Denis Bernard

Bio: Denis Bernard is an academic researcher from École Normale Supérieure. The author has contributed to research in topics: Branching fraction & B meson. The author has an hindex of 75, co-authored 624 publications receiving 20285 citations. Previous affiliations of Denis Bernard include Princeton University & University of Helsinki.

Introduction to classical integrable systems

Abstract: This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Observation of a broad structure in the pi(+)pi(-)J/psi mass spectrum around 4.26 GeV/c(2)

Abstract: We study initial-state radiation events, $e^+e^- \to \gamma_{ISR}\pi^+\pi^-J/\psi$, with data collected with the BaBar detector. We observe an accumulation of events near 4.26 GeV/$c^2$ in the invariant-mass spectrum of $\pi^+\pi^-J/\psi$. Fits of the mass spectrum indicate that a broad resonance with a mass of about 4.26 GeV/$c^2$ is required to describe the observed structure. The presence of additional narrow resonances cannot be excluded. The fitted width of the broad resonance is 50 to 90 MeV/$c^2$, depending on the fit hypothesis.

Study of the B- → J/ΨK -π+π- decay and measurement of the B - → X(3872)K- branching fraction

Abstract: The authors study the decay B{sup -} {yields} J/{psi}K{sup -}{pi}{sup +}{pi}{sup -} using 117 million B{bar B} events collected at the {Upsilon}(4S) resonance with the BaBar detector at the PEP-II e{sup +}e{sup -} asymmetric-energy storage ring. They measure the branching fractions {Beta}(B{sup -} {yields} J/{psi}K{sup -} {pi}{sup +}{pi}{sup -}) = (116 {+-} 7(stat.) {+-} 9(syst.)) x 10{sup -5} and {Beta}(B{sup -} {yields} X(3872)K{sup -}) x {Beta}(X(3872) {yields} J/{psi}{pi}{sup +}{pi}{sup -}) = (1.28 {+-} 0.41) x 10{sup -5} and find the mass of the X(3872) to be 3873.4 {+-} 1.4MeV/c{sup 2}. They search for the h{sub c} narrow state in the decay B{sup -} {yields} h{sub c} K{sup -}, h{sub c} {yields} J/{psi}{pi}{sup +}{pi}{sup -} and for the decay B{sup -} {yields} J/{psi}D{sup 0}{pi}{sup -}, with D{sup 0} {yields} K{sup -}{pi}{sup +}. They set the 90% C.L. limits {Beta}(B{sup -} {yields} h{sub c}K{sup -}) x {Beta}(h{sub c} {yields} J/{psi}{pi}{sup +}{pi}{sup -}) < 3.4 x 10{sup -6} and {Beta}(B{sup -} {yields} J/{psi}D{sup 0}{pi}{sup -}) < 5.2 x 10{sup -5}.

Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory.

Abstract: The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the ``supermultiplets'' of the spectrum in terms of generalized ``occupation numbers.'' We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.

Yang-Baxter equation in long-range interacting systems

Abstract: We consider the su(p) spin chains with long-range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities of the dynamical models and we diagonalise them. In the spin chain case, we establish the connection between the degeneracies of the spectrum and the representation theory of the Yangians. We use a correspondence with the dynamical models to diagonalise the Hamiltonian. Finally, we extend the previous results to the case of a trigonometric R-matrix.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The Structure and Function of Complex Networks

Abstract: Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Network pharmacology: the next paradigm in drug discovery.

Abstract: The dominant paradigm in drug discovery is the concept of designing maximally selective ligands to act on individual drug targets. However, many effective drugs act via modulation of multiple proteins rather than single targets. Advances in systems biology are revealing a phenotypic robustness and a network structure that strongly suggests that exquisitely selective compounds, compared with multitarget drugs, may exhibit lower than desired clinical efficacy. This new appreciation of the role of polypharmacology has significant implications for tackling the two major sources of attrition in drug development--efficacy and toxicity. Integrating network biology and polypharmacology holds the promise of expanding the current opportunity space for druggable targets. However, the rational design of polypharmacology faces considerable challenges in the need for new methods to validate target combinations and optimize multiple structure-activity relationships while maintaining drug-like properties. Advances in these areas are creating the foundation of the next paradigm in drug discovery: network pharmacology.

Classification of topological insulators and superconductors in three spatial dimensions

Abstract: We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial insulators or superconductors in five out of ten symmetry classes introduced in seminal work by Altland and Zirnbauer within the context of random matrix theory, more than a decade ago. One of these is the recently introduced ${\mathbb{Z}}_{2}$ topological insulator in the symplectic (or spin-orbit) symmetry class. We show that there exist precisely four more topological insulators. For these systems, all of which are time-reversal invariant in three dimensions, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. Three of the above five topologically nontrivial phases can be realized as time-reversal invariant superconductors. In these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a two-dimensional surface, they support a number (which may be an arbitrary nonvanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin-rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations of the Hamiltonian that preserve the characteristic discrete symmetries, including disorder. In particular, these surface modes completely evade Anderson localization from random impurities. These topological phases can be thought of as three-dimensional analogs of well-known paired topological phases in two spatial dimensions such as the spinless chiral $({p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y})$-wave superconductor (or Moore-Read Pfaffian state). In the corresponding topologically nontrivial (analogous to ``weak pairing'') and topologically trivial (analogous to ``strong pairing'') 3D phases, the wave functions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the superconducting phases with nonvanishing winding number possess nontrivial topological ground-state degeneracies.