Efficiently Exploring Ordering Problems through Conflict-directed Search

In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy complex hybrid specifications. The ordering problem is thus fundamental to planning. Promising recent works have explored the ordering problem as search, incorporating a special tree structure for efficiency. However, such approaches only reason over partial order specifications. Having observed that an ordering is inconsistent with respect to underlying constraints, prior works do not exploit the tree structure to efficiently generate orderings that resolve the inconsistency. In this paper, we present Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed search method to incrementally and systematically generate event total orders given ordering relations and conflicts returned by sub-solvers. Due to its ability to reason over conflicts, CDITO is much more efficient than Incremental Total Ordering. We demonstrate this by benchmarking on temporal network configuration problems that involve routing network flows and allocating bandwidth resources over time.Comment: Accepted at ICAPS2019. 9 pages, 4 figures, 2 tables

Effect of Local Population Uncertainty on Cooperation in Bacteria

Bacteria populations rely on mechanisms such as quorum sensing to coordinate complex tasks that cannot be achieved by a single bacterium. Quorum sensing is used to measure the local bacteria population density, and it controls cooperation by ensuring that a bacterium only commits the resources for cooperation when it expects its neighbors to reciprocate. This paper proposes a simple model for sharing a resource in a bacterial environment, where knowledge of the population influences each bacterium's behavior. Game theory is used to model the behavioral dynamics, where the net payoff (i.e., utility) for each bacterium is a function of its current behavior and that of the other bacteria. The game is first evaluated with perfect knowledge of the population. Then, the unreliability of diffusion introduces uncertainty in the local population estimate and changes the perceived payoffs. The results demonstrate the sensitivity to the system parameters and how population uncertainty can overcome a lack of explicit coordination.Comment: 5 pages, 6 figures. Will be presented as an invited paper at the 2017 IEEE Information Theory Workshop in November 2017 in Kaohsiung, Taiwa

Nonabelian dark matter: models and constraints

Numerous experimental anomalies hint at the existence of a dark matter (DM) multiplet chi_i with small mass splittings. We survey the simplest such models which arise from DM in the low representations of a new SU(2) gauge symmetry, whose gauge bosons have a small mass mu < 1 GeV. We identify preferred parameters M_chi ~ 1 TeV, mu ~ 100 MeV, alpha_g ~ 0.04 and the chi chi -> 4e annihilation channel, for explaining PAMELA, Fermi, and INTEGRAL/SPI lepton excesses, while remaining consistent with constraints from relic density, diffuse gamma rays and the CMB. This consistency is strengthened if DM annihilations occur mainly in subhalos, while excitations (relevant to the excited DM proposal to explain the 511 keV excess) occur in the galactic center (GC), due to higher velocity dispersions in the GC, induced by baryons. We derive new constraints and predictions which are generic to these models. Notably, decays of excited DM states chi' -> chi gamma arise at one loop and could provide a new signal for INTEGRAL/SPI; big bang nucleosynthesis (BBN) constraints on the density of dark SU(2) gauge bosons imply a lower bound on the mixing parameter epsilon between the SU(2) gauge bosons and photon. These considerations rule out the possibility of the gauge bosons that decay into e^+e^- being long-lived. We study in detail models of doublet, triplet and quintuplet DM, showing that both normal and inverted mass hierarchies can occur, with mass splittings that can be parametrically smaller, e.g., O(100) keV, than the generic MeV scale of splittings. A systematic treatment of Z_2 symmetry which insures the stability of the intermediate DM state is given for cases with inverted mass hierarchy, of interest for boosting the 511 keV signal from the excited dark matter mechanism.Comment: 28 pages, 17 figures; v2. added brief comment, reference

Hierarchical Orthogonal Matrix Generation and Matrix-Vector Multiplications in Rigid Body Simulations

In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body $p$ consisting of $n$ beads, the $6 \times 3n$ transformation matrix $Z$ that maps the force on each bead to $p$'s translational and rotational forces (a $6\times 1$ vector), and $V$ the row space of $Z$, we show how to explicitly construct the $(3n-6) \times 3n$ matrix $\tilde{Q}$ consisting of $(3n-6)$ orthonormal basis vectors of $V^{\perp}$ (orthogonal complement of $V$) using only $\mathcal{O}(n \log n)$ operations and storage. For applications where only the matrix-vector multiplications $\tilde{Q}{\bf v}$ and $\tilde{Q}^T {\bf v}$ are needed, we introduce asymptotically optimal $\mathcal{O}(n)$ hierarchical algorithms without explicitly forming $\tilde{Q}$. Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms