Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with Imprecision

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed - smaller - state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality.Comment: 9th International Conference on Soft Methods in Probability and Statistics (SMPS 2018

Zero-temperature phase diagram of binary boson-fermion mixtures

We calculate the phase diagram for dilute mixtures of bosons and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: a) a single uniform phase, b) a purely fermionic phase coexisting with a purely bosonic one and c) a purely fermionic phase coexisting with a mixed phase.Comment: 8 pages, revtex, 3 postscript figures; NORDITA-1999/71 C

Development of Grb2 SH2 Domain Signaling Antagonists: A Potential New Class of Antiproliferative Agents

Aberrant signaling through protein-tyrosine kinase (PTK)-dependent pathways is associated with several proliferative diseases. Accordingly, PTK inhibitors are being developed as new approaches for the treatment of certain cancers. Growth factor receptor bound protein 2 (Grb2) is an important downstream mediator of PTK signaling that serves obligatory roles in many pathogenic processes. One of the primary functions of Grb2 is to bind to specific phosphotyrosyl (pTyr)-containing sequences through its Src homology 2 (SH2) domain. Agents that bind to the Grb2 SH2 domain and prevent its normal function could disrupt associated PTK signaling and serve as alternatives to kinase-directed inhibitors. Starting from the X-ray crystal structure of a lead peptide bound to the Grb2 SH2 domain, this review will summarize important contributions to these efforts. The presentation will be thematically arranged according to the region of peptide modified, proceeding from the N-terminus to the C-terminus, with a special section devoted to aspects of conformational constraint

Ferromagnetism in a lattice of Bose condensates

We show that an ensemble of spinor Bose-Einstein condensates confined in a one dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.Comment: 4 pages, 2 figure

Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences—here limited to determining marginal or limit expectations—becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed—smaller—state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality

Measurement of relative phase diffusion between two Bose-Einstein condensates

We propose a method of measuring diffusion of the relative phase between two Bose-Einstein condensates occupying different nuclear or spin hyperfine states coupled by a two-photon transition via an intermediate level. Due to the macroscopic quantum coherence the condensates can be decoupled from the electromagnetic fields. The rate of decoherence and the phase collapse may be determined from the occupation of the intermediate level or the absorption of radiation.Comment: 4 pages, RevTex, 2 ps figure

Quantum tunneling across spin domains in a Bose-Einstein condensate

Quantum tunneling was observed in the decay of metastable spin domains in gaseous Bose-Einstein condensates. A mean-field description of the tunneling was developed and compared with measurement. The tunneling rates are a sensitive probe of the boundary between spin domains, and indicate a spin structure in the boundary between spin domains which is prohibited in the bulk fluid. These experiments were performed with optically trapped F=1 spinor Bose-Einstein condensates of sodium.Comment: 5 pages, 4 figure

Vortices in a Bose-Einstein Condensate

We have created vortices in two-component Bose-Einstein condensates. The vortex state was created through a coherent process involving the spatial and temporal control of interconversion between the two components. Using an interference technique, we map the phase of the vortex state to confirm that it possesses angular momentum. We can create vortices in either of the two components and have observed differences in the dynamics and stability.Comment: 4 pages with 3 figure

Calculations of collisions between cold alkaline earth atoms in a weak laser field

We calculate the light-induced collisional loss of laser-cooled and trapped magnesium atoms for detunings up to 50 atomic linewidths to the red of the ^1S_0-^1P_1 cooling transition. We evaluate loss rate coefficients due to both radiative and nonradiative state-changing mechanisms for temperatures at and below the Doppler cooling temperature. We solve the Schrodinger equation with a complex potential to represent spontaneous decay, but also give analytic models for various limits. Vibrational structure due to molecular photoassociation is present in the trap loss spectrum. Relatively broad structure due to absorption to the Mg_2 ^1Sigma_u state occurs for detunings larger than about 10 atomic linewidths. Much sharper structure, especially evident at low temperature, occurs even at smaller detunings due to of Mg_2 ^1Pi_g absorption, which is weakly allowed due to relativistic retardation corrections to the forbidden dipole transition strength. We also perform model studies for the other alkaline earth species Ca, Sr, and Ba and for Yb, and find similar qualitative behavior as for Mg.Comment: 20 pages, RevTex, 13 eps figures embedde