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A Relational Approach to Functional Decomposition of Logic CircuitsNov 06 2006Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is proposed. This approach ... More

The Effect of Mobility on Delayed Data OffloadingMar 27 2019Delayed offloading is a widely accepted solution for mobile users to offload their traffic through Wi-Fi when they are moving in urban areas. However, delayed offloading enhances offloading efficiency at the expense of delay performance. Previous works ... More

AWG-based Non-blocking Clos NetworksAug 21 2013Sep 13 2014The three-stage Clos networks remain the most popular solution to many practical switching systems to date. The aim of this paper is to show that the modular structure of Clos networks is invariant with respect to the technological changes. Due to the ... More

AWG-based Nonblocking Shuffle-Exchange NetworksJul 10 2019Optical shuffle-exchange networks (SENs) have wide application in different kinds of interconnection networks. This paper proposes an approach to construct modular optical SENs, using a set of arrayed waveguide gratings (AWGs) and tunable wavelength converters ... More

On Pollaczek-Khinchine Formula for Peer-to-Peer NetworksMay 26 2016The performance analysis of peer-to-peer (P2P) networks calls for a new kind of queueing model, in which jobs and service stations arrive randomly. Except in some simple special cases, in general, the queueing model with varying service rate is mathematically ... More

Parallel Scheduling Algorithm based on Complex Coloring for Input-Queued SwitchesJun 23 2016This paper explores the application of a new algebraic method of edge coloring, called complex coloring, to the scheduling problems of input queued switches. The proposed distributed parallel scheduling algorithm possesses two important features: optimality ... More

Power Efficiency and Delay Tradeoff of 10GBase-T Energy Efficient Ethernet ProtocolNov 09 2016In this paper, we study the power efficiency and delay performance of the IEEE 802.3az Energy Efficient Ethernet (EEE) protocol. A new approach is proposed to analyze the M/G/1 queue with the vacation time that is governed by the arrival process and the ... More

Optimum Transmission Window for EPONs with Gated-Limited ServiceMay 26 2017This paper studies the Ethernet Passive Optical Network (EPON) with gated-limited service. The transmission window (TW) is limited in this system to guaranteeing a bounded delay experienced by disciplined users, and to constrain malicious users from monopolizing ... More

Birkhoff-von-Neumann Switches with Deflection-Compensated MechanismAug 20 2013Despite the high throughput and low complexity achieved by input scheduling based on Birkhoff-von-Neumann (BvN) decomposition; the performance of the BvN switch becomes less predictable when the input traffic is bursty. In this paper, we propose a deflection-compensated ... More

Anomalous edge state in a non-Hermitian latticeMar 16 2016Apr 01 2016We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is described by ... More

The Mathematical Parallels Between Packet Switching and Information TransmissionOct 10 2006Nov 22 2006All communication networks comprise of transmission systems and switching systems, even though they are usually treated as two separate issues. Communication channels are generally disturbed by noise from various sources. In circuit switched networks, ... More

Reply to Comment on "Anomalous Edge State in a Non-Hermitian Lattice"Nov 01 2016The Comment by Xiong et al. (arXiv:1610.06275) criticizing my Letter [Phys. Rev. Lett. 116, 133903 (2016)] was rejected by Physical Review Letters. In this Reply, I show that all their claims are wrong.

Crosstalk-free Conjugate Networks for Optical Multicast SwitchingOct 09 2006High-speed photonic switching networks can switch optical signals at the rate of several terabits per second. However, they suffer from an intrinsic crosstalk problem when two optical signals cross at the same switch element. To avoid crosstalk, active ... More

Throughput and Delay Analysis of Wireless Random Access NetworksMay 09 2008This paper studies the network throughput and transport delay of a multihop wireless random access network based on a Markov renewal model of packet transportation. We show that the distribution of the source-to-destination (SD) distance plays a critical ... More

Stability and Throughput of Buffered Aloha with BackoffApr 22 2008This paper studies the buffered Aloha with K-exponential backoff collision resolution algorithms. The buffered Aloha network is modeled as a multi-queue single-server system. We adopt a widely used approach in packet switching systems to decompose the ... More

Solvability of Cubic Graphs - From Four Color Theorem to NP-CompleteJun 12 2013Jan 08 2014Similar to Euclidean geometry, graph theory is a science that studies figures that consist of points and lines. The core of Euclidean geometry is the parallel postulate, which provides the basis of the geometric invariant that the sum of the angles in ... More

Spatiotemporal dynamics of quantum jumps with Rydberg atomsFeb 07 2012May 24 2012We study the nonequilibrium dynamics of quantum jumps in a one-dimensional chain of atoms. Each atom is driven on a strong transition to a short-lived state and on a weak transition to a metastable state. We choose the metastable state to be a Rydberg ... More

Randomized $Δ$-Edge-Coloring via Quaternion of Complex ColorsApr 11 2011This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors, where $\Delta$ ... More

Ion crystals in anharmonic trapsOct 04 2016Jan 11 2017There is currently intensive research into creating a large-scale quantum computer with trapped ions. It is well known that for a linear ion crystal in a harmonic potential, the ions near the center are more closely spaced compared to the ions near the ... More

Entanglement and spin squeezing in non-Hermitian phase transitionsSep 24 2014Dec 17 2014We show that non-Hermitian dynamics generate substantial entanglement in many-body systems. We consider the non-Hermitian Lipkin-Meshkov-Glick model and show that its phase transition occurs with maximum multiparticle entanglement: there is full N-particle ... More

Heralded magnetism in non-Hermitian atomic systemsFeb 26 2014Oct 06 2014Quantum phase transitions are usually studied in terms of Hermitian Hamiltonians. However, cold-atom experiments are intrinsically non-Hermitian due to spontaneous decay. Here, we show that non-Hermitian systems exhibit quantum phase transitions that ... More

Pattern formation with trapped ionsNov 16 2010Jan 26 2011Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while ... More

Quantum synchronization of quantum van der Pol oscillators with trapped ionsJun 26 2013Nov 12 2013Van der Pol oscillators are prototypical self-sustaining oscillators which have been used to model nonlinear processes in biological and other classical processes. In this work, we investigate how quantum fluctuations affect phase-locking in one or many ... More

PT-symmetric Rabi model: Perturbation theoryAug 27 2015Oct 08 2015We study a non-Hermitian version of the Rabi model, where a two-level system is periodically driven with an imaginary-valued drive strength, leading to alternating gain and loss. In the Floquet picture, the model exhibits PT symmetry, which can be broken ... More

Quantum-classical transition of correlations of two coupled cavitiesSep 04 2012Sep 03 2013We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates periodically in time. ... More

Dissipative transverse-field Ising model: steady-state correlations and spin squeezingSep 12 2013Oct 30 2013We study the transverse-field Ising model with infinite-range coupling and spontaneous emission on every site. We find that there is spin squeezing in steady state due to the presence of the transverse field. This means that there is still entanglement, ... More

Deep Learning for Distributed Optimization: Applications to Wireless Resource ManagementMay 31 2019This paper studies a deep learning (DL) framework to solve distributed non-convex constrained optimizations in wireless networks where multiple computing nodes, interconnected via backhaul links, desire to determine an efficient assignment of their states ... More

Topology of two-color QCD at low temperature and high densityOct 30 2018Dec 04 2018The chemical potential ($\mu$) dependence of the topological susceptibility with two-color two-flavor QCD is studied. We find that at temperature $T \approx T_c /2$, where $T_c$ denotes the critical temperature at zero chemical potential, the topological ... More

Impact of Artificial Noise on Cellular Networks: A Stochastic Geometry ApproachAug 18 2016This paper studies the impact of artificial noise (AN) on the secrecy performance of a target cell in multi-cell cellular networks. Although AN turns out to be an efficient approach for securing a pointto-point/single cell confidential transmission, it ... More

Stability and Queueing Analysis of IEEE 802.11 Distributed Coordination FunctionMar 11 2011Jan 11 2012A widely adopted two-dimensional Markov chain model of the IEEE 802.11 DCF was introduced by Bianchi to characterize the backoff behavior of a single node under a saturated traffic condition. Using this approach, we propose a queuing model for the 802.11 ... More

Transport of quantum excitations via local and nonlocal fluctuationsFeb 11 2015In quantum systems, one usually seeks to minimize dephasing noise and disorder. The efficiency of transport in a quantum system is usually degraded by the presence of noise and disorder. However, it has been shown that the combination of the two can lead ... More

$\mathcal{PT}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological statesApr 15 2015May 04 2016Aubry-Andre Harper (AAH) lattice models, characterized by reflection-asymmetric, sinusoidally varying nearest-neighbor tunneling profile, are well-known for their topological properties. We consider the fate of such models in the presence of balanced ... More

Entanglement tongue and quantum synchronization of disordered oscillatorsDec 12 2013Jan 31 2014We study the synchronization of dissipatively-coupled van der Pol oscillators in the quantum limit, when each oscillator is near its quantum ground state. Two quantum oscillators with different frequencies exhibit an entanglement tongue, which is the ... More

Self-Controlled Jamming Resilient Design Using Physical Layer Secret KeysMar 20 2018Direct-sequence spread spectrum (DSSS) has been recognized as an effective jamming resilient technique. However, the effectiveness of DSSS relies on the use of either pre-shared unique secret keys or a bank of public codes, which can be prohibitively ... More

Limit cycle phase in driven-dissipative spin systemsJan 05 2015We explore the phase diagram of interacting spin-$1/2$ systems in the presence of anisotropic interactions, spontaneous decay and driving. We find a rich phase diagram featuring a limit cycle phase in which the magnetization oscillates in time. We analyze ... More

Collective quantum jumps of Rydberg atomsSep 29 2011We study an open quantum system of atoms with long-range Rydberg interaction, laser driving, and spontaneous emission. Over time, the system occasionally jumps between a state of low Rydberg population and a state of high Rydberg population. The jumps ... More

Cooperative Caching and Transmission Design in Cluster-Centric Small Cell NetworksJan 03 2016Wireless content caching in small cell networks (SCNs) has recently been considered as an efficient way to reduce the traffic and the energy consumption of the backhaul in emerging heterogeneous cellular networks (HetNets). In this paper, we consider ... More

Performance Analysis for Multi-layer Unmanned Aerial Vehicle NetworksJun 26 2018Jul 17 2018In this paper, we provide the model of the multilayer aerial network (MAN), composed unmanned aerial vehicles (UAVs) that distributed in Poisson point process (PPP) with different densities, heights, and transmission power. In our model, we consider the ... More

Performance Analysis of Markov Modulated 1-Persistent CSMA/CA Protocols with Exponential Backoff SchedulingAug 10 2010Mar 08 2011This paper proposes a Markovian model of 1-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms. The input buffer of each access node is modeled as a Geo/G/1 queue, and the service time distribution of each individual head-of-line ... More

Unconventional magnetism via optical pumping of interacting spin systemsApr 17 2013Jun 19 2013We consider strongly interacting systems of effective spins, subject to dissipative spin-flip processes associated with optical pumping. We predict the existence of novel magnetic phases in the steady-state of this system, which emerge due to the competition ... More

Multi-layer Unmanned Aerial Vehicle Networks: Modeling and Performance AnalysisApr 02 2019Since various types of unmanned aerial vehicles (UAVs) with different hardware capabilities are introduced, we establish a foundation for the multi-layer aerial network (MAN). First, the MAN is modeled as K layer ANs, and each layer has UAVs with different ... More

String order via Floquet interactions in atomic systemsMay 18 2016Aug 09 2016We study the transverse-field Ising model with interactions that are modulated in time. In a rotating frame, the system is described by a time-independent Hamiltonian with many-body interactions, similar to the cluster Hamiltonians of measurement-based ... More

Analysis of Non-Persistent CSMA Protocols with Exponential Backoff SchedulingMay 03 2010Dec 06 2010This paper studies the performance of Non-persistent CSMA/CA protocols with K-Exponential Backoff scheduling algorithms. A multi-queue single-server system is proposed to model multiple access networks. The input buffer of each access node is modeled ... More

Deep Learning Framework for Wireless Systems: Applications to Optical Wireless CommunicationsDec 13 2018Optical wireless communication (OWC) is a promising technology for future wireless communications owing to its potentials for cost-effective network deployment and high data rate. There are several implementation issues in the OWC which have not been ... More

Time-Series Anomaly Detection Service at MicrosoftJun 10 2019Large companies need to monitor various metrics (for example, Page Views and Revenue) of their applications and services in real time. At Microsoft, we develop a time-series anomaly detection service which helps customers to monitor the time-series continuously ... More

Low-Pump-Power, Low-Phase-Noise, and Microwave to Millimeter-wave Repetition Rate Operation in MicrocombsAug 26 2012Microresonator-based frequency combs (microcombs or Kerr-combs) can potentially miniaturize the numerous applications of conventional frequency combs. A priority is the realization of broad-band (ideally octave spanning) spectra at detectable repetition ... More

Chip-based Brillouin lasers as spectral purifiers for photonic systemsJan 20 2012High coherence lasers are essential in a wide range of applications, however, such performance is normally associated with large laser cavities, because increasing energy storage reduces quantum phase noise and also renders the laser frequency less sensitive ... More

Optimal Sensor Placement for Target Localization and Tracking in 2D and 3DOct 28 2012This paper analytically characterizes optimal sensor placements for target localization and tracking in 2D and 3D. Three types of sensors are considered: bearing-only, range-only, and received-signal-strength. The optimal placement problems of the three ... More

Multi-Antenna Transmission in Downlink Heterogeneous Cellular Networks under A Threshold-based Mobile Association PolicyOct 26 2016With the recent emergence of 5G era, heterogeneous cellular networks (HCNs) have invoked a popular research interest. In this paper, we provide a comprehensive analysis for multiantenna transmissions in a multi-tier downlink HCN. We first propose a reliability-oriented ... More

A Numerical Model for Flows in Porous and Open Domains Coupled at the Interface by Stress JumpApr 10 2006A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended model is used ... More

Inhomogeneous chiral condensates and non-analyticity under an external magnetic fieldJul 30 2015We investigate inhomogeneous chiral condensates, such as the so-called dual chiral density wave of dense quark matter, under an external magnetic field at finite real and imaginary chemical potentials. In a model-independent manner, we find that analytic ... More

DSR with Non-Optimal Route Suppression for MANETsMay 29 2006This paper revisits the issue of route discovery in dynamic source routing (DSR) for mobile ad hoc networks (MANETs), and puts forward a proposal of a lightweight non-optimal route suppression technique based on the observation of a rarely noted but commonly ... More

Confirmatory Bayesian Online Change Point Detection in the Covariance Structure of Gaussian ProcessesMay 30 2019In the analysis of sequential data, the detection of abrupt changes is important in predicting future changes. In this paper, we propose statistical hypothesis tests for detecting covariance structure changes in locally smooth time series modeled by Gaussian ... More

Role Playing Learning for Socially Concomitant Mobile Robot NavigationMay 29 2017In this paper, we present the Role Playing Learning (RPL) scheme for a mobile robot to navigate socially with its human companion in populated environments. Neural networks (NN) are constructed to parameterize a stochastic policy that directly maps sensory ... More

Longtime existence of Kähler Ricci flow and holomorphic sectional curvatureMay 31 2018In this work, we obtain a existence criteria for the longtime K\"ahler Ricci flow solution. Using the existence result, we generalize a result by Wu-Yau on the existence of K\"ahler Einstein metric to the case with possibly unbounded curvature. Moreover, ... More

Modular AWG-based Optical Shuffle NetworkJul 27 2017This paper proposes an arrayed-waveguide grating (AWG) based wavelength-division-multiplexing (WDM) shuffle network. Compared with previous optical shuffle networks, our proposal is compact, easy to implement, highly scalable, and cost effective.

Region Templates: Data Representation and Management for Large-Scale Image AnalysisMay 30 2014Distributed memory machines equipped with CPUs and GPUs (hybrid computing nodes) are hard to program because of the multiple layers of memory and heterogeneous computing configurations. In this paper, we introduce a region template abstraction for the ... More

Vortices and the entrainment transition in the 2D Kuramoto modelJun 18 2010Jun 25 2010We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We explain ... More

High-throughput Execution of Hierarchical Analysis Pipelines on Hybrid Cluster PlatformsSep 14 2012We propose, implement, and experimentally evaluate a runtime middleware to support high-throughput execution on hybrid cluster machines of large-scale analysis applications. A hybrid cluster machine consists of computation nodes which have multiple CPUs ... More

Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU MachinesSep 14 2012In this paper, we address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing ... More

Exploiting Trust Degree for Multiple-Antenna User CooperationMay 10 2017For a user cooperation system with multiple antennas, we consider a trust degree based cooperation techniques to explore the influence of the trustworthiness between users on the communication systems. For the system with two communication pairs, when ... More

Universality in the one-dimensional chain of phase-coupled oscillatorsJul 03 2009Sep 16 2009We apply a recently developed renormalization group (RG) method to study synchronization in a one-dimensional chain of phase-coupled oscillators in the regime of weak randomness. The RG predicts how oscillators with randomly distributed frequencies and ... More

The Relationship between CO Emission and Visual Extinction Traced by Dust Emission in the Magellanic CloudsApr 10 2015To test the theoretical understanding that finding bright CO emission depends primarily on dust shielding, we investigate the relationship between CO emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and expressed as "$A_V$") ... More

Tachyon physics with trapped ionsMar 23 2015Sep 29 2015It has been predicted that particles with imaginary mass, called tachyons, would be able to travel faster than the speed of light. There has not been any experimental evidence for tachyons occurring naturally. Here, we propose how to experimentally simulate ... More

Anisotropic Acoustic Plasmons in Black PhosphorusDec 29 2017Recently, it was demonstrated that a graphene/dielectric/metal configuration can support acoustic plasmons, which exhibit extreme plasmon confinement an order of magnitude higher than that of conventional graphene plasmons. Here, we investigate acoustic ... More

Anomalous Lattice Vibrations of Single and Few-Layer MoS2May 14 2010Molybdenum disulfide (MoS2) of single and few-layer thickness was exfoliated on SiO2/Si substrate and characterized by Raman spectroscopy. The number of S-Mo-S layers of the samples was independently determined by contact-mode atomic-force microscopy. ... More

Observation of tightly bound trions in monolayer MoS2Oct 31 2012Two-dimensional (2D) atomic crystals, such as graphene and transition-metal dichalcogenides, have emerged as a new class of materials with remarkable physical properties. In contrast to graphene, monolayer MoS2 is a non-centrosymmetric material with a ... More

Wireless Powered Asynchronous Backscatter Networks with Sporadic Short Packets: Performance Analysis and OptimizationJan 29 2018In the fifth generation era, the pervasive applications of Internet of Things and massive machine-type communications have initiated increasing research interests on the backscatter wireless powered communication (B-WPC) technique due to its ultra high ... More

Hybrid optical-thermal antennas for enhanced light focusing and local temperature controlAug 12 2016Metal nanoantennas supporting localized surface plasmon resonances have become an indispensable tool in bio(chemical) sensing and nanoscale imaging applications. The high plasmon-enhanced electric field intensity in the visible or near-IR range that enables ... More

Identification time-delayed fractional order chaos with functional extrema model via differential evolutionAug 12 2013In this paper, a novel inversion mechanism of functional extrema model via the differential evolution algorithms(DE), is proposed to exactly identify time-delays fractional order chaos systems. With the functional extrema model, the unknown time-delays, ... More

Image Retargeting by Content-Aware SynthesisMar 26 2014Aug 21 2014Real-world images usually contain vivid contents and rich textural details, which will complicate the manipulation on them. In this paper, we design a new framework based on content-aware synthesis to enhance content-aware image retargeting. By detecting ... More

Large-Scale Answerer in Questioner's Mind for Visual Dialog Question GenerationFeb 22 2019Answerer in Questioner's Mind (AQM) is an information-theoretic framework that has been recently proposed for task-oriented dialog systems. AQM benefits from asking a question that would maximize the information gain when it is asked. However, due to ... More

Development of a General Momentum Exchange Devices Fault Model for Spacecraft Fault-Tolerant Control System DesignJul 15 2019This paper investigates the mechanism of various faults of momentum exchange devices. These devices are modeled as a cascade electric motor EM - variable speed drive VSD system. Considering the mechanical part of the EM and the VSD system, the potential ... More

Ultra-high-Q wedge-resonator on a silicon chipDec 09 2011Ultra-high-Q optical resonators are being studied across a wide range of research subjects including quantum information, nonlinear optics, cavity optomechanics, and telecommunications. Here, we demonstrate a new, resonator on-a-chip with a record Q factor ... More

Connections between Minkowski and Cosmological Correlation FunctionsMar 26 2018Apr 14 2018We show how cosmological correlation functions of massless fields can be rewritten in terms of Minkowski correlation functions, by extracting symmetry-breaking operators from the cosmological correlators. This technique simplifies some cosmological calculations. ... More

Experimental comparison of tomography and self-testing in certifying entanglementJan 29 2019We assess the quality of a source of allegedly pure two-qubit states using both standard tomography and methods inspired by device-independent self-testing. Even when the detection and locality loopholes are open, the latter methods can dispense with ... More

Safeguarding Decentralized Wireless Networks Using Full-Duplex Jamming ReceiversOct 20 2016In this paper, we study the benefits of full-duplex (FD) receiver jamming in enhancing the physical-layer security of a two-tier decentralized wireless network with each tier deployed with a large number of pairs of a single-antenna transmitter and a ... More

Distributed Control of Angle-constrained Circular Formations using Bearing-only MeasurementsOct 28 2012Oct 30 2012This paper studies distributed formation control of multiple agents in the plane using bearing-only measurements. It is assumed that each agent only measures the local bearings of their neighbor agents. The target formation considered in this paper is ... More

Image RetargetabilityFeb 12 2018Real-world applications could benefit from the ability to automatically retarget an image to different aspect ratios and resolutions, while preserving its visually and semantically important content. However, not all images can be equally well processed ... More

Safeguarding Millimeter Wave Communications Against Randomly Located EavesdroppersJan 29 2018Millimeter wave offers a sensible solution to the capacity crunch faced by 5G wireless communications. This paper comprehensively studies physical layer security in a multi-input single-output (MISO) millimeter wave system where multiple single-antenna ... More

Physical Layer Security in Wireless Ad Hoc Networks Under A Hybrid Full-/Half-Duplex Receiver Deployment StrategyMar 27 2017This paper studies physical layer security in a wireless ad hoc network with numerous legitimate transmitter-receiver pairs and eavesdroppers. A hybrid full-/half-duplex receiver deployment strategy is proposed to secure legitimate transmissions, by letting ... More

Physical Layer Security in Heterogeneous Cellular NetworksJan 07 2016The heterogeneous cellular network (HCN) is a promising approach to the deployment of 5G cellular networks. This paper comprehensively studies physical layer security in a multi-tier HCN where base stations (BSs), authorized users and eavesdroppers are ... More

Covariant Functors and Asymptotic StabilityJul 30 2015Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then the sets of associated ... More

Représentations modulo $p$ de $\mathrm{GL}(m,D)$, $D$ algèbre à division sur un corps localSep 16 2014This Ph.D. thesis belongs to the realm of mod $p$ representation theory of $p$-adic groups. The main object of study is the inner form of the general linear group $\mathrm{GL}(m,D)$ where $D$ is a division algebra over a non-Archimedean local field. The ... More

The dynamic pressure in deep-water extreme Stokes wavesSep 08 2017In this paper we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maximum principles are applied to analyse the dynamic pressure in the fluid ... More

The 2-component dispersionless Burgers equation arising in the modelling of blood flowNov 23 2012This article investigates the properties of the solutions of the dispersionless two-component Burgers (B2) equation, derived as a model for blood-flow in arteries with elastic walls. The phenomenon of wave breaking is investigated as well as applications ... More

Tunable Graphene Metasurface Reflectarray for Cloaking, Illusion and FocusingDec 12 2017We present a graphene-based metasurface that can be actively tuned between different regimes of operation, such as anomalous beam steering and focusing, cloaking and illusion optics, by applying electrostatic gating without modifying the geometry of the ... More

Graph Reachability and Pebble Automata over Infinite AlphabetsOct 12 2011Apr 10 2012Let D denote an infinite alphabet -- a set that consists of infinitely many symbols. A word w = a_0 b_0 a_1 b_1 ... a_n b_n of even length over D can be viewed as a directed graph G_w whose vertices are the symbols that appear in w, and the edges are ... More

The pressure distribution in extreme Stokes wavesJan 22 2016Jan 29 2016In this paper we prove that the pressure beneath an extreme Stokes wave over finite depth is strictly increasing with depth. Additionally it is shown that the pressure decreases in moving between a crest-line and trough-line, while it is stationary with ... More

Electronic transport and device prospects of monolayer molybdenum disulphide grown by chemical vapour depositionJan 20 2014Layered transition metal dichalcogenides display a wide range of attractive physical and chemical properties and are potentially important for various device applications. Here we report the electronic transport and device properties of monolayer molybdenum ... More

pix2code: Generating Code from a Graphical User Interface ScreenshotMay 22 2017Sep 19 2017Transforming a graphical user interface screenshot created by a designer into computer code is a typical task conducted by a developer in order to build customized software, websites, and mobile applications. In this paper, we show that deep learning ... More

Effective Hasse principle for the intersection of two quadricsFeb 16 2016We consider a smooth system of two homogeneous quadratic equations over the rationals in at least 13 variables. In this case, the Hasse principle is known to hold, thanks to the work of Mordell in 1959. The only local obstruction is over the reals. In ... More

Adaptive high-order splitting schemes for large-scale differential Riccati equationsDec 02 2016Jun 26 2017We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical to employ structural ... More

Measurement of lateral and interfacial thermal conductivity of single- and bi-layer MoS2 and MoSe2 using refined optothermal Raman techniqueSep 23 2015Atomically thin materials such as graphene and semiconducting transition metal dichalcogenides (TMDCs) have attracted extensive interest in recent years, motivating investigation into multiple properties. In this work, we demonstrate a refined version ... More

An Alternating Property for Higher Brauer GroupsSep 23 2017Feb 04 2018Using the calculus of Steenrod operations in \'etale cohomology developed in [Feng17], we prove that the analogue of Tate's pairing on higher Brauer groups is alternating on 2-torsion. This improves upon a result of Jahn [Jahn15, Math. Annalen].

Etale Steenrod operations and the Artin-Tate pairingJun 01 2017Feb 05 2018We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the Brauer group of a surface over a finite field, which is the analogue of the Cassels-Tate pairing. Tate asked if this pairing is always alternating and we find an affirmative answer, ... More

The pressure in a deep-water Stokes wave of greatest heightAug 27 2015In this paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-crest of an extreme Stokes wave introduces a number of mathematical difficulties ... More

A LLT-like test for proving the primality of Fermat numbersMay 24 2007This paper provides a proof of a LLT-like test for Fermat numbers, based on the properties of Lucas Sequences and on the method of Lehmer.

The Dirichlet Problem for Harmonic Functions on Compact SetsApr 30 2010Jan 21 2011For any compact set $K\subset \mathbb{R}^n$ we develop the theory of Jensen measures and subharmonic peak points, which form the set $\mathcal{O}_K$, to study the Dirichlet problem on $K$. Initially we consider the space $h(K)$ of functions on $K$ which ... More

Singular value decay of operator-valued differential Lyapunov and Riccati equationsApr 06 2018Jun 25 2018We consider operator-valued differential Lyapunov and Riccati equations, where the operators $B$ and $C$ may be relatively unbounded with respect to $A$ (in the standard notation). In this setting, we prove that the singular values of the solutions decay ... More