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Nanoscale Communication with Brownian MotionMar 07 2007In this paper, the problem of communicating using chemical messages propagating using Brownian motion, rather than electromagnetic messages propagating as waves in free space or along a wire, is considered. This problem is motivated by nanotechnological ... More

Ordering Finite-State Markov Channels by Mutual InformationMay 08 2007In previous work, an ordering result was given for the symbolwise probability of error using general Markov channels, under iterative decoding of LDPC codes. In this paper, the ordering result is extended to mutual information, under the assumption of ... More

Molecular communication: Physically realistic models and achievable information ratesDec 08 2008Molecular communication is a biologically-inspired method of communication with attractive properties for microscale and nanoscale devices. In molecular communication, messages are transmitted by releasing a pattern of molecules at a transmitter, which ... More

Asynchronous Peak Detection for Demodulation in Molecular CommunicationNov 02 2016Molecular communication requires low-complexity symbol detection algorithms to deal with the many sources of uncertainty that are inherent in these channels. This paper proposes two variants of a high-performance asynchronous peak detection algorithm ... More

Design and Optimizing of On-Chip Kinesin Substrates for Molecular CommunicationMay 08 2015Lab-on-chip devices and point-of-care diagnostic chip devices are composed of many different components such as nanosensors that must be able to communicate with other components within the device. Molecular communication is a promising solution for on-chip ... More

Updating Beamformers to Respond to Changes in UsersMar 11 2018We consider a multi-user multiple-input single-output downlink system that provides each user with a prespecified level of quality-of-service. The base station (BS) designs the beamformers so that each user receives a certain signal-to-interference-and-noise ... More

Capacity of a Simple Intercellular Signal Transduction ChannelMay 10 2013We model the ligand-receptor molecular communication channel with a discrete-time Markov model, and show how to obtain the capacity of this channel. We show that the capacity-achieving input distribution is iid; further, unusually for a channel with memory, ... More

Shannon Capacity of Signal Transduction for Multiple Independent ReceptorsApr 12 2016Cyclic adenosine monophosphate (cAMP) is considered a model system for signal transduction, the mechanism by which cells exchange chemical messages. Our previous work calculated the Shannon capacity of a single cAMP receptor; however, a typical cell may ... More

Using Fractional Programming for Zero-Norm ApproximationOct 27 2018This paper proposes the use of fractional programming (FP) to solve problems involving the zero-norm. FP is used to transform a non-convex ratio to a convex problem that can be solved iteratively, and guaranteed to converge to the global optimum under ... More

Capacity of a Simple Intercellular Signal Transduction ChannelNov 06 2014Aug 08 2016We model biochemical signal transduction, based on a ligand-receptor binding mechanism, as a discrete-time finite-state Markov channel, which we call the BIND channel. We show how to obtain the capacity of this channel, for the case of binary output, ... More

Table-Top Molecular Communication: Text Messages Through Chemical SignalsSep 30 2013In this work, we describe the first modular, and programmable platform capable of transmitting a text message using chemical signalling -- a method also known as molecular communication. This form of communication is attractive for applications where ... More

Entropy of the Sum of Two Independent, Non-Identically-Distributed Exponential Random VariablesSep 09 2016In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy has not been ... More

RNA as a Nanoscale Data Transmission Medium: Error AnalysisSep 23 2016RNA can be used as a high-density medium for data storage and transmission; however, an important RNA process -- replication -- is noisy. This paper presents an error analysis for RNA as a data transmission medium, analyzing how deletion errors increase ... More

Molecular Communication Using Brownian Motion with DriftJun 17 2010Jul 23 2011Inspired by biological communication systems, molecular communication has been proposed as a viable scheme to communicate between nano-sized devices separated by a very short distance. Here, molecules are released by the transmitter into the medium, which ... More

Analyzing the Impact of Access Point Density on the Performance of Finite-Area NetworksDec 10 2015Assuming a network of infinite extent, several researchers have analyzed small-cell networks using a Poisson point process (PPP) location model, leading to simple analytic expressions. The general assumption has been that these results apply to finite-area ... More

Timing Control of Single Neuron Spikes with Optogenetic StimulationOct 31 2017Feb 13 2018This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a cortical neuron's ... More

Molecular communication in fluid media: The additive inverse Gaussian noise channelDec 01 2010Dec 09 2010We consider molecular communication, with information conveyed in the time of release of molecules. The main contribution of this paper is the development of a theoretical foundation for such a communication system. Specifically, we develop the additive ... More

Finite-State Channel Models for Signal Transduction in Neural SystemsSep 18 2016Information theory provides powerful tools for understanding communication systems. This analysis can be applied to intercellular signal transduction, which is a means of chemical communication among cells and microbes. We discuss how to apply information-theoretic ... More

Modeling Interference-Free Neuron Spikes with Optogenetic StimulationMay 14 2019This paper predicts the ability to externally control the firing times of a cortical neuron whose behavior follows the Izhikevich neuron model. The Izhikevich neuron model provides an efficient and biologically plausible method to track a cortical neuron's ... More

Thermodynamic Properties of Molecular CommunicationMay 09 2018In this paper, we consider the energy cost of communicating using molecular communication. In a simplified scenario, we show that the energy bound in Landauer's principle can be achieved, implying that molecular communication can approach fundamental ... More

Convex Optimization of Distributed Cooperative Detection in Multi-Receiver Molecular CommunicationNov 17 2016Mar 03 2018In this paper, the error performance achieved by cooperative detection among K distributed receivers in a diffusion-based molecular communication (MC) system is analyzed and optimized. In this system, the receivers first make local hard decisions on the ... More

Convex Optimization of Distributed Cooperative Detection in Multi-Receiver Molecular CommunicationNov 17 2016In this paper, the error performance achieved by cooperative detection among K distributed receivers in a diffusion-based molecular communication (MC) system is analyzed and optimized. In this system, the receivers first make local hard decisions on the ... More

Communication and Information Theory of Single Action Potential Signals in PlantsNov 08 2018Many plants, such as Mimosa pudica (the sensitive plant), employ electrochemical signals known as action potentials (APs) for rapid intercellular communication. In this paper, we consider a reaction diffusion model of individual AP signals to analyze ... More

Characterizing Information Propagation in PlantsApr 25 2018This paper considers an electro-chemical based communication model for intercellular communication in plants. Many plants, such as Mimosa pudica (the "sensitive plant"), employ electrochemical signals known as action potentials (APs) for communication ... More

Distributed Cooperative Detection for Multi-Receiver Molecular CommunicationApr 13 2016In this paper, a cooperative diffusion-based molecular communication system is considered where distributed receivers collaboratively determine a transmitter's signal. In this system, the receivers first make local hard decisions about the current transmitted ... More

Symbol-by-Symbol Maximum Likelihood Detection for Cooperative Molecular CommunicationJan 09 2018Dec 01 2018In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, the transmitter (TX) sends a common information symbol to multiple receivers (RXs) and ... More

Scheduling for VoLTE: Resource Allocation Optimization and Low-Complexity AlgorithmsJan 08 2019We consider scheduling and resource allocation in long-term evolution (LTE) networks across voice over LTE (VoLTE) and best-effort data users. The difference between these two is that VoLTE users get scheduling priority to receive their required quality ... More

A Universal Channel Model for Molecular Communication Systems with Metal-Oxide DetectorsMar 10 2015In this paper, we propose an end-to-end channel model for molecular communication systems with metal-oxide sensors. In particular, we focus on the recently developed table top molecular communication platform. The system is separated into two parts: the ... More

Channel and Noise Models for Nonlinear Molecular Communication SystemsNov 25 2013Recently, a tabletop molecular communication platform has been developed for transmitting short text messages across a room. The end-to-end system impulse response for this platform does not follow previously published theoretical works because of imperfect ... More

Using Game Theory for Real-Time Behavioural Dynamics in Microscopic Populations with Noisy SignallingNov 13 2017Feb 04 2019This paper introduces the application of game theory to understand noisy real-time signalling and the resulting behavioural dynamics in microscopic populations such as bacteria and other cells. It presents a bridge between the fields of molecular communication ... More

Maximum Likelihood Detection for Cooperative Molecular CommunicationApr 19 2017Mar 03 2018In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, a fusion center (FC) chooses the transmitter's symbol that is more likely, given the likelihood ... More

Stable Distributions as Noise Models for Molecular CommunicationDec 07 2015In this work, we consider diffusion-based molecular communication timing channels. Three different timing channels are presented based on three different modulation techniques, i.e., i) modulation of the release timing of the information particles, ii) ... More

Capacity Limits of Diffusion-Based Molecular Timing ChannelsFeb 25 2016This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival ... More

On the Capacity of Diffusion-Based Molecular Timing ChannelsApr 21 2016This work introduces capacity limits for molecular timing (MT) channels, where information is modulated on the release timing of small information particles, and decoded from the time of arrival at the receiver. It is shown that the random time of arrival ... More

Expectation Maximization as Message Passing - Part I: Principles and Gaussian MessagesOct 15 2009It is shown how expectation maximization (EM) may be viewed as a message passing algorithm in factor graphs. In particular, a general EM message computation rule is identified. As a factor graph tool, EM may be used to break cycles in a factor graph, ... More

Detection Algorithms for Molecular MIMOMar 12 2015In this paper, we propose a novel design for molecular communication in which both the transmitter and the receiver have, in a 3-dimensional environment, multiple bulges (in RF communication this corresponds to antenna). The proposed system consists of ... More

A Molecular Communication Link for Monitoring in Confined EnvironmentsMar 27 2014In this paper, we consider a molecular diffusion based communications link that can reliably transport data over-the-air. We show that the system can also reliably transport data across confined structural environments, especially in cases where conventional ... More

Communication System Design and Analysis for Asynchronous Molecular Timing ChannelsDec 08 2018Two new asynchronous modulation techniques for molecular timing (MT) channels are proposed. One based on modulating information on the time between two consecutive releases of indistinguishable information particles, and one based on using distinguishable ... More

On the Impact of Time-Synchronization in Molecular Timing ChannelsSep 07 2016This work studies the impact of time- synchronization in molecular timing (MT) channels by analyzing three different modulation techniques. The first requires transmitter-receiver synchronization and is based on modulating information on the release timing ... More

Molecular Communications: Channel Model and Physical Layer TechniquesJul 27 2015This article examines recent research in molecular communications from a telecommunications system design perspective. In particular, it focuses on channel models and state-of-the-art physical layer techniques. The goal is to provide a foundation for ... More

SMIET: Simultaneous Molecular Information and Energy TransferMay 31 2016Aug 17 2016The performance of communication systems is fundamentally limited by the loss of energy through propagation and circuit inefficiencies. In this article, we show that it is possible to achieve ultra low energy communications at the nano-scale, if diffusive ... More

Scaling laws for molecular communicationApr 01 2014In this paper, we investigate information-theoretic scaling laws, independent from communication strategies, for point-to-point molecular communication, where it sends/receives information-encoded molecules between nanomachines. Since the Shannon capacity ... More

Analyzing Dependent Placements of Small Cells in a Two-Layer Heterogeneous Network with a Rate Coverage ConstraintSep 21 2016We consider the downlink of a two-layer heterogeneous network, comprising macro cells (MCs) and small cells (SCs). The existing literature generally assumes independent placements of the access points (APs) in different layers; in contrast, we analyze ... More

On the Analysis of Bacterial Cooperation with a Characterization of 2D Signal PropagationDec 01 2018The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables microorganisms to respond to fluctuations of living environments by working together. In this ... More

Symbol interval optimization for molecular communication with driftJul 22 2014In this paper, we propose a symbol interval optimization algorithm in molecular communication with drift. Proper symbol intervals are important in practical communication systems since information needs to be sent as fast as possible with low error rates. ... More

Expected Density of Cooperative Bacteria in a 2D Quorum Sensing Based Molecular Communication SystemDec 01 2018May 04 2019The exchange of small molecular signals within microbial populations is generally referred to as quorum sensing (QS). QS is ubiquitous in nature and enables microorganisms to respond to fluctuations in living environments by working together. In this ... More

Continued fractions for some transcendental numbersSep 16 2015Mar 10 2016We consider series of the form $$ \frac{p}{q} +\sum_{j=2}^\infty \frac{1}{x_j}, $$ where $x_1=q$ and the integer sequence $(x_n)$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for $n\geq 1$. It is shown ... More

Laurent Polynomials and Superintegrable MapsFeb 10 2007This article is dedicated to the memory of Vadim Kuznetsov, and begins with some of the author's recollections of him. Thereafter, a brief review of Somos sequences is provided, with particular focus being made on the integrable structure of Somos-4 recurrences, ... More

Phases of Dense Quark Matter and the Structure of Compact ObjectsJan 11 2006The presence of quark matter in neutron stars may affect several neutron star observables and the neutrino signal in core-collapse supernovae. These observables are sensitive to the phase of quark matter that is present in compact objects. We present ... More

Moving Beyond Chi-Squared in Nuclei and Neutron StarsJul 01 2014Oct 14 2014There are several assumptions made in a standard $\chi^2$ analysis of data, including the frequent assumption that the likelihood function is well approximated by a multivariate Gaussian distribution. This article briefly reviews the standard approach ... More

Affine manifolds are rigid analytic spaces in characteristic one, IMay 26 2015May 28 2015I extend the definitions of schemes relative to monoids with zero - and therefore, toric geometry - to the world of formal schemes. This expands the usual framework to include, for instance, models for Mumford's degenerating Abelian varieties. Following ... More

How (Maximally) Contextual is Quantum Mechanics?Dec 11 2017Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some of the projectors ... More

Bounded Conjugators For Real Hyperbolic and Unipotent Elements in Semisimple Lie GroupsNov 13 2012Let $G$ be a real semisimple Lie group with trivial centre and no compact factors. Given a conjugate pair of either real hyperbolic elements or unipotent elements $a$ and $b$ in $G$ we find a conjugating element $g \in G$ such that $d_G(1,g) \leq L(d_G(1,u)+d_G(1,v))$, ... More

Conjugacy Length in Group ExtensionsNov 13 2012Oct 01 2013Determining the length of short conjugators in a group can be considered as an effective version of the conjugacy problem. The conjugacy length function provides a measure for these lengths. We study the behaviour of conjugacy length functions under group ... More

Non-autonomous Hénon-Heiles SystemsMar 12 1997Scaling similarity solutions of three integrable PDEs, namely the Sawada-Kotera, fifth order KdV and Kaup-Kupershmidt equations, are considered. It is shown that the resulting ODEs may be written as non-autonomous Hamiltonian equations, which are time-dependent ... More

Galactic morning: the Atacama Large Millimeter Array (ALMA) and the evolution of galaxiesNov 24 1999The importance of the Atacama Large Millimeter Array (ALMA) to the study of high-redshift dusty gas-rich galaxies is described. ALMA will have dramatically greater sensitivity and angular resolution than existing millimetre(mm) and submm-wave telescopes. ... More

Future millimeter, submillimeter and far-infrared surveys and their successful follow upJun 08 1999Dec 15 1999The first unbiased surveys for high-redshift galaxies in the submillimeter (submm) and far-infrared (FIR) wavebands have been made over the last two years. When combined with the intensity of extragalactic background radiation in the same wavebands, we ... More

Submillimetre-wave surveys: first results and prospectsJun 29 1998Aug 11 1998The population of distant dusty submm-luminous galaxies was first detected last year (Smail, Ivison and Blain 1997). Forms of evolution required to account for both this population and the intensity of background radiation have now been determined (Blain, ... More

Gravitational lensing and the Sunyaev-Zel'dovich effect in the millimetre/submillimetre wavebandJan 12 1998The intensity of the cosmic microwave background radiation in the fields of clusters of galaxies is modified by inverse Compton scattering in the hot intracluster gas - the Sunyaev-Zel'dovich (SZ) effect. The effect is expected to be most pronounced at ... More

SCUBA deep fields and source confusionNov 26 2000Deep submillimetre(submm)-wave surveys made over the last three years using the SCUBA camera at the 15-m James Clerk Maxwell Telescope (JCMT) have revealed a new population of very luminous high-redshift galaxies. The properties of this population, and ... More

A gravitational lens survey with Planck SurveyorJul 14 2000The Planck Surveyor cosmic microwave background (CMB) imaging mission will make very sensitive maps of the whole sky at microwave, millimetre (mm) and sub-mm wavelengths. The steep source counts expected in the highest frequency Planck bands are likely ... More

The differential magnification of high-redshift ultraluminous infrared galaxiesDec 22 1998Feb 08 1999A class of extremely luminous high-redshift galaxies has recently been detected in unbiased submillimetre-wave surveys using the Submillimetre Common-User Bolometer Array (SCUBA) camera at the James Clerk Maxwell Telescope. Most of the luminosity of these ... More

The Planck Surveyor mission and gravitational lensesJan 12 1998An extremely sensitive all-sky survey will be carried out in the millimetre/submillimetre waveband by the forthcoming ESA mission Planck Surveyor. The main scientific goal of the mission is to make very accurate measurements of the spatial power spectrum ... More

The Neutron Star Crust: Nuclear Physics InputNov 12 2007A fully self-consistent model of the neutron star inner crust based upon models of the nucleonic equation of state at zero temperature is constructed. The results nearly match those of previous calculations of the inner crust given the same input equation ... More

Skeleta in non-Archimedean and tropical geometryNov 03 2013Feb 26 2014I describe an algebro-geometric theory of skeleta, which provides a unified setting for the study of tropical varieties, skeleta of non-Archimedean analytic spaces, and affine manifolds with singularities. Skeleta are spaces equipped with a structure ... More

The universal property of derived geometryJan 29 2017Sep 08 2017Derived geometry can be defined as the universal way to adjoin finite homotopical limits to a given category of manifolds compatibly with products and glueing. The point of this paper is to show that a construction closely resembling existing approaches ... More

Bayesian Sequentially Monitored Multi-arm Experiments with Multiple Comparison AdjustmentsAug 29 2016Randomized experiments play a major role in data-driven decision making across many different fields and disciplines. In medicine, for example, randomized controlled trials (RCTs) are the backbone of clinical trial methodology for testing the efficacy ... More

On the computational complexity of detecting possibilistic localitySep 18 2016Oct 05 2016The proofs of quantum nonlocality due to GHZ and Hardy are quantitatively different from that of Bell insofar as they rely only on a consideration of whether events are possible or impossible, rather than relying on specific experimental probabilities. ... More

CZF does not have the Existence PropertyMar 14 2013Sep 04 2014Constructive theories usually have interesting metamathematical properties where explicit witnesses can be extracted from proofs of existential sentences. For relational theories, probably the most natural of these is the existence property, EP, sometimes ... More

Combinatorial Invariance of Relative R-polynomials in the Hermitian Symmetric CaseNov 30 2009We develop a marking system for an analog of Hasse diagrams of intervals $[u,v]$ with $u\leq v$ in a Hermitian symmetric pair $W/W_J$, and use this to create a closed form algorithm for computing relative R-polynomials. The uniform nature of this algorithm ... More

On the continued fraction expansion of certain Engel seriesAug 29 2015Sep 11 2015An Engel series is a sum of the reciprocals of an increasing sequence of positive integers, which is such that each term is divisible by the previous one. Here we consider a particular class of Engel series, for which each term of the sequence is divisible ... More

The Geometry of the Conjugacy Problem in Wreath Products and Free Solvable GroupsJul 25 2013We describe an effective version of the conjugacy problem and study it for wreath products and free solvable groups. The problem involves estimating the length of short conjugators between two elements of the group, a notion which leads to the definition ... More

Metric Behaviour of the Magnus EmbeddingFeb 23 2012Feb 17 2014The classic Magnus embedding is a very effective tool in the study of abelian extensions of a finitely generated group $G$, allowing us to see the extension as a subgroup of a wreath product of a free abelian group with $G$. In particular, the embedding ... More

Continued fractions and Hankel determinants from hyperelliptic curvesJul 11 2019Jul 25 2019Following van der Poorten, we consider a family of nonlinear maps which are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus $\mathrm{g}$. Using the connection with the classical theory of J-fractions and ... More

The history of starburst galaxiesNov 21 2000Dusty galaxies with luminosities in excess of 10^11 solar luminosities have been detected out to redshifts of about unity by the Infrared Space Observatory (ISO), and to higher redshifts using millimetre(mm)- and submm-wave cameras on ground-based telescopes. ... More

Prospects for future far-infrared/submillimeter studies of the high-redshift UniverseAug 30 2000Observations made using COBE, SCUBA, ISO and MAMBO have provided a reasonable working knowledge of both the intensity of the submm and far-infrared background radiation and the source counts of luminous high-redshift dusty galaxies. However, because there ... More

Dust temperature and the submillimeter-radio flux density ratio as a redshift indicatorMay 19 1999It is difficult to identify the distant galaxies selected in existing submillimeter (submm)-wave surveys, because their positional accuracy is only several arcseconds. Currently, centimeter-wave VLA observations are required in order to determine sub-arcsec ... More

The Discovery of Submillimeter GalaxiesFeb 10 2003I briefly describe some results about luminous distant dusty galaxies obtained in the 5 years since sensitive two-dimensional bolometer array cameras became available. The key requirements for making additional progress in understanding the properties ... More

The Color-Superconducting {'}t Hooft InteractionJun 23 2005Oct 03 2005We consider the effect of a six-fermion interaction of the {'}t Hooft form in the quark-quark channel on the ground state of matter at finite density. The coupling constant for this new term is varied within the limits suggested by naturalness. The flavor-mixing ... More

Fighting the flow: the stability of model flocks in a vortical flowJun 02 2016We investigate the stability of self-propelled particle flocks in the Taylor-Green vortex, a steady vortical flow. We consider a model where particles align themselves to a combination of the orientation and the acceleration of particles within a critical ... More

The operad that corepresents enrichmentFeb 24 2019I show that the theories of enrichment in a monoidal infinity-category defined by Hinich and by Gepner-Haugseng agree, and that the identification is unique. Among other things, this makes the Yoneda lemma available in the former model.

Deep Crustal Heating in a Multicomponent Accreted Neutron Star CrustFeb 15 2012May 16 2012A quasi-statistical equilibrium model is constructed to simulate the multicomponent composition of the crust of an accreting neutron star. The ashes of rp-process nucleosynthesis are driven by accretion through a series of electron captures, neutron emissions, ... More

The High-Density Symmetry Energy and Direct UrcaJul 18 2006The symmetry energy of nucleonic matter is usually assumed to be quadratic in the isospin density. While this may be justified at sub-saturation densities, there is no need to enforce this restriction at super-saturation densities. The presence of a quartic ... More

The ISM at high redshifts: ALMA results and a look to the futureMar 11 2015ALMA is revolutionizing the way we study and understand the astrophysics of galaxies, both as a whole and individually. By exploiting its unique sensitivity and resolution to make spatially and spectrally resolved images of the gas and dust in the interstellar ... More

The differential magnification of high-redshift ultraluminous infrared galaxiesMar 15 1999This proceeding discusses the potential modifications to the mid-infrared spectral energy distribution (SED) of a high-redshift dusty AGN that is graviationally lensed by a foreground galaxy. The mid-infrared colour of a lensed galaxy would typically ... More

Infrared galaxiesDec 15 1998To study large-scale structure in the Universe a full census of the contents are required. This is even more important when the processes of galaxy formation are being investigated. In the last year the population of distant galaxies that emit most of ... More

Exploiting magnification bias in ultradeep submillimetre-wave surveys using ALMAOct 17 2001The surface density of populations of galaxies with steep/shallow source counts is increased/decreased by gravitational lensing magnification. These effects are usually called `magnification bias' and `depletion' respectively. However, if sources are ... More

Selection effects in high-redshift submillimeter surveys and pointed observationsSep 01 2000The results of the first generation of submillimeter-wave surveys have been published. The opening of this new window on the distant Universe has added considerably to our understanding of the galaxy formation process, by revealing a numerous population ... More

Dust temperture and the submillimetre-radio flux density ratio as a redshift indicator for distant galaxiesJun 28 1999Aug 13 1999It is difficult to identify the distant galaxies selected in existing submillimetre-wave surveys, because their positions are known at best to only several arcseconds. Centimetre-wave VLA observations are required in order to determine positions to subarcsecond ... More

Painleve tests, singularity structure and integrabilityFeb 09 2005Oct 22 2008After a brief introduction to the Painlev\'{e} property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlev\'{e} tests. The tests are applied to several ... More

Skeleta in non-Archimedean and tropical geometryNov 03 2013Sep 08 2017I describe an algebro-geometric theory of skeleta, which provides a unified setting for the study of tropical varieties, skeleta of non-Archimedean analytic spaces, and affine manifolds with singularities. Skeleta are spaces equipped with a structure ... More

Projective modules over polyhedral semiringsJul 26 2015I classify projective modules over idempotent semirings that are free on a monoid. The analysis extends to the case of the semiring of convex, piecewise-affine functions on a polyhedron, for which projective modules correspond to convex families of weight ... More

On the difference between `tropical functions' and real-valued functionsJul 02 2015Mar 06 2016I introduce the concept of integral closure for elements and ideals in idempotent semirings, and establish how it corresponds to its namesake in commutative algebra. In the case of free semirings, integral closure can be understood in terms of a certain ... More

Continued fractions and Hankel determinants from hyperelliptic curvesJul 11 2019Following van der Poorten, we consider a family of nonlinear maps which are generated from the continued fraction expansion of a function on a hyperelliptic curve of genus $\mathrm{g}$. Using the connection with the classical theory of J-fractions and ... More

Curious continued fractions, nonlinear recurrences and transcendental numbersJun 30 2015Jul 20 2015We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear ... More

The geometry of the conjugacy problem in lamplighter groupsDec 12 2011Jan 13 2016In this note we investigate the conjugacy problem in lamplighter groups with particular interest in the role of their geometry. In particular we show that the conjugacy length function is linear.

Effect of Local Population Uncertainty on Cooperation in BacteriaAug 21 2017Bacteria 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 ... More

Objects in Kepler's Mirror May be Larger Than They Appear: Bias and Selection Effects in Transiting Planet SurveysNov 10 2012Statistical analyses of large surveys for transiting planets such as the Kepler mission must account for systematic errors and biases. Transit detection depends not only on the planet's radius and orbital period, but also on host star properties. Thus, ... More

Topology and Time ReversalOct 04 1995In this lecture we address some topological questions connected with the existence on a general spacetime manifold of diffeomorphisms connected to the identity which reverse the time-orientation.

Separation Logic for Small-step CminorJul 30 2007Cminor is a mid-level imperative programming language; there are proved-correct optimizing compilers from C to Cminor and from Cminor to machine language. We have redesigned Cminor so that it is suitable for Hoare Logic reasoning and we have designed ... More