hall states. We also provide several technical results on the general behavior of the gauge field fluctuations around these dyonic dilatonic black hole solutions: We specify a sufficient criterion for IR normalizability of the fluctuations, demonstrate the preservation of the gap under the SL(2,Z) action, and prove that the singularity of the fluctuation problem in the presence of a magnetic field is an accessory singularity. We finish with a preliminary investigation of the possible IR scaling solutions of our model and some speculations on how they could be important for the observed universality of quantum Hall transitions.Comment: 86 pages, 16 figures; v.2 references added, typos fixed, improved discussion of ref. [39]; v.3 more references added and typos fixed, several statements clarified, v.4 version accepted for publication in JHE

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure

Kinase-targeted cancer therapies: Progress, challenges and future directions

© 2018 The Author(s). The human genome encodes 538 protein kinases that transfer a γ-phosphate group from ATP to serine, threonine, or tyrosine residues. Many of these kinases are associated with human cancer initiation and progression. The recent development of small-molecule kinase inhibitors for the treatment of diverse types of cancer has proven successful in clinical therapy. Significantly, protein kinases are the second most targeted group of drug targets, after the G-protein-coupled receptors. Since the development of the first protein kinase inhibitor, in the early 1980s, 37 kinase inhibitors have received FDA approval for treatment of malignancies such as breast and lung cancer. Furthermore, about 150 kinase-targeted drugs are in clinical phase trials, and many kinase-specific inhibitors are in the preclinical stage of drug development. Nevertheless, many factors confound the clinical efficacy of these molecules. Specific tumor genetics, tumor microenvironment, drug resistance, and pharmacogenomics determine how useful a compound will be in the treatment of a given cancer. This review provides an overview of kinase-targeted drug discovery and development in relation to oncology and highlights the challenges and future potential for kinase-targeted cancer therapies

Scale Dependence of Dark Energy Antigravity

We investigate the effects of negative pressure induced by dark energy (cosmological constant or quintessence) on the dynamics at various astrophysical scales. Negative pressure induces a repulsive term (antigravity) in Newton's law which dominates on large scales. Assuming a value of the cosmological constant consistent with the recent SnIa data we determine the critical scale $r_c$ beyond which antigravity dominates the dynamics ($r_c \sim 1Mpc$) and discuss some of the dynamical effects implied. We show that dynamically induced mass estimates on the scale of the Local Group and beyond are significantly modified due to negative pressure. We also briefly discuss possible dynamical tests (eg effects on local Hubble flow) that can be applied on relatively small scales (a few $Mpc$) to determine the density and equation of state of dark energy.Comment: Contributed talk at the 2nd Hellenic Cosmology Workshop at NOA (Athens) Jan. 2001.To appear in the proceedings. Based on work done in collaboration with M. Axenides and E. Florato