On the equivalence of dynamically orthogonal and bi-orthogonal methods: Theory and numerical simulations

The Karhunen–Lòeve (KL) decomposition provides a low-dimensional representation for random fields as it is optimal in the mean square sense. Although for many stochastic systems of practical interest, described by stochastic partial differential equations (SPDEs), solutions possess this low-dimensional character, they also have a strongly time-dependent form and to this end a fixed-in-time basis may not describe the solution in an efficient way. Motivated by this limitation of standard KL expansion, Sapsis and Lermusiaux (2009) [26] developed the dynamically orthogonal (DO) field equations which allow for the simultaneous evolution of both the spatial basis where uncertainty ‘lives’ but also the stochastic characteristics of uncertainty. Recently, Cheng et al. (2013) [28] introduced an alternative approach, the bi-orthogonal (BO) method, which performs the exact same tasks, i.e. it evolves the spatial basis and the stochastic characteristics of uncertainty. In the current work we examine the relation of the two approaches and we prove theoretically and illustrate numerically their equivalence, in the sense that one method is an exact reformulation of the other. We show this by deriving a linear and invertible transformation matrix described by a matrix differential equation that connects the BO and the DO solutions. We also examine a pathology of the BO equations that occurs when two eigenvalues of the solution cross, resulting in an instantaneous, infinite-speed, internal rotation of the computed spatial basis. We demonstrate that despite the instantaneous duration of the singularity this has important implications on the numerical performance of the BO approach. On the other hand, it is observed that the BO is more stable in nonlinear problems involving a relatively large number of modes. Several examples, linear and nonlinear, are presented to illustrate the DO and BO methods as well as their equivalence.National Science Foundation (U.S.) (NSF/DMS (DMS-1216437))Pacific Northwest National Laboratory (U.S.). Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4) (DOE (DE-SC0009247))United States. Dept. of Defense (OSD/MURI (FA9550-09-1-0613)

Strain-tuned enhancement of ferromagnetic TC_{C} to 176 K in Sm-doped BiMnO3_{3} thin films and determination of magnetic phase diagram

BiMnO$_{3}$ is a promising multiferroic material but it’s ferromagnetic T$_{C}$ is well below room temperature and the magnetic phase diagram is unknown. In this work, the relationship between magnetic transition temperature (T$_{C}$) and the substrate induced (pseudo-) tetragonal distortion (ratio of out-of-plane to in-plane lattice parameters, c/a) in BiMnO$_{3}$ thin films, lightly doped to optimize lattice dimensions, was determined. For c/a > 0.99, hidden antiferromagnetism was revealed and the magnetisation versus temperature curves showed a tail behaviour, whereas for c/a < 0.99 clear ferromagnetism was observed. A peak T$_{C}$ of up to 176 K, more than 70 K higher than for bulk BiMnO$_{3}$, was achieved through precise strain tuning. The T$_{C}$ was maximised for strong tensile in-plane strain which produced weak octahedral rotations in the out-of-plane direction, an orthorhombic-like structure, and strong ferromagnetic coupling.This work was supported by the European Research Council (ERC) (Advanced Investigator grant ERC-2009-AdG-247276-NOVOX), the Engineering and Physical Sciences Research Council (EPSRC) (Equipment Account Grant EP/K035282/1) and the Isaac Newton Trust (Minute 13.38(k))

Mean-Payoff Optimization in Continuous-Time Markov Chains with Parametric Alarms

Continuous-time Markov chains with alarms (ACTMCs) allow for alarm events that can be non-exponentially distributed. Within parametric ACTMCs, the parameters of alarm-event distributions are not given explicitly and can be subject of parameter synthesis. An algorithm solving the $\varepsilon$-optimal parameter synthesis problem for parametric ACTMCs with long-run average optimization objectives is presented. Our approach is based on reduction of the problem to finding long-run average optimal strategies in semi-Markov decision processes (semi-MDPs) and sufficient discretization of parameter (i.e., action) space. Since the set of actions in the discretized semi-MDP can be very large, a straightforward approach based on explicit action-space construction fails to solve even simple instances of the problem. The presented algorithm uses an enhanced policy iteration on symbolic representations of the action space. The soundness of the algorithm is established for parametric ACTMCs with alarm-event distributions satisfying four mild assumptions that are shown to hold for uniform, Dirac and Weibull distributions in particular, but are satisfied for many other distributions as well. An experimental implementation shows that the symbolic technique substantially improves the efficiency of the synthesis algorithm and allows to solve instances of realistic size.Comment: This article is a full version of a paper accepted to the Conference on Quantitative Evaluation of SysTems (QEST) 201

Optimizing Performance of Continuous-Time Stochastic Systems using Timeout Synthesis

We consider parametric version of fixed-delay continuous-time Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters

Role of domain walls in the abnormal photovoltaic effect in BiFeO3

Recently, the anomalous photovoltaic (PV) effect in BiFeO3 (BFO) thin films, which resulted in open circuit voltages (V-oc) considerably larger than the band gap of the material, has generated a revival of the entire field of photoferroelectrics. Here, via temperature-dependent PV studies, we prove that the bulk photovoltaic (BPV) effect, which has been studied in the past for many non-centrosymmetric materials, is at the origin of the anomalous PV effect in BFO films. Moreover, we show that irrespective of the measurement geometry, V-oc as high as 50V can be achieved by controlling the conductivity of domain walls (DW). We also show that photoconductivity of the DW is markedly higher than in the bulk of BFO

Coherent Electron-Phonon Coupling in Tailored Quantum Systems

The coupling between a two-level system and its environment leads to decoherence. Within the context of coherent manipulation of electronic or quasiparticle states in nanostructures, it is crucial to understand the sources of decoherence. Here, we study the effect of electron-phonon coupling in a graphene and an InAs nanowire double quantum dot. Our measurements reveal oscillations of the double quantum dot current periodic in energy detuning between the two levels. These periodic peaks are more pronounced in the nanowire than in graphene, and disappear when the temperature is increased. We attribute the oscillations to an interference effect between two alternative inelastic decay paths involving acoustic phonons present in these materials. This interpretation predicts the oscillations to wash out when temperature is increased, as observed experimentally.Comment: 11 pages, 4 figure

Direct materials deposition: designed macro and microstructure

Solid freeform fabrication of engineering materials is now possible using the Direct Metal Deposition (DMD) technique. Closed loop optical feedback system for DMD makes realistic components with dimensional accuracy of 0.01 inch. On the other hand, close control of the process parameter can provide microstructure of choice. Such continued capability to control macro and microstructure is creating considerable interest. H13 tool steel is one of the difficult alloys for deposition due to residual stress accumulation from martensitic transformation. However, it is the material of choice for the die and tool industry. DMD offers Copper chill blocks and water cooling channels as the integral part of the tool. On the other hand ZrO 2 was co-deposited with nickel superalloys using DMD. This process thus is amenable to produce both macro and microstructure to a designed specification. This paper briefly reviews the state of the art of DMD and describes the microstructure and mechanical properties of selected engineering alloy systems deposited by DMD.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42335/1/10019-3-3-118_90030118.pd

Interface-Coupled BiFeO<inf>3</inf>/BiMnO<inf>3</inf> Superlattices with Magnetic Transition Temperature up to 410 K

This research was funded by the Engineering and Physical Sciences Research Council, (EP/P50385X/1), the European Research Council (ERC-2009-AdG 247276 NOVOX). The work at Texas A&M was funded by the U.S. National Science Foundation (DMR-1401266). The work at Los Alamos was supported by the U.S. Department of Energy through the LANL/LDRD program and was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. Use of the National Synchrotron Light Source, Brookhaven National Laboratory, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886.This is the final version of the article. It first appeared from Wiley via http://dx.doi.org/10.1002/admi.20150059

Phase I/II study of the deacetylase inhibitor panobinostat after allogeneic stem cell transplantation in patients with high-risk MDS or AML (PANOBEST trial)

Maintenance therapy after allogeneic hematopoietic stem cell transplantation (HSCT) for acute myeloid leukemia (AML) or myelodysplastic syndrome (MDS) is conceptually attractive to prevent relapse, but has been hampered by the limited number of suitable anti-leukemic agents. The deacetylase inhibitor (DACi) panobinostat demonstrated moderate anti-leukemic activity in a small subset of patients with advanced AML and high-risk MDS in phase I/II trials.1, 2 It also displays immunomodulatory activity3 that may enhance leukemia-specific cytotoxicity4 and mitigate graft versus host disease (GvHD), but conversely could impair T- and NK cell function.5, 6 We conducted this open-label, multi-center phase I/II trial (NCT01451268) to assess the feasibility and preliminary efficacy of prolonged prophylactic administration of panobinostat after HSCT for AML or MDS. The study protocol was approved by an independent ethics committee and conducted in compliance with the Declaration of Helsinki. All patients provided written informed consent. ..

Preconditioning of mesenchymal stromal cells with low-intensity ultrasound: influence on chondrogenesis and directed SOX9 signaling pathways

Background: Continuous low-intensity ultrasound (cLIUS) facilitates the chondrogenic differentiation of human mesenchymal stromal cells (MSCs) in the absence of exogenously added transforming growth factor-beta (TGFβ) by upregulating the expression of transcription factor SOX9, a master regulator of chondrogenesis. The present study evaluated the molecular events associated with the signaling pathways impacting SOX9 gene and protein expression under cLIUS. Methods: Human bone marrow-derived MSCs were exposed to cLIUS stimulation at 14 kPa (5 MHz, 2.5 Vpp) for 5 min. The gene and protein expression of SOX9 was evaluated. The specificity of SOX9 upregulation under cLIUS was determined by treating the MSCs with small molecule inhibitors of select signaling molecules, followed by cLIUS treatment. Signaling events regulating SOX9 expression under cLIUS were analyzed by gene expression, immunofluorescence staining, and western blotting. Results: cLIUS upregulated the gene expression of SOX9 and enhanced the nuclear localization of SOX9 protein when compared to non-cLIUS-stimulated control. cLIUS was noted to enhance the phosphorylation of the signaling molecule ERK1/2. Inhibition of MEK/ERK1/2 by PD98059 resulted in the effective abrogation of cLIUS-induced SOX9 expression, indicating that cLIUS-induced SOX9 upregulation was dependent on the phosphorylation of ERK1/2. Inhibition of integrin and TRPV4, the upstream cell-surface effectors of ERK1/2, did not inhibit the phosphorylation of ERK1/2 and therefore did not abrogate cLIUS-induced SOX9 expression, thereby suggesting the involvement of other mechanoreceptors. Consequently, the effect of cLIUS on the actin cytoskeleton, a mechanosensitive receptor regulating SOX9, was evaluated. Diffused and disrupted actin fibers observed in MSCs under cLIUS closely resembled actin disruption by treatment with cytoskeletal drug Y27632, which is known to increase the gene expression of SOX9. The upregulation of SOX9 under cLIUS was, therefore, related to cLIUS-induced actin reorganization. SOX9 upregulation induced by actin reorganization was also found to be dependent on the phosphorylation of ERK1/2. Conclusions: Collectively, preconditioning of MSCs by cLIUS resulted in the nuclear localization of SOX9, phosphorylation of ERK1/2 and disruption of actin filaments, and the expression of SOX9 was dependent on the phosphorylation of ERK1/2 under cLIUS