Matrix product states for anyonic systems and efficient simulation of dynamics

Matrix product states (MPS) have proven to be a very successful tool to study lattice systems with local degrees of freedom such as spins or bosons. Topologically ordered systems can support anyonic particles which are labeled by conserved topological charges and collectively carry non-local degrees of freedom. In this paper we extend the formalism of MPS to lattice systems of anyons. The anyonic MPS is constructed from tensors that explicitly conserve topological charge. We describe how to adapt the time-evolving block decimation (TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic TEBD algorithm, we used it to simulate (i) the ground state (using imaginary time evolution) of an infinite 1D critical system of (a) Ising anyons and (b) Fibonacci anyons both of which are well studied, and (ii) the real time dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a ladder geometry with an anyonic flux threading each island of the ladder. Our results pertaining to (ii) give insight into the transport properties of anyons. The anyonic MPS formalism can be readily adapted to study systems with conserved symmetry charges, as this is equivalent to a specialization of the more general anyonic case.Comment: 18 pages, 15 figue

Simulation of braiding anyons using Matrix Product States

Anyons exist as point like particles in two dimensions and carry braid statistics which enable interactions that are independent of the distance between the particles. Except for a relatively few number of models which are analytically tractable, much of the physics of anyons remain still unexplored. In this paper, we show how U(1)-symmetry can be combined with the previously proposed anyonic Matrix Product States to simulate ground states and dynamics of anyonic systems on a lattice at any rational particle number density. We provide proof of principle by studying itinerant anyons on a one dimensional chain where no natural notion of braiding arises and also on a two-leg ladder where the anyons hop between sites and possibly braid. We compare the result of the ground state energies of Fibonacci anyons against hardcore bosons and spinless fermions. In addition, we report the entanglement entropies of the ground states of interacting Fibonacci anyons on a fully filled two-leg ladder at different interaction strength, identifying gapped or gapless points in the parameter space. As an outlook, our approach can also prove useful in studying the time dynamics of a finite number of nonabelian anyons on a finite two-dimensional lattice.Comment: Revised version: 20 pages, 14 captioned figures, 2 new tables. We have moved a significant amount of material concerning symmetric tensors for anyons --- which can be found in prior works --- to Appendices in order to streamline our exposition of the modified Anyonic-U(1) ansat

A Theory of Cheap Control in Embodied Systems

We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machineComment: 27 pages, 10 figure

Hepatic Basolateral Efflux Contributes Significantly to Rosuvastatin Disposition I: Characterization of Basolateral Versus Biliary Clearance Using a Novel Protocol in Sandwich-Cultured Hepatocytes

Basolateral efflux clearance (CLBL) contributes significantly to rosuvastatin (RSV) elimination in sandwich-cultured hepatocytes (SCH). The contribution of CLBL to RSV hepatic elimination was determined in single-pass isolated perfused livers (IPLs) from wild-type (WT) and multidrug resistance–associated protein 2 (Mrp2)-deficient (TR−) rats in the absence and presence of the P-glycoprotein and breast cancer resistance protein (Bcrp) inhibitor, elacridar (GF120918); clearance values were compared with SCH. RSV biliary clearance (CLBile) was ablated almost completely by GF120918 in TR− IPLs, confirming that Mrp2 and Bcrp primarily are responsible for RSV CLBile. RSV appearance in outflow perfusate was attributed primarily to CLBL, which was impaired in TR− IPLs. CLBL was ∼6-fold greater than CLBile in the linear range in WT IPLs in the absence of GF120918. Recovery of unchanged RSV in liver tissue increased in TR− compared with WT (∼25 versus 6% of the administered dose) due to impaired CLBL and CLBile. RSV pentanoic acid, identified by high-resolution liquid chromatography–tandem mass spectroscopy, comprised ∼40% of total liver content and ∼16% of the administered dose in TR− livers at the end of perfusion, compared with ∼30 and 3% in WT livers, consistent with impaired RSV excretion and “shunting” to the metabolic pathway. In vitro–ex vivo extrapolation between WT SCH and IPLs (without GF120918) revealed that uptake clearance and CLBL were 4.2- and 6.4-fold lower, respectively, in rat SCH compared with IPLs; CLBile translated almost directly (1.1-fold). The present IPL data confirmed the significant role of CLBL in RSV hepatic elimination, and demonstrated that both CLBL and CLBile influence RSV hepatic and systemic exposure

Development of a chromium-thoria alloy

Low temperature ductility and high temperature strength of pure chromium and chromium-thoria alloy prepared from vapor deposited powder

Species Differences in Hepatobiliary Disposition of Taurocholic Acid in Human and Rat Sandwich-Cultured Hepatocytes: Implications for Drug-Induced Liver Injury

The bile salt export pump (BSEP) plays an important role in bile acid excretion. Impaired BSEP function may result in liver injury. Bile acids also undergo basolateral efflux, but the relative contributions of biliary (CLBile) versus basolateral efflux (CLBL) clearance to hepatocellular bile acid excretion have not been determined. In the present study, taurocholic acid (TCA; a model bile acid) disposition was characterized in human and rat sandwich-cultured hepatocytes (SCH) combined with pharmacokinetic modeling. In human SCH, biliary excretion of TCA predominated (CLBile = 0.14 ± 0.04 ml/min per g liver; CLBL = 0.042 ± 0.019 ml/min per g liver), whereas CLBile and CLBL contributed approximately equally to TCA hepatocellular excretion in rat SCH (CLBile = 0.34 ± 0.07 ml/min per g liver; CLBL = 0.26 ± 0.07 ml/min per g liver). Troglitazone decreased TCA uptake, CLBile, and CLBL; membrane vesicle assays revealed for the first time that the major metabolite, troglitazone sulfate, was a noncompetitive inhibitor of multidrug resistance–associated protein 4, a basolateral bile acid efflux transporter. Simulations revealed that decreased CLBile led to a greater increase in hepatic TCA exposure in human than in rat SCH. A decrease in both excretory pathways (CLBile and CLBL) exponentially increased hepatic TCA in both species, suggesting that 1) drugs that inhibit both pathways may have a greater risk for hepatotoxicity, and 2) impaired function of an alternate excretory pathway may predispose patients to hepatotoxicity when drugs that inhibit one pathway are administered. Simulations confirmed the protective role of uptake inhibition, suggesting that a drug’s inhibitory effects on bile acid uptake also should be considered when evaluating hepatotoxic potential. Overall, the current study precisely characterized basolateral efflux of TCA, revealed species differences in hepatocellular TCA efflux pathways, and provided insights about altered hepatic bile acid exposure when multiple transport pathways are impaired