Modularized and Scalable Compilation for Double Quantum Dot Quatum Computing

Any quantum program on a realistic quantum device must be compiled into an executable form while taking into account the underlying hardware constraints. Stringent restrictions on architecture and control imposed by physical platforms make this very challenging. In this paper, based on the quantum variational algorithm, we propose a novel scheme to train an Ansatz circuit and realize high-fidelity compilation of a set of universal quantum gates for singlet-triplet qubits in semiconductor double quantum dots, a fairly heavily constrained system. Furthermore, we propose a scalable architecture for a modular implementation of quantum programs in this constrained systems and validate its performance with two representative demonstrations, Grover's algorithm for the database searching (static compilation) and a variant of variational quantum eigensolver for the Max-Cut optimization (dynamic compilation). Our methods are potentially applicable to a wide range of physical devices. This work constitutes an important stepping-stone for exploiting the potential for advanced and complicated quantum algorithms on near-term devices.Comment: 10 pages, 4 figure

Online decentralized tracking for nonlinear time-varying optimal power flow of coupled transmission-distribution grids

The coordinated alternating current optimal power flow (ACOPF) for coupled transmission-distribution grids has become crucial to handle problems related to high penetration of renewable energy sources (RESs). However, obtaining all system details and solving ACOPF centrally is not feasible because of privacy concerns. Intermittent RESs and uncontrollable loads can swiftly change the operating condition of the power grid. Existing decentralized optimization methods can seldom track the optimal solutions of time-varying ACOPFs. Here, we propose an online decentralized optimization method to track the time-varying ACOPF of coupled transmission-distribution grids. First, the time-varying ACOPF problem is converted to a dynamic system based on Karush-Kuhn-Tucker conditions from the control perspective. Second, a prediction term denoted by the partial derivative with respect to time is developed to improve the tracking accuracy of the dynamic system. Third, a decentralized implementation for solving the dynamic system is designed based on only a few information exchanges with respect to boundary variables. Moreover, the proposed algorithm can be used to directly address nonlinear power flow equations without relying on convex relaxations or linearization techniques. Numerical test results reveal the effectiveness and fast-tracking performance of the proposed algorithm.Comment: 18 pages with 15 figure

HIGH ORDER SHOCK CAPTURING SCHEMES FOR HYPERBOLIC CONSERVATION LAWS AND THE APPLICATION IN OPEN CHANNEL FLOWS

Many applications in engineering practice can be described by thehyperbolic partial differential equations (PDEs). Numerical modeling of this typeof equations often involves large gradients or shocks, which makes it achallenging task for conventional numerical methods to accurately simulate suchsystems. Thus developing accurate and efficient shock capturing numericalschemes becomes important for the study of hyperbolic equations.In this dissertation, a detailed study of the numerical methods for linearand nonlinear unsteady hyperbolic equations was carried out. A new finitedifference shock capturing scheme of finite volume style was developed. Thisscheme is based on the high order Pad?? type compact central finite differencemethod with the weighted essentially non-oscillatory (WENO) reconstruction toeliminate non-physical oscillations near the discontinuities while maintain stablesolution in the smooth areas. The unconditionally stable semi-implicit Crank-Nicolson (CN) scheme is used for time integration.The theoretical development was conducted based on one-dimensionalhomogeneous scalar equation and system equations. Discussions were alsoextended to include source terms and to deal with problems of higher dimension.For the treatment of source terms, Strang splitting was used. For multidimensionalequations, the ?? -form Douglas-Gunn alternating direction implicit(ADI) method was employed. To compare the performance of the scheme withENO type interpolation, the current numerical framework was also applied usingENO reconstruction.The numerical schemes were tested on 1-D and 2-D benchmark problems,as well as published experimental results. The simulated results show thecapability of the proposed scheme to resolve discontinuities while maintainingaccuracy in smooth regions. Comparisons with the experimental results validatethe method for dam break problems. It is concluded that the proposed scheme isa useful tool for solving hyperbolic equations in general, and from engineeringapplication perspective it provides a new way of modeling open channel flows

Inference of functional neural connectivity and convergence acceleration methods

The knowledge of the maps of neuronal interactions is key for system neuroscience, but at the moment we possess relatively little of it . The recent development of experimental methods which allow a simultaneous recording of the spiking activity, but not the intracellular voltage, of thousands of neurons gives us an opportunity to start filling that gap. In Chapter 2, I present a method for the inference of the parameters of the leaky integrate-and-fire (LIF) model featuring time-dependent currents and conductances based only on the extracellular recording of spiking in the network. The fitted parameters can describe the functional connections in the network, as well as the internal properties of the cells. The method can also be used to determine whether a single-compartment model of a neuron should include conductance- or current-based synapses, or their mixture. In addition, because the same mathematical model describes some of the flavors of the Drift Diffusion Model (DDM), popular in the studies of decision making process, the presented method can be readily used to fit their parameters. Making the proposed inference procedure -- based on the expectation-maximization (EM) algorithm -- accurate and robust, necessitated a development of a new numerical adaptive-grid (AG) method for the forward-backward (FB) propagation of the probability density, which is required in the computation of the sufficient statistic in the EM algorithm. These topics are covered in Chapter 3. Another issue which had to be addressed in order to obtain a usable inference algorithm is the well known slow convergence of the EM algorithm in the flat regions of the loglikelihood. Two complementary approaches to this issue are presented in this dissertation. In Chapter 4, I present a new framework for the acceleration of convergence of iterative algorithms (not limited to the EM) which unifies all previously known methods and allows us to construct a new method demonstrating the best performance of them all. To make the computations even faster, I wrote a Matlab package which allows them to be done in parallel on several machines and clusters. As one can see, all the aforementioned projects were sprouted up from one "head" project on the inference of the LIF model parameters. At the end of the dissertation, I briefly describe a disconnected project which is devoted to the development of a flexible experimental setup (software and hardware) for behavioral experiments, with a specific application to a particular type of the virtual Morris water maze experiment (VMWM)

Full characterization of Parikh's Relevance-Sensitive Axiom for Belief Revision

© 2019 AI Access Foundation. In this article, the epistemic-entrenchment and partial-meet characterizations of Parikh's relevance-sensitive axiom for belief revision, known as axiom (P), are provided. In short, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information ' relates only to the first compartment, then the revision of K by ' should not affect the second compartment. Accordingly, we identify the subclass of epistemic-entrenchment and that of selection-function preorders, inducing AGM revision functions that satisfy axiom (P). Hence, together with the faithful-preorders characterization of (P) that has already been provided, Parikh's axiom is fully characterized in terms of all popular constructive models of Belief Revision. Since the notions of relevance and local change are inherent in almost all intellectual activity, the completion of the constructive view of (P) has a significant impact on many theoretical, as well as applied, domains of Artificial Intelligence

Combining induced protease fragment assembly and microarray analysis to monitor signaling in living cells.

Die Fähigkeit Signalkaskaden zu vermessen ist für das Verständnis komplexer biologischer Prozesse essentiell. Bis jetzt versorgt uns die DNA Microarray Technologie mit umfassenden Daten, deren Auflösung jedoch auf der Ebene der Genexpression endet. Diese Informationen reichen nicht aus um die vorgeschalteten regulatorischen Mechanismen der Genexpression zu verstehen. Die meisten proteomischen Technologien hängen von in vitro synthetisierten Peptiden ab oder benötigen weitere biochemische Manipulationen. Für die Charakterisierung und Beobachtung einzelner Bestandteile von Signalkaskaden in lebenden Zellen sind Hochdurchsatz-Verfahren notwendig. In der vorliegenden Arbeit wird ein experimentelles Verfahren namens EXTassay beschrieben, dass eine quantitative und parallele Messung multipler Signal-Ereignisse ermöglicht, die der mRNA Expression vorgelagert sind. EXTassays vereinen verschiedene zelluläre Assays, die an die Reporter Gen Expression gekoppelt sind. Um Multiplexing zu erreichen wurde eine komplexe und optimierte Bibliotek kurzer expressed oligonucleotide tags (EXTs) generiert. Jedes einzelne EXT ersetzt hierbei ein klassisches Reportergen und dient als eindeutiger Identifikator für einen definierten zellulären Assay. Es können verschiedene EXTs, die entweder in einer Zelle oder in einer Zellpopulation exprimiert sein können, über Microarray Hybridisierung analysiert werden. In dieser Arbeit wurden Protokolle für das verlässliche Auslesen von Microarrays für EXTs optimiert. Weiterhin wurden EXT-basierte Assays verwendet, um die durch Neuregulin-1 induzierte Dimerisierung und Aktivierung von Rezeptortyrosinkinasen der ErbB Familie zu untersuchen. Für die quantitative Messung von Rezeptordimeriserung und phosphorylationsabhängige Kopplung an Interaktionspartner wurden Protein-Komplementations-Assays der TEV Protease, split-TEV Assays, verwendet. Hierzu wurde jeder Assay an eindeutige EXT-Reporter gekoppelt. Zusätzlich wurde die Aktivierung von 30 verschiedenen EXT-gekoppelten cis-regulatorischen Elementen erfaßt, um so einen Einblick in die nachfolgende Aspekte der Signalverarbeitung zu erhalten. Alle Assays wurden mit eindeutigen EXTs durchgeführt und mittels Microarray analysiert. Die simultane Analyse dreier verschiedener und regulierter Rezeptor Komplexe (ErbB2/2, 2/3, 2/4) zeigte, dass EXT-basierte Assays geeignet sind rezeptor-spezifische Signalereignisse zu unterscheiden. EXTassays sind daher geeignet quantitative Profile aktivierter Signalkaskaden in Zellen erstellen zu können.The ability to monitor multiple signaling events simultaneously in living cells is essential to better understand complex biological processes. So far, DNA-microarray technologies provide global scale data mainly restricted to the level of gene expression. This information is not sufficient to understand the upstream regulatory mechanisms that lead to gene expression changes. Most proteomic technologies also provide large scale measurement but usually depend on in vitro synthesized peptides or require biochemical manipulations. High throughput technologies are required for functional characterization and monitoring of signaling components in living cells. Here, an experimental approach is presented termed EXTassay that enables quantitative and parallel measurements of various signaling events upstream of mRNA expression. EXTassay incorporates various cellular assays that are coupled to reporter gene expression. To achieve multiplexing, we have generated a complex and optimized library of short expressed oligonucleotide tags (EXTs). Each unique EXT can replace a classical reporter gene and serves as a unique identifier for tracking and quantification of a defined cellular assay. Multiple EXT-reporters expressed in the same cell or cell population can be isolated and analyzed by custom microarray hybridization. We have established protocols and optimized the microarray readout for reliable EXT quantification. We applied the EXTassay to analyze the neuregulin 1 induced ErbB receptor tyrosine kinase signaling in PC-12 cells. We used transcriptionally coupled split TEV protein complementation assays to monitor ErbB receptor dimerization and phosphorylation dependent interaction with downstream signaling proteins. In addition, we employed 30 different cis-regulatory elements to assess the downstream signaling. All assays were coupled to unique EXTs and analyzed by microarrays. By analyzing three different receptor complexes (ErbB 2/2, 2/3 and 2/4), we were able to measure receptor specific differential signaling effects and demonstrate that EXTassays can be applied for the quantitative profiling of activated signaling pathways

Linguistic Variation Issues: Case and Agreement in Northern Russian Participial Constructions

This study offers a novel approach to a longstanding problem in Slavic Linguistics, the formal representation of the Northern Russian participial constructions in -n(o)/-t(o). Unlike previous works, the methodological stance adopted by the author focuses on singling out all the relevant patterns of variation and on pursuing a unified explanation for them. The key to the solution of the puzzle is the idea that the participial affix -n-/-t- and the agreement inflections are not just pieces of morphology inserted post-syntactically, but true heads that enter the computation and are able to manipulate the argumental roles of the verb and to check the EPP. The author’s proposal is properly framed in the context of current debate on interlanguage variation

Shape theory and mathematical design of a general geometric kernel through regular stratified objects

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed